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The Urban Last Mile Problem: Autonomous Drone Delivery to Your Balcony | Drone delivery has been a hot topic in the industry in the past few years.
However, existing approaches either focus on rural areas or rely on centralized
drop-off locations from where the last mile delivery is performed. In this
paper we tackle the problem of autonomous last mile delivery in urban
environments using an off-the-shelf drone. We build a prototype system that is
able to fly to the approximate delivery location using GPS and then find the
exact drop-off location using visual navigation. The drop-off location could,
e.g., be on a balcony or porch, and simply needs to be indicated by a visual
marker on the wall or window. We test our system components in simulated
environments, including the visual navigation and collision avoidance. Finally,
we deploy our drone in a real-world environment and show how it can find the
drop-off point on a balcony. To stimulate future research in this topic we open
source our code.
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Extragalactic VLBI surveys in the MeerKAT era | The past decade has seen significant advances in cm-wave VLBI extragalactic
observations due to a wide range of technical successes, including the increase
in processed field-of-view and bandwidth. The future inclusion of MeerKAT into
global VLBI networks would provide further enhancement, particularly the
dramatic sensitivity boost to >7000 km baselines. This will not be without its
limitations, however, considering incomplete MeerKAT band overlap with current
VLBI arrays and the small (real-time) field-of-view afforded by the phased up
MeerKAT array. We provide a brief overview of the significant contributions
MeerKAT-VLBI could make, with an emphasis on the scientific output of several
MeerKAT extragalactic Large Survey Projects.
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Equicontinuity, orbit closures and invariant compact open sets for group actions on zero-dimensional spaces | Let $X$ be a locally compact zero-dimensional space, let $S$ be an
equicontinuous set of homeomorphisms such that $1 \in S = S^{-1}$, and suppose
that $\overline{Gx}$ is compact for each $x \in X$, where $G = \langle S
\rangle$. We show in this setting that a number of conditions are equivalent:
(a) $G$ acts minimally on the closure of each orbit; (b) the orbit closure
relation is closed; (c) for every compact open subset $U$ of $X$, there is $F
\subseteq G$ finite such that $\bigcap_{g \in F}g(U)$ is $G$-invariant. All of
these are equivalent to a notion of recurrence, which is a variation on a
concept of Auslander-Glasner-Weiss. It follows in particular that the action is
distal if and only if it is equicontinuous.
| 0 | 0 | 1 | 0 | 0 | 0 |
The Ramsey property for Banach spaces, Choquet simplices, and their noncommutative analogs | We show that the Gurarij space $\mathbb{G}$ and its noncommutative analog
$\mathbb{NG}$ both have extremely amenable automorphism group. We also compute
the universal minimal flows of the automorphism groups of the Poulsen simplex
$\mathbb{P}$ and its noncommutative analogue $\mathbb{NP}$. The former is
$\mathbb{P}$ itself, and the latter is the state space of the operator system
associated with $\mathbb{NP}$. This answers a question of Conley and
Törnquist. We also show that the pointwise stabilizer of any closed proper
face of $\mathbb{P}$ is extremely amenable. Similarly, the pointwise stabilizer
of any closed proper biface of the unit ball of the dual of the Gurarij space
(the Lusky simplex) is extremely amenable.
These results are obtained via the Kechris--Pestov--Todorcevic
correspondence, by establishing the approximate Ramsey property for several
classes of finite-dimensional operator spaces and operator systems (with
distinguished linear functionals), including: Banach spaces, exact operator
spaces, function systems with a distinguished state, and exact operator systems
with a distinguished state. This is the first direct application of the
Kechris--Pestov--Todorcevic correspondence in the setting of metric structures.
The fundamental combinatorial principle that underpins the proofs is the Dual
Ramsey Theorem of Graham and Rothschild.
In the second part of the paper, we obtain factorization theorems for
colorings of matrices and Grassmannians over $\mathbb{R}$ and ${\mathbb{C}}$,
which can be considered as continuous versions of the Dual Ramsey Theorem for
Boolean matrices and of the Graham-Leeb-Rothschild Theorem for Grassmannians
over a finite field.
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Evasion Attacks against Machine Learning at Test Time | In security-sensitive applications, the success of machine learning depends
on a thorough vetting of their resistance to adversarial data. In one
pertinent, well-motivated attack scenario, an adversary may attempt to evade a
deployed system at test time by carefully manipulating attack samples. In this
work, we present a simple but effective gradient-based approach that can be
exploited to systematically assess the security of several, widely-used
classification algorithms against evasion attacks. Following a recently
proposed framework for security evaluation, we simulate attack scenarios that
exhibit different risk levels for the classifier by increasing the attacker's
knowledge of the system and her ability to manipulate attack samples. This
gives the classifier designer a better picture of the classifier performance
under evasion attacks, and allows him to perform a more informed model
selection (or parameter setting). We evaluate our approach on the relevant
security task of malware detection in PDF files, and show that such systems can
be easily evaded. We also sketch some countermeasures suggested by our
analysis.
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Evaluation of Lightweight Block Ciphers in Hardware Implementation: A Comprehensive Survey | The conventional cryptography solutions are ill-suited to strict memory, size
and power limitations of resource-constrained devices, so lightweight
cryptography solutions have been specifically developed for this type of
applications. In this domain of cryptography, the term lightweight never refers
to inadequately low security, but rather to establishing the best balance to
maintain sufficient security. This paper presents the first comprehensive
survey evaluation of lightweight block ciphers in terms of their speed, cost,
performance, and balanced efficiency in hardware implementation, and
facilitates the comparison of studied ciphers in these respects. The cost of
lightweight block ciphers is evaluated with the metric of Gate Equivalent
(Fig.1), their speed with the metric of clock-cycle-per-block (Fig.2), their
performance with the metric of throughput (Fig.3) and their balanced efficiency
with the metric of Figure of Merit (Fig.4). The results of these evaluations
show that SIMON, SPECK, and Piccolo are the best lightweight block ciphers in
hardware implementation.(Abstract)
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The Sample Complexity of Online One-Class Collaborative Filtering | We consider the online one-class collaborative filtering (CF) problem that
consists of recommending items to users over time in an online fashion based on
positive ratings only. This problem arises when users respond only occasionally
to a recommendation with a positive rating, and never with a negative one. We
study the impact of the probability of a user responding to a recommendation,
p_f, on the sample complexity, i.e., the number of ratings required to make
`good' recommendations, and ask whether receiving positive and negative
ratings, instead of positive ratings only, improves the sample complexity. Both
questions arise in the design of recommender systems. We introduce a simple
probabilistic user model, and analyze the performance of an online user-based
CF algorithm. We prove that after an initial cold start phase, where
recommendations are invested in exploring the user's preferences, this
algorithm makes---up to a fraction of the recommendations required for updating
the user's preferences---perfect recommendations. The number of ratings
required for the cold start phase is nearly proportional to 1/p_f, and that for
updating the user's preferences is essentially independent of p_f. As a
consequence we find that, receiving positive and negative ratings instead of
only positive ones improves the number of ratings required for initial
exploration by a factor of 1/p_f, which can be significant.
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Coherent long-distance displacement of individual electron spins | Controlling nanocircuits at the single electron spin level is a possible
route for large-scale quantum information processing. In this context,
individual electron spins have been identified as versatile quantum information
carriers to interconnect different nodes of a spin-based semiconductor quantum
circuit. Despite important experimental efforts to control the electron
displacement over long distances, keeping the electron spin coherence after
transfer remained up to now elusive. Here we demonstrate that individual
electron spins can be displaced coherently over a distance of 5 micrometers.
This displacement is realized on a closed path made of three tunnel-coupled
lateral quantum dots. Using fast quantum dot control, the electrons tunnel from
one dot to another at a speed approaching 100 m/s. We find that the spin
coherence length is 8 times longer than expected from the electron spin
coherence without displacement. Such an enhanced spin coherence points at a
process similar to motional narrowing observed in nuclear magnetic resonance
experiments6. The demonstrated coherent displacement will enable long-range
interaction between distant spin-qubits and will open the route towards
non-abelian and holonomic manipulation of a single electron spin.
| 0 | 1 | 0 | 0 | 0 | 0 |
Transparency and Explanation in Deep Reinforcement Learning Neural Networks | Autonomous AI systems will be entering human society in the near future to
provide services and work alongside humans. For those systems to be accepted
and trusted, the users should be able to understand the reasoning process of
the system, i.e. the system should be transparent. System transparency enables
humans to form coherent explanations of the system's decisions and actions.
Transparency is important not only for user trust, but also for software
debugging and certification. In recent years, Deep Neural Networks have made
great advances in multiple application areas. However, deep neural networks are
opaque. In this paper, we report on work in transparency in Deep Reinforcement
Learning Networks (DRLN). Such networks have been extremely successful in
accurately learning action control in image input domains, such as Atari games.
In this paper, we propose a novel and general method that (a) incorporates
explicit object recognition processing into deep reinforcement learning models,
(b) forms the basis for the development of "object saliency maps", to provide
visualization of internal states of DRLNs, thus enabling the formation of
explanations and (c) can be incorporated in any existing deep reinforcement
learning framework. We present computational results and human experiments to
evaluate our approach.
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Refactoring Software Packages via Community Detection from Stability Point of View | As the complexity and size of software projects increases in real-world
environments, maintaining and creating maintainable and dependable code becomes
harder and more costly. Refactoring is considered as a method for enhancing the
internal structure of code for improving many software properties such as
maintainability.
In this thesis, the subject of refactoring software packages using community
detection algorithms is discussed, with a focus on the notion of package
stability. The proposed algorithm starts by extracting a package dependency
network from Java byte code and a community detection algorithm is used to find
possible changes in package structures. In this work, the reasons for the
importance of considering dependency directions while modeling package
dependencies with graphs are also discussed, and a proof for the relationship
between package stability and the modularity of package dependency graphs is
presented that shows how modularity is in favor of package stability.
For evaluating the proposed algorithm, a tool for live analysis of software
packages is implemented, and two software systems are tested. Results show that
modeling package dependencies with directed graphs and applying the presented
refactoring method, leads to a higher increase in package stability than
undirected graph modeling approaches that have been studied in the literature.
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Mechanism Design in Social Networks | This paper studies an auction design problem for a seller to sell a commodity
in a social network, where each individual (the seller or a buyer) can only
communicate with her neighbors. The challenge to the seller is to design a
mechanism to incentivize the buyers, who are aware of the auction, to further
propagate the information to their neighbors so that more buyers will
participate in the auction and hence, the seller will be able to make a higher
revenue. We propose a novel auction mechanism, called information diffusion
mechanism (IDM), which incentivizes the buyers to not only truthfully report
their valuations on the commodity to the seller, but also further propagate the
auction information to all their neighbors. In comparison, the direct extension
of the well-known Vickrey-Clarke-Groves (VCG) mechanism in social networks can
also incentivize the information diffusion, but it will decrease the seller's
revenue or even lead to a deficit sometimes. The formalization of the problem
has not yet been addressed in the literature of mechanism design and our
solution is very significant in the presence of large-scale online social
networks.
