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Large-sample approximations for variance-covariance matrices of high-dimensional time series
Distributional approximations of (bi--) linear functions of sample variance-covariance matrices play a critical role to analyze vector time series, as they are needed for various purposes, especially to draw inference on the dependence structure in terms of second moments and to analyze projections onto lower dimensi...
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Resilience: A Criterion for Learning in the Presence of Arbitrary Outliers
We introduce a criterion, resilience, which allows properties of a dataset (such as its mean or best low rank approximation) to be robustly computed, even in the presence of a large fraction of arbitrary additional data. Resilience is a weaker condition than most other properties considered so far in the literature, ...
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Non-Euclidean geometry, nontrivial topology and quantum vacuum effects
Space out of a topological defect of the Abrikosov-Nielsen-Olesen vortex type is locally flat but non-Euclidean. If a spinor field is quantized in such a space, then a variety of quantum effects is induced in the vacuum. Basing on the continuum model for long-wavelength electronic excitations, originating in the tigh...
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Spatial risk measures and rate of spatial diversification
An accurate assessment of the risk of extreme environmental events is of great importance for populations, authorities and the banking/insurance industry. Koch (2017) introduced a notion of spatial risk measure and a corresponding set of axioms which are well suited to analyze the risk due to events having a spatial ...
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Double Homotopy (Co)Limits for Relative Categories
We answer the question to what extent homotopy (co)limits in categories with weak equivalences allow for a Fubini-type interchange law. The main obstacle is that we do not assume our categories with weak equivalences to come equipped with a calculus for homotopy (co)limits, such as a derivator.
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Theory of ground states for classical Heisenberg spin systems I
We formulate part I of a rigorous theory of ground states for classical, finite, Heisenberg spin systems. The main result is that all ground states can be constructed from the eigenvectors of a real, symmetric matrix with entries comprising the coupling constants of the spin system as well as certain Lagrange paramet...
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A Pliable Index Coding Approach to Data Shuffling
A promising research area that has recently emerged, is on how to use index coding to improve the communication efficiency in distributed computing systems, especially for data shuffling in iterative computations. In this paper, we posit that pliable index coding can offer a more efficient framework for data shufflin...
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The statistical challenge of constraining the low-mass IMF in Local Group dwarf galaxies
We use Monte Carlo simulations to explore the statistical challenges of constraining the characteristic mass ($m_c$) and width ($\sigma$) of a lognormal sub-solar initial mass function (IMF) in Local Group dwarf galaxies using direct star counts. For a typical Milky Way (MW) satellite ($M_{V} = -8$), jointly constrai...
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Spatial analysis of airborne laser scanning point clouds for predicting forest variables
With recent developments in remote sensing technologies, plot-level forest resources can be predicted utilizing airborne laser scanning (ALS). The prediction is often assisted by mostly vertical summaries of the ALS point clouds. We present a spatial analysis of the point cloud by studying the horizontal distribution...
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Analytic and arithmetic properties of the $(Γ,χ)$-automorphic reproducing kernel function
We consider the reproducing kernel function of the theta Bargmann-Fock Hilbert space associated to given full-rank lattice and pseudo-character, and we deal with some of its analytical and arithmetical properties. Specially, the distribution and discreteness of its zeros are examined and analytic sets inside a produc...
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Concentration of $1$-Lipschitz functions on manifolds with boundary with Dirichlet boundary condition
In this paper, we consider a concentration of measure problem on Riemannian manifolds with boundary. We study concentration phenomena of non-negative $1$-Lipschitz functions with Dirichlet boundary condition around zero, which is called boundary concentration phenomena. We first examine relation between boundary conc...
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Simulated Annealing for JPEG Quantization
JPEG is one of the most widely used image formats, but in some ways remains surprisingly unoptimized, perhaps because some natural optimizations would go outside the standard that defines JPEG. We show how to improve JPEG compression in a standard-compliant, backward-compatible manner, by finding improved default qua...
