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Collaborative Summarization of Topic-Related Videos
Large collections of videos are grouped into clusters by a topic keyword, such as Eiffel Tower or Surfing, with many important visual concepts repeating across them. Such a topically close set of videos have mutual influence on each other, which could be used to summarize one of them by exploiting information from ot...
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ELICA: An Automated Tool for Dynamic Extraction of Requirements Relevant Information
Requirements elicitation requires extensive knowledge and deep understanding of the problem domain where the final system will be situated. However, in many software development projects, analysts are required to elicit the requirements from an unfamiliar domain, which often causes communication barriers between anal...
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Crystal field excitations and magnons: their roles in oxyselenides Pr2O2M2OSe2 (M = Mn, Fe)
We present the results of neutron scattering experiments to study the crystal and magnetic structures of the Mott-insulating transition metal oxyselenides Pr2O2M2OSe2 (M = Mn, Fe). The structural role of the non-Kramers Pr3+ ion is investigated and analysis of Pr3+ crystal field excitations performed. Long-range orde...
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Redistributing Funds across Charitable Crowdfunding Campaigns
On Kickstarter only 36% of crowdfunding campaigns successfully raise sufficient funds for their projects. In this paper, we explore the possibility of redistribution of crowdfunding donations to increase the chances of success. We define several intuitive redistribution policies and, using data from a real crowdfundi...
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Far-HO: A Bilevel Programming Package for Hyperparameter Optimization and Meta-Learning
In (Franceschi et al., 2018) we proposed a unified mathematical framework, grounded on bilevel programming, that encompasses gradient-based hyperparameter optimization and meta-learning. We formulated an approximate version of the problem where the inner objective is solved iteratively, and gave sufficient conditions...
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Analysis of Coupled Scalar Systems by Displacement Convexity
Potential functionals have been introduced recently as an important tool for the analysis of coupled scalar systems (e.g. density evolution equations). In this contribution, we investigate interesting properties of this potential. Using the tool of displacement convexity, we show that, under mild assumptions on the s...
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Deterministic subgraph detection in broadcast CONGEST
We present simple deterministic algorithms for subgraph finding and enumeration in the broadcast CONGEST model of distributed computation: -- For any constant $k$, detecting $k$-paths and trees on $k$ nodes can be done in $O(1)$ rounds. -- For any constant $k$, detecting $k$-cycles and pseudotrees on $k$ nodes can be...
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On Graded Lie Algebras of Characteristic Three With Classical Reductive Null Component
We consider finite-dimensional irreducible transitive graded Lie algebras $L = \sum_{i=-q}^rL_i$ over algebraically closed fields of characteristic three. We assume that the null component $L_0$ is classical and reductive. The adjoint representation of $L$ on itself induces a representation of the commutator subalgeb...
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Femtosecond mega-electron-volt electron microdiffraction
Instruments to visualize transient structural changes of inhomogeneous materials on the nanometer scale with atomic spatial and temporal resolution are demanded to advance materials science, bioscience, and fusion sciences. One such technique is femtosecond electron microdiffraction, in which a short pulse of electro...
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Deep Recurrent Neural Network for Protein Function Prediction from Sequence
As high-throughput biological sequencing becomes faster and cheaper, the need to extract useful information from sequencing becomes ever more paramount, often limited by low-throughput experimental characterizations. For proteins, accurate prediction of their functions directly from their primary amino-acid sequences...
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CubemapSLAM: A Piecewise-Pinhole Monocular Fisheye SLAM System
We present a real-time feature-based SLAM (Simultaneous Localization and Mapping) system for fisheye cameras featured by a large field-of-view (FoV). Large FoV cameras are beneficial for large-scale outdoor SLAM applications, because they increase visual overlap between consecutive frames and capture more pixels belo...
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$J$-holomorphic disks with pre-Lagrangian boundary conditions
The purpose of this paper is to carry out a classical construction of a non-constant holomorphic disk with boundary on (the suspension of) a Lagrangian submanifold in $\mathbb{R}^{2 n}$ in the case the Lagrangian is the lift of a coisotropic (a.k.a. pre-Lagrangian) submanifold in (a subset $U$ of) $\mathbb{R}^{2 n - ...
