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Automatic Variationally Stable Analysis for FE Computations: An IntroductionAug 06 2018Apr 13 2019We introduce an automatic variationally stable analysis (AVS) for finite element (FE) computations of scalar-valued convection-diffusion equations with non-constant and highly oscillatory coefficients. In the spirit of least squares FE methods, the AVS-FE ... More

Mode Decomposition Methods for Flows in High-Contrast Porous Media. Part I. Global ApproachJan 24 2013We apply dynamic mode decomposition (DMD) and proper orthogonal decomposition (POD) methods to flows in highly-heterogeneous porous media to extract the dominant coherent structures and derive reduced-order models via Galerkin projection. Permeability ... More

High-order generalized-$α$ methodsFeb 14 2019The generalized-$\alpha$ method encompasses a wide range of time integrators. The method possesses high-frequency dissipation while minimizing unwanted low-frequency dissipation and the numerical dissipation can be controlled by the user. The method is ... More

Higher-order generalized-$α$ methods for hyperbolic problemsJun 14 2019The generalized-$\alpha$ time-marching method provides second-order accuracy in time and controls the numerical dissipation in the high-frequency region of the discrete spectrum. This method includes a wide range of time integrators. We increase the order ... More

Automatically Stable Discontinuous Petrov-Galerkin Methods for Stationary Transport Problems: Quasi-Optimal Test Space NormJan 09 2012We investigate the application of the discontinuous Petrov-Galerkin (DPG) finite element framework to stationary convection-diffusion problems. In particular, we demonstrate how the quasi-optimal test space norm can be utilized to improve the robustness ... More

Higher order stable generalized finite element method for the elliptic eigenvalue problem with an interface in 1DOct 24 2018We study the generalized finite element methods (GFEMs) for the second-order elliptic eigenvalue problem with an interface in 1D. The linear stable generalized finite element methods (SGFEM) were recently developed for the elliptic source problem with ... More

Asymptotic Expansions for High-Contrast Linear ElasticityOct 01 2014Mar 09 2015We study linear elasticity problems with high contrast in the coefficients using asymptotic limits recently introduced. We derive an asymptotic expansion to solve heterogeneous elasticity problems in terms of the contrast in the coefficients. We study ... More

Analysis of the Discontinuous Petrov-Galerkin Method with Optimal Test Functions for the Reissner-Mindlin Plate Bending ModelJan 25 2013We analyze the discontinuous Petrov-Galerkin (DPG) method with optimal test functions when applied to solve the Reissner-Mindlin model of plate bending. We prove that the hybrid variational formulation underlying the DPG method is well-posed (stable) ... More

A variationally separable splitting for the generalized-$α$ method for parabolic equationsNov 23 2018We present a variationally separable splitting technique for the generalized-$\alpha$ method for solving parabolic partial differential equations. We develop a technique for a tensor-product mesh which results in a solver with a linear cost with respect ... More

Randomized Oversampling for Generalized Multiscale Finite Element MethodsSep 24 2014In this paper, we study the development of efficient multiscale methods for flows in heterogeneous media. Our approach uses the Generalized Multiscale Finite Element (GMsFEM) framework. The main idea of GMsFEM is to approximate the solution space locally ... More

Geometrically-Consistent Model Reduction of Polymer Chains in Solution. Application to Dissipative Particle Dynamics: Model DescriptionMay 12 2014We introduce a framework for model reduction of chain models for dissipative particle dynamics (DPD) simulations, where the characteristic size of the chain, pressure, density, and temperature are preserved. The proposed methodology reduces the number ... More

On the Shape Optimization of Flapping Wings and their Performance AnalysisNov 12 2012The present work is concerned with the shape optimization of flapping wings in forward flight. The analysis is performed by combining a gradient-based optimizer with the unsteady vortex lattice method (UVLM). We describe the UVLM implementation and provide ... More

