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Self-Organizing Maps as a Storage and Transfer Mechanism in Reinforcement Learning
The idea of reusing information from previously learned tasks (source tasks) for the learning of new tasks (target tasks) has the potential to significantly improve the sample efficiency reinforcement learning agents. In this work, we describe an approach to concisely store and represent learned task knowledge, and r...
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Distributed model predictive control for continuous-time nonlinear systems based on suboptimal ADMM
The paper presents a distributed model predictive control (DMPC) scheme for continuous-time nonlinear systems based on the alternating direction method of multipliers (ADMM). A stopping criterion in the ADMM algorithm limits the iterations and therefore the required communication effort during the distributed MPC sol...
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Implementing focal-plane phase masks optimized for real telescope apertures with SLM-based digital adaptive coronagraphy
Direct imaging of exoplanets or circumstellar disk material requires extreme contrast at the 10-6 to 10-12 levels at < 100 mas angular separation from the star. Focal-plane mask (FPM) coronagraphic imaging has played a key role in this field, taking advantage of progress in Adaptive Optics on ground-based 8+m class t...
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Verifying Asynchronous Interactions via Communicating Session Automata
The relationship between communicating automata and session types is the cornerstone of many diverse theories and tools, including type checking, code generation, and runtime verification. A serious limitation of session types is that, while endpoint programs interact asynchronously, the underlying property which gua...
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Phase induced transparency mediated structured beam generation in a closed-loop tripod configuration
We present a phase induced transparency based scheme to generate structured beam patterns in a closed four level atomic system. We employ phase structured probe beam and a transverse magnetic field (TMF) to create phase dependent medium susceptibility. We show that such phase dependent modulation of absorption holds ...
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Additional cases of positive twisted torus knots
A twisted torus knot is a knot obtained from a torus knot by twisting adjacent strands by full twists. The twisted torus knots lie in $F$, the genus 2 Heegaard surface for $S^3$. Primitive/primitive and primitive/Seifert knots lie in $F$ in a particular way. Dean gives sufficient conditions for the parameters of the ...
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Action-conditional Sequence Modeling for Recommendation
In many online applications interactions between a user and a web-service are organized in a sequential way, e.g., user browsing an e-commerce website. In this setting, recommendation system acts throughout user navigation by showing items. Previous works have addressed this recommendation setup through the task of p...
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Limits of End-to-End Learning
End-to-end learning refers to training a possibly complex learning system by applying gradient-based learning to the system as a whole. End-to-end learning system is specifically designed so that all modules are differentiable. In effect, not only a central learning machine, but also all "peripheral" modules like rep...
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Quantum Graphs: $ \mathcal{PT}$-symmetry and reflection symmetry of the spectrum
Not necessarily self-adjoint quantum graphs -- differential operators on metric graphs -- are considered. Assume in addition that the underlying metric graph possesses an automorphism (symmetry) $ \mathcal P $. If the differential operator is $ \mathcal P \mathcal T$-symmetric, then its spectrum has reflection symmet...
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On Diophantine equations involving sums of Fibonacci numbers and powers of $2$
In this paper, we completely solve the Diophantine equations $F_{n_1} + F_{n_2} = 2^{a_1} + 2^{a_2} + 2^{a_3}$ and $ F_{m_1} + F_{m_2} + F_{m_3} =2^{t_1} + 2^{t_2} $, where $F_k$ denotes the $k$-th Fibonacci number. In particular, we prove that $\max \{n_1, n_2, a_1, a_2, a_3 \}\leq 18$ and $\max \{ m_1, m_2, m_3, t_...
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T-duality in rational homotopy theory via $L_\infty$-algebras
We combine Sullivan models from rational homotopy theory with Stasheff's $L_\infty$-algebras to describe a duality in string theory. Namely, what in string theory is known as topological T-duality between $K^0$-cocycles in type IIA string theory and $K^1$-cocycles in type IIB string theory, or as Hori's formula, can ...
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Phasebook and Friends: Leveraging Discrete Representations for Source Separation
Deep learning based speech enhancement and source separation systems have recently reached unprecedented levels of quality, to the point that performance is reaching a new ceiling. Most systems rely on estimating the magnitude of a target source by estimating a real-valued mask to be applied to a time-frequency repre...
