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We present a new rank-adaptive tensor method to compute the numerical solution of high-dimensional nonlinear PDEs. The method combines functional tensor train (FTT) series expansions, operator splitting time integration, and a new rank-adaptive algorithm based on a thresholding criterion that limits the component of the PDE velocity vector normal to the FTT tensor manifold. This yields a scheme that can add or remove tensor modes adaptively from the PDE solution as time integration proceeds. The new method is designed to improve computational efficiency, accuracy and robustness in numerical integration of high-dimensional problems. In particular, it overcomes well-known computational challenges associated with dynamic tensor integration, including low-rank modeling errors and the need to invert covariance matrices of tensor cores at each time step. Numerical applications are presented and discussed for linear and nonlinear advection problems in two dimensions, and for a four-dimensional Fokker-Planck equation.
|
mathematics
|
Many techniques have been developed for the loop-shaping method in control design. While most loop-shaping methods apply a model of the open-loop controlled plant, the resulting performance depends on the accuracy of the dynamical model. This paper aims to develop a model-free loop-shaping technique. The core idea is to convert the model matching problem to a trajectory tracking problem. To achieve the desired loop gain, we need to determine the control input such that the system output tracks the impulse response of the loop gain function. In this paper, a model-free iterative learning control (ILC) algorithm is applied to solve this tracking problem. Once the ILC converges, the feedback controller that meets the desired loop gain can then be constructed. This method does not require the model of the controlled plant; hence it provides better performance of loop-shaping control design. The proposed method is validated through numerical simulation on a third order plant.
|
electrical engineering and systems science
|
Exploiting learning algorithms under scarce data regimes is a limitation and a reality of the medical imaging field. In an attempt to mitigate the problem, we propose a data augmentation protocol based on generative adversarial networks. We condition the networks at a pixel-level (segmentation mask) and at a global-level information (acquisition environment or lesion type). Such conditioning provides immediate access to the image-label pairs while controlling global class specific appearance of the synthesized images. To stimulate synthesis of the features relevant for the segmentation task, an additional passive player in a form of segmentor is introduced into the adversarial game. We validate the approach on two medical datasets: BraTS, ISIC. By controlling the class distribution through injection of synthetic images into the training set we achieve control over the accuracy levels of the datasets' classes.
|
electrical engineering and systems science
|
We present state-of-the-art predictions for transverse observables relevant to colour-singlet production at the LHC, in particular the transverse momentum of the colour singlet in gluon-fusion Higgs production and in neutral Drell-Yan lepton-pair production, as well as the $\phi^*_\eta$ observable in Drell Yan. We perform a next-to-next-to-next-to-leading logarithmic (N$^3$LL) resummation of such observables in momentum space according to the RadISH formalism, consistently including in our prediction all constant terms of relative order $\alpha_s^3$ with respect to the Born, thereby achieving N$^3$LL$^\prime$ accuracy. The calculation is fully exclusive with respect to the Born kinematics, which allows the application of arbitrary fiducial selection cuts on the decay products of the colour singlet. We supplement our results with a transverse-recoil prescription, accounting for dominant classes of subleading-power corrections in a fiducial setup. The resummed predictions are matched with fixed-order differential spectra at next-to-next-to-leading order (NNLO) accuracy. A phenomenological comparison is carried out with 13 TeV LHC data relevant to the Higgs to di-photon channel, as well as to neutral Drell-Yan lepton-pair production. Overall, the inclusion of ${\cal O}(\alpha_s^3)$ constant terms, and to a lesser extent of transverse-recoil effects, proves beneficial for the comparison of theoretical predictions to data, leaving a residual theoretical uncertainty in the resummation region at the 2-5% level for Drell-Yan observables, and 5-7% in Higgs production.
|
high energy physics phenomenology
|
The properties of current sheets forming in a ion-kinetically turbulent collisionless plasma are investigated by utilizing the results of two-dimensional hybrid-kinetic numerical simulations. For this sake the algorithm proposed by Zhdankin et al. (2013) for the analysis of current sheets forming in MHD-turbulent plasmas, was extended to analyse the role and propertes of current sheets formating in a much noisier kinetically turbulent plasma. The applicability of this approach to the analysis of kinetically-turbulent plasmas is verified. Invesigated are, e.g., the effects of the choice of parameters on the current sheet recognition, viz. the threshold current density, the minimum current density and of the local regions around current density peaks. The main current sheet properties are derived, their peak current density, the peak current carrier velocity (mainly electrons), the thickness and length of the current sheets, i.e. also their aspect ratio (length/thickness). By varying the grid resolution of the simulations it is shown that, as long as the electron inertia is not taken into account, the current sheets thin down well below ion inertial length scale until numerical (grid-resolution based) dissipation stops any the further thinning.
|
physics
|
I summarize what is known about the Euler-Heisenberg Lagrangian and its multiloop corrections for scalar and spinor QED, in various types of constant fields, and in various dimensions. Particular attention is given to the asymptotic properties of the weak-field expansion of the Lagrangian, which via Borel summation is related to Schwinger pair-creation, and the status of the "exponentiation conjecture" for the imaginary part of the Euler-Heisenberg to all loop orders.
|
high energy physics phenomenology
|
Cone-beam breast computed tomography (CT) provides true 3D breast images with isotropic resolution and high-contrast information, detecting calcifications as small as a few hundred microns and revealing subtle tissue differences. However, breast is highly sensitive to x-ray radiation. It is critically important for healthcare to reduce radiation dose. Few-view cone-beam CT only uses a fraction of x-ray projection data acquired by standard cone-beam breast CT, enabling significant reduction of the radiation dose. However, insufficient sampling data would cause severe streak artifacts in CT images reconstructed using conventional methods. In this study, we propose a deep-learning-based method to establish a residual neural network model for the image reconstruction, which is applied for few-view breast CT to produce high quality breast CT images. We respectively evaluate the deep-learning-based image reconstruction using one third and one quarter of x-ray projection views of the standard cone-beam breast CT. Based on clinical breast imaging dataset, we perform a supervised learning to train the neural network from few-view CT images to corresponding full-view CT images. Experimental results show that the deep learning-based image reconstruction method allows few-view breast CT to achieve a radiation dose <6 mGy per cone-beam CT scan, which is a threshold set by FDA for mammographic screening.
|
physics
|
The superconductivity of cuprates, which has been a mystery ever since its discovery decades ago, is created through doping electrons or holes into a Mott insulator. There, however, exists an inherent electron-hole asymmetry in cuprates. The layered crystal structures of cuprates enable collective charge excitations fundamentally different from those of three-dimensional metals, i.e., acoustic plasmons. Acoustic plasmons have been recently observed in electron-doped cuprates by resonant inelastic X-ray scattering (RIXS); in contrast, there is no evidence for acoustic plasmons in hole-doped cuprates, despite extensive measurements. This contrast led us to investigate whether the doped holes in cuprates La$_{2-x}$Sr$_x$CuO$_4$ are conducting carriers or are too incoherent to induce collective charge excitation. Here we present momentum-resolved RIXS measurements and calculations of collective charge response via the loss function to reconcile the aforementioned issues. Our results provide unprecedented spectroscopic evidence for the acoustic plasmons and long sought conducting p holes in hole-doped cuprates.
|
condensed matter
|
We propose a new broadband search strategy for ultralight axion dark matter that interacts with electromagnetism. An oscillating axion field induces transitions between two quasi-degenerate resonant modes of a superconducting cavity. In two broadband runs optimized for high and low masses, this setup can probe unexplored parameter space for axion-like particles covering fifteen orders of magnitude in mass, including astrophysically long-ranged fuzzy dark matter.
|
high energy physics phenomenology
|
We study the trade-off relations given by the l_1-norm coherence of general multipartite states. Explicit trade-off inequalities are derived with lower bounds given by the coherence of either bipartite or multipartite reduced density matrices. In particular, for pure three-qubit states, it is explicitly shown that the trade-off inequality is lower bounded by the three tangle of quantum entanglement.
|
quantum physics
|
We introduce and demonstrate a scheme for eliminating the inhomogeneous dephasing of a collective quantum state. The scheme employs off-resonant fields that continuously dress the collective state with an auxiliary sensor state, which has an enhanced and opposite sensitivity to the same source of inhomogeneity. We derive the optimal conditions under which the dressed state is fully protected from dephasing, when using either one or two dressing fields. The latter provides better protection, circumvents qubit phase rotation, and suppresses the sensitivity to drive noise. We further derive expressions for all residual, higher-order, sensitivities. We experimentally study the scheme by protecting a collective excitation of an atomic ensemble, where inhomogeneous dephasing originates from thermal motion. Using photon storage and retrieval, we demonstrate complete suppression of inhomogeneous dephasing and consequently a prolonged memory time. Our scheme may be applied to eliminate motional dephasing in other systems, improving the performance of quantum gates and memories with neutral atoms. It is also generally applicable to various gas, solid, and engineered systems, where sensitivity to variations in time, space, or other domains limits possible scale-up of the system.
|
quantum physics
|
In the Fall of 2017, two photon detector designs for the Deep Underground Neutrino Experiment (DUNE) Far Detector were installed and tested in the TallBo liquid argon (LAr) cryostat at the Proton Assembly (PAB) facility, Fermilab. The designs include two light bars developed at Indiana University and a photon detector based on the ARAPUCA light trap engineered by Colorado State University and Fermilab. The performance of these devices is determined by analyzing 8 weeks of cosmic ray data. The current paper focuses solely on the ARAPUCA device as the performance of the light bars will be reported separately. The paper briefly describes the ARAPUCA concept, the TallBo setup, and focuses on data analysis and results.
