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Calabi-Yau metrics on canonical bundles of complex flag manifolds
In the present paper we provide a description of complete Calabi-Yau metrics on the canonical bundle of generalized complex flag manifolds. By means of Lie theory we give an explicit description of complete Ricci-flat Kähler metrics obtained through the Calabi ansatz technique. We use this approach to provide several...
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The ratio of normalizing constants for Bayesian graphical Gaussian model selection
Many graphical Gaussian selection methods in a Bayesian framework use the G-Wishart as the conjugate prior on the precision matrix. The Bayes factor to compare a model governed by a graph G and a model governed by the neighboring graph G-e, derived from G by deleting an edge e, is a function of the ratios of prior an...
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Angiogenic Factors produced by Hypoxic Cells are a leading driver of Anastomoses in Sprouting Angiogenesis---a computational study
Angiogenesis - the growth of new blood vessels from a pre-existing vasculature - is key in both physiological processes and on several pathological scenarios such as cancer progression or diabetic retinopathy. For the new vascular networks to be functional, it is required that the growing sprouts merge either with an...
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Henri Bénard: Thermal convection and vortex shedding
We present in this article the work of Henri Bénard (1874-1939), French physicist who began the systematic experimental study of two hydrodynamic systems: the thermal convection of fluids heated from below (the Rayleigh-Bénard convection and the Bénard-Marangoni convection) and the periodical vortex shedding behind a...
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Surjective H-Colouring: New Hardness Results
A homomorphism from a graph G to a graph H is a vertex mapping f from the vertex set of G to the vertex set of H such that there is an edge between vertices f(u) and f(v) of H whenever there is an edge between vertices u and v of G. The H-Colouring problem is to decide whether or not a graph G allows a homomorphism t...
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Subband adaptive filter trained by differential evolution for channel estimation
The normalized subband adaptive filter (NSAF) is widely accepted as a preeminent adaptive filtering algorithm because of its efficiency under the colored excitation. However, the convergence rate of NSAF is slow. To address this drawback, in this paper, a variant of the NSAF, called the differential evolution (DE)-NS...
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Distributionally Robust Games: f-Divergence and Learning
In this paper we introduce the novel framework of distributionally robust games. These are multi-player games where each player models the state of nature using a worst-case distribution, also called adversarial distribution. Thus each player's payoff depends on the other players' decisions and on the decision of a v...
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Modeling and Reasoning About Wireless Networks: A Graph-based Calculus Approach
We propose a graph-based process calculus for modeling and reasoning about wireless networks with local broadcasts. Graphs are used at syntactical level to describe the topological structures of networks. This calculus is equipped with a reduction semantics and a labelled transition semantics. The former is used to d...
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Weyl's law on $RCD^*(K,N)$ metric measure spaces
In this paper, we will prove the Weyl's law for the asymptotic formula of Dirichlet eigenvalues on metric measure spaces with generalized Ricci curvature bounded from below.
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The area of the Mandelbrot set and Zagier's conjecture
We prove Zagier's conjecture regarding the 2-adic valuation of the coefficients $\{b_m\}$ that appear in Ewing and Schober's series formula for the area of the Mandelbrot set in the case where $m\equiv 2 \mod 4$.
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Accelerating Cross-Validation in Multinomial Logistic Regression with $\ell_1$-Regularization
We develop an approximate formula for evaluating a cross-validation estimator of predictive likelihood for multinomial logistic regression regularized by an $\ell_1$-norm. This allows us to avoid repeated optimizations required for literally conducting cross-validation; hence, the computational time can be significan...
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Realizing an optimization approach inspired from Piagets theory on cognitive development
The objective of this paper is to introduce an artificial intelligence based optimization approach, which is inspired from Piagets theory on cognitive development. The approach has been designed according to essential processes that an individual may experience while learning something new or improving his / her know...
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Catalyst design using actively learned machine with non-ab initio input features towards CO2 reduction reactions
In conventional chemisorption model, the d-band center theory (augmented sometimes with the upper edge of d-band for imporved accuarcy) plays a central role in predicting adsorption energies and catalytic activity as a function of d-band center of the solid surfaces, but it requires density functional calculations th...