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RankDCG: Rank-Ordering Evaluation Measure
Ranking is used for a wide array of problems, most notably information retrieval (search). There are a number of popular approaches to the evaluation of ranking such as Kendall's $\tau$, Average Precision, and nDCG. When dealing with problems such as user ranking or recommendation systems, all these measures suffer f...
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FUV Spectral Signatures of Molecules and the Evolution of the Gaseous Coma of Comet 67P/Churyumov-Gerasimenko
The Alice far-ultraviolet imaging spectrograph onboard Rosetta observed emissions from atomic and molecular species from within the coma of comet 67P/Churyumov-Gerasimenko during the entire escort phase of the mission from 2014 August to 2016 September. The initial observations showed that emissions of atomic hydroge...
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Adsorption and desorption of hydrogen at nonpolar GaN(1-100) surfaces: Kinetics and impact on surface vibrational and electronic properties
The adsorption of hydrogen at nonpolar GaN(1-100) surfaces and its impact on the electronic and vibrational properties is investigated using surface electron spectroscopy in combination with density functional theory (DFT) calculations. For the surface mediated dissociation of H2 and the subsequent adsorption of H, a...
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Application of the Fast Multipole Fully Coupled Poroelastic Displacement Discontinuity Method to Hydraulic Fracturing Problems
In this study, a fast multipole method (FMM) is used to decrease the computational time of a fully-coupled poroelastic hydraulic fracture model with a controllable effect on its accuracy. The hydraulic fracture model is based on the poroelastic formulation of the displacement discontinuity method (DDM) which is a spe...
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Conduction Channels of an InAs-Al nanowire Josephson weak link
We present a quantitative characterization of an electrically tunable Josephson junction defined in an InAs nanowire proximitized by an epitax-ially-grown superconducting Al shell. The gate-dependence of the number of conduction channels and of the set of transmission coefficients are extracted from the highly nonlin...
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Two-level Chebyshev filter based complementary subspace method: pushing the envelope of large-scale electronic structure calculations
We describe a novel iterative strategy for Kohn-Sham density functional theory calculations aimed at large systems (> 1000 electrons), applicable to metals and insulators alike. In lieu of explicit diagonalization of the Kohn-Sham Hamiltonian on every self-consistent field (SCF) iteration, we employ a two-level Cheby...
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Using the Tsetlin Machine to Learn Human-Interpretable Rules for High-Accuracy Text Categorization with Medical Applications
Medical applications challenge today's text categorization techniques by demanding both high accuracy and ease-of-interpretation. Although deep learning has provided a leap ahead in accuracy, this leap comes at the sacrifice of interpretability. To address this accuracy-interpretability challenge, we here introduce, ...
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Deep Learning with Experience Ranking Convolutional Neural Network for Robot Manipulator
Supervised learning, more specifically Convolutional Neural Networks (CNN), has surpassed human ability in some visual recognition tasks such as detection of traffic signs, faces and handwritten numbers. On the other hand, even state-of-the-art reinforcement learning (RL) methods have difficulties in environments wit...
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Isotope Shifts in the 7s$\rightarrow$8s Transition of Francium: Measurements and Comparison to \textit{ab initio} Theory
We observe the electric-dipole forbidden $7s\rightarrow8s$ transition in the francium isotopes $^{208-211}$Fr and $^{213}$Fr using a two-photon excitation scheme. We collect the atoms online from an accelerator and confine them in a magneto optical trap for the measurements. In combination with previous measurements ...
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SRM: An Efficient Framework for Autonomous Robotic Exploration in Indoor Environments
In this paper, we propose an integrated framework for the autonomous robotic exploration in indoor environments. Specially, we present a hybrid map, named Semantic Road Map (SRM), to represent the topological structure of the explored environment and facilitate decision-making in the exploration. The SRM is built inc...
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Mechanisms for bacterial gliding motility on soft substrates
The motility mechanism of certain rod-shaped bacteria has long been a mystery, since no external appendages are involved in their motion which is known as gliding. However, the physical principles behind gliding motility still remain poorly understood. Using myxobacteria as a canonical example of such organisms, we i...
