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Verifying Multipartite Entangled GHZ States via Multiple Quantum CoherencesMay 14 2019The ability to generate and verify multipartite entanglement is an important benchmark for near-term quantum devices devices. We develop a scalable entanglement metric based on multiple quantum coherences, and demonstrate experimentally on a 20-qubit ... More

Designing Statistical Language Learners: Experiments on Noun CompoundsSep 25 1996The goal of this thesis is to advance the exploration of the statistical language learning design space. In pursuit of that goal, the thesis makes two main theoretical contributions: (i) it identifies a new class of designs by specifying an architecture ... More

Conserving Fuel in Statistical Language Learning: Predicting Data RequirementsSep 07 1995In this paper I address the practical concern of predicting how much training data is sufficient for a statistical language learning system. First, I briefly review earlier results and show how these can be combined to bound the expected accuracy of a ... More

The evolution of Jordan curves on $\mathbb{S}^2$ by curve shortening flowJan 21 2016In this paper we prove that if $\gamma$ is a Jordan curve on $\mathbb{S}^2$ then there is a smooth curve shortening flow defined on $(0,T)$ which converges to $\gamma$ in $\mathcal{C}^0$ as $t\to 0^+ $. Another perspective is that the level-set flow of ... More

Convergence of mean curvature flows with surgeryFeb 19 2010Sep 20 2011Huisken and Sinestrari have recently defined a surgery process for mean curvature flow when the initial data is a two-convex hypersurface. The process depends on a parameter H. Its role is to initiate a surgery when the maximum of the mean curvature of ... More

On the complexity of switching linear regressionOct 23 2015Jul 04 2016This technical note extends recent results on the computational complexity of globally minimizing the error of piecewise-affine models to the related problem of minimizing the error of switching linear regression models. In particular, we show that, on ... More

On the exact minimization of saturated loss functions for robust regression and subspace estimationJun 15 2018Aug 24 2018This paper deals with robust regression and subspace estimation and more precisely with the problem of minimizing a saturated loss function. In particular, we focus on computational complexity issues and show that an exact algorithm with polynomial time-complexity ... More

A new length estimate for curve shortening flow and low regularity initial dataFeb 24 2011Dec 01 2011In this paper we introduce a geometric quantity, the $r$-multiplicity, that controls the length of a smooth curve as it evolves by curve shortening flow. The length estimates we obtain are used to prove results about the level set flow in the plane. If ... More

Risk Bounds for Learning Multiple Components with Permutation-Invariant LossesApr 16 2019This paper proposes a simple approach to derive efficient error bounds for learning multiple components with sparsity-inducing regularization. Indeed, we show that for such regularization schemes, known decompositions of the Rademacher complexity over ... More

Error Bounds for Piecewise Smooth and Switching RegressionJul 25 2017Jun 13 2018The paper deals with regression problems, in which the nonsmooth target is assumed to switch between different operating modes. Specifically, piecewise smooth (PWS) regression considers target functions switching deterministically via a partition of the ... More

Global optimization for low-dimensional switching linear regression and bounded-error estimationJul 18 2017Nov 23 2017The paper provides global optimization algorithms for two particularly difficult nonconvex problems raised by hybrid system identification: switching linear regression and bounded-error estimation. While most works focus on local optimization heuristics ... More

Single-particle spectral function of the $Λ$ hyperon in finite nucleiMar 17 2016The spectral function of the $\Lambda$ hyperon in finite nuclei is calculated from the corresponding $\Lambda$ self-energy, which is constructed within a perturbative many-body approach using some of the realistic hyperon-nucleon interactions of the J\"{u}lich ... More

Non-relativistic quantum theory consistent with principle of localityJul 09 2013Jan 25 2016Principle of locality means that any local change (perturbation) of the stationary state wave function field propagates with finite speed, and therefore reaches distant regions of the field with time delay. If a one-particle or multi-particle non-relativistic ... More

Modified Schrödinger equation, its analysis and experimental verificationFeb 07 2012According to classical non-relativistic Schr\"odinger equation, any local perturbation of wave function instantaneously affects all infinite region, because this equation is of parabolic type, and its solutions demonstrate infinite speed of perturbations ... More

