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Spline functions, the discrete biharmonic operator and approximate eigenvaluesFeb 27 2017Nov 30 2017The biharmonic operator plays a central role in a wide array of physical models, notably in elasticity theory and the streamfunction formulation of the Navier-Stokes equations. The need for corresponding numerical simulations has led, in recent years, ... More

Complex Relations in a Deep Structured Prediction Model for Fine Image SegmentationMay 24 2018Many deep learning architectures for semantic segmentation involve a Fully Convolutional Neural Network (FCN) followed by a Conditional Random Field (CRF) to carry out inference over an image. These models typically involve unary potentials based on local ... More

Structured learning and detailed interpretation of minimal object imagesNov 29 2017We model the process of human full interpretation of object images, namely the ability to identify and localize all semantic features and parts that are recognized by human observers. The task is approached by dividing the interpretation of the complete ... More

A model for interpreting social interactions in local image regionsDec 26 2017Understanding social interactions (such as 'hug' or 'fight') is a basic and important capacity of the human visual system, but a challenging and still open problem for modeling. In this work we study visual recognition of social interactions, based on ... More

Minimal Images in Deep Neural Networks: Fragile Object Recognition in Natural ImagesFeb 08 2019The human ability to recognize objects is impaired when the object is not shown in full. "Minimal images" are the smallest regions of an image that remain recognizable for humans. Ullman et al. 2016 show that a slight modification of the location and ... More

Efficient Single Writer ConcurrencyMar 23 2018May 13 2018Most research in concurrency focuses on providing safety and liveness guarantees under the worst possible conditions. However, workloads of many important concurrent applications are much less adversarial, leaving room for optimizations for the common ... More

Optimal Distributed Covering AlgorithmsFeb 25 2019We present a time-optimal deterministic distributed algorithm for approximating a minimum weight vertex cover in hypergraphs of rank $f$. This problem is equivalent to the Minimum Weight Set Cover problem in which the frequency of every element is bounded ... More

Remez-Type Inequality for Smooth FunctionsJun 16 2013The classical Remez inequality bounds the maximum of the absolute value of a polynomial $P(x)$ of degree $d$ on $[-1,1]$ through the maximum of its absolute value on any subset $Z$ of positive measure in $[-1,1]$. Similarly, in several variables the maximum ... More

Quark-Squark Alignment RevisitedJun 06 2002We re-examine the possibility that the solution to the supersymmetric flavor problem is related to small mixing angles in gaugino couplings induced by approximate horizontal Abelian symmetries. We prove that, for a large class of models, there is a single ... More

Effect of multiple degrees of ambivalence on the Naming GameAug 12 2013We examine a modified Naming Game in the mean field where there are multiple degrees of ambivalence. Once an agent in one state fears an opinion one way or another, he or she moves one step in the appropriate direction. In the absence of zealots, the ... More

Signal Acquisition from Measurements via Non-Linear ModelsOct 29 2008We consider the problem of reconstruction of a non-linear finite-parametric model $M=M_p(x),$ with $p=(p_1,...,p_r)$ a set of parameters, from a set of measurements $\mu_j(M)$. In this paper $\mu_j(M)$ are always the moments $m_j(M)=\int x^jM_p(x)dx$. ... More

Beyond MSSM BaryogenesisMay 01 2008May 20 2008Taking the MSSM as an effective low-energy theory, with a cut-off scale of a few TeV, can make significant modifications to the predictions concerning the Higgs and stop sectors. We investigate the consequences of such a scenario for electroweak baryogenesis. ... More

An observation on the Turán-Nazarov inequalityJun 30 2011Aug 07 2013The main observation of this note is that the Lebesgue measure $\mu$ in the Tur\'an-Nazarov inequality for exponential polynomials can be replaced with a certain geometric invariant $\omega \ge \mu$, which can be effectively estimated in terms of the ... More

