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LPCNet: Improving Neural Speech Synthesis Through Linear Prediction
Neural speech synthesis models have recently demonstrated the ability to synthesize high quality speech for text-to-speech and compression applications. These new models often require powerful GPUs to achieve real-time operation, so being able to reduce their complexity would open the way for many new applications. W...
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Coherent anti-Stokes Raman Scattering Lidar Using Slow Light: A Theoretical Study
We theoretically investigate a scheme in which backward coherent anti-Stokes Raman scattering (CARS) is significantly enhanced by using slow light. Specifically, we reduce the group velocity of the Stokes excitation pulse by introducing a coupling laser that causes electromagnetically induced transparency (EIT). When...
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Tests based on characterizations, and their efficiencies: a survey
A survey of goodness-of-fit and symmetry tests based on the characterization properties of distributions is presented. This approach became popular in recent years. In most cases the test statistics are functionals of $U$-empirical processes. The limiting distributions and large deviations of new statistics under the...
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Hyperprior on symmetric Dirichlet distribution
In this article we introduce how to put vague hyperprior on Dirichlet distribution, and we update the parameter of it by adaptive rejection sampling (ARS). Finally we analyze this hyperprior in an over-fitted mixture model by some synthetic experiments.
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On the interpretability and computational reliability of frequency-domain Granger causality
This is a comment to the paper 'A study of problems encountered in Granger causality analysis from a neuroscience perspective'. We agree that interpretation issues of Granger Causality in Neuroscience exist (partially due to the historical unfortunate use of the name 'causality', as nicely described in previous liter...
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Artificial topological models based on a one-dimensional spin-dependent optical lattice
Topological matter is a popular topic in both condensed matter and cold atom research. In the past decades, a variety of models have been identified with fascinating topological features. Some, but not all, of the models can be found in materials. As a fully controllable system, cold atoms trapped in optical lattices...
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Ramsey expansions of metrically homogeneous graphs
We discuss the Ramsey property, the existence of a stationary independence relation and the coherent extension property for partial isometries (coherent EPPA) for all classes of metrically homogeneous graphs from Cherlin's catalogue, which is conjectured to include all such structures. We show that, with the exceptio...
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Rapidly star-forming galaxies adjacent to quasars at redshifts exceeding 6
The existence of massive ($10^{11}$ solar masses) elliptical galaxies by redshift z~4 (when the Universe was 1.5 billion years old) necessitates the presence of galaxies with star-formation rates exceeding 100 solar masses per year at z>6 (corresponding to an age of the Universe of less than 1 billion years). Surveys...
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Regular irreducible characters of a hyperspecial compact group
A parametrization of irreducible unitary representations associated with the regular adjoint orbits of a hyperspecial compact subgroup of a reductive group over a non-dyadic non-archimedean local filed is presented. The parametrization is given by means of (a subset of) the character group of certain finite abelian g...
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Active Exploration Using Gaussian Random Fields and Gaussian Process Implicit Surfaces
In this work we study the problem of exploring surfaces and building compact 3D representations of the environment surrounding a robot through active perception. We propose an online probabilistic framework that merges visual and tactile measurements using Gaussian Random Field and Gaussian Process Implicit Surfaces....
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Doing good vs. avoiding bad in prosocial choice: A refined test and extension of the morality preference hypothesis
Prosociality is fundamental to human social life, and, accordingly, much research has attempted to explain human prosocial behavior. Capraro and Rand (Judgment and Decision Making, 13, 99-111, 2018) recently provided experimental evidence that prosociality in anonymous, one-shot interactions (such as Prisoner's Dilem...
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Measuring Territorial Control in Civil Wars Using Hidden Markov Models: A Data Informatics-Based Approach
Territorial control is a key aspect shaping the dynamics of civil war. Despite its importance, we lack data on territorial control that are fine-grained enough to account for subnational spatio-temporal variation and that cover a large set of conflicts. To resolve this issue, we propose a theoretical model of the rel...
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Virtual quandle for links in lens spaces
We construct a virtual quandle for links in lens spaces $L(p,q)$, with $q=1$. This invariant has two valuable advantages over an ordinary fundamental quandle for links in lens spaces: the virtual quandle is an essential invariant and the presentation of the virtual quandle can be easily written from the band diagram ...