Cosmological Evolution of GalaxiesDec 06 2012I review the subject of the cosmological evolution of galaxies, including different aspects of growth in disk galaxies, by focussing on the angular momentum problem, mergers, and their by-products. I discuss the alternative to merger-driven growth -- ... More

Statistical theory of perturbation waves in transport phenomena and its experimental verificationAug 14 2012In transport phenomena, perturbation waves are a result of interaction of molecules in gases and liquids, charged particles (ions, electrons) in plasma, conduction electrons and phonons in solid bodies. General statistical theory of the perturbation waves ... More

Deconvolution of band limited functions on non-compact symmetric spacesAug 29 2011It is shown that a band limited function on a non-compact symmetric space can be reconstructed in a stable way from some countable sets of values of its convolution with certain distributions of compact support. A reconstruction method in terms of frames ... More

Reconstruction of Paley-Wiener functions on the Heisenberg groupAug 29 2011Let $M$ be a Riemmanian manifold with bounded geometry. We consider a generalization of Paley-Wiener functions and Lagrangian splines on $M$. An analog of the Paley-Wiener theorem is given. We also show that every Paley-Wiener function on a manifold is ... More

Variational splines on Riemannian manifolds with applications to integral geometryApr 09 2011We extend the classical theory of variational interpolating splines to the case of compact Riemannian manifolds. Our consideration includes in particular such problems as interpolation of a function by its values on a discrete set of points and interpolation ... More

Dynamics of the Central kpc in Barred Galaxies: Theory and ModelingJan 31 2002The central kpc of barred galaxies exhibits a wealth of morphological information on different components with clear dynamical consequences. These include nuclear rings, spirals, bars, and more. We argue that this morphology is driven by large-scale stellar ... More

Model theory and the QWEP conjectureNov 02 2015We observe that Kirchberg's QWEP conjecture is equivalent to the statement that $C^*(\mathbb{F})$ is elementarily equivalent to a QWEP C$^*$ algebra. We also make a few other model-theoretic remarks about WEP and LLP C$^*$ algebras.

Multi-twist optical Mobius stripsOct 09 2009Circularly polarized Gauss-Laguerre GL(0,0) and GL(0,1) laser beams that cross at their waists at a small angle are shown to generate a quasi-paraxial field that contains an axial line of circular polarization, a C line, surrounded by polarization ellipses ... More

Optical Mobius Strips in Three Dimensional Ellipse Fields: Lines of Circular PolarizationMar 17 2009The major and minor axes of the polarization ellipses that surround singular lines of circular polarization in three dimensional optical ellipse fields are shown to be organized into Mobius strips. These strips can have either one or three half-twists, ... More

On the nonexistence of Følner setsJan 08 2019We show that there is $n\in \mathbf N$, a finite system $\Sigma(\vec x,\vec y)$ of equations and inequations having a solution in some group, where $\vec x$ has length $n$, and $\epsilon>0$ such that: for any group $G$ and any $\vec a\in G^n$, if the ... More

Two definable subcategories of maximal Cohen-Macaulay modulesApr 18 2019Over a Cohen-Macaulay ring we consider two extensions of the maximal Cohen-Macaulay modules from the viewpoint of definable subcategories, which are closed under direct limits, direct products and pure submodules. After describing these categories, we ... More

A mixed finite element for weakly-symmetric elasticityFeb 08 2018We develop a finite element discretization for the weakly symmetric equations of linear elasticity on tetrahedral meshes. The finite element combines, for $r \geq 0$, discontinuous polynomials of $r$ for the displacement, $H(\mathrm{div})$-conforming ... More

Proving probabilistic correctness statements: the case of Rabin's algorithm for mutual exclusionSep 19 1994The correctness of most randomized distributed algorithms is expressed by a statement of the form ``some predicate of the executions holds with high probability, regardless of the order in which actions are scheduled''. In this paper, we present a general ... More

Cotilting with balanced big Cohen-Macaualay modulesJul 12 2019Over a Cohen-Macaulay local ring admitting a canonical module the definable closure of the class of balanced big Cohen-Macaulay modules is cotilting and is the smallest such class containing the maximal Cohen-Macaulay modules. We describe its cotilting ... More

Detecting inclusions with a generalized impedance condition from electrostatic data via samplingAug 10 2017May 28 2019In this paper, we derive a Sampling Method to solve the inverse shape problem of recovering an inclusion with a generalized impedance condition from electrostatic Cauchy data. The generalized impedance condition is a second-order differential operator ... More

