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Weak solutions of the Landau--Lifshitz--Bloch equationMay 16 2016The Landau--Lifshitz--Bloch (LLB) equation is a formulation of dynamic micromagnetics valid at all temperatures, treating both the transverse and longitudinal relaxation components important for high-temperature applications. We study LLB equation in ... More

A convergent finite element approximation for the quasi-static Maxwell--Landau--Lifshitz--Gilbert equationsDec 13 2012We propose a $\theta$-linear scheme for the numerical solution of the quasi-static Maxwell-Landau-Lifshitz-Gilbert (MLLG) equations. Despite the strong nonlinearity of the Landau-Lifshitz-Gilbert equation, the proposed method results in a linear system ... More

Finite element approximation of a time-fractional diffusion problem in a non-convex polygonal domainJan 29 2016An initial-boundary value problem for the time-fractional diffusion equation is discretized in space using continuous piecewise-linear finite elements on a polygonal domain with a re-entrant corner. Known error bounds for the case of a convex polygon ... More

A semidiscrete finite element approximation of a time-fractional Fokker-Planck equation with nonsmooth initial dataFeb 08 2019We present a new stability and convergence analysis for the spatial discretization of a time-fractional Fokker--Planck equation in a convex polyhedral domain, using continuous, piecewise-linear, finite elements. The forcing may depend on time as well ... More

A finite element approximation for the stochastic Landau-Lifshitz-Gilbert equationAug 19 2013Feb 04 2015The stochastic Landau--Lifshitz--Gilbert (LLG) equation describes the behaviour of the magnetization under the influence of the effective field consisting of random fluctuations. We first reformulate the equation into an equation the unknown of which ... More

Numerical solution of the time-fractional Fokker-Planck equation with general forcingJul 21 2015We study two schemes for a time-fractional Fokker-Planck equation with space- and time-dependent forcing in one space dimension. The first scheme is continuous in time and is discretized in space using a piecewise-linear Galerkin finite element method. ... More

Existence, uniqueness and regularity of the solution of the time-fractional Fokker-Planck equation with general forcingFeb 07 2019A time-fractional Fokker-Planck initial-boundary value problem is considered, with differential operator $u_t-\nabla\cdot(\partial_t^{1-\alpha}\kappa_\alpha\nabla u-\textbf{F}\partial_t^{1-\alpha}u)$, where $0<\alpha <1$. The forcing function $\textbf{F} ... More

On a decoupled linear FEM integrator for Eddy-current-LLGJun 14 2013We propose a numerical integrator for the coupled system of the eddy-current equation with the nonlinear Landau-Lifshitz-Gilbert equation. The considered effective field contains a general field contribution, and we particularly cover exchange, anisotropy, ... More

The Positive Maximum Principle on Symmetric SpacesFeb 11 2019We investigate the Courr\`{e}ge theorem in the context of linear operators $A$ that satisfy the positive maximum principle on a space of continuous functions over a symmetric space. Applications are given to Feller--Markov processes. We also introduce ... More

Modules de cycles et classes non ramifiées sur un espace classifiantNov 01 2012Jan 31 2015Let G be a finite group of exponent m and let k be a field of characteristic prime to m, containing the m-th roots of unity. For any Rost cycle module M over k, we construct exact sequences detecting the unramified elements in Serre's group of invariants ... More

Deep Recurrent Level Set for Segmenting Brain TumorsOct 10 2018Variational Level Set (VLS) has been a widely used method in medical segmentation. However, segmentation accuracy in the VLS method dramatically decreases when dealing with intervening factors such as lighting, shadows, colors, etc. Additionally, results ... More

Temporal Non-Volume Preserving Approach to Facial Age-Progression and Age-Invariant Face RecognitionMar 24 2017Modeling the long-term facial aging process is extremely challenging due to the presence of large and non-linear variations during the face development stages. In order to efficiently address the problem, this work first decomposes the aging process into ... More

Deep Contextual Recurrent Residual Networks for Scene LabelingApr 12 2017Designed as extremely deep architectures, deep residual networks which provide a rich visual representation and offer robust convergence behaviors have recently achieved exceptional performance in numerous computer vision problems. Being directly applied ... More

