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Torsion of elliptic curves and unlikely intersections
We study effective versions of unlikely intersections of images of torsion points of elliptic curves on the projective line.
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BoostJet: Towards Combining Statistical Aggregates with Neural Embeddings for Recommendations
Recommenders have become widely popular in recent years because of their broader applicability in many e-commerce applications. These applications rely on recommenders for generating advertisements for various offers or providing content recommendations. However, the quality of the generated recommendations depends o...
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Fixed points of diffeomorphisms on nilmanifolds with a free nilpotent fundamental group
Let $M$ be a nilmanifold with a fundamental group which is free $2$-step nilpotent on at least 4 generators. We will show that for any nonnegative integer $n$ there exists a self-diffeomorphism $h_n$ of $M$ such that $h_n$ has exactly $n$ fixed points and any self-map $f$ of $M$ which is homotopic to $h_n$ has at lea...
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Offloading Execution from Edge to Cloud: a Dynamic Node-RED Based Approach
Fog computing enables use cases where data produced in end devices are stored, processed, and acted on directly at the edges of the network, yet computation can be offloaded to more powerful instances through the edge to cloud continuum. Such offloading mechanism is especially needed in case of modern multi-purpose I...
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A nested sampling code for targeted searches for continuous gravitational waves from pulsars
This document describes a code to perform parameter estimation and model selection in targeted searches for continuous gravitational waves from known pulsars using data from ground-based gravitational wave detectors. We describe the general workings of the code and characterise it on simulated data containing both no...
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Using Big Data to Enhance the Bosch Production Line Performance: A Kaggle Challenge
This paper describes our approach to the Bosch production line performance challenge run by Kaggle.com. Maximizing the production yield is at the heart of the manufacturing industry. At the Bosch assembly line, data is recorded for products as they progress through each stage. Data science methods are applied to this...
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Golden Elliptical Orbits in Newtonian Gravitation
In spherical symmetry with radial coordinate $r$, classical Newtonian gravitation supports circular orbits and, for $-1/r$ and $r^2$ potentials only, closed elliptical orbits [1]. Various families of elliptical orbits can be thought of as arising from the action of perturbations on corresponding circular orbits. We s...
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Learning Sparse Adversarial Dictionaries For Multi-Class Audio Classification
Audio events are quite often overlapping in nature, and more prone to noise than visual signals. There has been increasing evidence for the superior performance of representations learned using sparse dictionaries for applications like audio denoising and speech enhancement. This paper concentrates on modifying the t...
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Matter-wave solutions in the Bose-Einstein condensates with the harmonic and Gaussian potentials
We study exact solutions of the quasi-one-dimensional Gross-Pitaevskii (GP) equation with the (space, time)-modulated potential and nonlinearity and the time-dependent gain or loss term in Bose-Einstein condensates. In particular, based on the similarity transformation, we report several families of exact solutions o...
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Histogram Transform-based Speaker Identification
A novel text-independent speaker identification (SI) method is proposed. This method uses the Mel-frequency Cepstral coefficients (MFCCs) and the dynamic information among adjacent frames as feature sets to capture speaker's characteristics. In order to utilize dynamic information, we design super-MFCCs features by c...
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Towards self-adaptable robots: from programming to training machines
We argue that hardware modularity plays a key role in the convergence of Robotics and Artificial Intelligence (AI). We introduce a new approach for building robots that leads to more adaptable and capable machines. We present the concept of a self-adaptable robot that makes use of hardware modularity and AI technique...
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Incidence Results and Bounds of Trilinear and Quadrilinear Exponential Sums
We give a new bound on the number of collinear triples for two arbitrary subsets of a finite field. This improves on existing results which rely on the Cauchy inequality. We then us this to provide a new bound on trilinear and quadrilinear exponential sums.
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Comment on "Kinetic decoupling of WIMPs: Analytic expressions"
Visinelli and Gondolo (2015, hereafter VG15) derived analytic expressions for the evolution of the dark matter temperature in a generic cosmological model. They then calculated the dark matter kinetic decoupling temperature $T_{\mathrm{kd}}$ and compared their results to the Gelmini and Gondolo (2008, hereafter GG08)...