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Adaptation to Easy Data in Prediction with Limited Advice
We derive an online learning algorithm with improved regret guarantees for `easy' loss sequences. We consider two types of `easiness': (a) stochastic loss sequences and (b) adversarial loss sequences with small effective range of the losses. While a number of algorithms have been proposed for exploiting small effecti...
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Why Bohr was (Mostly) Right
After a discussion of the Frauchiger-Renner argument that no 'single- world' interpretation of quantum mechanics can be self-consistent, I propose a 'Bohrian' alternative to many-worlds or QBism as the rational option.
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Generalizing Distance Covariance to Measure and Test Multivariate Mutual Dependence
We propose three measures of mutual dependence between multiple random vectors. All the measures are zero if and only if the random vectors are mutually independent. The first measure generalizes distance covariance from pairwise dependence to mutual dependence, while the other two measures are sums of squared distan...
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Simultaneous Inference for High Dimensional Mean Vectors
Let $X_1, \ldots, X_n\in\mathbb{R}^p$ be i.i.d. random vectors. We aim to perform simultaneous inference for the mean vector $\mathbb{E} (X_i)$ with finite polynomial moments and an ultra high dimension. Our approach is based on the truncated sample mean vector. A Gaussian approximation result is derived for the latt...
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Joint Routing, Scheduling and Power Control Providing Hard Deadline in Wireless Multihop Networks
We consider optimal/efficient power allocation policies in a single/multihop wireless network in the presence of hard end-to-end deadline delay constraints on the transmitted packets. Such constraints can be useful for real time voice and video. Power is consumed in only transmission of the data. We consider the case...
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Activation of Microwave Fields in a Spin-Torque Nano-Oscillator by Neuronal Action Potentials
Action potentials are the basic unit of information in the nervous system and their reliable detection and decoding holds the key to understanding how the brain generates complex thought and behavior. Transducing these signals into microwave field oscillations can enable wireless sensors that report on brain activity...
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Responses in Large-Scale Structure
We introduce a rigorous definition of general power-spectrum responses as resummed vertices with two hard and $n$ soft momenta in cosmological perturbation theory. These responses measure the impact of long-wavelength perturbations on the local small-scale power spectrum. The kinematic structure of the responses (i.e...
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Graph isomorphisms in quasi-polynomial time
Let us be given two graphs $\Gamma_1$, $\Gamma_2$ of $n$ vertices. Are they isomorphic? If they are, the set of isomorphisms from $\Gamma_1$ to $\Gamma_2$ can be identified with a coset $H\cdot\pi$ inside the symmetric group on $n$ elements. How do we find $\pi$ and a set of generators of $H$? The challenge of giving...
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Hardware-Aware Machine Learning: Modeling and Optimization
Recent breakthroughs in Deep Learning (DL) applications have made DL models a key component in almost every modern computing system. The increased popularity of DL applications deployed on a wide-spectrum of platforms have resulted in a plethora of design challenges related to the constraints introduced by the hardwa...
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On the unit distance problem
The Erd\H os unit distance conjecture in the plane says that the number of pairs of points from a point set of size $n$ separated by a fixed (Euclidean) distance is $\leq C_{\epsilon} n^{1+\epsilon}$ for any $\epsilon>0$. The best known bound is $Cn^{\frac{4}{3}}$. We show that if the set under consideration is well-...
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Ordered states in the Kitaev-Heisenberg model: From 1D chains to 2D honeycomb
We study the ground state of the 1D Kitaev-Heisenberg (KH) model using the density-matrix renormalization group and Lanczos exact diagonalization methods. We obtain a rich ground-state phase diagram as a function of the ratio between Heisenberg ($J=\cos\phi)$ and Kitaev ($K=\sin\phi$) interactions. Depending on the r...
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Quadratic forms and Sobolev spaces of fractional order
We study quadratic functionals on $L^2(\mathbb{R}^d)$ that generate seminorms in the fractional Sobolev space $H^s(\mathbb{R}^d)$ for $0 < s < 1$. The functionals under consideration appear in the study of Markov jump processes and, independently, in recent research on the Boltzmann equation. The functional measures ...