SU(3) Relations and the CP Asymmetry in $B \to K_S K_S K_S$May 23 2005The CP asymmetry in the $B \to K_S K_S K_S$ decay is being measured by the two B factories. A large deviation of the CP asymmetry $S_{K_S K_S K_S}$ from $-S_{\psi K_S}$ and/or of $C_{K_S K_S K_S}$ from zero would imply new physics in $b \to s$ transitions. ... More

Numerical Relativity of Compact Binaries in the 21st CenturyAug 17 2018Sep 13 2018We review the dramatic progress in the simulations of compact objects and compact-object binaries that has taken place in the first two decades of the twenty-first century. This includes simulations of the inspirals and violent mergers of binaries containing ... More

Gaussian Mixture Generative Adversarial Networks for Diverse Datasets, and the Unsupervised Clustering of ImagesAug 30 2018Generative Adversarial Networks (GANs) have been shown to produce realistically looking synthetic images with remarkable success, yet their performance seems less impressive when the training set is highly diverse. In order to provide a better fit to ... More

Implications of Horizontal Symmetries on Baryon Number Violation in Supersymmetric ModelsAug 18 1994The smallness of the quark and lepton parameters and the hierarchy between them could be the result of selection rules due to a horizontal symmetry broken by a small parameter. The same selection rules apply to baryon number violating terms. Consequently, ... More

Constraining the Phase of B_s - \bar{B}_s MixingMay 02 2006Jul 27 2006New physics contributions to B_s-\bar{B}_s mixing can be parametrized by the size (r_s^2) and the phase (2\theta_s) of the total mixing amplitude relative to the Standard Model amplitude. The phase has so far been unconstrained. We first use the D0 measurement ... More

Relating leptogenesis parameters to light neutrino massesFeb 15 2007We obtain model independent relations among neutrino masses and leptogenesis parameters. We find exact relations that involve the CP asymmetries $\epsilon_{N_\alpha}$, the washout parameters $\tilde m_\alpha$ and $\theta_{\alpha\beta}$, and the neutrino ... More

The perimeter of uniform and geometric words: a probabilistic analysisAug 21 2017May 12 2018Let a word be a sequence of $n$ i.i.d. integer random variables. The perimeter $P$ of the word is the number of edges of the word, seen as a polyomino. In this paper, we present a probabilistic approach to the computation of the moments of $P$. This is ... More

$C^{1+α}$-Regularity for Two-Dimensional Almost-Minimal Sets in $\R^n$Jun 12 2008We give a new proof and a partial generalization of Jean Taylor's result [Ta] that says that Almgren almost-minimal sets of dimension 2 in $\R^3$ are locally $C^{1+\alpha}$-equivalent to minimal cones. The proof is rather elementary, but uses a local ... More

Hölder Regularity of Two-Dimensional Almost-Minimal Sets in $\R^n$Jun 10 2008We give a different and probably more elementary proof of a good part of Jean Taylor's regularity theorem for Almgren almost-minimal sets of dimension 2 in $\R^3$. We use this opportunity to settle some details about almost-minimal sets, extend a part ... More

Towards Unstructured Mesh Generation Using the Inverse Poisson ProblemFeb 17 2008A novel approach to unstructured quadrilateral mesh generation for planar domains is presented. Away from irregular vertices, the resulting meshes have the properties of nearly conformal grids. The technique is based on a theoretical relation between ... More

Expertises : procédures statistiques d'aide à la décisionFeb 27 2006In this study, we introduce a new approach to statistical decision theory. Without using a loss function, we select good decision rules to choice between two hypotheses. We call them "experts". They are globally unbiased but also conditionally unbiased ... More

Les p-values comme votes d'expertsFeb 07 2006The p-values are often implicitly used as a measure of evidence for the hypotheses of the tests. This practice has been analyzed with different approaches. It is generally accepted for the one-sided hypothesis problem, but it is often criticized for the ... More

