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A Consistent Bayesian Formulation for Stochastic Inverse Problems Based on Push-forward Measures
We formulate, and present a numerical method for solving, an inverse problem for inferring parameters of a deterministic model from stochastic observational data (quantities of interest). The solution, given as a probability measure, is derived using a Bayesian updating approach for measurable maps that finds a poste...
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Coherent State Mapping Ring-Polymer Molecular Dynamics for Non-Adiabatic quantum propagations
We introduce the coherent state mapping ring-polymer molecular dynamics (CS-RPMD), a new method that accurately describes electronic non-adiabatic dynamics with explicit nuclear quantization. This new approach is derived by using coherent state mapping representation for the electronic degrees of freedom (DOF) and th...
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Stochastic Gradient Descent in Continuous Time: A Central Limit Theorem
Stochastic gradient descent in continuous time (SGDCT) provides a computationally efficient method for the statistical learning of continuous-time models, which are widely used in science, engineering, and finance. The SGDCT algorithm follows a (noisy) descent direction along a continuous stream of data. The paramete...
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KMS states on $C^*$-algebras associated to a family of $*$-commuting local homeomorphisms
We consider a family of $*$-commuting local homeomorphisms on a compact space, and build a compactly aligned product system of Hilbert bimodules (in the sense of Fowler). This product system has a Nica-Toeplitz algebra and a Cuntz-Pimsner algebra. Both algebras carry a gauge action of a higher-dimensional torus, and ...
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Multi-Labelled Value Networks for Computer Go
This paper proposes a new approach to a novel value network architecture for the game Go, called a multi-labelled (ML) value network. In the ML value network, different values (win rates) are trained simultaneously for different settings of komi, a compensation given to balance the initiative of playing first. The ML...
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Lifting high-dimensional nonlinear models with Gaussian regressors
We study the problem of recovering a structured signal $\mathbf{x}_0$ from high-dimensional data $\mathbf{y}_i=f(\mathbf{a}_i^T\mathbf{x}_0)$ for some nonlinear (and potentially unknown) link function $f$, when the regressors $\mathbf{a}_i$ are iid Gaussian. Brillinger (1982) showed that ordinary least-squares estima...
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Functional Conceptual Substratum as a New Cognitive Mechanism for Mathematical Creation
We describe a new cognitive ability, i.e., functional conceptual substratum, used implicitly in the generation of several mathematical proofs and definitions. Furthermore, we present an initial (first-order) formalization of this mechanism together with its relation to classic notions like primitive positive definabi...
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Applying Gromov's Amenable Localization to Geodesic Flows
Let $M$ be a compact connected smooth Riemannian $n$-manifold with boundary. We combine Gromov's amenable localization technique with the Poincaré duality to study the traversally generic geodesic flows on $SM$, the space of the spherical tangent bundle. Such flows generate stratifications of $SM$, governed by rich u...
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Modeling the Ellsberg Paradox by Argument Strength
We present a formal measure of argument strength, which combines the ideas that conclusions of strong arguments are (i) highly probable and (ii) their uncertainty is relatively precise. Likewise, arguments are weak when their conclusion probability is low or when it is highly imprecise. We show how the proposed measu...
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Correction to the paper "Some remarks on Davie's uniqueness theorem"
The property 4 in Proposition 2.3 from the paper "Some remarks on Davie's uniqueness theorem" is replaced with a weaker assertion which is sufficient for the proof of the main results. Technical details and improvements are given.
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An Estimation and Analysis Framework for the Rasch Model
The Rasch model is widely used for item response analysis in applications ranging from recommender systems to psychology, education, and finance. While a number of estimators have been proposed for the Rasch model over the last decades, the available analytical performance guarantees are mostly asymptotic. This paper...
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Do planets remember how they formed?
One of the most directly observable features of a transiting multi-planet system is their size-ordering when ranked in orbital separation. Kepler has revealed a rich diversity of outcomes, from perfectly ordered systems, like Kepler-80, to ostensibly disordered systems, like Kepler-20. Under the hypothesis that syste...
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Demarcating circulation regimes of synchronously rotating terrestrial planets within the habitable zone
We investigate the atmospheric dynamics of terrestrial planets in synchronous rotation within the habitable zone of low-mass stars using the Community Atmosphere Model (CAM). The surface temperature contrast between day and night hemispheres decreases with an increase in incident stellar flux, which is opposite the t...