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Random Walk in a N-cube Without Hamiltonian Cycle to Chaotic Pseudorandom Number Generation: Theoretical and Practical Considerations
Designing a pseudorandom number generator (PRNG) is a difficult and complex task. Many recent works have considered chaotic functions as the basis of built PRNGs: the quality of the output would indeed be an obvious consequence of some chaos properties. However, there is no direct reasoning that goes from chaotic fun...
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A Hardware Platform for Efficient Multi-Modal Sensing with Adaptive Approximation
We present Warp, a hardware platform to support research in approximate computing, sensor energy optimization, and energy-scavenged systems. Warp incorporates 11 state-of-the-art sensor integrated circuits, computation, and an energy-scavenged power supply, all within a miniature system that is just 3.6 cm x 3.3 cm x...
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Electrocaloric effects in the lead-free Ba(Zr,Ti)O$_{3}$ relaxor ferroelectric from atomistic simulations
Atomistic effective Hamiltonian simulations are used to investigate electrocaloric (EC) effects in the lead-free Ba(Zr$_{0.5}$Ti$_{0.5}$)O$_{3}$ (BZT) relaxor ferroelectric. We find that the EC coefficient varies non-monotonically with the field at any temperature, presenting a maximum that can be traced back to the ...
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Accelerating Permutation Testing in Voxel-wise Analysis through Subspace Tracking: A new plugin for SnPM
Permutation testing is a non-parametric method for obtaining the max null distribution used to compute corrected $p$-values that provide strong control of false positives. In neuroimaging, however, the computational burden of running such an algorithm can be significant. We find that by viewing the permutation testin...
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Image restoration of solar spectra
When recording spectra from the ground, atmospheric turbulence causes degradation of the spatial resolution. We present a data reduction method that restores the spatial resolution of the spectra to their undegraded state. By assuming that the point spread function (PSF) estimated from a strictly synchronized, broadb...
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Who Said What: Modeling Individual Labelers Improves Classification
Data are often labeled by many different experts with each expert only labeling a small fraction of the data and each data point being labeled by several experts. This reduces the workload on individual experts and also gives a better estimate of the unobserved ground truth. When experts disagree, the standard approa...
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Automated Tiling of Unstructured Mesh Computations with Application to Seismological Modelling
Sparse tiling is a technique to fuse loops that access common data, thus increasing data locality. Unlike traditional loop fusion or blocking, the loops may have different iteration spaces and access shared datasets through indirect memory accesses, such as A[map[i]] -- hence the name "sparse". One notable example of...
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A copula approach for dependence modeling in multivariate nonparametric time series
This paper is concerned with modeling the dependence structure of two (or more) time-series in the presence of a (possible multivariate) covariate which may include past values of the time series. We assume that the covariate influences only the conditional mean and the conditional variance of each of the time series...
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A geometric second-order-rectifiable stratification for closed subsets of Euclidean space
Defining the $m$-th stratum of a closed subset of an $n$ dimensional Euclidean space to consist of those points, where it can be touched by a ball from at least $n-m$ linearly independent directions, we establish that the $m$-th stratum is second-order rectifiable of dimension $m$ and a Borel set. This was known for ...
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Probabilistic Formulations of Regression with Mixed Guidance
Regression problems assume every instance is annotated (labeled) with a real value, a form of annotation we call \emph{strong guidance}. In order for these annotations to be accurate, they must be the result of a precise experiment or measurement. However, in some cases additional \emph{weak guidance} might be given ...
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DCN+: Mixed Objective and Deep Residual Coattention for Question Answering
Traditional models for question answering optimize using cross entropy loss, which encourages exact answers at the cost of penalizing nearby or overlapping answers that are sometimes equally accurate. We propose a mixed objective that combines cross entropy loss with self-critical policy learning. The objective uses ...
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An optimal unrestricted learning procedure
We study learning problems involving arbitrary classes of functions $F$, distributions $X$ and targets $Y$. Because proper learning procedures, i.e., procedures that are only allowed to select functions in $F$, tend to perform poorly unless the problem satisfies some additional structural property (e.g., that $F$ is ...
