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Vortex Collapse for the L2-Critical Nonlinear Schrödinger EquationOct 28 2010The focusing cubic nonlinear Schr\"odinger equation in two dimensions admits vortex solitons, standing wave solutions with spatial structure, Qm(r,theta) = e^{i m theta} Rm(r). In the case of spin m = 1, we prove there exists a class of data that collapse ... More

Analytical and Numerical Results on the Positivity of Steady State Solutions of a Thin Film EquationJan 17 2011Oct 28 2011We consider an equation for a thin-film of fluid on a rotating cylinder and present several new analytical and numerical results on steady state solutions. First, we provide an elementary proof that both weak and classical steady states must be strictly ... More

Relative Entropy Minimization over Hilbert Spaces via Robbins-MonroJun 30 2015Jun 27 2017One way of getting insight into non-Gaussian measures, posed on infinite dimensional Hilbert spaces, is to first obtain best fit Gaussian approximations, which are more amenable to numerical approximation. These Gaussians can then be used to accelerate ... More

Relative Entropy Minimization over Hilbert Spaces via Robbins-MonroJun 30 2015Feb 26 2019One way of getting insight into non-Gaussian measures, posed on infinite dimensional Hilbert spaces, is to first obtain best fit Gaussian approximations, which are more amenable to numerical approximation. These Gaussians can then be used to accelerate ... More

Embedded Eigenvalues and the Nonlinear Schrodinger EquationJan 13 2011Jan 31 2011A common challenge to proving asymptotic stability of solitary waves is understanding the spectrum of the operator associated with the linearized flow. The existence of eigenvalues can inhibit the dispersive estimates key to proving stability. Following ... More

Solitary Wave Benchmarks in Magma DynamicsSep 01 2010We present a model problem for benchmarking codes that investigate magma migration in the Earth's interior. This system retains the essential features of more sophisticated models, yet has the advantage of possessing solitary wave solutions. The existence ... More

Relative Entropy Minimization over Hilbert Spaces via Robbins-MonroJun 30 2015May 22 2019One way of getting insight into non-Gaussian measures, posed on infinite dimensional Hilbert spaces, is to first obtain best fit Gaussian approximations, which are more amenable to numerical approximation. These Gaussians can then be used to accelerate ... More

Numerical Analysis of Parallel Replica DynamicsApr 03 2012Aug 31 2012Parallel replica dynamics is a method for accelerating the computation of processes characterized by a sequence of infrequent events. In this work, the processes are governed by the overdamped Langevin equation. Such processes spend much of their time ... More

Sampling from Rough Energy LandscapesMar 24 2019May 05 2019Rough energy landscapes appear in a variety of applications including disordered media and soft matter. In this work, we examine challenges to sampling from Boltzmann distributions associated with rough energy landscapes. Here, the roughness will correspond ... More

Relative Entropy Minimization over Hilbert Spaces via Robbins-MonroJun 30 2015Jul 07 2016One way of getting insight into non-Gaussian measures, posed on infinite dimensional Hilbert spaces, is to first obtain best fit Gaussian approximations, which are more amenable to numerical approximation. These Gaussians can then be used to accelerate ... More

Sampling from Rough Energy LandscapesMar 24 2019Rough energy landscapes appear in a variety of applications including disordered media and soft matter. In this work, we examine challenges to sampling from Boltzmann distributions associated with rough energy landscapes. Here, the roughness will correspond ... More

Spectral Analysis for Matrix Hamiltonian OperatorsMar 12 2010Apr 02 2010In this work, we study the spectral properties of matrix Hamiltonians generated by linearizing the nonlinear Schr\"odinger equation about soliton solutions. By a numerically assisted proof, we show that there are no embedded eigenvalues for the three ... More

Asymptotic Stability of Ascending Solitary Magma WavesJan 03 2008Jan 04 2008Coherent structures, such as solitary waves, appear in many physical problems, including fluid mechanics, optics, quantum physics, and plasma physics. A less studied setting is found in geophysics, where highly viscous fluids couple to evolving material ... More