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Versatile Large-Area Custom-Feature van der Waals Epitaxy of Topological Insulators
As the focus of applied research in topological insulators (TI) evolves, the need to synthesize large-area TI films for practical device applications takes center stage. However, constructing scalable and adaptable processes for high-quality TI compounds remains a challenge. To this end, a versatile van der Waals epi...
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Sharp off-diagonal weighted norm estimates for the Bergman projection
We prove that for $1<p\le q<\infty$, $qp\geq {p'}^2$ or $p'q'\geq q^2$, $\frac{1}{p}+\frac{1}{p'}=\frac{1}{q}+\frac{1}{q'}=1$, $$\|\omega P_\alpha(f)\|_{L^p(\mathcal{H},y^{\alpha+(2+\alpha)(\frac{q}{p}-1)}dxdy)}\le C_{p,q,\alpha}[\omega]_{B_{p,q,\alpha}}^{(\frac{1}{p'}+\frac{1}{q})\max\{1,\frac{p'}{q}\}}\|\omega f\|_...
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An Automated Scalable Framework for Distributing Radio Astronomy Processing Across Clusters and Clouds
The Low Frequency Array (LOFAR) radio telescope is an international aperture synthesis radio telescope used to study the Universe at low frequencies. One of the goals of the LOFAR telescope is to conduct deep wide-field surveys. Here we will discuss a framework for the processing of the LOFAR Two Meter Sky Survey (Lo...
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Learning multiple visual domains with residual adapters
There is a growing interest in learning data representations that work well for many different types of problems and data. In this paper, we look in particular at the task of learning a single visual representation that can be successfully utilized in the analysis of very different types of images, from dog breeds to...
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Cosmic quantum optical probing of quantum gravity through a gravitational lensLens
We consider the nonunitary quantum dynamics of neutral massless scalar particles used to model photons around a massive gravitational lens. The gravitational interaction between the lensing mass and asymptotically free particles is described by their second-quantized scattering wavefunctions. Remarkably, the zero-poi...
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Combinatorial Miller-Hagberg Algorithm for Randomization of Dense Networks
We propose a slightly revised Miller-Hagberg (MH) algorithm that efficiently generates a random network from a given expected degree sequence. The revision was to replace the approximated edge probability between a pair of nodes with a combinatorically calculated edge probability that better captures the likelihood o...
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Topological Insulators in Random Lattices
Our understanding of topological insulators is based on an underlying crystalline lattice where the local electronic degrees of freedom at different sites hybridize with each other in ways that produce nontrivial band topology, and the search for material systems to realize such phases have been strongly influenced b...
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DiGrad: Multi-Task Reinforcement Learning with Shared Actions
Most reinforcement learning algorithms are inefficient for learning multiple tasks in complex robotic systems, where different tasks share a set of actions. In such environments a compound policy may be learnt with shared neural network parameters, which performs multiple tasks concurrently. However such compound pol...
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Narratives of Quantum Theory in the Age of Quantum Technologies
Quantum technologies can be presented to the public with or without introducing a strange trait of quantum theory responsible for their non-classical efficiency. Traditionally the message was centered on the superposition principle, while entanglement and properties such as contextuality have been gaining ground rece...
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Is Information in the Brain Represented in Continuous or Discrete Form?
The question of continuous-versus-discrete information representation in the brain is a fundamental yet unresolved physiological question. Historically, most analyses assume a continuous representation without considering the alternative possibility of a discrete representation. Our work explores the plausibility of ...
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Real-Time Background Subtraction Using Adaptive Sampling and Cascade of Gaussians
Background-Foreground classification is a fundamental well-studied problem in computer vision. Due to the pixel-wise nature of modeling and processing in the algorithm, it is usually difficult to satisfy real-time constraints. There is a trade-off between the speed (because of model complexity) and accuracy. Inspired...
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Multilevel nested simulation for efficient risk estimation
We investigate the problem of computing a nested expectation of the form $\mathbb{P}[\mathbb{E}[X|Y] \!\geq\!0]\!=\!\mathbb{E}[\textrm{H}(\mathbb{E}[X|Y])]$ where $\textrm{H}$ is the Heaviside function. This nested expectation appears, for example, when estimating the probability of a large loss from a financial port...