Residual minimization for isogeometric analysis in reduced and mixed formsFeb 11 2019Most variational forms of isogeometric analysis use highly-continuous basis functions for both trial and test spaces. For a partial differential equation with a smooth solution, isogeometric analysis with highly-continuous basis functions for trial space ... More

Variational Formulations for Explicit Runge-Kutta MethodsJun 20 2018Variational space-time formulations for Partial Differential Equations have been of great interest in the last decades. While it is known that implicit time marching schemes have variational structure, the Galerkin formulation of explicit methods in time ... More

Computational complexity and memory usage for multi-frontal direct solvers in structured mesh finite elementsApr 08 2012The multi-frontal direct solver is the state-of-the-art algorithm for the direct solution of sparse linear systems. This paper provides computational complexity and memory usage estimates for the application of the multi-frontal direct solver algorithm ... More

Gaussian quadrature for splines via homotopy continuation: rules for $C^2$ cubic splinesMay 17 2015We introduce a new concept for generating optimal quadrature rules for splines. Given a target spline space where we aim to generate an optimal quadrature rule, we build an associated source space with known optimal quadrature and transfer the rule from ... More

An energy-stable convex splitting for the phase-field crystal equationMay 14 2014Jul 28 2015The phase-field crystal equation, a parabolic, sixth-order and nonlinear partial differential equation, has generated considerable interest as a possible solution to problems arising in molecular dynamics. This is because the phase-field crystal model ... More

Isogeometric Residual Minimization Method (iGRM) with Direction Splitting Preconditoner for Stationary Advection-Diffusion ProblemsJun 16 2019In this paper, we propose the Isogeometric Residual Minimization (iGRM) with direction splitting. The method mixes the benefits resulting from isogeometric analysis, residual minimization, and alternating direction solver. Namely, we utilize tensor product ... More

Gradient-based estimation of Manning's friction coefficient from noisy dataApr 08 2012We study the numerical recovery of Manning's roughness coefficient for the diffusive wave approximation of the shallow water equation. We describe a conjugate gradient method for the numerical inversion. Numerical results for one-dimensional model are ... More

Optimal spectral approximation of $2n$-order differential operators by mixed isogeometric analysisJun 12 2018We approximate the spectra of a class of $2n$-order differential operators using isogeometric analysis in mixed formulations. This class includes a wide range of differential operators such as those arising in elliptic, biharmonic, Cahn-Hilliard, Swift-Hohenberg, ... More

Isogeometric spectral approximation for elliptic differential operatorsFeb 02 2018We study the spectral approximation of a second-order elliptic differential eigenvalue problem that arises from structural vibration problems using isogeometric analysis. In this paper, we generalize recent work in this direction. We present optimally ... More

Explicit Gaussian quadrature rules for cubic splines with non-uniform knot sequencesOct 27 2014We provide explicit expressions for quadrature rules on the space of $C^1$ cubic splines with non-uniform, symmetrically stretched knot sequences. The quadrature nodes and weights are derived via an explicit recursion that avoids an intervention of any ... More

Dispersion-minimizing quadrature rules for $C^1$ quadratic isogeometric analysisMay 08 2017We develop quadrature rules for the isogeometric analysis of wave propagation and structural vibrations that minimize the discrete dispersion error of the approximation. The rules are optimal in the sense that they only require two quadrature points per ... More

Spectral approximation of elliptic operators by the Hybrid High-Order methodNov 03 2017Jul 20 2018We study the approximation of the spectrum of a second-order elliptic differential operator by the Hybrid High-Order (HHO) method. The HHO method is formulated using cell and face unknowns which are polynomials of some degree $k\geq0$. The key idea for ... More

Phase-coexistence Simulations of Fluid Mixtures by the Markov Chain Monte Carlo Method Using Single-Particle ModelsSep 10 2012We present a single-particle Lennard-Jones (L-J) model for CO2 and N2. Simplified L-J models for other small polyatomic molecules can be obtained following the methodology described herein. The phase-coexistence diagrams of single-component systems computed ... More