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Means of infinite sets I
We open a new field on how one can define means on infinite sets. We investigate many different ways on how such means can be constructed. One method is based on sequences of ideals, other deals with accumulation points, one uses isolated points, other deals with average using integral, other with limit of average on...
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On tamed almost complex four manifolds
This paper proves that on any tamed closed almost complex four-manifold $(M,J)$ whose dimension of $J$-anti-invariant cohomology is equal to self-dual second Betti number minus one, there exists a new symplectic form compatible with the given almost complex structure $J$. In particular, if the self-dual second Betti ...
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Evaluation and Prediction of Polygon Approximations of Planar Contours for Shape Analysis
Contours may be viewed as the 2D outline of the image of an object. This type of data arises in medical imaging as well as in computer vision and can be modeled as data on a manifold and can be studied using statistical shape analysis. Practically speaking, each observed contour, while theoretically infinite dimensio...
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Perturbative Expansion of Irreversible Work in Fokker-Planck Equation a la Quantum Mechanics
We discuss the systematic expansion of the solution of the Fokker-Planck equation with the help of the eigenfunctions of the time-dependent Fokker-Planck operator. The expansion parameter is the time derivative of the external parameter which controls the form of an external potential. Our expansion corresponds to th...
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Operational Semantics of Process Monitors
CSPe is a specification language for runtime monitors that can directly express concurrency in a bottom-up manner that composes the system from simpler, interacting components. It includes constructs to explicitly flag failures to the monitor, which unlike deadlocks and livelocks in conventional process algebras, pro...
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Anyonic Entanglement and Topological Entanglement Entropy
We study the properties of entanglement in two-dimensional topologically ordered phases of matter. Such phases support anyons, quasiparticles with exotic exchange statistics. The emergent nonlocal state spaces of anyonic systems admit a particular form of entanglement that does not exist in conventional quantum mecha...
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Water-based and Biocompatible 2D Crystal Inks: from Ink Formulation to All- Inkjet Printed Heterostructures
Fully exploiting the properties of 2D crystals requires a mass production method able to produce heterostructures of arbitrary complexity on any substrate, including plastic. Solution processing of graphene allows simple and low-cost techniques such as inkjet printing to be used for device fabrication. However, avail...
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Clustering to Reduce Spatial Data Set Size
Traditionally it had been a problem that researchers did not have access to enough spatial data to answer pressing research questions or build compelling visualizations. Today, however, the problem is often that we have too much data. Spatially redundant or approximately redundant points may refer to a single feature...
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Thermal diffusivity and chaos in metals without quasiparticles
We study the thermal diffusivity $D_T$ in models of metals without quasiparticle excitations (`strange metals'). The many-body quantum chaos and transport properties of such metals can be efficiently described by a holographic representation in a gravitational theory in an emergent curved spacetime with an additional...
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The Quest for Scalability and Accuracy in the Simulation of the Internet of Things: an Approach based on Multi-Level Simulation
This paper presents a methodology for simulating the Internet of Things (IoT) using multi-level simulation models. With respect to conventional simulators, this approach allows us to tune the level of detail of different parts of the model without compromising the scalability of the simulation. As a use case, we have...
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Harmonic spinors from twistors and potential forms
Symmetry operators of twistor spinors and harmonic spinors can be constructed from conformal Killing-Yano forms. Transformation operators relating twistors to harmonic spinors are found in terms of potential forms. These constructions are generalized to gauged twistor spinors and gauged harmonic spinors. The operator...
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Goodness-of-fit tests for the functional linear model based on randomly projected empirical processes
We consider marked empirical processes indexed by a randomly projected functional covariate to construct goodness-of-fit tests for the functional linear model with scalar response. The test statistics are built from continuous functionals over the projected process, resulting in computationally efficient tests that e...
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Efficient method for estimating the number of communities in a network
While there exist a wide range of effective methods for community detection in networks, most of them require one to know in advance how many communities one is looking for. Here we present a method for estimating the number of communities in a network using a combination of Bayesian inference with a novel prior and ...
