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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

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

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

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

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

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

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

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

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

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

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

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 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

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 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

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.

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

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

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

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

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

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

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

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

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

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

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

Strong Scaling for Numerical Weather Prediction at Petascale with the Atmospheric Model NUMANov 05 2015Sep 08 2016Numerical weather prediction (NWP) has proven to be computationally challenging due to its inherent multiscale nature. Currently, the highest resolution NWP models use a horizontal resolution of about 10km. In order to increase the resolution of NWP models ... 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

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

Sampling algorithms for validation of supervised learning models for Ising-like systemsNov 17 2016In this paper, we build and explore supervised learning models of ferromagnetic system behavior, using Monte-Carlo sampling of the spin configuration space generated by the 2D Ising model. Given the enormous size of the space of all possible Ising model ... More

Growing Live Disks Within Cosmologically Assembling Asymmetric Halos: Washing Out the Halo ProlatenessMar 17 2006We study the growth of galactic disks in live triaxial DM halos. The halos have been assembled through constrained realizations method and evolved from the linear regime using cosmological simulations. The `seed' disks have been inserted at redshift z=3 ... More

Thorn-Forking in Continuous LogicNov 18 2009We study thorn forking and rosiness in the context of continuous logic. We prove that the Urysohn sphere is rosy (with respect to finitary imaginaries), providing the first example of an essentially continuous unstable theory with a nice notion of independence. ... More

Poincaré-type inequalities and sampling and interpolation by average values on combinatorial graphsMay 06 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

Runaway of Line-Driven Winds Towards Critical and Overloaded solutionsFeb 17 2000Line-driven winds from hot stars and accretion disks are thought to adopt a unique, critical solution which corresponds to maximum mass loss rate and a particular velocity law. We show that in the presence of negative velocity gradients, radiative-acoustic ... More

Noise-resilient preparation of quantum many-body ground statesFeb 28 2017Certain quantum many-body ground states can be prepared by a large-depth quantum circuit consisting of geometrically local gates. In the presence of noise, local expectation values deviate from the correct value at most by an amount comparable to the ... More

Long-range entanglement is necessary for a topological storage of quantum informationApr 14 2013Oct 02 2013A general inequality between entanglement entropy and a number of topologically ordered states is derived, even without using the properties of the parent Hamiltonian or the formalism of topological quantum field theory. Given a quantum state $\ket{\psi}$, ... More

Perturbative analysis of topological entanglement entropy from conditional independenceOct 08 2012Dec 05 2012We use the structure of conditionally independent states to analyze the stability of topological entanglement entropy. For the ground state of quantum double or Levin-Wen model, we obtain a bound on the first order perturbation of topological entanglement ... More

On some estimates for bounded submartingales and the shift inequalityAug 03 2010It is well known that if a submartingale $X$ is bounded then the increasing predictable process $Y$ and the martingale $M$ from the Doob decomposition $% X=Y+M$ can be unbounded. In this paper for some classes of increasing convex functions $f$ we will ... 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

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