PetIGA: A Framework for High-Performance Isogeometric AnalysisMay 20 2013Jul 28 2015We present PetIGA, a code framework to approximate the solution of partial differential equations using isogeometric analysis. PetIGA can be used to assemble matrices and vectors which come from a Galerkin weak form, discretized with Non-Uniform Rational ... More

Automatic Variationally Stable Analysis for FE Computations: An IntroductionAug 06 2018Nov 21 2018We introduce an automatic variationally stable analysis (AVS) for finite element (FE) computations of scalar-valued convection-diffusion equations with non-constant and highly oscillatory coefficients. In the spirit of least squares FE methods, the AVS-FE ... More

Asymptotic expansions for high-contrast elliptic equationsApr 14 2012In this paper, we present a high-order expansion for elliptic equations in high-contrast media. The background conductivity is taken to be one and we assume the medium contains high (or low) conductivity inclusions. We derive an asymptotic expansion with ... More

Strain-minimising Stream SurfacesNov 05 2014We study the problem of finding strain-minimising stream surfaces in a divergence-free vector field. These surfaces are generated by motions of seed curves that propagate through the field in a strain minimising manner, i.e., they move without stretching ... More

O'KKLT at Finite TemperatureAug 30 2007May 12 2008We study whether finite temperature corrections decompactify the internal space in KKLT compactifications with an uplifting sector given by a system that exhibits metastable dynamical supersymmetry breaking. More precisely, we calculate the one-loop temperature ... More

PetIGA-MF: a multi-field high-performance toolbox for structure-preserving B-splines spacesFeb 28 2016We describe the development of a high-performance solution framework for isogeometric discrete differential forms based on B-splines: PetIGA-MF. Built on top of PetIGA, PetIGA-MF is a general multi-field discretization tool. To test the capabilities of ... More

Dispersion-minimized mass for isogeometric analysisNov 08 2017We introduce the dispersion-minimized mass for isogeometric analysis to approximate the structural vibration which we model as a second-order differential eigenvalue problem. The dispersion-minimized mass reduces the eigenvalue error significantly, from ... More

Mode Decomposition Methods for Flows in High-Contrast Porous Media. Part II. Local-Global ApproachJan 24 2013In this paper, we combine concepts of the generalized multiscale finite element method and mode decomposition methods to construct a robust local-global approach for model reduction of flows in high-contrast porous media. This is achieved by implementing ... More

Optimal quadrature rules for isogeometric analysisNov 12 2015We introduce optimal quadrature rules for spline spaces that are frequently used in Galerkin discretizations to build mass and stiffness matrices. Using the homotopy continuation concept [6] that transforms optimal quadrature rules from source spaces ... More

Localized Harmonic Characteristic Basis Functions for Multiscale Finite Element MethodsOct 01 2014Dec 10 2015We solve elliptic systems of equations posed on highly heterogeneous materials. Examples of this class of problems are composite structures and geological processes. We focus on a model problem which is a second-order elliptic equation with discontinuous ... More

Econophysics, Statistical Mechanics Approach toSep 23 2007Aug 03 2008This is a review article for Encyclopedia of Complexity and System Science, to be published by Springer http://refworks.springer.com/complexity/. The paper reviews statistical models for money, wealth, and income distributions developed in the econophysics ... More

Metals in high magnetic field: a new universality class of Fermi liquidsMay 14 1992Parquet equations, describing the competition between superconducting and density-wave instabilities, are solved for a three-dimensional isotropic metal in a high magnetic field when only the lowest Landau level is filled. In the case of a repulsive interaction ... More

Theory of Thermodynamic Magnetic Oscillations in Quasi-One-Dimensional ConductorsMay 14 1992The second order correction to free energy due to the interaction between electrons is calculated for a quasi-one-dimensional conductor exposed to a magnetic field perpendicular to the chains. It is found that specific heat, magnetization and torque oscillate ... More