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The Pluto System After New Horizons
The discovery of Pluto in 1930 presaged the discoveries of both the Kuiper Belt and ice dwarf planets, which are the third class of planets in our solar system. From the 1970s to the 19990s numerous fascinating attributes of the Pluto system were discovered, including multiple surface volatile species, Pluto's large ...
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Global-in-time Strichartz estimates and cubic Schrodinger equation on metric cone
We study the Strichartz estimates for Schrödinger equation on a metric cone $X$, where the metric cone $X=C(Y)=(0,\infty)_r\times Y$ and the cross section $Y$ is a $(n-1)$-dimensional closed Riemannian manifold $(Y,h)$. The equipped metric on $X$ is given by $g=dr^2+r^2h$, and let $\Delta_g$ be the Friedrich extensio...
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Compressive Embedding and Visualization using Graphs
Visualizing high-dimensional data has been a focus in data analysis communities for decades, which has led to the design of many algorithms, some of which are now considered references (such as t-SNE for example). In our era of overwhelming data volumes, the scalability of such methods have become more and more impor...
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Electrical control of metallic heavy-metal/ferromagnet interfacial states
Voltage control effects provide an energy-efficient means of tailoring material properties, especially in highly integrated nanoscale devices. However, only insulating and semiconducting systems can be controlled so far. In metallic systems, there is no electric field due to electron screening effects and thus no suc...
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An Expectation-Maximization Algorithm for the Fractal Inverse Problem
We present an Expectation-Maximization algorithm for the fractal inverse problem: the problem of fitting a fractal model to data. In our setting the fractals are Iterated Function Systems (IFS), with similitudes as the family of transformations. The data is a point cloud in ${\mathbb R}^H$ with arbitrary dimension $H...
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An Improved SCFlip Decoder for Polar Codes
This paper focuses on the recently introduced Successive Cancellation Flip (SCFlip) decoder of polar codes. Our contribution is twofold. First, we propose the use of an optimized metric to determine the flipping positions within the SCFlip decoder, which improves its ability to find the first error that occurred duri...
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Generation of controllable plasma wakefield noise in particle-in-cell simulations
Numerical simulations of beam-plasma instabilities may produce quantitatively incorrect results because of unrealistically high initial noise from which the instabilities develop. Of particular importance is the wakefield noise, the potential perturbations that have a phase velocity which is equal to the beam velocit...
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Variable Exponent Fock Spaces
In this article we introduce Variable exponent Fock spaces and study some of their basic properties such as the boundedness of evaluation functionals, density of polynomials, boundedness of a Bergman-type projection and duality.
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Pattern representation and recognition with accelerated analog neuromorphic systems
Despite being originally inspired by the central nervous system, artificial neural networks have diverged from their biological archetypes as they have been remodeled to fit particular tasks. In this paper, we review several possibilites to reverse map these architectures to biologically more realistic spiking networ...
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Dynamic Policies for Cooperative Networked Systems
A set of economic entities embedded in a network graph collaborate by opportunistically exchanging their resources to satisfy their dynamically generated needs. Under what conditions their collaboration leads to a sustainable economy? Which online policy can ensure a feasible resource exchange point will be attained,...
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On certain families of planar patterns and fractals
This survey article is dedicated to some families of fractals that were introduced and studied during the last decade, more precisely, families of Sierpiński carpets: limit net sets, generalised Sierpiński carpets and labyrinth fractals. We give a unifying approach of these fractals and several of their topological a...
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Static Dalvik VM bytecode instrumentation
This work proposes a novel approach to restricting the access for blacklisted Android system API calls. Main feature of the suggested method introduced in this paper is that it requires only rootless or (user-mode) access to the system unlike previous works. For that reason this method is valuable for end-users due t...
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PMU-Based Estimation of Dynamic State Jacobian Matrix
In this paper, a hybrid measurement- and model-based method is proposed which can estimate the dynamic state Jacobian matrix in near real-time. The proposed method is computationally efficient and robust to the variation of network topology. A numerical example is given to show that the proposed method is able to pro...