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Greedy Strategy Works for Clustering with Outliers and Coresets Construction
We study the problems of clustering with outliers in high dimension. Though a number of methods have been developed in the past decades, it is still quite challenging to design quality guaranteed algorithms with low complexities for the problems. Our idea is inspired by the greedy method, Gonzalez's algorithm, for so...
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All-but-the-Top: Simple and Effective Postprocessing for Word Representations
Real-valued word representations have transformed NLP applications; popular examples are word2vec and GloVe, recognized for their ability to capture linguistic regularities. In this paper, we demonstrate a {\em very simple}, and yet counter-intuitive, postprocessing technique -- eliminate the common mean vector and a...
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Detecting Near Duplicates in Software Documentation
Contemporary software documentation is as complicated as the software itself. During its lifecycle, the documentation accumulates a lot of near duplicate fragments, i.e. chunks of text that were copied from a single source and were later modified in different ways. Such near duplicates decrease documentation quality ...
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L-Graphs and Monotone L-Graphs
In an $\mathsf{L}$-embedding of a graph, each vertex is represented by an $\mathsf{L}$-segment, and two segments intersect each other if and only if the corresponding vertices are adjacent in the graph. If the corner of each $\mathsf{L}$-segment in an $\mathsf{L}$-embedding lies on a straight line, we call it a monot...
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ZigZag: A new approach to adaptive online learning
We develop a novel family of algorithms for the online learning setting with regret against any data sequence bounded by the empirical Rademacher complexity of that sequence. To develop a general theory of when this type of adaptive regret bound is achievable we establish a connection to the theory of decoupling ineq...
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Comparing Rule-Based and Deep Learning Models for Patient Phenotyping
Objective: We investigate whether deep learning techniques for natural language processing (NLP) can be used efficiently for patient phenotyping. Patient phenotyping is a classification task for determining whether a patient has a medical condition, and is a crucial part of secondary analysis of healthcare data. We a...
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Jackknife multiplier bootstrap: finite sample approximations to the $U$-process supremum with applications
This paper is concerned with finite sample approximations to the supremum of a non-degenerate $U$-process of a general order indexed by a function class. We are primarily interested in situations where the function class as well as the underlying distribution change with the sample size, and the $U$-process itself is...
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On the universality of anomalous scaling exponents of structure functions in turbulent flows
All previous experiments in open turbulent flows (e.g. downstream of grids, jet and atmospheric boundary layer) have produced quantitatively consistent values for the scaling exponents of velocity structure functions. The only measurement in closed turbulent flow (von Kármán swirling flow) using Taylor-hypothesis, ho...
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On the Heat Kernel and Weyl Anomaly of Schrödinger invariant theory
We propose a method inspired from discrete light cone quantization (DLCQ) to determine the heat kernel for a Schrödinger field theory (Galilean boost invariant with $z=2$ anisotropic scaling symmetry) living in $d+1$ dimensions, coupled to a curved Newton-Cartan background starting from a heat kernel of a relativisti...
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Tree-based networks: characterisations, metrics, and support trees
Phylogenetic networks generalise phylogenetic trees and allow for the accurate representation of the evolutionary history of a set of present-day species whose past includes reticulate events such as hybridisation and lateral gene transfer. One way to obtain such a network is by starting with a (rooted) phylogenetic ...
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Comparing People with Bibliometrics
Bibliometric indicators, citation counts and/or download counts are increasingly being used to inform personnel decisions such as hiring or promotions. These statistics are very often misused. Here we provide a guide to the factors which should be considered when using these so-called quantitative measures to evaluat...
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Urban Dreams of Migrants: A Case Study of Migrant Integration in Shanghai
Unprecedented human mobility has driven the rapid urbanization around the world. In China, the fraction of population dwelling in cities increased from 17.9% to 52.6% between 1978 and 2012. Such large-scale migration poses challenges for policymakers and important questions for researchers. To investigate the process...
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A computational method for estimating Burr XII parameters with complete and multiple censored data
Flexibility in shape and scale of Burr XII distribution can make close approximation of numerous well-known probability density functions. Due to these capabilities, the usages of Burr XII distribution are applied in risk analysis, lifetime data analysis and process capability estimation. In this paper the Cross-Entr...