Dynamic properties of solitons in the Frenkel-Kontorova Model. Application to incommensurate CDW conductorsNov 29 1998An impact of kink-type solitons on infrared lattice vibrations is studied for incommensurate Frenkel-Kontorova model. It is shown that the vibration of particles involved into the kink formation is very similar to that in a gap mode around the force constant ... More

Representation of fields associated with any moving point mass by means of fundamental fields corresponding to its trajectory in the frame of Einstein's special theory of relativityMar 01 2010Mar 02 2010Assume that in a Lorentzian frame is given a relativistically admissible trajectory of a point mass. An event in such a frame can be described by four coordinates, first three representing the position and the last one the time of the event. Let G denote ... More

Not all limit points of poles of the Padé approximants are obstructions for poinwise convergenceJan 09 2005Jan 19 2005In the work it is shown that not all limit points of poles of the Pad\'e approximants for the last intermediate row are obstructions for poinwise convergence of the whole row to an approximable function. The corresponding examples are constructed.

Applications of statistical mechanics to economics: Entropic origin of the probability distributions of money, income, and energy consumptionApr 29 2012This Chapter is written for the Festschrift celebrating the 70th birthday of the distinguished economist Duncan Foley from the New School for Social Research in New York. This Chapter reviews applications of statistical physics methods, such as the principle ... More

Novel method for photovoltaic energy conversion using surface acoustic waves in piezoelectric semiconductorsDec 29 2009Sep 28 2011This paper presents a novel principle for photovoltaic (PV) energy conversion using surface acoustic waves (SAWs) in piezoelectric semiconductors. A SAW produces a periodically modulated electric potential, which spatially segregates photoexcited electrons ... More

On random tomography with unobservable projection anglesSep 02 2009We formulate and investigate a statistical inverse problem of a random tomographic nature, where a probability density function on $\mathbb{R}^3$ is to be recovered from observation of finitely many of its two-dimensional projections in random and unobservable ... More

Play Ground for Victor's Magic SquaresJul 17 2008Mar 03 2012This article presents a new development of magic squares with a simple set up.

Polynomial dynamical systems and Korteweg--de Vries equationMay 13 2016In this work we explicitly construct polynomial vector fields $\mathcal{L}_k,\;k=0,1,2,3,4,6$ on the complex linear space $\mathbb{C}^6$ with coordinates $X=(x_2,x_3,x_4)$ and $Z=(z_4,z_5,z_6)$. The fields $\mathcal{L}_k$ are linearly independent outside ... More

Downsizing from the point of view of merging model (preliminary discussion)Jul 01 2015In four-particle scattering processes with transfer of mass, unlike mergers in which mass can only increase, mass of the most massive galaxies may be reduced. Elementary model describing such process is considered. In this way, it is supposed to explain ... More

Tilted loop currents in cuprate superconductorsSep 08 2014Oct 26 2014The paper briefly surveys theoretical models for the polar Kerr effect (PKE) and time-reversal symmetry breaking in the pseudogap phase of cuprate superconductors. By elimination, the most promising candidate is the tilted loop-current model, obtained ... More

Relativistic gravity fields and electromagnetic fields generated by flows of matterOct 05 2009One of the highlight of this note is that the author presents the relativistic gravity field that Einstein was looking for. The field is a byproduct of the matter in motion. This field can include both the discrete and continuous components. In free space ... More

On Henri Cartan's vectorial mean-value theorem and its applications to Lipschitzian operators and generalized Lebesgue-Bochner-Stieltjes integration theoryOct 13 2009H. Cartan in his book on differential calculus proved a theorem generalizing a Cauchy's mean-value theorem to the case of functions taking values in a Banach space. Cartan used this theorem in a masterful way to develop the entire theory of differential ... More