Accuracy of Algebraic Fourier Reconstruction for Shifts of Several SignalsNov 14 2013Apr 14 2014We consider the problem of "algebraic reconstruction" of linear combinations of shifts of several known signals $f_1,\ldots,f_k$ from the Fourier samples. Following \cite{Bat.Sar.Yom2}, for each $j=1,\ldots,k$ we choose sampling set $S_j$ to be a subset ... More

Neutrinoless double-beta decay with massive scalar emissionFeb 22 2018Aug 16 2018Searches for neutrino-less double-beta decay ($0\nu2\beta$) place an important constraint on models where light fields beyond the Standard Model participate in the neutrino mass mechanism. While $0\nu2\beta$ experimental collaborations often consider ... More

Enveloppe galoisienne d'une application rationnelle de P1Mar 21 2005The D-envelope (or galoisian envelope) of rational endomorphisms of P1 are computed. One obtain the following theorem : "the rational transformations of P1 with an invariant meromorphic G-structure are the integrables ones."

A refined and asymptotic analysis of optimal stopping problems of Bruss and WeberMay 26 2017The classical secretary problem has been generalized over the years into several directions. In this paper we confine our interest to those generalizations which have to do with the more general problem of stopping on a last observation of a specific ... More

Predicting interviewee attitude and body language from speech descriptorsSep 25 2017This present research investigated the relationship between personal impressions and the acoustic nonverbal communication conveyed by employees being interviewed. First, we investigated the extent to which different conversation topics addressed during ... More

Scalar-mediated $t\bar t$ forward-backward asymmetryJul 21 2011Aug 03 2011A large forward-backward asymmetry in $t\bar t$ production, for large invariant mass of the $t\bar t$ system, has been recently observed by the CDF collaboration. Among the scalar mediated mechanisms that can explain such a large asymmetry, only the t-channel ... More

Solution to Rubel's question about differentially algebraic dependence on initial valuesOct 31 2002Nov 28 2002We prove that, for generic systems of polynomial differential equations, the dependence of the solution on the initial conditions is not differentially algebraic. This answers, in the negative, a question posed by L.A. Rubel.

Super-resolution of near-colliding point sourcesApr 19 2019We consider the problem of stable recovery of sparse signals of the form $$F(x)=\sum_{j=1}^d a_j\delta(x-x_j),\quad x_j\in\mathbb{R},\;a_j\in\mathbb{C}, $$ from their spectral measurements, known in a bandwidth $\Omega$ with absolute error not exceeding ... More

Implications of large dimuon CP asymmetry in B_{d,s} decays on minimal flavor violation with low tan betaJul 12 2010Jul 29 2010The D0 collaboration has recently announced evidence for a dimuon CP asymmetry in B_{d,s} decays of order one percent. If confirmed, this asymmetry requires new physics. We argue that for minimally flavor violating (MFV) new physics, and at low tan beta=v_u/v_d, ... More

Constraining New Physics with the CDF Measurement of CP Violation in $B \to ψK_S$May 19 1999Oct 05 1999Recently, the CDF collaboration has reported a measurement of the CP asymmetry in the $B\to\psi K_S$ decay: $a_{\psi K_S}=0.79^{+0.41}_{-0.44}$. We analyze the constraints that follow from this measurement on the size and the phase of contributions from ... More

Geometry of error amplification in solving Prony system with near-colliding nodesJan 15 2017Jun 14 2018We consider a reconstruction problem for "spike-train" signals $F$ of an a priori known form $ F(x)=\sum_{j=1}^{d}a_{j}\delta\left(x-x_{j}\right),$ from their moments $m_k(F)=\int x^kF(x)dx.$ We assume that the moments $m_k(F)$, $k=0,1,\ldots,2d-1$, are ... More

Probing CP violation in neutrino oscillations with neutrino telescopesJun 14 2007Jul 03 2007Measurements of flavor ratios of astrophysical neutrino fluxes are sensitive to the two yet unknown mixing parameters $\theta_{13}$ and $\delta$ through the combination $\sin\theta_{13}\cos\delta$. We extend previous studies by considering the possibility ... More