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Locally stationary spatio-temporal interpolation of Argo profiling float data
Argo floats measure seawater temperature and salinity in the upper 2,000 m of the global ocean. Statistical analysis of the resulting spatio-temporal dataset is challenging due to its nonstationary structure and large size. We propose mapping these data using locally stationary Gaussian process regression where covar...
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Knowledge Reuse for Customization: Metamodels in an Open Design Community for 3d Printing
Theories of knowledge reuse posit two distinct processes: reuse for replication and reuse for innovation. We identify another distinct process, reuse for customization. Reuse for customization is a process in which designers manipulate the parameters of metamodels to produce models that fulfill their personal needs. ...
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Dynamic Rank Maximal Matchings
We consider the problem of matching applicants to posts where applicants have preferences over posts. Thus the input to our problem is a bipartite graph G = (A U P,E), where A denotes a set of applicants, P is a set of posts, and there are ranks on edges which denote the preferences of applicants over posts. A matchi...
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Early identification of important patents through network centrality
One of the most challenging problems in technological forecasting is to identify as early as possible those technologies that have the potential to lead to radical changes in our society. In this paper, we use the US patent citation network (1926-2010) to test our ability to early identify a list of historically sign...
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Central limit theorem for the variable bandwidth kernel density estimators
In this paper we study the ideal variable bandwidth kernel density estimator introduced by McKay (1993) and Jones, McKay and Hu (1994) and the plug-in practical version of the variable bandwidth kernel estimator with two sequences of bandwidths as in Giné and Sang (2013). Based on the bias and variance analysis of th...
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Distance-to-Mean Continuous Conditional Random Fields to Enhance Prediction Problem in Traffic Flow Data
The increase of vehicle in highways may cause traffic congestion as well as in the normal roadways. Predicting the traffic flow in highways especially, is demanded to solve this congestion problem. Predictions on time-series multivariate data, such as in the traffic flow dataset, have been largely accomplished throug...
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Submap-based Pose-graph Visual SLAM: A Robust Visual Exploration and Localization System
For VSLAM (Visual Simultaneous Localization and Mapping), localization is a challenging task, especially for some challenging situations: textureless frames, motion blur, etc.. To build a robust exploration and localization system in a given space or environment, a submap-based VSLAM system is proposed in this paper....
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Partial and Total Dielectronic Recombination Rate Coefficients for W$^{55+}$ to W$^{38+}$
Dielectronic recombination (DR) is the dominant mode of recombination in magnetically confined fusion plasmas for intermediate to low-charged ions of W. Complete, final-state resolved partial isonuclear W DR rate coefficient data is required for detailed collisional-radiative modelling for such plasmas in preparation...
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Congenial Causal Inference with Binary Structural Nested Mean Models
Structural nested mean models (SNMMs) are among the fundamental tools for inferring causal effects of time-dependent exposures from longitudinal studies. With binary outcomes, however, current methods for estimating multiplicative and additive SNMM parameters suffer from variation dependence between the causal SNMM p...
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Improving Search through A3C Reinforcement Learning based Conversational Agent
We develop a reinforcement learning based search assistant which can assist users through a set of actions and sequence of interactions to enable them realize their intent. Our approach caters to subjective search where the user is seeking digital assets such as images which is fundamentally different from the tasks ...
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Eco-Routing based on a Data Driven Fuel Consumption Model
A nonparametric fuel consumption model is developed and used for eco-routing algorithm development in this paper. Six months of driving information from the city of Ann Arbor is collected from 2,000 vehicles. The road grade information from more than 1,100 km of road network is modeled and the software Autonomie is u...
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SuperSpike: Supervised learning in multi-layer spiking neural networks
A vast majority of computation in the brain is performed by spiking neural networks. Despite the ubiquity of such spiking, we currently lack an understanding of how biological spiking neural circuits learn and compute in-vivo, as well as how we can instantiate such capabilities in artificial spiking circuits in-silic...