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Construction of a relativistic Ornstein-Uhlenbeck process
Based on a version of Dudley's Wiener process on the mass shell in the momentum Minkowski space of a massive point particle, a model of a relativistic Ornstein--Uhlenbeck process is constructed by addition of a specific drift term. The invariant distribution of this momentum process as well as other associated proces...
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Safe Trajectory Synthesis for Autonomous Driving in Unforeseen Environments
Path planning for autonomous vehicles in arbitrary environments requires a guarantee of safety, but this can be impractical to ensure in real-time when the vehicle is described with a high-fidelity model. To address this problem, this paper develops a method to perform trajectory design by considering a low-fidelity ...
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A Data and Model-Parallel, Distributed and Scalable Framework for Training of Deep Networks in Apache Spark
Training deep networks is expensive and time-consuming with the training period increasing with data size and growth in model parameters. In this paper, we provide a framework for distributed training of deep networks over a cluster of CPUs in Apache Spark. The framework implements both Data Parallelism and Model Par...
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ICLabel: An automated electroencephalographic independent component classifier, dataset, and website
The electroencephalogram (EEG) provides a non-invasive, minimally restrictive, and relatively low cost measure of mesoscale brain dynamics with high temporal resolution. Although signals recorded in parallel by multiple, near-adjacent EEG scalp electrode channels are highly-correlated and combine signals from many di...
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Inference on a New Class of Sample Average Treatment Effects
We derive new variance formulas for inference on a general class of estimands of causal average treatment effects in a Randomized Control Trial (RCT). We generalize Robins (1988) and show that when the estimand of interest is the Sample Average Treatment Effect of the Treated (SATT or SATC for controls), a consistent...
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A split step Fourier/discontinuous Galerkin scheme for the Kadomtsev--Petviashvili equation
In this paper we propose a method to solve the Kadomtsev--Petviashvili equation based on splitting the linear part of the equation from the nonlinear part. The linear part is treated using FFTs, while the nonlinear part is approximated using a semi-Lagrangian discontinuous Galerkin approach of arbitrary order. We dem...
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Dense Transformer Networks
The key idea of current deep learning methods for dense prediction is to apply a model on a regular patch centered on each pixel to make pixel-wise predictions. These methods are limited in the sense that the patches are determined by network architecture instead of learned from data. In this work, we propose the den...
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Tetragonal CH3NH3PbI3 Is Ferroelectric
Halide perovskite (HaP) semiconductors are revolutionizing photovoltaic (PV) solar energy conversion by showing remarkable performance of solar cells made with esp. tetragonal methylammonium lead tri-iodide (MAPbI3). In particular, the low voltage loss of these cells implies a remarkably low recombination rate of pho...
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A Simple and Efficient MapReduce Algorithm for Data Cube Materialization
Data cube materialization is a classical database operator introduced in Gray et al.~(Data Mining and Knowledge Discovery, Vol.~1), which is critical for many analysis tasks. Nandi et al.~(Transactions on Knowledge and Data Engineering, Vol.~6) first studied cube materialization for large scale datasets using the Map...
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Group Invariance, Stability to Deformations, and Complexity of Deep Convolutional Representations
The success of deep convolutional architectures is often attributed in part to their ability to learn multiscale and invariant representations of natural signals. However, a precise study of these properties and how they affect learning guarantees is still missing. In this paper, we consider deep convolutional repres...
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Completion of High Order Tensor Data with Missing Entries via Tensor-train Decomposition
In this paper, we aim at the completion problem of high order tensor data with missing entries. The existing tensor factorization and completion methods suffer from the curse of dimensionality when the order of tensor N>>3. To overcome this problem, we propose an efficient algorithm called TT-WOPT (Tensor-train Weigh...
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On the inner products of some Deligne--Lusztig type representations
In this paper we introduce a family of Deligne--Lusztig type varieties attached to connected reductive groups over quotients of discrete valuation rings, naturally generalising the higher Deligne--Lusztig varieties and some constructions related to the algebraisation problem raised by Lusztig. We establish the inner ...