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Evolutionary sequences for hydrogen-deficient white dwarfs
We present a set of full evolutionary sequences for white dwarfs with hydrogen-deficient atmospheres. We take into account the evolutionary history of the progenitor stars, all the relevant energy sources involved in the cooling, element diffusion in the very outer layers, and outer boundary conditions provided by ne...
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On the uniqueness of complete biconservative surfaces in $\mathbb{R}^3$
We study the uniqueness of complete biconservative surfaces in the Euclidean space $\mathbb{R}^3$, and prove that the only complete biconservative regular surfaces in $\mathbb{R}^3$ are either $CMC$ or certain surfaces of revolution. In particular, any compact biconservative regular surface in $\mathbb{R}^3$ is a rou...
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Quantum Annealing Applied to De-Conflicting Optimal Trajectories for Air Traffic Management
We present the mapping of a class of simplified air traffic management (ATM) problems (strategic conflict resolution) to quadratic unconstrained boolean optimization (QUBO) problems. The mapping is performed through an original representation of the conflict-resolution problem in terms of a conflict graph, where node...
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On rumour propagation among sceptics
Junior, Machado and Zuluaga (2011) studied a model to understand the spread of a rumour. Their model consists of individuals situated at the integer points of the line $\N$. An individual at the origin $0$ starts a rumour and passes it to all individuals in the interval $[0,R_0]$, where $R_0$ is a non-negative random...
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Neutron activation and prompt gamma intensity in Ar/CO$_{2}$-filled neutron detectors at the European Spallation Source
Monte Carlo simulations using MCNP6.1 were performed to study the effect of neutron activation in Ar/CO$_{2}$ neutron detector counting gas. A general MCNP model was built and validated with simple analytical calculations. Simulations and calculations agree that only the $^{40}$Ar activation can have a considerable e...
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Solving 1ODEs with functions
Here we present a new approach to deal with first order ordinary differential equations (1ODEs), presenting functions. This method is an alternative to the one we have presented in [1]. In [2], we have establish the theoretical background to deal, in the extended Prelle-Singer approach context, with systems of 1ODEs....
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System Level Framework for Assessing the Accuracy of Neonatal EEG Acquisition
Significant research has been conducted in recent years to design low-cost alternatives to the current EEG monitoring systems used in healthcare facilities. Testing such systems on a vulnerable population such as newborns is complicated due to ethical and regulatory considerations that slow down the technical develop...
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Strong Consistency of Spectral Clustering for Stochastic Block Models
In this paper we prove the strong consistency of several methods based on the spectral clustering techniques that are widely used to study the community detection problem in stochastic block models (SBMs). We show that under some weak conditions on the minimal degree, the number of communities, and the eigenvalues of...
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Extremely fast simulations of heat transfer in fluidized beds
Besides their huge technological importance, fluidized beds have attracted a large amount of research because they are perfect playgrounds to investigate highly dynamic particulate flows. Their over-all behavior is determined by short-lasting particle collisions and the interaction between solid and gas phase. Modern...
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Machine learning out-of-equilibrium phases of matter
Neural network based machine learning is emerging as a powerful tool for obtaining phase diagrams when traditional regression schemes using local equilibrium order parameters are not available, as in many-body localized or topological phases. Nevertheless, instances of machine learning offering new insights have been...
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Exact Tensor Completion from Sparsely Corrupted Observations via Convex Optimization
This paper conducts a rigorous analysis for provable estimation of multidimensional arrays, in particular third-order tensors, from a random subset of its corrupted entries. Our study rests heavily on a recently proposed tensor algebraic framework in which we can obtain tensor singular value decomposition (t-SVD) tha...
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On Triangle Inequality Based Approximation Error Estimation
The distance between the true and numerical solutions in some metric is considered as the discretization error magnitude. If error magnitude ranging is known, the triangle inequality enables the estimation of the vicinity of the approximate solution that contains the exact one (exact solution enclosure). The analysis...