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Distributions-oriented wind forecast verification by a hidden Markov model for multivariate circular-linear data
Winds from the North-West quadrant and lack of precipitation are known to lead to an increase of PM10 concentrations over a residential neighborhood in the city of Taranto (Italy). In 2012 the local government prescribed a reduction of industrial emissions by 10% every time such meteorological conditions are forecast...
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Mean Field Residual Networks: On the Edge of Chaos
We study randomly initialized residual networks using mean field theory and the theory of difference equations. Classical feedforward neural networks, such as those with tanh activations, exhibit exponential behavior on the average when propagating inputs forward or gradients backward. The exponential forward dynamic...
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Automorphisms and deformations of conformally Kähler, Einstein-Maxwell metrics
We obtain a structure theorem for the group of holomorphic automorphisms of a conformally Kähler, Einstein-Maxwell metric, extending the classical results of Matsushima, Licherowicz and Calabi in the Kähler-Einstein, cscK, and extremal Kähler cases. Combined with previous results of LeBrun, Apostolov-Maschler and Fut...
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Human-Level Intelligence or Animal-Like Abilities?
The vision systems of the eagle and the snake outperform everything that we can make in the laboratory, but snakes and eagles cannot build an eyeglass or a telescope or a microscope. (Judea Pearl)
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Wembedder: Wikidata entity embedding web service
I present a web service for querying an embedding of entities in the Wikidata knowledge graph. The embedding is trained on the Wikidata dump using Gensim's Word2Vec implementation and a simple graph walk. A REST API is implemented. Together with the Wikidata API the web service exposes a multilingual resource for ove...
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Meta-Learning for Contextual Bandit Exploration
We describe MELEE, a meta-learning algorithm for learning a good exploration policy in the interactive contextual bandit setting. Here, an algorithm must take actions based on contexts, and learn based only on a reward signal from the action taken, thereby generating an exploration/exploitation trade-off. MELEE addre...
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Population polarization dynamics and next-generation social media algorithms
We present a many-body theory that explains and reproduces recent observations of population polarization dynamics, is supported by controlled human experiments, and addresses the controversy surrounding the Internet's impact. It predicts that whether and how a population becomes polarized is dictated by the nature o...
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Ride Sharing and Dynamic Networks Analysis
The potential of an efficient ride-sharing scheme to significantly reduce traffic congestion, lower emission level, as well as facilitating the introduction of smart cities has been widely demonstrated. This positive thrust however is faced with several delaying factors, one of which is the volatility and unpredictab...
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Gas Adsorption and Dynamics in Pillared Graphene Frameworks
Pillared Graphene Frameworks are a novel class of microporous materials made by graphene sheets separated by organic spacers. One of their main features is that the pillar type and density can be chosen to tune the material properties. In this work, we present a computer simulation study of adsorption and dynamics of...
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DepthSynth: Real-Time Realistic Synthetic Data Generation from CAD Models for 2.5D Recognition
Recent progress in computer vision has been dominated by deep neural networks trained over large amounts of labeled data. Collecting such datasets is however a tedious, often impossible task; hence a surge in approaches relying solely on synthetic data for their training. For depth images however, discrepancies with ...
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Short Laws for Finite Groups and Residual Finiteness Growth
We prove that for every $n \in \mathbb{N}$ and $\delta>0$ there exists a word $w_n \in F_2$ of length $n^{2/3} \log(n)^{3+\delta}$ which is a law for every finite group of order at most $n$. This improves upon the main result of [A. Thom, About the length of laws for finite groups, Isr. J. Math.]. As an application w...
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Majorana Spin Liquids, Topology and Superconductivity in Ladders
We theoretically address spin chain analogs of the Kitaev quantum spin model on the honeycomb lattice. The emergent quantum spin liquid phases or Anderson resonating valence bond (RVB) states can be understood, as an effective model, in terms of p-wave superconductivity and Majorana fermions. We derive a generalized ...
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Conditional Mean and Quantile Dependence Testing in High Dimension
Motivated by applications in biological science, we propose a novel test to assess the conditional mean dependence of a response variable on a large number of covariates. Our procedure is built on the martingale difference divergence recently proposed in Shao and Zhang (2014), and it is able to detect a certain type ...