Automated Mutual Explicit Induction Proof in Separation LogicSep 04 2016Sep 06 2016We present a sequent-based deductive system for automatically proving entailments in separation logic by using mathematical induction. Our technique, called mutual explicit induction proof, is an instance of Noetherian induction. Specifically, we propose ... More

Towards a Deep Learning Framework for Unconstrained Face DetectionDec 16 2016Jan 02 2017Robust face detection is one of the most important pre-processing steps to support facial expression analysis, facial landmarking, face recognition, pose estimation, building of 3D facial models, etc. Although this topic has been intensely studied for ... More

On comparison principle and strict positivity of solutions to the nonlinear stochastic fractional heat equationsOct 02 2014In this paper, we prove a sample-path comparison principle for the nonlinear stochastic fractional heat equation on $\mathbb{R}$ with measure-valued initial data. We give quantitative estimates about how close to zero the solution can be. These results ... More

Nonlinear stochastic heat equation driven by spatially colored noise: moments and intermittencyOct 20 2015In this paper, we study the stochastic heat equation in the spatial domain $\mathbb{R}^d$ subject to a Gaussian noise which is white in time and colored in space. The spatial correlation can be any symmetric, nonnegative and nonnegative-definite function ... More

Learning from Longitudinal Face Demonstration - Where Tractable Deep Modeling Meets Inverse Reinforcement LearningNov 28 2017Feb 02 2019This paper presents a novel Subject-dependent Deep Aging Path (SDAP), which inherits the merits of both Generative Probabilistic Modeling and Inverse Reinforcement Learning to model the facial structures and the longitudinal face aging process of a given ... More

Scalar decay in a three-dimensional chaotic flowJan 31 2011Mar 15 2011The decay of a passive scalar in a three-dimensional chaotic flow is studied using high-resolution numerical simulations. The (volume-preserving) flow considered is a three-dimensional extension of the randomised alternating sine flow employed extensively ... More

Probing the elastic limit of DNA bendingMay 02 2014Many structures inside the cell such as nucleosomes and protein-mediated DNA loops contain sharply bent double-stranded (ds) DNA. Therefore, the energetics of strong dsDNA bending constitutes an essential part of cellular thermodynamics. Although the ... More

Decorrelation of total mass via energyOct 23 2014The main result of this small note is a quantified version of the assertion that if u and v solve two nonlinear stochastic heat equations, and if the mutual energy between the initial states of the two stochastic PDEs is small, then the total masses of ... More

A Boundedness Trichotomy for the Stochastic Heat EquationOct 15 2015We consider the stochastic heat equation with a multiplicative white noise forcing term under standard "intermitency conditions." The main finding of this paper is that, under mild regularity hypotheses, the a.s.-boundedness of the solution $x\mapsto ... More

Hybrid Video Signal Coding Technologies: Past, Current and FutureJul 20 2016The growing needs for high-quality video applications have resulted in a lot of studies and developments in video signal coding. This chapter presents some advanced techniques in enhancing the rate-distortion performance of the block-based hybrid video ... More

Using gaps in N-body tidal streams to probe missing satellitesNov 07 2013Jun 11 2014We use N-body simulations to model the tidal disruption of a star cluster in a Milky-Way-sized dark matter halo, which results in a narrow stream comparable to (but slightly wider than) Pal-5 or GD-1. The mean Galactic dark matter halo is modeled by a ... More

Variable-Length Feedback Codes under a Strict Delay ConstraintFeb 23 2015We study variable-length feedback (VLF) codes under a strict delay constraint to maximize their average transmission rate (ATR) in a discrete memoryless channel (DMC) while considering periodic decoding attempts. We first derive a lower bound on the maximum ... More

Dense blowup for parabolic SPDEsFeb 27 2017The main result of this paper is that there are examples of stochastic partial differential equations [hereforth, SPDEs] of the type $$ \partial_t u=\frac12\Delta u +\sigma(u)\eta \qquad\text{on $(0\,,\infty)\times\mathbb{R}^3$}$$ such that the solution ... More