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Maximal solutions for the Infinity-eigenvalue problem
In this article we prove that the first eigenvalue of the $\infty-$Laplacian $$ \left\{ \begin{array}{rclcl} \min\{ -\Delta_\infty v,\, |\nabla v|-\lambda_{1, \infty}(\Omega) v \} & = & 0 & \text{in} & \Omega v & = & 0 & \text{on} & \partial \Omega, \end{array} \right. $$ has a unique (up to scalar multiplication) ma...
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Algorithmic Decision Making in the Presence of Unmeasured Confounding
On a variety of complex decision-making tasks, from doctors prescribing treatment to judges setting bail, machine learning algorithms have been shown to outperform expert human judgments. One complication, however, is that it is often difficult to anticipate the effects of algorithmic policies prior to deployment, ma...
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BL-MNE: Emerging Heterogeneous Social Network Embedding through Broad Learning with Aligned Autoencoder
Network embedding aims at projecting the network data into a low-dimensional feature space, where the nodes are represented as a unique feature vector and network structure can be effectively preserved. In recent years, more and more online application service sites can be represented as massive and complex networks,...
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Multi-channel discourse as an indicator for Bitcoin price and volume movements
This research aims to identify how Bitcoin-related news publications and online discourse are expressed in Bitcoin exchange movements of price and volume. Being inherently digital, all Bitcoin-related fundamental data (from exchanges, as well as transactional data directly from the blockchain) is available online, so...
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Fano Resonances in a Photonic Crystal Covered with a Perforated Gold Film and its Application to Biosensing
Optical properties of the photonic crystal covered with a perforated metal film were investigated and the existence of the Fano-type resonances was shown. The Fano resonances originate from the interaction between the optical Tamm state and the waveguide modes of the photonic crystal. It manifests itself as a narrow ...
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Non-Stationary Bandits with Habituation and Recovery Dynamics
Many settings involve sequential decision-making where a set of actions can be chosen at each time step, each action provides a stochastic reward, and the distribution for the reward of each action is initially unknown. However, frequent selection of a specific action may reduce its expected reward, while abstaining ...
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Exception-Based Knowledge Updates
Existing methods for dealing with knowledge updates differ greatly depending on the underlying knowledge representation formalism. When Classical Logic is used, updates are typically performed by manipulating the knowledge base on the model-theoretic level. On the opposite side of the spectrum stand the semantics for...
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Dynamics of observables in rank-based models and performance of functionally generated portfolios
In the seminal work [9], several macroscopic market observables have been introduced, in an attempt to find characteristics capturing the diversity of a financial market. Despite the crucial importance of such observables for investment decisions, a concise mathematical description of their dynamics has been missing....
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An Approach to Controller Design Based on the Generalized Cloud Model
In this paper, an approach to controller design based on the cloud models, without using the analog plant model is presented.
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A 3pi Search for Planet Nine at 3.4 microns with WISE and NEOWISE
The recent 'Planet Nine' hypothesis has led to many observational and archival searches for this giant planet proposed to orbit the Sun at hundreds of astronomical units. While trans-Neptunian object searches are typically conducted in the optical, models suggest Planet Nine could be self-luminous and potentially bri...
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Integrable 7-point discrete equations and evolution lattice equations of order 2
We consider differential-difference equations that determine the continuous symmetries of discrete equations on the triangular lattice. It is shown that a certain combination of continuous flows can be represented as a scalar evolution lattice equation of order 2. The general scheme is illustrated by a number of exam...
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Complete Analysis of a Random Forest Model
Random forests have become an important tool for improving accuracy in regression problems since their popularization by [Breiman, 2001] and others. In this paper, we revisit a random forest model originally proposed by [Breiman, 2004] and later studied by [Biau, 2012], where a feature is selected at random and the s...
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Relative Chern character number and super-connection
For two complex vector bundles admitting a homomorphism, whose singularity locates in the disjoint union of some odd--dimensional spheres, we give a formula to compute the relative Chern characteristic number of these two complex vector bundles. In particular, for a spin manifold admitting some sphere bundle structur...
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Mental Sampling in Multimodal Representations
Both resources in the natural environment and concepts in a semantic space are distributed "patchily", with large gaps in between the patches. To describe people's internal and external foraging behavior, various random walk models have been proposed. In particular, internal foraging has been modeled as sampling: in ...