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Dimension preserving resolutions of singularities of Poisson structures
Some Poisson structures do admit resolutions by symplectic manifolds of the same dimension. We give examples and simple conditions under which such resolutions can not exist.
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Comparison of hidden Markov chain models and hidden Markov random field models in estimation of computed tomography images
There is an interest to replace computed tomography (CT) images with magnetic resonance (MR) images for a number of diagnostic and therapeutic workflows. In this article, predicting CT images from a number of magnetic resonance imaging (MRI) sequences using regression approach is explored. Two principal areas of appl...
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Spin-charge split pairing in underdoped cuprate superconductors: support from low-$T$ specific heat
We calculate the specific heat of a weakly interacting dilute system of bosons on a lattice and show that it is consistent with the measured electronic specific heat in the superconducting state of underdoped cuprates with boson concentration $\rho \sim x/2$, where $x$ is the hole (dopant) concentration. As usual, th...
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Iterative Amortized Inference
Inference models are a key component in scaling variational inference to deep latent variable models, most notably as encoder networks in variational auto-encoders (VAEs). By replacing conventional optimization-based inference with a learned model, inference is amortized over data examples and therefore more computat...
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Rethinking probabilistic prediction in the wake of the 2016 U.S. presidential election
To many statisticians and citizens, the outcome of the most recent U.S. presidential election represents a failure of data-driven methods on the grandest scale. This impression has led to much debate and discussion about how the election predictions went awry -- Were the polls inaccurate? Were the models wrong? Did w...
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$L^1$ solutions to one-dimensional BSDEs with sublinear growth generators in $z$
This paper aims at solving a one-dimensional backward stochastic differential equation (BSDE for short) with only integrable parameters. We first establish the existence of a minimal $L^1$ solution for the BSDE when the generator $g$ is stronger continuous in $(y,z)$ and monotonic in $y$ as well as it has a general g...
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Magnifying the early episodes of star formation: super star clusters at cosmological distances
We study the spectrophotometric properties of a highly magnified (\mu~40-70) pair of stellar systems identified at z=3.2222 behind the Hubble Frontier Field galaxy cluster MACS~J0416. Five multiple images (out of six) have been spectroscopically confirmed by means of VLT/MUSE and VLT/X-Shooter observations. Each imag...
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Ergodicity of a system of interacting random walks with asymmetric interaction
We study N interacting random walks on the positive integers. Each particle has drift {\delta} towards infinity, a reflection at the origin, and a drift towards particles with lower positions. This inhomogeneous mean field system is shown to be ergodic only when the interaction is strong enough. We focus on this latt...
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Extreme value statistics for censored data with heavy tails under competing risks
This paper addresses the problem of estimating, in the presence of random censoring as well as competing risks, the extreme value index of the (sub)-distribution function associated to one particular cause, in the heavy-tail case. Asymptotic normality of the proposed estimator (which has the form of an Aalen-Johansen...
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Response to "Counterexample to global convergence of DSOS and SDSOS hierarchies"
In a recent note [8], the author provides a counterexample to the global convergence of what his work refers to as "the DSOS and SDSOS hierarchies" for polynomial optimization problems (POPs) and purports that this refutes claims in our extended abstract [4] and slides in [3]. The goal of this paper is to clarify tha...
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Thermal memristor and neuromorphic networks for manipulating heat flow
A memristor is one of four fundamental two-terminal solid elements in electronics. In addition with the resistor, the capacitor and the inductor, this passive element relates the electric charges to current in solid state elements. Here we report the existence of a thermal analog for this element made with metal-insu...
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Asymptotic Distribution and Simultaneous Confidence Bands for Ratios of Quantile Functions
Ratio of medians or other suitable quantiles of two distributions is widely used in medical research to compare treatment and control groups or in economics to compare various economic variables when repeated cross-sectional data are available. Inspired by the so-called growth incidence curves introduced in poverty r...
