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Broadband topological slow light through higher momentum-space windingJan 16 2019Slow-light waveguides can strongly enhance light-matter interaction, but suffer from narrow bandwidth, increased backscattering, and Anderson localization. Edge states in photonic topological insulators resist backscattering and localization, but typically ... More

Bound states in the continuum through environmental designJan 22 2019We propose a new paradigm for realizing bound states in the continuum (BICs) by engineering the environment of a system to control the number of available radiation channels. Using this method, we demonstrate that a photonic crystal slab embedded in a ... More

Effective Dielectric Tensor for Electromagnetic Wave Propagation in Random MediaSep 12 2007We derive exact strong-contrast expansions for the effective dielectric tensor $\epeff$ of electromagnetic waves propagating in a two-phase composite random medium with isotropic components explicitly in terms of certain integrals over the $n$-point correlation ... More

Fractal waveguide arrays induce maximal localizationSep 18 2018Sep 22 2018The ability to transmit light through an array of closely packed waveguides while minimizing interwaveguide coupling has important implications for fields such as discrete imaging and telecommunications. Proposals for achieving these effects have leveraged ... More

Optimized Interactions for Targeted Self-Assembly: Application to Honeycomb LatticeAug 20 2005We devise an inverse statistical-mechanical methodology to find optimized interaction potentials that lead spontaneously to a target many-particle configuration. Target structures can possess varying degrees of disorder, thus extending the traditional ... More

Tachyonic Dispersion in Coherent NetworksAug 10 2015We propose a technique to realize a tachyonic band structure in a coherent network, such as an array of coupled ring resonators. This is achieved by adding "PT symmetric" spatially-balanced gain and loss to each node of the network. In a square-lattice ... More

Synthetic Diamond and Wurtzite Structures Self-Assemble with Isotropic Pair InteractionsSep 24 2007Using inverse statistical-mechanical optimization techniques, we have discovered isotropic pair interaction potentials with strongly repulsive cores that cause the tetrahedrally coordinated diamond and wurtzite lattices to stabilize, as evidenced by lattice ... More

Disorder-induced Floquet Topological InsulatorsMar 03 2014Feb 10 2015We investigate the possibility of realizing a disorder-induced topological Floquet spectrum in two-dimensional periodically-driven systems. Such a state would be a dynamical realization of the topological Anderson insulator. We establish that a disorder-induced ... More

Topological crystalline protection in a photonic systemDec 09 2015Topological crystalline insulators are a class of materials with a bulk energy gap and edge or surface modes, which are protected by crystalline symmetry, at their boundaries. They have been realized in electronic systems: in particular, in SnTe. In this ... More

PT-symmetry in honeycomb photonic latticesMar 17 2011Apr 20 2011We apply gain/loss to honeycomb photonic lattices and show that the dispersion relation is identical to tachyons - particles with imaginary mass that travel faster than the speed of light. This is accompanied by PT-symmetry breaking in this structure. ... More

Designed Interaction Potentials via Inverse Methods for Self-AssemblyMar 15 2006We formulate statistical-mechanical inverse methods in order to determine optimized interparticle interactions that spontaneously produce target many-particle configurations. Motivated by advances that give experimentalists greater and greater control ... More

Negative thermal expansion in single-component systems with isotropic interactionsJul 22 2008We have devised an isotropic interaction potential that gives rise to negative thermal expansion (NTE) behavior in equilibrium many-particle systems in both two and three dimensions over a wide temperature and pressure range (including zero pressure). ... More

Edge states protected by chiral symmetry in disordered photonic grapheneApr 25 2013We experimentally investigate the impact of uncorrelated composite and structural disorder in photonic graphene. We find that in case of structural disorder not only chiral symmetry, but also the vanishing of the density of states at zero energy is preserved. ... More

Negative Poisson's ratio materials via isotropic interactionsJul 22 2008We show that under tension, a classical many-body system with only isotropic pair interactions in a crystalline state can, counterintutively, have a negative Poisson's ratio, or auxetic behavior. We derive the conditions under which the triangular lattice ... More

Self-assembly of the simple cubic lattice with an isotropic potentialJun 26 2006Conventional wisdom presumes that low-coordinated crystal ground states require directional interactions. Using our recently introduced optimization procedure to achieve self-assembly of targeted structures (Phys. Rev. Lett. 95, 228301 (2005), Phys. Rev. ... More

