Results for "Tobin Isaac"

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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
Recursive Algorithms for Distributed Forests of OctreesMay 31 2014Aug 20 2015The forest-of-octrees approach to parallel adaptive mesh refinement and coarsening (AMR) has recently been demonstrated in the context of a number of large-scale PDE-based applications. Although linear octrees, which store only leaf octants, have an underlying ... 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
Support for Non-conformal Meshes in PETSc's DMPlex InterfaceAug 11 2015PETSc's DMPlex interface for unstructured meshes has been extended to support non-conformal meshes. The topological construct that DMPlex implements---the CW-complex---is by definition conformal, so representing non- conformal meshes in a way that hides ... More
Bounds on the number of discontinuities of Morton-type space-filling curvesMar 24 2015Apr 20 2017The 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. Similar curves have ... More
Solution of nonlinear Stokes equations discretized by high-order finite elements on nonconforming and anisotropic meshes, with application to ice sheet dynamicsJun 25 2014Jul 09 2015Motivated by the need for efficient and accurate simulation of the dynamics of the polar ice sheets, we design high-order finite element discretizations and scalable solvers for the solution of nonlinear incompressible Stokes equations. We focus on power-law, ... More
Knot Floer Filtration Classes of Topologically Slice KnotsSep 08 2013The knot Floer complex and the concordance invariant $\varepsilon$ can be used to define a filtration on the smooth concordance group. We exhibit an ordered subset of this filtration that is isomorphic to $\mathbb{N} \times \mathbb{N}$ and consists of ... 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
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
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
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.
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
On the adjustment coefficient, drawdowns and Lundberg-type bounds for random walkJul 22 2008Consider a random walk whose (light-tailed) increments have positive mean. Lower and upper bounds are provided for the expected maximal value of the random walk until it experiences a given drawdown d. These bounds, related to the Calmar ratio in Finance, ... 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
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
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.
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
Scalable and efficient algorithms for the propagation of uncertainty from data through inference to prediction for large-scale problems, with application to flow of the Antarctic ice sheetOct 05 2014Sep 02 2015The majority of research on efficient and scalable algorithms in computational science and engineering has focused on the forward problem: given parameter inputs, solve the governing equations to determine output quantities of interest. In contrast, here ... More
Inertial Motion in the Events Plane of Minkowski Space with Non-zero Rest Mass (Axiomatic Description)Mar 06 2014Inertial motion is considered in the plane of events characterized by the homogeneous Lorentz group L. On the basis of this group, a set of inertial movements and its decomposition into sets which are disconnected from one another with respect to the ... More
A quantum model of space-time-matterMar 24 2005We study a quantum mechanics with the usual postulates but in which the Heisenberg algebra of canonical commutation relations and the Poincare algebra are replaced by the Lie algebra of the homogeneous Lorentz group SO(5,1). It arises from the hypothesis ... More
Splines and Wavelets on Geophysically Relevant ManifoldsMar 04 2014Analysis on the unit sphere $\mathbb{S}^{2}$ found many applications in seismology, weather prediction, astrophysics, signal analysis, crystallography, computer vision, computerized tomography, neuroscience, and statistics. In the last two decades, the ... More
The Garman-Klass volatility estimator revisitedJul 22 2008Apr 18 2009The Garman-Klass unbiased estimator of the variance per unit time of a zero-drift Brownian Motion B, based on the usual financial data that reports for time windows of equal length the open (OPEN), minimum (MIN), maximum (MAX) and close (CLOSE) values, ... More
Dynamical Processes in the Central Kpc and Active Galactic NucleiJun 13 2003Jun 18 2003We discuss different aspects of nested bar dynamics and its effect on the gas flow and fueling of Active Galactic Nuclei. Specifically we focus on the dynamical decoupling between the primary and secondary bars and the gas flow across the bar-bar interface. ... More
About the nature of dark matter and dark energy and a model of cosmology that may solve the cosmic coincidence problemApr 01 2003A model of cosmology, that arises from the hypothesis that ordinary matter, dark matter and dark energy are made of the same stuff, is studied. It is argued that this hypothesis is a consequence of considering space and time in the same footing. The model ... More