Local Existence Theory for Derivative Nonlinear Schrödinger Equations with Non-Integer Power NonlinearitiesJan 28 2014We study a derivative nonlinear Schr\"{o}dinger equation, allowing non-integer powers in the nonlinearity, $|u|^{2\sigma} u_x$. Making careful use of the energy method, we are able to establish short-time existence of solutions with initial data in the ... More

Coherent Structures and Carrier Shocks in the Nonlinear Periodic Maxwell EquationsSep 20 2010Nov 18 2010We consider the one-dimensional propagation of electromagnetic waves in a weakly nonlinear and low-contrast spatially inhomogeneous medium with no energy dissipation. We focus on the case of a periodic medium, in which dispersion enters only through the ... More

On a Hamiltonian PDE arising in Magma DynamicsJan 03 2008Jan 17 2008In this article we discuss a new Hamiltonian PDE arising from a class of equations appearing in the study of magma, partially molten rock, in the Earth's interior. Under physically justifiable simplifications, a scalar, nonlinear, degenerate, dispersive ... More

Stability of Solitary Waves for a Generalized Derivative Nonlinear Schrödinger EquationJun 15 2012We consider a derivative nonlinear Schr\"odinger equation with a general nonlinearity. This equation has a two parameter family of solitary wave solutions. We prove orbital stability/instability results that depend on the strength of the nonlinearity ... More

Local structure of singular profiles for a Derivative Nonlinear Schrödinger EquationFeb 07 2016The Derivative Nonlinear Schr\"odinger equation is an $L^2$-critical nonlinear dispersive equation model for Alfv\'en waves in space plasmas. Recent numerical studies on an $L^2$-supercritical extension of this equation provide evidence of finite time ... More

Conservative Integrators for a Toy Model of Weak TurbulenceJul 01 2016Weak turbulence is a phenomenon by which a system generically transfers energy from low to high wave numbers, while persisting for all finite time. It has been conjectured by Bourgain that the 2D defocusing nonlinear Schr\"odinger equation (NLS) on the ... More

A Multiscale Model of Partial Melts 1: Effective EquationsMar 01 2009Sep 04 2009In this paper a model for partial melts is constructed using two-scale homogenization theory. While this technique is well known to the mathematics and materials communities, it is relatively novel to problems in the solid Earth. This approach begins ... More

Arrest of Langmuir wave collapse by quantum effectsOct 09 2009The arrest of Langmuir-wave collapse by quantum effects, first addressed by Haas and Shukla [Phys. Rev. E 79, 066402 (2009)] using a Rayleigh-Ritz trial-function method is revisited, using rigorous estimates and systematic asymptotic expansions. The absence ... More

Dynamics near a minimal-mass soliton for a Korteweg-de Vries equationNov 24 2012Jan 22 2013We study soliton solutions to a generalized Korteweg - de Vries (KdV) equation with a saturated nonlinearity, following the line of inquiry of the authors for the nonlinear Schr\"odinger equation (NLS). KdV with such a nonlinearity is known to possess ... More

Focusing Singularity in a Derivative Nonlinear Schrödinger EquationJan 06 2013We present a numerical study of a derivative nonlinear Schr\"odinger equation with a general power nonlinearity, $|\psi|^{2\sigma}\psi_x$. In the $L^2$-supercritical regime, $\sigma>1$, our simulations indicate that there is a finite time singularity. ... More

Scalar curvature and holomorphy potentialsApr 29 2008Jun 12 2011A holomorphy potential is a complex valued function whose complex gradient, with respect to some K\"ahler metric, is a holomorphic vector field. Given $k$ holomorphic vector fields on a compact complex manifold, form, for a given K\"ahler metric, a product ... More

On the joint behaviour of speed and entropy of random walks on groupsSep 01 2015For every $3/4\le \delta, \beta< 1$ satisfying $\delta\leq \beta < \frac{1+\delta}{2}$ we construct a finitely generated group $\Gamma$ and a (symmetric, finitely supported) random walk $X_n$ on $\Gamma$ so that its expected distance from its starting ... More

One-dimensional long-range diffusion-limited aggregation III -- The limit aggregateNov 01 2009Apr 06 2015In this paper we study the structure of the limit aggregate $A_\infty = \bigcup_{n\geq 0} A_n$ of the one-dimensional long range diffusion limited aggregation process defined in [AABK09]. We show (under some regularity conditions) that for walks with ... More