|
physics
|
The 1D AKLT model is a paradigm of antiferromagnetism, and its ground state exhibits symmetry-protected topological order. On a 2D lattice, the AKLT model has recently gained attention because it too displays symmetry-protected topological order, and its ground state can act as a resource state for measurement-based quantum computation. While the 1D model has been shown to be gapped, it remains an open problem to prove the existence of a spectral gap on the 2D square lattice, which would guarantee the robustness of the resource state. Recently, it has been shown that one can deduce this spectral gap by analyzing the model's boundary theory via a tensor network representation of the ground state. In this work, we express the boundary state of the 2D AKLT model in terms of a classical loop model, where loops, vertices, and crossings are each given a weight. We use numerical techniques to sample configurations of loops and subsequently evaluate the boundary state and boundary Hamiltonian on a square lattice. As a result, we evidence a spectral gap in the square lattice AKLT model. In addition, by varying the weights of the loops, vertices, and crossings, we indicate the presence of three distinct phases exhibited by the classical loop model.
|
quantum physics
|
We consider a minimal extension of the Standard Model which advocates a dark neutrino sector charged under a hidden $U(1)^\prime$. We show that neutrino masses can arise radiatively in this model. The observed values are compatible with a light dark sector below the electroweak scale and would imply new heavy fermions which may be testable in the next generation of beam dump searches at DUNE, NA62 and SHIP.
|
high energy physics phenomenology
|
Capacitated spatial clustering, a type of unsupervised machine learning method, is often used to tackle problems in compressing, classifying, logistic optimization and infrastructure optimization. Depending on the application at hand, a wide set of extensions may be necessary in clustering. In this article we propose a number of novel extensions to PACK that is a novel capacitated spatial clustering method. These extensions are relocation and location preference of cluster centers, outliers, and non-spatial attributes. The strength of PACK is that it can consider all of these extensions jointly. We demonstrate the usefulness PACK with a real world example in edge computing server placement for a city region with various different set ups, where we take into consideration outliers, center placement, and non-spatial attributes. Different setups are evaluated with summary statistics on spatial proximity and attribute similarity. As a result, the similarity of the clusters was improved at best by 53%, while simultaneously the proximity degraded only 18%. In alternate scenarios, both proximity and similarity were improved. The different extensions proved to provide a valuable way to include non-spatial information into the cluster analysis, and attain better overall proximity and similarity. Furthermore, we provide easy-to-use software tools (rpack) for conducting clustering analyses.
|
statistics
|
We study a frustrated two-leg spin ladder with alternate isotropic Heisenberg and Ising rung exchange interactions, whereas, interactions along legs and diagonals are Ising-type. All the interactions in the ladder are anti-ferromagnetic in nature and induce frustration in the system. This model shows four interesting quantum phases: (i) stripe rung ferromagnetic (SRFM), (ii) stripe rung ferromagnetic with edge singlet (SRFM-E), (iii) anisotropic antiferromagnetic (AAFM), and (iv) stripe leg ferromagnetic (SLFM) phase. We construct a quantum phase diagram for this model and show that in stripe rung ferromagnet (SRFM), the same type of sublattice spins (either $S$ or $\sigma$-type spins) are aligned in the same direction. Whereas, in anisotropic antiferromagnetic phase, both $S$ and $\sigma$-type of spins are anti-ferromagnetically aligned with each other, two nearest $S$ spins along the rung form an anisotropic singlet bond whereas two nearest $\sigma$ spins form an Ising bond. In large Heisenberg rung exchange interaction limit, spins on each leg are ferromagnetically aligned, but spins on different legs are anti-ferromagnetically aligned. The thermodynamic quantities like $Cv(T)$, $\chi(T)$ and $S(T)$ are also calculated using the transfer matrix method for different phase. The magnetic gap in the SRFM and the SLFM can be notice from $\chi(T)$ and $Cv(T)$ curves.
|
condensed matter
|
The goal of this work is to prove global controllability and stabilization properties for the fractional Schr\"odinger equation on $d$-dimensional compact Riemannian manifolds without boundary $(M,g)$. To prove our main results we use techniques of pseudo-differential calculus on manifolds. More precisely, by using microlocal analysis, we are able to prove propagation of singularities results which together with Strichartz type estimates and unique continuation property help us to achieve the main results of this work.
|
mathematics
|
We study vibrational statistics in current-carrying model molecular junctions using master equation approach. Especially, we concentrate on the validity of using an effective temperature $T_{\rm eff}$ to characterize the nonequilibrium steady state of a vibrational mode. We identify cases where a single $T_{\rm eff}$ can not fully describe one vibrational state. In such cases, the probability distribution among different vibrational states does not follow the Boltzmann type. Consequently, the actual entropy (free energy) of the vibrational mode is lower (higher) than the corresponding thermal value given by $T_{\rm eff}$, indicating extra work can be extracted from these states. Our results will be useful for the study of non-thermal vibrational state in thermodynamics of nanoscale systems, and its usage in nanoscale heat engines.
|
condensed matter
|
Automated analysis of mouse behaviours is crucial for many applications in neuroscience. However, quantifying mouse behaviours from videos or images remains a challenging problem, where pose estimation plays an important role in describing mouse behaviours. Although deep learning based methods have made promising advances in human pose estimation, they cannot be directly applied to pose estimation of mice due to different physiological natures. Particularly, since mouse body is highly deformable, it is a challenge to accurately locate different keypoints on the mouse body. In this paper, we propose a novel Hourglass network based model, namely Graphical Model based Structured Context Enhancement Network (GM-SCENet) where two effective modules, i.e., Structured Context Mixer (SCM) and Cascaded Multi-Level Supervision (CMLS) are subsequently implemented. SCM can adaptively learn and enhance the proposed structured context information of each mouse part by a novel graphical model that takes into account the motion difference between body parts. Then, the CMLS module is designed to jointly train the proposed SCM and the Hourglass network by generating multi-level information, increasing the robustness of the whole network.Using the multi-level prediction information from SCM and CMLS, we develop an inference method to ensure the accuracy of the localisation results. Finally, we evaluate our proposed approach against several baselines...
|
computer science
|
Plasma accelerators driven by intense laser or particle beams provide gigavolt-per-meter accelerating fields, promising to drastically shrink particle accelerators for high-energy physics and photon science. Applications such as linear colliders and free-electron lasers (FELs) require high energy and energy efficiency, but also high stability and beam quality. The latter includes low energy spread, which can be achieved by precise beam loading of the plasma wakefield using longitudinally shaped bunches, resulting in efficient and uniform acceleration. However, the plasma wavelength, which sets the scale for the region of very large accelerating fields to be 100 {\mu}m or smaller, requires bunches to be synchronized and shaped with extreme temporal precision, typically on the femtosecond scale. Here, a self-correction mechanism is introduced, greatly reducing the susceptibility to jitter. Using multiple accelerating stages, each with a small bunch compression between them, almost any initial bunch, regardless of current profile or injection phase, will self-correct into the current profile that flattens the wakefield, damping the relative energy spread and any energy offsets. As a consequence, staging can be used not only to reach high energies, but also to produce the exquisite beam quality and stability required for a variety of applications.
|
physics
|
Computable Stein discrepancies have been deployed for a variety of applications, ranging from sampler selection in posterior inference to approximate Bayesian inference to goodness-of-fit testing. Existing convergence-determining Stein discrepancies admit strong theoretical guarantees but suffer from a computational cost that grows quadratically in the sample size. While linear-time Stein discrepancies have been proposed for goodness-of-fit testing, they exhibit avoidable degradations in testing power---even when power is explicitly optimized. To address these shortcomings, we introduce feature Stein discrepancies ($\Phi$SDs), a new family of quality measures that can be cheaply approximated using importance sampling. We show how to construct $\Phi$SDs that provably determine the convergence of a sample to its target and develop high-accuracy approximations---random $\Phi$SDs (R$\Phi$SDs)---which are computable in near-linear time. In our experiments with sampler selection for approximate posterior inference and goodness-of-fit testing, R$\Phi$SDs perform as well or better than quadratic-time KSDs while being orders of magnitude faster to compute.
|
statistics
|
We present a new package for Mathematica system, called Libra. Its purpose is to provide convenient tools for the transformation of the first-order differential systems $\partial_i \boldsymbol j = M_i \boldsymbol j$ for one or several variables. In particular, Libra is designed for the reduction to $\epsilon$-form of the differential systems which appear in multiloop calculations. The package also contains some tools for the construction of general solution: both via perturbative expansion of path-ordered exponent and via generalized power series expansion near regular singular points.Libra also has tools to determine the minimal list of coefficients in the asymptotics of the original master integrals, sufficient for fixing the boundary conditions.
|
high energy physics phenomenology
|
Superconductivity results from an instability of the Fermi surface -- contour of \textit{poles} of the single particle propagator -- to an infinitesimally small attraction between electrons. Here, we instead discuss the analogous problem on a model \textit{Luttinger} surface, or contour of \textit{zeros} of the Green function. At zero temperature ($\beta \rightarrow \infty$) and a critical interaction strength ($u_{c\infty}$) characterized by the residue of self-energy pole, we find that the pair susceptibility diverges leading to a superconducting instability. We evaluate the pair fluctuation partition function and find that the spectral density in the normal state has an interaction-driven, power-law $\frac{1}{\sqrt{\omega}}$ type, van-Hove singularity (vHS) indicating non-Fermi liquid (NFL) physics. Crucially, in the strong coupling limit ($\beta u \gg 1$), the leading order fluctuation free energy terms in the normal state of this NFL-SC transition resemble the equivalent $\left(O(1)\right)$ terms of the Sachdev-Ye-Kitaev (SYK) model. This free energy contribution takes a simple form $-\beta F = \beta u_{c\infty} - \gamma~\text{ln}\left(\beta u_{c \infty}\right)$ where $\gamma$ is a constant equal to $\frac{1}{2}$. Weak impurity scattering ($\tau \gg \beta^{-1}$) leaves the low-energy spectral density unaffected, but leads to an interaction-driven enhancement of superconductivity. Our results shed light on the role played by order-parameter fluctuations in providing the key missing link between Mott physics and strongly coupled toy-models exhibiting gravity duals.