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Clustering with Temporal Constraints on Spatio-Temporal Data of Human Mobility
Extracting significant places or places of interest (POIs) using individuals' spatio-temporal data is of fundamental importance for human mobility analysis. Classical clustering methods have been used in prior work for detecting POIs, but without considering temporal constraints. Usually, the involved parameters for ...
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The maximum number of zeros of $r(z) - \overline{z}$ revisited
Generalizing several previous results in the literature on rational harmonic functions, we derive bounds on the maximum number of zeros of functions $f(z) = \frac{p(z)}{q(z)} - \overline{z}$, which depend on both $\mathrm{deg}(p)$ and $\mathrm{deg}(q)$. Furthermore, we prove that any function that attains one of thes...
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High Luminosity Large Hadron Collider HL-LHC
HL-LHC federates the efforts and R&D of a large international community towards the ambitious HL- LHC objectives and contributes to establishing the European Research Area (ERA) as a focal point of global research cooperation and a leader in frontier knowledge and technologies. HL-LHC relies on strong participation f...
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Adversarial Discriminative Sim-to-real Transfer of Visuo-motor Policies
Various approaches have been proposed to learn visuo-motor policies for real-world robotic applications. One solution is first learning in simulation then transferring to the real world. In the transfer, most existing approaches need real-world images with labels. However, the labelling process is often expensive or ...
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Algebraic Bethe ansatz for the trigonometric sl(2) Gaudin model with triangular boundary
In the derivation of the generating function of the Gaudin Hamiltonians with boundary terms, we follow the same approach used previously in the rational case, which in turn was based on Sklyanin's method in the periodic case. Our derivation is centered on the quasi-classical expansion of the linear combination of the...
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Marked Temporal Dynamics Modeling based on Recurrent Neural Network
We are now witnessing the increasing availability of event stream data, i.e., a sequence of events with each event typically being denoted by the time it occurs and its mark information (e.g., event type). A fundamental problem is to model and predict such kind of marked temporal dynamics, i.e., when the next event w...
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A Bayesian framework for distributed estimation of arrival rates in asynchronous networks
In this paper we consider a network of agents monitoring a spatially distributed arrival process. Each node measures the number of arrivals seen at its monitoring point in a given time-interval with the objective of estimating the unknown local arrival rate. We propose an asynchronous distributed approach based on a ...
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Rigidity of branching microstructures in shape memory alloys
We analyze generic sequences for which the geometrically linear energy \[E_\eta(u,\chi):= \eta^{-\frac{2}{3}}\int_{B_{0}(1)} \left| e(u)- \sum_{i=1}^3 \chi_ie_i\right|^2 d x+\eta^\frac{1}{3} \sum_{i=1}^3 |D\chi_i|(B_{0}(1))\] remains bounded in the limit $\eta \to 0$. Here $ e(u) :=1/2(Du + Du^T)$ is the (linearized)...
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Study and Observation of the Variation of Accuracies of KNN, SVM, LMNN, ENN Algorithms on Eleven Different Datasets from UCI Machine Learning Repository
Machine learning qualifies computers to assimilate with data, without being solely programmed [1, 2]. Machine learning can be classified as supervised and unsupervised learning. In supervised learning, computers learn an objective that portrays an input to an output hinged on training input-output pairs [3]. Most eff...
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Network Classification in Temporal Networks Using Motifs
Network classification has a variety of applications, such as detecting communities within networks and finding similarities between those representing different aspects of the real world. However, most existing work in this area focus on examining static undirected networks without considering directed edges or temp...
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The strength of Ramsey's theorem for pairs and arbitrarily many colors
In this paper, we show that $\mathrm{RT}^{2}+\mathsf{WKL}_0$ is a $\Pi^{1}_{1}$-conservative extension of $\mathrm{B}\Sigma^0_3$.
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Joint Power Allocation and Beamforming for Energy-Efficient Two-Way Multi-Relay Communications
This paper considers the joint design of user power allocation and relay beamforming in relaying communications, in which multiple pairs of single-antenna users exchange information with each other via multiple-antenna relays in two time slots. All users transmit their signals to the relays in the first time slot whi...