Broad Band Solitons in a Periodic and Nonlinear Maxwell SystemJun 18 2011We consider the one-dimensional Maxwell equations with low contrast periodic linear refractive index and weak Kerr nonlinearity. In this context, wave packet initial conditions with a single carrier frequency excite infinitely many resonances. On large ... More

A Multiscale Model of Partial Melts 2: Numerical ResultsMar 03 2009Sep 04 2009In a companion paper, equations for partially molten media were derived using two-scale homogenization theory. One advantage of homogenization is that material properties, such as permeability and viscosity, readily emerge. A caveat is that the dependence ... More

Degenerate dispersive equations arising in the study of magma dynamicsJul 18 2006An outstanding problem in Earth science is understanding the method of transport of magma in the Earth's mantle. Models for this process, transport in a viscously deformable porous media, give rise to scalar degenerate, dispersive, nonlinear wave equations. ... More

A Theoretical Examination of Diffusive Molecular DynamicsJun 08 2015Diffusive molecular dynamics is a novel model for materials with atomistic resolution that can reach diffusive time scales. The main ideas of diffusive molecular dynamics are to first minimize an approximate variational Gaussian free energy of the system ... More

Existence and Stability Properties of Radial Bound States for Schrödinger-Poisson with an External Coulomb Potential in Three Space DimensionsDec 11 2015Sep 12 2016We consider radial solutions to the Schr\"odinger-Poisson system in three dimensions with an external smooth potential with Coulomb-like decay. Such a system can be viewed as a model for the interaction of dark matter with a bright matter background in ... More

The parallel replica method for simulating long trajectories of Markov chainsJan 18 2014Jun 05 2014The parallel replica dynamics, originally developed by A.F. Voter, efficiently simulates very long trajectories of metastable Langevin dynamics. We present an analogous algorithm for discrete time Markov processes. Such Markov processes naturally arise, ... More

Conservative Integrators for a Toy Model of Weak TurbulenceJul 01 2016Jul 18 2017Weak turbulence is a phenomenon by which a system generically transfers energy from low to high wave numbers, while persisting for all finite time. It has been conjectured by Bourgain that the 2D defocusing nonlinear Schr\"odinger equation (NLS) on the ... More

A Generalized Parallel Replica DynamicsApr 24 2014Oct 08 2014Metastability is a common obstacle to performing long molecular dynamics simulations. Many numerical methods have been proposed to overcome it. One method is parallel replica dynamics, which relies on the rapid convergence of the underlying stochastic ... More

Three observations regarding Schatten p classesNov 17 2014Jan 27 2015The paper contains three results, the common feature of which is that they deal with the Schatten $p$ class. The first is a presentation of a new complemented subspace of $C_p$ in the reflexive range (and $p\not= 2$). This construction answers a question ... More

Conformally-Kähler Ricci solitons and base metrics for warped product Ricci solitonsApr 30 2015May 13 2015We investigate K\"ahler metrics conformal to gradient Ricci solitons, and base metrics of warped product gradient Ricci solitons. The latter we name quasi-solitons. A main assumption that is employed is functional dependence of the soliton potential, ... More

Correlation Estimation System Minimization Compared to Least Squares Minimization in Simple Linear RegressionFeb 07 2018A general method of minimization using correlation coefficients and order statistics is evaluated relative to least squares procedures in the estimation of parameters for normal data in simple linear regression.

Euclidean sections of convex bodies, series of lecturesOct 28 2011Jul 03 2012This is a somewhat expanded form of a four hours course given, with small variations, first at the educational workshop Probabilistic methods in Geometry, Bedlewo, Poland, July 6-12, 2008 and a few weeks later at the Summer school on Fourier analytic ... More

Dimension Reduction in $L_p$, $0<p<2$Oct 10 2011Complementing a recent observation of Newman and Rabinovich for $p=1$ we observe here that for all $0<p<2$ any $k$ points in $L_p$ embeds with distortion $(1+\e)$ into $\ell_p^n$ where $n$ is linear in $k$ (and polynomial in $\e^{-1}$).