New Approaches in designing a Zeeman-SlowerDec 10 2012Jan 17 2013We present two new approaches for the design of a Zeeman-Slower, which rely on optimal compliance with the adiabatic following condition and are applicable to a wide variety of systems. The first approach is an analytical one, based on the assumption ... More

The importance of N2 leptogenesisDec 15 2006Sep 17 2007We argue that fast interactions of the lightest singlet neutrino $N_1$ would project part of a preexisting lepton asymmetry $L_p$ onto a direction that is protected from $N_1$ washout effects, thus preventing it from being erased. In particular, we consider ... More

Time Variations in the Scale of Grand UnificationSep 12 2002Oct 08 2002We study the consequences of time variations in the scale of grand unification, $M_U$, when the Planck scale and the value of the unified coupling at the Planck scale are held fixed. We show that the relation between the variations of the low energy gauge ... More

High Quality a-axis outgrowth on c-axis YlCa1-xBa2Cu3O7-dApr 21 2004The large amplitude of the high Tc (HTS) superconducting gap is attractive for improved electronic applications. However, the study of such HTS cuprates has uncovered that unlike the s-wave order parameter of the low Tc, an angle dependent dx2-y2 wave ... More

The Pattern of CP Asymmetries in $b\to s$ TransitionsMar 16 2005Oct 06 2005New CP violating physics in $b\to s$ transitions will modify the CP asymmetries in B decays into final CP eigenstates ($\phi K_S$, $\eta^\prime K_S$, $\pi^0 K_S$, $\omega K_S$, $\rho^0 K_S$ and $\eta K_S$) from their Standard Model values. In a model ... More

On Optimal Allocation of a Continuous Resource Using an Iterative Approach and Total PositivityMar 01 2011We study a class of optimal allocation problems, including the well-known Bomber Problem, with the following common probabilistic structure. An aircraft equipped with an amount~$x$ of ammunition is intercepted by enemy airplanes arriving according to ... More

Mode coupling in the nonlinear response of black holesJun 23 2003Aug 14 2003We study the properties of the outgoing gravitational wave produced when a non-spinning black hole is excited by an ingoing gravitational wave. Simulations using a numerical code for solving Einstein's equations allow the study to be extended from the ... More

Colliding black holes from a null point of view: the close limitDec 29 2000We present a characteristic algorithm for computing the perturbations of a Schwarzschild spacetime by means of solving the Teukolsky equations. Our methods and results are expected to have direct bearing on the study of binary black holes presently underway ... More

Stability of partial Fourier matrices with clustered nodesSep 03 2018We prove sharp lower bounds for the smallest singular value of a partial Fourier matrix with arbitrary "off the grid" nodes (equivalently, a rectangular Vandermonde matrix with the nodes on the unit circle), in the case when some of the nodes are separated ... More

Exotic colored scalars at the LHCOct 20 2016We study the phenomenology of exotic color-triplet scalar particles $X$ with charge $|Q|=2/3, 4/3,5/3,7/3,8/3$ and $10/3$. If $X$ is a non-singlet of $SU(2)_W$ representation, mass splitting within the multiplet allows for cascade decays of the members ... More

On a possible large width 750 GeV diphoton resonance at ATLAS and CMSDec 17 2015Aug 31 2016The ATLAS and CMS experiments at the LHC have reported an excess of diphoton events with invariant mass around 750 GeV, with local significance of about $3.6 \sigma$ and $2.6 \sigma$, respectively. We entertain the possibility that this excess is due ... More

Exact Bounds for Some Hypergraph Saturation ProblemsSep 17 2012Jan 21 2014Let W_n(p,q) denote the minimum number of edges in an n x n bipartite graph G on vertex sets X,Y that satisfies the following condition; one can add the edges between X and Y that do not belong to G one after the other so that whenever a new edge is added, ... More