Gauss-Galerkin quadrature rules for quadratic and cubic spline spaces and their application to isogeometric analysisFeb 03 2016We introduce Gaussian quadrature rules for spline spaces that are frequently used in Galerkin discretizations to build mass and stiffness matrices. By definition, these spaces are of even degrees. The optimal quadrature rules we recently derived [5] act ... More

LARGE Volume String Compactifications at Finite TemperatureApr 01 2009Oct 02 2009We present a detailed study of the finite-temperature behaviour of the LARGE Volume type IIB flux compactifications. We show that certain moduli can thermalise at high temperatures. Despite that, their contribution to the finite-temperature effective ... More

Non Abelian Geometrical TachyonMar 31 2010Nov 14 2010We investigate the dynamics of a pair of coincident D5 branes in the background of $k$ NS5 branes. It has been proposed by Kutasov that the system with a single probing D-brane moving radially in this background is dual to the tachyonic DBI action for ... More

Multiscale stabilization for convection-dominated diffusion in heterogeneous mediaSep 23 2015We develop a Petrov-Galerkin stabilization method for multiscale convection-diffusion transport systems. Existing stabilization techniques add a limited number of degrees of freedom in the form of bubble functions or a modified diffusion, which may not ... More

Upper and lower bound theorems for graph-associahedraMay 10 2010May 17 2010From the paper of the first author it follows that upper and lower bounds for $\gamma$-vector of a simple polytope imply the bounds for its $g$-,$h$- and $f$-vectors. In the paper of the second author it was obtained unimprovable upper and lower bounds ... More

Hopf invariant for long-wavelength skyrmions in quantum Hall systems for integer and fractional fillingsFeb 18 1999Feb 26 2000We show that a Hopf term exists in the effective action of long-wavelength skyrmions in quantum Hall systems for both odd integer and fractional filling factors $\nu = 1/(2s +1)$, where $s$ is an integer. We evaluate the prefactor of the Hopf term using ... More

Epidemic Processes over Adaptive State-Dependent NetworksFeb 26 2016Jun 09 2016In this paper, we study the dynamics of epidemic processes taking place in adaptive networks of arbitrary topology. We focus our study on the adaptive susceptible-infected-susceptible (ASIS) model, where healthy individuals are allowed to temporarily ... More

Optimal Design of Switched Networks of Positive Linear Systems via Geometric ProgrammingApr 10 2015Sep 15 2015In this paper, we propose an optimization framework to design a network of positive linear systems whose structure switches according to a Markov process. The optimization framework herein proposed allows the network designer to optimize the coupling ... More

Stability of Markov regenerative switched linear systemsJan 14 2015Dec 05 2015In this paper, we give a necessary and sufficient condition for mean stability of switched linear systems having a Markov regenerative process as its switching signal. This class of switched linear systems, which we call Markov regenerative switched linear ... More

Fourier analysis of stationary time series in function spaceMay 09 2013We develop the basic building blocks of a frequency domain framework for drawing statistical inferences on the second-order structure of a stationary sequence of functional data. The key element in such a context is the spectral density operator, which ... More

Toric topology of the complex Grassmann manifoldsFeb 18 2018Feb 28 2018The family of complex Grassmann manifolds $G_{n,k}$ with the canonical action of the torus $T^n=\mathbb{T}^{n}$ and the analogous of the moment map $\mu : G_{n,k}\to \Delta_{n,k}$ for the hypersimplex $\Delta_{n,k}$, is well known. In this paper we study ... More

Statistical unfolding of elementary particle spectra: Empirical Bayes estimation and bias-corrected uncertainty quantificationMay 18 2015Nov 17 2015We consider the high energy physics unfolding problem where the goal is to estimate the spectrum of elementary particles given observations distorted by the limited resolution of a particle detector. This important statistical inverse problem arising ... More

Universal patterns of inequalityDec 24 2009Apr 18 2010Probability distributions of money, income, and energy consumption per capita are studied for ensembles of economic agents. The principle of entropy maximization for partitioning of a limited resource gives exponential distributions for the investigated ... More