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Forecasting Internally Displaced Population Migration Patterns in Syria and Yemen
Armed conflict has led to an unprecedented number of internally displaced persons (IDPs) - individuals who are forced out of their homes but remain within their country. IDPs often urgently require shelter, food, and healthcare, yet prediction of when large fluxes of IDPs will cross into an area remains a major chall...
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Entropy? Honest!
Here we deconstruct, and then in a reasoned way reconstruct, the concept of "entropy of a system," paying particular attention to where the randomness may be coming from. We start with the core concept of entropy as a COUNT associated with a DESCRIPTION; this count (traditionally expressed in logarithmic form for a n...
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Prior Convictions: Black-Box Adversarial Attacks with Bandits and Priors
We study the problem of generating adversarial examples in a black-box setting in which only loss-oracle access to a model is available. We introduce a framework that conceptually unifies much of the existing work on black-box attacks, and we demonstrate that the current state-of-the-art methods are optimal in a natu...
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A Dynamic Model of Central Counterparty Risk
We introduce a dynamic model of the default waterfall of derivatives CCPs and propose a risk sensitive method for sizing the initial margin (IM), and the default fund (DF) and its allocation among clearing members. Using a Markovian structure model of joint credit migrations, our evaluation of DF takes into account t...
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Half-Duplex Base Station with Adaptive Scheduling of the in-Band Uplink-Receptions and Downlink-Transmissions
In this paper, we propose a novel reception/transmission scheme for half-duplex base stations (BSs). In particular, we propose a half-duplex BS that employes in-band uplink-receptions from user 1 and downlink-transmissions to user 2, which occur in different time slots. Furthermore, we propose optimal adaptive schedu...
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HAT-P-26b: A Neptune-Mass Exoplanet with a Well Constrained Heavy Element Abundance
A correlation between giant-planet mass and atmospheric heavy elemental abundance was first noted in the past century from observations of planets in our own Solar System, and has served as a cornerstone of planet formation theory. Using data from the Hubble and Spitzer Space Telescopes from 0.5 to 5 microns, we cond...
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Robust Localization Using Range Measurements with Unknown and Bounded Errors
Cooperative geolocation has attracted significant research interests in recent years. A large number of localization algorithms rely on the availability of statistical knowledge of measurement errors, which is often difficult to obtain in practice. Compared with the statistical knowledge of measurement errors, it can...
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Intuitionistic Non-Normal Modal Logics: A general framework
We define a family of intuitionistic non-normal modal logics; they can bee seen as intuitionistic counterparts of classical ones. We first consider monomodal logics, which contain only one between Necessity and Possibility. We then consider the more important case of bimodal logics, which contain both modal operators...
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Externalities in Socially-Based Resource Sharing Network
This paper investigates the impact of link formation between a pair of agents on resource availability of other agents in a social cloud network, which is a special case of socially-based resource sharing systems. Specifically, we study the correlation between externalities, network size, and network density. We firs...
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Training Neural Networks as Learning Data-adaptive Kernels: Provable Representation and Approximation Benefits
Consider the problem: given data pair $(\mathbf{x}, \mathbf{y})$ drawn from a population with $f_*(x) = \mathbf{E}[\mathbf{y} | \mathbf{x} = x]$, specify a neural network and run gradient flow on the weights over time until reaching any stationarity. How does $f_t$, the function computed by the neural network at time...
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On utility maximization without passing by the dual problem
We treat utility maximization from terminal wealth for an agent with utility function $U:\mathbb{R}\to\mathbb{R}$ who dynamically invests in a continuous-time financial market and receives a possibly unbounded random endowment. We prove the existence of an optimal investment without introducing the associated dual pr...
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Stochastic Generative Hashing
Learning-based binary hashing has become a powerful paradigm for fast search and retrieval in massive databases. However, due to the requirement of discrete outputs for the hash functions, learning such functions is known to be very challenging. In addition, the objective functions adopted by existing hashing techniq...
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Nonlinear learning and learning advantages in evolutionary games
The idea of incompetence as a learning or adaptation function was introduced in the context of evolutionary games as a fixed parameter. However, live organisms usually perform different nonlinear adaptation functions such as a power law or exponential fitness growth. Here, we examine how the functional form of the le...