A Markovian Analysis of IEEE 802.11 Broadcast Transmission Networks with BufferingJun 19 2015The purpose of this paper is to analyze the so-called back-off technique of the IEEE 802.11 protocol in broadcast mode with waiting queues. In contrast to existing models, packets arriving when a station (or node) is in back-off state are not discarded, ... More

Kac-Moody Lie algebras graded by Kac-Moody root systemsJul 20 2012We look to gradations of Kac-Moody Lie algebras by Kac-Moody root systems with finite dimensional weight spaces. We extend, to general Kac-Moody Lie algebras, the notion of C-admissible pair as introduced by H. Rubenthaler and J. Nervi for semi-simple ... More

Generating connected acyclic digraphs uniformly at randomMar 25 2004We describe a simple algorithm based on a Markov chain process to generate simply connected acyclic directed graphs over a fixed set of vertices. This algorithm is an extension of a previous one, designed to generate acyclic digraphs, non necessarily ... More

Traffic Light Queues and the Poisson Clumping HeuristicOct 29 2018Jan 21 2019In discrete time, $\ell$-blocks of red lights are separated by $\ell$-blocks of green lights. Cars arrive at random. We seek the distribution of maximum line length of idle cars, and justify conjectured probabilistic asymptotics for $2 \leq \ell \leq ... More

Reifenberg Parameterizations for Sets with HolesOct 26 2009We extend the proof of Reifenberg's Topological Disk Theorem to allow the case of sets with holes, and give sufficient conditions on a set $E$ for the existence of a bi-Lipschitz parameterization of $E$ by a $d$-dimensional plane or smooth manifold. Such ... More

The close limit from a null point of view: the advanced solutionDec 28 2000Jun 07 2001We present a characteristic algorithm for computing the perturbation of a Schwarzschild spacetime by means of solving the Teukolsky equation. We implement the algorithm as a characteristic evolution code and apply it to compute the advanced solution to ... More

Testing minimal lepton flavor violation with extra vector-like leptons at the LHCJan 17 2010Models of minimal lepton flavor violation where the seesaw scale is higher than the relevant flavor scale predict that all lepton flavor violation is proportional to the charged lepton Yukawa matrix. If extra vector-like leptons are within the reach of ... More

Combining K-\bar K mixing and D-\bar D mixing to constrain the flavor structure of new physicsMar 12 2009New physics at high energy scale often contributes to K-\bar K and D-\bar D mixings in an approximately SU(2)_L invariant way. In such a case, the combination of measurements in these two systems is particularly powerful. The resulting constraints can ... More

CP violation Beyond the MSSM: Baryogenesis and Electric Dipole MomentsMar 11 2010We study electroweak baryogenesis and electric dipole moments in the presence of the two leading-order, non-renormalizable operators in the Higgs sector of the MSSM. Significant qualitative and quantitative differences from MSSM baryogenesis arise due ... More

Asymmetric Higgsino Dark MatterJan 12 2012In the supersymmetric framework, a higgsino asymmetry exists in the universe before the electroweak phase transition. We investigate whether the higgsino is a viable asymmetric dark matter candidate. We find that this is indeed possible. The gauginos, ... More

BMSSM Implications for CosmologyJun 25 2009Jul 15 2009The addition of non-renormalizable terms involving the Higgs fields to the MSSM (BMSSM) ameliorates the little hierarchy problem of the MSSM. We analyze in detail the two main cosmological issues affected by the BMSSM: dark matter and baryogenesis. The ... More

Tail estimates for the Brownian excursion area and other Brownian areasJul 06 2007Several Brownian areas are considered in this paper: the Brownian excursion area, the Brownian bridge area, the Brownian motion area, the Brownian meander area, the Brownian double meander area, the positive part of Brownian bridge area, the positive ... More