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General Latent Feature Modeling for Data Exploration Tasks
This paper introduces a general Bayesian non- parametric latent feature model suitable to per- form automatic exploratory analysis of heterogeneous datasets, where the attributes describing each object can be either discrete, continuous or mixed variables. The proposed model presents several important properties. Fir...
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The ALMA View of the OMC1 Explosion in Orion
Most massive stars form in dense clusters where gravitational interactions with other stars may be common. The two nearest forming massive stars, the BN object and Source I, located behind the Orion Nebula, were ejected with velocities of $\sim$29 and $\sim$13 km s$^{-1}$ about 500 years ago by such interactions. Thi...
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Neurology-as-a-Service for the Developing World
Electroencephalography (EEG) is an extensively-used and well-studied technique in the field of medical diagnostics and treatment for brain disorders, including epilepsy, migraines, and tumors. The analysis and interpretation of EEGs require physicians to have specialized training, which is not common even among most ...
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Estimation of Low-Rank Matrices via Approximate Message Passing
Consider the problem of estimating a low-rank symmetric matrix when its entries are perturbed by Gaussian noise, a setting that is known as `spiked model' or `deformed Wigner matrix'. If the empirical distribution of the entries of the spikes is known, optimal estimators that exploit this knowledge can substantially ...
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Simultaneous diagonalisation of the covariance and complementary covariance matrices in quaternion widely linear signal processing
Recent developments in quaternion-valued widely linear processing have established that the exploitation of complete second-order statistics requires consideration of both the standard covariance and the three complementary covariance matrices. Although such matrices have a tremendous amount of structure and their de...
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Arithmetic Siegel-Weil formula on $X_{0}(N)$
In this paper, we proved an arithmetic Siegel-Weil formula and the modularity of some arithmetic theta function on the modular curve $X_0(N)$ when $N$ is square free. In the process, we also construct some generalized Delta function for $\Gamma_0(N)$ and proved some explicit Kronecker limit formula for Eisenstein ser...
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Perturbation, Non-Gaussianity and Reheating in a GB-$α$-Attractor Model
Motivated by $\alpha$-attractor models, in this paper we consider a Gauss-Bonnet inflation with E-model type of potential. We consider the Gauss-Bonnet coupling function to be the same as the E-model potential. In the small $\alpha$ limit we obtain an attractor at $r=0$ as expected, and in the large $\alpha$ limit we...
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Experimental determination of the frequency and field dependence of Specific Loss Power in Magnetic Fluid Hyperthermia
Magnetic nanoparticles are promising systems for biomedical applications and in particular for Magnetic Fluid Hyperthermia, a promising therapy that utilizes the heat released by such systems to damage tumor cells. We present an experimental study of the physical properties that influences the capability of heat rele...
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Training wide residual networks for deployment using a single bit for each weight
For fast and energy-efficient deployment of trained deep neural networks on resource-constrained embedded hardware, each learned weight parameter should ideally be represented and stored using a single bit. Error-rates usually increase when this requirement is imposed. Here, we report large improvements in error rate...
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IP Based Traffic Recovery: An Optimal Approach using SDN Application for Data Center Network
With the passage of time and indulgence in Information Technology, network management has proved its significance and has become one of the most important and challenging task in today's era of information flow. Communication networks implement a high level of sophistication in managing and flowing the data through s...
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Performance of Optimal Data Shaping Codes
Data shaping is a coding technique that has been proposed to increase the lifetime of flash memory devices. Several data shaping codes have been described in recent work, including endurance codes and direct shaping codes for structured data. In this paper, we study information-theoretic properties of a general class...
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Finding influential nodes for integration in brain networks using optimal percolation theory
Global integration of information in the brain results from complex interactions of segregated brain networks. Identifying the most influential neuronal populations that efficiently bind these networks is a fundamental problem of systems neuroscience. Here we apply optimal percolation theory and pharmacogenetic inter...