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An invariant for embedded Fano manifolds covered by linear spaces
For an embedded Fano manifold $X$, we introduce a new invariant $S_X$ related to the dimension of covering linear spaces. The aim of this paper is to classify Fano manifolds $X$ which have large $S_X$.
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Delivery Latency Trade-Offs of Heterogeneous Contents in Fog Radio Access Networks
A Fog Radio Access Network (F-RAN) is a cellular wireless system that enables content delivery via the caching of popular content at edge nodes (ENs) and cloud processing. The existing information-theoretic analyses of F-RAN systems, and special cases thereof, make the assumption that all requests should be guarantee...
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Leaking Uninitialized Secure Enclave Memory via Structure Padding (Extended Abstract)
Intel software guard extensions (SGX) aims to provide an isolated execution environment, known as an enclave, for a user-level process to maximize its confidentiality and integrity. In this paper, we study how uninitialized data inside a secure enclave can be leaked via structure padding. We found that, during ECALL ...
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Asymptotic and numerical analysis of a stochastic PDE model of volume transmission
Volume transmission is an important neural communication pathway in which neurons in one brain region influence the neurotransmitter concentration in the extracellular space of a distant brain region. In this paper, we apply asymptotic analysis to a stochastic partial differential equation model of volume transmissio...
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Mixtures of Hidden Truncation Hyperbolic Factor Analyzers
The mixture of factor analyzers model was first introduced over 20 years ago and, in the meantime, has been extended to several non-Gaussian analogues. In general, these analogues account for situations with heavy tailed and/or skewed clusters. An approach is introduced that unifies many of these approaches into one ...
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Representations on Partially Holomorphic Cohomology Spaces, Revisited
This is a semi--expository update and rewrite of my 1974 AMS AMS Memoir describing Plancherel formulae and partial Dolbeault cohomology realizations for standard tempered representations for general real reductive Lie groups. Even after so many years, much of that Memoir is up to date, but of course there have been a...
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Underground tests of quantum mechanics. Whispers in the cosmic silence?
By performing X-rays measurements in the "cosmic silence" of the underground laboratory of Gran Sasso, LNGS-INFN, we test a basic principle of quantum mechanics: the Pauli Exclusion Principle (PEP), for electrons. We present the achieved results of the VIP experiment and the ongoing VIP2 measurement aiming to gain tw...
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Implications for Post-Processing Nucleosynthesis of Core-Collapse Supernova Models with Lagrangian Particles
We investigate core-collapse supernova (CCSN) nucleosynthesis with self-consistent, axisymmetric (2D) simulations performed using the radiation-hydrodynamics code Chimera. Computational costs have traditionally constrained the evolution of the nuclear composition within multidimensional CCSN models to, at best, a 14-...
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High Performance Parallel Image Reconstruction for New Vacuum Solar Telescope
Many technologies have been developed to help improve spatial resolution of observational images for ground-based solar telescopes, such as adaptive optics (AO) systems and post-processing reconstruction. As any AO system correction is only partial, it is indispensable to use post-processing reconstruction techniques...
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Approximation of Bandwidth for the Interactive Operation in Video on Demand System
An interactive session of video-on-demand (VOD) streaming procedure deserves smooth data transportation for the viewer, irrespective of their geographic location. To access the required video, bandwidth management during the video objects transportation at any interactive session is a mandatory prerequisite. It has b...
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Twisted Recurrence via Polynomial Walks
In this paper we show how polynomial walks can be used to establish a twisted recurrence for sets of positive density in $\mathbb{Z}^d$. In particular, we prove that if $\Gamma \leq \operatorname{GL}_d(\mathbb{Z})$ is finitely generated by unipotents and acts irreducibly on $\mathbb{R}^d$, then for any set $B \subset...
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Well-posedness and scattering for the Boltzmann equations: Soft potential with cut-off
We prove the global existence of the unique mild solution for the Cauchy problem of the cut-off Boltzmann equation for soft potential model $\gamma=2-N$ with initial data small in $L^N_{x,v}$ where $N=2,3$ is the dimension. The proof relies on the existing inhomogeneous Strichartz estimates for the kinetic equation b...
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Wikipedia in academia as a teaching tool: from averse to proactive faculty profiles
This study concerned the active use of Wikipedia as a teaching tool in the classroom in higher education, trying to identify different usage profiles and their characterization. A questionnaire survey was administrated to all full-time and part-time teachers at the Universitat Oberta de Catalunya and the Universitat ...