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DeepDownscale: a Deep Learning Strategy for High-Resolution Weather Forecast
Running high-resolution physical models is computationally expensive and essential for many disciplines. Agriculture, transportation, and energy are sectors that depend on high-resolution weather models, which typically consume many hours of large High Performance Computing (HPC) systems to deliver timely results. Ma...
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Open quantum random walks on the half-line: the Karlin-McGregor formula, path counting and Foster's Theorem
In this work we consider open quantum random walks on the non-negative integers. By considering orthogonal matrix polynomials we are able to describe transition probability expressions for classes of walks via a matrix version of the Karlin-McGregor formula. We focus on absorbing boundary conditions and, for simpler ...
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Nevanlinna classes associated to a closed set on $\partial$D
We introduce Nevanlinna classes of holomorphic functions associated to a closed set on the boundary of the unit disc in the complex plane and we get Blaschke type theorems relative to these classes by use of several complex variables methods. This gives alternative proofs of some results of Favorov \& Golinskii, usef...
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Exploring the nuances in the relationship "culture-strategy" for the business world
The current article explores interesting, significant and recently identified nuances in the relationship "culture-strategy". The shared views of leading scholars at the University of National and World Economy in relation with the essence, direction, structure, role and hierarchy of "culture-strategy" relation are d...
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Audio style transfer
'Style transfer' among images has recently emerged as a very active research topic, fuelled by the power of convolution neural networks (CNNs), and has become fast a very popular technology in social media. This paper investigates the analogous problem in the audio domain: How to transfer the style of a reference aud...
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Hyperbolic pseudoinverses for kinematics in the Euclidean group
The kinematics of a robot manipulator are described in terms of the mapping connecting its joint space and the 6-dimensional Euclidean group of motions $SE(3)$. The associated Jacobian matrices map into its Lie algebra $\mathfrak{se}(3)$, the space of twists describing infinitesimal motion of a rigid body. Control me...
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Nonlinear Unknown Input and State Estimation Algorithm in Mobile Robots
This technical report provides the description and the derivation of a novel nonlinear unknown input and state estimation algorithm (NUISE) for mobile robots. The algorithm is designed for real-world robots with nonlinear dynamic models and subject to stochastic noises on sensing and actuation. Leveraging sensor read...
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Acute sets
A set of points in $\mathbb{R}^d$ is acute, if any three points from this set form an acute triangle. In this note we construct an acute set in $\mathbb{R}^d$ of size at least $1.618^d$. Also, we present a simple example of an acute set of size at least $2^{\frac{d}{2}}$.
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Session Analysis using Plan Recognition
This paper presents preliminary results of our work with a major financial company, where we try to use methods of plan recognition in order to investigate the interactions of a costumer with the company's online interface. In this paper, we present the first steps of integrating a plan recognition algorithm in a rea...
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Personalized Driver Stress Detection with Multi-task Neural Networks using Physiological Signals
Stress can be seen as a physiological response to everyday emotional, mental and physical challenges. A long-term exposure to stressful situations can have negative health consequences, such as increased risk of cardiovascular diseases and immune system disorder. Therefore, a timely stress detection can lead to syste...
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Budgeted Experiment Design for Causal Structure Learning
We study the problem of causal structure learning when the experimenter is limited to perform at most $k$ non-adaptive experiments of size $1$. We formulate the problem of finding the best intervention target set as an optimization problem, which aims to maximize the average number of edges whose directions are resol...
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Evaluating the Robustness of Rogue Waves Under Perturbations
Rogue waves, and their periodic counterparts, have been shown to exist in a number of integrable models. However, relatively little is known about the existence of these objects in models where an exact formula is unattainable. In this work, we develop a novel numerical perspective towards identifying such states as ...
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Feeble fish in time-dependent waters and homogenization of the G-equation
We study the following control problem. A fish with bounded aquatic locomotion speed swims in fast waters. Can this fish, under reasonable assumptions, get to a desired destination? It can, even if the flow is time-dependent. Moreover, given a prescribed sufficiently large time $t$, it can be there at exactly the tim...
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Betti tables for indecomposable matrix factorizations of $XY(X-Y)(X-λY)$
We classify the Betti tables of indecomposable graded matrix factorizations over the simple elliptic singularity $f_\lambda = XY(X-Y)(X-\lambda Y)$ by making use of an associated weighted projective line of genus one.