Disk-Halo Interplay in Galaxy EvolutionOct 02 2007Some aspects of disk-halo interactions for models of in and out of equilibrium disk galaxies are reviewed. Specifically, we focus on disk-halo resonant interaction without and in the presence of a gas component. Another issue is the disk growth within ... More

Detecting inclusions with a generalized impedance condition from electrostatic data via samplingAug 10 2017Oct 15 2018In this paper, we derive a Sampling Method to solve the inverse shape problem of recovering an inclusion with a generalized impedance condition from electrostatic Cauchy data. The generalized impedance condition is a second-order differential operator ... More

Non Homogeneous Stochastic Diffusion on a JunctionMay 07 2019The purpose of this article is to give another proof on the existence of a diffusion on a junction, which has been already done by M.Freidlin and S-J.Sheu, in Diffusion processes on graphs, (2000). We generalize the result to time dependent and borel ... More

Nonparametric Identification and Estimation with Independent, Discrete InstrumentsJun 12 2019In a nonparametric instrumental regression model, we strengthen the conventional moment independence assumption towards full statistical independence between instrument and error term. This allows us to prove identification results and develop estimators ... More

A proof that the square root of s for s not a perfect square is simply normal to base 2Sep 03 2013Sep 19 2018Since E. Borel proved in 1909 that almost all real numbers with respect to Lebesgue measure are normal to all bases, an open problem has been whether simple irrationals like square root of 2 are normal to any base. We show that each number of the form ... More

Single-particle spectral function of the $Λ$ hyperon in finite nucleiMar 17 2016Nov 04 2016The spectral function of the $\Lambda$ hyperon in finite nuclei is calculated from the corresponding $\Lambda$ self-energy, which is constructed within a perturbative many-body approach using some of the hyperon-nucleon interactions of the J\"{u}lich ... More

Nonstandard hulls of locally uniform groupsMar 29 2012We present a nonstandard hull construction for locally uniform groups in a spirit similar to Luxembourg's construction of the nonstandard hull of a uniform space. Our nonstandard hull is a local group rather than a global group. We investigate how this ... More

Nuclear symmetry energy and the r-mode instability of neutron starsFeb 21 2012Apr 24 2012We analyze the role of the symmetry energy slope parameter $L$ on the {\it r}-mode instability of neutron stars. Our study is performed using both microscopic and phenomenological approaches of the nuclear equation of state. The microscopic ones include ... More

A Discrete Helgason-Fourier transform for Sobolev and Besov functions on noncompact symmetric spacesApr 09 2011Let $f$ be a Paley-Wiener function in the space $L_{2}(X)$, where $X$ is a symmetric space of noncompact type. It is shown that by using the values of $f$ on a sufficiently dense and separated set of points of $X$ one can give an exact formula for the ... More

Definable Operators on Hilbert SpacesOct 11 2010Let H be an infinite-dimensional (real or complex) Hilbert space, viewed as a metric structure in its natural signature. We characterize the definable linear operators on H as exactly the "scalar plus compact" operators.

Quantum algorithm for distributed clock synchronizationMay 22 2000The clock synchronization problem is to determine the time difference $\Delta$ between two spatially separated clocks. When message delivery times between the two clocks are uncertain, $O(2^{2n})$ classical messages must be exchanged between the clocks ... More

Modeling Dynamics in the Central Regions of Disk GalaxiesDec 07 2004The central regions of disk galaxies are hosts to supermassive black holes whose masses show a tight correlation with the properties of surrounding stellar bulges. While the exact origin of this dependency is not clear, it can be related to the very basic ... More

On a sufficient condition that the square root of s is simply normal to base 2, for s not a perfect squareApr 08 2011A simple proof is given of a sufficient condition that the square root of s is simply normal to base 2, for s not a perfect square. This relates to previous work of the author.