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A trans-disciplinary review of deep learning research for water resources scientists
Deep learning (DL), a new-generation of artificial neural network research, has transformed industries, daily lives and various scientific disciplines in recent years. DL represents significant progress in the ability of neural networks to automatically engineer problem-relevant features and capture highly complex da...
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A new NS3 Implementation of CCNx 1.0 Protocol
The ccns3Sim project is an open source implementation of the CCNx 1.0 protocols for the NS3 simulator. We describe the implementation and several important features including modularity and process delay simulation. The ccns3Sim implementation is a fresh NS3-specific implementation. Like NS3 itself, it uses C++98 sta...
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MultiRefactor: Automated Refactoring To Improve Software Quality
In this paper, a new approach is proposed for automated software maintenance. The tool is able to perform 26 different refactorings. It also contains a large selection of metrics to measure the impact of the refactorings on the software and six different search based optimization algorithms to improve the software. T...
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Learning Postural Synergies for Categorical Grasping through Shape Space Registration
Every time a person encounters an object with a given degree of familiarity, he/she immediately knows how to grasp it. Adaptation of the movement of the hand according to the object geometry happens effortlessly because of the accumulated knowledge of previous experiences grasping similar objects. In this paper, we p...
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Perturbations of self-adjoint operators in semifinite von Neumann algebras: Kato-Rosenblum theorem
In the paper, we prove an analogue of the Kato-Rosenblum theorem in a semifinite von Neumann algebra. Let $\mathcal{M}$ be a countably decomposable, properly infinite, semifinite von Neumann algebra acting on a Hilbert space $\mathcal{H}$ and let $\tau$ be a faithful normal semifinite tracial weight of $\mathcal M$. ...
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Dust radiative transfer modelling of the infrared ring around the magnetar SGR 1900$+$14
A peculiar infrared ring-like structure was discovered by {\em Spitzer} around the strongly magnetised neutron star SGR 1900$+$14. This infrared structure was suggested to be due to a dust-free cavity, produced by the SGR Giant Flare occurred in 1998, and kept illuminated by surrounding stars. Using a 3D dust radiati...
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Application of transfer matrix and transfer function analysis to grating-type dielectric laser accelerators: ponderomotive focusing of electrons
The question of suitability of transfer matrix description of electrons traversing grating-type dielectric laser acceleration (DLA) structures is addressed. It is shown that although matrix considerations lead to interesting insights, the basic transfer properties of DLA cells cannot be described by a matrix. A more ...
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Discretization-free Knowledge Gradient Methods for Bayesian Optimization
This paper studies Bayesian ranking and selection (R&S) problems with correlated prior beliefs and continuous domains, i.e. Bayesian optimization (BO). Knowledge gradient methods [Frazier et al., 2008, 2009] have been widely studied for discrete R&S problems, which sample the one-step Bayes-optimal point. When used o...
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Measuring the Robustness of Graph Properties
In this paper, we propose a perturbation framework to measure the robustness of graph properties. Although there are already perturbation methods proposed to tackle this problem, they are limited by the fact that the strength of the perturbation cannot be well controlled. We firstly provide a perturbation framework o...
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Better Software Analytics via "DUO": Data Mining Algorithms Using/Used-by Optimizers
This paper claims that a new field of empirical software engineering research and practice is emerging: data mining using/used-by optimizers for empirical studies, or DUO. For example, data miners can generate the models that are explored by optimizers.Also, optimizers can advise how to best adjust the control parame...
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Lesion detection and Grading of Diabetic Retinopathy via Two-stages Deep Convolutional Neural Networks
We propose an automatic diabetic retinopathy (DR) analysis algorithm based on two-stages deep convolutional neural networks (DCNN). Compared to existing DCNN-based DR detection methods, the proposed algorithm have the following advantages: (1) Our method can point out the location and type of lesions in the fundus im...
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DRYVR:Data-driven verification and compositional reasoning for automotive systems
We present the DRYVR framework for verifying hybrid control systems that are described by a combination of a black-box simulator for trajectories and a white-box transition graph specifying mode switches. The framework includes (a) a probabilistic algorithm for learning sensitivity of the continuous trajectories from...