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The Simulator: Understanding Adaptive Sampling in the Moderate-Confidence Regime
We propose a novel technique for analyzing adaptive sampling called the {\em Simulator}. Our approach differs from the existing methods by considering not how much information could be gathered by any fixed sampling strategy, but how difficult it is to distinguish a good sampling strategy from a bad one given the lim...
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A new method to suppress the bias in polarized intensity
Computing polarised intensities from noisy data in Stokes U and Q suffers from a positive bias that should be suppressed. To develop a correction method that, when applied to maps, should provide a distribution of polarised intensity that closely follows the signal from the source. We propose a new method to suppress...
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Bootstrapping kernel intensity estimation for nonhomogeneous point processes depending on spatial covariates
In the spatial point process context, kernel intensity estimation has been mainly restricted to exploratory analysis due to its lack of consistency. Different methods have been analysed to overcome this problem, and the inclusion of covariates resulted to be one possible solution. In this paper we focus on de\-fi\-ni...
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Levi-Kahler reduction of CR structures, products of spheres, and toric geometry
We study CR geometry in arbitrary codimension, and introduce a process, which we call the Levi-Kahler quotient, for constructing Kahler metrics from CR structures with a transverse torus action. Most of the paper is devoted to the study of Levi-Kahler quotients of toric CR manifolds, and in particular, products of od...
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Network Representation Learning: A Survey
With the widespread use of information technologies, information networks are becoming increasingly popular to capture complex relationships across various disciplines, such as social networks, citation networks, telecommunication networks, and biological networks. Analyzing these networks sheds light on different as...
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Confidence intervals for the area under the receiver operating characteristic curve in the presence of ignorable missing data
Receiver operating characteristic (ROC) curves are widely used as a measure of accuracy of diagnostic tests and can be summarized using the area under the ROC curve (AUC). Often, it is useful to construct a confidence intervals for the AUC, however, since there are a number of different proposed methods to measure va...
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Maximum Entropy Flow Networks
Maximum entropy modeling is a flexible and popular framework for formulating statistical models given partial knowledge. In this paper, rather than the traditional method of optimizing over the continuous density directly, we learn a smooth and invertible transformation that maps a simple distribution to the desired ...
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Overcoming the Sign Problem at Finite Temperature: Quantum Tensor Network for the Orbital $e_g$ Model on an Infinite Square Lattice
The variational tensor network renormalization approach to two-dimensional (2D) quantum systems at finite temperature is applied for the first time to a model suffering the notorious quantum Monte Carlo sign problem --- the orbital $e_g$ model with spatially highly anisotropic orbital interactions. Coarse-graining of...
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Nonasymptotic estimation and support recovery for high dimensional sparse covariance matrices
We propose a general framework for nonasymptotic covariance matrix estimation making use of concentration inequality-based confidence sets. We specify this framework for the estimation of large sparse covariance matrices through incorporation of past thresholding estimators with key emphasis on support recovery. This...
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Most Complex Deterministic Union-Free Regular Languages
A regular language $L$ is union-free if it can be represented by a regular expression without the union operation. A union-free language is deterministic if it can be accepted by a deterministic one-cycle-free-path finite automaton; this is an automaton which has one final state and exactly one cycle-free path from a...
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Piecewise Deterministic Markov Processes and their invariant measure
Piecewise Deterministic Markov Processes (PDMPs) are studied in a general framework. First, different constructions are proven to be equivalent. Second, we introduce a coupling between two PDMPs following the same differential flow which implies quantitative bounds on the total variation between the marginal distribu...
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Visual Speech Language Models
Language models (LM) are very powerful in lipreading systems. Language models built upon the ground truth utterances of datasets learn grammar and structure rules of words and sentences (the latter in the case of continuous speech). However, visual co-articulation effects in visual speech signals damage the performan...
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Millisecond Pulsars as Standards: Timing, positioning and communication
Millisecond pulsars (MSPs) have a great potential to set standards in timekeeping, positioning and metadata communication.