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Information-theoretic Limits for Community Detection in Network Models
We analyze the information-theoretic limits for the recovery of node labels in several network models. This includes the Stochastic Block Model, the Exponential Random Graph Model, the Latent Space Model, the Directed Preferential Attachment Model, and the Directed Small-world Model. For the Stochastic Block Model, t...
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Proofs of life: molecular-biology reasoning simulates cell behaviors from first principles
We axiomatize the molecular-biology reasoning style, verify compliance of the standard reference: Ptashne, A Genetic Switch, and present proof-theory-induced technologies to predict phenotypes and life cycles from genotypes. The key is to note that `reductionist discipline' entails constructive reasoning, i.e., that ...
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Beyond recursion operators
We briefly recall the history of the Nijenhuis torsion of (1,1)-tensors on manifolds and of the lesser-known Haantjes torsion. We then show how the Haantjes manifolds of Magri and the symplectic-Haantjes structures of Tempesta and Tondo generalize the classical approach to integrable systems in the bi-hamiltonian and...
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On Classical Integrability of the Hydrodynamics of Quantum Integrable Systems
Recently, a hydrodynamic description of local equilibrium dynamics in quantum integrable systems was discovered. In the diffusionless limit, this is equivalent to a certain "Bethe-Boltzmann" kinetic equation, which has the form of an integro-differential conservation law in $(1+1)$D. The purpose of the present work i...
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Transition to turbulence when the Tollmien-Schlichting and bypass routes coexist
Plane Poiseuille flow, the pressure driven flow between parallel plates, shows a route to turbulence connected with a linear instability to Tollmien-Schlichting (TS) waves, and another one, the bypass transition, that is triggered with finite amplitude perturbation. We use direct numerical simulations to explore the ...
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Interactive Exploration and Discovery of Scientific Publications with PubVis
With an exponentially growing number of scientific papers published each year, advanced tools for exploring and discovering publications of interest are becoming indispensable. To empower users beyond a simple keyword search provided e.g. by Google Scholar, we present the novel web application PubVis. Powered by a va...
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Improving phase II oncology trials using best observed RECIST response as an endpoint by modelling continuous tumour measurements
In many phase II trials in solid tumours, patients are assessed using endpoints based on the Response Evaluation Criteria in Solid Tumours (RECIST) scale. Often, analyses are based on the response rate. This is the proportion of patients who have an observed tumour shrinkage above a pre-defined level and no new tumou...
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Evans-Selberg potential on planar domains
We provide explicit formulas of Evans kernels, Evans-Selberg potentials and fundamental metrics on potential-theoretically parabolic planar domains.
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Bridging the Gap Between Computational Photography and Visual Recognition
What is the current state-of-the-art for image restoration and enhancement applied to degraded images acquired under less than ideal circumstances? Can the application of such algorithms as a pre-processing step to improve image interpretability for manual analysis or automatic visual recognition to classify scene co...
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On some conjectures of Samuels and Feige
Let $\mu_1 \ge \dotsc \ge \mu_n > 0$ and $\mu_1 + \dotsm + \mu_n = 1$. Let $X_1, \dotsc, X_n$ be independent non-negative random variables with $EX_1 = \dotsc = EX_n = 1$, and let $Z = \sum_{i=1}^n \mu_i X_i$. Let $M = \max_{1 \le i \le n} \mu_i = \mu_1$, and let $\delta > 0$ and $T = 1 + \delta$. Both Samuels and Fe...
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Adaptive Behavior Generation for Autonomous Driving using Deep Reinforcement Learning with Compact Semantic States
Making the right decision in traffic is a challenging task that is highly dependent on individual preferences as well as the surrounding environment. Therefore it is hard to model solely based on expert knowledge. In this work we use Deep Reinforcement Learning to learn maneuver decisions based on a compact semantic ...
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Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows
We present Sequential Neural Likelihood (SNL), a new method for Bayesian inference in simulator models, where the likelihood is intractable but simulating data from the model is possible. SNL trains an autoregressive flow on simulated data in order to learn a model of the likelihood in the region of high posterior de...