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A Topological proof that $O_2$ is $2$-MCFL
We give a new proof of Salvati's theorem that the group language $O_2$ is $2$ multiple context free. Unlike Salvati's proof, our arguments do not use any idea specific to two-dimensions. This raises the possibility that the argument might generalize to $O_n$.
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Projected Variational Integrators for Degenerate Lagrangian Systems
We propose and compare several projection methods applied to variational integrators for degenerate Lagrangian systems, whose Lagrangian is of the form $L = \vartheta(q) \cdot \dot{q} - H(q)$ and thus linear in velocities. While previous methods for such systems only work reliably in the case of $\vartheta$ being a l...
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Boosted Generative Models
We propose a novel approach for using unsupervised boosting to create an ensemble of generative models, where models are trained in sequence to correct earlier mistakes. Our meta-algorithmic framework can leverage any existing base learner that permits likelihood evaluation, including recent deep expressive models. F...
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The Geometry of Strong Koszul Algebras
Koszul algebras with quadratic Groebner bases, called strong Koszul algebras, are studied. We introduce affine algebraic varieties whose points are in one-to-one correspondence with certain strong Koszul algebras and we investigate the connection between the varieties and the algebras.
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Overlapping community detection using superior seed set selection in social networks
Community discovery in the social network is one of the tremendously expanding areas which earn interest among researchers for the past one decade. There are many already existing algorithms. However, new seed-based algorithms establish an emerging drift in this area. The basic idea behind these strategies is to iden...
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Debugging Transactions and Tracking their Provenance with Reenactment
Debugging transactions and understanding their execution are of immense importance for developing OLAP applications, to trace causes of errors in production systems, and to audit the operations of a database. However, debugging transactions is hard for several reasons: 1) after the execution of a transaction, its inp...
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How LinkedIn Economic Graph Bonds Information and Product: Applications in LinkedIn Salary
The LinkedIn Salary product was launched in late 2016 with the goal of providing insights on compensation distribution to job seekers, so that they can make more informed decisions when discovering and assessing career opportunities. The compensation insights are provided based on data collected from LinkedIn members...
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Fast quantum logic gates with trapped-ion qubits
Quantum bits based on individual trapped atomic ions constitute a promising technology for building a quantum computer, with all the elementary operations having been achieved with the necessary precision for some error-correction schemes. However, the essential two-qubit logic gate used for generating quantum entang...
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Generative Adversarial Network based Autoencoder: Application to fault detection problem for closed loop dynamical systems
Fault detection problem for closed loop uncertain dynamical systems, is investigated in this paper, using different deep learning based methods. Traditional classifier based method does not perform well, because of the inherent difficulty of detecting system level faults for closed loop dynamical system. Specifically...
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Non-Asymptotic Rates for Manifold, Tangent Space, and Curvature Estimation
Given an $n$-sample drawn on a submanifold $M \subset \mathbb{R}^D$, we derive optimal rates for the estimation of tangent spaces $T\_X M$, the second fundamental form $II\_X^M$, and the submanifold $M$.After motivating their study, we introduce a quantitative class of $\mathcal{C}^k$-submanifolds in analogy with H{ö...
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Learning to Optimize Neural Nets
Learning to Optimize is a recently proposed framework for learning optimization algorithms using reinforcement learning. In this paper, we explore learning an optimization algorithm for training shallow neural nets. Such high-dimensional stochastic optimization problems present interesting challenges for existing rei...
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A space-time finite element method for neural field equations with transmission delays
We present and analyze a new space-time finite element method for the solution of neural field equations with transmission delays. The numerical treatment of these systems is rare in the literature and currently has several restrictions on the spatial domain and the functions involved, such as connectivity and delay ...
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Notes on complexity of packing coloring
A packing $k$-coloring for some integer $k$ of a graph $G=(V,E)$ is a mapping $\varphi:V\to\{1,\ldots,k\}$ such that any two vertices $u, v$ of color $\varphi(u)=\varphi(v)$ are in distance at least $\varphi(u)+1$. This concept is motivated by frequency assignment problems. The \emph{packing chromatic number} of $G$ ...