Strain-induced pseudomagnetic field and Landau levels in photonic structuresJul 16 2012Magnetic effects at optical frequencies are notoriously weak. This is evidenced by the fact that the magnetic permeability of nearly all materials is unity in the optical frequency range, and that magneto-optical devices (such as Faraday isolators) must ... More

Amorphous Photonic Lattices: Band Gaps, Effective Mass and Suppressed TransportDec 15 2010We present, theoretically and experimentally, amorphous photonic lattices exhibiting a band-gap yet completely lacking Bragg diffraction: 2D waveguides distributed randomly according to a liquid-like model responsible for the absence of Bragg peaks as ... More

Topological creation and destruction of edge states in photonic grapheneNov 24 2012We demonstrate theoretically and experimentally a topological transition of classical light in "photonic graphene": an array of waveguides arranged in the honeycomb geometry. As the system is uniaxially strained (compressed), the two unique Dirac points ... More

Photonic Floquet Topological InsulatorsDec 13 2012The topological insulator is a fundamentally new phase of matter, with the striking property that the conduction of electrons occurs only on its surface, not within the bulk, and that conduction is topologically protected. Topological protection, the ... More

Topological Protection of Photonic Path EntanglementMay 06 2016The recent advent of photonic topological insulators has opened the door to using the robustness of topologically protected transport (originated in the domain of condensed matter physics) in optical devices and in quantum simulation. Concurrently, quantum ... More

Experimental observation of optical Weyl pointsOct 04 2016Weyl fermions are hypothetical two-component massless relativistic particles in three-dimensional (3D) space, proposed by Hermann Weyl in 1929. Their band-crossing points, called 'Weyl points,' carry a topological charge and are therefore highly robust. ... More

Experimental realization of a Weyl exceptional ringAug 28 2018Sep 04 2018Weyl points are isolated degeneracies in reciprocal space that are monopoles of the Berry curvature. This topological charge makes them inherently robust to Hermitian perturbations of the system. However, non-Hermitian effects, usually inaccessible in ... More

Probing topological invariants in the bulk of a non-Hermitian optical systemAug 10 2014Topological insulators are insulating in the bulk but feature conducting states on their surfaces. Standard methods for probing their topological properties largely involve probing the surface, even though topological invariants are defined via the bulk ... More

Anomalous Topological Phases and Unpaired Dirac Cones in Photonic Floquet Topological InsulatorsJan 08 2016Jun 07 2016We propose a class of photonic Floquet topological insulators based on staggered helical lattices and an efficient numerical method for calculating their Floquet bandstructure. The lattices support anomalous Floquet topological insulator phases with vanishing ... More

Topological protection of photonic mid-gap cavity modesNov 08 2016Defect modes in two-dimensional periodic photonic structures have found use in a highly diverse set of optical devices. For example, photonic crystal cavities confine optical modes to subwavelength volumes and can be used for Purcell enhancement of nonlinearity, ... More

Zero modes for the magnetic Pauli operator in even-dimensional Euclidean spaceOct 22 2007We study the ground state of the Pauli Hamiltonian with a magnetic field in R^(2d). We consider the case where a scalar potential W is present and the magnetic field B is given by $B=2i\partial\bar\partial W$. The main result is that there are no zero ... More

Asymptotic Expansions for Moment Functionals of Perturbed Discrete Time Semi-Markov ProcessesMar 18 2016Apr 26 2016In this paper, we study mixed power-exponential moment functionals of nonlinearly perturbed semi-Markov processes in discrete time. Conditions under which the moment functionals of interest can be expanded in asymptotic power series with respect to the ... More

Asymptotics for Quasi-Stationary Distributions of Perturbed Discrete Time Semi-Markov ProcessesMar 18 2016Apr 26 2016In this paper, we study quasi-stationary distributions of nonlinearly perturbed semi-Markov processes in discrete time. This type of distributions is of interest for the analysis of stochastic systems which have finite lifetimes, but are expected to persist ... More

Sur les espaces mesures singuliers II - Etude spectraleDec 13 2004We are mainly interested here in Kazhdan's property T for measured equivalence relations. Among our main results are characterizations of strong ergodicity and Kazhdan's property in terms of the spectra of diffusion operators, associated to random walks ... More