Two definable subcategories of maximal Cohen-Macaulay modulesApr 18 2019Apr 19 2019Over a Cohen-Macaulay ring we consider two extensions of the maximal Cohen-Macaulay modules from the viewpoint of definable subcategories, which are closed under direct limits, direct products and pure submodules. After describing these categories, we ... More

A bijective proof and generalization of Siladić's TheoremMay 31 2019In a recent paper, Dousse introduced a refinement of Siladi\'c's theorem on partitions, where parts occur in two primary and three secondary colors. Her proof used the method of weighted words and $q$-difference equations. The purpose of this paper is ... More

Cores and the Kinematics of Early-Type GalaxiesSep 19 2012I have combined the Emsellem et al. ATLAS3D rotation measures of a large sample of early-type galaxies with HST-based classifications of their central structure to characterize the rotation velocities of galaxies with cores. "Core galaxies" rotate slowly, ... More

Quasi linear parabolic PDE in a junction with non linear Neumann vertex conditionJul 11 2018The purpose of this article is to study quasi linear parabolic partial differential equations of second order, on a bounded junction, satisfying a nonlinear and non dynamical Neumann boundary condition at the junction point. We prove the existence and ... More

Orders of $π$-basesDec 30 2007We extend the scope of B. Shapirovskii's results [B.E Shapirovskii, "Cardinal invariants in Compact Hausdorff Spaces," Amer. Math. Soc. Transl. (2) Vol. 134, 1987, pp. 93-118] on the order of $\pi$-bases in compact spaces and answer some questions of ... More

The Cauchy Problem for nonlinear Quadratic Interactions of the Schrödinger type in one dimensional spaceApr 04 2017Jul 02 2018In this work I study the well-posedness of the Cauchy problem associated with the coupled Schr\"odinger equations {with quadratic nonlinearities}, which appears modeling problems in nonlinear optics. I obtain the local well-posedness for data {in Sobolev ... More

Electronic Structure of Liquid Water and a Platinum SurfaceJul 29 2014Many-body perturbation theory within the G$_0$W$_0$ approximation is used to determine molecular orbital level alignment at a liquid water/Pt(111) interface generated through $ab~ initio$ molecular dynamics. Molecular orbital energy levels are shown to ... More

A proof that the square root of s for s not a perfect square is simply normal to base 2Sep 03 2013Jul 20 2016Since E. Borel proved in 1909 that almost all real numbers with respect to Lebesgue measure are normal to all bases, an open problem has been whether simple irrationals like square root of 2 are normal to any base. We show that each number of the form ... More

Variational Splines and Paley--Wiener Spaces on Combinatorial GraphsNov 25 2011Notions of interpolating variational splines and Paley-Wiener spaces are introduced on a combinatorial graph G. Both of these definitions explore existence of a combinatorial Laplace operator onG. The existence and uniqueness of interpolating variational ... More

Building Galactic Disks in Triaxial Dark Matter HalosOct 24 2006We review our recent work on the formation and evolution of disks with in triaxial dark matter (DM) halos by means of numerical simulations, including star formation and feedback from stellar evolution. The growing disks are strongly in fluenced by shapes ... More

An approximate Herbrand's theorem and definable functions in metric structuresJul 19 2011We develop a version of Herbrand's theorem for continuous logic and use it to prove that definable functions in infinite-dimensional Hilbert spaces are piecewise approximable by affine functions. We obtain similar results for definable functions in Hilbert ... More

Optical Möbius SingularitiesDec 17 2008M\"{o}bius strips with one, two, three, and four, half-twists are shown to be generic features of three-dimensional (nonparaxial) elliptically polarized light. The geometry and topology of these unusual singularities is described and the multitude of ... More

Dynamics of Inner Galactic Disks: The Striking Case of M100Feb 29 1996We investigate gas dynamics in the presence of a double inner Lindblad resonance within a barred disk galaxy. Using an example of a prominent spiral, M100, we reproduce the basic central morphology, including four dominant regions of star formation corresponding ... More

Galactic Bars in Cosmological ContextDec 03 2008Galactic disks can form in asymmetric potentials of the assembling dark matter (DM) halos, giving rise to the first generation of gas-rich bars. Properties of these bars differ from canonical bars analyzed so far. Moreover, rapid disk growth is associated ... More

On the simple normality to base 2 of the square root of s, for s not a perfect squareDec 16 2005Sep 21 2006We show that each number of the form, the square root of s for s not a perfect square, is simply normal to the base 2. The argument uses some elementary ideas from the calculus of finite differences.