|
condensed matter
|
Fix $d \ge 3$. We show the existence of a constant $c>0$ such that any graph of diameter at most $d$ has average distance at most $d-c \frac{d^{3/2}}{\sqrt n}$, where $n$ is the number of vertices. Moreover, we exhibit graphs certifying sharpness of this bound up to the choice of $c$. This constitutes an asymptotic solution to a longstanding open problem of Plesn\'{i}k. Furthermore we solve the problem exactly for digraphs if the order is large compared with the diameter.
|
mathematics
|
In this paper, we propose a turbo receiver for joint activity detection and data decoding in grant-free massive random access, which iterates between a detector and a belief propagation (BP)-based channel decoder. Specifically, responsible for user activity detection, channel estimation and soft data symbol detection, the detector is developed based on a bilinear inference problem that exploits the common sparsity pattern in the received pilot and data signals. The bilinear generalized approximate message passing (BiG-AMP) algorithm is adopted to solve the problem using probabilities of the transmitted data symbols estimated by the channel decoder as prior knowledge. In addition, extrinsic information is also derived from the detector to improve the channel decoding accuracy in the decoder. Simulation results show significant improvements achieved by the proposed turbo receiver compared with conventional designs.
|
electrical engineering and systems science
|
Stimulated by recent progress made by the LHCb Collaboration in discoveries of new bottom baryons, e.g., the $\Xi _{b}(6227)^{-}$ and the $\Sigma_{b}(6097)^{\pm}$, we re-examine the orbitally excited spectrum of the charmed and bottom baryons using Regge approach in the heavy quark-diquark picture. The results indicate that the spin-averaged mass spectrum of the orbitally-excited charmed and bottom baryons can be described by a linear Regge relation, which is derived from the rotating QCD string model. By giving further mass-splitting analysis of spin-dependent interactions, we explain the baryons $\Xi_{b}(6227)^{-}$ and the $\Sigma_{b}(6097)^{\pm}$,and the $\Sigma _{c}(2800)$ and $\Xi _{c}^{\prime }(2930)$ to be the $1P$%-wave baryons, all with the spin-parity $J^{P}=3/2^{-}$ preferably. Mass prediction of the bottom baryon $\Xi_{b}$ in its P- and D-waves are presented, providing clues for the coming experiments like the LHCb to find them.
|
high energy physics phenomenology
|
Novel coronavirus disease 2019 (COVID-19) is rapidly spreading throughout the world and while pregnant women present the same adverse outcome rates, they are underrepresented in clinical research. In this paper, we model categorical variables of 89 test-positive COVID-19 pregnant women within the unsupervised Bayesian framework. We model the data using latent Gaussian processes for density estimation of multivariate categorical data. The results show that the model can find latent patterns in the data, which in turn could provide additional insights into the study of pregnant women that are COVID-19 positive.
|
statistics
|
The correlations arising from sequential measurements on a single quantum system form a polytope. This is defined by the arrow-of-time (AoT) constraints, meaning that future choices of measurement settings cannot influence past outcomes. We discuss the resources needed to simulate the extreme points of the AoT polytope, where resources are quantified in terms of the minimal dimension, or "internal memory" of the physical system. First, we analyze the equivalence classes of the extreme points under symmetries. Second, we characterize the minimal dimension necessary to obtain a given extreme point of the AoT polytope, including a lower scaling bound in the asymptotic limit of long sequences. Finally, we present a general method to derive dimension-sensitive temporal inequalities for longer sequences, based on inequalities for shorter ones, and investigate their robustness to imperfections.
|
quantum physics
|
Suppose that $X$ is a Polish space, $E$ is a countable Borel equivalence relation on $X$, and $\mu$ is an $E$-invariant Borel probability measure on $X$. We consider the circumstances under which for every countable non-abelian free group $\Gamma$, there is a Borel sequence $(\cdot_r)_{r \in \mathbb{R}}$ of free actions of $\Gamma$ on $X$, generating subequivalence relations $E_r$ of $E$ with respect to which $\mu$ is ergodic, with the further property that $(E_r)_{r \in \mathbb{R}}$ is an increasing sequence of relations which are pairwise incomparable under $\mu$-reducibility. In particular, we show that if $E$ satisfies a natural separability condition, then this is the case as long as there exists a free Borel action of a countable non-abelian free group on $X$, generating a subequivalence relation of $E$ with respect to which $\mu$ is ergodic.
|
mathematics
|
Difference-in-differences (DID) is a widely used approach for drawing causal inference from observational panel data. Two common estimation strategies for DID are outcome regression and propensity score weighting. In this paper, motivated by a real application in traffic safety research, we propose a new double-robust DID estimator that hybridizes regression and propensity score weighting. We particularly focus on the case of discrete outcomes. We show that the proposed double-robust estimator possesses the desirable large-sample robustness property. We conduct a simulation study to examine its finite-sample performance and compare with alternative methods. Our empirical results from a Pennsylvania Department of Transportation data suggest that rumble strips are marginally effective in reducing vehicle crashes.
|
statistics
|
In this work, the results of Ultra-Wideband air-to-ground measurements carried out in a real-world factory environment are presented and discussed. With intelligent in-dustrial deployments in mind, we envision a scenario where the Unmanned Aerial Vehicle can be used as a supplementary tool for factory operation, optimization and control. Measurements address narrow band and wide band characterization of the wireless radio channel, and can be used for link budget calculation, interference studies and time dispersion assessment in real factories, without the usual limitation for both radio terminals to be close to ground. The measurements are performed at different locations and different heights over the 3.1-5.3 GHz band. Some fundamental propagation parameters values are determined vs. distance, height and propagation conditions. The measurements are complemented with, and compared to, conventional ground-to-ground measurements with the same setup. The conducted measurement campaign gives an insight for realizing wireless applications in smart connected factories, including UAV-assisted applications.
|
electrical engineering and systems science
|
Chiral Lagrangian mesonic fields can be connected to QCD quark operators via matrix operators containing scale factors. These scale factor matrices are shown to be constrained by chiral symmetry, resulting in a universal scale factor for each Chiral Lagrangian nonet. QCD sum-rules, combined with mixing angles from Chiral Lagrangian analyses, are used to determine the scale factors for the $a_0$ isotriplet and $K_0^*$ isodoublet scalar mesons. The resulting scale factors verify the universality property, providing a validation of the scale factor matrices connecting Chiral Lagrangian mesonic fields and quark operators.
|
high energy physics phenomenology
|
The partition function of three dimensional gravity in the quantum regime, where the AdS radius $\ell$ is Planck scale, is dual to the Ising conformal field theory when the central charge $c=3\ell/2G$ equals $1/2$. Mathematically, we show that the three dimensional gravity can be described by Schramm-Loewner Evolution (SLE) with certain $\kappa$. In fact, SLE depends on the choice of parameter $\kappa$ which controls the rate of diffusion of the Brownian motion, and the behavior of SLE depends critically on its value. Each value of $c < 1$ corresponds to two values of $\kappa$, which may hint that the three dimensional gravity has two different phases at certain central charge c. Moreover, phase transition is also discussed in AdS and Ising model.
|
high energy physics theory
|
The phenomenon of Bose-Einstein condensation is investigated in the context of the Color-Glass-Condensate description of the initial state of ultrarelativistic heavy-ion collisions. For the first time, in this paper we study the influence of particle-number changing $2 \leftrightarrow 3$ processes on the transient formation of a Bose-Einstein Condensate within an isotropic system of scalar bosons by including $2 \leftrightarrow 3$ interactions of massive bosons with constant and isotropic cross sections, following a Boltzmann equation. The one-particle distribution function is decomposed in a condensate part and a non-zero momentum part of excited modes, leading to coupled integro-differential equations for the time evolution of the condensate and phase-space distribution function, which are then solved numerically. Our simulations converge to the expected equilibrium state, and only for $\sigma_{23}/\sigma_{22} \ll 1$ we find that a Bose-Einstein condensate emerges and decays within a finite lifetime in contrast to the case where only binary scattering processes are taken into account, and the condensate is stable due to particle-number conservation. Our calculations demonstrate that Bose-Einstein Condensates in the very early stage of heavy-ion collisions are highly unlikely, if inelastic collisions are significantly participating in the dynamical gluonic evolution.
|
high energy physics phenomenology
|
Fracture functions are parton distributions of an initial hadron in the presence of an almost collinear particle observed in the final state. They are important ingredients in QCD factorization for processes where a particle is produced diffractively. There are different fracture functions for a process in different kinematic regions. We take the production of a lepton pair combined with a diffractively produced particle in hadron collisions to discuss this. Those fracture functions can be factorized further if there are large energy scales involved. They can be factorized with twist-2 parton distribution functions and fragmentation functions. We perform one-loop calculations to illustrate the factorization in the case with the diffractively produced particle as a real photon. Evolution equations of different fracture functions are derived from our explicit calculations. They agree with expectations. These equations can be used for re-summations of large log terms in perturbative expansions.
|
high energy physics phenomenology
|
Hybrid SiN-QD microlasers coupled to a passive SiN output waveguide with 7{\mu}m diameter and record low threshold density of 27 {\mu}J cm-2 are demonstrated. A new design and unique processing scheme starting from SiN/QD/SiN stacks offer long term stability and facilitate in depth laser characterization. This approach opens up new paths for optical communication, lab-on-a-chip, gas sensing and, potentially, on-chip cavity quantum electrodynamics and quantum optics.
|
physics
|
We investigate the properties of a discrete-time martingale $\{X_m\}_{m\in \mathbb Z_{\geq 0}}$, where all differences between adjacent random variables are limited to be not more than a constant as a promise. In this situation, it is known that the Azuma-Hoeffding inequality holds, which gives an upper bound of a probability for exceptional events. The inequality gives a simple form of the upper bound, and it has been utilized for many investigations. However, the inequality is not tight. We give an explicit expression of a tight upper bound, and we show that it and the bound obtained from the Azuma-Hoeffding inequality have different asymptotic behaviors.