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Automatic Music Highlight Extraction using Convolutional Recurrent Attention Networks
Music highlights are valuable contents for music services. Most methods focused on low-level signal features. We propose a method for extracting highlights using high-level features from convolutional recurrent attention networks (CRAN). CRAN utilizes convolution and recurrent layers for sequential learning with an a...
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On Oracle-Efficient PAC RL with Rich Observations
We study the computational tractability of PAC reinforcement learning with rich observations. We present new provably sample-efficient algorithms for environments with deterministic hidden state dynamics and stochastic rich observations. These methods operate in an oracle model of computation -- accessing policy and ...
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Noise induced transition in Josephson junction with second harmonic
We show a noise-induced transition in Josephson junction with fundamental as well as second harmonic. A periodically modulated multiplicative colored noise can stabilize an unstable configuration in such a system. The stabilization of the unstable configuration has been captured in the effective potential of the syst...
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Distributed Estimation of Principal Eigenspaces
Principal component analysis (PCA) is fundamental to statistical machine learning. It extracts latent principal factors that contribute to the most variation of the data. When data are stored across multiple machines, however, communication cost can prohibit the computation of PCA in a central location and distribute...
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Invariant algebraic surfaces of the FitzHugh-Nagumo system
In this paper, we characterize all the irreducible Darboux polynomials and polynomial first integrals of FitzHugh-Nagumo (F-N) system. The method of the weight homogeneous polynomials and the characteristic curves is widely used to give a complete classification of Darboux polynomials of a system. However, this metho...
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Local and global boundary rigidity and the geodesic X-ray transform in the normal gauge
In this paper we analyze the local and global boundary rigidity problem for general Riemannian manifolds with boundary $(M,g)$ whose boundary is strictly convex. We show that the boundary distance function, i.e., $d_g|_{\partial M\times\partial M}$, known over suitable open sets of $\partial M$ determines $g$ in suit...
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Adversarial Source Identification Game with Corrupted Training
We study a variant of the source identification game with training data in which part of the training data is corrupted by an attacker. In the addressed scenario, the defender aims at deciding whether a test sequence has been drawn according to a discrete memoryless source $X \sim P_X$, whose statistics are known to ...
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Toric actions and convexity in cosymplectic geometry
We prove a convexity theorem for Hamiltonian torus actions on compact cosymplectic manifolds. We show that compact toric cosymplectic manifolds are mapping tori of equivariant symplectomorphisms of toric symplectic manifolds.
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Localization and Stationary Phase Approximation on Supermanifolds
Given an odd vector field $Q$ on a supermanifold $M$ and a $Q$-invariant density $\mu$ on $M$, under certain compactness conditions on $Q$, the value of the integral $\int_{M}\mu$ is determined by the value of $\mu$ on any neighborhood of the vanishing locus $N$ of $Q$. We present a formula for the integral in the ca...
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An Analytical Design Optimization Method for Electric Propulsion Systems of Multicopter UAVs with Desired Hovering Endurance
Multicopters are becoming increasingly important in both civil and military fields. Currently, most multicopter propulsion systems are designed by experience and trial-and-error experiments, which are costly and ineffective. This paper proposes a simple and practical method to help designers find the optimal propulsi...
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A Reassessment of Absolute Energies of the X-ray L Lines of Lanthanide Metals
We introduce a new technique for determining x-ray fluorescence line energies and widths, and we present measurements made with this technique of 22 x-ray L lines from lanthanide-series elements. The technique uses arrays of transition-edge sensors, microcalorimeters with high energy-resolving power that simultaneous...
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Limitations of Source-Filter Coupling In Phonation
The coupling of vocal fold (source) and vocal tract (filter) is one of the most critical factors in source-filter articulation theory. The traditional linear source-filter theory has been challenged by current research which clearly shows the impact of acoustic loading on the dynamic behavior of the vocal fold vibrat...
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Correlation between clustering and degree in affiliation networks
We are interested in the probability that two randomly selected neighbors of a random vertex of degree (at least) $k$ are adjacent. We evaluate this probability for a power law random intersection graph, where each vertex is prescribed a collection of attributes and two vertices are adjacent whenever they share a com...