Petviashvilli's Method for the Dirichlet ProblemNov 15 2014Nov 26 2014We examine the Petviashvilli method for solving the equation $ \phi - \Delta \phi = |\phi|^{p-1} \phi$ on a bounded domain $\Omega \subset \mathbb{R}^d$ with Dirichlet boundary conditions. We prove a local convergence result, using spectral analysis, ... More

Kullback-Leibler Approximation for Probability Measures on Infinite Dimensional SpacesOct 29 2013Mar 28 2014In a variety of applications it is important to extract information from a probability measure $\mu$ on an infinite dimensional space. Examples include the Bayesian approach to inverse problems and possibly conditioned) continuous time Markov processes. ... More

Algorithms for Kullback-Leibler Approximation of Probability Measures in Infinite DimensionsAug 08 2014In this paper we study algorithms to find a Gaussian approximation to a target measure defined on a Hilbert space of functions; the target measure itself is defined via its density with respect to a reference Gaussian measure. We employ the Kullback-Leibler ... More

Asymptotic Stability of high-dimensional Zakharov-Kuznetsov solitonsJun 12 2014Sep 08 2015We prove that solitons (or solitary waves) of the Zakharov-Kuznetsov (ZK) equation, a physically relevant high dimensional generalization of the Korteweg-de Vries (KdV) equation appearing in Plasma Physics, and having mixed KdV and nonlinear Schr\"odinger ... More

Spin-Diffusions and Diffusive Molecular DynamicsFeb 05 2017Sep 23 2017Metastable condensed matter typically fluctuates about local energy minima at the femtosecond time scale before transitioning between local minima after nanoseconds or microseconds. This vast scale separation limits the applicability of classical molecular ... More

Behavior of a Model Dynamical System with Applications to Weak TurbulenceSep 04 2012Sep 13 2012We experimentally explore solutions to a model Hamiltonian dynamical system derived in Colliander et al., 2012, to study frequency cascades in the cubic defocusing nonlinear Schr\"odinger equation on the torus. Our results include a statistical analysis ... More

Instability of Bubbles Near the Hadron--Quark-Gluon-Plasma Phase TransitionOct 09 1992May 28 2005The small surface tension of the interface between hadronic and quark-gluon-plasma domains, along with a negative curvature tension, implies that the uniform plasma is unstable against spontaneous formation of hadronic bubbles. We furthermore show that ... More

A special set of exceptional times for dynamical random walk on $\Z^2$Sep 10 2006Sep 17 2006Benjamini,Haggstrom, Peres and Steif introduced the model of dynamical random walk on Z^d. This is a continuum of random walks indexed by a parameter t. They proved that for d=3,4 there almost surely exist t such that the random walk at time t visits ... More

Speed exponents of random walks on groupsMar 28 2012Oct 06 2015For every 3/4 <= beta < 1 we construct a finitely generated group so that the expected distance of the simple random walk from its starting point is within a constant factor of n^beta. In fact, the speed can be set precisely to equal any nice prescribed ... More

Every exponential group supports a positive harmonic functionOct 31 2017May 20 2018We prove that all groups of exponential growth support non-constant positive harmonic functions. In fact, out results hold in the more general case of strongly connected, finitely supported Markov chains invariant under some transitive group of automorphisms ... More

Transverse thermoelectric transport in a model of many competing order parametersOct 01 2014Coexisting fluctuations towards various ordered states are ubiquitous in strongly correlated electronic systems. In particular, measurements of underdoped cuprate high-temperature superconductors reveal evidence for short range charge order in parallel ... More

The Role of the Core Energy in the Vortex Nernst EffectOct 11 2013Oct 02 2014We present an analytical study of diamagnetism and transport in a film with superconducting phase fluctuations, formulated in terms of vortex dynamics within the Debye-H\"uckle approximation. We find that the diamagnetic and Nernst signals decay strongly ... More

Development of novel electrical characterization methods and measurements of G4-DNA and DNA DerivativesNov 23 2015Dec 04 2015This dissertation presents an investigation into the electrical properties of two types of G4-DNA and several DNA-based molecules, targeting them as candidates for molecular wires and devices. Atomic force microscopy (AFM) and electrostatic force microscopy ... More