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Prototype Matching Networks for Large-Scale Multi-label Genomic Sequence Classification | One of the fundamental tasks in understanding genomics is the problem of
predicting Transcription Factor Binding Sites (TFBSs). With more than hundreds
of Transcription Factors (TFs) as labels, genomic-sequence based TFBS
prediction is a challenging multi-label classification task. There are two
major biological mechanisms for TF binding: (1) sequence-specific binding
patterns on genomes known as "motifs" and (2) interactions among TFs known as
co-binding effects. In this paper, we propose a novel deep architecture, the
Prototype Matching Network (PMN) to mimic the TF binding mechanisms. Our PMN
model automatically extracts prototypes ("motif"-like features) for each TF
through a novel prototype-matching loss. Borrowing ideas from few-shot matching
models, we use the notion of support set of prototypes and an LSTM to learn how
TFs interact and bind to genomic sequences. On a reference TFBS dataset with
$2.1$ $million$ genomic sequences, PMN significantly outperforms baselines and
validates our design choices empirically. To our knowledge, this is the first
deep learning architecture that introduces prototype learning and considers
TF-TF interactions for large-scale TFBS prediction. Not only is the proposed
architecture accurate, but it also models the underlying biology.
| 1 | 0 | 0 | 1 | 0 | 0 |
Quantum Multicriticality near the Dirac-Semimetal to Band-Insulator Critical Point in Two Dimensions: A Controlled Ascent from One Dimension | We compute the effects of generic short-range interactions on gapless
electrons residing at the quantum critical point separating a two-dimensional
Dirac semimetal (DSM) and a symmetry-preserving band insulator (BI). The
electronic dispersion at this critical point is anisotropic ($E_{\mathbf k}=\pm
\sqrt{v^2 k^2_x + b^2 k^{2n}_y}$ with $n=2$), which results in unconventional
scaling of physical observables. Due to the vanishing density of states
($\varrho(E) \sim |E|^{1/n}$), this anisotropic semimetal (ASM) is stable
against weak short-range interactions. However, for stronger interactions the
direct DSM-BI transition can either $(i)$ become a first-order transition, or
$(ii)$ get avoided by an intervening broken-symmetry phase (BSP). We perform a
renormalization group analysis by perturbing away from the one-dimensional
limit with the small parameter $\epsilon = 1/n$, augmented with a $1/n$
expansion (parametrically suppressing quantum fluctuations in higher
dimension). We identify charge density wave (CDW), antiferromagnet (AFM) and
singlet s-wave superconductor as the three dominant candidates for the BSP. The
onset of any such order at strong coupling $(\sim \epsilon)$ takes place
through a continuous quantum phase transition across multicritical point. We
also present the phase diagram of an extended Hubbard model for the ASM,
obtained via the controlled deformation of its counterpart in one dimension.
The latter displays spin-charge separation and instabilities to CDW, spin
density wave, and Luther-Emery liquid phases at arbitrarily weak coupling. The
spin density wave and Luther-Emery liquid phases deform into pseudospin
SU(2)-symmetric quantum critical points separating the ASM from the AFM and
superconducting orders, respectively. Our results can be germane for a
uniaxially strained honeycomb lattice or organic compound
$\alpha$-(BEDT-TTF)$_2\text{I}_3$.
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Wider frequency domain for negative refraction index in a quantized composite right-left handed transmission line | The refraction index of the quantized lossy composite right-left handed
transmission line (CRLH-TL) is deduced in the thermal coherence state. The
results show that the negative refraction index (herein the left-handedness)
can be implemented by the electric circuit dissipative factors(i.e., the
resistances \(R\) and conductances \( G\)) in a higher frequency band
(1.446GHz\(\leq\omega\leq \) 15GHz), and flexibly adjusted by the left-handed
circuit components (\(C_l\), \(L_l\)) and the right-handed circuit components
(\(C_r\), \(L_r\)) at a lower frequency (\(\omega\)=0.995GHz) . The flexible
adjustment for left-handedness in a wider bandwidth will be significant for the
microscale circuit design of the CRLH-TL and may make the theoretical
preparation for its compact applications.
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Model Averaging and its Use in Economics | The method of model averaging has become an important tool to deal with model
uncertainty, for example in situations where a large amount of different
theories exist, as are common in economics. Model averaging is a natural and
formal response to model uncertainty in a Bayesian framework, and most of the
paper deals with Bayesian model averaging. The important role of the prior
assumptions in these Bayesian procedures is highlighted. In addition,
frequentist model averaging methods are also discussed. Numerical methods to
implement these methods are explained, and I point the reader to some freely
available computational resources. The main focus is on uncertainty regarding
the choice of covariates in normal linear regression models, but the paper also
covers other, more challenging, settings, with particular emphasis on sampling
models commonly used in economics. Applications of model averaging in economics
are reviewed and discussed in a wide range of areas, among which growth
economics, production modelling, finance and forecasting macroeconomic
quantities.
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Dropout Feature Ranking for Deep Learning Models | Deep neural networks (DNNs) achieve state-of-the-art results in a variety of
domains. Unfortunately, DNNs are notorious for their non-interpretability, and
thus limit their applicability in hypothesis-driven domains such as biology and
healthcare. Moreover, in the resource-constraint setting, it is critical to
design tests relying on fewer more informative features leading to high
accuracy performance within reasonable budget. We aim to close this gap by
proposing a new general feature ranking method for deep learning. We show that
our simple yet effective method performs on par or compares favorably to eight
strawman, classical and deep-learning feature ranking methods in two
simulations and five very different datasets on tasks ranging from
classification to regression, in both static and time series scenarios. We also
illustrate the use of our method on a drug response dataset and show that it
identifies genes relevant to the drug-response.
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Per-instance Differential Privacy | We consider a refinement of differential privacy --- per instance
differential privacy (pDP), which captures the privacy of a specific individual
with respect to a fixed data set. We show that this is a strict generalization
of the standard DP and inherits all its desirable properties, e.g.,
composition, invariance to side information and closedness to postprocessing,
except that they all hold for every instance separately. When the data is drawn
from a distribution, we show that per-instance DP implies generalization.
Moreover, we provide explicit calculations of the per-instance DP for the
output perturbation on a class of smooth learning problems. The result reveals
an interesting and intuitive fact that an individual has stronger privacy if
he/she has small "leverage score" with respect to the data set and if he/she
can be predicted more accurately using the leave-one-out data set. Our
simulation shows several orders-of-magnitude more favorable privacy and utility
trade-off when we consider the privacy of only the users in the data set. In a
case study on differentially private linear regression, provide a novel
analysis of the One-Posterior-Sample (OPS) estimator and show that when the
data set is well-conditioned it provides $(\epsilon,\delta)$-pDP for any target
individuals and matches the exact lower bound up to a
$1+\tilde{O}(n^{-1}\epsilon^{-2})$ multiplicative factor. We also demonstrate
how we can use a "pDP to DP conversion" step to design AdaOPS which uses
adaptive regularization to achieve the same results with
$(\epsilon,\delta)$-DP.
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Dual quadratic differentials and entire minimal graphs in Heisenberg space | We define holomorphic quadratic differentials for spacelike surfaces with
constant mean curvature in the Lorentzian homogeneous spaces
$\mathbb{L}(\kappa,\tau)$ with isometry group of dimension 4, which are dual to
the Abresch-Rosenberg differentials in the Riemannian counterparts
$\mathbb{E}(\kappa,\tau)$, and obtain some consequences. On the one hand, we
give a very short proof of the Bernstein problem in Heisenberg space, and
provide a geometric description of the family of entire graphs sharing the same
differential in terms of a 2-parameter conformal deformation. On the other
hand, we prove that entire minimal graphs in Heisenberg space have negative
Gauss curvature.
| 0 | 0 | 1 | 0 | 0 | 0 |
Adaptive Modular Exponentiation Methods v.s. Python's Power Function | In this paper we use Python to implement two efficient modular exponentiation
methods: the adaptive m-ary method and the adaptive sliding-window method of
window size k, where both m's are adaptively chosen based on the length of
exponent. We also conduct the benchmark for both methods. Evaluation results
show that compared to the industry-standard efficient implementations of
modular power function in CPython and Pypy, our algorithms can reduce 1-5%
computing time for exponents with more than 3072 bits.
| 1 | 0 | 0 | 0 | 0 | 0 |
Bayesian radiocarbon modelling for beginners | Due to freely available, tailored software, Bayesian statistics is fast
becoming the dominant paradigm in archaeological chronology construction. Such
software provides users with powerful tools for Bayesian inference for
chronological models with little need to undertake formal study of statistical
modelling or computer programming. This runs the risk that it is reduced to the
status of a black-box which is not sensible given the power and complexity of
the modelling tools it implements. In this paper we seek to offer intuitive
insight to ensure that readers from the archaeological research community who
use Bayesian chronological modelling software will be better able to make well
educated choices about the tools and techniques they adopt. Our hope is that
they will then be both better informed about their own research designs and
better prepared to offer constructively critical assessments of the modelling
undertaken by others.
| 0 | 0 | 0 | 1 | 0 | 0 |
Suspended Load Path Tracking Control Using a Tilt-rotor UAV Based on Zonotopic State Estimation | This work addresses the problem of path tracking control of a suspended load
using a tilt-rotor UAV. The main challenge in controlling this kind of system
arises from the dynamic behavior imposed by the load, which is usually coupled
to the UAV by means of a rope, adding unactuated degrees of freedom to the
whole system. Furthermore, to perform the load transportation it is often
needed the knowledge of the load position to accomplish the task. Since
available sensors are commonly embedded in the mobile platform, information on
the load position may not be directly available. To solve this problem in this
work, initially, the kinematics of the multi-body mechanical system are
formulated from the load's perspective, from which a detailed dynamic model is
derived using the Euler-Lagrange approach, yielding a highly coupled, nonlinear
state-space representation of the system, affine in the inputs, with the load's
position and orientation directly represented by state variables. A zonotopic
state estimator is proposed to solve the problem of estimating the load
position and orientation, which is formulated based on sensors located at the
aircraft, with different sampling times, and unknown-but-bounded measurement
noise. To solve the path tracking problem, a discrete-time mixed
$\mathcal{H}_2/\mathcal{H}_\infty$ controller with pole-placement constraints
is designed with guaranteed time-response properties and robust to unmodeled
dynamics, parametric uncertainties, and external disturbances. Results from
numerical experiments, performed in a platform based on the Gazebo simulator
and on a Computer Aided Design (CAD) model of the system, are presented to
corroborate the performance of the zonotopic state estimator along with the
designed controller.
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Decay Estimates and Strichartz Estimates of Fourth-order Schrödinger Operator | We study time decay estimates of the fourth-order Schrödinger operator
$H=(-\Delta)^{2}+V(x)$ in $\mathbb{R}^{d}$ for $d=3$ and $d\geq5$. We analyze
the low energy and high energy behaviour of resolvent $R(H; z)$, and then
derive the Jensen-Kato dispersion decay estimate and local decay estimate for
$e^{-itH}P_{ac}$ under suitable spectrum assumptions of $H$. Based on
Jensen-Kato decay estimate and local decay estimate, we obtain the
$L^1\rightarrow L^{\infty}$ estimate of $e^{-itH}P_{ac}$ in $3$-dimension by
Ginibre argument, and also establish the endpoint global Strichartz estimates
of $e^{-itH}P_{ac}$ for $d\geq5$. Furthermore, using the local decay estimate
and the Georgescu-Larenas-Soffer conjugate operator method, we prove the
Jensen-Kato type decay estimates for some functions of $H$.
| 0 | 0 | 1 | 0 | 0 | 0 |
On the Uniqueness of FROG Methods | The problem of recovering a signal from its power spectrum, called phase
retrieval, arises in many scientific fields. One of many examples is
ultra-short laser pulse characterization in which the electromagnetic field is
oscillating with ~10^15 Hz and phase information cannot be measured directly
due to limitations of the electronic sensors. Phase retrieval is ill-posed in
most cases as there are many different signals with the same Fourier transform
magnitude. To overcome this fundamental ill-posedness, several measurement
techniques are used in practice. One of the most popular methods for complete
characterization of ultra-short laser pulses is the Frequency-Resolved Optical
Gating (FROG). In FROG, the acquired data is the power spectrum of the product
of the unknown pulse with its delayed replica. Therefore the measured signal is
a quartic function of the unknown pulse. A generalized version of FROG, where
the delayed replica is replaced by a second unknown pulse, is called blind
FROG. In this case, the measured signal is quadratic with respect to both
pulses. In this letter we introduce and formulate FROG-type techniques. We then
show that almost all band-limited signals are determined uniquely, up to
trivial ambiguities, by blind FROG measurements (and thus also by FROG), if in
addition we have access to the signals power spectrum.