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Automatic Disambiguation of French Discourse Connectives
Discourse connectives (e.g. however, because) are terms that can explicitly convey a discourse relation within a text. While discourse connectives have been shown to be an effective clue to automatically identify discourse relations, they are not always used to convey such relations, thus they should first be disambi...
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Predicting Financial Crime: Augmenting the Predictive Policing Arsenal
Financial crime is a rampant but hidden threat. In spite of this, predictive policing systems disproportionately target "street crime" rather than white collar crime. This paper presents the White Collar Crime Early Warning System (WCCEWS), a white collar crime predictive model that uses random forest classifiers to ...
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Polar codes with a stepped boundary
We consider explicit polar constructions of blocklength $n\rightarrow\infty$ for the two extreme cases of code rates $R\rightarrow1$ and $R\rightarrow0.$ For code rates $R\rightarrow1,$ we design codes with complexity order of $n\log n$ in code construction, encoding, and decoding. These codes achieve the vanishing o...
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Resonant Scattering Characteristics of Homogeneous Dielectric Sphere
In the present article the classical problem of electromagnetic scattering by a single homogeneous sphere is revisited. Main focus is the study of the scattering behavior as a function of the material contrast and the size parameters for all electric and magnetic resonances of a dielectric sphere. Specifically, the P...
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An efficient global optimization algorithm for maximizing the sum of two generalized Rayleigh quotients
Maximizing the sum of two generalized Rayleigh quotients (SRQ) can be reformulated as a one-dimensional optimization problem, where the function value evaluations are reduced to solving semi-definite programming (SDP) subproblems. In this paper, we first use the dual SDP subproblem to construct an explicit overestima...
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Location Dependent Dirichlet Processes
Dirichlet processes (DP) are widely applied in Bayesian nonparametric modeling. However, in their basic form they do not directly integrate dependency information among data arising from space and time. In this paper, we propose location dependent Dirichlet processes (LDDP) which incorporate nonparametric Gaussian pr...
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Poisson brackets symmetry from the pentagon-wheel cocycle in the graph complex
Kontsevich designed a scheme to generate infinitesimal symmetries $\dot{\mathcal{P}} = \mathcal{Q}(\mathcal{P})$ of Poisson brackets $\mathcal{P}$ on all affine manifolds $M^r$; every such deformation is encoded by oriented graphs on $n+2$ vertices and $2n$ edges. In particular, these symmetries can be obtained by or...
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Shadows of characteristic cycles, Verma modules, and positivity of Chern-Schwartz-MacPherson classes of Schubert cells
Chern-Schwartz-MacPherson (CSM) classes generalize to singular and/or noncompact varieties the classical total homology Chern class of the tangent bundle of a smooth compact complex manifold. The theory of CSM classes has been extended to the equivariant setting by Ohmoto. We prove that for an arbitrary complex proje...
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An Iterative Scheme for Leverage-based Approximate Aggregation
The current data explosion poses great challenges to the approximate aggregation with an efficiency and accuracy. To address this problem, we propose a novel approach to calculate the aggregation answers with a high accuracy using only a small portion of the data. We introduce leverages to reflect individual differen...
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A Game of Martingales
We consider a two player dynamic game played over $T \leq \infty$ periods. In each period each player chooses any probability distribution with support on $[0,1]$ with a given mean, where the mean is the realized value of the draw from the previous period. The player with the highest realization in the period achieve...
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Effects of tunnelling and asymmetry for system-bath models of electron transfer
We apply the newly derived nonadiabatic golden-rule instanton theory to asymmetric models describing electron-transfer in solution. The models go beyond the usual spin-boson description and have anharmonic free-energy surfaces with different values for the reactant and product reorganization energies. The instanton m...
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Self-Modifying Morphology Experiments with DyRET: Dynamic Robot for Embodied Testing
If robots are to become ubiquitous, they will need to be able to adapt to complex and dynamic environments. Robots that can adapt their bodies while deployed might be flexible and robust enough to meet this challenge. Previous work on dynamic robot morphology has focused on simulation, combining simple modules, or sw...