Dissipation and high disorderNov 24 2014Given a field $\{B(x)\}_{x\in\mathbf{Z}^d}$ of independent standard Brownian motions, indexed by $\mathbf{Z}^d$, the generator of a suitable Markov process on $\mathbf{Z}^d,\,\,\mathcal{G},$ and sufficiently nice function $\sigma:[0,\infty)\to[0,\infty),$ ... More

Spin-wave contributions to current-induced domain wall dynamicsDec 22 2008We examine theoretically the role of spin-waves on current-induced domain wall dynamics in a ferromagnetic wire. At room temperature, we find that an interaction between the domain wall and the spin waves appears when there is a finite difference between ... More

The MBHBM* Project -- I: Measurement of the Central Black Hole Mass in Dwarf Galaxy NGC 3504 Using Molecular Gas KinematicsFeb 11 2019We present the first measurement of the mass of a supermassive black hole (SMBH) in the nearby double-barred spiral galaxy NGC 3504 as part of the Measuring Black Holes Below the Milky Way ($M_{\star}$) mass galaxies (MBHBM$_{\star}$) Project. Our analysis ... More

Simple 3-3-1 model and implication for dark matterJul 14 2014Oct 06 2014We propose a new and realistic 3-3-1 model with the minimal lepton and scalar contents, named the simple 3-3-1 model. The scalar sector contains two new heavy Higgs bosons, one neutral H and another singly-charged H^\pm, besides the standard model Higgs ... More

Watch out for This Commit! A Study of Influential Software ChangesJun 10 2016One single code change can significantly influence a wide range of software systems and their users. For example, 1) adding a new feature can spread defects in several modules, while 2) changing an API method can improve the performance of all client ... More

Semantic Context Forests for Learning-Based Knee Cartilage Segmentation in 3D MR ImagesJul 11 2013Apr 22 2014The automatic segmentation of human knee cartilage from 3D MR images is a useful yet challenging task due to the thin sheet structure of the cartilage with diffuse boundaries and inhomogeneous intensities. In this paper, we present an iterative multi-class ... More

Polyaromatic disordered carbon grains as carriers of the UV bump: FUV to mid-infrared spectroscopy of laboratory analogsNov 16 2017A multiwavelength study of laboratory carbons with varying degrees of hydrogenation and sp$^2$ hybridization is required to characterize the structure of the carbonaceous carriers of interstellar and circumstellar extinction. Analogs to carbonaceous interstellar ... More

Interleaved Text/Image Deep Mining on a Large-Scale Radiology Database for Automated Image InterpretationMay 04 2015Despite tremendous progress in computer vision, there has not been an attempt for machine learning on very large-scale medical image databases. We present an interleaved text/image deep learning system to extract and mine the semantic interactions of ... More

Unsupervised Category Discovery via Looped Deep Pseudo-Task Optimization Using a Large Scale Radiology Image DatabaseMar 25 2016Obtaining semantic labels on a large scale radiology image database (215,786 key images from 61,845 unique patients) is a prerequisite yet bottleneck to train highly effective deep convolutional neural network (CNN) models for image recognition. Nevertheless, ... More

Two-magnon Raman scattering and pseudospin-lattice interactions in Sr2IrO4 and Sr3Ir2O7Sep 11 2015We have used Raman scattering to investigate the magnetic excitations and lattice dynamics in the prototypical spin-orbit Mott insulators Sr2IrO4 and Sr3Ir2O7. Both compounds exhibit pronounced two-magnon Raman scattering features with different energies, ... More

FixMiner: Mining Relevant Fix Patterns for Automated Program RepairOct 03 2018Code comprehension is critical in software maintenance. Towards providing tools and approaches to support maintenance tasks, researchers have investigated various research lines related to how software code can be described in an abstract form. So far, ... More

Medium Resolution Near-Infrared Spectra of the Host Galaxies of Nearby QuasarsMay 20 2014Jun 09 2014We present medium resolution near-infrared host galaxy spectra of low redshift quasars, PG 0844 + 349 (z=0.064), PG 1226 + 023 (z=0.158), and PG 1426+015 (z=0.086). The observations were done by using the Infrared Camera and Spectrograph (IRCS) at the ... More