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Predicting Positive and Negative Links with Noisy Queries: Theory & Practice
Social networks involve both positive and negative relationships, which can be captured in signed graphs. The {\em edge sign prediction problem} aims to predict whether an interaction between a pair of nodes will be positive or negative. We provide theoretical results for this problem that motivate natural improvemen...
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Simulating a Topological Transition in a Superconducting Phase Qubit by Fast Adiabatic Trajectories
The significance of topological phases has been widely recognized in the community of condensed matter physics. The well controllable quantum systems provide an artificial platform to probe and engineer various topological phases. The adiabatic trajectory of a quantum state describes the change of the bulk Bloch eige...
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Improved Absolute Frequency Measurement of the 171Yb Optical Lattice Clock at KRISS Relative to the SI Second
We measured the absolute frequency of the $^1S_0$ - $^3P_0$ transition of $^{171}$Yb atoms confined in a one-dimensional optical lattice relative to the SI second. The determined frequency was 518 295 836 590 863.38(57) Hz. The uncertainty was reduced by a factor of 14 compared with our previously reported value in 2...
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Theoretical properties of quasi-stationary Monte Carlo methods
This paper gives foundational results for the application of quasi-stationarity to Monte Carlo inference problems. We prove natural sufficient conditions for the quasi-limiting distribution of a killed diffusion to coincide with a target density of interest. We also quantify the rate of convergence to quasi-stationar...
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A Hilbert Space of Stationary Ergodic Processes
Identifying meaningful signal buried in noise is a problem of interest arising in diverse scenarios of data-driven modeling. We present here a theoretical framework for exploiting intrinsic geometry in data that resists noise corruption, and might be identifiable under severe obfuscation. Our approach is based on unc...
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Total variation regularized non-negative matrix factorization for smooth hyperspectral unmixing
Hyperspectral analysis has gained popularity over recent years as a way to infer what materials are displayed on a picture whose pixels consist of a mixture of spectral signatures. Computing both signatures and mixture coefficients is known as unsupervised unmixing, a set of techniques usually based on non-negative m...
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Efficient Antihydrogen Detection in Antimatter Physics by Deep Learning
Antihydrogen is at the forefront of antimatter research at the CERN Antiproton Decelerator. Experiments aiming to test the fundamental CPT symmetry and antigravity effects require the efficient detection of antihydrogen annihilation events, which is performed using highly granular tracking detectors installed around ...
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Spin controlled atom-ion inelastic collisions
The control of the ultracold collisions between neutral atoms is an extensive and successful field of study. The tools developed allow for ultracold chemical reactions to be managed using magnetic fields, light fields and spin-state manipulation of the colliding particles among other methods. The control of chemical ...
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Nonparametric Cusum Charts for Angular Data with Applications in Health Science and Astrophysics
This paper develops non-parametric rotation invariant CUSUMs suited to the detection of changes in the mean direction as well as changes in the concentration parameter of angular data. The properties of the CUSUMs are illustrated by theoretical calculations, Monte Carlo simulation and application to sequentially obse...
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Origin of Weak Turbulence in the Outer Regions of Protoplanetary Disks
The mechanism behind angular momentum transport in protoplanetary disks, and whether this transport is turbulent in nature, is a fundamental issue in planet formation studies. Recent ALMA observations have suggested that turbulent velocities in the outer regions of these disks are less than ~5-10% of the sound speed,...
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Real-time Monocular Visual Odometry for Turbid and Dynamic Underwater Environments
In the context of robotic underwater operations, the visual degradations induced by the medium properties make difficult the exclusive use of cameras for localization purpose. Hence, most localization methods are based on expensive navigational sensors associated with acoustic positioning. On the other hand, visual o...
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Casper the Friendly Finality Gadget
We introduce Casper, a proof of stake-based finality system which overlays an existing proof of work blockchain. Casper is a partial consensus mechanism combining proof of stake algorithm research and Byzantine fault tolerant consensus theory. We introduce our system, prove some desirable features, and show defenses ...