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Dropout is a special case of the stochastic delta rule: faster and more accurate deep learning
Multi-layer neural networks have lead to remarkable performance on many kinds of benchmark tasks in text, speech and image processing. Nonlinear parameter estimation in hierarchical models is known to be subject to overfitting. One approach to this overfitting and related problems (local minima, colinearity, feature ...
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Kernel Regression with Sparse Metric Learning
Kernel regression is a popular non-parametric fitting technique. It aims at learning a function which estimates the targets for test inputs as precise as possible. Generally, the function value for a test input is estimated by a weighted average of the surrounding training examples. The weights are typically computed...
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Learning MSO-definable hypotheses on string
We study the classification problems over string data for hypotheses specified by formulas of monadic second-order logic MSO. The goal is to design learning algorithms that run in time polynomial in the size of the training set, independently of or at least sublinear in the size of the whole data set. We prove negati...
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From semimetal to chiral Fulde-Ferrell superfluids
The recent realization of two-dimensional (2D) synthetic spin-orbit (SO) coupling opens a broad avenue to study novel topological states for ultracold atoms. Here, we propose a new scheme to realize exotic chiral Fulde-Ferrell superfluid for ultracold fermions, with a generic theory being shown that the topology of s...
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TumorNet: Lung Nodule Characterization Using Multi-View Convolutional Neural Network with Gaussian Process
Characterization of lung nodules as benign or malignant is one of the most important tasks in lung cancer diagnosis, staging and treatment planning. While the variation in the appearance of the nodules remains large, there is a need for a fast and robust computer aided system. In this work, we propose an end-to-end t...
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An apparatus architecture for femtosecond transmission electron microscopy
The motion of electrons in or near solids, liquids and gases can be tracked by forcing their ejection with attosecond x-ray pulses, derived from femtosecond lasers. The momentum of these emitted electrons carries the imprint of the electronic state. Aberration corrected transmission electron microscopes have observed...
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HourGlass: Predictable Time-based Cache Coherence Protocol for Dual-Critical Multi-Core Systems
We present a hardware mechanism called HourGlass to predictably share data in a multi-core system where cores are explicitly designated as critical or non-critical. HourGlass is a time-based cache coherence protocol for dual-critical multi-core systems that ensures worst-case latency (WCL) bounds for memory requests ...
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Frictional Effects on RNA Folding: Speed Limit and Kramers Turnover
We investigated frictional effects on the folding rates of a human telomerase hairpin (hTR HP) and H-type pseudoknot from the Beet Western Yellow Virus (BWYV PK) using simulations of the Three Interaction Site (TIS) model for RNA. The heat capacity from TIS model simulations, calculated using temperature replica exch...
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Learning to Rank based on Analogical Reasoning
Object ranking or "learning to rank" is an important problem in the realm of preference learning. On the basis of training data in the form of a set of rankings of objects represented as feature vectors, the goal is to learn a ranking function that predicts a linear order of any new set of objects. In this paper, we ...
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Modeling Spatial Overdispersion with the Generalized Waring Process
Modeling spatial overdispersion requires point processes models with finite dimensional distributions that are overdisperse relative to the Poisson. Fitting such models usually heavily relies on the properties of stationarity, ergodicity, and orderliness. And, though processes based on negative binomial finite dimens...
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Adversarial examples for generative models
We explore methods of producing adversarial examples on deep generative models such as the variational autoencoder (VAE) and the VAE-GAN. Deep learning architectures are known to be vulnerable to adversarial examples, but previous work has focused on the application of adversarial examples to classification tasks. De...
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Sparse covariance matrix estimation in high-dimensional deconvolution
We study the estimation of the covariance matrix $\Sigma$ of a $p$-dimensional normal random vector based on $n$ independent observations corrupted by additive noise. Only a general nonparametric assumption is imposed on the distribution of the noise without any sparsity constraint on its covariance matrix. In this h...
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Dynamic controllers for column synchronization of rotation matrices: a QR-factorization approach
In the multi-agent systems setting, this paper addresses continuous-time distributed synchronization of columns of rotation matrices. More precisely, k specific columns shall be synchronized and only the corresponding k columns of the relative rotations between the agents are assumed to be available for the control d...