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Finding low-tension communities
Motivated by applications that arise in online social media and collaboration networks, there has been a lot of work on community-search and team-formation problems. In the former class of problems, the goal is to find a subgraph that satisfies a certain connectivity requirement and contains a given collection of see...
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Cohomology of the flag variety under PBW degenerations
PBW degenerations are a particularly nice family of flat degenerations of type A flag varieties. We show that the cohomology of any PBW degeneration of the flag variety surjects onto the cohomology of the original flag variety, and that this holds in an equivariant setting too. We also prove that the same is true in ...
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Exact MAP inference in general higher-order graphical models using linear programming
This paper is concerned with the problem of exact MAP inference in general higher-order graphical models by means of a traditional linear programming relaxation approach. In fact, the proof that we have developed in this paper is a rather simple algebraic proof being made straightforward, above all, by the introducti...
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Dissolution of topological Fermi arcs in a dirty Weyl semimetal
Weyl semimetals (WSMs) have recently attracted a great deal of attention as they provide condensed matter realization of chiral anomaly, feature topologically protected Fermi arc surface states and sustain sharp chiral Weyl quasiparticles up to a critical disorder at which a continuous quantum phase transition (QPT) ...
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Performance Improvement in Noisy Linear Consensus Networks with Time-Delay
We analyze performance of a class of time-delay first-order consensus networks from a graph topological perspective and present methods to improve it. The performance is measured by network's square of H-2 norm and it is shown that it is a convex function of Laplacian eigenvalues and the coupling weights of the under...
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Use of First and Third Person Views for Deep Intersection Classification
We explore the problem of intersection classification using monocular on-board passive vision, with the goal of classifying traffic scenes with respect to road topology. We divide the existing approaches into two broad categories according to the type of input data: (a) first person vision (FPV) approaches, which use...
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On the Liouville heat kernel for k-coarse MBRW and nonuniversality
We study the Liouville heat kernel (in the $L^2$ phase) associated with a class of logarithmically correlated Gaussian fields on the two dimensional torus. We show that for each $\varepsilon>0$ there exists such a field, whose covariance is a bounded perturbation of that of the two dimensional Gaussian free field, an...
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Bounding the convergence time of local probabilistic evolution
Isoperimetric inequalities form a very intuitive yet powerful characterization of the connectedness of a state space, that has proven successful in obtaining convergence bounds. Since the seventies they form an essential tool in differential geometry, graph theory and Markov chain analysis. In this paper we use isope...
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Excitable behaviors
This chapter revisits the concept of excitability, a basic system property of neurons. The focus is on excitable systems regarded as behaviors rather than dynamical systems. By this we mean open systems modulated by specific interconnection properties rather than closed systems classified by their parameter ranges. M...
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Laplacian solitons: questions and homogeneous examples
We give the first examples of closed Laplacian solitons which are shrinking, and in particular produce closed Laplacian flow solutions with a finite-time singularity. Extremally Ricci pinched G2-structures (introduced by Bryant) which are steady Laplacian solitons have also been found. All the examples are left-invar...
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The Markoff Group of Transformations in Prime and Composite Moduli
The Markoff group of transformations is a group $\Gamma$ of affine integral morphisms, which is known to act transitively on the set of all positive integer solutions to the equation $x^{2}+y^{2}+z^{2}=xyz$. The fundamental strong approximation conjecture for the Markoff equation states that for every prime $p$, the ...
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The equivariant index of twisted dirac operators and semi-classical limits
Consider a spin manifold M, equipped with a line bundle L and an action of a compact Lie group G. We can attach to this data a family Theta(k) of distributions on the dual of the Lie algebra of G. The aim of this paper is to study the asymptotic behaviour of Theta(k) when k is large, and M possibly non compact, and t...
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Proportionally Representative Participatory Budgeting: Axioms and Algorithms
Participatory budgeting is one of the exciting developments in deliberative grassroots democracy. We concentrate on approval elections and propose proportional representation axioms in participatory budgeting, by generalizing relevant axioms for approval-based multi-winner elections. We observe a rich landscape with ...