On the Dirac and Pauli operators with several Aharonov-Bohm solenoidsApr 04 2006We study the self-adjoint Pauli operators that can be realized as the square of a self-adjoint Dirac operator and correspond to a magnetic field consisting of a finite number of Aharonov-Bohm solenoids and a regular part, and prove an Aharonov-Casher ... More

Sur les espaces mesures singuliers I - Etude metrique-mesureeDec 13 2004Recall Jones-Schmidt theorem that an ergodic measured equivalence relation is strongly ergodic if and only if it has no nontrivial amenable quotient. We give two new characterizations of strong ergodicity, in terms of metric-measured spaces. The first ... More

On low degree regular sequences in group cohomologyOct 11 2006We investigate small $p$-groups with cohomology rings of depth higher than predicted by Duflot's theorem. In these groups, a sampling would suggest several naive conjectures about the degrees of the additional regular sequence elements. We arrive at counterexamples ... More

SUSY model and dark matter determination in the compressed-spectrum region at the ILCNov 14 2016It is an appealing possibility that the observed dark matter density in the universe can be fully explained by SUSY. The current experimental knowledge indicates that this possibility strongly favors a co-annihilation scenario. In such scenarios, the ... More

Eigenvalue asymptotics of the even-dimensional exterior Landau-Neumann HamiltonianJun 27 2008We study the Schroedinger operator with a constant magnetic field in the exterior of a compact domain in $\mathbb{R}^{2d}$, $d\geq 1$. The spectrum of this operator consists of clusters of eigenvalues around the Landau levels. We give asymptotic formulas ... More

Almost Sharp Global Well-Posedness for a class of Dissipative and Dispersive Equations on R in Low Regularity Sobolev SpacesSep 12 2014Jan 08 2015In this paper we obtain global well-posedness in low order Sobolev spaces of higher order KdV type equations with dissipation. The result is optimal in the sense that the flow-map is not twice continuously differentiable in rougher spaces. The solution ... More

Computation of Poincare-Betti series for monomial ringsFeb 16 2005The multigraded Poincare-Betti series P_R^k(x_1,...,x_n; t) of a monomial ring k[x_1,...,x_n]/<M> on a finite number of monomial generators has the form (1+tx_1)(1+tx_2)...(1+tx_n)/b_(R,k)(x_1,...,x_n; t), where b_(R,k)(x_1,...,x_n;t) is a polynomial ... More

Quasi-Stationary Asymptotics for Perturbed Semi-Markov Processes in Discrete TimeMar 18 2016We consider a discrete time semi-Markov process where the characteristics defining the process depend on a small perturbation parameter. It is assumed that the state space consists of one finite communicating class of states and, in addition, one absorbing ... More

Observation of novel edge states in photonic grapheneOct 19 2012The intriguing properties of graphene, a two-dimensional material composed of a honeycomb lattice of carbon atoms, have attracted a great deal of interest in recent years. Specifically, the fact that electrons in graphene behave as massless relativistic ... More

Crouzeix's conjecture holds for tridiagonal $3\times 3$ matrices with elliptic numerical range centered at an eigenvalueJan 05 2017Dec 23 2017M. Crouzeix formulated the following conjecture in (Integral Equations Operator Theory 48, 2004, 461--477): For every square matrix $A$ and every polynomial $p$, $$ \|p(A)\| \le 2 \max_{z\in W(A)}|p(z)|, $$ where $W(A)$ is the numerical range of $A$. ... More

Topological PhotonicsFeb 12 2018Topological photonics is a rapidly-emerging field of research in which geometrical and topological ideas are exploited to design and control the behavior of light. Drawing inspiration from the discovery of the quantum Hall effects and topological insulators ... More

Word Sense Disambiguation using a Bidirectional LSTMJun 11 2016In this paper we present a model that leverages a bidirectional long short-term memory network to learn word sense disambiguation directly from data. The approach is end-to-end trainable and makes effective use of word order. Further, to improve the robustness ... More

On the use of Hahn's asymptotic formula and stabilized recurrence for a fast, simple, and stable Chebyshev--Jacobi transformFeb 08 2016We describe a fast, simple, and stable transform of Chebyshev expansion coefficients to Jacobi expansion coefficients and its inverse based on the numerical evaluation of Jacobi expansions at the Chebyshev--Lobatto points. This is achieved via a decomposition ... More