Deconvolution With a Spatially-Variant PSFAug 12 2002Application of deconvolution algorithms to astronomical images is often limited by variations in PSF structure over the domain of the images. One major difficulty is that Fourier methods can no longer be used for fast convolutions over the entire images. ... More

Combining Undersampled Dithered ImagesOct 23 1998Undersampled images, such as those produced by the HST WFPC-2, misrepresent fine-scale structure intrinsic to the astronomical sources being imaged. Analyzing such images is difficult on scales close to their resolution limits and may produce erroneous ... More

The Photometry of Undersampled Point Spread FunctionsJul 07 1999An undersampled point spread function may interact with the microstructure of a solid-state detector such that the total flux detected can depend sensitively on where the PSF center falls within a pixel. Such intra-pixel sensitivity variations will not ... More

The level-set flow of the topologist's sine curve is smoothJan 11 2016In this note we prove that the level-set flow of the topologist's sine curve is a smooth closed curve. In previous work it was shown by the second author that under level-set flow, a locally-connected set in the plane evolves to be smooth, either as a ... More

Nonparametric estimation of risk measures of collective risksApr 10 2015Sep 16 2015We consider two nonparametric estimators for the risk measure of the sum of $n$ i.i.d. individual insurance risks where the number of historical single claims that are used for the statistical estimation is of order $n$. This framework matches the situation ... More

SentiMATE: Learning to play Chess through Natural Language ProcessingJul 18 2019We present SentiMATE, a novel end-to-end Deep Learning model for Chess, employing Natural Language Processing that aims to learn an effective evaluation function assessing move quality. This function is pre-trained on the sentiment of commentary associated ... More

Eliminating Higher-Multiplicity Intersections, II. The Deleted Product Criterion in the $r$-Metastable RangeJan 05 2016Motivated by Tverberg-type problems in topological combinatorics and by classical results about embeddings (maps without double points), we study the question whether a finite simplicial complex K can be mapped into R^d without higher-multiplicity intersections. ... More

Small and Large Scale Granular StaticsAug 28 2003Dec 29 2003Recent experimental results on the static or quasistatic response of granular materials have been interpreted to suggest the inapplicability of the traditional engineering approaches, which are based on elasto-plastic models (which are elliptic in nature). ... More

Model problems for two equations, which type depends on solutionApr 01 2013In this work there are considered model problems for two nonlinear equations, which type depends on the solution. One of the equations may be called a nonlinear analog of the Lavrent'ev-Bitsadze equation.

Sampling formulas for one-parameter groups of operators in Banach spacesMar 03 2014We extend some results about sampling of entire functions of exponential type to Banach spaces. By using generator $D$ of one-parameter group $e^{tD}$ of isometries of a Banach space $E$ we introduce Bernstein subspaces $\mathbf{B}_{\sigma}(D),\>\>\sigma>0,$ ... More

Shannon Sampling and Parseval Frames on Compact ManifoldsDec 06 2013Our article is a summary of some results for Riemannian manifolds that were obtained in \cite{gpes}-\cite{Pesssubm}. To the best of our knowledge these are the pioneering papers which contain the most general results about frames, Shannon sampling, and ... More

Boas-type formulas in Banach spaces with applications to analysis on manifoldsNov 23 2013Apr 24 2014The paper contains Boas-type formulas for trajectories of one-parameter groups of operators in Banach spaces. The results are illustrated using one-parameter groups of operators which appear in representations of Lie groups.

The fundamental group of a locally finite graph with ends: a hyperfinite approachMar 20 2012Mar 29 2012The end compactification |\Gamma| of the locally finite graph \Gamma is the union of the graph and its ends, endowed with a suitable topology. We show that \pi_1(|\Gamma|) embeds into a nonstandard free group with hyperfinitely many generators, i.e. an ... More

Fragmentation of protoplanetary disks around M-dwarfsJul 23 2016We investigate the conditions required for planet formation via gravitational instability (GI) and protoplanetary disk (PPD) fragmentation around M-dwarfs. Using a suite of 64 SPH simulations with $10^6$ particles, the parameter space of disk mass, temperature, ... More

Near field imaging of small isotropic and extended anisotropic scatterersJan 12 2016Sep 11 2016In this paper, we consider two time-harmonic inverse scattering problems of reconstructing penetrable inhomogeneous obstacles from near field measurements. First we appeal to the Born approximation for reconstructing small isotropic scatterers via the ... More

