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Differentially Private ANOVA Testing | Modern society generates an incredible amount of data about individuals, and
releasing summary statistics about this data in a manner that provably protects
individual privacy would offer a valuable resource for researchers in many
fields. We present the first algorithm for analysis of variance (ANOVA) that
preserves differential privacy, allowing this important statistical test to be
conducted (and the results released) on databases of sensitive information. In
addition to our private algorithm for the F test statistic, we show a rigorous
way to compute p-values that accounts for the added noise needed to preserve
privacy. Finally, we present experimental results quantifying the statistical
power of this differentially private version of the test, finding that a sample
of several thousand observations is frequently enough to detect variation
between groups. The differentially private ANOVA algorithm is a promising
approach for releasing a common test statistic that is valuable in fields in
the sciences and social sciences.
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The $E$-cohomological Conley Index, Cup-Lengths and the Arnold Conjecture on $T^{2n}$ | We give a new proof of the strong Arnold conjecture for $1$-periodic
solutions of Hamiltonian systems on tori, that was first shown by C. Conley and
E. Zehnder in 1983. Our proof uses other methods and is shorter than the
previous one. We first show that the $E$-cohomological Conley index, that was
introduced by the first author recently, has a natural module structure. This
yields a new cup-length and a lower bound for the number of critical points of
functionals. Then an existence result for the $E$-cohomological Conley index,
which applies to the setting of the Arnold conjecture, paves the way to a new
proof of it on tori.
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Compiling Diderot: From Tensor Calculus to C | Diderot is a parallel domain-specific language for analysis and visualization
of multidimensional scientific images, such as those produced by CT and MRI
scanners. In particular, it supports algorithms where tensor fields (i.e.,
functions from 3D points to tensor values) are used to represent the underlying
physical objects that were scanned by the imaging device. Diderot supports
higher-order programming where tensor fields are first-class values and where
differential operators and lifted linear-algebra operators can be used to
express mathematical reasoning directly in the language. While such lifted
field operations are central to the definition and computation of many
scientific visualization algorithms, to date they have required extensive
manual derivations and laborious implementation.
The challenge for the Diderot compiler is to effectively translate the
high-level mathematical concepts that are expressible in the surface language
to a low-level and efficient implementation in C. This paper describes our
approach to this challenge, which is based around the careful design of an
intermediate representation (IR), called EIN, and a number of compiler
transformations that lower the program from tensor calculus to C while avoiding
combinatorial explosion in the size of the IR. We describe the challenges in
compiling a language like Diderot, the design of EIN, and the transformation
used by the compiler. We also present an evaluation of EIN with respect to both
compiler efficiency and quality of generated code.
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Semi-Supervised and Active Few-Shot Learning with Prototypical Networks | We consider the problem of semi-supervised few-shot classification where a
classifier needs to adapt to new tasks using a few labeled examples and
(potentially many) unlabeled examples. We propose a clustering approach to the
problem. The features extracted with Prototypical Networks are clustered using
$K$-means with the few labeled examples guiding the clustering process. We note
that in many real-world applications the adaptation performance can be
significantly improved by requesting the few labels through user feedback. We
demonstrate good performance of the active adaptation strategy using image
data.
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Inhomogeneous exponential jump model | We introduce and study the inhomogeneous exponential jump model - an
integrable stochastic interacting particle system on the continuous half line
evolving in continuous time. An important feature of the system is the presence
of arbitrary spatial inhomogeneity on the half line which does not break the
integrability. We completely characterize the macroscopic limit shape and
asymptotic fluctuations of the height function (= integrated current) in the
model. In particular, we explain how the presence of inhomogeneity may lead to
macroscopic phase transitions in the limit shape such as shocks or traffic
jams. Away from these singularities the asymptotic fluctuations of the height
function around its macroscopic limit shape are governed by the GUE Tracy-Widom
distribution. A surprising result is that while the limit shape is
discontinuous at a traffic jam caused by a macroscopic slowdown in the
inhomogeneity, fluctuations on both sides of such a traffic jam still have the
GUE Tracy-Widom distribution (but with different non-universal normalizations).
The integrability of the model comes from the fact that it is a degeneration
of the inhomogeneous stochastic higher spin six vertex models studied earlier
in arXiv:1601.05770 [math.PR]. Our results on fluctuations are obtained via an
asymptotic analysis of Fredholm determinantal formulas arising from contour
integral expressions for the q-moments in the stochastic higher spin six vertex
model. We also discuss "product-form" translation invariant stationary
distributions of the exponential jump model which lead to an alternative
hydrodynamic-type heuristic derivation of the macroscopic limit shape.
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Evidence accumulation in a Laplace domain decision space | Evidence accumulation models of simple decision-making have long assumed that
the brain estimates a scalar decision variable corresponding to the
log-likelihood ratio of the two alternatives. Typical neural implementations of
this algorithmic cognitive model assume that large numbers of neurons are each
noisy exemplars of the scalar decision variable. Here we propose a neural
implementation of the diffusion model in which many neurons construct and
maintain the Laplace transform of the distance to each of the decision bounds.
As in classic findings from brain regions including LIP, the firing rate of
neurons coding for the Laplace transform of net accumulated evidence grows to a
bound during random dot motion tasks. However, rather than noisy exemplars of a
single mean value, this approach makes the novel prediction that firing rates
grow to the bound exponentially, across neurons there should be a distribution
of different rates. A second set of neurons records an approximate inversion of
the Laplace transform, these neurons directly estimate net accumulated
evidence. In analogy to time cells and place cells observed in the hippocampus
and other brain regions, the neurons in this second set have receptive fields
along a "decision axis." This finding is consistent with recent findings from
rodent recordings. This theoretical approach places simple evidence
accumulation models in the same mathematical language as recent proposals for
representing time and space in cognitive models for memory.
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Improved Energy Pooling Efficiency Through Inhibited Spontaneous Emission | The radiative lifetime of molecules or atoms can be increased by placing them
within a tuned conductive cavity that inhibits spontaneous emission. This was
examined as a possible means of enhancing three-body, singlet-based
upconversion, known as energy pooling. Achieving efficient upconversion of
light has potential applications in the fields of photovoltaics, biofuels, and
medicine. The affect of the photonically constrained environment on pooling
efficiency was quantified using a kinetic model populated with data from
molecular quantum electrodynamics, perturbation theory, and ab initio
calculations. This model was applied to a system with fluorescein donors and a
hexabenzocoronene acceptor. Placing the molecules within a conducting cavity
was found to increase the efficiency of energy pooling by increasing both the
donor lifetime and the acceptor emission rate--i.e. a combination of inhibited
spontaneous emission and the Purcell effect. A model system with a free-space
pooling efficiency of 23% was found to have an efficiency of 47% in a
rectangular cavity.
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A unified, mechanistic framework for developmental and evolutionary change | The two most fundamental processes describing change in biology -development
and evolution- occur over drastically different timescales, difficult to
reconcile within a unified framework. Development involves a temporal sequence
of cell states controlled by a hierarchy of regulatory structures. It occurs
over the lifetime of a single individual, and is associated to the gene
expression level change of a given genotype. Evolution, by contrast entails
genotypic change through the acquisition or loss of genes, and involves the
emergence of new, environmentally selected phenotypes over the lifetimes of
many individ- uals. Here we present a model of regulatory network evolution
that accounts for both timescales. We extend the framework of boolean models of
gene regulatory network (GRN)-currently only applicable to describing
development-to include evolutionary processes. As opposed to one-to-one maps to
specific attractors, we identify the phenotypes of the cells as the relevant
macrostates of the GRN. A pheno- type may now correspond to multiple
attractors, and its formal definition no longer require a fixed size for the
genotype. This opens the possibility for a quantitative study of the phenotypic
change of a genotype, which is itself changing over evolutionary timescales. We
show how the realization of specific phenotypes can be controlled by gene
duplication events, and how successive events of gene duplication lead to new
regulatory structures via selection. It is these structures that enable control
of macroscale patterning, as in development. The proposed framework therefore
provides a mechanistic explanation for the emergence of regulatory structures
controlling development over evolutionary time.
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Coinfection in a stochastic model for bacteriophage systems | A system modeling bacteriophage treatments with coinfections in a noisy
context is analyzed. We prove that in a small noise regime, the system
converges in the long term to a bacteria free equilibrium. Moreover, we compare
the treatment with coinfection with the treatment without coinfection, showing
how the coinfection affects the dose of bacteriophages that is needed to
eliminate the bacteria and the velocity of convergence to the free bacteria
equilibrium.
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Field dependence of non-reciprocal magnons in chiral MnSi | Spin waves in chiral magnetic materials are strongly influenced by the
Dzyaloshinskii-Moriya interaction resulting in intriguing phenomena like
non-reciprocal magnon propagation and magnetochiral dichroism. Here, we study
the non-reciprocal magnon spectrum of the archetypical chiral magnet MnSi and
its evolution as a function of magnetic field covering the field-polarized and
conical helix phase. Using inelastic neutron scattering, the magnon energies
and their spectral weights are determined quantitatively after deconvolution
with the instrumental resolution. In the field-polarized phase the imaginary
part of the dynamical susceptibility $\chi''(\varepsilon, {\bf q})$ is shown to
be asymmetric with respect to wavevectors ${\bf q}$ longitudinal to the applied
magnetic field ${\bf H}$, which is a hallmark of chiral magnetism. In the
helimagnetic phase, $\chi''(\varepsilon, {\bf q})$ becomes increasingly
symmetric with decreasing ${\bf H}$ due to the formation of helimagnon bands
and the activation of additional spinflip and non-spinflip scattering channels.
The neutron spectra are in excellent quantitative agreement with the low-energy
theory of cubic chiral magnets with a single fitting parameter being the
damping rate of spin waves.
| 0 | 1 | 0 | 0 | 0 | 0 |
On the Simpson index for the Moran process with random selection and immigration | Moran or Wright-Fisher processes are probably the most well known model to
study the evolution of a population under various effects. Our object of study
will be the Simpson index which measures the level of diversity of the
population, one of the key parameter for ecologists who study for example
forest dynamics. Following ecological motivations, we will consider here the
case where there are various species with fitness and immigration parameters
being random processes (and thus time evolving). To measure biodiversity,
ecologists generally use the Simpson index, who has no closed formula, except
in the neutral (no selection) case via a backward approach, and which is
difficult to evaluate even numerically when the population size is large. Our
approach relies on the large population limit in the "weak" selection case, and
thus to give a procedure which enable us to approximate, with controlled rate,
the expectation of the Simpson index at fixed time. Our approach will be
forward and valid for all time, which is the main difference with the
historical approach of Kingman, or Krone-Neuhauser. We will also study the long
time behaviour of the Wright-Fisher process in a simplified setting, allowing
us to get a full picture for the approximation of the expectation of the
Simpson index.
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Small animal whole body imaging with metamaterial-inspired RF coil | Preclinical magnetic resonance imaging often requires the entire body of an
animal to be imaged with sufficient quality. This is usually performed by
combining regions scanned with small coils with high sensitivity or long scans
using large coils with low sensitivity. Here, a metamaterial-inspired design
employing of a parallel array of wires operating on the principle of eigenmode
hybridization is used to produce a small animal whole-body imaging coil. The
coil field distribution responsible for the coil field of view and sensitivity
is simulated in an electromagnetic simulation package and the coil geometrical
parameters are optimized for the chosen application. A prototype coil is then
manufactured and assembled using brass telescopic tubes and copper plates as
distributed capacitance, its field distribution is measured experimentally
using B1+ mapping technique and found to be in close correspondence with
simulated results. The coil field distribution is found to be suitable for
whole-body small animal imaging and coil image quality is compared with a
number of commercially available coils by whole-body living mice scanning.