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Discrete Integrable Systems, Supersymmetric Quantum Mechanics, and Framed BPS States - I
It is possible to understand whether a given BPS spectrum is generated by a relevant deformation of a 4D N=2 SCFT or of an asymptotically free theory from the periodicity properties of the corresponding quantum monodromy. With the aim of giving a better understanding of the above conjecture, in this paper we revisit ...
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Generalized Robust Bayesian Committee Machine for Large-scale Gaussian Process Regression
In order to scale standard Gaussian process (GP) regression to large-scale datasets, aggregation models employ factorized training process and then combine predictions from distributed experts. The state-of-the-art aggregation models, however, either provide inconsistent predictions or require time-consuming aggregat...
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Network Inference from a Link-Traced Sample using Approximate Bayesian Computation
We present a new inference method based on approximate Bayesian computation for estimating parameters governing an entire network based on link-traced samples of that network. To do this, we first take summary statistics from an observed link-traced network sample, such as a recruitment network of subjects in a hard-...
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Variational Dropout Sparsifies Deep Neural Networks
We explore a recently proposed Variational Dropout technique that provided an elegant Bayesian interpretation to Gaussian Dropout. We extend Variational Dropout to the case when dropout rates are unbounded, propose a way to reduce the variance of the gradient estimator and report first experimental results with indiv...
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A note on clustered cells
This note contains additions to the paper 'Clustered cell decomposition in P-minimal structures' (arXiv:1612.02683). We discuss a question which was raised in that paper, on the order of clustered cells. We also consider a notion of cells of minimal order, which is a slight optimalisation of the theorem from the orig...
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Record statistics of a strongly correlated time series: random walks and Lévy flights
We review recent advances on the record statistics of strongly correlated time series, whose entries denote the positions of a random walk or a Lévy flight on a line. After a brief survey of the theory of records for independent and identically distributed random variables, we focus on random walks. During the last f...
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On nonlinear instability of Prandtl's boundary layers: the case of Rayleigh's stable shear flows
In this paper, we study Prandtl's boundary layer asymptotic expansion for incompressible fluids on the half-space in the inviscid limit. In \cite{Gr1}, E. Grenier proved that Prandtl's Ansatz is false for data with Sobolev regularity near Rayleigh's unstable shear flows. In this paper, we show that this Ansatz is als...
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Subspace Clustering with Missing and Corrupted Data
Given full or partial information about a collection of points that lie close to a union of several subspaces, subspace clustering refers to the process of clustering the points according to their subspace and identifying the subspaces. One popular approach, sparse subspace clustering (SSC), represents each sample as...
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Monte Carlo Tensor Network Renormalization
Techniques for approximately contracting tensor networks are limited in how efficiently they can make use of parallel computing resources. In this work we demonstrate and characterize a Monte Carlo approach to the tensor network renormalization group method which can be used straightforwardly on modern computing arch...
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Experimental study of electron and phonon dynamics in nanoscale materials by ultrafast laser time-domain spectroscopy
With the rapid advances in the development of nanotechnology, nowadays, the sizes of elementary unit, i.e. transistor, of micro- and nanoelectronic devices are well deep into nanoscale. For the pursuit of cheaper and faster nanoscale electronic devices, the size of transistors keeps scaling down. As the miniaturizati...
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SSGP topologies on abelian groups of positive finite divisible rank
Let G be an abelian group. For a subset A of G, Cyc(A) denotes the set of all elements x of G such that the cyclic subgroup generated by x is contained in A, and G is said to have the small subgroup generating property (abbreviated to SSGP) if the smallest subgroup of G generated by Cyc(U) is dense in G for every nei...
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Intelligent Pothole Detection and Road Condition Assessment
Poor road conditions are a public nuisance, causing passenger discomfort, damage to vehicles, and accidents. In the U.S., road-related conditions are a factor in 22,000 of the 42,000 traffic fatalities each year. Although we often complain about bad roads, we have no way to detect or report them at scale. To address ...