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The ELEGANT NMR Spectrometer
Compact and portable in-situ NMR spectrometers which can be dipped in the liquid to be measured, and are easily maintained, with affordable coil constructions and electronics, together with an apparatus to recover depleted magnets are presented, that provide a new real-time processing method for NMR spectrum acquisit...
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What Would a Graph Look Like in This Layout? A Machine Learning Approach to Large Graph Visualization
Using different methods for laying out a graph can lead to very different visual appearances, with which the viewer perceives different information. Selecting a "good" layout method is thus important for visualizing a graph. The selection can be highly subjective and dependent on the given task. A common approach to ...
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A sure independence screening procedure for ultra-high dimensional partially linear additive models
We introduce a two-step procedure, in the context of ultra-high dimensional additive models, which aims to reduce the size of covariates vector and distinguish linear and nonlinear effects among nonzero components. Our proposed screening procedure, in the first step, is constructed based on the concept of cumulative ...
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Unbiased Multi-index Monte Carlo
We introduce a new class of Monte Carlo based approximations of expectations of random variables such that their laws are only available via certain discretizations. Sampling from the discretized versions of these laws can typically introduce a bias. In this paper, we show how to remove that bias, by introducing a ne...
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Hilbert Transformation and $r\mathrm{Spin}(n)+\mathbb{R}^n$ Group
In this paper we study symmetry properties of the Hilbert transformation of several real variables in the Clifford algebra setting. In order to describe the symmetry properties we introduce the group $r\mathrm{Spin}(n)+\mathbb{R}^n, r>0,$ which is essentially an extension of the ax+b group. The study concludes that t...
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Asymptotic limit and decay estimates for a class of dissipative linear hyperbolic systems in several dimensions
In this paper, we study the large-time behavior of solutions to a class of partially dissipative linear hyperbolic systems with applications in velocity-jump processes in several dimensions. Given integers $n,d\ge 1$, let $\mathbf A:=(A^1,\dots,A^d)\in (\mathbb R^{n\times n})^d$ be a matrix-vector, where $A^j\in\math...
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(G, μ)-displays and Rapoport-Zink spaces
Let (G, \mu) be a pair of a reductive group G over the p-adic integers and a minuscule cocharacter {\mu} of G defined over an unramified extension. We introduce and study "(G, \mu)-displays" which generalize Zink's Witt vector displays. We use these to define certain Rapoport-Zink formal schemes purely group theoreti...
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Selecting Representative Examples for Program Synthesis
Program synthesis is a class of regression problems where one seeks a solution, in the form of a source-code program, mapping the inputs to their corresponding outputs exactly. Due to its precise and combinatorial nature, program synthesis is commonly formulated as a constraint satisfaction problem, where input-outpu...
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Semistable rank 2 sheaves with singularities of mixed dimension on $\mathbb{P}^3$
We describe new irreducible components of the Gieseker-Maruyama moduli scheme $\mathcal{M}(3)$ of semistable rank 2 coherent sheaves with Chern classes $c_1=0,\ c_2=3,\ c_3=0$ on $\mathbb{P}^3$, general points of which correspond to sheaves whose singular loci contain components of dimensions both 0 and 1. These shea...
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From jamming to collective cell migration through a boundary induced transition
Cell monolayers provide an interesting example of active matter, exhibiting a phase transition from a flowing to jammed state as they age. Here we report experiments and numerical simulations illustrating how a jammed cellular layer rapidly reverts to a flowing state after a wound. Quantitative comparison between exp...
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An Approximate Bayesian Long Short-Term Memory Algorithm for Outlier Detection
Long Short-Term Memory networks trained with gradient descent and back-propagation have received great success in various applications. However, point estimation of the weights of the networks is prone to over-fitting problems and lacks important uncertainty information associated with the estimation. However, exact ...
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Estimates of covering type and the number of vertices of minimal triangulations
The covering type of a space $X$ is defined as the minimal cardinality of a good cover of a space that is homotopy equivalent to $X$. We derive estimates for the covering type of $X$ in terms of other invariants of $X$, namely the ranks of the homology groups, the multiplicative structure of the cohomology ring and t...