Physics of the Interplay Between the Top Quark and the Higgs BosonMar 05 2013Mar 27 2013We discuss some aspects of the interplay between the top quark and the Higgs boson at the LHC. First we describe what indirect information on the top Yukawa coupling can be extracted from measurements in the Higgs sector. We then show that the study of ... More

The Jiang-Su algebra revisitedJan 15 2008We give a number of new characterizations of the Jiang-Su algebra Z, both intrinsic and extrinsic, in terms of C*-algebraic, dynamical, topological and K-theoretic conditions. Along the way we study divisibility properties of C*-algebras, we give a precise ... More

A free product formula for the sofic dimensionAug 03 2013It is proved that if $G=G_1*_{G_3}G_2$ is free product of probability measure preserving $s$-regular ergodic discrete groupoids amalgamated over an amenable subgroupoid $G_3$, then the sofic dimension $s(G)$ satisfies the equality \[ s(G)=\h(G_1^0)s(G_1)+\h(G_2^0)s(G_2)-\h(G_3^0)s(G_3) ... More

Random groups and nonarchimedean latticesAug 10 2013Sep 24 2014We consider models of random groups in which the typical group is of intermediate rank (in particular, it is not hyperbolic). These models are parallel to M. Gromov's well-known constructions and include for example a "density model" for groups of intermediate ... More

Mixed state non-Abelian holonomy for subsystemsApr 29 2004Feb 01 2005Non-Abelian holonomy in dynamical systems may arise in adiabatic transport of energetically degenerate sets of states. We examine such a holonomy structure for mixtures of energetically degenerate quantal states. We demonstrate that this structure has ... More

On M-ideals and o-O type spacesDec 17 2014Sep 15 2015We consider pairs of Banach spaces (M_0, M) such that M_0 is defined in terms of a little-o condition, and M is defined by the corresponding big-O condition. The construction is general and pairs include function spaces of vanishing and bounded mean oscillation, ... More

Approximability of the Vertex Cover Problem in Power Law GraphsApr 04 2012Apr 05 2012In this paper we construct an approximation algorithm for the Minimum Vertex Cover Problem (Min-VC) with an expected approximation ratio of 2-f(beta) for random Power Law Graphs (PLG) in the (alpha,beta)-model of Aiello et. al., where f(beta) is a strictly ... More

Linear wave systems on $n$-D spatial domainsMay 08 2014Nov 26 2014In this paper we study the linear wave equation on an $n$-dimensional spatial domain. We show that there is a boundary triplet associated to the undamped wave equation. This enables us to characterise all boundary conditions for which the undamped wave ... More

Purely infinite C*-algebras: ideal-preserving zero homotopiesDec 15 2003We show that if A is a separable, nuclear, O_infty-absorbing (or strongly purely infinite) C*-algebra, which is homotopic to zero in an ideal-system preserving way, then A is the inductive limit of C*-algebras of the form M_k(C_0(G,v)), where G is a finite ... More

Strong Haagerup inequality with operator coefficientsMar 02 2009Jun 10 2009We prove a Strong Haagerup inequality with operator coefficients. If for an integer d, H_d denotes the subspace of the von Neumann algebra of a free group F_I spanned by the words of length d in the generators (but not their inverses), then we provide ... More

Debris of asteroid disruptions close to the SunFeb 05 2019The under-abundance of asteroids on orbits with small perihelion distances suggests that thermally-driven disruption may be an important process in the removal of rocky bodies in the Solar System. Here we report our study of how the debris streams arise ... More

La propriete de decroissance rapide pour le groupe de WiseNov 11 2012We show that the group of presentation $< a,b,c,s,t\mid c=ab=ba,\, c^2=sas^{-1}=tbt^{-1}>$ (introduced by D. Wise) has the property of rapid decay.