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Riesz sequences and generalized arithmetic progressions | The purpose of this note is to verify that the results attained in [6] admit
an extension to the multidimensional setting. Namely, for subsets of the two
dimensional torus we find the sharp growth rate of the step(s) of a generalized
arithmetic progression in terms of its size which may be found in an
exponential systems satisfying the Riesz sequence property.
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Positive Scalar Curvature and Minimal Hypersurface Singularities | In this paper we develop methods to extend the minimal hypersurface approach
to positive scalar curvature problems to all dimensions. This includes a proof
of the positive mass theorem in all dimensions without a spin assumption. It
also includes statements about the structure of compact manifolds of positive
scalar curvature extending the work of \cite{sy1} to all dimensions. The
technical work in this paper is to construct minimal slicings and associated
weight functions in the presence of small singular sets and to show that the
singular sets do not become too large in the lower dimensional slices. It is
shown that the singular set in any slice is a closed set with Hausdorff
codimension at least three. In particular for arguments which involve slicing
down to dimension $1$ or $2$ the method is successful. The arguments can be
viewed as an extension of the minimal hypersurface regularity theory to this
setting of minimal slicings.
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Moving Beyond Sub-Gaussianity in High-Dimensional Statistics: Applications in Covariance Estimation and Linear Regression | Concentration inequalities form an essential toolkit in the study of
high-dimensional statistical methods. Most of the relevant statistics
literature is based on the assumptions of sub-Gaussian/sub-exponential random
vectors. In this paper, we bring together various probability inequalities for
sums of independent random variables under much weaker exponential type
(sub-Weibull) tail assumptions. These results extract a part sub-Gaussian tail
behavior in finite samples, matching the asymptotics governed by the central
limit theorem, and are compactly represented in terms of a new Orlicz
quasi-norm - the Generalized Bernstein-Orlicz norm - that typifies such tail
behaviors.
We illustrate the usefulness of these inequalities through the analysis of
four fundamental problems in high-dimensional statistics. In the first two
problems, we study the rate of convergence of the sample covariance matrix in
terms of the maximum elementwise norm and the maximum k-sub-matrix operator
norm which are key quantities of interest in bootstrap procedures and
high-dimensional structured covariance matrix estimation. The third example
concerns the restricted eigenvalue condition, required in high dimensional
linear regression, which we verify for all sub-Weibull random vectors under
only marginal (not joint) tail assumptions on the covariates. To our knowledge,
this is the first unified result obtained in such generality. In the final
example, we consider the Lasso estimator for linear regression and establish
its rate of convergence under much weaker tail assumptions (on the errors as
well as the covariates) than those in the existing literature. The common
feature in all our results is that the convergence rates under most exponential
tails match the usual ones under sub-Gaussian assumptions. Finally, we also
establish a high-dimensional CLT and tail bounds for empirical processes for
sub-Weibulls.
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The additive groups of $\mathbb{Z}$ and $\mathbb{Q}$ with predicates for being square-free | We consider the four structures $(\mathbb{Z}; \mathrm{Sqf}^\mathbb{Z})$,
$(\mathbb{Z}; <, \mathrm{Sqf}^\mathbb{Z})$, $(\mathbb{Q};
\mathrm{Sqf}^\mathbb{Q})$, and $(\mathbb{Q}; <, \mathrm{Sqf}^\mathbb{Q})$ where
$\mathbb{Z}$ is the additive group of integers, $\mathrm{Sqf}^\mathbb{Z}$ is
the set of $a \in \mathbb{Z}$ such that $v_{p}(a) < 2$ for every prime $p$ and
corresponding $p$-adic valuation $v_{p}$, $\mathbb{Q}$ and
$\mathrm{Sqf}^\mathbb{Q}$ are defined likewise for rational numbers, and $<$
denotes the natural ordering on each of these domains. We prove that the second
structure is model-theoretically wild while the other three structures are
model-theoretically tame. Moreover, all these results can be seen as examples
where number-theoretic randomness yields model-theoretic consequences.
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Particle-hole symmetry of charge excitation spectra in the paramagnetic phase of the Hubbard model | The Kotliar and Ruckenstein slave-boson representation of the Hubbard model
allows to obtain an approximation of the charge dynamical response function
resulting from the Gaussian fluctuations around the paramagnetic saddle-point
in analytical form. Numerical evaluation in the thermodynamical limit yields
charge excitation spectra consisting of a continuum, a gapless collective mode
with anisotropic zero-sound velocity, and a correlation induced high-frequency
mode at $\omega\approx U$. In this work we show that this analytical expression
obeys the particle-hole symmetry of the model on any bipartite lattice with one
atom in the unit cell. Other formal aspects of the approach are also addressed.
| 0 | 1 | 0 | 0 | 0 | 0 |
OLÉ: Orthogonal Low-rank Embedding, A Plug and Play Geometric Loss for Deep Learning | Deep neural networks trained using a softmax layer at the top and the
cross-entropy loss are ubiquitous tools for image classification. Yet, this
does not naturally enforce intra-class similarity nor inter-class margin of the
learned deep representations. To simultaneously achieve these two goals,
different solutions have been proposed in the literature, such as the pairwise
or triplet losses. However, such solutions carry the extra task of selecting
pairs or triplets, and the extra computational burden of computing and learning
for many combinations of them. In this paper, we propose a plug-and-play loss
term for deep networks that explicitly reduces intra-class variance and
enforces inter-class margin simultaneously, in a simple and elegant geometric
manner. For each class, the deep features are collapsed into a learned linear
subspace, or union of them, and inter-class subspaces are pushed to be as
orthogonal as possible. Our proposed Orthogonal Low-rank Embedding (OLÉ) does
not require carefully crafting pairs or triplets of samples for training, and
works standalone as a classification loss, being the first reported deep metric
learning framework of its kind. Because of the improved margin between features
of different classes, the resulting deep networks generalize better, are more
discriminative, and more robust. We demonstrate improved classification
performance in general object recognition, plugging the proposed loss term into
existing off-the-shelf architectures. In particular, we show the advantage of
the proposed loss in the small data/model scenario, and we significantly
advance the state-of-the-art on the Stanford STL-10 benchmark.
| 1 | 0 | 0 | 1 | 0 | 0 |
Decidability problems in automaton semigroups | We consider decidability problems in self-similar semigroups, and in
particular in semigroups of automatic transformations of $X^*$. We describe
algorithms answering the word problem, and bound its complexity under some
additional assumptions. We give a partial algorithm that decides in a group
generated by an automaton, given $x,y$, whether an Engel identity
($[\cdots[[x,y],y],\dots,y]=1$ for a long enough commutator sequence) is
satisfied. This algorithm succeeds, importantly, in proving that Grigorchuk's
$2$-group is not Engel. We consider next the problem of recognizing Engel
elements, namely elements $y$ such that the map $x\mapsto[x,y]$ attracts to
$\{1\}$. Although this problem seems intractable in general, we prove that it
is decidable for Grigorchuk's group: Engel elements are precisely those of
order at most $2$. We include, in the text, a large number of open problems.
Our computations were implemented using the package "Fr" within the computer
algebra system "Gap".
| 1 | 0 | 1 | 0 | 0 | 0 |
Migration of a Carbon Adatom on a Charged Single-Walled Carbon Nanotube | We find that negative charges on an armchair single-walled carbon nanotube
(SWCNT) can significantly enhance the migration of a carbon adatom on the
external surfaces of SWCNTs, along the direction of the tube axis. Nanotube
charging results in stronger binding of adatoms to SWCNTs and consequent longer
lifetimes of adatoms before desorption, which in turn increases their migration
distance several orders of magnitude. These results support the hypothesis of
diffusion enhanced SWCNT growth in the volume of arc plasma. This process could
enhance effective carbon flux to the metal catalyst.
| 0 | 1 | 0 | 0 | 0 | 0 |
Function Norms and Regularization in Deep Networks | Deep neural networks (DNNs) have become increasingly important due to their
excellent empirical performance on a wide range of problems. However,
regularization is generally achieved by indirect means, largely due to the
complex set of functions defined by a network and the difficulty in measuring
function complexity. There exists no method in the literature for additive
regularization based on a norm of the function, as is classically considered in
statistical learning theory. In this work, we propose sampling-based
approximations to weighted function norms as regularizers for deep neural
networks. We provide, to the best of our knowledge, the first proof in the
literature of the NP-hardness of computing function norms of DNNs, motivating
the necessity of an approximate approach. We then derive a generalization bound
for functions trained with weighted norms and prove that a natural stochastic
optimization strategy minimizes the bound. Finally, we empirically validate the
improved performance of the proposed regularization strategies for both convex
function sets as well as DNNs on real-world classification and image
segmentation tasks demonstrating improved performance over weight decay,
dropout, and batch normalization. Source code will be released at the time of
publication.
| 1 | 0 | 0 | 1 | 0 | 0 |
Efficiently Clustering Very Large Attributed Graphs | Attributed graphs model real networks by enriching their nodes with
attributes accounting for properties. Several techniques have been proposed for
partitioning these graphs into clusters that are homogeneous with respect to
both semantic attributes and to the structure of the graph. However, time and
space complexities of state of the art algorithms limit their scalability to
medium-sized graphs. We propose SToC (for Semantic-Topological Clustering), a
fast and scalable algorithm for partitioning large attributed graphs. The
approach is robust, being compatible both with categorical and with
quantitative attributes, and it is tailorable, allowing the user to weight the
semantic and topological components. Further, the approach does not require the
user to guess in advance the number of clusters. SToC relies on well known
approximation techniques such as bottom-k sketches, traditional graph-theoretic
concepts, and a new perspective on the composition of heterogeneous distance
measures. Experimental results demonstrate its ability to efficiently compute
high-quality partitions of large scale attributed graphs.
| 1 | 1 | 0 | 0 | 0 | 0 |
Thermochemistry and vertical mixing in the tropospheres of Uranus and Neptune: How convection inhibition can affect the derivation of deep oxygen abundances | Thermochemical models have been used in the past to constrain the deep oxygen
abundance in the gas and ice giant planets from tropospheric CO spectroscopic
measurements. Knowing the oxygen abundance of these planets is a key to better
understand their formation. These models have widely used dry and/or moist
adiabats to extrapolate temperatures from the measured values in the upper
troposphere down to the level where the thermochemical equilibrium between
H$_2$O and CO is established. The mean molecular mass gradient produced by the
condensation of H$_2$O stabilizes the atmosphere against convection and results
in a vertical thermal profile and H$_2$O distribution that departs
significantly from previous estimates. We revisit O/H estimates using an
atmospheric structure that accounts for the inhibition of the convection by
condensation. We use a thermochemical network and the latest observations of CO
in Uranus and Neptune to calculate the internal oxygen enrichment required to
satisfy both these new estimates of the thermal profile and the observations.