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Concrete Autoencoders for Differentiable Feature Selection and Reconstruction
We introduce the concrete autoencoder, an end-to-end differentiable method for global feature selection, which efficiently identifies a subset of the most informative features and simultaneously learns a neural network to reconstruct the input data from the selected features. Our method is unsupervised, and is based ...
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Emergence and complexity in theoretical models of self-organized criticality
In this thesis we present few theoretical studies of the models of self-organized criticality. Following a brief introduction of self-organized criticality, we discuss three main problems. The first problem is about growing patterns formed in the abelian sandpile model (ASM). The patterns exhibit proportionate growth...
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An Extension of Averaged-Operator-Based Algorithms
Many of the algorithms used to solve minimization problems with sparsity-inducing regularizers are generic in the sense that they do not take into account the sparsity of the solution in any particular way. However, algorithms known as semismooth Newton are able to take advantage of this sparsity to accelerate their ...
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Along the sun-drenched roadside: On the interplay between urban street orientation entropy and the buildings' solar potential
We explore the relation between urban road network characteristics particularly circuitry, street orientation entropy and the city's topography on the one hand and the building's orientation entropy on the other in order to quantify their effect on the city's solar potential. These statistical measures of the road ne...
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$HD(M\setminus L)>0.353$
The complement $M\setminus L$ of the Lagrange spectrum $L$ in the Markov spectrum $M$ was studied by many authors (including Freiman, Berstein, Cusick and Flahive). After their works, we disposed of a countable collection of points in $M\setminus L$. In this article, we describe the structure of $M\setminus L$ near a...
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Comparing the dark matter models, modified Newtonian dynamics and modified gravity in accounting for the galaxy rotation curves
We compare six models (including the baryonic model, two dark matter models, two modified Newtonian dynamics models and one modified gravity model) in accounting for the galaxy rotation curves. For the dark matter models, we assume NFW profile and core-modified profile for the dark halo, respectively. For the modifie...
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Good Clusterings Have Large Volume
The clustering of a data set is one of the core tasks in data analytics. Many clustering algorithms exhibit a strong contrast between a favorable performance in practice and bad theoretical worst-cases. Prime examples are least-squares assignments and the popular $k$-means algorithm. We are interested in this contras...
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Regularity of Lie Groups
We solve the regularity problem for Milnor's infinite dimensional Lie groups in the $C^0$-topological context, and provide necessary and sufficient regularity conditions for the standard setting ($C^k$-topology). We prove that the evolution map is $C^0$-continuous on its domain $\textit{iff}\hspace{1pt}$ the Lie grou...
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A study on text-score disagreement in online reviews
In this paper, we focus on online reviews and employ artificial intelligence tools, taken from the cognitive computing field, to help understanding the relationships between the textual part of the review and the assigned numerical score. We move from the intuitions that 1) a set of textual reviews expressing differe...
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Convergence rates for nonequilibrium Langevin dynamics
We study the exponential convergence to the stationary state for nonequilibrium Langevin dynamics, by a perturbative approach based on hypocoercive techniques developed for equilibrium Langevin dynamics. The Hamiltonian and overdamped limits (corresponding respectively to frictions going to zero or infinity) are care...
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Natural Extension of Hartree-Fock through extremal $1$-fermion information: Overview and application to the lithium atom
Fermionic natural occupation numbers do not only obey Pauli's exclusion principle but are even stronger restricted by so-called generalized Pauli constraints. Whenever given natural occupation numbers lie on the boundary of the allowed region the corresponding $N$-fermion quantum state has a significantly simpler str...
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Homotopy Parametric Simplex Method for Sparse Learning
High dimensional sparse learning has imposed a great computational challenge to large scale data analysis. In this paper, we are interested in a broad class of sparse learning approaches formulated as linear programs parametrized by a {\em regularization factor}, and solve them by the parametric simplex method (PSM)....
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Fractional Operators with Inhomogeneous Boundary Conditions: Analysis, Control, and Discretization
In this paper we introduce new characterizations of spectral fractional Laplacian to incorporate nonhomogeneous Dirichlet and Neumann boundary conditions. The classical cases with homogeneous boundary conditions arise as a special case. We apply our definition to fractional elliptic equations of order $s \in (0,1)$ w...
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