Universal properties of group actions on locally compact spacesDec 20 2013Dec 06 2014We study universal properties of locally compact G-spaces for countable infinite groups G. In particular we consider open invariant subsets of the \beta-compactification of G (which is a G-space in a natural way), and their minimal closed invariant subspaces. ... More

Interleaved equivalence of categories of persistence modulesOct 30 2012We demonstrate that an equivalence of categories using $\varepsilon$-interleavings as a fundamental component exists between the model of persistence modules as graded modules over a polynomial ring and the model of persistence modules as modules over ... More

Axiomatizability of the stable rank of C*-algebrasNov 25 2016We show that the class of C*-algebras with stable rank greater than a given positive integer is axiomatizable in logic of metric structures. As a consequence we show that the stable rank is continuous with respect to forming ultrapowers of C*-algebras, ... More

Solutions to the generalized Towers of Hanoi problemApr 19 2012Apr 21 2012The purpose of this paper is to prove the Frame-Stewart algorithm for the generalized Towers of Hanoi problem as well as finding the number of moves required to solve the problem and studying the multitude of optimal solutions. The main idea is to study ... More

Complete isometries between subspaces of noncommutative Lp-spacesJul 03 2007Dec 04 2007We prove some noncommutative analogues of a theorem by Plotkin and Rudin about isometries between subspaces of Lp-spaces. Let 0<p<\infty, p not an even integer. The main result of this paper states that in the category of unital subspaces of noncommutative ... More

Operator space valued Hankel matricesSep 28 2009If $E$ is an operator space, the non-commutative vector valued $L^p$ spaces $S^p[E]$ have been defined by Pisier for any $1 \leq p \leq \infty$. In this paper a necessary and sufficient condition for a Hankel matrix of the form $(a_{i+j})_{0 \le i,j}$ ... More

$Hb\bar{b}$ production in Composite Higgs ModelsMay 08 2013New vector-like quarks with electric charge 2/3 and -1/3 can be singly produced at hadron colliders through the exchange of a color octet vector resonance in models of strong electroweak symmetry breaking. We show that electroweak symmetry breaking effects ... More

Composite Dark SectorsApr 01 2015Jun 01 2015We introduce a new paradigm in Composite Dark Sectors, where the full Standard Model (including the Higgs boson) is extended with a strongly-interacting composite sector with global symmetry group $\mathcal{G}$ spontaneously broken to $\mathcal{H}\subset ... More

Symmetric Private Information Retrieval For MDS Coded Distributed StorageOct 14 2016A user wants to retrieve a file from a database without revealing the identity of the file retrieved at the database, which is known as the problem of private information retrieval (PIR). If it is further required that the user obtains no information ... More

Surgery on discrete groupsNov 25 2016We study constructions of groups, in particular of groups of intermediate rank, which are accessible to surgery techniques.

Aut(F2) puzzlesOct 28 2014This paper studies Aut(F2) and groups closely related to it from a geometric perspective.

Removing chambers in Bruhat-Tits buildingsMar 24 2010Nov 11 2012We introduce and study a family of countable groups constructed from Euclidean buildings by "removing" suitably chosen subsets of chambers.

Le coût est un invariant isopérimétriqueMar 05 2009Mar 06 2009For a type II_1 ergodic measured equivalence relation R on a probability space without atom, we prove that h(R)=2C(R)-2, where C(R) is the cost, and h(R) the isoperimetric constant. This follows recent result by Lyons and the authors.

Exclusion statistics for quantum Hall states in Tao-Thouless limitNov 08 2010Jan 26 2011We consider spin-polarized abelian quantum Hall states in the Tao-Thouless limit, {\it ie} on a thin torus. For any filling factor $\nu=p/q$ a well-defined sector of low-energy states is identified and the exclusion statistics of the excitations is determined. ... More

Enumerating the Saneblidze-Umble diagonal termsJul 30 2007The author presents a computer implementation, calculating the terms of the Saneblidze-Umble diagonals on the permutahedron and the associahedron. The code is analyzed for correctness and presented in the paper, the source code of which simultaneously ... More

Amoebas and coamoebas of linear spacesMay 12 2012Sep 13 2016We give a complete description of amoebas and coamoebas of $k$-dimensional very affine linear spaces in $(\mathbb{C}^*)^{n}$. This include an upper bound of their dimension, and we show that if a $k$-dimensional very affine linear space in $(\mathbb{C}^*)^{n}$ ... More

Discriminant coamoebas through homologyJan 31 2012Aug 02 2012Understanding the complement of the coamoeba of a (reduced) A-discriminant is one approach to studying the monodromy of solutions to the corresponding system of A-hypergeometric differential equations. Nilsson and Passare described the structure of the ... More