Impact of Tool Support in Patch ConstructionDec 18 2018In this work, we investigate the practice of patch construction in the Linux kernel development, focusing on the differences between three patching processes: (1) patches crafted entirely manually to fix bugs, (2) those that are derived from warnings ... More

You Cannot Fix What You Cannot Find! An Investigation of Fault Localization Bias in Benchmarking Automated Program Repair SystemsDec 18 2018Properly benchmarking Automated Program Repair (APR) systems should contribute to the development and adoption of the research outputs by practitioners. To that end, the research community must ensure that it reaches significant milestones by reliably ... More

Machine Learning for Vehicular NetworksDec 19 2017Feb 26 2018The emerging vehicular networks are expected to make everyday vehicular operation safer, greener, and more efficient, and pave the path to autonomous driving in the advent of the fifth generation (5G) cellular system. Machine learning, as a major branch ... More

D&C: A Divide-and-Conquer Approach to IR-based Bug LocalizationFeb 07 2019Many automated tasks in software maintenance rely on information retrieval techniques to identify specific information within unstructured data. Bug localization is such a typical task, where text in a bug report is analyzed to identify file locations ... More

Optical Characterization of PtSi/Si by Spectroscopic EllipsometryJun 12 2016We report optical characterization of PtSi films for thermoelectric device applications by nondestructive spectroscopic ellipsometry (SE). Pt monolayer and Pt-Si multilayer which consists of 3 pairs of Pt and Si layers were deposited on p-doped-silicon ... More

Improving Computer-aided Detection using Convolutional Neural Networks and Random View AggregationMay 12 2015Sep 15 2015Automated computer-aided detection (CADe) in medical imaging has been an important tool in clinical practice and research. State-of-the-art methods often show high sensitivities but at the cost of high false-positives (FP) per patient rates. We design ... More

Unsupervised Joint Mining of Deep Features and Image Labels for Large-scale Radiology Image Categorization and Scene RecognitionJan 23 2017Dec 27 2017The recent rapid and tremendous success of deep convolutional neural networks (CNN) on many challenging computer vision tasks largely derives from the accessibility of the well-annotated ImageNet and PASCAL VOC datasets. Nevertheless, unsupervised image ... More

Survey of Promising Technologies for 5G NetworksDec 21 2016As an enhancement of cellular networks, the future-generation 5G network can be considered an ultra-high-speed technology. The proposed 5G network might include all types of advanced dominant technologies to provide remarkable services. Consequently, ... More

Simulating tidal streams in a high resolution dark matter haloNov 13 2014Apr 20 2015We simulate tidal streams in the presence and absence of substructures inside the zero redshift snapshot of the Via Lactea II (VL-2) simulation. A halo finder is used to remove and isolate the subhalos found inside the high resolution dark matter halo ... More

Preliminary DIMM and MASS Nighttime Seeing Measurements at PEARL, in the Canadian High ArcticMay 24 2013Results of deploying a Differential Image Motion Monitor (DIMM) and a DIMM combined with a Multi-Aperture Scintillation Sensor (MASS/DIMM) are reported for campaigns in 2011 and 2012 on the roof of the Polar Environment Atmospheric Research Laboratory ... More

Crystal growth and intrinsic magnetic behavior of Sr$_2$IrO$_4$Sep 21 2015Oct 01 2015We report on the growth of stoichiometric Sr$_2$IrO$_4$ single crystals, which allow us to unveil their intrinsic magnetic properties. The effect of different growth conditions has been investigated for crystals grown by the flux method. We find that ... More

Anatomy-specific classification of medical images using deep convolutional netsApr 15 2015Automated classification of human anatomy is an important prerequisite for many computer-aided diagnosis systems. The spatial complexity and variability of anatomy throughout the human body makes classification difficult. "Deep learning" methods such ... More

Limits to the sensitivity of a low noise compact atomic gravimeterJan 08 2008A detailed analysis of the most relevant sources of phase noise in an atomic interferometer is carried out, both theoretically and experimentally. Even a short interrogation time of 100 ms allows our cold atom gravimeter to reach an excellent short term ... More