A Short Proof of Gowers' Lower Bound for the Regularity LemmaAug 24 2013A celebrated result of Gowers states that for every \epsilon > 0 there is a graph G so that every \epsilon-regular partition of G (in the sense of Szemeredi's regularity lemma) has order given by a tower of exponents of height polynomial in 1/\epsilon. ... More

Numerical Modeling of Multi-wavelength Spectra of M87 Core EmissionSep 13 2011Dec 19 2011Spectral fits to M87 core data from radio to hard x-ray are generated via a specially selected software suite, comprised of the HARM GRMHD accretion disk model and a 2D Monte Carlo radiation transport code. By determining appropriate parameter changes ... More

New classes of domains with explicit Bergman kernelJan 28 2003Mar 31 2003We introduce two classes of "egg type" domains, built on general bounded symmetric domains, for which we compute the Bergmann kernel in explicit form. We use the characterization of bounded symmetric domains through Jordan triple systems. The egg type ... More

Event Shape Analysis in ALICEDec 04 2009Dec 07 2009The jets are the final state manifestation of the hard parton scattering. Since at LHC energies the production of hard processes in proton-proton collisions will be copious and varied, it is important to develop methods to identify them through the study ... More

Singular solutions of the L^2-supercritical biharmonic Nonlinear Schrodinger equationNov 24 2010We use asymptotic analysis and numerical simulations to study peak-type singular solutions of the supercritical biharmonic NLS. These solutions have a quartic-root blowup rate, and collapse with a quasi self-similar universal profile, which is a zero-Hamiltonian ... More

Single-mode interferometric field of view in partial turbulence correction. Application to the observation of the environment of Sgr A* with GRAVITYMar 26 2019Context. The GRAVITY instrument on the ESO VLTI is setting a new mark in the landscape of optical interferometers. Long exposures are possible for the first time in this wavelength domain, delivering a dramatic improvement for astrophysics. In particular, ... More

Optimal design problems for Schrödinger operators with noncompact resolventsJan 31 2015We consider optimization problems for cost functionals which depend on the negative spectrum of Schr\"odinger operators of the form $-\Delta+V(x)$, where $V$ is a potential, with prescribed compact support, which has to be determined. Under suitable assumptions ... More

The isomorphism problem for complete Pick algebras: a surveyDec 25 2014Complete Pick algebras - these are, roughly, the multiplier algebras in which Pick's interpolation theorem holds true - have been the focus of much research in the last twenty years or so. All (irreducible) complete Pick algebras may be realized concretely ... More

Memory Effects In Nonequilibrium Quantum Impurity ModelsMay 26 2011Memory effects play a key role in the dynamics of strongly correlated systems driven out of equilibrium. In the present study, we explore the nature of memory in the nonequilibrium Anderson impurity model. The Nakajima--Zwanzig--Mori formalism is used ... More

Negative Differential Spin Conductance by Population SwitchingOct 30 2007An examination of the properties of many-electron conduction through spin-degenerate systems can lead to situations where increasing the bias voltage applied to the system is predicted to decrease the current flowing through it, for the electrons of a ... More

On finiteness of the sum of negative eigenvalues of Schroedinger operatorsFeb 14 2008Jul 03 2008We prove conditions on potentials which imply that the sum of the negative eigenvalues of the Schroeodinger operator is finite. We use a method for bounding eigenvalues based on estimates of the Hilbert-Schmidt norm of semigroup differences and on complex ... More

Conjectures about Traffic Light QueuesOct 09 2018Oct 31 2018In discrete time, $\ell$-blocks of red lights are separated by $\ell$-blocks of green lights. Cars arrive at random. The maximum line length of idle cars is fully understood for $\ell = 1$, but only partially for $2 \leq \ell \leq 3$.