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Deep Reinforcement Learning for Programming Language Correction
Novice programmers often struggle with the formal syntax of programming languages. To assist them, we design a novel programming language correction framework amenable to reinforcement learning. The framework allows an agent to mimic human actions for text navigation and editing. We demonstrate that the agent can be ...
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Dispersionless and multicomponent BKP hierarchies with quantum torus symmetries
In this article, we will construct the additional perturbative quantum torus symmetry of the dispersionless BKP hierarchy basing on the $W_{\infty}$ infinite dimensional Lie symmetry. These results show that the complete quantum torus symmetry is broken from the BKP hierarchy to its dispersionless hierarchy. Further ...
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A Sampling Framework for Solving Physics-driven Inverse Source Problems
Partial differential equations are central to describing many physical phenomena. In many applications these phenomena are observed through a sensor network, with the aim of inferring their underlying properties. Leveraging from certain results in sampling and approximation theory, we present a new framework for solv...
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An Application of $h$-principle to Manifold Calculus
Manifold calculus is a form of functor calculus that analyzes contravariant functors from some categories of manifolds to topological spaces by providing analytic approximations to them. In this paper we apply the theory of h-principle to construct several examples of analytic functors in this sense. We prove that th...
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Grasping Unknown Objects in Clutter by Superquadric Representation
In this paper, a quick and efficient method is presented for grasping unknown objects in clutter. The grasping method relies on real-time superquadric (SQ) representation of partial view objects and incomplete object modelling, well suited for unknown symmetric objects in cluttered scenarios which is followed by opti...
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Learning to Play with Intrinsically-Motivated Self-Aware Agents
Infants are experts at playing, with an amazing ability to generate novel structured behaviors in unstructured environments that lack clear extrinsic reward signals. We seek to mathematically formalize these abilities using a neural network that implements curiosity-driven intrinsic motivation. Using a simple but eco...
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$\ell_1$-minimization method for link flow correction
A computational method, based on $\ell_1$-minimization, is proposed for the problem of link flow correction, when the available traffic flow data on many links in a road network are inconsistent with respect to the flow conservation law. Without extra information, the problem is generally ill-posed when a large porti...
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Current Flow Group Closeness Centrality for Complex Networks
Current flow closeness centrality (CFCC) has a better discriminating ability than the ordinary closeness centrality based on shortest paths. In this paper, we extend this notion to a group of vertices in a weighted graph, and then study the problem of finding a subset $S$ of $k$ vertices to maximize its CFCC $C(S)$, ...
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Visualization of Constraint Handling Rules: Semantics and Applications
The work in the paper presents an animation extension ($CHR^{vis}$) to Constraint Handling Rules (CHR). Visualizations have always helped programmers understand data and debug programs. A picture is worth a thousand words. It can help identify where a problem is or show how something works. It can even illustrate a r...
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Simplified Energy Landscape for Modularity Using Total Variation
Networks capture pairwise interactions between entities and are frequently used in applications such as social networks, food networks, and protein interaction networks, to name a few. Communities, cohesive groups of nodes, often form in these applications, and identifying them gives insight into the overall organiza...
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A Hard Look at the Neutron Stars and Accretion Disks in 4U 1636-53, GX 17+2, and 4U 1705-44 with $\emph{NuSTAR}$
We present $\emph{NuSTAR}$ observations of neutron star (NS) low-mass X-ray binaries: 4U 1636-53, GX 17+2, and 4U 1705-44. We observed 4U 1636-53 in the hard state, with an Eddington fraction, $F_{\mathrm{Edd}}$, of 0.01; GX 17+2 and 4U 1705-44 were in the soft state with fractions of 0.57 and 0.10, respectively. Eac...
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Approximating Weighted Duo-Preservation in Comparative Genomics
Motivated by comparative genomics, Chen et al. [9] introduced the Maximum Duo-preservation String Mapping (MDSM) problem in which we are given two strings $s_1$ and $s_2$ from the same alphabet and the goal is to find a mapping $\pi$ between them so as to maximize the number of duos preserved. A duo is any two consec...
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On the virtual singular braid monoid
We study the algebraic structures of the virtual singular braid monoid, $VSB_n$, and the virtual singular pure braid monoid, $VSP_n$. The monoid $VSB_n$ is the splittable extension of $VSP_n$ by the symmetric group $S_n$. We also construct a representation of $VSB_n$.