We also present the current limitations of such modeling.
| 0 | 1 | 0 | 0 | 0 | 0 |
Attentive cross-modal paratope prediction | Antibodies are a critical part of the immune system, having the function of
directly neutralising or tagging undesirable objects (the antigens) for future
destruction. Being able to predict which amino acids belong to the paratope,
the region on the antibody which binds to the antigen, can facilitate antibody
design and contribute to the development of personalised medicine. The
suitability of deep neural networks has recently been confirmed for this task,
with Parapred outperforming all prior physical models. Our contribution is
twofold: first, we significantly outperform the computational efficiency of
Parapred by leveraging à trous convolutions and self-attention. Secondly, we
implement cross-modal attention by allowing the antibody residues to attend
over antigen residues. This leads to new state-of-the-art results on this task,
along with insightful interpretations.
| 0 | 0 | 0 | 1 | 1 | 0 |
Tomonaga-Luttinger spin liquid in the spin-1/2 inequilateral diamond-chain compound K$_3$Cu$_3$AlO$_2$(SO$_4$)$_4$ | K$_3$Cu$_3$AlO$_2$(SO$_4$)$_4$ is a highly one-dimensional spin-1/2
inequilateral diamond-chain antiferromagnet. Spinon continuum and spin-singlet
dimer excitations are observed in the inelastic neutron scattering spectra,
which is in excellent agreement with a theoretical prediction: a dimer-monomer
composite structure, where the dimer is caused by strong antiferromagnetic
(AFM) coupling and the monomer forms an almost isolated quantum AFM chain
controlling low-energy excitations. Moreover, muon spin rotation/relaxation
spectroscopy shows no long-range ordering down to 90~mK, which is roughly three
orders of magnitude lower than the exchange interaction of the quantum AFM
chain. K$_3$Cu$_3$AlO$_2$(SO$_4$)$_4$ is, thus, regarded as a compound that
exhibits a Tomonaga-Luttinger spin liquid behavior at low temperatures close to
the ground state.
| 0 | 1 | 0 | 0 | 0 | 0 |
Weak Convergence of Stationary Empirical Processes | We offer an umbrella type result which extends weak convergence of the
classical empirical process on the line to that of more general processes
indexed by functions of bounded variation. This extension is not contingent on
the type of dependence of the underlying sequence of random variables. As a
consequence we establish weak convergence for stationary empirical processes
indexed by general classes of functions under alpha mixing conditions.
| 0 | 0 | 1 | 1 | 0 | 0 |
Syntax Error Recovery in Parsing Expression Grammars | Parsing Expression Grammars (PEGs) are a formalism used to describe top-down
parsers with backtracking. As PEGs do not provide a good error recovery
mechanism, PEG-based parsers usually do not recover from syntax errors in the
input, or recover from syntax errors using ad-hoc, implementation-specific
features. The lack of proper error recovery makes PEG parsers unsuitable for
using with Integrated Development Environments (IDEs), which need to build
syntactic trees even for incomplete, syntactically invalid programs.
We propose a conservative extension, based on PEGs with labeled failures,
that adds a syntax error recovery mechanism for PEGs. This extension associates
recovery expressions to labels, where a label now not only reports a syntax
error but also uses this recovery expression to reach a synchronization point
in the input and resume parsing. We give an operational semantics of PEGs with
this recovery mechanism, and use an implementation based on such semantics to
build a robust parser for the Lua language. We evaluate the effectiveness of
this parser, alone and in comparison with a Lua parser with automatic error
recovery generated by ANTLR, a popular parser generator.
| 1 | 0 | 0 | 0 | 0 | 0 |
Collaborative Pressure Ulcer Prevention: An Automated Skin Damage and Pressure Ulcer Assessment Tool for Nursing Professionals, Patients, Family Members and Carers | This paper describes the Pressure Ulcers Online Website, which is a first
step solution towards a new and innovative platform for helping people to
detect, understand and manage pressure ulcers. It outlines the reasons why the
project has been developed and provides a central point of contact for pressure
ulcer analysis and ongoing research. Using state-of-the-art technologies in
convolutional neural networks and transfer learning along with end-to-end web
technologies, this platform allows pressure ulcers to be analysed and findings
to be reported. As the system evolves through collaborative partnerships,
future versions will provide decision support functions to describe the complex
characteristics of pressure ulcers along with information on wound care across
multiple user boundaries. This project is therefore intended to raise awareness
and support for people suffering with or providing care for pressure ulcers.
| 0 | 0 | 0 | 1 | 0 | 0 |
Brain networks reveal the effects of antipsychotic drugs on schizophrenia patients and controls | The study of brain networks, including derived from functional neuroimaging
data, attracts broad interest and represents a rapidly growing
interdisciplinary field. Comparing networks of healthy volunteers with those of
patients can potentially offer new, quantitative diagnostic methods, and a
framework for better understanding brain and mind disorders. We explore resting
state fMRI data through network measures, and demonstrate that not only is
there a distinctive network architecture in the healthy brain that is disrupted
in schizophrenia, but also that both networks respond to medication. We
construct networks representing 15 healthy individuals and 12 schizophrenia
patients (males and females), all of whom are administered three drug
treatments: (i) a placebo; and two antipsychotic medications (ii) aripiprazole
and; (iii) sulpiride. We first reproduce the established finding that brain
networks of schizophrenia patients exhibit increased efficiency and reduced
clustering compared to controls. Our data then reveals that the antipsychotic
medications mitigate this effect, shifting the metrics towards those observed
in healthy volunteers, with a marked difference in efficacy between the two
drugs. Additionally, we find that aripiprazole considerably alters the network
statistics of healthy controls. Using a test of cognitive ability, we establish
that aripiprazole also adversely affects their performance. This provides
evidence that changes to macroscopic brain network architecture result in
measurable behavioural differences. This is the first time different
medications have been assessed in this way. Our results lay the groundwork for
an objective methodology with which to calculate and compare the efficacy of
different treatments of mind and brain disorders.
| 0 | 0 | 0 | 0 | 1 | 0 |
New approach to Minkowski fractional inequalities using generalized k-fractional integral operator | In this paper, we obtain new results related to Minkowski fractional integral
inequality using generalized k-fractional integral operator which is in terms
of the Gauss hypergeometric function.
| 0 | 0 | 1 | 0 | 0 | 0 |
Segmentation of nearly isotropic overlapped tracks in photomicrographs using successive erosions as watershed markers | The major challenges of automatic track counting are distinguishing tracks
and material defects, identifying small tracks and defects of similar size, and
detecting overlapping tracks. Here we address the latter issue using WUSEM, an
algorithm which combines the watershed transform, morphological erosions and
labeling to separate regions in photomicrographs. WUSEM shows reliable results
when used in photomicrographs presenting almost isotropic objects. We tested
this method in two datasets of diallyl phthalate (DAP) photomicrographs and
compared the results when counting manually and using the classic watershed.
The mean automatic/manual efficiency ratio when using WUSEM in the test
datasets is 0.97 +/- 0.11.
| 1 | 1 | 0 | 0 | 0 | 0 |
A Bayesian Hyperprior Approach for Joint Image Denoising and Interpolation, with an Application to HDR Imaging | Recently, impressive denoising results have been achieved by Bayesian
approaches which assume Gaussian models for the image patches. This improvement
in performance can be attributed to the use of per-patch models. Unfortunately
such an approach is particularly unstable for most inverse problems beyond
denoising. In this work, we propose the use of a hyperprior to model image
patches, in order to stabilize the estimation procedure. There are two main
advantages to the proposed restoration scheme: Firstly it is adapted to
diagonal degradation matrices, and in particular to missing data problems (e.g.
inpainting of missing pixels or zooming). Secondly it can deal with signal
dependent noise models, particularly suited to digital cameras. As such, the
scheme is especially adapted to computational photography. In order to
illustrate this point, we provide an application to high dynamic range imaging
from a single image taken with a modified sensor, which shows the effectiveness
of the proposed scheme.
| 1 | 0 | 0 | 1 | 0 | 0 |
Development and evaluation of a deep learning model for protein-ligand binding affinity prediction | Structure based ligand discovery is one of the most successful approaches for
augmenting the drug discovery process. Currently, there is a notable shift
towards machine learning (ML) methodologies to aid such procedures. Deep
learning has recently gained considerable attention as it allows the model to
"learn" to extract features that are relevant for the task at hand. We have
developed a novel deep neural network estimating the binding affinity of
ligand-receptor complexes. The complex is represented with a 3D grid, and the
model utilizes a 3D convolution to produce a feature map of this
representation, treating the atoms of both proteins and ligands in the same
manner. Our network was tested on the CASF "scoring power" benchmark and Astex
Diverse Set and outperformed classical scoring functions. The model, together
with usage instructions and examples, is available as a git repository at
this http URL
| 1 | 0 | 0 | 1 | 0 | 0 |
The Bayesian update: variational formulations and gradient flows | The Bayesian update can be viewed as a variational problem by characterizing
the posterior as the minimizer of a functional. The variational viewpoint is
far from new and is at the heart of popular methods for posterior
approximation. However, some of its consequences seem largely unexplored. We
focus on the following one: defining the posterior as the minimizer of a
functional gives a natural path towards the posterior by moving in the
direction of steepest descent of the functional. This idea is made precise
through the theory of gradient flows, allowing to bring new tools to the study
of Bayesian models and algorithms. Since the posterior may be characterized as
the minimizer of different functionals, several variational formulations may be
considered. We study three of them and their three associated gradient flows.
We show that, in all cases, the rate of convergence of the flows to the
posterior can be bounded by the geodesic convexity of the functional to be
minimized. Each gradient flow naturally suggests a nonlinear diffusion with the
posterior as invariant distribution. These diffusions may be discretized to
build proposals for Markov chain Monte Carlo (MCMC) algorithms. By
construction, the diffusions are guaranteed to satisfy a certain optimality
condition, and rates of convergence are given by the convexity of the
functionals. We use this observation to propose a criterion for the choice of
metric in Riemannian MCMC methods.
| 0 | 0 | 1 | 1 | 0 | 0 |
Magnetic diode at $T$ = 300 K | We report the finding of unidirectional electronic properties, analogous to a
semiconductor diode, in two-dimensional artificial permalloy honeycomb lattice
of ultra-small bond, with a typical length of ~ 12 nm. The unidirectional
transport behavior, characterized by the asymmetric colossal enhancement in
differential conductivity at a modest current application of ~ 10-15 $\mu$A,
persists to T = 300 K in honeycomb lattice of thickness ~ 6 nm. The asymmetric
behavior arises without the application of magnetic field. A qualitative
analysis of experimental data suggests the role of magnetic charge or monopoles
in the unusual observations with strong implication for spintronics.
| 0 | 1 | 0 | 0 | 0 | 0 |
Efficient mixture model for clustering of sparse high dimensional binary data | In this paper we propose a mixture model, SparseMix, for clustering of sparse
high dimensional binary data, which connects model-based with centroid-based
clustering. Every group is described by a representative and a probability
distribution modeling dispersion from this representative. In contrast to
classical mixture models based on EM algorithm, SparseMix:
-is especially designed for the processing of sparse data,
-can be efficiently realized by an on-line Hartigan optimization algorithm,
-is able to automatically reduce unnecessary clusters.
We perform extensive experimental studies on various types of data, which
confirm that SparseMix builds partitions with higher compatibility with
reference grouping than related methods. Moreover, constructed representatives
often better reveal the internal structure of data.
| 1 | 0 | 0 | 1 | 0 | 0 |
Normalized Total Gradient: A New Measure for Multispectral Image Registration | Image registration is a fundamental issue in multispectral image processing.
In filter wheel based multispectral imaging systems, the non-coplanar placement
of the filters always causes the misalignment of multiple channel images. The
selective characteristic of spectral response in multispectral imaging raises
two challenges to image registration. First, the intensity levels of a local
region may be different in individual channel images. Second, the local
intensity may vary rapidly in some channel images while keeps stationary in
others. Conventional multimodal measures, such as mutual information,
correlation coefficient, and correlation ratio, can register images with
different regional intensity levels, but will fail in the circumstance of
severe local intensity variation. In this paper, a new measure, namely
normalized total gradient (NTG), is proposed for multispectral image
registration. The NTG is applied on the difference between two channel images.