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The Arctic Ocean seasonal cycles of heat and freshwater fluxes: observation-based inverse estimates
This paper presents the first estimate of the seasonal cycle of ocean and sea ice net heat and freshwater (FW) fluxes around the boundary of the Arctic Ocean. The ocean transports are estimated primarily using 138 moored instruments deployed in September 2005 to August 2006 across the four main Arctic gateways: Davis...
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Standard Zero-Free Regions for Rankin--Selberg L-Functions via Sieve Theory
We give a simple proof of a standard zero-free region in the $t$-aspect for the Rankin--Selberg $L$-function $L(s,\pi \times \widetilde{\pi})$ for any unitary cuspidal automorphic representation $\pi$ of $\mathrm{GL}_n(\mathbb{A}_F)$ that is tempered at every nonarchimedean place outside a set of Dirichlet density ze...
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Mass transfer in asymptotic-giant-branch binary systems
Binary stars can interact via mass transfer when one member (the primary) ascends onto a giant branch. The amount of gas ejected by the binary and the amount of gas accreted by the secondary over the lifetime of the primary influence the subsequent binary phenomenology. Some of the gas ejected by the binary will rema...
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On polar relative normalizations of ruled surfaces
This paper deals with skew ruled surfaces in the Euclidean space $\mathbb{E}^{3}$ which are equipped with polar normalizations, that is, relative normalizations such that the relative normal at each point of the ruled surface lies on the corresponding polar plane. We determine the invariants of a such normalized rule...
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Femtosecond X-ray Fourier holography imaging of free-flying nanoparticles
Ultrafast X-ray imaging provides high resolution information on individual fragile specimens such as aerosols, metastable particles, superfluid quantum systems and live biospecimen, which is inaccessible with conventional imaging techniques. Coherent X-ray diffractive imaging, however, suffers from intrinsic loss of ...
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The Rank Effect
We decompose returns for portfolios of bottom-ranked, lower-priced assets relative to the market into rank crossovers and changes in the relative price of those bottom-ranked assets. This decomposition is general and consistent with virtually any asset pricing model. Crossovers measure changes in rank and are smoothl...
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The Generalized Label Correcting Method for Optimal Kinodynamic Motion Planning
Nearly all autonomous robotic systems use some form of motion planning to compute reference motions through their environment. An increasing use of autonomous robots in a broad range of applications creates a need for efficient, general purpose motion planning algorithms that are applicable in any of these new applic...
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Learning to Compose Task-Specific Tree Structures
For years, recursive neural networks (RvNNs) have been shown to be suitable for representing text into fixed-length vectors and achieved good performance on several natural language processing tasks. However, the main drawback of RvNNs is that they require structured input, which makes data preparation and model impl...
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Navier-Stokes flow past a rigid body: attainability of steady solutions as limits of unsteady weak solutions, starting and landing cases
Consider the Navier-Stokes flow in 3-dimensional exterior domains, where a rigid body is translating with prescribed translational velocity $-h(t)u_\infty$ with constant vector $u_\infty\in \mathbb R^3\setminus\{0\}$. Finn raised the question whether his steady slutions are attainable as limits for $t\to\infty$ of un...
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Flux cost functions and the choice of metabolic fluxes
Metabolic fluxes in cells are governed by physical, biochemical, physiological, and economic principles. Cells may show "economical" behaviour, trading metabolic performance against the costly side-effects of high enzyme or metabolite concentrations. Some constraint-based flux prediction methods score fluxes by heuri...
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Finding Archetypal Spaces for Data Using Neural Networks
Archetypal analysis is a type of factor analysis where data is fit by a convex polytope whose corners are "archetypes" of the data, with the data represented as a convex combination of these archetypal points. While archetypal analysis has been used on biological data, it has not achieved widespread adoption because ...
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Formally continuous functions on Baire space
A function from Baire space to the natural numbers is called formally continuous if it is induced by a morphism between the corresponding formal spaces. We compare formal continuity to two other notions of continuity on Baire space working in Bishop constructive mathematics: one is a function induced by a Brouwer-ope...