Feedback theory extended for proving generation of contraction semigroupsMar 14 2014Nov 06 2015Recently, the following novel method for proving the existence of solutions for certain linear time-invariant PDEs was introduced: The operator associated to a given PDE is represented by a (larger) operator with an internal loop. If the larger operator ... More

Purely infinite C*-algebras arising from crossed productsJun 07 2010Oct 27 2010We study conditions that will ensure that a crossed product of a C*-algebra by a discrete exact group is purely infinite (simple or non-simple). We are particularly interested in the case of a discrete non-amenable exact group acting on a commutative ... More

The transmission problem on a three-dimensional wedgeMay 31 2018Sep 03 2018We consider the transmission problem for the Laplace equation on an infinite three-dimensional wedge, determining the complex parameters for which the problem is well-posed, and characterizing the infinite multiplicity nature of the spectrum. This is ... More

Virtual Particle Interpretation of Quantum Mechanics - a non-dualistic model of QM with a natural probability interpretationJun 03 2012Jun 07 2012An interpretation of non-relativistic quantum mechanics is presented in the spirit of Erwin Madelung's hydrodynamic formulation of QM and Louis de Broglie's and David Bohm's pilot wave models. The aims of the approach are as follows: 1) to have a clear ... More

The essential norm of a weighted composition operator on BMOADec 05 2013We provide an estimate for the essential norm of a weighted composition operator $W_{\psi,\varphi}\colon f\mapsto \psi(f\circ\varphi)$ acting on the space $BMOA$ in terms of the weight function $\psi$ and the $n$-th power $\varphi^n$ of the analytic self-map ... More

Universal entropy invariantsSep 24 2014We define entropy invariants for abstract algebraic structures using an asymptotic Boltzmann formula.

The 4-string Braid group $B_4$ has property RD and exponential mesoscopic rankSep 03 2008Feb 03 2009We prove that the braid group $B_4$ on 4 strings, as well as its central quotient $B_4/< z>$, have the property RD of Haagerup-Jolissaint. It follows that the automorphism group $\Aut(F_2)$ of the free group $F_2$ on 2 generators has property RD. We also ... More

Observables of QCD DiffractionDec 03 2016A new combinatorial vector space measurement model is introduced for soft QCD diffraction. The model independent mathematical construction resolves experimental complications; the theoretical framework of the approach includes the Good-Walker view of ... More

Conquering the pre-computation in two-dimensional harmonic polynomial transformsNov 21 2017We describe a skeletonization of the spherical harmonic connection problem that reduces the storage and pre-computation to superoptimal complexities at the cost of increasing the execution time by the modest multiplicative factor of $\mathcal{O}(\log ... More

AF-embeddings into C*-algebras of real rank zeroOct 21 2003It is proved that every separable $C^*$-algebra of real rank zero contains an AF-sub-$C^*$-algebra such that the inclusion mapping induces an isomorphism of the ideal lattices of the two $C^*$-algebras and such that every projection in a matrix algebra ... More

Asymptotic convergence of spectral inverse iterations for stochastic eigenvalue problemsJun 12 2017We consider and analyze applying a spectral inverse iteration algorithm and its subspace iteration variant for computing eigenpairs of an elliptic operator with random coefficients. With these iterative algorithms the solution is sought from a finite ... More

Multiparametric shell eigenvalue problemsMar 10 2018Mar 16 2018The eigenproblem for thin shells of revolution under uncertainty in material parameters is discussed. Here the focus is on the smallest eigenpairs. Shells of revolution have natural eigenclusters due to symmetries, moreover, the eigenpairs depend on a ... More

A non-existence result for the Ginzburg-Landau equationsJul 11 2009Sep 30 2009We consider the stationary Ginzburg-Landau equations in $\R^d$, $d=2,3$. We exhibit a class of applied magnetic fields (including constant fields) such that the Ginzburg-Landau equations do not admit finite energy solutions.

An exotic group with the Haagerup propertyMay 05 2012Nov 11 2012We prove the Haagerup property for an infinite discrete group constructed using surgery on a Euclidean Tits building of type $\tilde A_2$.