Influence of lasers propagation delay on the sensitivity of atom interferometersJan 02 2007In atom interferometers based on two photon transitions, the delay induced by the difference of the laser beams paths makes the interferometer sensitive to the fluctuations of the frequency of the lasers. We first study, in the general case, how the laser ... More

Non-Gaussian errors of baryonic acoustic oscillationsJun 28 2011Jan 11 2012We revisit the uncertainty in baryon acoustic oscillation (BAO) forecasts and data analyses. In particular, we study how much the uncertainties on both the measured mean dilation scale and the associated error bar are affected by the non-Gaussianity of ... More

Phenomenology of the SU(3)_C \otimes SU(2)_L \otimes SU(3)_R \otimes U(1)_X gauge modelSep 12 2016We study the left-right asymmetric model based on SU(3)_C\otimes SU(2)_L \otimes SU(3)_R\otimes U(1)_X gauge group, which improves the theoretical and phenomenological aspects of the known left-right symmetric model. This new gauge symmetry yields that ... More

Dispersal of tidal debris in a Milky-Way-sized dark matter haloJan 18 2016Mar 02 2016We simulate the tidal disruption of a collisionless N-body globular star cluster in a total of 300 different orbits selected to have galactocentric radii between 10 and 30 kpc in four dark matter halos: (a) a spherical halo with no subhalos, (b) a spherical ... More

Probing Neutrino and Higgs sectors in SU(2)_1 X SU(2)_2 X U(1)_Y model with lepton-flavor non-universalityNov 21 2016The neutrino and Higgs sectors in the SU(2}_1 X SU(2)_2 X U(1)_Y model with lepton-flavor non-universality are discussed. We show that active neutrinos can get Majorana masses from radiative corrections, after adding only new singly charged Higgs bosons. ... More

3D Facial Expression Reconstruction using Cascaded RegressionDec 10 2017Aug 17 2018This paper proposes a novel model fitting algorithm for 3D facial expression reconstruction from a single image. Face expression reconstruction from a single image is a challenging task in computer vision. Most state-of-the-art methods fit the input image ... More

Temperature-Dependent Interplay of Dzyaloshinskii-Moriya Interaction and Single-Ion Anisotropy in Multiferroic BiFeO$_3$Aug 13 2014Sep 12 2014Low-energy magnon excitations in multiferroic BiFeO$_3$ were measured in detail as a function of temperature around several Brillouin zone centers by inelastic neutron scattering experiments on single crystals. Unique features around 1 meV are directly ... More

Deviation from Fermi-liquid behavior in two-dimensional surface states of Au-induced nanowires on Ge(001) by correlation and localizationFeb 17 2016The electronic states of Au-induced atomic nanowires on Ge(001) (Au/Ge(001) NWs) have been investigated by angle-resolved photoelectron spectroscopy with linearly polarized light. We have found three electron pockets around $\bar{J}\bar{K}$, where the ... More

Compressed DiffusionJan 31 2019Diffusion maps are a commonly used kernel-based method for manifold learning, which can reveal intrinsic structures in data and embed them in low dimensions. However, as with most kernel methods, its implementation requires a heavy computational load, ... More

Application of machine learning algorithms to the study of noise artifacts in gravitational-wave dataMar 27 2013The sensitivity of searches for astrophysical transients in data from the LIGO is generally limited by the presence of transient, non-Gaussian noise artifacts, which occur at a high-enough rate such that accidental coincidence across multiple detectors ... More

Doping dependence of magnetic excitations in Sr$_{2-x}$La$_x$IrO$_4$Mar 24 2016We have studied the magnetic excitations of electron-doped Sr$_{2-x}$La$_x$IrO$_4$ ($0 \leq x \leq 0.10$) using resonant inelastic x-ray scattering (RIXS) at the Ir L$_3$-edge. The long range magnetic order is rapidly lost with increasing $x$, but two-dimensional ... More