Computation of the Power Spectrum in Chaotic $1/4 λφ^4$ InflationDec 06 2011The phase-integral approximation devised by Fr\"oman and Fr\"oman, is used for computing cosmological perturbations in the quartic chaotic inflationary model. The phase-integral formulas for the scalar power spectrum are explicitly obtained up to fifth ... More

Scattering of a Klein-Gordon particle by a Woods-Saxon potentialMar 11 2005We solve the Klein-Gordon equation in the presence of a spatially one-dimensional Woods-Saxon potential. The scattering solutions are obtained in terms of hypergeometric functions and the condition for the existence of transmission resonances is derived. ... More

What is the dimension of a stochastic process? Testing for the rank of a covariance operatorJan 08 2019How can we discern whether a mean-square continuous stochastic process is finite-dimensional, and if so, what its precise dimension is? And how can we do so at a given level of confidence? This question is central to a great deal of methods for functional ... More

Construction of fullerenesOct 10 2015We present an infinite series of operations on fullerenes generalizing the Endo-Kroto operation, such that each combinatorial fullerene is obtained from the dodecahedron by a sequence of such operations. We prove that these operations are invertible in ... More

Toric topology of the complex Grassmann manifoldsFeb 18 2018Apr 02 2019The family of the complex Grassmann manifolds $G_{n,k}$ with a canonical action of the torus $T^n=\mathbb{T}^{n}$ and the analogue of the moment map $\mu : G_{n,k}\to \Delta _{n,k}$ for the hypersimplex $\Delta _{n,k}$, is well known. In this paper we ... More

Fullerenes, Polytopes and Toric TopologySep 09 2016The lectures are devoted to a remarkable class of $3$-dimensional polytopes, which are mathematical models of the important object of quantum physics, quantum chemistry and nanotechnology -- fullerenes. The main goal is to show how results of toric topology ... More

Fréchet Means and Procrustes Analysis in Wasserstein SpaceJan 24 2017Jan 17 2018We consider two statistical problems at the intersection of functional and non-Euclidean data analysis: the determination of a Fr\'echet mean in the Wasserstein space of multivariate distributions; and the optimal registration of deformed random measures ... More

Traffic Optimization to Control Epidemic Outbreaks in Metapopulation ModelsAug 17 2013We propose a novel framework to study viral spreading processes in metapopulation models. Large subpopulations (i.e., cities) are connected via metalinks (i.e., roads) according to a metagraph structure (i.e., the traffic infrastructure). The problem ... More

Topology Identification of Directed Dynamical Networks via Power Spectral AnalysisAug 09 2013We address the problem of identifying the topology of an unknown weighted, directed network of LTI systems stimulated by wide-sense stationary noises of unknown power spectral densities. We propose several reconstruction algorithms based on the cross-power ... More

Robust Topology Identification and Control of LTI NetworksJun 17 2014This paper reports a robust scheme for topology identification and control of networks running on linear dynamics. In the proposed method, the unknown network is enforced to asymptotically follow a reference dynamics using the combination of Lyapunov ... More

From Local Measurements to Network Spectral Properties: Beyond Degree DistributionsApr 20 2010Jan 13 2011It is well-known that the behavior of many dynamical processes running on networks is intimately related to the eigenvalue spectrum of the network. In this paper, we address the problem of inferring global information regarding the eigenvalue spectrum ... More

Topology Classes of Flat U(1) Bundles and Diffeomorphic Covariant Representations of the Heisenberg AlgebraAug 04 1999Sep 01 1999The general construction of self-adjoint configuration space representations of the Heisenberg algebra over an arbitrary manifold is considered. All such inequivalent representations are parametrised in terms of the topology classes of flat U(1) bundles ... More