Weak compactness of operators acting on o-O type spacesMay 02 2014Dec 18 2014We consider operators T : M_0 -> Z and T : M -> Z, where Z is a Banach space and (M_0, M) is a pair of Banach spaces belonging to a general construction in which M is defined by a "big-O" condition and M_0 is given by the corresponding "little-o" condition. ... More

Duality and Distance Formulas in Spaces Defined by Means of OscillationOct 31 2011Dec 12 2011For the classical space of functions with bounded mean oscillation, it is well known that VMO** = BMO and there are many characterizations of the distance from a function f in BMO to VMO. When considering the Bloch space, results in the same vein are ... More

Efficient Parallel Computation of Nearest Neighbor Interchange DistancesMay 15 2012The nni-distance is a well-known distance measure for phylogenetic trees. We construct an efficient parallel approximation algorithm for the nni-distance in the CRCW-PRAM model running in O(log n) time on O(n) processors. Given two phylogenetic trees ... More

A partial $A_\infty$-structure on the cohomology of $C_n\times C_m$Jul 11 2007May 13 2010Suppose k is a field of characteristic 2, and $n,m\geq 4$ powers of 2. Then the $A_\infty$-structure of the group cohomology algebras $H^*(C_n,k)$ and $(H^*(C_m,k)$ are well known. We give results characterizing an $A_\infty$-structure on $H^*(C_n\times ... More

Spectral properties of higher order anharmonic oscillatorsDec 04 2009We discuss spectral properties of the self-adjoint operator \[ -d^2/dt^2 + (t^{k+1}/(k+1)-\alpha)^2 \] in $L^2(\mathbb{R})$ for odd integers $k$. We prove that the minimum over $\alpha$ of the ground state energy of this operator is attained at a unique ... 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

Perturbation of Hausdorff moment sequences, and an application to the theory of C*-algebras of real rank zeroFeb 11 2005We investigate the class of unital C*-algebras that admit a unital embedding into every unital C*-algebra of real rank zero, that has no finite-dimensional quotients. We refer to a C*-algebra in this class as an initial object. We show that there are ... More

On the use of conformal maps for the acceleration of convergence of the trapezoidal rule and Sinc numerical methodsJun 12 2014We investigate the use of conformal maps for the acceleration of convergence of the trapezoidal rule and Sinc numerical methods. The conformal map is a polynomial adjustment to the $\sinh$ map, and allows the treatment of a finite number of singularities ... More

A fast and well-conditioned spectral method for singular integral equationsJul 02 2015We develop a spectral method for solving univariate singular integral equations over unions of intervals by utilizing Chebyshev and ultraspherical polynomials to reformulate the equations as almost-banded infinite-dimensional systems. This is accomplished ... More

Spectral bounds for the Neumann-Poincaré operator on planar domains with cornersSep 18 2012The boundary double layer potential, or the Neumann-Poincare operator, is studied on the Sobolev space of order 1/2 along the boundary, coinciding with the space of charges giving rise to double layer potentials with finite energy in the whole space. ... More

On Helson matrices: moment problems, non-negativity, boundedness, and finite rankNov 11 2016We study Helson matrices (also known as multiplicative Hankel matrices), i.e. infinite matrices of the form $M(\alpha) = \{\alpha(nm)\}_{n,m=1}^\infty$, where $\alpha$ is a sequence of complex numbers. Helson matrices are considered as linear operators ... More

The essential spectrum of the Neumann--Poincare operator on a domain with cornersJan 13 2016Feb 12 2016Exploiting the homogeneous structure of a wedge in the complex plane, we compute the spectrum of the anti-linear Ahlfors-Beurling transform acting on the associated Bergman space. Consequently, the similarity equivalence between the Ahlfors-Beurling transform ... More

On the semi-classical analysis of the groundstate energy of the Dirichlet Pauli operator in non-simply connected domainsFeb 08 2017Feb 13 2017We consider the Dirichlet Pauli operator in bounded connected domains in the plane, with a semi-classical parameter. We show, in particular, that the ground state energy of this Pauli operator will be exponentially small as the semi-classical parameter ... More

Curvature-Exploiting Acceleration of Elastic Net ComputationsJan 24 2019This paper introduces an efficient second-order method for solving the elastic net problem. Its key innovation is a computationally efficient technique for injecting curvature information in the optimization process which admits a strong theoretical performance ... More