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Rating Protocol Design for Extortion and Cooperation in the Crowdsourcing Contest Dilemma
Crowdsourcing has emerged as a paradigm for leveraging human intelligence and activity to solve a wide range of tasks. However, strategic workers will find enticement in their self-interest to free-ride and attack in a crowdsourcing contest dilemma game. Hence, incentive mechanisms are of great importance to overcome...
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Form factors of local operators in supersymmetric quantum integrable models
We apply the nested algebraic Bethe ansatz to the models with gl(2|1) and gl}(1|2) supersymmetry. We show that form factors of local operators in these models can be expressed in terms of the universal form factors. Our derivation is based on the use of the RTT-algebra only. It does not refer to any specific represen...
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On the $E$-polynomial of parabolic $\mathrm{Sp}_{2n}$-character varieties
We find the $E$-polynomials of a family of parabolic $\mathrm{Sp}_{2n}$-character varieties $\mathcal{M}^{\xi}_{n}$ of Riemann surfaces by constructing a stratification, proving that each stratum has polynomial count, applying a result of Katz regarding the counting functions, and finally adding up the resulting $E$-...
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Goldstone and Higgs Hydrodynamics in the BCS-BEC Crossover
We discuss the derivation of a low-energy effective field theory of phase (Goldstone) and amplitude (Higgs) modes of the pairing field from a microscopic theory of attractive fermions. The coupled equations for Goldstone and Higgs fields are critically analyzed in the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein ...
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A note on knot concordance and involutive knot Floer homology
We prove that if two knots are concordant, their involutive knot Floer complexes satisfy a certain type of stable equivalence.
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$M$-QAM Precoder Design for MIMO Directional Modulation Transceivers
Spectrally efficient multi-antenna wireless communication systems are a key challenge as service demands continue to increase. At the same time, powering up radio access networks is facing environmental and regulation limitations. In order to achieve more power efficiency, we design a directional modulation precoder ...
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Ivanov-Regularised Least-Squares Estimators over Large RKHSs and Their Interpolation Spaces
We study kernel least-squares estimation under a norm constraint. This form of regularisation is known as Ivanov regularisation and it provides better control of the norm of the estimator than the well-established Tikhonov regularisation. This choice of regularisation allows us to dispose of the standard assumption t...
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Using Ice and Dust Lines to Constrain the Surface Densities of Protoplanetary Disks
We present a novel method for determining the surface density of protoplanetary disks through consideration of disk 'dust lines' which indicate the observed disk radial scale at different observational wavelengths. This method relies on the assumption that the processes of particle growth and drift control the radial...
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Quaternionic Projective Bundle Theorem and Gysin Triangle in MW-Motivic Cohomology
In this paper, we show that the motive $HP^n$ of the quaternionic Grassmannian (as defined by I. Panin and C. Walter) splits in the category of effective MW-motives (as defined by B. Calmès, F. Déglise and J. Fasel). Moreover, we extend this result to an arbitrary symplectic bundle, obtaining the so-called quaternion...
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Green function for linearized Navier-Stokes around a boundary layer profile: near critical layers
This is a continuation and completion of the program (initiated in \cite{GrN1,GrN2}) to derive pointwise estimates on the Green function and sharp bounds on the semigroup of linearized Navier-Stokes around a generic stationary boundary layer profile. This is done via a spectral analysis approach and a careful study o...
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Summary of a Literature Review in Scalability of QoS-aware Service Composition
This paper shows that authors have no consistent way to characterize the scalability of their solutions, and so consider only a limited number of scaling characteristics. This review aimed at establishing the evidence that the route for designing and evaluating the scalability of dynamic QoS-aware service composition...
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Interacting superradiance samples: modified intensities and timescales, and frequency shifts
We consider the interaction between distinct superradiance (SR) systems and use the dressed state formalism to solve the case of two interacting two-atom SR samples at resonance. We show that the ensuing entanglement modifies the transition rates and intensities of radiation, as well as introduces a potentially measu...