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Creativity: Generating Diverse Questions using Variational Autoencoders
Generating diverse questions for given images is an important task for computational education, entertainment and AI assistants. Different from many conventional prediction techniques is the need for algorithms to generate a diverse set of plausible questions, which we refer to as "creativity". In this paper we propo...
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Cooling dynamics of a single trapped ion via elastic collisions with small-mass atoms
We demonstrated sympathetic cooling of a single ion in a buffer gas of ultracold atoms with small mass. Efficient collisional cooling was realized by suppressing collision-induced heating. We attempt to explain the experimental results with a simple rate equation model and provide a quantitative discussion of the coo...
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Modulational instability in the full-dispersion Camassa-Holm equation
We determine the stability and instability of a sufficiently small and periodic traveling wave to long wavelength perturbations, for a nonlinear dispersive equation which extends a Camassa-Holm equation to include all the dispersion of water waves and the Whitham equation to include nonlinearities of medium amplitude...
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Evaluating and Modelling Hanabi-Playing Agents
Agent modelling involves considering how other agents will behave, in order to influence your own actions. In this paper, we explore the use of agent modelling in the hidden-information, collaborative card game Hanabi. We implement a number of rule-based agents, both from the literature and of our own devising, in ad...
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Rank-related dimension bounds for subspaces of bilinear forms over finite fields
Let q be a power of a prime and let V be a vector space of finite dimension n over the field of order q. Let Bil(V) denote the set of all bilinear forms defined on V x V, let Symm(V) denote the subspace of Bil(V) consisting of symmetric bilinear forms, and Alt(V) denote the subspace of alternating bilinear forms. Let...
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Multi-objective optimization to explicitly account for model complexity when learning Bayesian Networks
Bayesian Networks have been widely used in the last decades in many fields, to describe statistical dependencies among random variables. In general, learning the structure of such models is a problem with considerable theoretical interest that still poses many challenges. On the one hand, this is a well-known NP-comp...
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Simultaneous Localization and Layout Model Selection in Manhattan Worlds
In this paper, we will demonstrate how Manhattan structure can be exploited to transform the Simultaneous Localization and Mapping (SLAM) problem, which is typically solved by a nonlinear optimization over feature positions, into a model selection problem solved by a convex optimization over higher order layout struc...
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Robust method for finding sparse solutions to linear inverse problems using an L2 regularization
We analyzed the performance of a biologically inspired algorithm called the Corrected Projections Algorithm (CPA) when a sparseness constraint is required to unambiguously reconstruct an observed signal using atoms from an overcomplete dictionary. By changing the geometry of the estimation problem, CPA gives an analy...
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Humanoid Robot-Application and Influence
Application of humanoid robots has been common in the field of healthcare and education. It has been recurrently used to improve social behavior and mollify distress level among children with autism, cancer and cerebral palsy. This article discusses the same from a human factors perspective. It shows how people of di...
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Onsager's Conjecture for the Incompressible Euler Equations in Bounded Domains
The goal of this note is to show that, also in a bounded domain $\Omega \subset \mathbb{R}^n$, with $\partial \Omega\in C^2$, any weak solution, $(u(x,t),p(x,t))$, of the Euler equations of ideal incompressible fluid in $\Omega\times (0,T) \subset \mathbb{R}^n\times\mathbb{R}_t$, with the impermeability boundary cond...
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Fuzzy logic based approaches for gene regulatory network inference
The rapid advancement in high-throughput techniques has fueled the generation of large volume of biological data rapidly with low cost. Some of these techniques are microarray and next generation sequencing which provides genome level insight of living cells. As a result, the size of most of the biological databases,...
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Instrumentation for nuclear magnetic resonance in zero and ultralow magnetic field
We review instrumentation for nuclear magnetic resonance (NMR) in zero and ultra-low magnetic field (ZULF, below 0.1 $\mu$T) where detection is based on a low-cost, non-cryogenic, spin-exchange relaxation free (SERF) $^{87}$Rb atomic magnetometer. The typical sensitivity is 20-30 fT/Hz$^{1/2}$ for signal frequencies ...
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Countable dense homogeneity and the Cantor set
It is shown that CH implies the existence of a compact Hausdorff space that is countable dense homogeneous, crowded and does not contain topological copies of the Cantor set. This contrasts with a previous result by the author which says that for any crowded Hausdorff space $X$ of countable $\pi$-weight, if ${}^\omeg...