Decomposing a Graph Into Expanding SubgraphsFeb 02 2015A paradigm that was successfully applied in the study of both pure and algorithmic problems in graph theory can be colloquially summarized as stating that "any graph is close to being the disjoint union of expanders". Our goal in this paper is to show ... More

Quantitative relation between noise sensitivity and influencesMar 09 2010A Boolean function $f:\{0,1\}^n \to \{0,1\}$ is said to be noise sensitive if inserting a small random error in its argument makes the value of the function almost unpredictable. Benjamini, Kalai and Schramm showed that if the sum of squares of influences ... More

A new presentation of the cyclotomic Cherednik algebraSep 18 2016We give an alternate presentation of the cyclotomic rational Cherednik algebra. This presentation has a diagrammatic flavor, and it provides a simple explanation of several surprising facts about this algebra. It allows direct proof of the connection ... More

Big Bang Models in String TheoryMay 19 2006Dec 20 2006These proceedings are based on lectures delivered at the "RTN Winter School on Strings, Supergravity and Gauge Theories", CERN, January 16 - January 20, 2006. The school was mainly aimed at Ph.D. students and young postdocs. The lectures start with a ... More

Dimension-free Maximal Inequalities for Spherical Means in the HypercubeSep 17 2013Dec 08 2014We extend the main result of \cite{HKS} -- the existence of dimension-free $L^2$-bounds for the spherical maximal function in the hypercube -- to all $L^p, p > 1$. Our approach is motivated by the spectral technique developed in \cite{S} and \cite{NS} ... More

Improved mixing time bounds for the Thorp shuffle and L-reversal chainFeb 04 2008We prove a theorem that reduces bounding the mixing time of a card shuffle to verifying a condition that involves only pairs of cards, then we use it to obtain improved bounds for two previously studied models. E. Thorp introduced the following card shuffling ... More

Caustic Rings and Cold Dark MatterMar 06 2001The hierarchical cold dark matter (CDM) model for structure formation is a well defined and testable model. Direct detection is the best technique for confirming the model yet predictions for the energy and density distribution of particles on earth remain ... More

The Nature Of Dark MatterFeb 03 1994Collisionless particles, such as cold dark matter, interact only by gravity and do not have any associated length scale, therefore the dark halos of galaxies should have negligible core radii. This expectation has been supported by numerical experiments ... More

Evolutionary processes in clustersJun 27 2003Are the morphologies of galaxies imprinted during an early and rapid formation epoch or are they due to environmental processes that subsequently transform galaxies between morphological classes? Recent numerical simulations demonstrate that the cluster ... More

Construction of Maximal Hypersurfaces with Boundary ConditionsAug 22 2014Oct 07 2016We construct maximal hypersurfaces with a Neumann boundary condition in Minkowski space via mean curvature flow. In doing this we give general conditions for long time existence of the flow with boundary conditions with assumptions on the curvature of ... More

The chart based approach to studying the global structure of a spacetime induces a coordinate invariant boundaryJan 07 2014Feb 25 2014I demonstrate that the chart based approach to the study of the global structure of Lorentzian manifolds induces a homeomorphism of the manifold into a topological space as an open dense set. The topological boundary of this homeomorphism is a chart independent ... More

Relative entropy and the Pinsker product formula for sofic groupsMay 05 2016We continue our study of the outer Pinsker factor for probability measure-preserving actions of sofic groups. Using the notion of doubly quenched convergence developed by Austin, we prove that in many cases the outer Pinsker factor of a product action ... More

Infinite-dimensional $\ell^1$ minimization and function approximation from pointwise dataMar 09 2015Jun 23 2016We consider the problem of approximating a smooth function from finitely-many pointwise samples using $\ell^1$ minimization techniques. In the first part of this paper, we introduce an infinite-dimensional approach to this problem. Three advantages of ... More

Subelliptic Resolvent Estimates for Non-self-adjoint Semiclassical Schrodinger OperatorsSep 02 2016Oct 01 2016In this paper we prove a subelliptic resolvent estimate for a class of semiclassical non-self-adjoint Schr\"odinger operators with purely imaginary potentials when the spectral parameter is in a parabolic neighborhood of the imaginary axis.