Frames for spaces of Paley-Wiener functions on Riemannian manifoldsApr 09 2011It is shown that Paley-Wiener functions on Riemannian manifolds of bounded geometry can be reconstructed in a stable way from some countable sets of their inner products with certain distributions of compact support. A reconstruction method in terms of ... More
Ends of groups: a nonstandard perspectiveAug 16 2010We give a nonstandard treatment of the notion of ends of proper geodesic metric spaces. We then apply this nonstandard treatment to Cayley graphs of finitely generated groups and give nonstandard proofs of many of the fundamental results concerning ends ... More
Definable Functions in Urysohn's Metric SpaceJan 27 2010Let U denote the Urysohn sphere and consider U as a metric structure in the empty continuous signature. We prove that every definable function from U^n to U is either a projection function or else has relatively compact range. As a consequence, we prove ... More
Dark Matter Substructure, Filaments and Assembling DisksFeb 16 2009We review some general properties of assembling galactic dark matter (DM) halos which have a direct effect on the baryon dynamics. Specifically, we focus on the mutual dynamical feedback between baryons and DM which influence disk formation and evolution, ... 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
Hilbert's Fifth Problem for Local GroupsAug 28 2007Oct 08 2009We solve Hilbert's fifth problem for local groups: every locally euclidean local group is locally isomorphic to a Lie group. Jacoby claimed a proof of this in 1957, but this proof is seriously flawed. We use methods from nonstandard analysis and model ... More
Extensible Pattern Matching in an Extensible LanguageJun 14 2011Pattern matching is a widely used technique in functional languages, especially those in the ML and Haskell traditions, where it is at the core of the semantics. In languages in the Lisp tradition, in contrast, pattern matching it typically provided by ... More
Three conjectures in extremal spectral graph theoryJun 06 2016We prove three conjectures regarding the maximization of spectral invariants over certain families of graphs. Our most difficult result is that the join of $P_2$ and $P_{n-2}$ is the unique graph of maximum spectral radius over all planar graphs. This ... 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
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
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
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
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
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
Characterizing graphs of maximum principal ratioNov 19 2015The principal ratio of a connected graph, denoted $\gamma(G)$, is the ratio of the maximum and minimum entries of its first eigenvector. Cioab\u{a} and Gregory conjectured that the graph on $n$ vertices maximizing $\gamma(G)$ is a kite graph: a complete ... 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
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
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
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.
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
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
Dividing and weak quasidimensions in arbitary theoriesSep 25 2014Oct 14 2014We show that any countable model of a model complete theory has an elementary extension with a "pseudofinite-like" quasidimension that detects dividing.
On Kirchberg's Embedding ProblemApr 07 2014Feb 27 2015Kirchberg's Embedding Problem (KEP) asks whether every separable C$^*$ algebra embeds into an ultrapower of the Cuntz algebra $\mathcal{O}_2$. In this paper, we use model theory to show that this conjecture is equivalent to a local approximate nuclearity ... More
Sampling solutions of Schrödinger equations on combinatorial graphsFeb 12 2015Apr 30 2015We consider functions on a graph $G$ whose evolution in time $-\infty<t<\infty$ is governed by a Schr\"{o}dinger type equation with a combinatorial Laplace operator on the right side. For a given subset $S$ of vertices of $G$ we compute a cut-off frequency ... More
Bernstein-Nikolskii and Plancherel-Polya inequalities in $L_{p}$-norms on non-compact symmetric spacesMar 18 2014By using Bernstein-type inequality we define analogs of spaces of entire functions of exponential type in $L_{p}(X), 1\leq p\leq \infty$, where $X$ is a symmetric space of non-compact. We give estimates of $L_{p}$-norms, $1\leq p\leq \infty$, of such ... More
Splitting matters: how monotone transformation of predictor variables may improve the predictions of decision tree modelsNov 14 2016It is widely believed that the prediction accuracy of decision tree models is invariant under any strictly monotone transformation of the individual predictor variables. However, this statement may be false when predicting new observations with values ... More
Structural characterizations of water-metal interfacesNov 07 2016We analyze and compare the structural, dynamical, and electronic properties of liquid water next to prototypical metals including Pt, graphite, and graphene. Our analysis is built on Born-Oppenheimer molecular dynamics (BOMD) generated using density functional ... More