Scaled variational computation of the energy spectrum of a two-dimensional hydrogenic donor in a magnetic field of arbitrary strengthJan 20 1999We compute the energy levels of a 2D Hydrogen atom when a constant magnetic field is applied. With the help of a mixed-basis variational method and a genera lization of virial theorem, which consists in scaling the wave function, we calculate the binding ... More

Energy spectrum of the ground state of a two dimensional relativistic hydrogen atom in the presence of a constant magnetic fieldFeb 12 2004We compute the energy spectrum of the ground state of a 2D Dirac electron in the presence of a Coulomb potential and a constant magnetic field perpendicular to the plane where the the electron is confined. With the help of a mixed-basis variational method ... More

Analytic computation of the energy levels of a two-dimensional hydrogenic donor in a constant magnetic fieldAug 26 1998We compute the energy levels of a 2D Hydrogen atom when a constant magnetic field is applied. With the help of a mixed-basis variational method, we calculate the energy eigenvalues of the 1S, 2P- and 3D- levels. We compare the computed energy spectra ... More

Spontaneous spin accumulation in singlet-triplet Josephson junctionsJul 09 2008Feb 27 2009We study the Andreev bound states in a Josephson junction between a singlet and a triplet superconductors. Because of the mismatch in the spin symmetries of pairing, the energies of the spin up and down quasiparticles are generally different. This results ... More

Quantum Hall effect anomaly and collective modes in the magnetic-field-induced spin-density-wave phases of quasi-one-dimensional conductorsJun 25 1998Dec 16 1998We study the collective modes in the magnetic-field-induced spin-density-wave (FISDW) phases experimentally observed in organic conductors of the Bechgaard salts family. In phases that exhibit a sign reversal of the quantum Hall effect (Ribault anomaly), ... More

Vacuum effects in an asymptotically uniformly accelerated frame with a constant magnetic fieldOct 07 1999In the present article we solve the Dirac-Pauli and Klein Gordon equations in an asymptotically uniformly accelerated frame when a constant magnetic field is present. We compute, via the Bogoliubov coefficients, the density of scalar and spin 1/2 particles ... More

Flag manifolds and the Landweber-Novikov algebraJun 03 1998We investigate geometrical interpretations of various structure maps associated with the Landweber-Novikov algebra S^* and its integral dual S_*. In particular, we study the coproduct and antipode in S_*, together with the left and right actions of S^* ... More

Two-valued groups, Kummer varieties and integrable billiardsNov 11 2010A natural and important question of study two-valued groups associated with hyperelliptic Jacobians and their relationship with integrable systems is motivated by seminal examples of relationship between algebraic two-valued groups related to elliptic ... More

The Class of Random Graphs Arising from Exchangeable Random MeasuresDec 07 2015We introduce a class of random graphs that we argue meets many of the desiderata one would demand of a model to serve as the foundation for a statistical analysis of real-world networks. The class of random graphs is defined by a probabilistic symmetry: ... More

Functional Lagged Regression with Sparse Noisy ObservationsMay 17 2019A (lagged) time series regression model involves the regression of scalar response time series on a time series of regressors that consists of a sequence of random functions (curves), also known as a functional time series. In practice, the underlying ... More

Extensions and results from a method for evaluating fractional integralsNov 28 1994We present a method derived from Laplace transform theory that enables the evaluation of fractional integrals. This method is adapted and extended in a variety of ways to demonstrate its utility in deriving alternative representations for other classes ... More

Topological invariants for the fractional quantum Hall statesJan 16 2013We calculate a topological invariant, whose value would coincide with the Chern number in case of integer quantum Hall effect, for fractional quantum Hall states. In case of Abelian fractional quantum Hall states, this invariant is shown to be equal to ... More

Bulk-boundary correspondence of topological insulators from their Green's functionsApr 08 2011Aug 25 2011Topological insulators are noninteracting, gapped fermionic systems which have gapless boundary excitations. They are characterized by topological invariants, which can be written in many different ways, including in terms of Green's functions. Here we ... More