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An optimal XP algorithm for Hamiltonian cycle on graphs of bounded clique-width
In this paper, we prove that, given a clique-width $k$-expression of an $n$-vertex graph, \textsc{Hamiltonian Cycle} can be solved in time $n^{\mathcal{O}(k)}$. This improves the naive algorithm that runs in time $n^{\mathcal{O}(k^2)}$ by Espelage et al. (WG 2001), and it also matches with the lower bound result by F...
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On the functional window of the avian compass
The functional window is an experimentally observed property of the avian compass that refers to its selectivity around the geomagnetic field strength. We show that the radical-pair model, using biologically feasible hyperfine parameters, can qualitatively explain the salient features of the avian compass as observed...
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Automated text summarisation and evidence-based medicine: A survey of two domains
The practice of evidence-based medicine (EBM) urges medical practitioners to utilise the latest research evidence when making clinical decisions. Because of the massive and growing volume of published research on various medical topics, practitioners often find themselves overloaded with information. As such, natural...
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Generalized Moran sets Generated by Step-wise Adjustable Iterated Function Systems
In this article we provide a systematic way of creating generalized Moran sets using an analogous iterated function system (IFS) procedure. We use a step-wise adjustable IFS to introduce some variance (such as non-self-similarity) in the fractal limit sets. The process retains the computational simplicity of a standa...
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On the lateral instability analysis of MEMS comb-drive electrostatic transducers
This paper investigates the lateral pull-in effect of an in-plane overlap-varying transducer. The instability is induced by the translational and rotational displacements. Based on the principle of virtual work, the equilibrium conditions of force and moment in lateral directions are derived. The analytical solutions...
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Isospectrality For Orbifold Lens Spaces
We answer Mark Kac's famous question, "can one hear the shape of a drum?" in the positive for orbifolds that are 3-dimensional and 4-dimensional lens spaces; we thus complete the answer to this question for orbifold lens spaces in all dimensions. We also show that the coefficients of the asymptotic expansion of the t...
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How Wrong Am I? - Studying Adversarial Examples and their Impact on Uncertainty in Gaussian Process Machine Learning Models
Machine learning models are vulnerable to Adversarial Examples: minor perturbations to input samples intended to deliberately cause misclassification. Current defenses against adversarial examples, especially for Deep Neural Networks (DNN), are primarily derived from empirical developments, and their security guarant...
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Energy Efficient Adaptive Network Coding Schemes for Satellite Communications
In this paper, we propose novel energy efficient adaptive network coding and modulation schemes for time variant channels. We evaluate such schemes under a realistic channel model for open area environments and Geostationary Earth Orbit (GEO) satellites. Compared to non-adaptive network coding and adaptive rate effic...
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DCCO: Towards Deformable Continuous Convolution Operators
Discriminative Correlation Filter (DCF) based methods have shown competitive performance on tracking benchmarks in recent years. Generally, DCF based trackers learn a rigid appearance model of the target. However, this reliance on a single rigid appearance model is insufficient in situations where the target undergoe...
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Multitarget search on complex networks: A logarithmic growth of global mean random cover time
We investigate multitarget search on complex networks and derive an exact expression for the mean random cover time that quantifies the expected time a walker needs to visit multiple targets. Based on this, we recover and extend some interesting results of multitarget search on networks. Specifically, we observe the ...
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New X-ray bound on density of primordial black holes
We set a new upper limit on the abundance of primordial black holes (PBH) based on existing X-ray data. PBH interactions with interstellar medium should result in significant fluxes of X-ray photons, which would contribute to the observed number density of compact X-ray objects in galaxies. The data constrain PBH num...
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Hierarchical Clustering with Prior Knowledge
Hierarchical clustering is a class of algorithms that seeks to build a hierarchy of clusters. It has been the dominant approach to constructing embedded classification schemes since it outputs dendrograms, which capture the hierarchical relationship among members at all levels of granularity, simultaneously. Being gr...