|
mathematics
|
Nowadays, offensive content in social media has become a serious problem, and automatically detecting offensive language is an essential task. In this paper, we build an offensive language detection system, which combines multi-task learning with BERT-based models. Using a pre-trained language model such as BERT, we can effectively learn the representations for noisy text in social media. Besides, to boost the performance of offensive language detection, we leverage the supervision signals from other related tasks. In the OffensEval-2020 competition, our model achieves 91.51% F1 score in English Sub-task A, which is comparable to the first place (92.23%F1). An empirical analysis is provided to explain the effectiveness of our approaches.
|
computer science
|
In this paper, non-orthogonal multiple access (NOMA) networks assisted by multiple intelligent reflecting surfaces (IRSs) with discrete phase shifts are investigated, in which each user device (UD) is served by an IRS to improve the quality of the received signal. Two scenarios are considered based on whether there is a direct link or not between the base station (BS) and each UD, and the outage performance is analyzed for each of them. Specifically, the outage probability is approximated in the high signal-to-noise ratio (SNR) regime, and the diversity order is obtained. Orthogonal multiple access (OMA) can be regarded as a special case of NOMA, and the outage performance of the multi-IRS assisted OMA system is also characterized. It is demonstrated that NOMA outperforms OMA in multi-IRS assisted networks. Furthermore, it is shown that the use of discrete phase shifts does not degrade the diversity order. More importantly, simulation results further reveal that a 3-bit resolution for discrete phase shifts is sufficient to achieve near-optimal outage performance.
|
electrical engineering and systems science
|
The interaction between quantum two-level systems is typically short-range in free space and most photonic environments. Here we show that diminishing momentum isosurfaces with equal frequencies can create a significantly extended range of interaction between distant quantum systems. The extended range is robust and does not rely on a specific location or orientation of the transition dipoles. A general relation between the interaction range and properties of the isosurface is described for structured photonic media. It provides a new way to mediate long-range quantum behavior.
|
physics
|
The current context of launchers reusability requires the improvement of control algorithms for their liquid-propellant rocket engines. Their transient phases are generally still performed in open loop. In this paper, it is aimed at enhancing the control performance and robustness during the fully continuous phase of the start-up transient of a generic gas-generator cycle. The main control goals concern end-state tracking in terms of combustion-chamber pressure and chambers mixture ratios, as well as the verification of a set of hard operational constraints. A controller based on a nonlinear preprocessor and on linear MPC (Model-Predictive Control) has been synthesised, making use of nonlinear state-space models of the engine. The former generates the full-state reference to be tracked while the latter achieves the aforementioned goals with sufficient accuracy and verifying constraints for the required pressure levels. Robustness considerations are included in the MPC algorithm via an epigraph formulation of the minimax robust optimisation problem, where a finite set of perturbation scenarios is considered.
|
electrical engineering and systems science
|
In game-theoretic learning, several agents are simultaneously following their individual interests, so the environment is non-stationary from each player's perspective. In this context, the performance of a learning algorithm is often measured by its regret. However, no-regret algorithms are not created equal in terms of game-theoretic guarantees: depending on how they are tuned, some of them may drive the system to an equilibrium, while others could produce cyclic, chaotic, or otherwise divergent trajectories. To account for this, we propose a range of no-regret policies based on optimistic mirror descent, with the following desirable properties: i) they do not require any prior tuning or knowledge of the game; ii) they all achieve O(\sqrt{T}) regret against arbitrary, adversarial opponents; and iii) they converge to the best response against convergent opponents. Also, if employed by all players, then iv) they guarantee O(1) social regret; while v) the induced sequence of play converges to Nash equilibrium with O(1) individual regret in all variationally stable games (a class of games that includes all monotone and convex-concave zero-sum games).
|
computer science
|
We propose the dynamical stabilization of a nonequilibrium order in a driven dissipative system comprised an atomic Bose-Einstein condensate inside a high finesse optical cavity, pumped with an optical standing wave operating in the regime of anomalous dispersion. When the amplitude of the pump field is modulated close to twice the characteristic limit-cycle frequency of the unmodulated system, a stable subharmonic response is found. The dynamical phase diagram shows that this subharmonic response occurs in a region expanded with respect to that where stable limit-cycle dynamics occurs for the unmodulated system. In turning on the modulation we tune the atom-cavity system from a continuous to a discrete time crystal.
|
condensed matter
|
Our bimetric spacetime model of glitching pulsars is applied to the remnant of GW170817. Accordingly, pulsars are born with embryonic incompressible superconducting gluon-quark superfluid cores (SuSu-matter) that are embedded in Minkowski spacetime, whereas the ambient compressible and dissipative media (CDM) are imbedded in curved spacetime. As pulsars cool down, the equilibrium between both spacetime is altered, thereby triggering the well-observed glitch phenomena. Based thereon and assuming all neutron stars (NSs) to be born with the same initial mass of $M_{NS}(t=0) \approx 1.25\,\mathcal{M}_{\odot},$ we argue that the remnant of GW170817 should be a relatively faint NS with a hypermassive central core made of SuSu-matter. The effective mass and radius of the remnant are predicted to be $[2.8 \mathcal{M}_{\odot} < \mathcal{M}_{rem} \le 3.351 \mathcal{M}_{\odot}]$ and $R_{rem}=10.764$ km, whereas the mass of the enclosed SuSu-core is $\mathcal{M}_{core}=1.7 \mathcal{M}_{\odot}.$ Here, about $1/2~ \mathcal{M}_{core}$ is an energy enhancement triggered by the phase transition of the gluon-quark-plasma from the microscopic into macroscopic scale. The current compactness of the remnant is $\alpha_c = 0.918,$ but predicted to increase as the CDM and cools down, rendering the remnant an invisible dark energy object, and therefore to an excellent black hole candidate.
|
astrophysics
|
We propose a visual analytics system to help a user analyze and steer zero-shot learning models. Zero-shot learning has emerged as a viable scenario for categorizing data that consists of no labeled examples, and thus a promising approach to minimize data annotation from humans. However, it is challenging to understand where zero-shot learning fails, the cause of such failures, and how a user can modify the model to prevent such failures. Our visualization system is designed to help users diagnose and understand mispredictions in such models, so that they may gain insight on the behavior of a model when applied to data associated with categories not seen during training. Through usage scenarios, we highlight how our system can help a user improve performance in zero-shot learning.
|
computer science
|
With a combination of numerical methods, including quantum Monte Carlo, exact diagonalization, and a simplified dynamical mean-field model, we consider the attosecond charge dynamics of electrons induced by strong-field laser pulses in two-dimensional Mott insulators. The necessity to go beyond single-particle approaches in these strongly correlated systems has made the simulation of two-dimensional extended materials challenging, and we contrast their resulting high-harmonic emission with more widely studied one-dimensional analogues. As well as considering the photo-induced breakdown of the Mott insulating state and magnetic order, we also resolve the time and ultra-high frequency domains of emission, which are used to characterize both the photo-transition, and the sub-cycle structure of the electron dynamics. This extends simulation capabilities and understanding of the photo-melting of these Mott insulators in two-dimensions, at the frontier of attosecond non-equilibrium science of correlated materials.
|
condensed matter
|
The $Z'$-portal is one of most popular and well-explored scenarios of dark matter (DM). To avoid the strong constraints coming from dilepton resonance searches at the LHC and direct detection of DM, it is usually required that in addition to being leptophobic, the $Z'$ is axially coupled to either the (fermionic) DM or the standard model (SM) quarks. The first possibility has been extensively studied both in the context of simplified model and UV complete scenarios. However, the studies on the second possibiliy are largely confined to simplified models only. Here, we construct the minimal UV completion of these models satisfying both the criteria of leptophobia and purely axial $Z'-$quark coupling. The anomaly cancellation conditions demand highly non-trivial structures, not only in the dark sector, but also in the Higgs sector.
|
high energy physics phenomenology
|
For a finite group $G$ and $U: = U(\mathbb{Z}G)$, the group of units of the integral group ring of $G$, we study the implications of the structure of $G$ on the abelianization $U/U'$ of $U$. We pose questions on the connections between the exponent of $G/G'$ and the exponent of $U/U'$ as well as between the ranks of the torsion-free parts of $Z(U)$, the center of $U$, and $U/U'$. We show that the units originating from known generic constructions of units in $\mathbb{Z}G$ are well-behaved under the projection from $U$ to $U/U'$ and that our questions have a positive answer for many examples. We then exhibit an explicit example which shows that the general statement on the torsion-free part does not hold, which also answers questions from [BJJ$^+$18].
|
mathematics
|
Particles are spontaneously created from the vacuum by time-varying gravitational or electromagnetic backgrounds. It has been proven that the particle number operator in an expanding universe is an adiabatic invariant. In this paper we show that, in some special cases, the expected adiabatic invariance of the particle number fails in presence of electromagnetic backgrounds. In order to do this, we consider as a prototype a Sauter-type electric pulse. Furthermore, we also show a close relation between the breaking of the adiabatic invariance and the emergence of the axial anomaly.
|
high energy physics theory
|
The European Open Science Cloud (EOSC) initiative faces the challenge of developing an agile, fit-for-purpose, and sustainable service-oriented platform that can address the evolving needs of scientific communities. The NEANIAS project plays an active role in the materialization of the EOSC ecosystem by actively contributing to the technological, procedural, strategic and business development of EOSC. We present the first outcomes of the NEANIAS activities relating to co-design and delivery of new innovative services for space research for data management and visualization (SPACE-VIS), map making and mosaicing (SPACE-MOS) and pattern and structure detection (SPACE-ML). We include a summary of collected user requirements driving our services and methodology for their delivery, together with service access details and pointers to future works.