Successive spin-flop transitions of Neel-type antiferromagnet Li$_2$MnO$_3$ single crystal with honeycomb-latticeSep 03 2014We have carried out high magnetic field studies of single-crystalline Li$_2$MnO$_3$, a honeycomb lattice antiferromagnet. Its magnetic phase diagram was mapped out using magnetization measurements at applied fields up to 35 T. Our results show that it ... More

Power-laws and the Conservation of Information in discrete token systems: Part 2 The role of defectSep 07 2012In a matching paper (arXiv:1207.5027), I proved that Conservation of Size and Information in a discrete token based system is overwhelmingly likely to lead to a power-law component size distribution with respect to the size of its unique alphabet. This ... More

A proof of the Kazdan-Warner identity via the Minkowski spacetimeFeb 05 2016Any 2-dim Riemannian manifold with spherical topology can be embedded isometrically into a lightcone of the Minkowski spacetime. We apply this fact to give a proof of the Kazdan-Warner identity.

A diffusion process associated with Fréchet meansOct 23 2015This paper studies rescaled images, under $\exp^{-1}_{\mu}$, of the sample Fr\'{e}chet means of i.i.d. random variables $\{X_k\vert k\geq 1\}$ with Fr\'{e}chet mean $\mu$ on a Riemannian manifold. We show that, with appropriate scaling, these images converge ... More

Intrinsic Prices Of RiskMar 03 2014Aug 18 2014We review the nature of some well-known phenomena such as volatility smiles, convexity adjustments and parallel derivative markets. We propose that the market is incomplete and postulate the existence of intrinsic risks in every contingent claim as a ... More

Homology torsion growth and Mahler measureOct 20 2010Nov 14 2012We prove a conjecture of K. Schmidt in algebraic dynamical system theory on the growth of the number of components of fixed point sets. We also generalize a result of Silver and Williams on the growth of homology torsions of finite abelian covering of ... More

Self-adjoint, unitary, and normal weighted composition operators in several variablesJul 25 2012We study weighted composition operators on Hilbert spaces of analytic functions on the unit ball with kernels of the form $(1-<z,w>)^{-\gamma}$ for $\gamma>0$. We find necessary and sufficient conditions for the adjoint of a weighted composition operator ... More

Compact Hankel operators on generalized Bergman spaces of the polydiscApr 07 2010We show that for $f$ a continuous function on the closed polydisc $\bar{\mathbb{D}^n}$ with $n\geq 2$, the Hankel operator $H_{f}$ is compact on the Bergman space of $\mathbb{D}^n$ if and only if there is a decomposition $f=h+g$, where $h$ is in the ball ... More

Global Existence and Regularity Results for Large Cross Diffusion Models on Planar DomainsApr 29 2016The global existence of classical solutions to cross diffusion systems of more than 2 equations given on a planar domain is established. The results can apply to generalized Shigesada-Kawasaki-Teramoto (SKT) and food pyramid models whose diffusion and ... More

Irreducible characters of Sylow p-subgroups of the Steinberg triality groups $^3D_4(p^{3m})$Sep 06 2013In this notes we construct and count all ordinary irreducible characters of Sylow $p$-subgroups of the Steinberg triality groups ${}^3D_4(p^{3m})$.

The action dimension of Artin groupsAug 29 2016Sep 29 2016The \emph{action dimension} of a discrete group $G$ is the minimum dimension of a contractible manifold, which admits a proper $G$-action. In this paper, we study the action dimension of general Artin groups. The main result is that the action dimension ... More

Some properties of Fréchet medians in Riemannian manifoldsOct 18 2011Dec 03 2011The consistency of Fr\'echet medians is proved for probability measures in proper metric spaces. In the context of Riemannian manifolds, assuming that the probability measure has more than a half mass lying in a convex ball and verifies some concentration ... More

The intersection of a hyperplane with a lightcone in the Minkowski spacetimeJan 07 2016Klainerman, Luk and Rodnianski derived an anisotropic criterion for formation of trapped surfaces in vacuum, extending the original trapped surface formation theorem of Christodoulou. The effort to understand their result led us to study the intersection ... More