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Discrete Games in Endogenous Networks: Equilibria and Policy
In games of friendship links and behaviors, I propose $k$-player Nash stability---a family of equilibria, indexed by a measure of robustness given by the number of permitted link changes, which is (ordinally and cardinally) ranked in a probabilistic sense. Application of the proposed framework to adolescents' tobacco...
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Evaluating regulatory reform of network industries: a survey of empirical models based on categorical proxies
Proxies for regulatory reforms based on categorical variables are increasingly used in empirical evaluation models. We surveyed 63 studies that rely on such indices to analyze the effects of entry liberalization, privatization, unbundling, and independent regulation of the electricity, natural gas, and telecommunicat...
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Theory of ground states for classical Heisenberg spin systems II
We apply the theory of ground states for classical, finite, Heisenberg spin systems previously published to a couple of spin systems that can be considered as finite models $K_{12},\,K_{15}$ and $K_{18}$ of the AF Kagome lattice. The model $K_{12}$ is isomorphic to the cuboctahedron. In particular, we find three-dime...
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Relative Property (T) for Nilpotent Subgroups
We show that relative Property (T) for the abelianization of a nilpotent normal subgroup implies relative Property (T) for the subgroup itself. This and other results are a consequence of a theorem of independent interest, which states that if $H$ is a closed subgroup of a locally compact group $G$, and $A$ is a clos...
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Discriminant analysis in small and large dimensions
We study the distributional properties of the linear discriminant function under the assumption of normality by comparing two groups with the same covariance matrix but different mean vectors. A stochastic representation for the discriminant function coefficients is derived which is then used to obtain their asymptot...
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Sparse Bayesian Inference for Dense Semantic Mapping
Despite impressive advances in simultaneous localization and mapping, dense robotic mapping remains challenging due to its inherent nature of being a high-dimensional inference problem. In this paper, we propose a dense semantic robotic mapping technique that exploits sparse Bayesian models, in particular, the releva...
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Singularities and Semistable Degenerations for Symplectic Topology
We overview our recent work defining and studying normal crossings varieties and subvarieties in symplectic topology. This work answers a question of Gromov on the feasibility of introducing singular (sub)varieties into symplectic topology in the case of normal crossings singularities. It also provides a necessary an...
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One-step Local M-estimator for Integrated Jump-Diffusion Models
In this paper, robust nonparametric estimators, instead of local linear estimators, are adapted for infinitesimal coefficients associated with integrated jump-diffusion models to avoid the impact of outliers on accuracy. Furthermore, consider the complexity of iteration of the solution for local M-estimator, we propo...
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Python Open Source Waveform Extractor (POWER): An open source, Python package to monitor and post-process numerical relativity simulations
Numerical simulations of Einstein's field equations provide unique insights into the physics of compact objects moving at relativistic speeds, and which are driven by strong gravitational interactions. Numerical relativity has played a key role to firmly establish gravitational wave astrophysics as a new field of res...
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Uniform confidence bands for nonparametric errors-in-variables regression
This paper develops a method to construct uniform confidence bands for a nonparametric regression function where a predictor variable is subject to a measurement error. We allow for the distribution of the measurement error to be unknown, but assume that there is an independent sample from the measurement error distr...
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Unconventional superconductivity in the BiS$_2$-based layered superconductor NdO$_{0.71}$F$_{0.29}$BiS$_2$
We investigate the superconducting-gap anisotropy in one of the recently discovered BiS$_2$-based superconductors, NdO$_{0.71}$F$_{0.29}$BiS$_2$ ($T_c$ $\sim$ 5 K), using laser-based angle-resolved photoemission spectroscopy. Whereas the previously discovered high-$T_c$ superconductors such as copper oxides and iron-...
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Low noise sensitivity analysis of Lq-minimization in oversampled systems
The class of Lq-regularized least squares (LQLS) are considered for estimating a p-dimensional vector \b{eta} from its n noisy linear observations y = X\b{eta}+w. The performance of these schemes are studied under the high-dimensional asymptotic setting in which p grows linearly with n. In this asymptotic setting, ph...