|
astrophysics
|
In this study, we propose an encoder-decoder structured system with fully convolutional networks to implement voice activity detection (VAD) directly on the time-domain waveform. The proposed system processes the input waveform to identify its segments to be either speech or non-speech. This novel waveform-based VAD algorithm, with a short-hand notation "WVAD", has two main particularities. First, as compared to most conventional VAD systems that use spectral features, raw-waveforms employed in WVAD contain more comprehensive information and thus are supposed to facilitate more accurate speech/non-speech predictions. Second, based on the multi-branched architecture, WVAD can be extended by using an ensemble of encoders, referred to as WEVAD, that incorporate multiple attribute information in utterances, and thus can yield better VAD performance for specified acoustic conditions. We evaluated the presented WVAD and WEVAD for the VAD task in two datasets: First, the experiments conducted on AURORA2 reveal that WVAD outperforms many state-of-the-art VAD algorithms. Next, the TMHINT task confirms that through combining multiple attributes in utterances, WEVAD behaves even better than WVAD.
|
electrical engineering and systems science
|
In this paper, we prove the Kobayashi hyperbolicity of the coarse moduli spaces of canonically polarized or polarized Calabi-Yau manifolds in the sense of complex $V$-spaces (a generalization of complex $V$-manifolds in the sense of Satake). As an application, we prove the following hyperbolic version of Campana's isotriviality conjecture: for the smooth family of canonically polarized or polarized Calabi-Yau manifolds, when the Kobayashi pseudo-distance of the base vanishes identically, the family must be isotrivial, that is, any two fibers are isomorphic. We also prove that for the smooth projective family of polarized Calabi-Yau manifolds, its variation of the family is less than or equal to the essential dimension of the base.
|
mathematics
|
This paper considers the problem of testing if a sequence of means $(\mu_t)_{t =1,\ldots ,n }$ of a non-stationary time series $(X_t)_{t =1,\ldots ,n }$ is stable in the sense that the difference of the means $\mu_1$ and $\mu_t$ between the initial time $t=1$ and any other time is smaller than a given level, that is $ | \mu_1 - \mu_t | \leq c $ for all $t =1,\ldots ,n $. A test for hypotheses of this type is developed using a biascorrected monotone rearranged local linear estimator and asymptotic normality of the corresponding test statistic is established. As the asymptotic variance depends on the location and order of the critical roots of the equation $| \mu_1 - \mu_t | = c$ a new bootstrap procedure is proposed to obtain critical values and its consistency is established. As a consequence we are able to quantitatively describe relevant deviations of a non-stationary sequence from its initial value. The results are illustrated by means of a simulation study and by analyzing data examples.
|
statistics
|
In the simple random walk the steps are independent, whereas in the Elephant Random Walk (ERW), which was introduced by Sch\"utz and Trimper in 2004, the next step always depends on the whole path so far. In an earlier paper we investigated Elephant Random Walks when the elephant has a restricted memory. Inspired by a suggestion by Bercu et al. (arXiv:1902.11220v1) we extended our results to the case when delays are allowed. In this paper we examine how the number of delays (that possibly stop the process) increases as time goes by.
|
mathematics
|
Predicting which words are considered hard to understand for a given target population is a vital step in many NLP applications such as text simplification. This task is commonly referred to as Complex Word Identification (CWI). With a few exceptions, previous studies have approached the task as a binary classification task in which systems predict a complexity value (complex vs. non-complex) for a set of target words in a text. This choice is motivated by the fact that all CWI datasets compiled so far have been annotated using a binary annotation scheme. Our paper addresses this limitation by presenting the first English dataset for continuous lexical complexity prediction. We use a 5-point Likert scale scheme to annotate complex words in texts from three sources/domains: the Bible, Europarl, and biomedical texts. This resulted in a corpus of 9,476 sentences each annotated by around 7 annotators.
|
computer science
|
It was conjectured by Escobar [J. Funct. Anal. 165 (1999), 101-116] that for an $n$-dimensional ($n\geq 3$) smooth compact Riemannian manifold with boundary, which has nonnegative Ricci curvature and boundary principal curvatures bounded below by $c>0$, the first nonzero Steklov eigenvalue is greater than or equal to $c$ with equality holding only on isometrically Euclidean balls with radius $1/c$. In this paper, we confirm this conjecture in the case of nonnegative sectional curvature. The proof is based on a combination of Qiu-Xia's weighted Reilly type formula with a special choice of the weight function depending on the distance function to the boundary, as well as a generalized Pohozaev type identity.
|
mathematics
|
We introduce SPFlow, an open-source Python library providing a simple interface to inference, learning and manipulation routines for deep and tractable probabilistic models called Sum-Product Networks (SPNs). The library allows one to quickly create SPNs both from data and through a domain specific language (DSL). It efficiently implements several probabilistic inference routines like computing marginals, conditionals and (approximate) most probable explanations (MPEs) along with sampling as well as utilities for serializing, plotting and structure statistics on an SPN. Moreover, many of the algorithms proposed in the literature to learn the structure and parameters of SPNs are readily available in SPFlow. Furthermore, SPFlow is extremely extensible and customizable, allowing users to promptly distill new inference and learning routines by injecting custom code into a lightweight functional-oriented API framework. This is achieved in SPFlow by keeping an internal Python representation of the graph structure that also enables practical compilation of an SPN into a TensorFlow graph, C, CUDA or FPGA custom code, significantly speeding-up computations.
|
computer science
|
While the use of combination therapy is increasing in prevalence for cancer treatment, it is often difficult to predict the exact interactions between different treatment forms, and their synergistic/antagonistic effects on patient health and therapy outcome. In this research, a system of ordinary differential equations is constructed to model nonlinear dynamics between tumor cells, immune cells, and three forms of therapy: chemotherapy, immunotherapy, and radiotherapy. This model is then used to generate optimized combination therapy plans using optimal control theory. In-silico experiments are conducted to simulate the response of the patient model to various treatment plans. This is the first mathematical model in current literature to introduce radiotherapy as an option alongside immuno- and chemotherapy, permitting more flexible and effective treatment plans that reflect modern therapeutic approaches.
|
mathematics
|
Thousands of transiting exoplanets have been discovered to date, thanks in great part to the {\em Kepler} space mission. As in all populations, and certainly in the case of exoplanets, one finds unique objects with distinct characteristics. Here we will describe the properties and behaviour of a small group of `disintegrating' exoplanets discovered over the last few years (KIC 12557548b, K2-22b, and others). They evaporate, lose mass unraveling their naked cores, produce spectacular dusty comet-like tails, and feature highly variable asymmetric transits. Apart from these exoplanets, there is observational evidence for even smaller `exo-'objects orbiting other stars: exoasteroids and exocomets. Most probably, such objects are also behind the mystery of Boyajian's star. Ongoing and upcoming space missions such as {\em TESS} and PLATO will hopefully discover more objects of this kind, and a new era of the exploration of small extrasolar systems bodies will be upon us.
|
astrophysics
|
In this work we study a significantly enlarged truncation of conformally reduced quantum gravity in the context of Asymptotic Safety, including all operators that can be resolved in such a truncation including up to the sixth order in derivatives. A fixed point analysis suggests that there is no asymptotically safe fixed point in this system once one goes beyond an Einstein-Hilbert approximation. We will put these findings into context and discuss some lessons that can be learned from these results for general non-perturbative renormalisation group flows.
|
high energy physics theory
|
Massive connectivity for Internet of Things applications is expected to challenge the way access reservation protocols are designed in 5G networks. Since the number of devices and their density are envisioned to be orders of magnitude larger, state-of-the-art access reservation, Random Access (RA) procedure, might be a bottleneck for end-to-end delay. This would be especially challenging for burst arrival scenarios: Semi-synchronous triggering of a large number of devices due to a common event (blackout, emergency alarm, etc.). In this article, to improve RA procedure scalability, we propose to combine Binary Countdown Contention Resolution (BCCR) with the state-of-the-art Access Class Barring (ACB). We present a joint analysis of ACB and BCCR and apply a framework for treating RA as a bi-objective optimization, minimizing the resource consumption and maximizing the throughput of the procedure in every contention round. We use this framework to devise dynamic load-adaptive algorithm and simulatively illustrate that the proposed algorithm reduces the burst resolution delay while consuming less resources compared to the state-of-the-art techniques.
|
computer science
|
Compressed sensing techniques enable efficient acquisition and recovery of sparse, high-dimensional data signals via low-dimensional projections. In this work, we propose Uncertainty Autoencoders, a learning framework for unsupervised representation learning inspired by compressed sensing. We treat the low-dimensional projections as noisy latent representations of an autoencoder and directly learn both the acquisition (i.e., encoding) and amortized recovery (i.e., decoding) procedures. Our learning objective optimizes for a tractable variational lower bound to the mutual information between the datapoints and the latent representations. We show how our framework provides a unified treatment to several lines of research in dimensionality reduction, compressed sensing, and generative modeling. Empirically, we demonstrate a 32% improvement on average over competing approaches for the task of statistical compressed sensing of high-dimensional datasets.
|
statistics
|
Following Caron-Huot and combining results for the thermal dependence of spectral functions at large time-like momenta, we write an explicit expression for the thermal width of the Higgs boson to $\mathcal{O}(\alpha_\mathrm{s})$ for $T \ll M_H$. It is an $\mathcal{O}( \alpha_\mathrm{s} (T/M_H)^4 )$ correction for $H\to gg$ and $H\to q\bar{q}$. We also compile corresponding results for the thermal width of the $Z$-boson, and we recall which generic structures of the field theory, accessible via the operator product expansion, fix the $T/M$-dependence of the decay of heavy particles.
|
high energy physics phenomenology
|
In the previous work we give a microscopic explanation of the entropy for the BTZ black hole and four-dimensional Kerr black hole based on the massless scalar field theory on the horizon. An essential input is the central charges of those black holes. In this paper, we calculate the central charges for Kerr black holes and Kerr-AdS black holes in diverse dimensions by rewriting the entropy formula in a suggesting way. Then we also give the statistical explanation for the entropy of those black holes based on the scalar field on the horizon which similar to 4D kerr black hole.