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Multipole resonances and directional scattering by hyperbolic-media antennas
We propose to use optical antennas made out of natural hyperbolic material hexagonal boron nitride (hBN), and we demonstrate that this medium is a promising alternative to plasmonic and all-dielectric materials for realizing efficient subwavelength scatterers and metasurfaces based on them. We theoretically show that...
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Discerning Dark Energy Models with High-Redshift Standard Candles
Following the success of type Ia supernovae in constraining cosmologies at lower redshift $(z\lesssim2)$, effort has been spent determining if a similarly useful standardisable candle can be found at higher redshift. {In this work we determine the largest possible magnitude discrepancy between a constant dark energy ...
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Controlling Physical Attributes in GAN-Accelerated Simulation of Electromagnetic Calorimeters
High-precision modeling of subatomic particle interactions is critical for many fields within the physical sciences, such as nuclear physics and high energy particle physics. Most simulation pipelines in the sciences are computationally intensive -- in a variety of scientific fields, Generative Adversarial Networks h...
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Max-value Entropy Search for Efficient Bayesian Optimization
Entropy Search (ES) and Predictive Entropy Search (PES) are popular and empirically successful Bayesian Optimization techniques. Both rely on a compelling information-theoretic motivation, and maximize the information gained about the $\arg\max$ of the unknown function; yet, both are plagued by the expensive computat...
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On stochastic differential equations with arbitrarily slow convergence rates for strong approximation in two space dimensions
In the recent article [Jentzen, A., Müller-Gronbach, T., and Yaroslavtseva, L., Commun. Math. Sci., 14(6), 1477--1500, 2016] it has been established that for every arbitrarily slow convergence speed and every natural number $d \in \{4,5,\ldots\}$ there exist $d$-dimensional stochastic differential equations (SDEs) wi...
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Energy Dissipation in Monolayer MoS$_2$ Electronics
The advancement of nanoscale electronics has been limited by energy dissipation challenges for over a decade. Such limitations could be particularly severe for two-dimensional (2D) semiconductors integrated with flexible substrates or multi-layered processors, both being critical thermal bottlenecks. To shed light in...
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Adaptive Estimation of Nonparametric Geometric Graphs
This article studies the recovery of graphons when they are convolution kernels on compact (symmetric) metric spaces. This case is of particular interest since it covers the situation where the probability of an edge depends only on some unknown nonparametric function of the distance between latent points, referred t...
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Angular and Temporal Correlation of V2X Channels Across Sub-6 GHz and mmWave Bands
5G millimeter wave (mmWave) technology is envisioned to be an integral part of next-generation vehicle-to-everything (V2X) networks and autonomous vehicles due to its broad bandwidth, wide field of view sensing, and precise localization capabilities. The reliability of mmWave links may be compromised due to difficult...
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Comparison of Decision Tree Based Classification Strategies to Detect External Chemical Stimuli from Raw and Filtered Plant Electrical Response
Plants monitor their surrounding environment and control their physiological functions by producing an electrical response. We recorded electrical signals from different plants by exposing them to Sodium Chloride (NaCl), Ozone (O3) and Sulfuric Acid (H2SO4) under laboratory conditions. After applying pre-processing t...
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Interactive Reinforcement Learning for Object Grounding via Self-Talking
Humans are able to identify a referred visual object in a complex scene via a few rounds of natural language communications. Success communication requires both parties to engage and learn to adapt for each other. In this paper, we introduce an interactive training method to improve the natural language conversation ...
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Adaptive Bayesian Sampling with Monte Carlo EM
We present a novel technique for learning the mass matrices in samplers obtained from discretized dynamics that preserve some energy function. Existing adaptive samplers use Riemannian preconditioning techniques, where the mass matrices are functions of the parameters being sampled. This leads to significant complexi...
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Neutrino Fluxes from a Core-Collapse Supernova in a Model with Three Sterile Neutrinos
The characteristics of the gravitational collapse of a supernova and the fluxes of active and sterile neutrinos produced during the formation of its protoneutron core have been calculated numerically. The relative yields of active and sterile neutrinos in core matter with different degrees of neutronization have been...