Signal to noise measurements in living mice show outstanding coil performance
compared to commercially available coils with large receptive fields, and
rivaling performance compared to small receptive field and high-sensitivity
coils. The coil is deemed suitable for whole-body small animal preclinical
applications.
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Entropic Trace Estimates for Log Determinants | The scalable calculation of matrix determinants has been a bottleneck to the
widespread application of many machine learning methods such as determinantal
point processes, Gaussian processes, generalised Markov random fields, graph
models and many others. In this work, we estimate log determinants under the
framework of maximum entropy, given information in the form of moment
constraints from stochastic trace estimation. The estimates demonstrate a
significant improvement on state-of-the-art alternative methods, as shown on a
wide variety of UFL sparse matrices. By taking the example of a general Markov
random field, we also demonstrate how this approach can significantly
accelerate inference in large-scale learning methods involving the log
determinant.
| 1 | 0 | 0 | 1 | 0 | 0 |
A Mixture of Matrix Variate Bilinear Factor Analyzers | Over the years data has become increasingly higher dimensional, which has
prompted an increased need for dimension reduction techniques. This is perhaps
especially true for clustering (unsupervised classification) as well as
semi-supervised and supervised classification. Although dimension reduction in
the area of clustering for multivariate data has been quite thoroughly
discussed within the literature, there is relatively little work in the area of
three-way, or matrix variate, data. Herein, we develop a mixture of matrix
variate bilinear factor analyzers (MMVBFA) model for use in clustering
high-dimensional matrix variate data. This work can be considered both the
first matrix variate bilinear factor analysis model as well as the first MMVBFA
model. Parameter estimation is discussed, and the MMVBFA model is illustrated
using simulated and real data.
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The application of the competency-based approach to assess the training and employment adequacy problem | This review paper fits in the context of the adequate matching of training to
employment, which is one of the main challenges that universities around the
world strive to meet. In higher education, the revision of curricula
necessitates a return to the skills required by the labor market to train
skilled labors.
In this research, we started with the presentation of the conceptual
framework. Then we quoted different currents that discussed the problematic of
the job training match from various perspectives. We proceeded to choose some
studies that have attempted to remedy this problem by adopting the
competency-based approach that involves the referential line. This approach has
as a main characteristic the attainment of the match between training and
employment. Therefore, it is a relevant solution for this problem. We
scrutinized the selected studies, presenting their objectives, methodologies
and results, and we provided our own analysis. Then, we focused on the Moroccan
context through observations and studies already conducted. And finally, we
introduced the problematic of our future project.
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Prediction and Generation of Binary Markov Processes: Can a Finite-State Fox Catch a Markov Mouse? | Understanding the generative mechanism of a natural system is a vital
component of the scientific method. Here, we investigate one of the fundamental
steps toward this goal by presenting the minimal generator of an arbitrary
binary Markov process. This is a class of processes whose predictive model is
well known. Surprisingly, the generative model requires three distinct
topologies for different regions of parameter space. We show that a previously
proposed generator for a particular set of binary Markov processes is, in fact,
not minimal. Our results shed the first quantitative light on the relative
(minimal) costs of prediction and generation. We find, for instance, that the
difference between prediction and generation is maximized when the process is
approximately independently, identically distributed.
| 1 | 1 | 0 | 0 | 0 | 0 |
Topological orders of strongly interacting particles | We investigate the self-organization of strongly interacting particles
confined in 1D and 2D. We consider hardcore bosons in spinless Hubbard lattice
models with short range interactions. We show that, many-body orders with
topological characteristics emerge, at different energy bands separated by
large gaps. These topological orders manifest in the way the particles organize
in real space to form states with different energy. Each of these states
contains topological defects/condensations whose Euler characteristic can be
used as a topological number to categorize states belonging to the same energy
band. We provide analytical formulas for this topological number and the full
energy spectrum of the system for both sparsely and densely filled systems.
Furthermore, we discuss the connection with the Gauss-Bonnet theorem of
differential geometry, by using the curvature generated in real space by the
particle structures. Our result is a demonstration of how topological orders
can arise in strongly interacting many-body systems with simple underlying
rules, without considering the spin, long-range microscopic interactions, or
external fields.
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Virtual unknotting numbers of certain virtual torus knots | The virtual unknotting number of a virtual knot is the minimal number of
crossing changes that makes the virtual knot to be the unknot, which is defined
only for virtual knots virtually homotopic to the unknot. We focus on the
virtual knot obtained from the standard (p,q)-torus knot diagram by replacing
all crossings on one overstrand into virtual crossings and prove that its
virtual unknotting number is equal to the unknotting number of the
$(p,q)$-torus knot, i.e. it is (p-1)(q-1)/2.
| 0 | 0 | 1 | 0 | 0 | 0 |
Computing the Lambert W function in arbitrary-precision complex interval arithmetic | We describe an algorithm to evaluate all the complex branches of the Lambert
W function with rigorous error bounds in interval arithmetic, which has been
implemented in the Arb library. The classic 1996 paper on the Lambert W
function by Corless et al. provides a thorough but partly heuristic numerical
analysis which needs to be complemented with some explicit inequalities and
practical observations about managing precision and branch cuts.
| 1 | 0 | 0 | 0 | 0 | 0 |
An Architecture for Embedded Systems Supporting Assisted Living | The rise in life expectancy is one of the great achievements of the twentieth
century. This phenomenon originates a still increasing interest in Ambient
Assisted Living (AAL) technological solutions that may support people in their
daily routines allowing an independent and safe lifestyle as long as possible.
AAL systems generally acquire data from the field and reason on them and the
context to accomplish their tasks. Very often, AAL systems are vertical
solutions, thus making hard their reuse and adaptation to different domains
with respect to the ones for which they have been developed. In this paper we
propose an architectural solution that allows the acquisition level of an ALL
system to be easily built, configured, and extended without affecting the
reasoning level of the system. We experienced our proposal in a fall detection
system.
| 1 | 0 | 0 | 0 | 0 | 0 |
Hunting Rabbits on the Hypercube | We explore the Hunters and Rabbits game on the hypercube. In the process, we
find the solution for all classes of graphs with an isoperimetric nesting
property and find the exact hunter number of $Q^n$ to be
$1+\sum\limits_{i=0}^{n-2} \binom{i}{\lfloor i/2 \rfloor}$. In addition, we
extend results to the situation where we allow the rabbit to not move between
shots.
| 0 | 0 | 1 | 0 | 0 | 0 |
Mixed Effect Dirichlet-Tree Multinomial for Longitudinal Microbiome Data and Weight Prediction | Quantifying the relation between gut microbiome and body weight can provide
insights into personalized strategies for improving digestive health. In this
paper, we present an algorithm that predicts weight fluctuations using gut
microbiome in a healthy cohort of newborns from a previously published dataset.
Microbial data has been known to present unique statistical challenges that
defy most conventional models. We propose a mixed effect Dirichlet-tree
multinomial (DTM) model to untangle these difficulties as well as incorporate
covariate information and account for species relatedness. The DTM setup allows
one to easily invoke empirical Bayes shrinkage on each node for enhanced
inference of microbial proportions. Using these estimates, we subsequently
apply random forest for weight prediction and obtain a microbiome-inferred
weight metric. Our result demonstrates that microbiome-inferred weight is
significantly associated with weight changes in the future and its non-trivial
effect size makes it a viable candidate to forecast weight progression.
| 0 | 0 | 0 | 1 | 0 | 0 |
Approximating Throughput and Packet Decoding Delay in Linear Network Coded Wireless Broadcast | In this paper, we study a wireless packet broadcast system that uses linear
network coding (LNC) to help receivers recover data packets that are missing
due to packet erasures. We study two intertwined performance metrics, namely
throughput and average packet decoding delay (APDD) and establish strong/weak
approximation relations based on whether the approximation holds for the
performance of every receiver (strong) or for the average performance across
all receivers (weak). We prove an equivalence between strong throughput
approximation and strong APDD approximation. We prove that throughput-optimal
LNC techniques can strongly approximate APDD, and partition-based LNC
techniques may weakly approximate throughput. We also prove that memoryless LNC
techniques, including instantly decodable network coding techniques, are not
strong throughput and APDD approximation nor weak throughput approximation
techniques.
| 1 | 0 | 1 | 0 | 0 | 0 |
Search for electromagnetic super-preshowers using gamma-ray telescopes | Any considerations on propagation of particles through the Universe must
involve particle interactions: processes leading to production of particle
cascades. While one expects existence of such cascades, the state of the art
cosmic-ray research is oriented purely on a detection of single particles,
gamma rays or associated extensive air showers. The natural extension of the
cosmic-ray research with the studies on ensembles of particles and air showers
is being proposed by the CREDO Collaboration. Within the CREDO strategy the
focus is put on generalized super-preshowers (SPS): spatially and/or temporally
extended cascades of particles originated above the Earth atmosphere, possibly
even at astrophysical distances. With CREDO we want to find out whether SPS can
be at least partially observed by a network of terrestrial and/or satellite
detectors receiving primary or secondary cosmic-ray signal. This paper
addresses electromagnetic SPS, e.g. initiated by VHE photons interacting with
the cosmic microwave background, and the SPS signatures that can be seen by
gamma-ray telescopes, exploring the exampleof Cherenkov Telescope Array. The
energy spectrum of secondary electrons and photons in an electromagnetic
super-preshower might be extended over awide range of energy, down to TeV or
even lower, as it is evident from the simulation results. This means that
electromagnetic showers induced by such particles in the Earth atmosphere could
be observed by imaging atmospheric Cherenkov telescopes. We present preliminary
results from the study of response of the Cherenkov Telescope Array to SPS
events, including the analysis of the simulated shower images on the camera
focal plane and implementedgeneric reconstruction chains based on the Hillas
parameters.
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Gromov-Hausdorff limit of Wasserstein spaces on point clouds | We consider a point cloud $X_n := \{ x_1, \dots, x_n \}$ uniformly
distributed on the flat torus $\mathbb{T}^d : = \mathbb{R}^d / \mathbb{Z}^d $,
and construct a geometric graph on the cloud by connecting points that are
within distance $\epsilon$ of each other. We let $\mathcal{P}(X_n)$ be the
space of probability measures on $X_n$ and endow it with a discrete Wasserstein
distance $W_n$ as introduced independently by Maas and Zhou et al. for general
finite Markov chains. We show that as long as $\epsilon= \epsilon_n$ decays
towards zero slower than an explicit rate depending on the level of uniformity
of $X_n$, then the space $(\mathcal{P}(X_n), W_n)$ converges in the
Gromov-Hausdorff sense towards the space of probability measures on
$\mathbb{T}^d$ endowed with the Wasserstein distance.
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Minimal axiomatic frameworks for definable hyperreals with transfer | We modify the definable ultrapower construction of Kanovei and Shelah (2004)
to develop a ZF-definable extension of the continuum with transfer provable
using countable choice only, with an additional mild hypothesis on
well-ordering implying properness. Under the same assumptions, we also prove
the existence of a definable, proper elementary extension of the standard
superstructure over the reals.
Keywords: definability; hyperreal; superstructure; elementary embedding.
