Results for "Mikael Rechtsman"

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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
Bulk soliton dynamics in bosonic topological insulatorsApr 21 2019We theoretically explore the dynamics of spatial solitons in nonlinear/interacting bosonic topological insulators. We employ a time-reversal broken Lieb-lattice analog of a Chern insulator and find that in the presence of a saturable nonlinearity, solitons ... 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
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
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
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
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
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
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
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
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
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 Photonic Quasicrystals: Fractal Topological Spectrum and Protected TransportMay 25 2017We show that it is possible to have a topological phase in two-dimensional quasicrystals without any magnetic field applied, but instead introducing an artificial gauge field via dynamic modulation. This topological quasicrystal exhibits scatter-free ... More
Photonic Realization of a Transition Between Topological Phases Residing in the Weak and Strong Floquet Driving RegimesNov 07 2017A photonic Floquet topological insulator has previously been experimentally realized in an array of evanescently-coupled helical waveguides. In the topological regime probed by that experiment, the chirality of the single topological edge mode was the ... 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
Observation of Photonic Topological Valley-Hall Edge StatesMay 31 2017We experimentally demonstrate topological edge states arising from the valley-Hall effect in twodimensional honeycomb photonic lattices with broken inversion symmetry. We break inversion symmetry by detuning the refractive indices of the two honeycomb ... 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
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
Photonic topological pumping through the edges of a dynamical four-dimensional quantum Hall systemMay 23 2017When a two-dimensional electron gas is exposed to a perpendicular magnetic field and an in-plane electric field, its conductance becomes quantized in the transverse in-plane direction: this is known as the quantum Hall (QH) effect. This effect is a result ... 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
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
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
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
Success and failure of the plasma analogy for Laughlin states on a torusMar 27 2015Nov 29 2016We investigate the nature of the plasma analogy for the Laughlin wave function on a torus describing the quantum Hall plateau at $\nu=\frac{1}{q}$. We first establish, as expected, that the plasma is screening if there are no short nontrivial paths around ... More
Simplified SUSY at the ILCAug 07 2013At the ILC, one has the possibility to search for SUSY in an model-independent way: The corner-stone of SUSY is that sparticles couple as particles. This is independent of the mechanism responsible for SUSY breaking. Any model will have one Lightest SUSY ... More
$h \rightarrow γγ$ excess and Dark Matter from Composite Higgs ModelsOct 23 2012Dec 25 2012Composite Higgs Models are very appealing candidates for a natural realization of electroweak symmetry breaking. Non minimal models could explain the recent Higgs data from ATLAS, CMS and Tevatron experiments, including the excess in the amount of diphoton ... More
Priors for the Bayesian star paradoxNov 04 2009Nov 19 2010We show that the Bayesian star paradox, first proved mathematically by Steel and Matsen for a specific class of prior distributions, occurs in a wider context including less regular, possibly discontinuous, prior distributions.
Reconstructing sleptons in cascade-decays at the linear colliderAug 24 2005A method to reconstruct sleptons in cascade-decays at the FLC is presented. It is shown that experimental mass-resolutions as low as 8.7 MeV/c^2 are attainable.