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Resource Allocation for Wireless Networks: A Distributed Optimization Approach
We consider the multi-cell joint power control and scheduling problem in cellular wireless networks as a weighted sum-rate maximization problem. This formulation is very general and applies to a wide range of applications and QoS requirements. The problem is inherently hard due to objective's non-convexity and the kn...
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Modular operads and Batalin-Vilkovisky geometry
This is a copy of the article published in IMRN (2007). I describe the noncommutative Batalin-Vilkovisky geometry associated naturally with arbitrary modular operad. The classical limit of this geometry is the noncommutative symplectic geometry of the corresponding tree-level cyclic operad. I show, in particular, tha...
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Response of QD to structured beams via convolution integrals
We propose a new expression for the response of a quadrant detector using convolution integrals. This expression is easier to evaluate by hand, exploiting the properties of the convolution. Computationally, it is also practicable to use since a large number of computer programs can right away evaluate convolutions. W...
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Regularized arrangements of cellular complexes
In this paper we propose a novel algorithm to combine two or more cellular complexes, providing a minimal fragmentation of the cells of the resulting complex. We introduce here the idea of arrangement generated by a collection of cellular complexes, producing a cellular decomposition of the embedding space. The algor...
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Duality of deconfined quantum critical point in two dimensional Dirac semimetals
In this paper we discuss the N$\acute{e}$el and Kekul$\acute{e}$ valence bond solids quantum criticality in graphene Dirac semimetal. Considering the quartic four-fermion interaction $g(\bar{\psi}_i\Gamma_{ij}\psi_j)^2$ that contains spin,valley, and sublattice degrees of freedom in the continuum field theory, we fin...
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A Survey on Cloud Video Multicasting Over Mobile Networks
Since multimedia streaming has become very popular research topic in the recent years, this paper surveys the state of art techniques introduced for multimedia multicasting over mobile networks. In this paper, we give an overview of multimedia multicasting mechanisms in respect to cloud mobile communications, and we ...
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The Brauer trees of unipotent blocks
In this paper we complete the determination of the Brauer trees of unipotent blocks (with cyclic defect groups) of finite groups of Lie type. These trees were conjectured by the first author. As a consequence, the Brauer trees of principal $\ell$-blocks of finite groups are known for $\ell>71$.
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An Empirical Bayes Approach to Regularization Using Previously Published Models
This manuscript proposes a novel empirical Bayes technique for regularizing regression coefficients in predictive models. When predictions from a previously published model are available, this empirical Bayes method provides a natural mathematical framework for shrinking coefficients toward the estimates implied by t...
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On minimum distance of locally repairable codes
Distributed and cloud storage systems are used to reliably store large-scale data. Erasure codes have been recently proposed and used in real-world distributed and cloud storage systems such as Google File System, Microsoft Azure Storage, and Facebook HDFS-RAID, to enhance the reliability. In order to decrease the re...
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The MoEDAL experiment at the LHC: status and results
The MoEDAL experiment at the LHC is optimised to detect highly ionising particles such as magnetic monopoles, dyons and (multiply) electrically charged stable massive particles predicted in a number of theoretical scenarios. MoEDAL, deployed in the LHCb cavern, combines passive nuclear track detectors with magnetic m...
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Towards a population synthesis model of self-gravitating disc fragmentation and tidal downsizing II: The effect of fragment-fragment interactions
It is likely that most protostellar systems undergo a brief phase where the protostellar disc is self-gravitating. If these discs are prone to fragmentation, then they are able to rapidly form objects that are initially of several Jupiter masses and larger. The fate of these disc fragments (and the fate of planetary ...
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Credit Risk Meets Random Matrices: Coping with Non-Stationary Asset Correlations
We review recent progress in modeling credit risk for correlated assets. We start from the Merton model which default events and losses are derived from the asset values at maturity. To estimate the time development of the asset values, the stock prices are used whose correlations have a strong impact on the loss dis...
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Peptide-Spectra Matching from Weak Supervision
As in many other scientific domains, we face a fundamental problem when using machine learning to identify proteins from mass spectrometry data: large ground truth datasets mapping inputs to correct outputs are extremely difficult to obtain. Instead, we have access to imperfect hand-coded models crafted by domain exp...