This measure is based on the key assumption (observation) that the gradient of
difference image between two aligned channel images is sparser than that
between two misaligned ones. A registration framework, which incorporates image
pyramid and global/local optimization, is further introduced for rigid
transform. Experimental results validate that the proposed method is effective
for multispectral image registration and performs better than conventional
methods.
| 1 | 0 | 0 | 0 | 0 | 0 |
Graphical-model based estimation and inference for differential privacy | Many privacy mechanisms reveal high-level information about a data
distribution through noisy measurements. It is common to use this information
to estimate the answers to new queries. In this work, we provide an approach to
solve this estimation problem efficiently using graphical models, which is
particularly effective when the distribution is high-dimensional but the
measurements are over low-dimensional marginals. We show that our approach is
far more efficient than existing estimation techniques from the privacy
literature and that it can improve the accuracy and scalability of many
state-of-the-art mechanisms.
| 1 | 0 | 0 | 1 | 0 | 0 |
Hierarchical Kriging for multi-fidelity aero-servo-elastic simulators - Application to extreme loads on wind turbines | In the present work, we consider multi-fidelity surrogate modelling to fuse
the output of multiple aero-servo-elastic computer simulators of varying
complexity. In many instances, predictions from multiple simulators for the
same quantity of interest on a wind turbine are available. In this type of
situation, there is strong evidence that fusing the output from multiple
aero-servo-elastic simulators yields better predictive ability and lower model
uncertainty than using any single simulator. Hierarchical Kriging is a
multi-fidelity surrogate modelling method in which the Kriging surrogate model
of the cheap (low-fidelity) simulator is used as a trend of the Kriging
surrogate model of the higher fidelity simulator. We propose a parametric
approach to Hierarchical Kriging where the best surrogate models are selected
based on evaluating all possible combinations of the available Kriging
parameters candidates. The parametric Hierarchical Kriging approach is
illustrated by fusing the extreme flapwise bending moment at the blade root of
a large multi-megawatt wind turbine as a function of wind velocity, turbulence
and wind shear exponent in the presence of model uncertainty and
heterogeneously noisy output. The extreme responses are obtained by two widely
accepted wind turbine specific aero-servo-elastic computer simulators, FAST and
Bladed. With limited high-fidelity simulations, Hierarchical Kriging produces
more accurate predictions of validation data compared to conventional Kriging.
In addition, contrary to conventional Kriging, Hierarchical Kriging is shown to
be a robust surrogate modelling technique because it is less sensitive to the
choice of the Kriging parameters and the choice of the estimation error.
| 0 | 0 | 0 | 1 | 0 | 0 |
Unifying PAC and Regret: Uniform PAC Bounds for Episodic Reinforcement Learning | Statistical performance bounds for reinforcement learning (RL) algorithms can
be critical for high-stakes applications like healthcare. This paper introduces
a new framework for theoretically measuring the performance of such algorithms
called Uniform-PAC, which is a strengthening of the classical Probably
Approximately Correct (PAC) framework. In contrast to the PAC framework, the
uniform version may be used to derive high probability regret guarantees and so
forms a bridge between the two setups that has been missing in the literature.
We demonstrate the benefits of the new framework for finite-state episodic MDPs
with a new algorithm that is Uniform-PAC and simultaneously achieves optimal
regret and PAC guarantees except for a factor of the horizon.
| 1 | 0 | 0 | 1 | 0 | 0 |
Alternative Semantic Representations for Zero-Shot Human Action Recognition | A proper semantic representation for encoding side information is key to the
success of zero-shot learning. In this paper, we explore two alternative
semantic representations especially for zero-shot human action recognition:
textual descriptions of human actions and deep features extracted from still
images relevant to human actions. Such side information are accessible on Web
with little cost, which paves a new way in gaining side information for
large-scale zero-shot human action recognition. We investigate different
encoding methods to generate semantic representations for human actions from
such side information. Based on our zero-shot visual recognition method, we
conducted experiments on UCF101 and HMDB51 to evaluate two proposed semantic
representations . The results suggest that our proposed text- and image-based
semantic representations outperform traditional attributes and word vectors
considerably for zero-shot human action recognition. In particular, the
image-based semantic representations yield the favourable performance even
though the representation is extracted from a small number of images per class.
| 1 | 0 | 0 | 0 | 0 | 0 |
Being Corrupt Requires Being Clever, But Detecting Corruption Doesn't | We consider a variation of the problem of corruption detection on networks
posed by Alon, Mossel, and Pemantle '15. In this model, each vertex of a graph
can be either truthful or corrupt. Each vertex reports about the types
(truthful or corrupt) of all its neighbors to a central agency, where truthful
nodes report the true types they see and corrupt nodes report adversarially.
The central agency aggregates these reports and attempts to find a single
truthful node. Inspired by real auditing networks, we pose our problem for
arbitrary graphs and consider corruption through a computational lens. We
identify a key combinatorial parameter of the graph $m(G)$, which is the
minimal number of corrupted agents needed to prevent the central agency from
identifying a single corrupt node. We give an efficient (in fact, linear time)
algorithm for the central agency to identify a truthful node that is successful
whenever the number of corrupt nodes is less than $m(G)/2$. On the other hand,
we prove that for any constant $\alpha > 1$, it is NP-hard to find a subset of
nodes $S$ in $G$ such that corrupting $S$ prevents the central agency from
finding one truthful node and $|S| \leq \alpha m(G)$, assuming the Small Set
Expansion Hypothesis (Raghavendra and Steurer, STOC '10). We conclude that
being corrupt requires being clever, while detecting corruption does not.
Our main technical insight is a relation between the minimum number of
corrupt nodes required to hide all truthful nodes and a certain notion of
vertex separability for the underlying graph. Additionally, this insight lets
us design an efficient algorithm for a corrupt party to decide which graphs
require the fewest corrupted nodes, up to a multiplicative factor of $O(\log
n)$.
| 1 | 0 | 0 | 0 | 0 | 0 |
Computing the homology of basic semialgebraic sets in weak exponential time | We describe and analyze an algorithm for computing the homology (Betti
numbers and torsion coefficients) of basic semialgebraic sets which works in
weak exponential time. That is, out of a set of exponentially small measure in
the space of data the cost of the algorithm is exponential in the size of the
data. All algorithms previously proposed for this problem have a complexity
which is doubly exponential (and this is so for almost all data).
| 1 | 0 | 1 | 0 | 0 | 0 |
Deterministic and Randomized Diffusion based Iterative Generalized Hard Thresholding (DiFIGHT) for Distributed Sparse Signal Recovery | In this paper, we propose a distributed iterated hard thresholding algorithm
termed DiFIGHT over a network that is built on the diffusion mechanism and also
propose a modification of the proposed algorithm termed MoDiFIGHT, that has low
complexity in terms of communication in the network. We additionally propose
four different strategies termed RP, RNP, RGPr, and RGNPr that are used to
randomly select a subset of nodes that are subsequently activated to take part
in the distributed algorithm, so as to reduce the mean number of communications
during the run of the distributed algorithm. We present theoretical estimates
of the long run communication per unit time for these different strategies,
when used by the two proposed algorithms. Also, we present an analysis of the
two proposed algorithms and provide provable bounds on their recovery
performance with or without using the random node selection strategies.
Finally, we use numerical studies to show that both when the random strategies
are used as well as when they are not used, the proposed algorithms display
performances far superior to distributed IHT algorithm using consensus
mechanism.
| 1 | 0 | 0 | 0 | 0 | 0 |
Iterated doubles of the Joker and their realisability | Let $\mathcal{A}(1)^*$ be the subHopf algebra of the mod~$2$ Steenrod algebra
$\mathcal{A}^*$ generated by $\mathrm{Sq}^1$ and $\mathrm{Sq}^2$. The
\emph{Joker} is the cyclic $\mathcal{A}(1)^*$-module
$\mathcal{A}(1)^*/\mathcal{A}(1)^*\{\mathrm{Sq}^3\}$ which plays a special
rôle in the study of $\mathcal{A}(1)^*$-modules. We discuss realisations of
the Joker both as an $\mathcal{A}^*$-module and as the cohomology of a
spectrum. We also consider analogous $\mathcal{A}(n)^*$-modules for $n\geq2$
and prove realisability results (both stable and unstable) for $n=2,3$ and
non-realisability results for $n\geq4$.
| 0 | 0 | 1 | 0 | 0 | 0 |
On subtrees of the representation tree in rational base numeration systems | Every rational number p/q defines a rational base numeration system in which
every integer has a unique finite representation, up to leading zeroes. This
work is a contribution to the study of the set of the representations of
integers. This prefix-closed subset of the free monoid is naturally represented
as a highly non-regular tree. Its nodes are the integers, its edges bear labels
taken in {0,1,...,p-1}, and its subtrees are all distinct.
We associate with each subtree (or with its root n) three infinite words. The
bottom word of n is the lexicographically smallest word that is the label of a
branch of the subtree. The top word of n is defined similarly. The span-word of
n is the digitwise difference between the latter and the former.
First, we show that the set of all the span-words is accepted by an infinite
automaton whose underlying graph is essentially the same as the tree itself.
Second, we study the function that computes for all n the bottom word
associated with n+1 from the one associated with n, and show that it is
realised by an infinite sequential transducer whose underlying graph is once
again essentially the same as the tree itself.
An infinite word may be interpreted as an expansion in base p/q after the
radix point, hence evaluated to a real number. If T is a subtree whose root is
n, then the evaluations of the labels of the branches of T form an interval of
$\mathbb{R}$. The length of this interval is called the span of n and is equal
to the evaluation of the span-word of n. The set of all spans is then a subset
of R and we use the preceding construction to study its topological closure. We
show that it is an interval when p is greater than or equal to 2q-1, and a
Cantor set of measure zero otherwise.
| 1 | 0 | 0 | 0 | 0 | 0 |
A Practical Method for Solving Contextual Bandit Problems Using Decision Trees | Many efficient algorithms with strong theoretical guarantees have been
proposed for the contextual multi-armed bandit problem. However, applying these
algorithms in practice can be difficult because they require domain expertise
to build appropriate features and to tune their parameters. We propose a new
method for the contextual bandit problem that is simple, practical, and can be
applied with little or no domain expertise. Our algorithm relies on decision
trees to model the context-reward relationship. Decision trees are
non-parametric, interpretable, and work well without hand-crafted features. To
guide the exploration-exploitation trade-off, we use a bootstrapping approach
which abstracts Thompson sampling to non-Bayesian settings. We also discuss
several computational heuristics and demonstrate the performance of our method
on several datasets.
| 1 | 0 | 0 | 1 | 0 | 0 |
Trainable back-propagated functional transfer matrices | Connections between nodes of fully connected neural networks are usually
represented by weight matrices. In this article, functional transfer matrices
are introduced as alternatives to the weight matrices: Instead of using real
weights, a functional transfer matrix uses real functions with trainable
parameters to represent connections between nodes. Multiple functional transfer
matrices are then stacked together with bias vectors and activations to form
deep functional transfer neural networks. These neural networks can be trained
within the framework of back-propagation, based on a revision of the delta
rules and the error transmission rule for functional connections. In
experiments, it is demonstrated that the revised rules can be used to train a
range of functional connections: 20 different functions are applied to neural
networks with up to 10 hidden layers, and most of them gain high test
accuracies on the MNIST database. It is also demonstrated that a functional
transfer matrix with a memory function can roughly memorise a non-cyclical
sequence of 400 digits.
| 1 | 0 | 0 | 1 | 0 | 0 |
Multiple Exciton Generation in Chiral Carbon Nanotubes: Density Functional Theory Based Computation | We use Boltzmann transport equation (BE) to study time evolution of a
photo-excited state in a nanoparticle including phonon-mediated exciton
relaxation and the multiple exciton generation (MEG) processes, such as
exciton-to-biexciton multiplication and biexciton-to-exciton recombination. BE
collision integrals are computed using Kadanoff-Baym-Keldysh many-body
perturbation theory (MBPT) based on density functional theory (DFT)
simulations, including exciton effects. We compute internal quantum efficiency
(QE), which is the number of excitons generated from an absorbed photon in the
course of the relaxation. We apply this approach to chiral single-wall carbon
nanotubes (SWCNTs), such as (6,2), and (6,5). We predict efficient MEG in the
(6,2) and (6,5) SWCNTs within the solar spectrum range starting at the $2 E_g$
energy threshold and with QE reaching $\sim 1.6$ at about $3 E_g,$ where $E_g$
is the electronic gap.