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Dimension Estimation Using Random Connection Models
Information about intrinsic dimension is crucial to perform dimensionality reduction, compress information, design efficient algorithms, and do statistical adaptation. In this paper we propose an estimator for the intrinsic dimension of a data set. The estimator is based on binary neighbourhood information about the ...
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Optimal projection of observations in a Bayesian setting
Optimal dimensionality reduction methods are proposed for the Bayesian inference of a Gaussian linear model with additive noise in presence of overabundant data. Three different optimal projections of the observations are proposed based on information theory: the projection that minimizes the Kullback-Leibler diverge...
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Notes on the Multiplicative Ergodic Theorem
The Oseledets Multiplicative Ergodic theorem is a basic result with numerous applications throughout dynamical systems. These notes provide an introduction to this theorem, as well as subsequent generalizations. They are based on lectures at summer schools in Brazil, France, and Russia.
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Targeted Learning with Daily EHR Data
Electronic health records (EHR) data provide a cost and time-effective opportunity to conduct cohort studies of the effects of multiple time-point interventions in the diverse patient population found in real-world clinical settings. Because the computational cost of analyzing EHR data at daily (or more granular) sca...
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Stripe-Based Fragility Analysis of Concrete Bridge Classes Using Machine Learning Techniques
A framework for the generation of bridge-specific fragility utilizing the capabilities of machine learning and stripe-based approach is presented in this paper. The proposed methodology using random forests helps to generate or update fragility curves for a new set of input parameters with less computational effort a...
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Accountability of AI Under the Law: The Role of Explanation
The ubiquity of systems using artificial intelligence or "AI" has brought increasing attention to how those systems should be regulated. The choice of how to regulate AI systems will require care. AI systems have the potential to synthesize large amounts of data, allowing for greater levels of personalization and pre...
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Frequency-oriented sub-sampling by photonic Fourier transform and I/Q demodulation
Sub-sampling can acquire directly a passband within a broad radio frequency (RF) range, avoiding down-conversion and low-phase-noise tunable local oscillation (LO). However, sub-sampling suffers from band folding and self-image interference. In this paper we propose a frequency-oriented sub-sampling to solve the two ...
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A moment map picture of relative balanced metrics on extremal Kähler manifolds
We give a moment map interpretation of some relatively balanced metrics. As an application, we extend a result of S. K. Donaldson on constant scalar curvature Kähler metrics to the case of extremal metrics. Namely, we show that a given extremal metric is the limit of some specific relatively balanced metrics. As a co...
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Traffic models with adversarial vehicle behaviour
We examine the impact of adversarial actions on vehicles in traffic. Current advances in assisted/autonomous driving technologies are supposed to reduce the number of casualties, but this seems to be desired despite the recently proved insecurity of in-vehicle communication buses or components. Fortunately to some ex...
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Robust Cooperative Manipulation without Force/Torque Measurements: Control Design and Experiments
This paper presents two novel control methodologies for the cooperative manipulation of an object by N robotic agents. Firstly, we design an adaptive control protocol which employs quaternion feedback for the object orientation to avoid potential representation singularities. Secondly, we propose a control protocol t...
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Conditionally conjugate mean-field variational Bayes for logistic models
Variational Bayes (VB) is a common strategy for approximate Bayesian inference, but simple methods are only available for specific classes of models including, in particular, representations having conditionally conjugate constructions within an exponential family. Models with logit components are an apparently notab...
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A $\frac{3}{2}$-Approximation Algorithm for Tree Augmentation via Chvátal-Gomory Cuts
The weighted tree augmentation problem (WTAP) is a fundamental network design problem. We are given an undirected tree $G = (V,E)$, an additional set of edges $L$ called links and a cost vector $c \in \mathbb{R}^L_{\geq 1}$. The goal is to choose a minimum cost subset $S \subseteq L$ such that $G = (V, E \cup S)$ is ...
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On Identifying Disaster-Related Tweets: Matching-based or Learning-based?
Social media such as tweets are emerging as platforms contributing to situational awareness during disasters. Information shared on Twitter by both affected population (e.g., requesting assistance, warning) and those outside the impact zone (e.g., providing assistance) would help first responders, decision makers, an...