Robinson forcing and the quasidiagonality problemAug 02 2016Aug 23 2016We introduce weakenings of two of the more prominent open problems in the classification of $\mathrm{C}^*$-algebras, namely the quasidiagonality problem and the UCT problem. We show that the a positive solution of the conjunction of the two weaker problems ... More

On the theories of McDuff's II$_1$ factorsFeb 04 2016Recently, Boutonnet, Chifan, and Ioana proved that McDuff's family of continuum many pairwise nonisomorphic separable II$_1$ factors are in fact pairwise non-elementarily equivalent by proving that any ultrapowers of two distinct members of the family ... More

Model-theoretic aspects of the Gurarij operator systemJan 18 2015Apr 28 2015We establish some of the basic model theoretic facts about the Gurarij operator system $\mathbb{GS}$ recently constructed by the second-named author. In particular, we show: (1) $\mathbb{GS}$ is the unique separable 1-exact existentially closed operator ... More

Irregular sampling and the Radon transformAug 29 2011In image reconstruction there are techniques that use analytical formulae for the Radon transform to recover an image from a continuum of data. In practice, however, one has only discrete data available. Thus one often resorts to sampling and interpolation ... More

Angular Momentum Transfer and Lack of Fragmentation in Self-Gravitating Accretion FlowsApr 27 2009Jul 23 2009Rapid inflows associated with early galaxy formation lead to the accumulation of self-gravitating gas in the centers of proto-galaxies. Such gas accumulations are prone to non-axisymmetric instabilities, as in the well-known Maclaurin sequence of rotating ... More

Morton curve segments produce no more than two distinct face-connected subdomainsMar 24 2015Aug 01 2015The Morton- or z-curve is one example for a space filling curve: Given a level of refinement L, it maps the interval [0, 2**dL) one-to-one to a set of d-dimensional cubes of edge length 2**-L that form a subdivision of the unit cube. In contrast to the ... More

Nested Bars in Disk Galaxies: No Offset Dust Lanes in Secondary Nuclear BarsSep 28 2001Under certain conditions, sub-kpc nuclear bars form inside large-scale stellar bars of disk galaxies. These secondary bars spend a fraction of their lifetime in a dynamically-decoupled state, tumbling in the gravitational field of the outer bars. We analyze ... More

Phase space sampling and operator confidence with generative adversarial networksOct 23 2017We demonstrate that a generative adversarial network can be trained to produce Ising model configurations in distinct regions of phase space. In training a generative adversarial network, the discriminator neural network becomes very good a discerning ... More

Spinodal instabilities of asymmetric nuclear matter within the Brueckner--Hartree--Fock approachMay 14 2008Sep 19 2008We study the spinodal instabilities of asymmetric nuclear matter at finite temperature within the microscopic Brueckner--Hartree--Fock (BHF) approximation using the realistic Argonne V18 nucleon-nucleon potential plus a three-body force of Urbana type. ... More

Modulus of convexity for operator convex functionsOct 02 2013Jul 08 2014Given an operator convex function $f(x)$, we obtain an operator-valued lower bound for $cf(x) + (1-c)f(y) - f(cx + (1-c)y)$, $c \in [0,1]$. The lower bound is expressed in terms of the matrix Bregman divergence. A similar inequality is shown to be false ... More

Holographic quantum simulationFeb 07 2017Feb 28 2017A one-dimensional quantum simulator can simulate two-dimensional quantum many-body systems. A representation of a low-energy state is obtained by applying a feedback loop.

Hindman's theorem and idempotent typesAug 12 2015Motivated by a question of Di Nasso, we prove that Hindman's theorem is equivalent to the existence of idempotent types in countable complete extensions of Peano Arithmetic.