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A Tight Excess Risk Bound via a Unified PAC-Bayesian-Rademacher-Shtarkov-MDL Complexity | We present a novel notion of complexity that interpolates between and
generalizes some classic existing complexity notions in learning theory: for
estimators like empirical risk minimization (ERM) with arbitrary bounded
losses, it is upper bounded in terms of data-independent Rademacher complexity;
for generalized Bayesian estimators, it is upper bounded by the data-dependent
information complexity (also known as stochastic or PAC-Bayesian,
$\mathrm{KL}(\text{posterior} \operatorname{\|} \text{prior})$ complexity. For
(penalized) ERM, the new complexity reduces to (generalized) normalized maximum
likelihood (NML) complexity, i.e. a minimax log-loss individual-sequence
regret. Our first main result bounds excess risk in terms of the new
complexity. Our second main result links the new complexity via Rademacher
complexity to $L_2(P)$ entropy, thereby generalizing earlier results of Opper,
Haussler, Lugosi, and Cesa-Bianchi who did the log-loss case with $L_\infty$.
Together, these results recover optimal bounds for VC- and large (polynomial
entropy) classes, replacing localized Rademacher complexity by a simpler
analysis which almost completely separates the two aspects that determine the
achievable rates: 'easiness' (Bernstein) conditions and model complexity.
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A Naive Algorithm for Feedback Vertex Set | Given a graph on $n$ vertices and an integer $k$, the feedback vertex set
problem asks for the deletion of at most $k$ vertices to make the graph
acyclic. We show that a greedy branching algorithm, which always branches on an
undecided vertex with the largest degree, runs in single-exponential time,
i.e., $O(c^k\cdot n^2)$ for some constant $c$.
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Query Complexity of Clustering with Side Information | Suppose, we are given a set of $n$ elements to be clustered into $k$
(unknown) clusters, and an oracle/expert labeler that can interactively answer
pair-wise queries of the form, "do two elements $u$ and $v$ belong to the same
cluster?". The goal is to recover the optimum clustering by asking the minimum
number of queries. In this paper, we initiate a rigorous theoretical study of
this basic problem of query complexity of interactive clustering, and provide
strong information theoretic lower bounds, as well as nearly matching upper
bounds. Most clustering problems come with a similarity matrix, which is used
by an automated process to cluster similar points together. Our main
contribution in this paper is to show the dramatic power of side information
aka similarity matrix on reducing the query complexity of clustering. A
similarity matrix represents noisy pair-wise relationships such as one computed
by some function on attributes of the elements. A natural noisy model is where
similarity values are drawn independently from some arbitrary probability
distribution $f_+$ when the underlying pair of elements belong to the same
cluster, and from some $f_-$ otherwise. We show that given such a similarity
matrix, the query complexity reduces drastically from $\Theta(nk)$ (no
similarity matrix) to $O(\frac{k^2\log{n}}{\cH^2(f_+\|f_-)})$ where $\cH^2$
denotes the squared Hellinger divergence. Moreover, this is also
information-theoretic optimal within an $O(\log{n})$ factor. Our algorithms are
all efficient, and parameter free, i.e., they work without any knowledge of $k,
f_+$ and $f_-$, and only depend logarithmically with $n$. Along the way, our
work also reveals intriguing connection to popular community detection models
such as the {\em stochastic block model}, significantly generalizes them, and
opens up many venues for interesting future research.
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On Prediction Properties of Kriging: Uniform Error Bounds and Robustness | Kriging based on Gaussian random fields is widely used in reconstructing
unknown functions. The kriging method has pointwise predictive distributions
which are computationally simple. However, in many applications one would like
to predict for a range of untried points simultaneously. In this work we obtain
some error bounds for the (simple) kriging predictor under the uniform metric.
It works for a scattered set of input points in an arbitrary dimension, and
also covers the case where the covariance function of the Gaussian process is
misspecified. These results lead to a better understanding of the rate of
convergence of kriging under the Gaussian or the Matérn correlation
functions, the relationship between space-filling designs and kriging models,
and the robustness of the Matérn correlation functions.
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Robust Submodular Maximization: A Non-Uniform Partitioning Approach | We study the problem of maximizing a monotone submodular function subject to
a cardinality constraint $k$, with the added twist that a number of items
$\tau$ from the returned set may be removed. We focus on the worst-case setting
considered in (Orlin et al., 2016), in which a constant-factor approximation
guarantee was given for $\tau = o(\sqrt{k})$. In this paper, we solve a key
open problem raised therein, presenting a new Partitioned Robust (PRo)
submodular maximization algorithm that achieves the same guarantee for more
general $\tau = o(k)$. Our algorithm constructs partitions consisting of
buckets with exponentially increasing sizes, and applies standard submodular
optimization subroutines on the buckets in order to construct the robust
solution. We numerically demonstrate the performance of PRo in data
summarization and influence maximization, demonstrating gains over both the
greedy algorithm and the algorithm of (Orlin et al., 2016).
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Value Directed Exploration in Multi-Armed Bandits with Structured Priors | Multi-armed bandits are a quintessential machine learning problem requiring
the balancing of exploration and exploitation. While there has been progress in
developing algorithms with strong theoretical guarantees, there has been less
focus on practical near-optimal finite-time performance. In this paper, we
propose an algorithm for Bayesian multi-armed bandits that utilizes
value-function-driven online planning techniques. Building on previous work on
UCB and Gittins index, we introduce linearly-separable value functions that
take both the expected return and the benefit of exploration into consideration
to perform n-step lookahead. The algorithm enjoys a sub-linear performance
guarantee and we present simulation results that confirm its strength in
problems with structured priors. The simplicity and generality of our approach
makes it a strong candidate for analyzing more complex multi-armed bandit
problems.
| 1 | 0 | 0 | 1 | 0 | 0 |
Adaptive Mantel Test for AssociationTesting in Imaging Genetics Data | Mantel's test (MT) for association is conducted by testing the linear
relationship of similarity of all pairs of subjects between two observational
domains. Motivated by applications to neuroimaging and genetics data, and
following the succes of shrinkage and kernel methods for prediction with
high-dimensional data, we here introduce the adaptive Mantel test as an
extension of the MT. By utilizing kernels and penalized similarity measures,
the adaptive Mantel test is able to achieve higher statistical power relative
to the classical MT in many settings. Furthermore, the adaptive Mantel test is
designed to simultaneously test over multiple similarity measures such that the
correct type I error rate under the null hypothesis is maintained without the
need to directly adjust the significance threshold for multiple testing. The
performance of the adaptive Mantel test is evaluated on simulated data, and is
used to investigate associations between genetics markers related to
Alzheimer's Disease and heatlhy brain physiology with data from a working
memory study of 350 college students from Beijing Normal University.
| 0 | 0 | 0 | 1 | 0 | 0 |
Approximation of Functions over Manifolds: A Moving Least-Squares Approach | We present an algorithm for approximating a function defined over a
$d$-dimensional manifold utilizing only noisy function values at locations
sampled from the manifold with noise. To produce the approximation we do not
require any knowledge regarding the manifold other than its dimension $d$. The
approximation scheme is based upon the Manifold Moving Least-Squares (MMLS).
The proposed algorithm is resistant to noise in both the domain and function
values. Furthermore, the approximant is shown to be smooth and of approximation
order of $\mathcal{O}(h^{m+1})$ for non-noisy data, where $h$ is the mesh size
with respect to the manifold domain, and $m$ is the degree of a local
polynomial approximation utilized in our algorithm. In addition, the proposed
algorithm is linear in time with respect to the ambient-space's dimension.
Thus, in case of extremely large ambient space dimension, we are able to avoid
the curse of dimensionality without having to perform non-linear dimension
reduction, which introduces distortions to the manifold data. Using numerical
experiments, we compare the presented method to state-of-the-art algorithms for
regression over manifolds and show its potential.
| 1 | 0 | 0 | 1 | 0 | 0 |
Delay sober up drunkers: Control of diffusion in random walkers | Time delay in general leads to instability in some systems, while a specific
feedback with delay can control fluctuated motion in nonlinear deterministic
systems to a stable state. In this paper, we consider a non-stationary
stochastic process, i.e., a random walk and observe its diffusion phenomenon
with time delayed feedback. Surprisingly, the diffusion coefficient decreases
with increasing the delay time. We analytically illustrate this suppression of
diffusion by using stochastic delay differential equations and justify the
feasibility of this suppression by applying the time-delay feedback to a
molecular dynamics model.
| 0 | 1 | 0 | 0 | 0 | 0 |
Gravitational Wave signatures of inflationary models from Primordial Black Hole Dark Matter | Primordial Black Holes (PBH) could be the cold dark matter of the universe.
They could have arisen from large (order one) curvature fluctuations produced
during inflation that reentered the horizon in the radiation era. At reentry,
these fluctuations source gravitational waves (GW) via second order anisotropic
stresses. These GW, together with those (possibly) sourced during inflation by
the same mechanism responsible for the large curvature fluctuations, constitute
a primordial stochastic GW background (SGWB) that unavoidably accompanies the
PBH formation. We study how the amplitude and the range of frequencies of this
signal depend on the statistics (Gaussian versus $\chi^2$) of the primordial
curvature fluctuations, and on the evolution of the PBH mass function due to
accretion and merging. We then compare this signal with the sensitivity of
present and future detectors, at PTA and LISA scales. We find that this SGWB
will help to probe, or strongly constrain, the early universe mechanism of PBH
production. The comparison between the peak mass of the PBH distribution and
the peak frequency of this SGWB will provide important information on the
merging and accretion evolution of the PBH mass distribution from their
formation to the present era. Different assumptions on the statistics and on
the PBH evolution also result in different amounts of CMB $\mu$-distortions.
Therefore the above results can be complemented by the detection (or the
absence) of $\mu$-distortions with an experiment such as PIXIE.
| 0 | 1 | 0 | 0 | 0 | 0 |
Linear Parsing Expression Grammars | PEGs were formalized by Ford in 2004, and have several pragmatic operators
(such as ordered choice and unlimited lookahead) for better expressing modern
programming language syntax. Since these operators are not explicitly defined
in the classic formal language theory, it is significant and still challenging
to argue PEGs' expressiveness in the context of formal language theory.Since
PEGs are relatively new, there are several unsolved problems.One of the
problems is revealing a subclass of PEGs that is equivalent to DFAs. This
allows application of some techniques from the theory of regular grammar to
PEGs. In this paper, we define Linear PEGs (LPEGs), a subclass of PEGs that is
equivalent to DFAs. Surprisingly, LPEGs are formalized by only excluding some
patterns of recursive nonterminal in PEGs, and include the full set of ordered
choice, unlimited lookahead, and greedy repetition, which are characteristic of
PEGs. Although the conversion judgement of parsing expressions into DFAs is
undecidable in general, the formalism of LPEGs allows for a syntactical
judgement of parsing expressions.