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Robust Transceiver Design Based on Interference Alignment for Multi-User Multi-Cell MIMO Networks with Channel Uncertainty
In this paper, we firstly exploit the inter-user interference (IUI) and inter-cell interference (ICI) as useful references to develop a robust transceiver design based on interference alignment for a downlink multi-user multi-cell multiple-input multiple-output (MIMO) interference network under channel estimation err...
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Machine learning quantum mechanics: solving quantum mechanics problems using radial basis function networks
Inspired by the recent work of Carleo and Troyer[1], we apply machine learning methods to quantum mechanics in this article. The radial basis function network in a discrete basis is used as the variational wavefunction for the ground state of a quantum system. Variational Monte Carlo(VMC) calculations are carried out...
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Scale-free networks are rare
A central claim in modern network science is that real-world networks are typically "scale free," meaning that the fraction of nodes with degree $k$ follows a power law, decaying like $k^{-\alpha}$, often with $2 < \alpha < 3$. However, empirical evidence for this belief derives from a relatively small number of real...
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Enlargeability, foliations, and positive scalar curvature
We extend the deep and important results of Lichnerowicz, Connes, and Gromov-Lawson which relate geometry and characteristic numbers to the existence and non-existence of metrics of positive scalar curvature (PSC). In particular, we show: that a spin foliation with Hausdorff homotopy groupoid of an enlargeable manifo...
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A simple mathematical model for unemployment: a case study in Portugal with optimal control
We propose a simple mathematical model for unemployment. Despite its simpleness, we claim that the model is more realistic and useful than recent models available in the literature. A case study with real data from Portugal supports our claim. An optimal control problem is formulated and solved, which provides some n...
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Interpreting Deep Neural Networks Through Variable Importance
While the success of deep neural networks (DNNs) is well-established across a variety of domains, our ability to explain and interpret these methods is limited. Unlike previously proposed local methods which try to explain particular classification decisions, we focus on global interpretability and ask a universally ...
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Conformality of $1/N$ corrections in SYK-like models
The Sachdev-Ye--Kitaev is a quantum mechanical model of $N$ Majorana fermions which displays a number of appealing features -- solvability in the strong coupling regime, near-conformal invariance and maximal chaos -- which make it a suitable model for black holes in the context of the AdS/CFT holography. In this pape...
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Segal-type models of higher categories
Higher category theory is an exceedingly active area of research, whose rapid growth has been driven by its penetration into a diverse range of scientific fields. Its influence extends through key mathematical disciplines, notably homotopy theory, algebraic geometry and algebra, mathematical physics, to encompass imp...
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Low-Mass Dark Matter Search with CDMSlite
The SuperCDMS experiment is designed to directly detect weakly interacting massive particles (WIMPs) that may constitute the dark matter in our Galaxy. During its operation at the Soudan Underground Laboratory, germanium detectors were run in the CDMSlite mode to gather data sets with sensitivity specifically for WIM...
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Gravity with free initial conditions: a solution to the cosmological constant problem testable by CMB B-mode polarization
In standard general relativity the universe cannot be started with arbitrary initial conditions, because four of the ten components of the Einstein's field equations (EFE) are constraints on initial conditions. In the previous work it was proposed to extend the gravity theory to allow free initial conditions, with a ...
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Gradual Learning of Recurrent Neural Networks
Recurrent Neural Networks (RNNs) achieve state-of-the-art results in many sequence-to-sequence modeling tasks. However, RNNs are difficult to train and tend to suffer from overfitting. Motivated by the Data Processing Inequality (DPI), we formulate the multi-layered network as a Markov chain, introducing a training m...
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Borel subsets of the real line and continuous reducibility
We study classes of Borel subsets of the real line $\mathbb{R}$ such as levels of the Borel hierarchy and the class of sets that are reducible to the set $\mathbb{Q}$ of rationals, endowed with the Wadge quasi-order of reducibility with respect to continuous functions on $\mathbb{R}$. Notably, we explore several stru...
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Pairing from dynamically screened Coulomb repulsion in bismuth
Recently, Prakash et. al. have discovered bulk superconductivity in single crystals of bismuth, which is a semi metal with extremely low carrier density. At such low density, we argue that conventional electron-phonon coupling is too weak to be responsible for the binding of electrons into Cooper pairs. We study a dy...
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