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Principal Floquet subspaces and exponential separations of type II with applications to random delay differential equations
This paper deals with the study of principal Lyapunov exponents, principal Floquet subspaces, and exponential separation for positive random linear dynamical systems in ordered Banach spaces. The main contribution lies in the introduction of a new type of exponential separation, called of type II, important for its a...
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DNA insertion mutations can be predicted by a periodic probability function
It is generally difficult to predict the positions of mutations in genomic DNA at the nucleotide level. Retroviral DNA insertion is one mode of mutation, resulting in host infections that are difficult to treat. This mutation process involves the integration of retroviral DNA into the host-infected cellular genomic D...
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Machine Learning Molecular Dynamics for the Simulation of Infrared Spectra
Machine learning has emerged as an invaluable tool in many research areas. In the present work, we harness this power to predict highly accurate molecular infrared spectra with unprecedented computational efficiency. To account for vibrational anharmonic and dynamical effects -- typically neglected by conventional qu...
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Statistically Optimal and Computationally Efficient Low Rank Tensor Completion from Noisy Entries
In this article, we develop methods for estimating a low rank tensor from noisy observations on a subset of its entries to achieve both statistical and computational efficiencies. There have been a lot of recent interests in this problem of noisy tensor completion. Much of the attention has been focused on the fundam...
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The cohomology of the full directed graph complex
In his seminal paper "Formality conjecture", M. Kontsevich introduced a graph complex $GC_{1ve}$ closely connected with the problem of constructing a formality quasi-isomorphism for Hochschild cochains. In this paper, we express the cohomology of the full directed graph complex explicitly in terms of the cohomology o...
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Model equations and structures formation for the media with memory
We propose new types of models of the appearance of small- and large scale structures in media with memory, including a hyperbolic modification of the Navier-Stokes equations and a class of dynamical low-dimensional models with memory effects. On the basis of computer modeling, the formation of the small-scale struct...
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On the Support Recovery of Jointly Sparse Gaussian Sources using Sparse Bayesian Learning
In this work, we provide non-asymptotic, probabilistic guarantees for successful sparse support recovery by the multiple sparse Bayesian learning (M-SBL) algorithm in the multiple measurement vector (MMV) framework. For joint sparse Gaussian sources, we show that M-SBL perfectly recovers their common nonzero support ...
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A Critical-like Collective State Leads to Long-range Cell Communication in Dictyostelium discoideum Aggregation
The transition from single-cell to multicellular behavior is important in early development but rarely studied. The starvation-induced aggregation of the social amoeba Dictyostelium discoideum into a multicellular slug is known to result from single-cell chemotaxis towards emitted pulses of cyclic adenosine monophosp...
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Twistor theory at fifty: from contour integrals to twistor strings
We review aspects of twistor theory, its aims and achievements spanning thelast five decades. In the twistor approach, space--time is secondary with events being derived objects that correspond to compact holomorphic curves in a complex three--fold -- the twistor space. After giving an elementary construction of this...
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Strong convergence rates of probabilistic integrators for ordinary differential equations
Probabilistic integration of a continuous dynamical system is a way of systematically introducing model error, at scales no larger than errors introduced by standard numerical discretisation, in order to enable thorough exploration of possible responses of the system to inputs. It is thus a potentially useful approac...
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The G-centre and gradable derived equivalences
We propose a generalisation for the notion of the centre of an algebra in the setup of algebras graded by an arbitrary abelian group G. Our generalisation, which we call the G-centre, is designed to control the endomorphism category of the grading shift functors. We show that the G-centre is preserved by gradable der...
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RFCDE: Random Forests for Conditional Density Estimation
Random forests is a common non-parametric regression technique which performs well for mixed-type data and irrelevant covariates, while being robust to monotonic variable transformations. Existing random forest implementations target regression or classification. We introduce the RFCDE package for fitting random fore...
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The symplectic approach of gauged linear $σ$-model
Witten's Gauged Linear $\sigma$-Model (GLSM) unifies the Gromov-Witten theory and the Landau-Ginzburg theory, and provides a global perspective on mirror symmetry. In this article, we summarize a mathematically rigorous construction of the GLSM in the geometric phase using methods from symplectic geometry.
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