|
high energy physics theory
|
Behavioral research can provide important insights for SE practices. But in performing it, many studies of SE are committing a normative fallacy - they misappropriate normative and prescriptive theories for descriptive purposes. The evidence from reviews of empirical studies of decision making in SE suggests that the normative fallacy may is common. This article draws on cognitive psychology and behavioral economics to explains this fallacy. Because data collection is framed by narrow and empirically invalid theories, flawed assumptions baked into those theories lead to misleading interpretations of observed behaviors and ultimately, to invalid conclusions and flawed recommendations. Researchers should be careful not to rely solely on engineering methods to explain what people do when they do engineering. Instead, insist that descriptive research be based on validated descriptive theories, listen carefully to skilled practitioners, and only rely on validated findings to prescribe what they should do.
|
computer science
|
We study the charge-to-mass ratios of BPS states in four-dimensional $\mathcal{N}=2$ supergravities arising from Calabi-Yau threefold compactifications of Type IIB string theory. We present a formula for the asymptotic charge-to-mass ratio valid for all limits in complex structure moduli space. This is achieved by using the sl(2)-structure that emerges in any such limit as described by asymptotic Hodge theory. The asymptotic charge-to-mass formula applies for sl(2)-elementary states that couple to the graviphoton asymptotically. Using this formula, we determine the radii of the ellipsoid that forms the extremality region of electric BPS black holes, which provides us with a general asymptotic bound on the charge-to-mass ratio for these theories. Finally, we comment on how these bounds for the Weak Gravity Conjecture relate to their counterparts in the asymptotic de Sitter Conjecture and Swampland Distance Conjecture.
|
high energy physics theory
|
A connected Kuga-Sato variety $\mathbf{W}^r$ parameterizes tuples of $r$ points on elliptic curves (with level structure). A special point of $\mathbf{W}^r$ is a tuple of torsion points on a CM elliptic curve. A sequence of special points is strict if any CM elliptic curve appears at most finitely many times and no relation between the points in the tuple is satisfied infinitely often. The genus orbit of a special point is the $\operatorname{Gal}(\bar{\mathbb{Q}}/\mathbb{Q}^{\mathrm{ab}})$-orbit. We show that genus orbits of special points in a strict sequence equidistribute in $\mathbf{W}^r(\mathbb{C})$, assuming a congruence condition at two fixed primes. A genus orbit can be very sparse in the full Galois orbit. In particular, the number of torsion points on each elliptic curve in a genus orbit is not bounded below by the torsion order. A genus orbit corresponds to a toral packet in an extension of $\mathbf{SL}_2$ by a vector representation. These packets also arise in the study by Aka, Einsiedler and Shapira of grids orthogonal to lattice points on the $2$-sphere. As an application we establish their joint equidistribution conjecture assuming two split primes.
|
mathematics
|
We translate the construction of the chiral operad by Beilinson and Drinfeld to the purely algebraic language of vertex algebras. Consequently, the general construction of a cohomology complex associated to a linear operad produces a vertex algebra cohomology complex. Likewise, the associated graded of the chiral operad leads to a classical operad, which produces a Poisson vertex algebra cohomology complex. The latter is closely related to the variational Poisson cohomology studied by two of the authors.
|
mathematics
|
Gaia Photometric Science Alerts (GPSA) publishes Gaia G magnitudes and Blue Photometer (BP) and Red Photometer (RP) low-resolution epoch spectra of transient events. 27 high-resolution spectra from Gaia's Radial Velocity Spectrometer (RVS) of 12 GPSAs have also been published. These 27 RVS epoch spectra are presented next to their corresponding BP and RP epoch spectra in a single place for the first time. We also present one new RVS spectrum of a 13th GPSA that could not be published by the GPSA system. Of the 13 GPSA with RVS spectra, five are photometrically classified as unknown, five as supernovae (three as SN Ia, one as SN II, one as SN IIP), one as a cataclysmic variable, one as a binary microlensing event and one as a young stellar object. The five GPSAs classified as unknown are potential scientific opportunities, while all of them are a preview of the epoch RVS spectra that will be published in Gaia's fourth data release.
|
astrophysics
|
In recent years, arrays of atomic ions in a linear RF trap have proven to be a particularly successful platform for quantum simulation. However, a wide range of quantum models and phenomena have, so far, remained beyond the reach of such simulators. In this work we introduce a technique that can substantially extend this reach using an external field gradient along the ion chain and a global, uniform driving field. The technique can be used to generate both static and time-varying synthetic gauge fields in a linear chain of trapped ions, and enables continuous simulation of a variety of coupling geometries and topologies, including periodic boundary conditions and high dimensional Hamiltonians. We describe the technique, derive the corresponding effective Hamiltonian, propose a number of variations, and discuss the possibility of scaling to quantum-advantage sized simulators. Additionally, we suggest several possible implementations and briefly examine two: the Aharonov-Bohm ring and the frustrated triangular ladder.
|
quantum physics
|
We prove differential Harnack inequalities for flows of strictly convex hypersurfaces by powers $p$, $0<p<1$, of the mean curvature in Einstein manifolds with a positive lower bound on the sectional curvature. We assume that this lower bound is sufficiently large compared to the derivatives of the curvature tensor of the ambient space and that the mean curvature of the initial hypersurface is sufficiently large compared to the ambient geometry. We also obtain some new Harnack inequalities for more general curvature flows in the sphere, as well as a monotonicity estimate for the mean curvature flow in non-negatively curved, locally symmetric spaces.
|
mathematics
|
Current unmanned aerial vehicle (UAV) visual tracking algorithms are primarily limited with respect to: (i) the kind of size variation they can deal with, (ii) the implementation speed which hardly meets the real-time requirement. In this work, a real-time UAV tracking algorithm with powerful size estimation ability is proposed. Specifically, the overall tracking task is allocated to two 2D filters: (i) translation filter for location prediction in the space domain, (ii) size filter for scale and aspect ratio optimization in the size domain. Besides, an efficient two-stage re-detection strategy is introduced for long-term UAV tracking tasks. Large-scale experiments on four UAV benchmarks demonstrate the superiority of the presented method which has computation feasibility on a low-cost CPU.
|
computer science
|
Ultraviolet microdisk lasers are integrated monolithically into photonic circuits using a III-nitride on silicon platform with gallium nitride (GaN) as the main waveguiding layer. The photonic circuits consist of a microdisk and a pulley waveguide terminated by out-coupling gratings. We measure quality factors up to 3500 under continuous-wave excitation. Lasing is observed from 374 nm to 399 nm under pulsed excitation, achieving low threshold energies of $0.14 ~\text{mJ/cm}^2$ per pulse (threshold peak powers of $35 ~\text{kW/cm}^2$). A large peak to background dynamic of around 200 is observed at the out-coupling grating for small gaps of 50 nm between the disk and waveguide. These devices operate at the limit of what can be achieved with GaN in terms of operation wavelength.
|
physics
|
We present an analysis of the spatial clustering of a large sample of high-resolution, interferometically identified, submillimetre galaxies (SMGs). We measure the projected cross-correlation function of ~350 SMGs in the UKIDSS Ultra Deep-Survey Field across a redshift range of $z=1.5-3$ utilising a method that incorporates the uncertainties in the redshift measurements for both the SMGs and cross-correlated galaxies through sampling their full probability distribution functions. By measuring the absolute linear bias of the SMGs we derive halo masses of $\log_{10}(M_{\rm halo}[{h^{-1}\,\rm M_{\odot}}])\sim12.8$ with no evidence of evolution in the halo masses with redshift, contrary to some previous work. From considering models of halo mass growth rates we predict that the SMGs will reside in haloes of mass $\log_{10}(M_{\rm halo}[{h^{-1}\,\rm M_{\odot}}])\sim13.2$ at $z=0$, consistent with the expectation that the majority of $z=1.5-3$ SMGs will evolve into present-day spheroidal galaxies. Finally, comparing to models of stellar-to-halo mass ratios, we show that SMGs may correspond to systems that are maximally efficient at converting their gas reservoirs into stars. We compare them to a simple model for gas cooling in halos that suggests that the unique properties of the SMG population, including their high levels of star-formation and their redshift distribution, are a result of the SMGs being the most massive galaxies that are still able to accrete cool gas from their surrounding intragalactic medium.
|
astrophysics
|
We report on how $J/\psi$- and $\Upsilon$-pair production are promising processes to access the polarised and unpolarised gluon TMDs at the LHC. We present the formalism used, as well as resulting observables that could be extracted from data.
|
high energy physics phenomenology
|
Lightweight super resolution networks have extremely importance for real-world applications. In recent years several SR deep learning approaches with outstanding achievement have been introduced by sacrificing memory and computational cost. To overcome this problem, a novel lightweight super resolution network is proposed, which improves the SOTA performance in lightweight SR and performs roughly similar to computationally expensive networks. Multi-Path Residual Network designs with a set of Residual concatenation Blocks stacked with Adaptive Residual Blocks: ($i$) to adaptively extract informative features and learn more expressive spatial context information; ($ii$) to better leverage multi-level representations before up-sampling stage; and ($iii$) to allow an efficient information and gradient flow within the network. The proposed architecture also contains a new attention mechanism, Two-Fold Attention Module, to maximize the representation ability of the model. Extensive experiments show the superiority of our model against other SOTA SR approaches.
|
electrical engineering and systems science
|
We investigate the dynamics of axion-like particle (ALP) dark matter where the field range is enlarged by a monodromy. The monodromy potential allows sufficient production of dark matter also at larger couplings to the Standard Model particles. The potential typically features a number of "wiggles" that lead to a rapid growth of fluctuations. Using classical-statistical field theory simulations we go beyond the linear regime and treat the system in the non-linear and even non-perturbative regime. For sufficiently strong wiggles the initially homogeneous field is completely converted into fluctuations. The fluctuations correspond to dark matter particles with a non-vanishing velocity and we consider the corresponding restrictions from structure formation as well as the effects on today's dark matter density. Since all the dark matter is made up from these strong fluctuations, the dark matter density features large, $\mathcal{O}(1)$ fluctuations at scales $\lesssim 10^{6}\,{\rm km}\sqrt{{\rm eV}/m_a}$.