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Self-Stabilizing Disconnected Components Detection and Rooted Shortest-Path Tree Maintenance in Polynomial Steps
We deal with the problem of maintaining a shortest-path tree rooted at some process r in a network that may be disconnected after topological changes. The goal is then to maintain a shortest-path tree rooted at r in its connected component, V\_r, and make all processes of other components detecting that r is not part...
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Optimizing wearable assistive devices with neuromuscular models and optimal control
The coupling of human movement dynamics with the function and design of wearable assistive devices is vital to better understand the interaction between the two. Advanced neuromuscular models and optimal control formulations provide the possibility to study and improve this interaction. In addition, optimal control c...
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Preferential placement for community structure formation
Various models have been recently proposed to reflect and predict different properties of complex networks. However, the community structure, which is one of the most important properties, is not well studied and modeled. In this paper, we suggest a principle called "preferential placement", which allows to model a r...
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Lower Bounds on Regret for Noisy Gaussian Process Bandit Optimization
In this paper, we consider the problem of sequentially optimizing a black-box function $f$ based on noisy samples and bandit feedback. We assume that $f$ is smooth in the sense of having a bounded norm in some reproducing kernel Hilbert space (RKHS), yielding a commonly-considered non-Bayesian form of Gaussian proces...
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Hirota bilinear equations for Painlevé transcendents
We present some observations on the tau-function for the fourth Painlevé equation. By considering a Hirota bilinear equation of order four for this tau-function, we describe the general form of the Taylor expansion around an arbitrary movable zero. The corresponding Taylor series for the tau-functions of the first an...
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Gradient-based Representational Similarity Analysis with Searchlight for Analyzing fMRI Data
Representational Similarity Analysis (RSA) aims to explore similarities between neural activities of different stimuli. Classical RSA techniques employ the inverse of the covariance matrix to explore a linear model between the neural activities and task events. However, calculating the inverse of a large-scale covari...
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Diffeomorphic random sampling using optimal information transport
In this article we explore an algorithm for diffeomorphic random sampling of nonuniform probability distributions on Riemannian manifolds. The algorithm is based on optimal information transport (OIT)---an analogue of optimal mass transport (OMT). Our framework uses the deep geometric connections between the Fisher-R...
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On approximations by trigonometric polynomials of classes of functions defined by moduli of smoothness
In this paper, we give a characterization of Nikol'ski\u{\i}-Besov type classes of functions, given by integral representations of moduli of smoothness, in terms of series over the moduli of smoothness. Also, necessary and sufficient conditions in terms of monotone or lacunary Fourier coefficients for a function to b...
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Topologically protected Dirac plasmons in graphene
Topological optical states exhibit unique immunity to defects and the ability to propagate without losses rendering them ideal for photonic applications.A powerful class of such states is based on time-reversal symmetry breaking of the optical response.However, existing proposals either involve sophisticated and bulk...
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The K-Nearest Neighbour UCB algorithm for multi-armed bandits with covariates
In this paper we propose and explore the k-Nearest Neighbour UCB algorithm for multi-armed bandits with covariates. We focus on a setting where the covariates are supported on a metric space of low intrinsic dimension, such as a manifold embedded within a high dimensional ambient feature space. The algorithm is conce...
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Proportional Mean Residual Life Model with Censored Survival Data under Case-cohort Design
Proportional mean residual life model is studied for analysing survival data from the case-cohort design. To simultaneously estimate the regression parameters and the baseline mean residual life function, weighted estimating equations based on an inverse selection probability are proposed. The resulting regression co...
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Shape differentiation of a steady-state reaction-diffusion problem arising in Chemical Engineering: the case of non-smooth kinetic with dead core
In this paper we consider an extension of the results in shape differentiation of semilinear equations with smooth nonlinearity presented in J.I. Díaz and D. Gómez-Castro: An Application of Shape Differentiation to the Effectiveness of a Steady State Reaction-Diffusion Problem Arising in Chemical Engineering. Electro...