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Universal Joint Image Clustering and Registration using Partition Information
We consider the problem of universal joint clustering and registration of images and define algorithms using multivariate information functionals. We first study registering two images using maximum mutual information and prove its asymptotic optimality. We then show the shortcomings of pairwise registration in multi...
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Quantitative statistical stability and speed of convergence to equilibrium for partially hyperbolic skew products
We consider a general relation between fixed point stability of suitably perturbed transfer operators and convergence to equilibrium (a notion which is strictly related to decay of correlations). We apply this relation to deterministic perturbations of a class of (piecewise) partially hyperbolic skew products whose b...
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Minimax Rényi Redundancy
The redundancy for universal lossless compression of discrete memoryless sources in Campbell's setting is characterized as a minimax Rényi divergence, which is shown to be equal to the maximal $\alpha$-mutual information via a generalized redundancy-capacity theorem. Special attention is placed on the analysis of the...
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DeepArchitect: Automatically Designing and Training Deep Architectures
In deep learning, performance is strongly affected by the choice of architecture and hyperparameters. While there has been extensive work on automatic hyperparameter optimization for simple spaces, complex spaces such as the space of deep architectures remain largely unexplored. As a result, the choice of architectur...
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Dynamical control of atoms with polarized bichromatic weak field
We propose ultranarrow dynamical control of population oscillation (PO) between ground states through the polarization content of an input bichromatic field. Appropriate engineering of classical interference between optical fields results in PO arising exclusively from optical pumping. Contrary to the expected broad ...
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Cycle packings of the complete multigraph
Bryant, Horsley, Maenhaut and Smith recently gave necessary and sufficient conditions for when the complete multigraph can be decomposed into cycles of specified lengths $m_1,m_2,\ldots,m_\tau$. In this paper we characterise exactly when there exists a packing of the complete multigraph with cycles of specified lengt...
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Statistical Inference for the Population Landscape via Moment Adjusted Stochastic Gradients
Modern statistical inference tasks often require iterative optimization methods to approximate the solution. Convergence analysis from optimization only tells us how well we are approximating the solution deterministically, but overlooks the sampling nature of the data. However, due to the randomness in the data, sta...
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Super cavity solitons and the coexistence of multiple nonlinear states in a tristable passive Kerr resonator
Passive Kerr cavities driven by coherent laser fields display a rich landscape of nonlinear physics, including bistability, pattern formation, and localised dissipative structures (solitons). Their conceptual simplicity has for several decades offered an unprecedented window into nonlinear cavity dynamics, providing ...
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Twisting and Mixing
We present a framework that connects three interesting classes of groups: the twisted groups (also known as Suzuki-Ree groups), the mixed groups and the exotic pseudo-reductive groups. For a given characteristic p, we construct categories of twisted and mixed schemes. Ordinary schemes are a full subcategory of the mi...
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KeyVec: Key-semantics Preserving Document Representations
Previous studies have demonstrated the empirical success of word embeddings in various applications. In this paper, we investigate the problem of learning distributed representations for text documents which many machine learning algorithms take as input for a number of NLP tasks. We propose a neural network model, K...
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Integer Factorization with a Neuromorphic Sieve
The bound to factor large integers is dominated by the computational effort to discover numbers that are smooth, typically performed by sieving a polynomial sequence. On a von Neumann architecture, sieving has log-log amortized time complexity to check each value for smoothness. This work presents a neuromorphic siev...
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Probabilistic Assessment of PV-Battery System Impacts on LV Distribution Networks
The increasing uptake of residential batteries has led to suggestions that the prevalence of batteries on LV networks will serendipitously mitigate the technical problems induced by PV installations. However, in general, the effects of PV-battery systems on LV networks have not been well studied. Given this backgroun...
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Simulating Cellular Communications in Vehicular Networks: Making SimuLTE Interoperable with Veins
The evolution of cellular technologies toward 5G progressively enables efficient and ubiquitous communications in an increasing number of fields. Among these, vehicular networks are being considered as one of the most promising and challenging applications, requiring support for communications in high-speed mobility ...