The Fabric of the Universe: Exploring the cosmic web in 3D prints and woven textilesFeb 07 2017Apr 19 2017We introduce The Fabric of the Universe, an art and science collaboration focused on exploring the cosmic web of dark matter with unconventional techniques and materials. We discuss two of our projects in detail. First, we describe a pipeline for translating ... More

The Alexander polynomial for Virtual Twist KnotsAug 26 2015We define a family of virtual knots generalizing the classical twist knots. We develop a recursive formula for the Alexander polynomial $\Delta_0$ (as defined by Silver and Williams) of these virtual twist knots. These results are applied to provide evidence ... More

Abbott Wave-Triggered Runaway in Line-Driven Winds from Stars and Accretion DisksOct 11 2001Line-driven winds from stars and accretion disks are accelerated by scattering in numerous line transitions. The wind is believed to adopt a unique critical solution, out of the infinite variety of shallow and steep solutions. We study the inherent dynamics ... More

Dynamics of Line-Driven Winds from Disks in Cataclysmic Variables. I. Solution Topology and Wind GeometryFeb 09 1999We analyze the dynamics of 2-D stationary, line-driven winds from accretion disks in cataclysmic variable stars. The driving force is that of line radiation pressure, in the formalism developed by Castor, Abbott & Klein for O stars. Our main assumption ... More

Average sampling and average splines on combinatorial graphsJan 25 2019In the setting of a weighted combinatorial finite or infinite countable graph $G$ we introduce functional Paley-Wiener spaces $PW_{\omega}(L),\>\omega>0,$ defined in terms of the spectral resolution of the combinatorial Laplace operator $L$ in the space ... More

A purely geometrical method of determining the location of a smartphone accelerometerMar 27 2019In a paper ( posthumously ) co-authored by Isaac Newton himself, the primacy of geometric notions in pedagogical expositions of centripetal acceleration has been clearly asserted. In the present paper we demonstrate how this pedagogical prerogative can ... More

Deep neural networks for direct, featureless learning through observation: the case of 2d spin modelsJun 29 2017Mar 16 2018We demonstrate the capability of a convolutional deep neural network in predicting the nearest-neighbor energy of the 4x4 Ising model. Using its success at this task, we motivate the study of the larger 8x8 Ising model, showing that the deep neural network ... More

On the informational completeness of local observablesMay 01 2014For a general multipartite quantum state, we formulate a locally checkable condition, under which the expectation values of certain nonlocal observables are completely determined by the expectation values of some local observables. The condition is satisfied ... More

Entropic topological invariant for a gapped one-dimensional systemJun 20 2013Aug 20 2014We propose an order parameter for a general one-dimensional gapped system with an open boundary condition. The order parameter can be computed from the ground state entanglement entropy of some regions near one of the boundaries. Hence, it is well-defined ... More

3D local qupit quantum code without string logical operatorJan 31 2012Recently Haah introduced a new quantum error correcting code embedded on a cubic lattice. One of the defining properties of this code is the absence of string logical operator. We present new codes with similar properties by relaxing the condition on ... More

Analysis of new direct sampling indicators for far-field measurementsJan 08 2019Feb 12 2019This article focuses on the analysis of three direct sampling indicators which can be used for recovering scatterers from the far-field pattern of time-harmonic acoustic measurements. These methods fall under the category of sampling methods where an ... More

Independent Events in a Simple Random Experiment and the Meaning of IndependenceApr 30 2012We count the number and patterns of pairs and tuples of independent events in a simple random experiment: first a fair coin is flipped and then a fair die is tossed. The first number, equal to 888,888, suggest that there are some open questions about ... More

Convex bodies with many elliptic sectionsAug 25 2014{We show in this paper that two normal elliptic sections through every point of the boundary of a smooth convex body essentially characterize an ellipsoid and furthermore, that four different pairwise non-tangent elliptic sections through every point ... More

Asymptotic Properties of Random Voronoi Cells with Arbitrary Underlying DensityNov 28 2018Dec 31 2018We consider the Voronoi diagram generated by $n$ i.i.d. $\mathbb{R}^{d}$-valued random variables with an arbitrary underlying probability density function $f$ on $\mathbb{R}^{d}$, and analyse the asymptotic behaviours of certain geometric properties, ... More

Boundary amenability of groups via ultrapowersOct 28 2016We use $\mathrm{C}^{\ast}$-algebra ultrapowers to give a new construction of the Stone-Cech compactification of a separable, locally compact space. We use this construction to give a new proof of the fact that groups that act isometrically, properly, ... More

Spectral order statistics of Gaussian random matrices: large deviations for trapped fermions and associated phase transitionsJul 11 2014Jul 29 2014We compute the full order statistics of a one-dimensional gas of fermions in a harmonic trap at zero temperature, including its large deviation tails. The problem amounts to computing the probability distribution of the $k$th smallest eigenvalue $\lambda_{(k)}$ ... More