|
high energy physics phenomenology
|
We propose an approach to constructing iterative methods for finding polynomial roots simultaneously. One feature of this approach is using the fundamental theorem of symmetric polynomials. Within this framework, we reconstruct many of the existing root finding methods. The new results presented in this paper are some modifications of the Durand-Kerner method.
|
mathematics
|
Miniaturization of devices has been a primary objective in microelectronics and photonics for decades, aiming at denser integration, enhanced functionalities and drastic reduction of power consumption. Headway in nanophotonics is currently linked to the progress in concepts and technologies necessary for applications in information and communication, brain inspired computing, medicine and sensing and quantum information. Amongst all nanostructures, semiconductor photonic crystals (PhCs) occupy a prominent position as they enable the fabrication of quasi ultimate optical cavities. Low threshold laser diodes or Raman lasers , low power consuming optical memories , efficient single photon sources or single photon quantum gates are impressive examples of their capabilities. We report the demonstration of about 20 micron long PhC semiconductor optical parametric oscillator (OPO) at telecom wavelength exploiting nearly diffraction limited optical modes. The pump power threshold is measured below 0.2 mW. Parametric oscillation was reached through the drastic enhancement of Kerr optical Four Wave Mixing by thermally tuning the high Q modes of a nanocavity into a triply resonant configuration. Miniaturization of this paradigmatic source of coherent light paves the way for quantum optical circuits, dense integration of highly efficient nonlinear sources of squeezed light or entangled photons pairs.
|
physics
|
Gravitational wave (GW) oscillations occur whenever there are additional tensor modes interacting with the perturbations of the metric coupled to matter. These extra modes can arise from new spin-2 fields (as in e.g. bigravity theories) or from non-trivial realisations of the cosmological principle induced by background vector fields with internal symmetries (e.g. Yang-Mills, gaugids or multi-Proca). We develop a general cosmological framework to study such novel features due to oscillations. The evolution of the two tensor modes is described by a linear system of coupled second order differential equations exhibiting friction, velocity, chirality and mass mixing. We follow appropriate schemes to obtain approximate solutions for the evolution of both modes and show the corresponding phenomenology for different mixings. Observational signatures include modulations of the wave-form, oscillations of the GW luminosity distance, anomalous GW speed and chirality. We discuss the prospects of observing these effects with present and future GW observatories such as LIGO/VIRGO and LISA.
|
astrophysics
|
We consider incorporating incomplete physics knowledge, expressed as differential equations with latent functions, into Gaussian processes (GPs) to improve their performance, especially for limited data and extrapolation. While existing works have successfully encoded such knowledge via kernel convolution, they only apply to linear equations with analytical Green's functions. The convolution can further restrict us from fusing physics with highly expressive kernels, e.g., deep kernels. To overcome these limitations, we propose Physics Regularized Gaussian Process (PRGP) that can incorporate both linear and nonlinear equations, does not rely on Green's functions, and is free to use arbitrary kernels. Specifically, we integrate the standard GP with a generative model to encode the differential equation in a principled Bayesian hybrid framework. For efficient and effective inference, we marginalize out the latent variables and derive a simplified model evidence lower bound (ELBO), based on which we develop a stochastic collapsed inference algorithm. Our ELBO can be viewed as a posterior regularization objective. We show the advantage of our approach in both simulation and real-world applications.
|
statistics
|
In this paper, we develop a new method for constructing $m$-ovoids in the symplectic polar space $\W(2r-1,\q)$ from some strongly regular Cayley graphs in \cite{Brouwer1999Journal}. Using this method, we obtain many new $m$-ovoids which can not be derived by field reduction.
|
mathematics
|
Purpose. Precise placement of needles is a challenge in a number of clinical applications such as brachytherapy or biopsy. Forces acting at the needle cause tissue deformation and needle deflection which in turn may lead to misplacement or injury. Hence, a number of approaches to estimate the forces at the needle have been proposed. Yet, integrating sensors into the needle tip is challenging and a careful calibration is required to obtain good force estimates. Methods. We describe a fiber-optical needle tip force sensor design using a single OCT fiber for measurement. The fiber images the deformation of an epoxy layer placed below the needle tip which results in a stream of 1D depth profiles. We study different deep learning approaches to facilitate calibration between this spatio-temporal image data and the related forces. In particular, we propose a novel convGRU-CNN architecture for simultaneous spatial and temporal data processing. Results. The needle can be adapted to different operating ranges by changing the stiffness of the epoxy layer. Likewise, calibration can be adapted by training the deep learning models. Our novel convGRU-CNN architecture results in the lowest mean absolute error of 1.59 +- 1.3 mN and a cross-correlation coefficient of 0.9997, and clearly outperforms the other methods. Ex vivo experiments in human prostate tissue demonstrate the needle's application. Conclusions. Our OCT-based fiber-optical sensor presents a viable alternative for needle tip force estimation. The results indicate that the rich spatio-temporal information included in the stream of images showing the deformation throughout the epoxy layer can be effectively used by deep learning models. Particularly, we demonstrate that the convGRU-CNN architecture performs favorably, making it a promising approach for other spatio-temporal learning problems.
|
electrical engineering and systems science
|
In this article, we consider the phenomenon of complete coincidence of the key properties of pairs of Calabi-Yau manifolds realized as hypersurfaces in two different weighted projective spaces. More precisely, the first manifold in such a pair is realized as a hypersurface in a weighted projective space, and the second as a hypersurface in the orbifold of another weighted projective space. The two manifolds in each pair have the same Hodge numbers and special K\"ahler geometry on the complex structure moduli space and are associated with the same $N=2$ gauge linear sigma model. We give the explanation of this interesting coincidence using the Batyrev's correspondence between Calabi-Yau manifolds and the reflexive polyhedra.
|
high energy physics theory
|
The theory of cellular automata in operational probabilistic theories is developed. We start introducing the composition of infinitely many elementary systems, and then use this notion to define update rules for such infinite composite systems. The notion of causal influence is introduced, and its relation with the usual property of signalling is discussed. We then introduce homogeneity, namely the property of an update rule to evolve every system in the same way, and prove that systems evolving by a homogeneous rule always correspond to vertices of a Cayley graph. Next, we define the notion of locality for update rules. Cellular automata are then defined as homogeneous and local update rules. Finally, we prove a general version of the wrapping lemma, that connects CA on different Cayley graphs sharing some small-scale structure of neighbourhoods.
|
quantum physics
|
A precise security analysis of practical quantum key distribution (QKD) systems is an important step for improving their performance. Here we consider a class of quantum soft filtering operations, which generalizes the unambiguous state discrimination (USD) technique. These operations can be applied as a basis for a security analysis of the original coherent one-way (COW) QKD protocol since their application interpolates between beam-splitting (BS) and USD attacks. We demonstrate that a zero-error attack based on quantum soft filtering operations gives a larger amount of the information for Eve at a given level of losses. We calculate the Eve information as a function of the channel length. The efficiency of the proposed attack highly depends on the level of the monitoring under the maintenance of the statistics of control (decoy) states, and best-case results are achieved in the case of the absence of maintenance of control state statistics. Our results form additional requirements for the analysis of practical QKD systems based on the COW QKD protocol and its variants by providing an upper bound on the security.
|
quantum physics
|
Through millennia humans exploited the natural property of metals to get stronger or hardened when mechanically deformed. Ultimately rooted in the motion of dislocations, mechanisms of metal hardening remained in the crosshairs of physical metallurgists for over a century. Here, we performed atomistic simulations at the limits of supercomputing, which are sufficiently large to be statistically representative of macroscopic crystal plasticity yet fully resolved to examine the origins of metal hardening at its most fundamental level of atomic motion. We demonstrate that the notorious staged (inflection) hardening of metals is a direct consequence of crystal rotation under uniaxial straining. At variance with widely divergent and contradictory views in the literature, we observe that basic mechanisms of dislocation behavior are the same across all stages of metal hardening.
|
condensed matter
|
Arms control treaties are necessary to reduce the large stockpiles of the nuclear weapons that constitute one of the biggest dangers to the world. However, an impactful treaty hinges on effective inspection exercises to verify the participants' compliance to the treaty terms. Such procedures would require verification of the authenticity of a warhead undergoing dismantlement. Previously proposed solutions lacked the combination of isotopic sensitivity and information security. Here we present the experimental feasibility proof of a novel technique that uses neutron induced nuclear resonances and is sensitive to the combination of isotopics and geometry. The information is physically encrypted to prevent the leakage of sensitive information. Our approach can significantly increase the trustworthiness of future arms control treaties while expanding their scope to include the verified dismantlement of nuclear warheads themselves.
|
physics
|
Chirality is ubiquitous from microscopic to macroscopic phenomena in physics and biology, such as fermionic interactions and DNA duplication. In photonics, chirality has traditionally represented differentiated optical responses for right and left circular polarizations. This definition of optical chirality in the polarization domain includes handedness-dependent phase velocities or optical absorption inside chiral media, which enable polarimetry for measuring the material concentration and circular dichroism spectroscopy for sensing biological or chemical enantiomers. Recently, the emerging field of non-Hermitian photonics, which explores exotic phenomena in gain or loss media, has provided a new viewpoint on chirality in photonics that is not restricted to the traditional polarization domain but is extended to other physical quantities such as the orbital angular momentum, propagation direction, and system parameter space. Here, we introduce recent milestones in chiral light-matter interactions in non-Hermitian photonics and show an enhanced degree of design freedom in photonic devices for spin and orbital angular momenta, directionality, and asymmetric modal conversion.