Cluster Structures on Higher Teichmuller Spaces for Classical GroupsMar 11 2016Let $S$ be a surface, $G$ a simply-connected classical group, and $G'$ the associated adjoint form of the group. We show that the spaces of moduli spaces of framed local systems $\X_{G',S}$ and $\A_{G,S}$, which were constructed by Fock and Goncharov ... More

Overview of the T2K long baseline neutrino oscillation experimentOct 22 2009Neutrino oscillations were discovered by atmospheric and solar neutrino experiments, and have been confirmed by experiments using neutrinos from accelerators and nuclear reactors. It has been found that there are large mixing angles in the $\nu_e \to ... More

String spectral sequenceSep 30 2004Jan 06 2005We define shriek map for a finite codimensionnal embedding of fibration. We study the morphisms induced by shriek maps in the Leray-Serre spectral sequence. As a byproduct, we get two multiplicative spectral sequences of algebra wich converge to the Chas ... More

Nonlinear stochastic time-fractional diffusion equations on $\mathbb{R}$: moments, Hölder regularity and intermittencyOct 07 2014We study the nonlinear stochastic time-fractional diffusion equations in the spatial domain $\mathbb{R}$, driven by multiplicative space-time white noise. The fractional index $\beta$ varies continuously from $0$ to $2$. The case $\beta=1$ (resp. $\beta=2$) ... More

On some nonadmissible smooth irreducible representations of $\mathrm{GL}_2$Sep 26 2018Let $p>2$ be a prime. We give examples of smooth absolutely irreducible representations of $\mathrm{GL}_2(\mathbb{Q}_{p^3})$ over $\mathbb{F}_{p^3}$ which are not admissible.

Riemannian Median and Its EstimationNov 18 2009In this paper, we define the geometric median of a probability measure on a Riemannian manifold, give its characterization and a natural condition to ensure its uniqueness. In order to calculate the median in practical cases, we also propose a subgradient ... More

Local and Global Existence of Strong Solutions to Large Cross Diffusion SystemsAug 22 2016We study the solvability of a general class of cross diffusion systems and establish the local and global existence of their strong solutions under the weakest assumption that they are VMO. This work simplifies the setting in our previous work [16] and ... More

Existence of Strong and Nontrivial Solutions to Strongly Coupled Elliptic SystemsMar 17 2016We establish the existence of strong solutions to a class of nonlinear strongly coupled and uniform elliptic systems consisting of more than two equations. The existence of of nontrivial and non constant solutions (or pattern formations) will also be ... More

Regular Decomposition of Ordinarity in Generic Exponential SumsAug 22 2012Dec 24 2012In papers published in 1993 and 2004 Wan establishes a decomposition theory for the generic Newton polygon associated to a family of $L$-functions of $n$-dimensional exponential sums over finite fields. In this work we generalize the star, parallel hyperplane ... More

A PTAS for subset TSP in minor-free graphsApr 04 2018We give the first polynomial time approximation scheme for the subset Traveling Salesperson Problem (subset TSP) in $H$-minor-free graphs. Our main technical contribution is a polynomial time algorithm that, given an edge-weighted $H$-minor-free graph ... More

Power-Laws and the Conservation of Information in discrete token systems: Part 1 General TheoryJul 20 2012The Conservation of Energy plays a pivotal part in the development of the physical sciences. With the growth of computation and the study of other discrete token based systems such as the genome, it is useful to ask if there are conservation principles ... More

Growth of homology torsion in finite coverings and hyperbolic volumeDec 24 2014May 22 2016We give an upper bound for the growth of homology torsions of finite coverings of irreducible 3-manifolds with tori boundary in terms of hyperbolic volume.