| 1 | 0 | 0 | 0 | 0 | 0 |
Pre-Synaptic Pool Modification (PSPM): A Supervised Learning Procedure for Spiking Neural Networks | A central question in neuroscience is how to develop realistic models that
predict output firing behavior based on provided external stimulus. Given a set
of external inputs and a set of output spike trains, the objective is to
discover a network structure which can accomplish the transformation as
accurately as possible. Due to the difficulty of this problem in its most
general form, approximations have been made in previous work. Past
approximations have sacrificed network size, recurrence, allowed spiked count,
or have imposed layered network structure. Here we present a learning rule
without these sacrifices, which produces a weight matrix of a leaky
integrate-and-fire (LIF) network to match the output activity of both
deterministic LIF networks as well as probabilistic integrate-and-fire (PIF)
networks. Inspired by synaptic scaling, our pre-synaptic pool modification
(PSPM) algorithm outputs deterministic, fully recurrent spiking neural networks
that can provide a novel generative model for given spike trains. Similarity in
output spike trains is evaluated with a variety of metrics including a
van-Rossum like measure and a numerical comparison of inter-spike interval
distributions. Application of our algorithm to randomly generated networks
improves similarity to the reference spike trains on both of these stated
measures. In addition, we generated LIF networks that operate near criticality
when trained on critical PIF outputs. Our results establish that learning rules
based on synaptic homeostasis can be used to represent input-output
relationships in fully recurrent spiking neural networks.
| 0 | 0 | 0 | 0 | 1 | 0 |
The Bright and Dark Sides of High-Redshift starburst galaxies from {\it Herschel} and {\it Subaru} observations | We present rest-frame optical spectra from the FMOS-COSMOS survey of twelve
$z \sim 1.6$ \textit{Herschel} starburst galaxies, with Star Formation Rate
(SFR) elevated by $\times$8, on average, above the star-forming Main Sequence
(MS). Comparing the H$\alpha$ to IR luminosity ratio and the Balmer Decrement
we find that the optically-thin regions of the sources contain on average only
$\sim 10$ percent of the total SFR whereas $\sim90$ percent comes from an
extremely obscured component which is revealed only by far-IR observations and
is optically-thick even in H$\alpha$. We measure the [NII]$_{6583}$/H$\alpha$
ratio, suggesting that the less obscured regions have a metal content similar
to that of the MS population at the same stellar masses and redshifts. However,
our objects appear to be metal-rich outliers from the metallicity-SFR
anticorrelation observed at fixed stellar mass for the MS population. The
[SII]$_{6732}$/[SII]$_{6717}$ ratio from the average spectrum indicates an
electron density $n_{\rm e} \sim 1,100\ \mathrm{cm}^{-3}$, larger than what
estimated for MS galaxies but only at the 1.5$\sigma$ level. Our results
provide supporting evidence that high-$z$ MS outliers are the analogous of
local ULIRGs, and are consistent with a major merger origin for the starburst
event.
| 0 | 1 | 0 | 0 | 0 | 0 |
Edge Estimation with Independent Set Oracles | We study the task of estimating the number of edges in a graph with access to
only an independent set oracle. Independent set queries draw motivation from
group testing and have applications to the complexity of decision versus
counting problems. We give two algorithms to estimate the number of edges in an
$n$-vertex graph, using (i) $\mathrm{polylog}(n)$ bipartite independent set
queries, or (ii) ${n}^{2/3} \cdot\mathrm{polylog}(n)$ independent set queries.
| 1 | 0 | 0 | 0 | 0 | 0 |
Threshold-activated transport stabilizes chaotic populations to steady states | We explore Random Scale-Free networks of populations, modelled by chaotic
Ricker maps, connected by transport that is triggered when population density
in a patch is in excess of a critical threshold level. Our central result is
that threshold-activated dispersal leads to stable fixed populations, for a
wide range of threshold levels. Further, suppression of chaos is facilitated
when the threshold-activated migration is more rapid than the intrinsic
population dynamics of a patch. Additionally, networks with large number of
nodes open to the environment, readily yield stable steady states. Lastly we
demonstrate that in networks with very few open nodes, the degree and
betweeness centrality of the node open to the environment has a pronounced
influence on control. All qualitative trends are corroborated by quantitative
measures, reflecting the efficiency of control, and the width of the steady
state window.
| 0 | 1 | 0 | 0 | 0 | 0 |
Bounding and Counting Linear Regions of Deep Neural Networks | We investigate the complexity of deep neural networks (DNN) that represent
piecewise linear (PWL) functions. In particular, we study the number of linear
regions, i.e. pieces, that a PWL function represented by a DNN can attain, both
theoretically and empirically. We present (i) tighter upper and lower bounds
for the maximum number of linear regions on rectifier networks, which are exact
for inputs of dimension one; (ii) a first upper bound for multi-layer maxout
networks; and (iii) a first method to perform exact enumeration or counting of
the number of regions by modeling the DNN with a mixed-integer linear
formulation. These bounds come from leveraging the dimension of the space
defining each linear region. The results also indicate that a deep rectifier
network can only have more linear regions than every shallow counterpart with
same number of neurons if that number exceeds the dimension of the input.
| 1 | 0 | 0 | 1 | 0 | 0 |
The reactive-telegraph equation and a related kinetic model | We study the long-range, long-time behavior of the reactive-telegraph
equation and a related reactive-kinetic model. The two problems are equivalent
in one spatial dimension. We point out that the reactive-telegraph equation,
meant to model a population density, does not preserve positivity in higher
dimensions. In view of this, in dimensions larger than one, we consider a
reactive-kinetic model and investigate the long-range, long-time limit of the
solutions. We provide a general characterization of the speed of propagation
and we compute it explicitly in one and two dimensions. We show that a phase
transition between parabolic and hyperbolic behavior takes place only in one
dimension. Finally, we investigate the hydrodynamic limit of the limiting
problem.
| 0 | 0 | 1 | 0 | 0 | 0 |
Finiteness theorems for K3 surfaces and abelian varieties of CM type | We study abelian varieties and K3 surfaces with complex multiplication
defined over number fields of fixed degree. We show that these varieties fall
into finitely many isomorphism classes over an algebraic closure of the field
of rational numbers. As an application we confirm finiteness conjectures of
Shafarevich and Coleman in the CM case. In addition we prove the uniform
boundedness of the Galois invariant subgroup of the geometric Brauer group for
forms of a smooth projective variety satisfying the integral Mumford--Tate
conjecture. When applied to K3 surfaces, this affirms a conjecture of
Várilly-Alvarado in the CM case.
| 0 | 0 | 1 | 0 | 0 | 0 |
Rheology of inelastic hard spheres at finite density and shear rate | Considering a granular fluid of inelastic smooth hard spheres we discuss the
conditions delineating the rheological regimes comprising Newtonian,
Bagnoldian, shear thinning, and shear thickening behavior. Developing a kinetic
theory, valid at finite shear rates and densities around the glass transition
density, we predict the viscosity and Bagnold coefficient at practically
relevant values of the control parameters. The determination of full flow
curves relating the shear stress $\sigma$ to the shear rate $\dot\gamma$, and
predictions of the yield stress complete our discussion of granular rheology
derived from first principles.
| 0 | 1 | 0 | 0 | 0 | 0 |
The Flash ADC system and PMT waveform reconstruction for the Daya Bay Experiment | To better understand the energy response of the Antineutrino Detector (AD),
the Daya Bay Reactor Neutrino Experiment installed a full Flash ADC readout
system on one AD that allowed for simultaneous data taking with the current
readout system. This paper presents the design, data acquisition, and
simulation of the Flash ADC system, and focuses on the PMT waveform
reconstruction algorithms. For liquid scintillator calorimetry, the most
critical requirement to waveform reconstruction is linearity. Several common
reconstruction methods were tested but the linearity performance was not
satisfactory. A new method based on the deconvolution technique was developed
with 1% residual non-linearity, which fulfills the requirement. The performance
was validated with both data and Monte Carlo (MC) simulations, and 1%
consistency between them has been achieved.
| 0 | 1 | 0 | 0 | 0 | 0 |
Quasitoric totally normally split representatives in unitary cobordism ring | The present paper generalises the results of Ray and Buchstaber-Ray,
Buchstaber-Panov-Ray in unitary cobordism theory. I prove that any class $x\in
\Omega^{*}_{U}$ of the unitary cobordism ring contains a quasitoric totally
normally and tangentially split manifold.
| 0 | 0 | 1 | 0 | 0 | 0 |
Interpretable Feature Recommendation for Signal Analytics | This paper presents an automated approach for interpretable feature
recommendation for solving signal data analytics problems. The method has been
tested by performing experiments on datasets in the domain of prognostics where
interpretation of features is considered very important. The proposed approach
is based on Wide Learning architecture and provides means for interpretation of
the recommended features. It is to be noted that such an interpretation is not
available with feature learning approaches like Deep Learning (such as
Convolutional Neural Network) or feature transformation approaches like
Principal Component Analysis. Results show that the feature recommendation and
interpretation techniques are quite effective for the problems at hand in terms
of performance and drastic reduction in time to develop a solution. It is
further shown by an example, how this human-in-loop interpretation system can
be used as a prescriptive system.
| 1 | 0 | 0 | 1 | 0 | 0 |
Learning One-hidden-layer ReLU Networks via Gradient Descent | We study the problem of learning one-hidden-layer neural networks with
Rectified Linear Unit (ReLU) activation function, where the inputs are sampled
from standard Gaussian distribution and the outputs are generated from a noisy
teacher network. We analyze the performance of gradient descent for training
such kind of neural networks based on empirical risk minimization, and provide
algorithm-dependent guarantees. In particular, we prove that tensor
initialization followed by gradient descent can converge to the ground-truth
parameters at a linear rate up to some statistical error. To the best of our
knowledge, this is the first work characterizing the recovery guarantee for
practical learning of one-hidden-layer ReLU networks with multiple neurons.
Numerical experiments verify our theoretical findings.
| 0 | 0 | 0 | 1 | 0 | 0 |
Exclusion of GNSS NLOS Receptions Caused by Dynamic Objects in Heavy Traffic Urban Scenarios Using Real-Time 3D Point Cloud: An Approach without 3D Maps | Absolute positioning is an essential factor for the arrival of autonomous
driving. Global Navigation Satellites System (GNSS) receiver provides absolute
localization for it. GNSS solution can provide satisfactory positioning in open
or sub-urban areas, however, its performance suffered in super-urbanized area
due to the phenomenon which are well-known as multipath effects and NLOS
receptions. The effects dominate GNSS positioning performance in the area. The
recent proposed 3D map aided (3DMA) GNSS can mitigate most of the multipath
effects and NLOS receptions caused by buildings based on 3D city models.
However, the same phenomenon caused by moving objects in urban area is
currently not modelled in the 3D geographic information system (GIS). Moving
objects with tall height, such as the double-decker bus, can also cause NLOS
receptions because of the blockage of GNSS signals by surface of objects.
Therefore, we present a novel method to exclude the NLOS receptions caused by
double-decker bus in highly urbanized area, Hong Kong. To estimate the geometry
dimension and orientation relative to GPS receiver, a Euclidean cluster
algorithm and a classification method are used to detect the double-decker
buses and calculate their relative locations. To increase the accuracy and
reliability of the proposed NLOS exclusion method, an NLOS exclusion criterion
is proposed to exclude the blocked satellites considering the elevation, signal
noise ratio (SNR) and horizontal dilution of precision (HDOP). Finally, GNSS
positioning is estimated by weighted least square (WLS) method using the
remaining satellites after the NLOS exclusion. A static experiment was
performed near a double-decker bus stop in Hong Kong, which verified the
effectiveness of the proposed method.
| 1 | 0 | 0 | 0 | 0 | 0 |
Energy Distribution in Intrinsically Coupled Systems: The Spring Pendulum Paradigm | Intrinsically nonlinear coupled systems present different oscillating
components that exchange energy among themselves. We present a new approach to
deal with such energy exchanges and to investigate how it depends on the system
control parameters. The method consists in writing the total energy of the
system, and properly identifying the energy terms for each component and,
especially, their coupling. To illustrate the proposed approach, we work with
the bi-dimensional spring pendulum, which is a paradigm to study nonlinear
coupled systems, and is used as a model for several systems. For the spring
pendulum, we identify three energy components, resembling the spring and
pendulum like motions, and the coupling between them. With these analytical
expressions, we analyze the energy exchange for individual trajectories, and we
also obtain global characteristics of the spring pendulum energy distribution
by calculating spatial and time average energy components for a great number of
trajectories (periodic, quasi-periodic and chaotic) throughout the phase space.