A new infinite family of non-abelian strongly real Beauville $p$-groups for every odd prime $p$Aug 02 2016We prove that there exist infinitely many a non-abelian strongly real Beauville $p$-group for every prime $p$. Previously only finitely many in the case $p=2$ have been constructed.

The Deligne-Mostow list and special families of surfacesJul 14 2016We study whether there exist infinitely many surfaces with given discrete invariants for which the H^2 is of CM type. This is a surface analogue of a conjecture of Coleman about curves. We construct a large number of examples of families of surfaces with ... More

Strongly Real Beauville GroupsMay 29 2014A strongly real Beauville group is a Beauville group that defines a real Beauville surface. Here we discuss efforts to find examples of these groups, emphasising on the one extreme finite simple groups and on the other abelian and nilpotent groups. We ... More

Sparse 3D convolutional neural networksMay 12 2015Aug 25 2015We have implemented a convolutional neural network designed for processing sparse three-dimensional input data. The world we live in is three dimensional so there are a large number of potential applications including 3D object recognition and analysis ... More

A Data Science Course for Undergraduates: Thinking with DataMar 18 2015Data science is an emerging interdisciplinary field that combines elements of mathematics, statistics, computer science, and knowledge in a particular application domain for the purpose of extracting meaningful information from the increasingly sophisticated ... More

A compactness result in approach theory with an application to the continuity approach structureApr 28 2015Jun 17 2015We establish a compactness result in approach theory which we apply to obtain a generalization of Prokhorov's Theorem for the continuity approach structure.

The critical CoHA of a quiver with potentialNov 27 2013Oct 27 2016Pursuing the similarity between the Kontsevich--Soibelman construction of the cohomological Hall algebra of BPS states and Lusztig's construction of canonical bases for quantum enveloping algebras, and the similarity between the inetgrality conjecture ... More

Invariance of orientation data for ind-constructible Calabi-Yau $A_{\infty}$ categories under derived equivalenceJun 28 2010Oct 25 2011We study orientation data, as introduced by Kontsevich and Soibelman in order to define well-behaved integration maps from the motivic Hall algebra of 3-dimensional Calabi-Yau categories to rings of motives. We start with an example that demonstrates ... More

Max-Min theorems for weak containment, square summable homoclinic points, and completely positive entropyFeb 18 2019We prove a max-min theorem for weak containment in the context of algebraic actions. Namely, we show that given an algebraic action of $G$ on $X,$ there is a maximal, closed $G$-invariant subgroup $Y$ of $X$ so that the action of $G$ on $Y$ is weakly ... More

Independence Tuples and Deninger's ProblemFeb 12 2015Apr 27 2016Motivated by our results in "Polish Models and Sofic Entropy," we define modified version of the independence tuples for sofic entropy developed by Kerr and Li. These modified version essentially require that the independence sequences give rise to representations ... More

Polish Models and Sofic EntropyNov 06 2014Dec 31 2015For actions of a sofic group on probability spaces, the entropy has been defined by Bowen, with an extension by Kerr-Li. In particular, when the action is by homeomorphisms of a compact space preserving a given measure, Kerr-Li show one can compute the ... More

Stabilization phenomena in Kac-Moody algebras and quiver varietiesMay 30 2005Aug 29 2006Let X be the Dynkin diagram of a symmetrizable Kac-Moody algebra, and X_0 a subgraph with all vertices of degree 1 or 2. Using the crystal structure on the components of quiver varieties for X, we show that if we expand X by extending X_0, the branching ... More

Relations between tautological cycles on JacobiansJun 23 2007Jul 09 2007We study tautological cycle classes on the Jacobian of a curve. We prove a new result about the ring of tautological classes on a general curve that allows, among other things, easy dimension calculations and leads to some general results about the structure ... More