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Overcoming data scarcity with transfer learning
Despite increasing focus on data publication and discovery in materials science and related fields, the global view of materials data is highly sparse. This sparsity encourages training models on the union of multiple datasets, but simple unions can prove problematic as (ostensibly) equivalent properties may be measu...
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Dirichlet Bayesian Network Scores and the Maximum Relative Entropy Principle
A classic approach for learning Bayesian networks from data is to identify a maximum a posteriori (MAP) network structure. In the case of discrete Bayesian networks, MAP networks are selected by maximising one of several possible Bayesian Dirichlet (BD) scores; the most famous is the Bayesian Dirichlet equivalent uni...
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Thermal lattice Boltzmann method for multiphase flows
New method to simulate heat transport in multiphase lattice Boltzmann (LB) method is proposed. The energy transport equation needs to be solved when phase boundaries are present. Internal energy is represented by an additional set of distribution functions, which evolve according to a LB-like equation simulating the ...
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Control for Schrödinger equation on hyperbolic surfaces
We show that the any nonempty open set on a hyperbolic surface provides observability and control for the time dependent Schrödinger equation. The only other manifolds for which this was previously known are flat tori. The proof is based on the main estimate in Dyatlov-Jin and standard arguments of control theory.
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Grand Fujii-Fujii-Nakamoto operator inequality dealing with operator order and operator chaotic order
In this paper, we shall prove that a grand Fujii-Fujii-Nakamoto operator inequality implies operator order and operator chaotic order under different conditions.
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Stability for gains from large investors' strategies in M1/J1 topologies
We prove continuity of a controlled SDE solution in Skorokhod's $M_1$ and $J_1$ topologies and also uniformly, in probability, as a non-linear functional of the control strategy. The functional comes from a finance problem to model price impact of a large investor in an illiquid market. We show that $M_1$-continuity ...
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Apparent and Intrinsic Evolution of Active Region Upflows
We analyze the evolution of Fe XII coronal plasma upflows from the edges of ten active regions (ARs) as they cross the solar disk using the Hinode Extreme Ultraviolet Imaging Spectrometer (EIS). Confirming the results of Demoulin et al. (2013, Sol. Phys. 283, 341), we find that for each AR there is an observed long t...
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Size scaling of failure strength with fat-tailed disorder in a fiber bundle model
We investigate the size scaling of the macroscopic fracture strength of heterogeneous materials when microscopic disorder is controlled by fat-tailed distributions. We consider a fiber bundle model where the strength of single fibers is described by a power law distribution over a finite range. Tuning the amount of d...
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Time-dependent focusing Mean-Field Games: the sub-critical case
We consider time-dependent viscous Mean-Field Games systems in the case of local, decreasing and unbounded coupling. These systems arise in mean-field game theory, and describe Nash equilibria of games with a large number of agents aiming at aggregation. We prove the existence of weak solutions that are minimisers of...
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Evolution of protoplanetary disks from their taxonomy in scattered light: Group I vs. Group II
High-resolution imaging reveals a large morphological variety of protoplanetary disks. To date, no constraints on their global evolution have been found from this census. An evolutionary classification of disks was proposed based on their IR spectral energy distribution, with the Group I sources showing a prominent c...
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Sandwich semigroups in locally small categories II: Transformations
Fix sets $X$ and $Y$, and write $\mathcal{PT}_{XY}$ for the set of all partial functions $X\to Y$. Fix a partial function $a:Y\to X$, and define the operation $\star_a$ on $\mathcal{PT}_{XY}$ by $f\star_ag=fag$ for $f,g\in\mathcal{PT}_{XY}$. The sandwich semigroup $(\mathcal{PT}_{XY},\star_a)$ is denoted $\mathcal{PT...
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Environmental feedback drives cooperation in spatial social dilemmas
Exploiting others is beneficial individually but it could also be detrimental globally. The reverse is also true: a higher cooperation level may change the environment in a way that is beneficial for all competitors. To explore the possible consequence of this feedback we consider a coevolutionary model where the loc...