| 0 | 1 | 0 | 0 | 0 | 0 |
Turaev-Viro invariants, colored Jones polynomials and volume | We obtain a formula for the Turaev-Viro invariants of a link complement in
terms of values of the colored Jones polynomial of the link. As an application
we give the first examples for which the volume conjecture of Chen and the
third named author\,\cite{Chen-Yang} is verified. Namely, we show that the
asymptotics of the Turaev-Viro invariants of the Figure-eight knot and the
Borromean rings complement determine the corresponding hyperbolic volumes. Our
calculations also exhibit new phenomena of asymptotic behavior of values of the
colored Jones polynomials that seem not to be predicted by neither the
Kashaev-Murakami-Murakami volume conjecture and various of its generalizations
nor by Zagier's quantum modularity conjecture. We conjecture that the
asymptotics of the Turaev-Viro invariants of any link complement determine the
simplicial volume of the link, and verify it for all knots with zero simplicial
volume. Finally we observe that our simplicial volume conjecture is stable
under connect sum and split unions of links.
| 0 | 0 | 1 | 0 | 0 | 0 |
Credit card fraud detection through parenclitic network analysis | The detection of frauds in credit card transactions is a major topic in
financial research, of profound economic implications. While this has hitherto
been tackled through data analysis techniques, the resemblances between this
and other problems, like the design of recommendation systems and of diagnostic
/ prognostic medical tools, suggest that a complex network approach may yield
important benefits. In this contribution we present a first hybrid data mining
/ complex network classification algorithm, able to detect illegal instances in
a real card transaction data set. It is based on a recently proposed network
reconstruction algorithm that allows creating representations of the deviation
of one instance from a reference group. We show how the inclusion of features
extracted from the network data representation improves the score obtained by a
standard, neural network-based classification algorithm; and additionally how
this combined approach can outperform a commercial fraud detection system in
specific operation niches. Beyond these specific results, this contribution
represents a new example on how complex networks and data mining can be
integrated as complementary tools, with the former providing a view to data
beyond the capabilities of the latter.
| 1 | 1 | 0 | 0 | 0 | 0 |
On the Consistency of Graph-based Bayesian Learning and the Scalability of Sampling Algorithms | A popular approach to semi-supervised learning proceeds by endowing the input
data with a graph structure in order to extract geometric information and
incorporate it into a Bayesian framework. We introduce new theory that gives
appropriate scalings of graph parameters that provably lead to a well-defined
limiting posterior as the size of the unlabeled data set grows. Furthermore, we
show that these consistency results have profound algorithmic implications.
When consistency holds, carefully designed graph-based Markov chain Monte Carlo
algorithms are proved to have a uniform spectral gap, independent of the number
of unlabeled inputs. Several numerical experiments corroborate both the
statistical consistency and the algorithmic scalability established by the
theory.
| 1 | 0 | 0 | 1 | 0 | 0 |
Bayesian Optimization for Parameter Tuning of the XOR Neural Network | When applying Machine Learning techniques to problems, one must select model
parameters to ensure that the system converges but also does not become stuck
at the objective function's local minimum. Tuning these parameters becomes a
non-trivial task for large models and it is not always apparent if the user has
found the optimal parameters. We aim to automate the process of tuning a Neural
Network, (where only a limited number of parameter search attempts are
available) by implementing Bayesian Optimization. In particular, by assigning
Gaussian Process Priors to the parameter space, we utilize Bayesian
Optimization to tune an Artificial Neural Network used to learn the XOR
function, with the result of achieving higher prediction accuracy.
| 1 | 0 | 0 | 1 | 0 | 0 |
A differential model for growing sandpiles on networks | We consider a system of differential equations of Monge-Kantorovich type
which describes the equilibrium configurations of granular material poured by a
constant source on a network. Relying on the definition of viscosity solution
for Hamilton-Jacobi equations on networks, recently introduced by P.-L. Lions
and P. E. Souganidis, we prove existence and uniqueness of the solution of the
system and we discuss its numerical approximation. Some numerical experiments
are carried out.
| 0 | 0 | 1 | 0 | 0 | 0 |
DCT-like Transform for Image Compression Requires 14 Additions Only | A low-complexity 8-point orthogonal approximate DCT is introduced. The
proposed transform requires no multiplications or bit-shift operations. The
derived fast algorithm requires only 14 additions, less than any existing DCT
approximation. Moreover, in several image compression scenarios, the proposed
transform could outperform the well-known signed DCT, as well as
state-of-the-art algorithms.
| 1 | 0 | 0 | 1 | 0 | 0 |
On realizability of sign patterns by real polynomials | The classical Descartes' rule of signs limits the number of positive roots of
a real polynomial in one variable by the number of sign changes in the sequence
of its coefficients. One can ask the question which pairs of nonnegative
integers $(p,n)$, chosen in accordance with this rule and with some other
natural conditions, can be the pairs of numbers of positive and negative roots
of a real polynomial with prescribed signs of the coefficients. The paper
solves this problem for degree $8$ polynomials.
| 0 | 0 | 1 | 0 | 0 | 0 |
HAlign-II: efficient ultra-large multiple sequence alignment and phylogenetic tree reconstruction with distributed and parallel computing | Multiple sequence alignment (MSA) plays a key role in biological sequence
analyses, especially in phylogenetic tree construction. Extreme increase in
next-generation sequencing results in shortage of efficient ultra-large
biological sequence alignment approaches for coping with different sequence
types. Distributed and parallel computing represents a crucial technique for
accelerating ultra-large sequence analyses. Based on HAlign and Spark
distributed computing system, we implement a highly cost-efficient and
time-efficient HAlign-II tool to address ultra-large multiple biological
sequence alignment and phylogenetic tree construction. After comparing with
most available state-of-the-art methods, our experimental results indicate the
following: 1) HAlign-II can efficiently carry out MSA and construct
phylogenetic trees with ultra-large biological sequences; 2) HAlign-II shows
extremely high memory efficiency and scales well with increases in computing
resource; 3) HAlign-II provides a user-friendly web server based on our
distributed computing infrastructure. HAlign-II with open-source codes and
datasets was established at this http URL.
| 1 | 0 | 0 | 0 | 0 | 0 |
Search for Evergreens in Science: A Functional Data Analysis | Evergreens in science are papers that display a continual rise in annual
citations without decline, at least within a sufficiently long time period.
Aiming to better understand evergreens in particular and patterns of citation
trajectory in general, this paper develops a functional data analysis method to
cluster citation trajectories of a sample of 1699 research papers published in
1980 in the American Physical Society (APS) journals. We propose a functional
Poisson regression model for individual papers' citation trajectories, and fit
the model to the observed 30-year citations of individual papers by functional
principal component analysis and maximum likelihood estimation. Based on the
estimated paper-specific coefficients, we apply the K-means clustering
algorithm to cluster papers into different groups, for uncovering general types
of citation trajectories. The result demonstrates the existence of an evergreen
cluster of papers that do not exhibit any decline in annual citations over 30
years.
| 1 | 0 | 0 | 1 | 0 | 0 |
Tied Hidden Factors in Neural Networks for End-to-End Speaker Recognition | In this paper we propose a method to model speaker and session variability
and able to generate likelihood ratios using neural networks in an end-to-end
phrase dependent speaker verification system. As in Joint Factor Analysis, the
model uses tied hidden variables to model speaker and session variability and a
MAP adaptation of some of the parameters of the model. In the training
procedure our method jointly estimates the network parameters and the values of
the speaker and channel hidden variables. This is done in a two-step
backpropagation algorithm, first the network weights and factor loading
matrices are updated and then the hidden variables, whose gradients are
calculated by aggregating the corresponding speaker or session frames, since
these hidden variables are tied. The last layer of the network is defined as a
linear regression probabilistic model whose inputs are the previous layer
outputs. This choice has the advantage that it produces likelihoods and
additionally it can be adapted during the enrolment using MAP without the need
of a gradient optimization. The decisions are made based on the ratio of the
output likelihoods of two neural network models, speaker adapted and universal
background model. The method was evaluated on the RSR2015 database.
| 1 | 0 | 0 | 0 | 0 | 0 |
An Optimal Control Formulation of Pulse-Based Control Using Koopman Operator | In many applications, and in systems/synthetic biology, in particular, it is
desirable to compute control policies that force the trajectory of a bistable
system from one equilibrium (the initial point) to another equilibrium (the
target point), or in other words to solve the switching problem. It was
recently shown that, for monotone bistable systems, this problem admits
easy-to-implement open-loop solutions in terms of temporal pulses (i.e., step
functions of fixed length and fixed magnitude). In this paper, we develop this
idea further and formulate a problem of convergence to an equilibrium from an
arbitrary initial point. We show that this problem can be solved using a static
optimization problem in the case of monotone systems. Changing the initial
point to an arbitrary state allows to build closed-loop, event-based or
open-loop policies for the switching/convergence problems. In our derivations
we exploit the Koopman operator, which offers a linear infinite-dimensional
representation of an autonomous nonlinear system. One of the main advantages of
using the Koopman operator is the powerful computational tools developed for
this framework. Besides the presence of numerical solutions, the
switching/convergence problem can also serve as a building block for solving
more complicated control problems and can potentially be applied to
non-monotone systems. We illustrate this argument on the problem of
synchronizing cardiac cells by defibrillation. Potentially, our approach can be
extended to problems with different parametrizations of control signals since
the only fundamental limitation is the finite time application of the control
signal.
| 1 | 0 | 1 | 0 | 0 | 0 |
A Converse to Banach's Fixed Point Theorem and its CLS Completeness | Banach's fixed point theorem for contraction maps has been widely used to
analyze the convergence of iterative methods in non-convex problems. It is a
common experience, however, that iterative maps fail to be globally contracting
under the natural metric in their domain, making the applicability of Banach's
theorem limited. We explore how generally we can apply Banach's fixed point
theorem to establish the convergence of iterative methods when pairing it with
carefully designed metrics.
Our first result is a strong converse of Banach's theorem, showing that it is
a universal analysis tool for establishing global convergence of iterative
methods to unique fixed points, and for bounding their convergence rate. In
other words, we show that, whenever an iterative map globally converges to a
unique fixed point, there exists a metric under which the iterative map is
contracting and which can be used to bound the number of iterations until
convergence. We illustrate our approach in the widely used power method,
providing a new way of bounding its convergence rate through contraction
arguments.
We next consider the computational complexity of Banach's fixed point
theorem. Making the proof of our converse theorem constructive, we show that
computing a fixed point whose existence is guaranteed by Banach's fixed point
theorem is CLS-complete. We thus provide the first natural complete problem for
the class CLS, which was defined in [Daskalakis, Papadimitriou 2011] to capture
the complexity of problems such as P-matrix LCP, computing KKT-points, and
finding mixed Nash equilibria in congestion and network coordination games.
| 1 | 0 | 1 | 1 | 0 | 0 |
Improved Discrete RRT for Coordinated Multi-robot Planning | This paper addresses the problem of coordination of a fleet of mobile robots
- the problem of finding an optimal set of collision-free trajectories for
individual robots in the fleet. Many approaches have been introduced during the
last decades, but a minority of them is practically applicable, i.e. fast,
producing near-optimal solutions, and complete. We propose a novel
probabilistic approach based on the Rapidly Exploring Random Tree algorithm
(RRT) by significantly improving its multi-robot variant for discrete
environments. The presented experimental results show that the proposed
approach is fast enough to solve problems with tens of robots in seconds.
Although the solutions generated by the approach are slightly worse than one of
the best state-of-the-art algorithms presented in (ter Mors et al., 2010), it
solves problems where ter Mors's algorithm fails.
| 1 | 0 | 0 | 0 | 0 | 0 |
A note on the stratification by automorphisms of smooth plane curves of genus 6 | In this note, we give a so-called representative classification for the
strata by automorphism group of smooth $\bar{k}$-plane curves of genus $6$,
where $\bar{k}$ is a fixed separable closure of a field $k$ of characteristic
$p = 0$ or $p > 13$. We start with a classification already obtained by the
first author and we use standard techniques.
Interestingly, in the way to get these families for the different strata, we
find two remarkable phenomenons that did not appear before. One is the
existence of a non $0$-dimensional final stratum of plane curves. At a first
sight it may sound odd, but we will see that this is a normal situation for
higher degrees and we will give a explanation for it.