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Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations
We introduce physics informed neural networks -- neural networks that are trained to solve supervised learning tasks while respecting any given law of physics described by general nonlinear partial differential equations. In this second part of our two-part treatise, we focus on the problem of data-driven discovery o...
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The HoTT reals coincide with the Escardó-Simpson reals
Escardó and Simpson defined a notion of interval object by a universal property in any category with binary products. The Homotopy Type Theory book defines a higher-inductive notion of reals, and suggests that the interval may satisfy this universal property. We show that this is indeed the case in the category of se...
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Noise2Noise: Learning Image Restoration without Clean Data
We apply basic statistical reasoning to signal reconstruction by machine learning -- learning to map corrupted observations to clean signals -- with a simple and powerful conclusion: it is possible to learn to restore images by only looking at corrupted examples, at performance at and sometimes exceeding training usi...
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Simple Root Cause Analysis by Separable Likelihoods
Root Cause Analysis for Anomalies is challenging because of the trade-off between the accuracy and its explanatory friendliness, required for industrial applications. In this paper we propose a framework for simple and friendly RCA within the Bayesian regime under certain restrictions (that Hessian at the mode is dia...
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Jeffrey's prior sampling of deep sigmoidal networks
Neural networks have been shown to have a remarkable ability to uncover low dimensional structure in data: the space of possible reconstructed images form a reduced model manifold in image space. We explore this idea directly by analyzing the manifold learned by Deep Belief Networks and Stacked Denoising Autoencoders...
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Computing the quality of the Laplace approximation
Bayesian inference requires approximation methods to become computable, but for most of them it is impossible to quantify how close the approximation is to the true posterior. In this work, we present a theorem upper-bounding the KL divergence between a log-concave target density $f\left(\boldsymbol{\theta}\right)$ a...
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Correlations between thresholds and degrees: An analytic approach to model attacks and failure cascades
Two node variables determine the evolution of cascades in random networks: a node's degree and threshold. Correlations between both fundamentally change the robustness of a network, yet, they are disregarded in standard analytic methods as local tree or heterogeneous mean field approximations because of the bad tract...
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Faster Learning by Reduction of Data Access Time
Nowadays, the major challenge in machine learning is the Big Data challenge. The big data problems due to large number of data points or large number of features in each data point, or both, the training of models have become very slow. The training time has two major components: Time to access the data and time to p...
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Optimal Control for Constrained Coverage Path Planning
The problem of constrained coverage path planning involves a robot trying to cover maximum area of an environment under some constraints that appear as obstacles in the map. Out of the several coverage path planning methods, we consider augmenting the linear sweep-based coverage method to achieve minimum energy/ time...
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ScaleSimulator: A Fast and Cycle-Accurate Parallel Simulator for Architectural Exploration
Design of next generation computer systems should be supported by simulation infrastructure that must achieve a few contradictory goals such as fast execution time, high accuracy, and enough flexibility to allow comparison between large numbers of possible design points. Most existing architecture level simulators ar...
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Annihilating wild kernels
Let $L/K$ be a finite Galois extension of number fields with Galois group $G$. Let $p$ be an odd prime and $r>1$ be an integer. Assuming a conjecture of Schneider, we formulate a conjecture that relates special values of equivariant Artin $L$-series at $s=r$ to the compact support cohomology of the étale $p$-adic she...
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Trading the Twitter Sentiment with Reinforcement Learning
This paper is to explore the possibility to use alternative data and artificial intelligence techniques to trade stocks. The efficacy of the daily Twitter sentiment on predicting the stock return is examined using machine learning methods. Reinforcement learning(Q-learning) is applied to generate the optimal trading ...
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Kahler-Einstein metrics and algebraic geometry
This is a survey article, based on the author's lectures in the 2015 Current developments in Mathematics meeting; published in "Current developments in Mathematics". Version 2, references corrected and added.
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Hemihelical local minimizers in prestrained elastic bi-strips
We consider a double layered prestrained elastic rod in the limit of vanishing cross section. For the resulting limit Kirchoff-rod model with intrinsic curvature we prove a supercritical bifurcation result, rigorously showing the emergence of a branch of hemihelical local minimizers from the straight configuration, a...