Considering an energy term due to the nonlinear coupling, we identify regions
in the parameter space that correspond to strong and weak coupling. The
presented procedure can be applied to nonlinear coupled systems to reveal how
the coupling mediates internal energy exchanges, and how the energy
distribution varies according to the system parameters.
| 0 | 1 | 0 | 0 | 0 | 0 |
Cayley deformations of compact complex surfaces | In this article, we consider Cayley deformations of a compact complex surface
in a Calabi--Yau four-fold. We will study complex deformations of compact
complex submanifolds of Calabi--Yau manifolds with a view to explaining why
complex and Cayley deformations of a compact complex surface are the same. We
in fact prove that the moduli space of complex deformations of any compact
complex embedded submanifold of a Calabi--Yau manifold is a smooth manifold.
| 0 | 0 | 1 | 0 | 0 | 0 |
Ensemble Inhibition and Excitation in the Human Cortex: an Ising Model Analysis with Uncertainties | The pairwise maximum entropy model, also known as the Ising model, has been
widely used to analyze the collective activity of neurons. However, controversy
persists in the literature about seemingly inconsistent findings, whose
significance is unclear due to lack of reliable error estimates. We therefore
develop a method for accurately estimating parameter uncertainty based on
random walks in parameter space using adaptive Markov Chain Monte Carlo after
the convergence of the main optimization algorithm. We apply our method to the
spiking patterns of excitatory and inhibitory neurons recorded with
multielectrode arrays in the human temporal cortex during the wake-sleep cycle.
Our analysis shows that the Ising model captures neuronal collective behavior
much better than the independent model during wakefulness, light sleep, and
deep sleep when both excitatory (E) and inhibitory (I) neurons are modeled;
ignoring the inhibitory effects of I-neurons dramatically overestimates
synchrony among E-neurons. Furthermore, information-theoretic measures reveal
that the Ising model explains about 80%-95% of the correlations, depending on
sleep state and neuron type. Thermodynamic measures show signatures of
criticality, although we take this with a grain of salt as it may be merely a
reflection of long-range neural correlations.
| 0 | 0 | 0 | 0 | 1 | 0 |
Generalized Self-Concordant Functions: A Recipe for Newton-Type Methods | We study the smooth structure of convex functions by generalizing a powerful
concept so-called self-concordance introduced by Nesterov and Nemirovskii in
the early 1990s to a broader class of convex functions, which we call
generalized self-concordant functions. This notion allows us to develop a
unified framework for designing Newton-type methods to solve convex optimiza-
tion problems. The proposed theory provides a mathematical tool to analyze both
local and global convergence of Newton-type methods without imposing
unverifiable assumptions as long as the un- derlying functionals fall into our
generalized self-concordant function class. First, we introduce the class of
generalized self-concordant functions, which covers standard self-concordant
functions as a special case. Next, we establish several properties and key
estimates of this function class, which can be used to design numerical
methods. Then, we apply this theory to develop several Newton-type methods for
solving a class of smooth convex optimization problems involving the
generalized self- concordant functions. We provide an explicit step-size for
the damped-step Newton-type scheme which can guarantee a global convergence
without performing any globalization strategy. We also prove a local quadratic
convergence of this method and its full-step variant without requiring the
Lipschitz continuity of the objective Hessian. Then, we extend our result to
develop proximal Newton-type methods for a class of composite convex
minimization problems involving generalized self-concordant functions. We also
achieve both global and local convergence without additional assumption.
Finally, we verify our theoretical results via several numerical examples, and
compare them with existing methods.
| 0 | 0 | 1 | 1 | 0 | 0 |
On Joint Functional Calculus For Ritt Operators | In this paper, we study joint functional calculus for commuting $n$-tuple of
Ritt operators. We provide an equivalent characterisation of boundedness for
joint functional calculus for Ritt operators on $L^p$-spaces, $1< p<\infty$. We
also investigate joint similarity problem and joint bounded functional calculus
on non-commutative $L^p$-spaces for $n$-tuple of Ritt operators. We get our
results by proving a suitable multivariable transfer principle between
sectorial and Ritt operators as well as an appropriate joint dilation result in
a general setting.
| 0 | 0 | 1 | 0 | 0 | 0 |
Controlling plasmon modes and damping in buckled two-dimensional material open systems | Full ranges of both hybrid plasmon-mode dispersions and their damping are
studied systematically by our recently developed mean-field theory in open
systems involving a conducting substrate and a two-dimensional (2D) material
with a buckled honeycomb lattice, such as silicene, germanene, and a group
\rom{4} dichalcogenide as well. In this hybrid system, the single plasmon mode
for a free-standing 2D layer is split into one acoustic-like and one
optical-like mode, leading to a dramatic change in the damping of plasmon
modes. In comparison with gapped graphene, critical features associated with
plasmon modes and damping in silicene and molybdenum disulfide are found with
various spin-orbit and lattice asymmetry energy bandgaps, doping types and
levels, and coupling strengths between 2D materials and the conducting
substrate. The obtained damping dependence on both spin and valley degrees of
freedom is expected to facilitate measuring the open-system dielectric property
and the spin-orbit coupling strength of individual 2D materials. The unique
linear dispersion of the acoustic-like plasmon mode introduces additional
damping from the intraband particle-hole modes which is absent for a
free-standing 2D material layer, and the use of molybdenum disulfide with a
large bandgap simultaneously suppresses the strong damping from the interband
particle-hole modes.
| 0 | 1 | 0 | 0 | 0 | 0 |
A high-order nonconservative approach for hyperbolic equations in fluid dynamics | It is well known, thanks to Lax-Wendroff theorem, that the local conservation
of a numerical scheme for a conservative hyperbolic system is a simple and
systematic way to guarantee that, if stable, a scheme will provide a sequence
of solutions that will converge to a weak solution of the continuous problem.
In [1], it is shown that a nonconservative scheme will not provide a good
solution. The question of using, nevertheless, a nonconservative formulation of
the system and getting the correct solution has been a long-standing debate. In
this paper, we show how get a relevant weak solution from a pressure-based
formulation of the Euler equations of fluid mechanics. This is useful when
dealing with nonlinear equations of state because it is easier to compute the
internal energy from the pressure than the opposite. This makes it possible to
get oscillation free solutions, contrarily to classical conservative methods.
An extension to multiphase flows is also discussed, as well as a
multidimensional extension.
| 0 | 0 | 1 | 0 | 0 | 0 |
Improving Resilience of Autonomous Moving Platforms by Real Time Analysis of Their Cooperation | Environmental changes, failures, collisions or even terrorist attacks can
cause serious malfunctions of the delivery systems. We have presented a novel
approach improving resilience of Autonomous Moving Platforms AMPs. The approach
is based on multi-level state diagrams describing environmental trigger
specifications, movement actions and synchronization primitives. The upper
level diagrams allowed us to model advanced interactions between autonomous
AMPs and detect irregularities such as deadlocks live-locks etc. The techniques
were presented to verify and analyze combined AMPs' behaviors using model
checking technique. The described system, Dedan verifier, is still under
development. In the near future, a graphical form of verified system
representation is planned.
| 1 | 0 | 0 | 0 | 0 | 0 |
Power series expansions for the planar monomer-dimer problem | We compute the free energy of the planar monomer-dimer model. Unlike the
classical planar dimer model, an exact solution is not known in this case. Even
the computation of the low-density power series expansion requires heavy and
nontrivial computations. Despite of the exponential computational complexity,
we compute almost three times more terms than were previously known. Such an
expansion provides both lower and upper bound for the free energy, and allows
to obtain more accurate numerical values than previously possible. We expect
that our methods can be applied to other similar problems.
| 1 | 0 | 0 | 0 | 0 | 0 |
Neural Networks Compression for Language Modeling | In this paper, we consider several compression techniques for the language
modeling problem based on recurrent neural networks (RNNs). It is known that
conventional RNNs, e.g, LSTM-based networks in language modeling, are
characterized with either high space complexity or substantial inference time.
This problem is especially crucial for mobile applications, in which the
constant interaction with the remote server is inappropriate. By using the Penn
Treebank (PTB) dataset we compare pruning, quantization, low-rank
factorization, tensor train decomposition for LSTM networks in terms of model
size and suitability for fast inference.
| 1 | 0 | 0 | 1 | 0 | 0 |
Relativistic effects in the non-resonant two-photon K-shell ionization of neutral atoms | Relativistic effects in the non-resonant two-photon K-shell ionization of
neutral atoms are studied theoretically within the framework of second-order
perturbation theory. The non-relativistic results are compared with the
relativistic calculations in the dipole and no-pair approximations as well as
with the complete relativistic approach. The calculations are performed in both
velocity and length gauges. Our results show a significant decrease of the
total cross section for heavy atoms as compared to the non-relativistic
treatment, which is mainly due to the relativistic wavefunction contraction.
The effects of higher multipoles and negative continuum energy states
counteract the relativistic contraction contribution, but are generally much
weaker. While the effects beyond the dipole approximation are equally important
in both gauges, the inclusion of negative continuum energy states visibly
contributes to the total cross section only in the velocity gauge.
| 0 | 1 | 0 | 0 | 0 | 0 |
Local Okounkov bodies and limits in prime characteristic | This article is concerned with the asymptotic behavior of certain sequences
of ideals in rings of prime characteristic. These sequences, which we call
$p$-families of ideals, are ubiquitous in prime characteristic commutative
algebra (e.g., they occur naturally in the theories of tight closure,
Hilbert-Kunz multiplicity, and $F$-signature). We associate to each $p$-family
of ideals an object in Euclidean space that is analogous to the Newton-Okounkov
body of a graded family of ideals, which we call a $p$-body. Generalizing the
methods used to establish volume formulas for the Hilbert-Kunz multiplicity and
$F$-signature of semigroup rings, we relate the volume of a $p$-body to a
certain asymptotic invariant determined by the corresponding $p$-family of
ideals. We apply these methods to obtain new existence results for limits in
positive characteristic, an analogue of the Brunn-Minkowski theorem for
Hilbert-Kunz multiplicity, and a uniformity result concerning the positivity of
a $p$-family.
| 0 | 0 | 1 | 0 | 0 | 0 |
Two-Dimensional Systolic Complexes Satisfy Property A | We show that 2-dimensional systolic complexes are quasi-isometric to quadric
complexes with flat intervals. We use this fact along with the weight function
of Brodzki, Campbell, Guentner, Niblo and Wright to prove that 2-dimensional
systolic complexes satisfy Property A.
| 0 | 0 | 1 | 0 | 0 | 0 |
Application of the Computer Capacity to the Analysis of Processors Evolution | The notion of computer capacity was proposed in 2012, and this quantity has
been estimated for computers of different kinds.