We explicitly describe representative families for all strata, except for the
stratum with automorphism group $\mathbb{Z}/5\mathbb{Z}$. Here we find the
second difference with the lower genus cases where the previous techniques do
not fully work. Fortunately, we are still able to prove the existence of such
family by applying a version of Luroth's theorem in dimension $2$.
| 0 | 0 | 1 | 0 | 0 | 0 |
Relativistic verifiable delegation of quantum computation | The importance of being able to verify quantum computation delegated to
remote servers increases with recent development of quantum technologies. In
some of the proposed protocols for this task, a client delegates her quantum
computation to non-communicating servers. The fact that the servers do not
communicate is not physically justified and it is essential for the proof of
security of such protocols. For the best of our knowledge, we present in this
work the first verifiable delegation scheme where a classical client delegates
her quantum computation to two entangled servers that are allowed to
communicate, but respecting the plausible assumption that information cannot be
propagated faster than speed of light. We achieve this result by proposing the
first one-round two-prover game for the Local Hamiltonian problem where provers
only need polynomial time quantum computation and access to copies of the
groundstate of the Hamiltonian.
| 1 | 0 | 0 | 0 | 0 | 0 |
Finiteness of étale fundamental groups by reduction modulo $p$ | We introduce a spreading out technique to deduce finiteness results for
étale fundamental groups of complex varieties by characteristic $p$ methods,
and apply this to recover a finiteness result proven recently for local
fundamental groups in characteristic $0$ using birational geometry.
| 0 | 0 | 1 | 0 | 0 | 0 |
Morphological Error Detection in 3D Segmentations | Deep learning algorithms for connectomics rely upon localized classification,
rather than overall morphology. This leads to a high incidence of erroneously
merged objects. Humans, by contrast, can easily detect such errors by acquiring
intuition for the correct morphology of objects. Biological neurons have
complicated and variable shapes, which are challenging to learn, and merge
errors take a multitude of different forms. We present an algorithm, MergeNet,
that shows 3D ConvNets can, in fact, detect merge errors from high-level
neuronal morphology. MergeNet follows unsupervised training and operates across
datasets. We demonstrate the performance of MergeNet both on a variety of
connectomics data and on a dataset created from merged MNIST images.
| 1 | 0 | 0 | 1 | 0 | 0 |
Structural Feature Selection for Event Logs | We consider the problem of classifying business process instances based on
structural features derived from event logs. The main motivation is to provide
machine learning based techniques with quick response times for interactive
computer assisted root cause analysis. In particular, we create structural
features from process mining such as activity and transition occurrence counts,
and ordering of activities to be evaluated as potential features for
classification. We show that adding such structural features increases the
amount of information thus potentially increasing classification accuracy.
However, there is an inherent trade-off as using too many features leads to too
long run-times for machine learning classification models. One way to improve
the machine learning algorithms' run-time is to only select a small number of
features by a feature selection algorithm. However, the run-time required by
the feature selection algorithm must also be taken into account. Also, the
classification accuracy should not suffer too much from the feature selection.
The main contributions of this paper are as follows: First, we propose and
compare six different feature selection algorithms by means of an experimental
setup comparing their classification accuracy and achievable response times.
Second, we discuss the potential use of feature selection results for computer
assisted root cause analysis as well as the properties of different types of
structural features in the context of feature selection.
| 1 | 0 | 0 | 1 | 0 | 0 |
Counting $G$-Extensions by Discriminant | The problem of analyzing the number of number field extensions $L/K$ with
bounded (relative) discriminant has been the subject of renewed interest in
recent years, with significant advances made by Schmidt, Ellenberg-Venkatesh,
Bhargava, Bhargava-Shankar-Wang, and others. In this paper, we use the geometry
of numbers and invariant theory of finite groups, in a manner similar to
Ellenberg and Venkatesh, to give an upper bound on the number of extensions
$L/K$ with fixed degree, bounded relative discriminant, and specified Galois
closure.
| 0 | 0 | 1 | 0 | 0 | 0 |
Robust and Efficient Transfer Learning with Hidden-Parameter Markov Decision Processes | We introduce a new formulation of the Hidden Parameter Markov Decision
Process (HiP-MDP), a framework for modeling families of related tasks using
low-dimensional latent embeddings. Our new framework correctly models the joint
uncertainty in the latent parameters and the state space. We also replace the
original Gaussian Process-based model with a Bayesian Neural Network, enabling
more scalable inference. Thus, we expand the scope of the HiP-MDP to
applications with higher dimensions and more complex dynamics.
| 1 | 0 | 0 | 1 | 0 | 0 |
Lattice Gaussian Sampling by Markov Chain Monte Carlo: Bounded Distance Decoding and Trapdoor Sampling | Sampling from the lattice Gaussian distribution plays an important role in
various research fields. In this paper, the Markov chain Monte Carlo
(MCMC)-based sampling technique is advanced in several fronts. Firstly, the
spectral gap for the independent Metropolis-Hastings-Klein (MHK) algorithm is
derived, which is then extended to Peikert's algorithm and rejection sampling;
we show that independent MHK exhibits faster convergence. Then, the performance
of bounded distance decoding using MCMC is analyzed, revealing a flexible
trade-off between the decoding radius and complexity. MCMC is further applied
to trapdoor sampling, again offering a trade-off between security and
complexity. Finally, the independent multiple-try Metropolis-Klein (MTMK)
algorithm is proposed to enhance the convergence rate. The proposed algorithms
allow parallel implementation, which is beneficial for practical applications.
| 1 | 0 | 0 | 0 | 0 | 0 |
$S$-Leaping: An adaptive, accelerated stochastic simulation algorithm, bridging $τ$-leaping and $R$-leaping | We propose the $S$-leaping algorithm for the acceleration of Gillespie's
stochastic simulation algorithm that combines the advantages of the two main
accelerated methods; the $\tau$-leaping and $R$-leaping algorithms. These
algorithms are known to be efficient under different conditions; the
$\tau$-leaping is efficient for non-stiff systems or systems with partial
equilibrium, while the $R$-leaping performs better in stiff system thanks to an
efficient sampling procedure. However, even a small change in a system's set up
can critically affect the nature of the simulated system and thus reduce the
efficiency of an accelerated algorithm. The proposed algorithm combines the
efficient time step selection from the $\tau$-leaping with the effective
sampling procedure from the $R$-leaping algorithm. The $S$-leaping is shown to
maintain its efficiency under different conditions and in the case of large and
stiff systems or systems with fast dynamics, the $S$-leaping outperforms both
methods. We demonstrate the performance and the accuracy of the $S$-leaping in
comparison with the $\tau$-leaping and $R$-leaping on a number of benchmark
systems involving biological reaction networks.
| 0 | 0 | 0 | 0 | 1 | 0 |
Diclofenac sodium ion exchange resin complex loaded melt cast films for sustained release ocular delivery | The goal of the present study is to develop polymeric matrix films loaded
with a combination of free diclofenac sodium (DFSfree) and DFS:Ion exchange
resin complexes (DFS:IR) for immediate and sustained release profiles,
respectively. Effect of ratio of DFS and IR on the DFS:IR complexation
efficiency was studied using batch processing. DFS:IR complex, DFSfree, or a
combination of DFSfree+DFS:IR loaded matrix films were prepared by melt-cast
technology. DFS content was 20% w/w in these matrix films. In vitro
transcorneal permeability from the film formulations were compared against DFS
solution, using a side-by-side diffusion apparatus, over a 6 h period. Ocular
disposition of DFS from the solution, films and corresponding suspensions were
evaluated in conscious New Zealand albino rabbits, 4 h and 8 h post-topical
administration. All in vivo studies were carried out as per the University of
Mississippi IACUC approved protocol. Complexation efficiency of DFS:IR was
found to be 99% with a 1:1 ratio of DFS:IR. DFS release from DFS:IR suspension
and the film were best-fit to a Higuchi model. In vitro transcorneal flux with
the DFSfree+DFS:IR(1:1)(1 + 1) was twice that of only DFS:IR(1:1) film. In
vivo, DFS solution and DFS:IR(1:1) suspension formulations were not able to
maintain therapeutic DFS levels in the aqueous humor (AH). Both DFSfree and
DFSfree+DFS:IR(1:1)(3 + 1) loaded matrix films were able to achieve and
maintain high DFS concentrations in the AH, but elimination of DFS from the
ocular tissues was much faster with the DFSfree formulation. DFSfree+DFS:IR
combination loaded matrix films were able to deliver and maintain therapeutic
DFS concentrations in the anterior ocular chamber for up to 8 h. Thus, free
drug/IR complex loaded matrix films could be a potential topical ocular
delivery platform for achieving immediate and sustained release
characteristics.
| 0 | 1 | 0 | 0 | 0 | 0 |
Method of precision increase by averaging with application to numerical differentiation | If several independent algorithms for a computer-calculated quantity exist,
then one can expect their results (which differ because of numerical errors) to
follow approximately Gaussian distribution. The mean of this distribution,
interpreted as the value of the quantity of interest, can be determined with
better precision than what is the precision provided by a single algorithm.
Often, with lack of enough independent algorithms, one can proceed differently:
many practical algorithms introduce a bias using a parameter, e.g. a small but
finite number to compute a limit or a large but finite number (cutoff) to
approximate infinity. One may vary such parameter of a single algorithm and
interpret the resulting numbers as generated by several algorithms. A numerical
evidence for the validity of this approach is shown for differentiation.
| 0 | 0 | 1 | 0 | 0 | 0 |
On-line Building Energy Optimization using Deep Reinforcement Learning | Unprecedented high volumes of data are becoming available with the growth of
the advanced metering infrastructure. These are expected to benefit planning
and operation of the future power system, and to help the customers transition
from a passive to an active role. In this paper, we explore for the first time
in the smart grid context the benefits of using Deep Reinforcement Learning, a
hybrid type of methods that combines Reinforcement Learning with Deep Learning,
to perform on-line optimization of schedules for building energy management
systems. The learning procedure was explored using two methods, Deep Q-learning
and Deep Policy Gradient, both of them being extended to perform multiple
actions simultaneously. The proposed approach was validated on the large-scale
Pecan Street Inc. database. This highly-dimensional database includes
information about photovoltaic power generation, electric vehicles as well as
buildings appliances. Moreover, these on-line energy scheduling strategies
could be used to provide real-time feedback to consumers to encourage more
efficient use of electricity.
| 1 | 0 | 1 | 0 | 0 | 0 |
A KL-LUCB Bandit Algorithm for Large-Scale Crowdsourcing | This paper focuses on best-arm identification in multi-armed bandits with
bounded rewards. We develop an algorithm that is a fusion of lil-UCB and
KL-LUCB, offering the best qualities of the two algorithms in one method. This
is achieved by proving a novel anytime confidence bound for the mean of bounded
distributions, which is the analogue of the LIL-type bounds recently developed
for sub-Gaussian distributions. We corroborate our theoretical results with
numerical experiments based on the New Yorker Cartoon Caption Contest.
| 0 | 0 | 1 | 1 | 0 | 0 |
Refractive index tomography with structured illumination | This work introduces a novel reinterpretation of structured illumination (SI)
microscopy for coherent imaging that allows three-dimensional imaging of
complex refractive index (RI). To do so, we show that coherent SI is
mathematically equivalent to a superposition of angled illuminations. It
follows that raw acquisitions for standard SI-enhanced quantitative-phase
images can be processed into complex electric-field maps describing sample
diffraction under angled illuminations. Standard diffraction tomography (DT)
computation can then be used to reconstruct the sample 3D RI distribution at
sub-diffraction resolutions. We demonstrate this concept by using a
SI-quantitative-phase imaging system to computationally reconstruct 3D RI
distributions of human breast (MCF-7) and colorectal (HT-29) adenocarcinoma
cells. Our experimental setup uses a spatial light modulator to generate
structured patterns at the sample and collects angle-dependent sample
diffraction using a common-path, off-axis interference configuration with no
moving components. Furthermore, this technique holds promise for easy pairing
with SI fluorescence microscopy, and important future extensions may include
multimodal, sub-diffraction resolution, 3D RI and fluorescent visualizations.
| 0 | 1 | 0 | 0 | 0 | 0 |
Foreign English Accent Adjustment by Learning Phonetic Patterns | State-of-the-art automatic speech recognition (ASR) systems struggle with the
lack of data for rare accents. For sufficiently large datasets, neural engines
tend to outshine statistical models in most natural language processing
problems. However, a speech accent remains a challenge for both approaches.