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AdaBatch: Adaptive Batch Sizes for Training Deep Neural Networks
Training deep neural networks with Stochastic Gradient Descent, or its variants, requires careful choice of both learning rate and batch size. While smaller batch sizes generally converge in fewer training epochs, larger batch sizes offer more parallelism and hence better computational efficiency. We have developed a...
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Extremely broadband ultralight thermally emissive metasurfaces
We report the design, fabrication and characterization of ultralight highly emissive metaphotonic structures with record-low mass/area that emit thermal radiation efficiently over a broad spectral (2 to 35 microns) and angular (0-60 degrees) range. The structures comprise one to three pairs of alternating nanometer-s...
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Wright-Fisher diffusions for evolutionary games with death-birth updating
We investigate spatial evolutionary games with death-birth updating in large finite populations. Within growing spatial structures subject to appropriate conditions, the density processes of a fixed type are proven to converge to the Wright-Fisher diffusions with drift. In addition, convergence in the Wasserstein dis...
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Quantized Compressed Sensing for Partial Random Circulant Matrices
We provide the first analysis of a non-trivial quantization scheme for compressed sensing measurements arising from structured measurements. Specifically, our analysis studies compressed sensing matrices consisting of rows selected at random, without replacement, from a circulant matrix generated by a random subgauss...
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Optimal Scheduling of Multi-Energy Systems with Flexible Electrical and Thermal Loads
This paper proposes a detailed optimal scheduling model of an exemplar multi-energy system comprising combined cycle power plants (CCPPs), battery energy storage systems, renewable energy sources, boilers, thermal energy storage systems,electric loads and thermal loads. The proposed model considers the detailed start...
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On the sharpness and the injective property of basic justification models
Justification Awareness Models, JAMs, were proposed by S.~Artemov as a tool for modelling epistemic scenarios like Russel's Prime Minister example. It was demonstrated that the sharpness and the injective property of a model play essential role in the epistemic usage of JAMs. The problem to axiomatize these propertie...
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AFT*: Integrating Active Learning and Transfer Learning to Reduce Annotation Efforts
The splendid success of convolutional neural networks (CNNs) in computer vision is largely attributed to the availability of large annotated datasets, such as ImageNet and Places. However, in biomedical imaging, it is very challenging to create such large annotated datasets, as annotating biomedical images is not onl...
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Do triangle-free planar graphs have exponentially many 3-colorings?
Thomassen conjectured that triangle-free planar graphs have an exponential number of $3$-colorings. We show this conjecture to be equivalent to the following statement: there exists a positive real $\alpha$ such that whenever $G$ is a planar graph and $A$ is a subset of its edges whose deletion makes $G$ triangle-fre...
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Smart TWAP trading in continuous-time equilibria
This paper presents a continuous-time equilibrium model of TWAP trading and liquidity provision in a market with multiple strategic investors with heterogeneous intraday trading targets. We solve the model in closed-form and show there are infinitely many equilibria. We compare the competitive equilibrium with differ...
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Self-sustained activity in balanced networks with low firing-rate
The brain can display self-sustained activity (SSA), which is the persistent firing of neurons in the absence of external stimuli. This spontaneous activity shows low neuronal firing rates and is observed in diverse in vitro and in vivo situations. In this work, we study the influence of excitatory/inhibitory balance...
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Fixed-Rank Approximation of a Positive-Semidefinite Matrix from Streaming Data
Several important applications, such as streaming PCA and semidefinite programming, involve a large-scale positive-semidefinite (psd) matrix that is presented as a sequence of linear updates. Because of storage limitations, it may only be possible to retain a sketch of the psd matrix. This paper develops a new algori...
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A New Perspective on Robust $M$-Estimation: Finite Sample Theory and Applications to Dependence-Adjusted Multiple Testing
Heavy-tailed errors impair the accuracy of the least squares estimate, which can be spoiled by a single grossly outlying observation. As argued in the seminal work of Peter Huber in 1973 [{\it Ann. Statist.} {\bf 1} (1973) 799--821], robust alternatives to the method of least squares are sorely needed. To achieve rob...
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