Katz Centrality of Markovian Temporal Networks: Analysis and OptimizationSep 19 2016Identifying important nodes in complex networks is a fundamental problem in network analysis. Although a plethora of measures has been proposed to identify important nodes in static (i.e., time-invariant) networks, there is a lack of tools in the context ... More

Stability of Spreading Processes with General Transmission and Recovery TimesJun 28 2016Although viral spreading processes taking place in networks are commonly analyzed using Markovian models in which both the transmission times and the recovery times follow exponential distributions, empirical studies show that, in most real scenarios, ... More

Protection of Complex Networks against SIR Spreading ProcessesMar 14 2016This paper introduces a theoretical framework for the analysis and control of the stochastic susceptible-infected-removed (SIR) spreading process over a network of heterogeneous agents. In our analysis, we analyze the exact networked Markov process describing ... More

Optimal Design of Networks of Positive Linear Systems under Stochastic UncertaintySep 29 2015In this paper, we study networks of positive linear systems subject to time-invariant and random uncertainties. We present linear matrix inequalities for checking the stability of the whole network around the origin with prescribed probability and decay ... More

Sign reversals of the quantum Hall effect and helicoidal magnetic-field-induced spin-density waves in quasi-one-dimensional organic conductorsDec 17 1997We study the effect of umklapp scattering on the magnetic-field-induced spin-density-wave phases, which are experimentally observed in the quasi-one-dimensional organic conductors of the Bechgaard salts family. Within the framework of the quantized nesting ... More

Statistical Aspects of Wasserstein DistancesJun 14 2018Apr 09 2019Wasserstein distances are metrics on probability distributions inspired by the problem of optimal mass transportation. Roughly speaking, they measure the minimal effort required to reconfigure the probability mass of one distribution in order to recover ... More

The foundations of $(2n,k)$-manifoldsMar 15 2018Apr 02 2019In the focus of our paper is a system of axioms that serves as a basis for introducing structural data for $(2n,k)$-manifolds $M^{2n}$, where $M^{2n}$ is a smooth, compact $2n$-dimensional manifold with a smooth effective action of the $k$-dimensional ... More

Finite sets of operations sufficient to construct any fullerene from $C_{20}$Nov 16 2016We study the well-known problem of combinatorial classification of fullerenes. By a (mathematical) fullerene we mean a convex simple three dimensional polytope with all facets pentagons and hexagons. We analyse approaches of construction of arbitrary ... More

Topology and geometry of the canonical action of $T^4$ on the complex Grassmannian $G_{4,2}$ and the complex projective space $CP^{5}$Oct 09 2014Jan 20 2016We consider the canonical action of the compact torus $T^4$ on the Grassmann manifold $G_{4,2}$ and prove that the orbit space $G_{4,2}/T^4$ is homeomorphic to the sphere $S^5$. We prove that the induced differentiable structure on $S^5$ is not the smooth ... More

Sampling and Estimation for (Sparse) Exchangeable GraphsNov 02 2016Sparse exchangeable graphs on $\mathbb{R}_+$, and the associated graphex framework for sparse graphs, generalize exchangeable graphs on $\mathbb{N}$, and the associated graphon framework for dense graphs. We develop the graphex framework as a tool for ... More

Empirical Bayes unfolding of elementary particle spectra at the Large Hadron ColliderJan 31 2014We consider the so-called unfolding problem in experimental high energy physics, where the goal is to estimate the true spectrum of elementary particles given observations distorted by measurement error due to the limited resolution of a particle detector. ... More

Dispersion optimized quadratures for isogeometric analysisFeb 15 2017Jul 17 2018We develop and analyze quadrature blending schemes that minimize the dispersion error of isogeometric analysis up to polynomial order seven with maximum continuity in the span ($C^{p-1}$). The schemes yield two extra orders of convergence (superconvergence) ... More