Do hyperons exist in the interior of neutron stars ?Oct 21 2015Nov 06 2015In this work we review the role of hyperons on the properties of neutron and proto-neutron stars. In particular, we revise the so-called "hyperon puzzle", go over some of the solutions proposed to tackle it, and discuss the implications that the recent ... More
A computability-theoretic reformulation of the Connes Embedding ProblemAug 12 2013The Connes Embedding Problem (CEP) asks whether every separable II_1 factor embeds into an ultrapower of the hyperfinite II_1 factor. We show that the CEP is equivalent to the computability of the universal theory of every type II_1 von Neumann algebra. ... More
Paley-Wiener-Schwartz nearly Parseval frames and Besov spaces on noncompact symmetric spacesAug 08 2013Feb 08 2014Let $X$ be a symmetric space of the noncompact type. The goal of the paper is to construct in the space $L_{2}(X)$ nearly Parseval frames consisting of functions which simultaneously belong to Paley-Wiener spaces and to Schwartz space on $X$. We call ... More
The AGN Obscuring Torus -- End of the "Doughnut" Paradigm?May 28 2006Aug 04 2006Unified schemes of active galactic nuclei (AGN) require an obscuring dusty torus around the central engine. The compact sizes (only a few pc) determined in recent high-resolution observations require that the obscuring matter be clumpy and located inside ... More
An approximate logic for measuresJun 15 2011Nov 04 2012We present a logical framework for formalizing connections between finitary combinatorics and measure theory or ergodic theory that have appeared various places throughout the literature. We develop the basic syntax and semantics of this logic and give ... More
Local non-CSS quantum error correcting code on a three-dimensional latticeDec 03 2010Apr 25 2013We present a family of non-CSS quantum error-correcting code consisting of geometrically local stabilizer generators on a 3D lattice. We study the Hamiltonian constructed from ferromagnetic interaction of overcomplete set of local stabilizer generators. ... More
Quamtumness, Generalized Spherical 2-Design and Symmetric Informationally Complete POVMAug 02 2006Mar 25 2007C. A. Fuchs and M. Sasaki defined the quantumness of a set of quantum states in \cite{Quantumness}, which is closely related to the fidelity loss in transmission of the quantum states through a classical channel. In \cite{Fuchs}, Fuchs showed that in ... More
Operator extension of strong subadditivity of entropyOct 18 2012Dec 05 2012We prove an operator inequality that extends strong subadditivity of entropy: after taking a trace, the operator inequality becomes the strong subadditivity of entropy.
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
Eliminating Higher-Multiplicity Intersections, I. A Whitney Trick for Tverberg-Type ProblemsAug 10 2015Motivated by topological Tverberg-type problems 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 triple, quadruple, or, more generally, r-fold ... 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
Phi-transform on domainsAug 25 2012Jan 09 2014The goal of the present paper is to construct bandlimited highly localized and nearly tight frames on domains with smooth boundaries in Euclidean spaces. These frames are used do describe corresponding Besov spaces.
Kolmogorov and Linear Widths of Balls in Sobolev and Besov Norms on Compact ManifoldsApr 04 2011Apr 27 2012We determine upper asymptotic estimates of Kolmogorov and linear $n$-widths of unit balls in Sobolev and Besov norms in $L_{p}$-spaces on smooth compact Riemannian manifolds. For compact homogeneous manifolds, we establish estimates which are asymptotically ... More
A Beaming-Independent Estimate of the Energy Distribution of Long Gamma-Ray Bursts: Initial Results and Future ProspectsJan 03 2011We present single-epoch radio afterglow observations of 24 long-duration gamma-ray burst (GRB) on a timescale of >100 d after the burst. These observations trace the afterglow evolution when the blastwave has decelerated to mildly- or non-relativistic ... More
Sampling, splines and frames on compact manifoldsMay 27 2014Feb 28 2015Analysis on the unit sphere $\mathbb{S}^{2}$ found many applications in seismology, weather prediction, astrophysics, signal analysis, crystallography, computer vision, computerized tomography, neuroscience, and statistics. In the last two decades, the ... More
An approach to spectral problems on Riemannian manifoldsMar 19 2014It is shown that eigenvalues of Laplace-Beltrami operators on compact Riemannian manifolds can be determined as limits of eigenvalues of certain finite-dimensional operators in spaces of polyharmonic functions with singularities. In particular, a bounded ... More
Quantum Digital SignaturesMay 08 2001Nov 15 2001We present a quantum digital signature scheme whose security is based on fundamental principles of quantum physics. It allows a sender (Alice) to sign a message in such a way that the signature can be validated by a number of different people, and all ... More