Thin elastic shells with variable thickness for lithospheric flexure of one-plate planetsApr 12 2007Sep 14 2007Planetary topography can either be modeled as a load supported by the lithosphere, or as a dynamical effect due to lithospheric flexure caused by mantle convection. In both cases the response of the lithosphere to external forces can be calculated with ... More
Static cylindrically symmetric spacetimesApr 12 2006Mar 04 2007We prove existence of static solutions to the cylindrically symmetric Einstein-Vlasov system, and we show that the matter cylinder has finite extension. The same results are also proved for a quite general class of equations of state for perfect fluids ... More
Propagation et oscillations en theorie des champsOct 06 2000After a review of the problems associated with the conventional treatment of particle oscillations, an oscillation formula is derived within the framework of quantum field theory. The oscillating particle is represented by its propagator and the initial ... More
Ohmic Decay of Magnetic Fields due to non-spherical accretion in the Crusts of Neutron StarsApr 04 1998We consider magnetic field evolution of neutron stars during polar-cap accretion. The size of the polar cap increases as the field decays, and is set by the last open field line before the accretion disk. Below the polar cap we find the temperature to ... More
Direct Bounds on Heavy Top-Like Quarks With Standard and Exotic DecaysMay 08 2017Aug 14 2017Heavy vector-like quarks with electric charge $Q=2/3$ (also called \textit{heavy tops}) appear naturally in many extensions of the Standard Model. Although these typically predict the existence of further particles below the TeV scale, direct searches ... More
Fixed-points in the cone of traces on a C*-algebraMar 29 2018Jan 02 2019Nicolas Monod introduced the class of groups with the fixed-point property for cones, characterized by always admitting a non-zero fixed point whenever acting (suitably) on proper weakly complete cones. He proved that his class of groups contains the ... More
Just-infinite C*-algebras and their invariantsMay 08 2017Dec 28 2017Just-infinite C*-algebras, i.e., infinite dimensional C*-algebras, whose proper quotients are finite dimensional, were investigated in [Grigorchuk-Musat-Rordam, 2016]. One particular example of a just-infinite residually finite dimensional AF-algebras ... More
The stable and the real rank of Z-absorbing C*-algebrasAug 02 2004Aug 30 2004Suppose that A is a C*-algebra for which A is isomorphic to A tensor Z, where Z is the Jiang-Su algebra: a unital, simple, stably finite, separable, nuclear, infinite dimensional C*-algebra with the same Elliott invariant as the complex numbers. We show ... More
Phylogenetic distances for neighbour dependent substitution processesDec 10 2008Jan 04 2010We consider models of nucleotidic substitution processes where the rate of substitution at a given site depends on the state of its neighbours. For a wide class of such nonreversible models, we show how to compute consistent, mathematically exact, estimators ... More
Massively parallel implementation in Python of a pseudo-spectral DNS code for turbulent flowsJul 01 2016Direct Numerical Simulations (DNS) of the Navier Stokes equations is a valuable research tool in fluid dynamics, but there are very few publicly available codes and, due to heavy number crunching, codes are usually written in low-level languages. In this ... More
The Bruhat order on conjugation-invariant sets of involutions in the symmetric groupFeb 12 2015Let $I_n$ be the set of involutions in the symmetric group $S_n$, and for $A \subseteq \{0,1,\ldots,n\}$, let \[ F_n^A=\{\sigma \in I_n \mid \text{$\sigma$ has $a$ fixed points for some $a \in A$}\}. \] We give a complete characterisation of the sets ... More
Free Energy of ABJM TheoryMar 24 2011The free energy of ABJM theory has previously been computed in the strong and weak coupling limits. In this note, we report on results for the computation of the first non-vanishing quantum correction to the free energy, from the field theory side. The ... More
ILC Beam-Parameters and New PhysicsJul 18 2010A brief overview of the linear collider design is given, with emphasis on the elements of particular importance for the performance. The modifications of the RDR design suggested in the SB2009 proposal are presented, once again with emphasis on those ... More
East-west faults due to planetary contractionJun 30 2010Contraction, expansion and despinning have been common in the past evolution of Solar System bodies. These processes deform the lithosphere until it breaks along faults. The type and orientation of faults are usually determined under the assumption of ... More
Enceladus's crust as a non-uniform thin shell: II tidal dissipationMar 06 2019Tidal heating is the prime suspect behind Enceladus's south polar heating anomaly and global subsurface ocean. No model of internal tidal dissipation, however, can explain at the same time the total heat budget and the focusing of the energy at the south ... More