In this paper we show that, when designing new processors, the manufacturers
change the parameters that affect the computer capacity. This allows us to
predict the values of parameters of future processors. As the main example we
use Intel processors, due to the accessibility of detailed description of all
their technical characteristics.
| 1 | 0 | 0 | 0 | 0 | 0 |
On absolutely normal numbers and their discrepancy estimate | We construct the base $2$ expansion of an absolutely normal real number $x$
so that, for every integer $b$ greater than or equal to $2$, the discrepancy
modulo $1$ of the sequence $(b^0 x, b^1 x, b^2 x , \ldots)$ is essentially the
same as that realized by almost all real numbers.
| 1 | 0 | 1 | 0 | 0 | 0 |
Multispectral computational ghost imaging with multiplexed illumination | Computational ghost imaging is a robust and compact system that has drawn
wide attentions over the last two decades. Multispectral imaging possesses
spatial and spectral resolving abilities, is very useful for surveying scenes
and extracting detailed information. Existing multispectral imagers mostly
utilize narrow band filters or dispersive optical devices to separate lights of
different wavelengths, and then use multiple bucket detectors or an array
detector to record them separately. Here, we propose a novel multispectral
ghost imaging method that uses one single bucket detector with multiplexed
illumination to produce colored image. The multiplexed illumination patterns
are produced by three binary encoded matrices (corresponding to red, green,
blue colored information, respectively) and random patterns. The results of
simulation and experiment have verified that our method can be effective to
recover the colored object. Our method has two major advantages: one is that
the binary encoded matrices as cipher keys can protect the security of private
contents; the other is that multispectral images are produced simultaneously by
one single-pixel detector, which significantly reduces the amount of the data
acquisition.
| 0 | 1 | 0 | 0 | 0 | 0 |
Combined MEG and fMRI Exponential Random Graph Modeling for inferring functional Brain Connectivity | Estimated connectomes by the means of neuroimaging techniques have enriched
our knowledge of the organizational properties of the brain leading to the
development of network-based clinical diagnostics. Unfortunately, to date, many
of those network-based clinical diagnostics tools, based on the mere
description of isolated instances of observed connectomes are noisy estimates
of the true connectivity network. Modeling brain connectivity networks is
therefore important to better explain the functional organization of the brain
and allow inference of specific brain properties. In this report, we present
pilot results on the modeling of combined MEG and fMRI neuroimaging data
acquired during an n-back memory task experiment. We adopted a pooled
Exponential Random Graph Model (ERGM) as a network statistical model to capture
the underlying process in functional brain networks of 9 subjects MEG and fMRI
data out of 32 during a 0-back vs 2-back memory task experiment. Our results
suggested strong evidence that all the functional connectomes of the 9 subjects
have small world properties. A group level comparison using comparing the
conditions pairwise showed no significant difference in the functional
connectomes across the subjects. Our pooled ERGMs successfully reproduced
important brain properties such as functional segregation and functional
integration. However, the ERGMs reproducing the functional segregation of the
brain networks discriminated between the 0-back and 2-back conditions while the
models reproducing both properties failed to successfully discriminate between
both conditions. Our results are promising and would improve in robustness with
a larger sample size. Nevertheless, our pilot results tend to support previous
findings that functional segregation and integration are sufficient to
statistically reproduce the main properties of brain network.
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An updated Type II supernova Hubble diagram | We present photometry and spectroscopy of nine Type II-P/L supernovae (SNe)
with redshifts in the 0.045 < z < 0.335 range, with a view to re-examining
their utility as distance indicators. Specifically, we apply the expanding
photosphere method (EPM) and the standardized candle method (SCM) to each
target, and find that both methods yield distances that are in reasonable
agreement with each other. The current record-holder for the highest-redshift
spectroscopically confirmed SN II-P is PS1-13bni (z = 0.335 +0.009 -0.012), and
illustrates the promise of Type II SNe as cosmological tools. We updated
existing EPM and SCM Hubble diagrams by adding our sample to those previously
published. Within the context of Type II SN distance measuring techniques, we
investigated two related questions. First, we explored the possibility of
utilising spectral lines other than the traditionally used Fe II 5169 to infer
the photospheric velocity of SN ejecta. Using local well-observed objects, we
derive an epoch-dependent relation between the strong Balmer line and Fe II
5169 velocities that is applicable 30 to 40 days post-explosion. Motivated in
part by the continuum of key observables such as rise time and decline rates
exhibited from II-P to II-L SNe, we assessed the possibility of using
Hubble-flow Type II-L SNe as distance indicators. These yield similar distances
as the Type II-P SNe. Although these initial results are encouraging, a
significantly larger sample of SNe II-L would be required to draw definitive
conclusions.
| 0 | 1 | 0 | 0 | 0 | 0 |
Digital Identity: The Effect of Trust and Reputation Information on User Judgement in the Sharing Economy | The Sharing Economy (SE) is a growing ecosystem focusing on peer-to-peer
enterprise. In the SE the information available to assist individuals (users)
in making decisions focuses predominantly on community generated trust and
reputation information. However, how such information impacts user judgement is
still being understood. To explore such effects, we constructed an artificial
SE accommodation platform where we varied the elements related to hosts'
digital identity, measuring users' perceptions and decisions to interact.
Across three studies, we find that trust and reputation information increases
not only the users' perceived trustworthiness, credibility, and sociability of
hosts, but also the propensity to rent a private room in their home. This
effect is seen when providing users both with complete profiles and profiles
with partial user-selected information. Closer investigations reveal that three
elements relating to the host's digital identity are sufficient to produce such
positive perceptions and increased rental decisions, regardless of which three
elements are presented. Our findings have relevant implications for human
judgment and privacy in the SE, and question its current culture of ever
increasing information-sharing.
| 1 | 0 | 0 | 0 | 0 | 0 |
Can Deep Clinical Models Handle Real-World Domain Shifts? | The hypothesis that computational models can be reliable enough to be adopted
in prognosis and patient care is revolutionizing healthcare. Deep learning, in
particular, has been a game changer in building predictive models, thereby
leading to community-wide data curation efforts. However, due to the inherent
variabilities in population characteristics and biological systems, these
models are often biased to the training datasets. This can be limiting when
models are deployed in new environments, particularly when there are systematic
domain shifts not known a priori. In this paper, we formalize these challenges
by emulating a large class of domain shifts that can occur in clinical
settings, and argue that evaluating the behavior of predictive models in light
of those shifts is an effective way of quantifying the reliability of clinical
models. More specifically, we develop an approach for building challenging
scenarios, based on analysis of \textit{disease landscapes}, and utilize
unsupervised domain adaptation to compensate for the domain shifts. Using the
openly available MIMIC-III EHR dataset for phenotyping, we generate a large
class of scenarios and evaluate the ability of deep clinical models in those
cases. For the first time, our work sheds light into data regimes where deep
clinical models can fail to generalize, due to significant changes in the
disease landscapes between the source and target landscapes. This study
emphasizes the need for sophisticated evaluation mechanisms driven by
real-world domain shifts to build effective AI solutions for healthcare.
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Fabrication of grain boundary junctions using NdFeAs(O,F) superconducting thin films | We report on the growth of NdFeAs(O,F) thin films on [001]-tilt MgO bicrystal
substrates with misorientation angle theta_GB=6°, 12°, 24° and
45°, and their inter- and intra-grain transport properties. X-ray
diffraction study confirmed that all our NdFeAs(O,F) films are epitaxially
grown on the MgO bicrystals. The theta_GB dependence of the inter-grain
critical current density Jc shows that, unlike Co-doped BaFe2As2 and Fe(Se,Te),
its decay with theta_GB is rather significant. As a possible reason of this
result, fluorine may have diffused preferentially to the grain boundary region
and eroded the crystal structure.
| 0 | 1 | 0 | 0 | 0 | 0 |
Panchromatic Hubble Andromeda Treasury XVIII. The High-mass Truncation of the Star Cluster Mass Function | We measure the mass function for a sample of 840 young star clusters with
ages between 10-300 Myr observed by the Panchromatic Hubble Andromeda Treasury
(PHAT) survey in M31. The data show clear evidence of a high-mass truncation:
only 15 clusters more massive than $10^4$ $M_{\odot}$ are observed, compared to
$\sim$100 expected for a canonical $M^{-2}$ pure power-law mass function with
the same total number of clusters above the catalog completeness limit.
Adopting a Schechter function parameterization, we fit a characteristic
truncation mass of $M_c = 8.5^{+2.8}_{-1.8} \times 10^3$ $M_{\odot}$. While
previous studies have measured cluster mass function truncations, the
characteristic truncation mass we measure is the lowest ever reported.
Combining this M31 measurement with previous results, we find that the cluster
mass function truncation correlates strongly with the characteristic star
formation rate surface density of the host galaxy, where $M_c \propto$ $\langle
\Sigma_{\mathrm{SFR}} \rangle^{\sim1.1}$. We also find evidence that suggests
the observed $M_c$-$\Sigma_{\mathrm{SFR}}$ relation also applies to globular
clusters, linking the two populations via a common formation pathway. If so,
globular cluster mass functions could be useful tools for constraining the star
formation properties of their progenitor host galaxies in the early Universe.
| 0 | 1 | 0 | 0 | 0 | 0 |
Cohomology and overconvergence for representations of powers of Galois groups | We show that the Galois cohomology groups of $p$-adic representations of a
direct power of $\operatorname{Gal}(\overline{\mathbb{Q}_p}/\mathbb{Q}_p)$ can
be computed via the generalization of Herr's complex to multivariable
$(\varphi,\Gamma)$-modules. Using Tate duality and a pairing for multivariable
$(\varphi,\Gamma)$-modules we extend this to analogues of the Iwasawa
cohomology. We show that all $p$-adic representations of a direct power of
$\operatorname{Gal}(\overline{\mathbb{Q}_p}/\mathbb{Q}_p)$ are overconvergent
and, moreover, passing to overconvergent multivariable
$(\varphi,\Gamma)$-modules is an equivalence of categories. Finally, we prove
that the overconvergent Herr complex also computes the Galois cohomology
groups.
| 0 | 0 | 1 | 0 | 0 | 0 |
Global algorithms for maximal eigenpair | This paper is a continuation of \ct{cmf16} where an efficient algorithm for
computing the maximal eigenpair was introduced first for tridiagonal matrices
and then extended to the irreducible matrices with nonnegative off-diagonal
elements. This paper introduces two global algorithms for computing the maximal
eigenpair in a rather general setup, including even a class of real (with some
negative off-diagonal elements) or complex matrices.
| 0 | 0 | 1 | 1 | 0 | 0 |
Entanglement and entropy production in coupled single-mode Bose-Einstein condensates | We investigate the time evolution of the entanglement entropy of coupled
single-mode Bose-Einstein condensates in a double well potential at $T=0$
temperature, by combining numerical results with analytical approximations. We
find that the coherent oscillations of the condensates result in entropy
oscillations on the top of a linear entropy generation at short time scales.