Boundedness and compactness of composition operators on Segal-Bargmann spacesNov 30 2011For $E$ a Hilbert space, let $\mathcal{H}(E)$ denote the Segal-Bargmann space (also known as the Fock space) over $E$, which is a reproducing kernel Hilbert space with kernel $K(x,y)=\exp(< x,y>)$ for $x,y$ in $E$. If $\phi$ is a mapping on $E$, the composition ... More

Toeplitz operators on generalized harmonic Bergman spacesApr 06 2010We study Toeplitz operators with uniformly continuous symbols on generalized harmonic Bergman spaces of the unit ball in $\mathbb{R}^n$. We describe their essential spectra and establish a short exact sequence associated with the $C^{*}$-algebra generated ... More

A refined Luecking's theorem and finite-rank products of Toeplitz operatorsFeb 26 2008For any function $f$ in $L^{\infty}(\mathbb{D})$, let $T_f$ denote the corresponding Toeplitz operator the Bergman space $A^2(\mathbb{D})$. A recent result of D. Luecking shows that if $T_f$ has finite rank then $f$ must be the zero function. Using a ... More

Coalescence times for the continuous time Bienaymé-Galton-Watson processMay 08 2014We investigate the distribution of the coalescence time (most recent common ancestor) for two individuals picked at random (uniformly) in the current generation of a continuous time Bienaym\'e-Galton-Watson process founded $t$ units of time ago. We also ... More

Global Existence and Global Attractors of Cross Diffusion Systems on Planar DomainsMay 17 2016May 18 2016Global existence of strong solutions and the existence of global and atrractors are established for generalized Shigesada-Kawasaki-Teramoto models on planar domains. The cross diffusion and reaction can have polynomial growth of any order.

Comparative Assembly Hubs: Web Accessible Browsers for Comparative GenomicsNov 05 2013We introduce a pipeline to easily generate collections of web accessible UCSC genome browsers interrelated by an alignment. Using the alignment, all annotations and the alignment itself can be efficiently viewed with reference to any genome in the collection, ... More

Multifunctional in vivo vascular imaging using near-infrared II fluorescenceNov 18 2012In vivo real-time epifluorescence imaging of mouse hindlimb vasculatures in the second near-infrared region (NIR-II, 1.1~1.4 microns) is performed using single-walled carbon nanotubes (SWNTs) as fluorophores. Both high spatial resolution (~30 microns) ... More

Characterizing Near-Infrared Sky Brightness in the Canadian High ArcticJun 28 2012We present the first measurements of the near-infrared (NIR), specifically the J-band, sky background in the Canadian High Arctic. There has been considerable recent interest in the development of an astronomical observatory in Ellesmere Island; initial ... More

An Approach to to Cluster Structures on Moduli of Local Systems for General GroupsJun 03 2016Let $S$ be a surface, $G$ a simply-connected classical group, and $G'$ the associated adjoint form of the group. In \cite{FG1}, it was shown that the moduli spaces of framed local systems $\X_{G',S}$ and $\A_{G,S}$ have the structure of cluster varieties, ... More

Relatively Hyperbolic Coxeter Groups with maximal Flats of codimension 1Jun 04 2015We study relatively hyperbolic Coxeter groups of type $HM$ with maximal Euclidean Coxeter subgroups of codimension 1. Our main result in this paper is that the dimension of these groups is bounded above.

The commutants of certain Toeplitz operators on weighted Bergman spacesFeb 26 2008For $\alpha>-1$, let $A^2_{\alpha}$ be the corresponding weighted Bergman space of the unit ball in $\mathbb{C}^n$. For a bounded measurable function $f$, let $T_f$ be the Toeplitz operator with symbol $f$ on $A^2_{\alpha}$. This paper describes all the ... More

The zero-product problem for Toeplitz operators with radial symbolsDec 02 2007For any bounded measurable function $f$ on the unit ball $B_n$, let $T_f$ be the Toeplitz operator with symbol $f$ acting on the Bergman space $A^2(B_n)$. The Zero-Product Problem asks: if $f_1,..., f_N$ are bounded measurable functions such that $T_{f_1}... ... More

On a Class of Ideals of the Toeplitz Algebra on the Bergman Space of the Unit BallMay 07 2007Let $\mathfrak{T}$ denote the full Toeplitz algebra on the Bergman space of the unit ball $\mathbb{B}_n.$ For each subset $G$ of $L^{\infty},$ let $\mathfrak{CI}(G)$ denote the closed two-sided ideal of $\mathfrak{T}$ generated by all $T_fT_g-T_gT_f$ ... More