A simple C*-algebra with a finite and an infinite projectionApr 29 2002Aug 28 2002An example is given of a simple, unital C*-algebra which contains an infinite and a non-zero finite projection. This C*-algebra is also an example of an infinite simple C*-algebra which is not purely infinite. A corner of this C*-algebra is a finite, ... 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
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
Algorithmics of DiffractionNov 05 2018Dec 31 2018We discuss novel ways to probe high energy diffraction, first inclusive diffraction and then central exclusive processes at the LHC. Our new Monte Carlo synthesis and analysis framework, Graniitti, includes differential screening, an expendable set of ... More
A spectral-Galerkin turbulent channel flow solver for large-scale simulationsJan 13 2017A fully (pseudo-)spectral solver for direct numerical simulations of large-scale turbulent channel flows is described. The solver utilizes the Chebyshev base functions suggested by J. Shen [SIAM J. Sci. Comput., 16, 1, 1995], that lead to stable and robust ... More
Tidal Love numbers of membrane worlds: Europa, Titan, and CoApr 17 2015May 29 2015Under tidal forcing, icy satellites with subsurface oceans deform as if the surface were a membrane stretched around a fluid layer. `Membrane worlds' is thus a fitting name for these bodies and membrane theory provides the perfect toolbox to predict tidal ... More
Spatial patterns of tidal heatingDec 19 2012In a body periodically strained by tides, heating produced by viscous friction is far from homogeneous. I show here that the distribution of the dissipated power within a spherically stratified body is a linear combination of three angular functions. ... More
On the cylindrically symmetric Einstein-Vlasov systemMar 23 2005For the cylindrically symmetric ''asymptotically flat'' Einstein equations in the case of electro-vacuum it is known that solutions exist globally and also that this class of spacetimes is causally geodesically complete. Hence strong cosmic censorship ... More
The effect of Hall drift on the evolution of magnetic fields in the crusts of neutron starsSep 20 1996We consider the effect of Hall-drift on the evolution of magnetic fields in neutorn star crusts using a finite difference code. Previously, most studies have focused on the situation where the ohmic term dominates the evolution. Here, we investigate the ... More
Well-posedness of time-varying linear systemsApr 28 2019In this paper, we give easily verifiable sufficient conditions for two classes of perturbed linear, passive PDE systems to be well-posed, and we provide an energy inequality for the perturbed systems as well. Our conditions are in terms of smoothness ... 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
A purely infinite AH-algebra and an application to AF-embeddabilityMay 28 2002Jan 02 2004We show that there exists a purely infinite AH-algebra. The AH-algebra arises as an inductive limit of C*-algebras of the form C_0([0,1),M_k) and it absorbs the Cuntz algebra O_\infty tensorially. Thus one can reach an O_\infty-absorbing C*-algebra as ... 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 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
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
Tides on Europa: the membrane paradigmOct 17 2014Jupiter's moon Europa has a thin icy crust which is decoupled from the mantle by a subsurface ocean. The crust thus responds to tidal forcing as a deformed membrane, cold at the top and near melting point at the bottom. In this paper I develop the membrane ... More
Applying Compression to a Game's Network ProtocolMay 28 2012This report presents the results of applying different compression algorithms to the network protocol of an online game. The algorithm implementations compared are zlib, liblzma and my own implementation based on LZ77 and a variation of adaptive Huffman ... More
Structure of the core of magnetic vortices in d-wave superconductors with a subdominant triplet pairing mechanismMar 18 2011Aug 06 2011The quasiparticle states found in the vortex core of a high-T$_{\rm{c}}$ cuprate superconductor may be probed by scanning tunneling spectroscopy. Results of such experiments have revealed typical spectra that are quite different from what is seen in conventional ... 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
On the modular covariance properties of composite fermions on the torusOct 24 2018In this work we show that the composite fermion construction for the torus geometry is modular covariant. We show that this is the case both before and after projection, and that modular covariance properties are preserved under both exact projection ... More
Shenfun -- automating the spectral Galerkin methodAug 10 2017With the shenfun Python module (github.com/spectralDNS/shenfun) an effort is made towards automating the implementation of the spectral Galerkin method for simple tensor product domains, consisting of (currently) one non-periodic and any number of periodic ... 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
How to compute $\sum 1/n^2$ by solving trianglesJan 01 2007A new simple geometric method is presented for finding the exact value of $\sum_{n=1}^\infty 1/n^2$.