Due to dephasing, the entropy eventually saturates to a stationary value, in
spite of the lack of equilibration. We show that this long time limit of the
entropy reflects the semiclassical dynamics of the system, revealing the
self-trapping phase transition of the condensates at large interaction strength
by a sudden entropy jump. We compare the stationary limit of the entropy to the
prediction of a classical microcanonical ensemble, and find surprisingly good
agreement in spite of the non-equilibrium state of the system. Our predictions
should be experimentally observable on a Bose-Einstein condensate in a double
well potential or on a two-component condensate with inter-state coupling.
| 0 | 1 | 0 | 0 | 0 | 0 |
Sparse Poisson Regression with Penalized Weighted Score Function | We proposed a new penalized method in this paper to solve sparse Poisson
Regression problems. Being different from $\ell_1$ penalized log-likelihood
estimation, our new method can be viewed as penalized weighted score function
method. We show that under mild conditions, our estimator is $\ell_1$
consistent and the tuning parameter can be pre-specified, which shares the same
good property of the square-root Lasso.
| 0 | 0 | 1 | 1 | 0 | 0 |
Bubble size statistics during reionization from 21-cm tomography | The upcoming SKA1-Low radio interferometer will be sensitive enough to
produce tomographic imaging data of the redshifted 21-cm signal from the Epoch
of Reionization. Due to the non-Gaussian distribution of the signal, a power
spectrum analysis alone will not provide a complete description of its
properties. Here, we consider an additional metric which could be derived from
tomographic imaging data, namely the bubble size distribution of ionized
regions. We study three methods that have previously been used to characterize
bubble size distributions in simulation data for the hydrogen ionization
fraction - the spherical-average, mean-free-path and friends-of-friends methods
- and apply them to simulated 21-cm data cubes. Our simulated data cubes have
the (sensitivity-dictated) resolution expected for the SKA1-Low reionization
experiment and we study the impact of both the light-cone and redshift space
distortion effects. To identify ionized regions in the 21-cm data we introduce
a new, self-adjusting thresholding approach based on the K-Means algorithm. We
find that the fraction of ionized cells identified in this way consistently
falls below the mean volume-averaged ionized fraction. From a comparison of the
three bubble size methods, we conclude that all three methods are useful, but
that the mean-free-path method performs best in terms of tracking the progress
of reionization and separating different reionization scenarios. The light-cone
effect is found to affect data spanning more than about 10~MHz in frequency
($\Delta z\sim0.5$). We find that redshift space distortions only marginally
affect the bubble size distributions.
| 0 | 1 | 0 | 0 | 0 | 0 |
Robust Stochastic Configuration Networks with Kernel Density Estimation | Neural networks have been widely used as predictive models to fit data
distribution, and they could be implemented through learning a collection of
samples. In many applications, however, the given dataset may contain noisy
samples or outliers which may result in a poor learner model in terms of
generalization. This paper contributes to a development of robust stochastic
configuration networks (RSCNs) for resolving uncertain data regression
problems. RSCNs are built on original stochastic configuration networks with
weighted least squares method for evaluating the output weights, and the input
weights and biases are incrementally and randomly generated by satisfying with
a set of inequality constrains. The kernel density estimation (KDE) method is
employed to set the penalty weights for each training samples, so that some
negative impacts, caused by noisy data or outliers, on the resulting learner
model can be reduced. The alternating optimization technique is applied for
updating a RSCN model with improved penalty weights computed from the kernel
density estimation function. Performance evaluation is carried out by a
function approximation, four benchmark datasets and a case study on engineering
application. Comparisons to other robust randomised neural modelling
techniques, including the probabilistic robust learning algorithm for neural
networks with random weights and improved RVFL networks, indicate that the
proposed RSCNs with KDE perform favourably and demonstrate good potential for
real-world applications.
| 1 | 0 | 0 | 1 | 0 | 0 |
Density of the spectrum of Jacobi matrices with power asymptotics | We consider Jacobi matrices $J$ whose parameters have the power asymptotics
$\rho_n=n^{\beta_1} \left( x_0 + \frac{x_1}{n} + {\rm
O}(n^{-1-\epsilon})\right)$ and $q_n=n^{\beta_2} \left( y_0 + \frac{y_1}{n} +
{\rm O}(n^{-1-\epsilon})\right)$ for the off-diagonal and diagonal,
respectively. We show that for $\beta_1 > \beta_2$, or $\beta_1=\beta_2$ and
$2x_0 > |y_0|$, the matrix $J$ is in the limit circle case and the convergence
exponent of its spectrum is $1/\beta_1$. Moreover, we obtain upper and lower
bounds for the upper density of the spectrum. When the parameters of the matrix
$J$ have a power asymptotic with one more term, we characterise the occurrence
of the limit circle case completely (including the exceptional case $\lim_{n\to
\infty} |q_n|\big/ \rho_n = 2$) and determine the convergence exponent in
almost all cases.
| 0 | 0 | 1 | 0 | 0 | 0 |
Modeling of a self-sustaining ignition in a solid energetic material | In the present work we analyze some necessary conditions for ignition of
solid energetic materials by low velocity impact ignition mechanism. Basing on
reported results of {\it ab initio} computations we assume that the energetic
activation barriers for the primary endothermic dissociation in some energetic
materials may be locally lowered due to the effect of shear strain caused by
the impact. We show that the ignition may be initiated in regions with the
reduced activation barriers, even at moderately low exothermicity of the
subsequent exothermic reactions thus suggesting that the above regions may
serve as "hot spots" for the ignition. We apply our results to analyze initial
steps of ignition in DADNE and TATB molecular crystals.
| 0 | 1 | 0 | 0 | 0 | 0 |
Election Bias: Comparing Polls and Twitter in the 2016 U.S. Election | While the polls have been the most trusted source for election predictions
for decades, in the recent presidential election they were called inaccurate
and biased. How inaccurate were the polls in this election and can social media
beat the polls as an accurate election predictor? Polls from several news
outlets and sentiment analysis on Twitter data were used, in conjunction with
the results of the election, to answer this question and outline further
research on the best method for predicting the outcome of future elections.
| 1 | 0 | 0 | 0 | 0 | 0 |
Versality of the relative Fukaya category | Seidel introduced the notion of a Fukaya category `relative to an ample
divisor', explained that it is a deformation of the Fukaya category of the
affine variety that is the complement of the divisor, and showed how the
relevant deformation theory is controlled by the symplectic cohomology of the
complement. We elaborate on Seidel's definition of the relative Fukaya
category, and give a criterion under which the deformation is versal.
| 0 | 0 | 1 | 0 | 0 | 0 |
Hot Phonon and Carrier Relaxation in Si(100) Determined by Transient Extreme Ultraviolet Spectroscopy | The thermalization of hot carriers and phonons gives direct insight into the
scattering processes that mediate electrical and thermal transport. Obtaining
the scattering rates for both hot carriers and phonons currently requires
multiple measurements with incommensurate timescales. Here, transient
extreme-ultraviolet (XUV) spectroscopy on the silicon 2p core level at 100 eV
is used to measure hot carrier and phonon thermalization in Si(100) from tens
of femtoseconds to 200 ps following photoexcitation of the indirect transition
to the {\Delta} valley at 800 nm. The ground state XUV spectrum is first
theoretically predicted using a combination of a single plasmon pole model and
the Bethe-Salpeter equation (BSE) with density functional theory (DFT). The
excited state spectrum is predicted by incorporating the electronic effects of
photo-induced state-filling, broadening, and band-gap renormalization into the
ground state XUV spectrum. A time-dependent lattice deformation and expansion
is also required to describe the excited state spectrum. The kinetics of these
structural components match the kinetics of phonons excited from the
electron-phonon and phonon-phonon scattering processes following
photoexcitation. Separating the contributions of electronic and structural
effects on the transient XUV spectra allows the carrier population, the
population of phonons involved in inter- and intra-valley electron-phonon
scattering, and the population of phonons involved in phonon-phonon scattering
to be quantified as a function of delay time.
| 0 | 1 | 0 | 0 | 0 | 0 |
Counting Quasi-Idempotent Irreducible Integral Matrices | Given any polynomial $p$ in $C[X]$, we show that the set of irreducible
matrices satisfying $p(A)=0$ is finite. In the specific case $p(X)=X^2-nX$, we
count the number of irreducible matrices in this set and analyze the arising
sequences and their asymptotics. Such matrices turn out to be related to
generalized compositions and generalized partitions.
| 0 | 0 | 1 | 0 | 0 | 0 |
On sound-based interpretation of neonatal EEG | Significant training is required to visually interpret neonatal EEG signals.
This study explores alternative sound-based methods for EEG interpretation
which are designed to allow for intuitive and quick differentiation between
healthy background activity and abnormal activity such as seizures. A novel
method based on frequency and amplitude modulation (FM/AM) is presented. The
algorithm is tuned to facilitate the audio domain perception of rhythmic
activity which is specific to neonatal seizures. The method is compared with
the previously developed phase vocoder algorithm for different time compressing
factors. A survey is conducted amongst a cohort of non-EEG experts to
quantitatively and qualitatively examine the performance of sound-based methods
in comparison with the visual interpretation. It is shown that both
sonification methods perform similarly well, with a smaller inter-observer
variability in comparison with visual. A post-survey analysis of results is
performed by examining the sensitivity of the ear to frequency evolution in
audio.
| 0 | 0 | 0 | 1 | 1 | 0 |
OAuthGuard: Protecting User Security and Privacy with OAuth 2.0 and OpenID Connect | Millions of users routinely use Google to log in to websites supporting OAuth
2.0 or OpenID Connect; the security of OAuth 2.0 and OpenID Connect is
therefore of critical importance. As revealed in previous studies, in practice
RPs often implement OAuth 2.0 incorrectly, and so many real-world OAuth 2.0 and
OpenID Connect systems are vulnerable to attack. However, users of such flawed
systems are typically unaware of these issues, and so are at risk of attacks
which could result in unauthorised access to the victim user's account at an
RP. In order to address this threat, we have developed OAuthGuard, an OAuth 2.0
and OpenID Connect vulnerability scanner and protector, that works with RPs
using Google OAuth 2.0 and OpenID Connect services. It protects user security
and privacy even when RPs do not implement OAuth 2.0 or OpenID Connect
correctly. We used OAuthGuard to survey the 1000 top-ranked websites supporting
Google sign-in for the possible presence of five OAuth 2.0 or OpenID Connect
security and privacy vulnerabilities, of which one has not previously been
described in the literature. Of the 137 sites in our study that employ Google
Sign-in, 69 were found to suffer from at least one serious vulnerability.