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AspEm: Embedding Learning by Aspects in Heterogeneous Information Networks
Heterogeneous information networks (HINs) are ubiquitous in real-world applications. Due to the heterogeneity in HINs, the typed edges may not fully align with each other. In order to capture the semantic subtlety, we propose the concept of aspects with each aspect being a unit representing one underlying semantic fa...
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Nonlinear Information Bottleneck
Information bottleneck [IB] is a technique for extracting information in some `input' random variable that is relevant for predicting some different 'output' random variable. IB works by encoding the input in a compressed 'bottleneck variable' from which the output can then be accurately decoded. IB can be difficult ...
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Top-k Overlapping Densest Subgraphs: Approximation and Complexity
A central problem in graph mining is finding dense subgraphs, with several applications in different fields, a notable example being identifying communities. While a lot of effort has been put on the problem of finding a single dense subgraph, only recently the focus has been shifted to the problem of finding a set o...
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The energy-momentum tensor of electromagnetic fields in matter
We present a complete resolution of the Abraham-Minkowski controversy . This is done by considering several new aspects which invalidate previous discussions. We show that: 1)For polarized matter the center of mass theorem is no longer valid in its usual form. A contribution related to microscopic spin should be cons...
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Pinhole induced efficiency variation in perovskite solar cells
Process induced efficiency variation is a major concern for all thin film solar cells, including the emerging perovskite based solar cells. In this manuscript, we address the effect of pinholes or process induced surface coverage aspects on the efficiency of such solar cells through detailed numerical simulations. In...
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An Overview of Robust Subspace Recovery
This paper will serve as an introduction to the body of work on robust subspace recovery. Robust subspace recovery involves finding an underlying low-dimensional subspace in a dataset that is possibly corrupted with outliers. While this problem is easy to state, it has been difficult to develop optimal algorithms due...
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Tuning Free Orthogonal Matching Pursuit
Orthogonal matching pursuit (OMP) is a widely used compressive sensing (CS) algorithm for recovering sparse signals in noisy linear regression models. The performance of OMP depends on its stopping criteria (SC). SC for OMP discussed in literature typically assumes knowledge of either the sparsity of the signal to be...
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New constructions of MDS codes with complementary duals
Linear complementary-dual (LCD for short) codes are linear codes that intersect with their duals trivially. LCD codes have been used in certain communication systems. It is recently found that LCD codes can be applied in cryptography. This application of LCD codes renewed the interest in the construction of LCD codes...
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Porosity and regularity in metric measure spaces
This is a report of a joint work with E. Järvenpää, M. Järvenpää, T. Rajala, S. Rogovin, and V. Suomala. In [3], we characterized uniformly porous sets in $s$-regular metric spaces in terms of regular sets by verifying that a set $A$ is uniformly porous if and only if there is $t < s$ and a $t$-regular set $F \supset...
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Strong-coupling superconductivity induced by calcium intercalation in bilayer transition-metal dichalcogenides
We theoretically investigate the possibility of achieving a superconducting state in transition-metal dichalcogenide bilayers through intercalation, a process previously and widely used to achieve metallization and superconducting states in novel superconductors. For the Ca-intercalated bilayers MoS$_2$ and WS$_2$, w...
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Interval-type theorems concerning quasi-arithmetic means
Family of quasi-arithmetic means has a natural, partial order (point-wise order) $A^{[f]}\le A^{[g]}$ if and only if $A^{[f]}(v)\le A^{[g]}(v)$ for all admissible vectors $v$ ($f,\,g$ and, later, $h$ are continuous and monotone and defined on a common interval). Therefore one can introduce the notion of interval-type...
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Integrable flows between exact CFTs
We explicitly construct families of integrable $\sigma$-model actions smoothly interpolating between exact CFTs. In the ultraviolet the theory is the direct product of two current algebras at levels $k_1$ and $k_2$. In the infrared and for the case of two deformation matrices the CFT involves a coset CFT, whereas for...
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