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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

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

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

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

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

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

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

Nested Bars and Associated Morphology of Central Kpc in Disk GalaxiesFeb 28 2002We discuss different aspects of nested bar systems, both observational and theoretical. Such systems consist of a large-scale primary bar leading to the formation of a sub-kpc size secondary bar, whose pattern speed differs substantially from that of ... More

Optical M0bius Strips in Three Dimensional Ellipse Fields: Lines of Linear PolarizationMay 20 2009The minor axes of, and the normals to, the polarization ellipses that surround singular lines of linear polarization in three dimensional optical ellipse fields are shown to be organized into Mobius strips and into structures we call rippled rings (r-rings). ... More

Sampling in paley-wiener spaces on combinatorial graphsNov 25 2011A notion of Paley-Wiener spaces is introduced on combinatorial graphs. It is shown that functions from some of these spaces are uniquely determined by their values on some sets of vertices which are called the uniqueness sets. Such uniqueness sets are ... More

Hyperons in Neutron StarsSep 11 2015In this work I briefly review some of the effects of hyperons on the properties of neutron and proto-neutron stars. In particular, I revise the problem of the strong softening of the EoS, and the consequent reduction of the maximum mass, induced by the ... 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

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

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

Nonstandard Hulls of Locally Exponential Lie AlgebrasApr 03 2008We show how to construct the nonstandard hull of certain infinite-dimensional Lie algebras in order to generalize a theorem of Pestov on the enlargeability of Banach-Lie algebras. In the process, we consider a nonstandard smoothness condition on functions ... 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

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

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

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

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

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

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

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

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

Memristor - The fictional circuit elementAug 17 2018The memory resistor abbreviated memristor was a harmless postulate in 1971. In the decade since 2008, a device claiming to be the missing memristor is on the prowl, seeking recognition as a fundamental circuit element, sometimes wanting electronics textbooks ... 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

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

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

Finding sparse solutions of systems of polynomial equations via group-sparsity optimizationNov 22 2013Jul 16 2014The paper deals with the problem of finding sparse solutions to systems of polynomial equations possibly perturbed by noise. In particular, we show how these solutions can be recovered from group-sparse solutions of a derived system of linear equations. ... More

Omitting types in operator systemsJan 26 2015Dec 21 2015We show that the class of 1-exact operator systems is not uniformly definable by a sequence of types. We use this fact to show that there is no finitary version of Arveson's extension theorem. Next, we show that WEP is equivalent to a certain notion of ... More

Large deviations of the shifted index number in the Gaussian ensembleOct 15 2014Oct 24 2015We show that, using the Coulomb fluid approach, we are able to derive a rate function $\Psi(c,x)$ of two variables that captures: (i) the large deviations of bulk eigenvalues; (ii) the large deviations of extreme eigenvalues (both left and right large ... More

Bernstein-Nikolskii inequalities and Riesz interpolation formula on compact homogeneous manifoldsMar 18 2014Apr 24 2014Bernstein-Nikolskii inequalities and Riesz interpolation formula are established for eigenfunctions of Laplace operators and polynomials on compact homogeneous manifolds.

Superfluidity of $Σ^-$ hyperons in $β$-stable neutron star matterMay 05 2004Jul 14 2004In this work we evaluate the $^1S_0$ energy gap of $\Sigma^-$ hyperons in $\beta$-stable neutron star matter. We solve the BCS gap equation for an effective $\Sigma^-\Sigma^-$ pairing interaction derived from the most recent parametrization of the hyperon-hyperon ... More

Transseries and Todorov-Vernaeve's asymptotic fieldsMay 04 2012We study the relationship between fields of transseries and residue fields of convex subrings of non-standard extensions of the real numbers. This was motivated by a question of Todorov and Vernaeve, answered in this paper.

Estimates of Kolmogorov, Gelfand and linear $n$- widths on Compact Riemannian ManifoldsAug 30 2015We determine lower and exact estimates of Kolmogorov, Gelfand and linear $n$-widths of unit balls in Sobolev norms in $L_{p}$-spaces on compact Riemannian manifolds. As it was shown by us previously these lower estimates are exact asymptotically in the ... More

Lower Central Series Ideal Quotients Over F_p and ZJun 28 2015Given a graded associative algebra $A$, its lower central series is defined by $L_1 = A$ and $L_{i+1} = [L_i, A]$. We consider successive quotients $N_i(A) = M_i(A) / M_{i+1}(A)$, where $M_i(A) = AL_i(A) A$. These quotients are direct sums of graded components. ... 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

A purely geometrical method of determining the location of a smartphone accelerometerMar 27 2019Mar 28 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

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

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

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

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

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