Phonologists manually create general rules describing a speaker's accent, but
their results remain underutilized. In this paper, we propose a model that
automatically retrieves phonological generalizations from a small dataset. This
method leverages the difference in pronunciation between a particular dialect
and General American English (GAE) and creates new accented samples of words.
The proposed model is able to learn all generalizations that previously were
manually obtained by phonologists. We use this statistical method to generate a
million phonological variations of words from the CMU Pronouncing Dictionary
and train a sequence-to-sequence RNN to recognize accented words with 59%
accuracy.
| 1 | 0 | 0 | 1 | 0 | 0 |
The geometry of hypothesis testing over convex cones: Generalized likelihood tests and minimax radii | We consider a compound testing problem within the Gaussian sequence model in
which the null and alternative are specified by a pair of closed, convex cones.
Such cone testing problem arise in various applications, including detection of
treatment effects, trend detection in econometrics, signal detection in radar
processing, and shape-constrained inference in non-parametric statistics. We
provide a sharp characterization of the GLRT testing radius up to a universal
multiplicative constant in terms of the geometric structure of the underlying
convex cones. When applied to concrete examples, this result reveals some
interesting phenomena that do not arise in the analogous problems of estimation
under convex constraints. In particular, in contrast to estimation error, the
testing error no longer depends purely on the problem complexity via a
volume-based measure (such as metric entropy or Gaussian complexity), other
geometric properties of the cones also play an important role. To address the
issue of optimality, we prove information-theoretic lower bounds for minimax
testing radius again in terms of geometric quantities. Our general theorems are
illustrated by examples including the cases of monotone and orthant cones, and
involve some results of independent interest.
| 1 | 0 | 1 | 1 | 0 | 0 |
Permutation methods for factor analysis and PCA | Researchers often have datasets measuring features $x_{ij}$ of samples, such
as test scores of students. In factor analysis and PCA, these features are
thought to be influenced by unobserved factors, such as skills. Can we
determine how many components affect the data? This is an important problem,
because it has a large impact on all downstream data analysis. Consequently,
many approaches have been developed to address it. Parallel Analysis is a
popular permutation method. It works by randomly scrambling each feature of the
data. It selects components if their singular values are larger than those of
the permuted data. Despite widespread use in leading textbooks and scientific
publications, as well as empirical evidence for its accuracy, it currently has
no theoretical justification.
In this paper, we show that the parallel analysis permutation method
consistently selects the large components in certain high-dimensional factor
models. However, it does not select the smaller components. The intuition is
that permutations keep the noise invariant, while "destroying" the low-rank
signal. This provides justification for permutation methods in PCA and factor
models under some conditions. Our work uncovers drawbacks of permutation
methods, and paves the way to improvements.
| 0 | 0 | 1 | 1 | 0 | 0 |
Adapting the CVA model to Leland's framework | We consider the framework proposed by Burgard and Kjaer (2011) that derives
the PDE which governs the price of an option including bilateral counterparty
risk and funding. We extend this work by relaxing the assumption of absence of
transaction costs in the hedging portfolio by proposing a cost proportional to
the amount of assets traded and the traded price. After deriving the nonlinear
PDE, we prove the existence of a solution for the corresponding
initial-boundary value problem. Moreover, we develop a numerical scheme that
allows to find the solution of the PDE by setting different values for each
parameter of the model. To understand the impact of each variable within the
model, we analyze the Greeks of the option and the sensitivity of the price to
changes in all the risk factors.
| 0 | 0 | 0 | 0 | 0 | 1 |
Blue Sky Ideas in Artificial Intelligence Education from the EAAI 2017 New and Future AI Educator Program | The 7th Symposium on Educational Advances in Artificial Intelligence
(EAAI'17, co-chaired by Sven Koenig and Eric Eaton) launched the EAAI New and
Future AI Educator Program to support the training of early-career university
faculty, secondary school faculty, and future educators (PhD candidates or
postdocs who intend a career in academia). As part of the program, awardees
were asked to address one of the following "blue sky" questions:
* How could/should Artificial Intelligence (AI) courses incorporate ethics
into the curriculum?
* How could we teach AI topics at an early undergraduate or a secondary
school level?
* AI has the potential for broad impact to numerous disciplines. How could we
make AI education more interdisciplinary, specifically to benefit
non-engineering fields?
This paper is a collection of their responses, intended to help motivate
discussion around these issues in AI education.
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Network Analysis of Particles and Grains | The arrangements of particles and forces in granular materials have a complex
organization on multiple spatial scales that ranges from local structures to
mesoscale and system-wide ones. This multiscale organization can affect how a
material responds or reconfigures when exposed to external perturbations or
loading. The theoretical study of particle-level, force-chain, domain, and bulk
properties requires the development and application of appropriate physical,
mathematical, statistical, and computational frameworks. Traditionally,
granular materials have been investigated using particulate or continuum
models, each of which tends to be implicitly agnostic to multiscale
organization. Recently, tools from network science have emerged as powerful
approaches for probing and characterizing heterogeneous architectures across
different scales in complex systems, and a diverse set of methods have yielded
fascinating insights into granular materials. In this paper, we review work on
network-based approaches to studying granular matter and explore the potential
of such frameworks to provide a useful description of these systems and to
enhance understanding of their underlying physics. We also outline a few open
questions and highlight particularly promising future directions in the
analysis and design of granular matter and other kinds of material networks.
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Perfect Sequences and Arrays over the Unit Quaternions | We introduce several new constructions for perfect periodic autocorrelation
sequences and arrays over the unit quaternions. This paper uses both
mathematical proofs and com- puter experiments to prove the (bounded) array
constructions have perfect periodic auto- correlation. Furthermore, the first
sequence construction generates odd-perfect sequences of unbounded lengths,
with good ZCZ.
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Schwarzian conditions for linear differential operators with selected differential Galois groups (unabridged version) | We show that non-linear Schwarzian differential equations emerging from
covariance symmetry conditions imposed on linear differential operators with
hypergeometric function solutions, can be generalized to arbitrary order linear
differential operators with polynomial coefficients having selected
differential Galois groups. For order three and order four linear differential
operators we show that this pullback invariance up to conjugation eventually
reduces to symmetric powers of an underlying order-two operator. We give,
precisely, the conditions to have modular correspondences solutions for such
Schwarzian differential equations, which was an open question in a previous
paper. We analyze in detail a pullbacked hypergeometric example generalizing
modular forms, that ushers a pullback invariance up to operator homomorphisms.
We expect this new concept to be well-suited in physics and enumerative
combinatorics. We finally consider the more general problem of the equivalence
of two different order-four linear differential
Calabi-Yau operators up to pullbacks and conjugation, and clarify the cases
where they have the same Yukawa couplings.
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Robust Bayesian Filtering and Smoothing Using Student's t Distribution | State estimation in heavy-tailed process and measurement noise is an
important challenge that must be addressed in, e.g., tracking scenarios with
agile targets and outlier-corrupted measurements. The performance of the Kalman
filter (KF) can deteriorate in such applications because of the close relation
to the Gaussian distribution. Therefore, this paper describes the use of
Student's t distribution to develop robust, scalable, and simple filtering and
smoothing algorithms.
After a discussion of Student's t distribution, exact filtering in linear
state-space models with t noise is analyzed. Intermediate approximation steps
are used to arrive at filtering and smoothing algorithms that closely resemble
the KF and the Rauch-Tung-Striebel (RTS) smoother except for a nonlinear
measurement-dependent matrix update. The required approximations are discussed
and an undesirable behavior of moment matching for t densities is revealed. A
favorable approximation based on minimization of the Kullback-Leibler
divergence is presented. Because of its relation to the KF, some properties and
algorithmic extensions are inherited by the t filter. Instructive simulation
examples demonstrate the performance and robustness of the novel algorithms.
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Multi-pass configuration for Improved Squeezed Vacuum Generation in Hot Rb Vapor | We study a squeezed vacuum field generated in hot Rb vapor via the
polarization self-rotation effect. Our previous experiments showed that the
amount of observed squeezing may be limited by the contamination of the
squeezed vacuum output with higher-order spatial modes, also generated inside
the cell. Here, we demonstrate that the squeezing can be improved by making the
light interact several times with a less dense atomic ensemble. With
optimization of some parameters we can achieve up to -2.6 dB of squeezing in
the multi-pass case, which is 0.6 dB improvement compared to the single-pass
experimental configuration. Our results show that other than the optical depth
of the medium, the spatial mode structure and cell configuration also affect
the squeezing level.
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Improved Computation of Involutive Bases | In this paper, we describe improved algorithms to compute Janet and Pommaret
bases. To this end, based on the method proposed by Moller et al., we present a
more efficient variant of Gerdt's algorithm (than the algorithm presented by
Gerdt-Hashemi-M.Alizadeh) to compute minimal involutive bases. Further, by
using the involutive version of Hilbert driven technique, along with the new
variant of Gerdt's algorithm, we modify the algorithm, given by Seiler, to
compute a linear change of coordinates for a given homogeneous ideal so that
the new ideal (after performing this change) possesses a finite Pommaret basis.
All the proposed algorithms have been implemented in Maple and their efficiency
is discussed via a set of benchmark polynomials.
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Dynamic Stochastic Approximation for Multi-stage Stochastic Optimization | In this paper, we consider multi-stage stochastic optimization problems with
convex objectives and conic constraints at each stage. We present a new
stochastic first-order method, namely the dynamic stochastic approximation
(DSA) algorithm, for solving these types of stochastic optimization problems.
We show that DSA can achieve an optimal ${\cal O}(1/\epsilon^4)$ rate of
convergence in terms of the total number of required scenarios when applied to
a three-stage stochastic optimization problem. We further show that this rate
of convergence can be improved to ${\cal O}(1/\epsilon^2)$ when the objective
function is strongly convex. We also discuss variants of DSA for solving more
general multi-stage stochastic optimization problems with the number of stages
$T > 3$. The developed DSA algorithms only need to go through the scenario tree
once in order to compute an $\epsilon$-solution of the multi-stage stochastic
optimization problem. To the best of our knowledge, this is the first time that
stochastic approximation type methods are generalized for multi-stage
stochastic optimization with $T \ge 3$.
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Stability Analysis of Piecewise Affine Systems with Multi-model Model Predictive Control | Constrained model predictive control (MPC) is a widely used control strategy,
which employs moving horizon-based on-line optimisation to compute the optimum
path of the manipulated variables. Nonlinear MPC can utilize detailed models
but it is computationally expensive; on the other hand linear MPC may not be
adequate. Piecewise affine (PWA) models can describe the underlying nonlinear
dynamics more accurately, therefore they can provide a viable trade-off through
their use in multi-model linear MPC configurations, which avoid integer
programming. However, such schemes may introduce uncertainty affecting the
closed loop stability. In this work, we propose an input to output stability
analysis for closed loop systems, consisting of PWA models, where an observer
and multi-model linear MPC are applied together, under unstructured
uncertainty. Integral quadratic constraints (IQCs) are employed to assess the
robustness of MPC under uncertainty. We create a model pool, by performing
linearisation on selected transient points. All the possible uncertainties and
nonlinearities (including the controller) can be introduced in the framework,
assuming that they admit the appropriate IQCs, whilst the dissipation
inequality can provide necessary conditions incorporating IQCs. We demonstrate
the existence of static multipliers, which can reduce the conservatism of the
stability analysis significantly. The proposed methodology is demonstrated
through two engineering case studies.
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