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Analytic evaluation of Coulomb integrals for one, two and three-electron distance operators, $R_{C1}^{-n}R_{D1}^{-m}$, $R_{C1}^{-n}r_{12}^{-m}$ and $r_{12}^{-n}r_{13}^{-m}$ with $n, m=0,1,2$
The state of the art for integral evaluation is that analytical solutions to integrals are far more useful than numerical solutions. We evaluate certain integrals analytically that are necessary in some approaches in quantum chemistry. In the title, where R stands for nucleus-electron and r for electron-electron dist...
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Herschel-PACS photometry of faint stars
Our aims are to determine flux densities and their photometric accuracy for a set of seventeen stars that range in flux from intermediately bright (<2.5 Jy) to faint (>5 mJy) in the far-infrared (FIR). We also aim to derive signal-to-noise dependence with flux and time, and compare the results with predictions from t...
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Role of zero synapses in unsupervised feature learning
Synapses in real neural circuits can take discrete values, including zero (silent or potential) synapses. The computational role of zero synapses in unsupervised feature learning of unlabeled noisy data is still unclear, thus it is important to understand how the sparseness of synaptic activity is shaped during learn...
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On the Pervasiveness of Difference-Convexity in Optimization and Statistics
With the increasing interest in applying the methodology of difference-of-convex (dc) optimization to diverse problems in engineering and statistics, this paper establishes the dc property of many well-known functions not previously known to be of this class. Motivated by a quadratic programming based recourse functi...
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Stochastic Dynamic Optimal Power Flow in Distribution Network with Distributed Renewable Energy and Battery Energy Storage
The penetration of distributed renewable energy (DRE) greatly raises the risk of distribution network operation such as peak shaving and voltage stability. Battery energy storage (BES) has been widely accepted as the most potential application to cope with the challenge of high penetration of DRE. To cope with the un...
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Achievable Rate Region of the Zero-Forcing Precoder in a 2 X 2 MU-MISO Broadcast VLC Channel with Per-LED Peak Power Constraint and Dimming Control
In this paper, we consider the 2 X 2 multi-user multiple-input-single-output (MU-MISO) broadcast visible light communication (VLC) channel with two light emitting diodes (LEDs) at the transmitter and a single photo diode (PD) at each of the two users. We propose an achievable rate region of the Zero-Forcing (ZF) prec...
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Autonomous Electric Race Car Design
Autonomous driving and electric vehicles are nowadays very active research and development areas. In this paper we present the conversion of a standard Kyburz eRod into an autonomous vehicle that can be operated in challenging environments such as Swiss mountain passes. The overall hardware and software architectures...
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Temporal Stable Community in Time-Varying Networks
Identifying community structure of a complex network provides insight to the interdependence between the network topology and emergent collective behaviors of networks, while detecting such invariant communities in a time-varying network is more challenging. In this paper, we define the temporal stable community and ...
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The shape of a rapidly rotating polytrope with index unity
We show that the solutions obtained in the paper `An exact solution for arbitrarily rotating gaseous polytropes with index unity' by Kong, Zhang, and Schubert represent only approximate solutions of the free-boundary Euler-Poisson system of equations describing uniformly rotating, self-gravitating polytropes with ind...
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Measurement of the Planck constant at the National Institute of Standards and Technology from 2015 to 2017
Researchers at the National Institute of Standards and Technology(NIST) have measured the value of the Planck constant to be $h =6.626\,069\,934(89)\times 10^{-34}\,$J$\,$s (relative standard uncertainty $13\times 10^{-9}$). The result is based on over 10$\,$000 weighings of masses with nominal values ranging from 0....
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Event Stream-Based Process Discovery using Abstract Representations
The aim of process discovery, originating from the area of process mining, is to discover a process model based on business process execution data. A majority of process discovery techniques relies on an event log as an input. An event log is a static source of historical data capturing the execution of a business pr...
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On $C$-bases, partition pairs and filtrations for induced or restricted Specht modules
We obtain alternative explicit Specht filtrations for the induced and the restricted Specht modules in the Hecke algebra of the symmetric group (defined over the ring $A=\mathbb Z[q^{1/2},q^{-1/2}]$ where $q$ is an indeterminate) using $C$-bases for these modules. Moreover, we provide a link between a certain $C$-bas...
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