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Finitely forcible graph limits are universal
The theory of graph limits represents large graphs by analytic objects called graphons. Graph limits determined by finitely many graph densities, which are represented by finitely forcible graphons, arise in various scenarios, particularly within extremal combinatorics. Lovasz and Szegedy conjectured that all such gr...
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Sex-biased dispersal: a review of the theory
Dispersal is ubiquitous throughout the tree of life: factors selecting for dispersal include kin competition, inbreeding avoidance and spatiotemporal variation in resources or habitat suitability. These factors differ in whether they promote male and female dispersal equally strongly, and often selection on dispersal...
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Nonequilibrium quantum dynamics of partial symmetry breaking for ultracold bosons in an optical lattice ring trap
A vortex in a Bose-Einstein condensate on a ring undergoes quantum dynamics in response to a quantum quench in terms of partial symmetry breaking from a uniform lattice to a biperiodic one. Neither the current, a macroscopic measure, nor fidelity, a microscopic measure, exhibit critical behavior. Instead, the symmetr...
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Learning Hidden Quantum Markov Models
Hidden Quantum Markov Models (HQMMs) can be thought of as quantum probabilistic graphical models that can model sequential data. We extend previous work on HQMMs with three contributions: (1) we show how classical hidden Markov models (HMMs) can be simulated on a quantum circuit, (2) we reformulate HQMMs by relaxing ...
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Gradient Descent using Duality Structures
Gradient descent is commonly used to solve optimization problems arising in machine learning, such as training neural networks. Although it seems to be effective for many different neural network training problems, it is unclear if the effectiveness of gradient descent can be explained using existing performance guar...
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On the Universal Approximation Property and Equivalence of Stochastic Computing-based Neural Networks and Binary Neural Networks
Large-scale deep neural networks are both memory intensive and computation-intensive, thereby posing stringent requirements on the computing platforms. Hardware accelerations of deep neural networks have been extensively investigated in both industry and academia. Specific forms of binary neural networks (BNNs) and s...
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Riemannian stochastic quasi-Newton algorithm with variance reduction and its convergence analysis
Stochastic variance reduction algorithms have recently become popular for minimizing the average of a large, but finite number of loss functions. The present paper proposes a Riemannian stochastic quasi-Newton algorithm with variance reduction (R-SQN-VR). The key challenges of averaging, adding, and subtracting multi...
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Higher cohomology vanishing of line bundles on generalized Springer's resolution
We give a proof of a conjecture raised by Michael Finkelberg and Andrei Ionov. As a corollary, the coefficients of multivariable version of Kostka functions introduced by Finkelberg and Ionov are non-negative.
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Strong instability of ground states to a fourth order Schrödinger equation
In this note we prove the instability by blow-up of the ground state solutions for a class of fourth order Schr\" odinger equations. This extends the first rigorous results on blowing-up solutions for the biharmonic NLS due to Boulenger and Lenzmann \cite{BoLe} and confirm numerical conjectures from \cite{BaFi, BaFiM...
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Coalescing particle systems and applications to nonlinear Fokker-Planck equations
We study a stochastic particle system with a logarithmically-singular inter-particle interaction potential which allows for inelastic particle collisions. We relate the squared Bessel process to the evolution of localized clusters of particles, and develop a numerical method capable of detecting collisions of many po...
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Periodic solution for strongly nonlinear oscillators by He's new amplitude-frequency relationship
This paper applies He's new amplitude-frequency relationship recently established by Ji-Huan He (Int J Appl Comput Math 3 1557-1560, 2017) to study periodic solutions of strongly nonlinear systems with odd nonlinearities. Some examples are given to illustrate the effectiveness, ease and convenience of the method. In ...
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Singular Degenerations of Lie Supergroups of Type $D(2,1;a)$
The complex Lie superalgebras $\mathfrak{g}$ of type $D(2,1;a)$ - also denoted by $\mathfrak{osp}(4,2;a) $ - are usually considered for "non-singular" values of the parameter $a$, for which they are simple. In this paper we introduce five suitable integral forms of $\mathfrak{g}$, that are well-defined at singular va...
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