Oscillations of neutrinos and mesons in quantum field theorySep 13 2001Oct 15 2002This report deals with the quantum field theory of particle oscillations in vacuum. We first review the various controversies regarding quantum-mechanical derivations of the oscillation formula, as well as the different field-theoretical approaches proposed ... More
Josephson currents through spin-active interfacesAug 04 2000The Josephson coupling of two isotropic s-wave superconductors through a small, magnetically active junction is studied. This is done as a function of junction transparency and of the degree of spin-mixing occurring in the barrier. In the tunneling limit, ... 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
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
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 2018Apr 02 2019Topological 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
Spontaneously broken time-reversal symmetry in high-temperature superconductorsNov 04 2014Conventional superconductors are strong diamagnets that through the Meissner effect expel magnetic fields. It would therefore be surprising if a superconducting ground state would support spontaneous magnetics fields. Such time-reversal symmetry broken ... More
Complex Edge-State Phase Transitions in 1D Topological Laser ArraysSep 02 2017We report the first observation of lasing in topological edge states in a 1D Su-Schrieffer-Heeger active array of resonators. We show that in the presence of chiral-time ($\mathcal{CT}$) symmetry, this non-Hermitian topological structure can experience ... 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
Percolation thresholds of two-dimensional continuum systems of rectangles [with erratum]Apr 05 2016The present work introduces an efficient Monte Carlo algorithm for continuum percolation composed of randomly-oriented rectangles. By conducting extensive simulations, we report high precision percolation thresholds for a variety of homogeneous systems ... More
Convergence analysis of approximate primal solutions in dual first-order methodsFeb 23 2015Dual first-order methods are powerful techniques for large-scale convex optimization. Although an extensive research effort has been devoted to studying their convergence properties, explicit convergence rates for the primal iterates have only been established ... More
Secret Key Agreement Using Correlated Sources over the Generalized Multiple Access ChannelApr 13 2012A secret key agreement setup between three users is considered in which each of the users 1 and 2 intends to share a secret key with user 3 and users 1 and 2 are eavesdroppers with respect to each other. The three users observe i.i.d. outputs of correlated ... More
Mapping properties for the Bargmann transform on modulation spacesFeb 16 2010Jun 01 2010We investigate mapping properties for the Bargmann transform and prove that this transform is isometric and bijective from modulation spaces to convenient Banach spaces of analytic functions.
Interleaved computation for persistent homologyMay 31 2011We describe an approach to bounded-memory computation of persistent homology and betti barcodes, in which a computational state is maintained with updates introducing new edges to the underlying neighbourhood graph and percolating the resulting changes ... More
Prediction of transcription factor binding to DNA using rule induction methodsMay 13 2005Jul 03 2005The transcription of DNA into mRNA is initiated and aided by a number of transcription factors (TFs), proteins with DNA-binding regions that attach themselves to binding sites in the DNA (transcription factor binding sites, TFBSs). As it has become apparent ... More
Effective inverse spectral problem for rational Lax matrices and applicationsMay 01 2007Aug 19 2007We reconstruct a rational Lax matrix of size R+1 from its spectral curve (the desingularization of the characteristic polynomial) and some additional data. Using a twisted Cauchy--like kernel (a bi-differential of bi-weight (1-nu,nu)) we provide a residue-formula ... More
Theme Enrichment Analysis: A Statistical Test for Identifying Significantly Enriched Themes in a List of Stories with an Application to the Star Trek Television FranchiseJul 19 2017Aug 14 2018In this paper, we describe how the hypergeometric test can be used to determine whether a given theme of interest occurs in a storyset at a frequency more than would be expected by chance. By a storyset we mean simply a list of stories defined according ... More
Intermediate rank and property RDOct 08 2007Nov 11 2012We introduce concepts of intermediate rank for countable groups that "interpolate" between consecutive values of the classical (integer-valued) rank. Various classes of groups are proved to have intermediate rank behaviors. We are especially interested ... More
Purely infinite C*-algebras of real rank zeroJun 15 2006Jul 04 2006We show that a separable purely infinite C*-algebra is of real rank zero if and only if its primitive ideal space has a basis consisting of compact-open sets and the natural map K_0(I) -> K_0(I/J) is surjective for all closed two-sided ideals J contained ... 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
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
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