OAuthGuard was able to protect user security and privacy for 56 of these 69
RPs, and for the other 13 was able to warn users that they were using an
insecure implementation.
| 1 | 0 | 0 | 0 | 0 | 0 |
Aspiration dynamics generate robust predictions in structured populations | Evolutionary game dynamics in structured populations are strongly affected by
updating rules. Previous studies usually focus on imitation-based rules, which
rely on payoff information of social peers. Recent behavioral experiments
suggest that whether individuals use such social information for strategy
updating may be crucial to the outcomes of social interactions. This hints at
the importance of considering updating rules without dependence on social
peers' payoff information, which, however, is rarely investigated. Here, we
study aspiration-based self-evaluation rules, with which individuals
self-assess the performance of strategies by comparing own payoffs with an
imaginary value they aspire, called the aspiration level. We explore the fate
of strategies on population structures represented by graphs or networks. Under
weak selection, we analytically derive the condition for strategy dominance,
which is found to coincide with the classical condition of risk-dominance. This
condition holds for all networks and all distributions of aspiration levels,
and for individualized ways of self-evaluation. Our condition can be
intuitively interpreted: one strategy prevails over the other if the strategy
brings more satisfaction to individuals than the other does. Our work thus
sheds light on the intrinsic difference between evolutionary dynamics induced
by aspiration-based and imitation-based rules.
| 0 | 0 | 0 | 0 | 1 | 0 |
Memory Efficient Experience Replay for Streaming Learning | In supervised machine learning, an agent is typically trained once and then
deployed. While this works well for static settings, robots often operate in
changing environments and must quickly learn new things from data streams. In
this paradigm, known as streaming learning, a learner is trained online, in a
single pass, from a data stream that cannot be assumed to be independent and
identically distributed (iid). Streaming learning will cause conventional deep
neural networks (DNNs) to fail for two reasons: 1) they need multiple passes
through the entire dataset; and 2) non-iid data will cause catastrophic
forgetting. An old fix to both of these issues is rehearsal. To learn a new
example, rehearsal mixes it with previous examples, and then this mixture is
used to update the DNN. Full rehearsal is slow and memory intensive because it
stores all previously observed examples, and its effectiveness for preventing
catastrophic forgetting has not been studied in modern DNNs. Here, we describe
the ExStream algorithm for memory efficient rehearsal and compare it to
alternatives. We find that full rehearsal can eliminate catastrophic forgetting
in a variety of streaming learning settings, with ExStream performing well
using far less memory and computation.
| 0 | 0 | 0 | 1 | 0 | 0 |
New integrable semi-discretizations of the coupled nonlinear Schrodinger equations | We have undertaken an algorithmic search for new integrable
semi-discretizations of physically relevant nonlinear partial differential
equations. The search is performed by using a compatibility condition for the
discrete Lax operators and symbolic computations. We have discovered a new
integrable system of coupled nonlinear Schrodinger equations which combines
elements of the Ablowitz-Ladik lattice and the triangular-lattice ribbon
studied by Vakhnenko. We show that the continuum limit of the new integrable
system is given by uncoupled complex modified Korteweg-de Vries equations and
uncoupled nonlinear Schrodinger equations.
| 0 | 1 | 1 | 0 | 0 | 0 |
Provable Alternating Gradient Descent for Non-negative Matrix Factorization with Strong Correlations | Non-negative matrix factorization is a basic tool for decomposing data into
the feature and weight matrices under non-negativity constraints, and in
practice is often solved in the alternating minimization framework. However, it
is unclear whether such algorithms can recover the ground-truth feature matrix
when the weights for different features are highly correlated, which is common
in applications. This paper proposes a simple and natural alternating gradient
descent based algorithm, and shows that with a mild initialization it provably
recovers the ground-truth in the presence of strong correlations. In most
interesting cases, the correlation can be in the same order as the highest
possible. Our analysis also reveals its several favorable features including
robustness to noise. We complement our theoretical results with empirical
studies on semi-synthetic datasets, demonstrating its advantage over several
popular methods in recovering the ground-truth.
| 1 | 0 | 0 | 1 | 0 | 0 |
Bayesian mean-variance analysis: Optimal portfolio selection under parameter uncertainty | The paper solves the problem of optimal portfolio choice when the parameters
of the asset returns distribution, like the mean vector and the covariance
matrix are unknown and have to be estimated by using historical data of the
asset returns. The new approach employs the Bayesian posterior predictive
distribution which is the distribution of the future realization of the asset
returns given the observable sample. The parameters of the posterior predictive
distributions are functions of the observed data values and, consequently, the
solution of the optimization problem is expressed in terms of data only and
does not depend on unknown quantities. In contrast, the optimization problem of
the traditional approach is based on unknown quantities which are estimated in
the second step leading to a suboptimal solution. We also derive a very useful
stochastic representation of the posterior predictive distribution whose
application leads not only to the solution of the considered optimization
problem, but provides the posterior predictive distribution of the optimal
portfolio return used to construct a prediction interval. A Bayesian efficient
frontier, a set of optimal portfolios obtained by employing the posterior
predictive distribution, is constructed as well. Theoretically and using real
data we show that the Bayesian efficient frontier outperforms the sample
efficient frontier, a common estimator of the set of optimal portfolios known
to be overoptimistic.
| 0 | 0 | 0 | 0 | 0 | 1 |
Selective inference after likelihood- or test-based model selection in linear models | Statistical inference after model selection requires an inference framework
that takes the selection into account in order to be valid. Following recent
work on selective inference, we derive analytical expressions for inference
after likelihood- or test-based model selection for linear models.
| 0 | 0 | 0 | 1 | 0 | 0 |
Sampling and Reconstruction of Graph Signals via Weak Submodularity and Semidefinite Relaxation | We study the problem of sampling a bandlimited graph signal in the presence
of noise, where the objective is to select a node subset of prescribed
cardinality that minimizes the signal reconstruction mean squared error (MSE).
To that end, we formulate the task at hand as the minimization of MSE subject
to binary constraints, and approximate the resulting NP-hard problem via
semidefinite programming (SDP) relaxation. Moreover, we provide an alternative
formulation based on maximizing a monotone weak submodular function and propose
a randomized-greedy algorithm to find a sub-optimal subset. We then derive a
worst-case performance guarantee on the MSE returned by the randomized greedy
algorithm for general non-stationary graph signals. The efficacy of the
proposed methods is illustrated through numerical simulations on synthetic and
real-world graphs. Notably, the randomized greedy algorithm yields an
order-of-magnitude speedup over state-of-the-art greedy sampling schemes, while
incurring only a marginal MSE performance loss.
| 1 | 0 | 0 | 1 | 0 | 0 |
DLTK: State of the Art Reference Implementations for Deep Learning on Medical Images | We present DLTK, a toolkit providing baseline implementations for efficient
experimentation with deep learning methods on biomedical images. It builds on
top of TensorFlow and its high modularity and easy-to-use examples allow for a
low-threshold access to state-of-the-art implementations for typical medical
imaging problems. A comparison of DLTK's reference implementations of popular
network architectures for image segmentation demonstrates new top performance
on the publicly available challenge data "Multi-Atlas Labeling Beyond the
Cranial Vault". The average test Dice similarity coefficient of $81.5$ exceeds
the previously best performing CNN ($75.7$) and the accuracy of the challenge
winning method ($79.0$).
| 1 | 0 | 0 | 0 | 0 | 0 |
A homotopy theory of Nakaoka twin cotorsion pairs | We show that the Verdier quotients can be realized as subfactors by the
homotopy theory of additive categories with suspensions developed in
\cite{ZWLi2, ZWLi3}. As applications, we develop the homotopy theory of Nakaoka
twin cotorsion pairs of triangulated categories and prove that Iyama-Yoshino
triangulated subfactors are Verdier quotients under suitable conditions.
| 0 | 0 | 1 | 0 | 0 | 0 |
Categorical relations between Langlands dual quantum affine algebras: Doubly laced types | We prove that the Grothendieck rings of category $\mathcal{C}^{(t)}_Q$ over
quantum affine algebras $U_q'(\g^{(t)})$ $(t=1,2)$ associated to each Dynkin
quiver $Q$ of finite type $A_{2n-1}$ (resp. $D_{n+1}$) is isomorphic to one of
category $\mathcal{C}_{\mQ}$ over the Langlands dual $U_q'({^L}\g^{(2)})$ of
$U_q'(\g^{(2)})$ associated to any twisted adapted class $[\mQ]$ of $A_{2n-1}$
(resp. $D_{n+1}$). This results provide partial answers of conjectures of
Frenkel-Hernandez on Langlands duality for finite-dimensional representation of
quantum affine algebras.
| 0 | 0 | 1 | 0 | 0 | 0 |
Strategic Dynamic Pricing with Network Effects | We study the optimal pricing strategy of a monopolist selling homogeneous
goods to customers over multiple periods. The customers choose their time of
purchase to maximize their payoff that depends on their valuation of the
product, the purchase price, and the utility they derive from past purchases of
others, termed the network effect. We first show that the optimal price
sequence is non-decreasing. Therefore, by postponing purchase to future rounds,
customers trade-off a higher utility from the network effects with a higher
price. We then show that a customer's equilibrium strategy can be characterized
by a threshold rule in which at each round a customer purchases the product if
and only if her valuation exceeds a certain threshold. This implies that
customers face an inference problem regarding the valuations of others, i.e.,
observing that a customer has not yet purchased the product, signals that her
valuation is below a threshold. We consider a block model of network
interactions, where there are blocks of buyers subject to the same network
effect. A natural benchmark, this model allows us to provide an explicit
characterization of the optimal price sequence asymptotically as the number of
agents goes to infinity, which notably is linearly increasing in time with a
slope that depends on the network effect through a scalar given by the sum of
entries of the inverse of the network weight matrix. Our characterization shows
that increasing the "imbalance" in the network defined as the difference
between the in and out degree of the nodes increases the revenue of the
monopolist. We further study the effects of price discrimination and show that
in earlier periods monopolist offers lower prices to blocks with higher
Bonacich centrality to encourage them to purchase, which in turn further
incentivizes other customers to buy in subsequent periods.
| 1 | 0 | 0 | 0 | 0 | 0 |
Semisimple Leibniz algebras and their derivations and automorphisms | The present paper is devoted to the description of finite-dimensional
semisimple Leibniz algebras over complex numbers, their derivations and
automorphisms.
| 0 | 0 | 1 | 0 | 0 | 0 |
Vandermonde Matrices with Nodes in the Unit Disk and the Large Sieve | We derive bounds on the extremal singular values and the condition number of
NxK, with N>=K, Vandermonde matrices with nodes in the unit disk. The
mathematical techniques we develop to prove our main results are inspired by a
link---first established by by Selberg [1] and later extended by Moitra
[2]---between the extremal singular values of Vandermonde matrices with nodes
on the unit circle and large sieve inequalities. Our main conceptual
contribution lies in establishing a connection between the extremal singular
values of Vandermonde matrices with nodes in the unit disk and a novel large
sieve inequality involving polynomials in z \in C with |z|<=1. Compared to
Bazán's upper bound on the condition number [3], which, to the best of our
knowledge, constitutes the only analytical result---available in the
literature---on the condition number of Vandermonde matrices with nodes in the
unit disk, our bound not only takes a much simpler form, but is also sharper
for certain node configurations. Moreover, the bound we obtain can be evaluated
consistently in a numerically stable fashion, whereas the evaluation of
Bazán's bound requires the solution of a linear system of equations which has
the same condition number as the Vandermonde matrix under consideration and can
therefore lead to numerical instability in practice. As a byproduct, our
result---when particularized to the case of nodes on the unit circle---slightly
improves upon the Selberg-Moitra bound.
| 1 | 0 | 1 | 0 | 0 | 0 |
High-buckled R3 stanene with topologically nontrivial energy gap | Stanene has been predicted to be a two-dimensional topological insulator
(2DTI). Its low-buckled atomic geometry and the enhanced spin-orbit coupling
are expected to cause a prominent quantum spin hall (QSH) effect. However, most
of the experimentally grown stanene to date displays a metallic state without a
real gap, possibly due to the chemical coupling with the substrate and the
stress applied by the substrate. Here,we demonstrate an efficient way of tuning
the atomic buckling in stanene to open a topologically nontrivial energy gap.
Via tuning the growth kinetics, we obtain not only the low-buckled 1x1 stanene
but also an unexpected high-buckled R3xR3 stanene on the Bi(111) substrate.
Scanning tunneling microscopy (STM) study combined with density functional
theory (DFT) calculation confirms that the R3xR3 stanene is a distorted 1x1
structure with a high-buckled Sn in every three 1x1 unit cells. The
high-buckled R3xR3 stanene favors a large band inversion at the {\Gamma} point,
and the spin orbital coupling open a topologically nontrivial energy gap. The
existence of edge states as verified in both STM measurement and DFT
calculation further confirms the topology of the R3xR3 stanene. This study
provides an alternate way to tune the topology of monolayer 2DTI materials.
| 0 | 1 | 0 | 0 | 0 | 0 |
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