|
physics
|
Capabilities for collecting and storing data on mobile objects have increased dramatically over the past few decades. A persistent difficulty is summarizing large collections of mobile objects. This paper develops methods for extracting and analyzing hotspots or locations with relatively high levels of mobility activity. We use kernel density estimation (KDE) to convert a large collection of mobile objects into a smooth, continuous surface. We then develop a topological algorithm to extract critical geometric features of the surface; these include critical points (peaks, pits and passes) and critical lines (ridgelines and course-lines). We connect the peaks and corresponding ridgelines to produce a surface network that summarizes the topological structure of the surface. We apply graph theoretic indices to analytically characterize the surface and its changes over time. To illustrate our approach, we apply the techniques to taxi cab data collected in Shanghai, China. We find increases in the complexity of the hotspot spatial distribution during normal activity hours in the late morning, afternoon and evening and a spike in the connectivity of the hotspot spatial distribution in the morning as taxis concentrate on servicing travel to work. These results match with scientific and anecdotal knowledge about human activity patterns in the study area.
|
statistics
|
Significant improvements have been achieved in motion control systems with the availability of high speed power switches and microcomputers on the market. Even though motor drivers are able to provide high torque control bandwidth under nominal conditions, they suffer from various physical constraints which degrade both output amplitude and bandwidth of torque control loop. In this context, peak power limit of a power source, as one of those constraints, has not been fully explored from the control perspective so far. A conventional and practical way of considering peak power limit in control systems is to model it as a trivial torque saturation derived from the allowable torque at maximum speed satisfying the constraint. However, this model is overly conservative leading to poor closed loop performance when actuators operate below their maximum speed. In this paper, novel ways of incorporating peak power limits into both classical and optimal controllers are presented upon a theoretical analysis revealing its effects on stability and performance.
|
electrical engineering and systems science
|
We describe a viscocapillary instability that can perturb the spherical symmetry of cellular aggregates in culture, also called multicellular spheroids. In the condition where the cells constituting the spheroid get their necessary metabolites from the immediate, outer microenvironment, a permanent cell flow exists within the spheroid from its outer rim where cells divide toward its core where they die. A perturbation of the spherical symmetry induces viscous shear stresses within the tissue that can destabilise the aggregate. The proposed instability is viscocapillary in nature and does not rely on external heterogeneities, such as a pre-existing pattern of blood vessels or the presence of a substrate on which the cells can exert pulling forces. It arises for sufficiently large cell-cell adhesion strengths, cell-renewal rates, and metabolite supplies, as described by our model parameters. Since multicellular spheroids in culture are good model systems of small, avascular tumours, mimicking the metabolite concentration gradients found in vivo, we can speculate that our description applies to microtumour instabilities in cancer progression.
|
physics
|
We study a special dynamical regime of a Bose-Einstein condensate in a ring-shaped lattice where the populations in each site remain constant during the time evolution. The states in this regime are characterized by equal occupation numbers in alternate wells and non-trivial phases, while the phase differences between neighboring sites evolve in time yielding persistent currents that oscillate around the lattice. We show that the velocity circulation around the ring lattice alternates between two values determined by the number of wells and with a specific time period that is only driven by the onsite interaction energy parameter. In contrast to the self-trapping regime present in optical lattices, the occupation number at each site does not show any oscillation and the particle imbalance does not possess a lower bound for the phenomenon to occur. These findings are predicted with a multimode model and confirmed by full three-dimensional Gross-Pitaevskii simulations using an effective onsite interaction energy parameter.
|
condensed matter
|
The amplified spontaneous emission (ASE) noise has been extensively studied and employed to build quantum random number generators (QRNGs). While the previous relative works mainly focus on the realization and verification of the QRNG system, the comprehensive physical model and randomness quantification for the general detection of the ASE noise are still incomplete, which is essential for the quantitative security analysis. In this paper, a systematical physical model for the emission, detection and acquisition of the ASE noise with added electronic noise is developed and verified, based on which the numerical simulations are performed under various setups and the simulation results all significantly fit well with the corresponding experimental data. Then, a randomness quantification method and the corresponding experimentally verifiable approach are proposed and validated, which quantifies the randomness purely resulted from the quantum process and improves the security analysis for the QRNG based on the detection of the ASE noise. The physical model and the randomness quantification method proposed in this paper are of significant feasibility and applicable for the QRNG system with randomness originating from the detection of the photon number with arbitrary distributions.
|
quantum physics
|
We consider an optically thick spherical agglomerate of magneto-optical scatterers with a central isotropic, unpolarized light source, placed in a homogeneous magnetic field. The Photon Hall Effect induces a rotating Poynting vector, both inside and outside the medium. We show that electromagnetic (orbital) angular momentum leaks out and induces a torque proportional to the injection power of the source and the photon Hall angle. This effect represents a novel class of optical phenomena, generating angular momentum from diffusive magneto-transport.
|
physics
|
In state-of-the-art quantum computing platforms, including superconducting qubits and trapped ions, imperfections in the 2-qubit entangling gates are the dominant contributions of error to system-wide performance. Recently, a novel 2-qubit parametric gate was proposed and demonstrated with superconducting transmon qubits. This gate is activated through RF modulation of the transmon frequency and can be operated at an amplitude where the performance is first-order insensitive to flux-noise. In this work we experimentally validate the existence of this AC sweet spot and demonstrate its dependence on white noise power from room temperature electronics. With these factors in place, we measure coherence-limited entangling-gate fidelities as high as 99.2 $\pm$ 0.15%.
|
quantum physics
|
This paper studies an Internet-of-Things (IoT) network employing a reconfigurable intelligent surface (RIS) over generalized fading channels. Inspired by the promising potential of RIS-based transmission, we investigate a RIS-enabled IoT network with the source node employing a RIS-based access point. The system is modelled with reference to a receiver transmitter pair and the Fisher-Snedecor F model is adopted to analyse the composite fading and shadowing channel. Closed-form expressions are derived for the system with regards to the average capacity, average bit error rate (BER) and outage probability. Monte-Carlo simulations are provided throughout to validate the results. The results investigated and reported in this study extend early results reported in the emerging literature on RIS-enabled technologies and provides a framework for the evaluation of a basic RIS-enabled IoT network over the most common multipath fading channels. The results indicate the clear benefit of employing a RIS-enabled access point, as well as the versatility of the derived expressions in analysing the effects of fading and shadowing on the network. The results further demonstrate that for a RIS-enabled IoT network, there is the need to balance between the cost and benefit of increasing the RIS cells against other parameters such as increasing transmit power, especially at low SNR and/or high to moderate fading/shadowing severity.
|
electrical engineering and systems science
|
We study a family of polynomials which are orthogonal with respect to the varying, highly oscillatory complex weight function $e^{ni\lambda z}$ on $[-1,1]$, where $\lambda$ is a positive parameter. This family of polynomials has appeared in the literature recently in connection with complex quadrature rules, and their asymptotics have been previously studied when $\lambda$ is smaller than a certain critical value, $\lambda_c$. Our main goal is to compute their asymptotics when $\lambda>\lambda_c$. We first provide a geometric description, based on the theory of quadratic differentials, of the curves in the complex plane which will eventually support the asymptotic zero distribution of these polynomials. Next, using the powerful Riemann-Hilbert formulation of the orthogonal polynomials due to Fokas, Its, and Kitaev, along with its method of asymptotic solution via Deift-Zhou nonlinear steepest descent, we provide uniform asymptotics of the polynomials throughout the complex plane. Although much of this asymptotic analysis follows along the lines of previous works in the literature, the main obstacle appears in the construction of the so-called global parametrix. This construction is carried out in an explicit way with the help of certain integrals of elliptic type. In stark contrast to the situation one typically encounters in the presence of real orthogonality, an interesting byproduct of this construction is that there is a discrete set of values of $\lambda$ for which one cannot solve the model Riemann-Hilbert problem, and as such the corresponding polynomials fail to exist.
|
mathematics
|
PURPOSE: We propose a fully unsupervised method to learn latent disease networks directly from unstructured biomedical text corpora. This method addresses current challenges in unsupervised knowledge extraction, such as the detection of long-range dependencies and requirements for large training corpora. METHODS: Let C be a corpus of n text chunks. Let V be a set of p disease terms occurring in the corpus. Let X indicate the occurrence of V in C. Gextext identifies disease similarities by positively correlated occurrence patterns. This information is combined to generate a graph on which geodesic distance describes dissimilarity. Diseasomes were learned by Gextext and GloVE on corpora of 100-1000 PubMed abstracts. Similarity matrix estimates were validated against biomedical semantic similarity metrics and gene profile similarity. RESULTS: Geodesic distance on Gextext-inferred diseasomes correlated inversely with external measures of semantic similarity. Gene profile similarity also correlated significant with proximity on the inferred graph. Gextext outperformed GloVE in our experiments. The information contained on the Gextext graph exceeded the explicit information content within the text. CONCLUSIONS: Gextext extracts latent relationships from unstructured text, enabling fully unsupervised modelling of diseasome graphs from PubMed abstracts.
|
computer science
|
The work discusses the diffusional growth in particulate systems such as atmospheric clouds. It focuses on the Eulerian modeling approach in which the evolution of the probability density function describing the particle size spectrum is carried out using a fixed-bin discretization. The numerical diffusion problem inherent to the employment of the fixed-bin discretization is scrutinized. The work focuses on the applications of MPDATA family of numerical schemes. Several MPDATA variants are explored including: infinite-gauge, non-oscillatory, third-order-terms and recursive antidiffusive correction (double pass donor cell, DPDC) options. Methodology for handling coordinate transformations associated with both particle size distribution variable choice and numerical grid layout are expounded. The study uses PyMPDATA - a new open-source Python implementation of MPDATA. Analysis of the performance of the scheme for different discretization parameters and different settings of the algorithm is performed using an analytically solvable test case pertinent to condensational growth of cloud droplets. The analysis covers spatial and temporal convergence, computational cost, conservativeness and quantification of the numerical broadening of the particle size spectrum. Presented results demonstrate that, for the problem considered, even a tenfold decrease of the spurious numerical spectral broadening can be obtained by a proper choice of the MPDATA variant (maintaining the same spatial and temporal resolution).
|
physics
|
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