Symmetric Strong Duality for a Class of Continuous Linear Programs with Constant CoefficientsMar 01 2014We consider Continuous Linear Programs over a continuous finite time horizon $T$, with linear cost coefficient functions and linear right hand side functions and a constant coefficient matrix, where we search for optimal solutions in the space of measures ... More

Structure of Solutions for Continuous Linear Programs with Constant CoefficientsMar 10 2014Nov 29 2014We consider Continuous Linear Programs over a continuous finite time horizon $T$, with linear cost coefficient functions, linear right hand side functions, and a constant coefficient matrix, as well as their symmetric dual. We search for optimal solutions ... More

Positive speed for high-degree automaton groupsFeb 24 2011Mother groups are the basic building blocks for polynomial automaton groups. We show that, in contrast with mother groups of degree 0 or 1, any bounded, symmetric, generating random walk on the mother groups of degree at least 3 has positive speed. The ... More

Momentum Reconstruction and Triggering in the TALAS DetectorNov 19 2000A neural network solution for a complicated experimental High Energy Physics problem is described. The method is used to reconstruct the momentum and charge of muons produced in collisions of particle in the ATLAS detector. The information used for the ... More

Measure of $π$'s and $Λ$'s emitter radius via Bose-Einstein and Fermi-Dirac StatisticsNov 16 1998This report summarises the recent studies of the Bose-Einstein Correlations (BEC) carried out by the four LEP experiments using hadronic Z$^0$ decay events and $e^+ e^-$ reactions leading to the WW decay final states. The three identical charged pion ... More

Excited MobJul 23 2013Feb 17 2014We show that for an i.i.d. bounded and weakly elliptic cookie environment, one dimensional excited random walk on the $k$-time leftover environment is right transient if and only if $\delta > k+1$ and has positive speed if and only if $\delta > k+2$, ... More

The Mutating Contact Process: Model Introduction and Qualitative Analysis of Phase Transitions in its SurvivalJan 04 2018We introduce and study the mutating contact process, a variant of the multitype contact process, where one type mutates at a constant rate to the other type. We prove that on $\mathbb{Z}$ a single mutant cannot survive while on $\mathbb{T}_{d}$ there ... More

Signatures of thermally excited vortices in a superconductor with competing ordersOct 16 2014Experimental evidence for the existence of a fluctuating charge-density wave order in the pseudogap regime of YBa$_2$Cu$_3$O$_{6+x}$ has renewed interest in its interplay with superconductivity. Here, we consider the problem within a nonlinear sigma model, ... More

Coalitions in Routing Games: A Worst-Case PerspectiveOct 13 2013Oct 31 2016We investigate a routing game that allows for the creation of coalitions, within the framework of cooperative game theory. Specifically, we describe the cost of each coalition as its maximin value. This represents the performance that the coalition can ... More

How Good is Bargained Routing?Jan 17 2016In the context of networking, research has focused on non-cooperative games, where the selfish agents cannot reach a binding agreement on the way they would share the infrastructure. Many approaches have been proposed for mitigating the typically inefficient ... More

A simplex-type algorithm for continuous linear programs with constant coefficientsMay 14 2017May 01 2019We consider continuous linear programs over a continuous finite time horizon $T$, with a constant coefficient matrix, linear right hand side functions and linear cost coefficient functions, where we search for optimal solutions in the space of measures ... More

Groups with minimal harmonic functions as small as you like (With an appendix by Nicolas Matte Bon)May 24 2016Feb 05 2017For any order of growth $f(n)=o(\log n)$ we construct a finitely-generated group $G$ and a set of generators $S$ such that the Cayley graph of $G$ with respect to $S$ supports a harmonic function with growth $f$ but does not support any harmonic function ... More

On two biased graph processesAug 03 2006In [Amir et al.], the authors consider the generalization $\Gor$ of the Erd\H{o}s-R\'enyi random graph process $G$, where instead of adding new edges uniformly, $\Gor$ gives a weight of size 1 to missing edges between pairs of isolated vertices, and a ... More

The Hilbert Schmidt version of the commutator theorem for zero trace matricesMar 27 2015Let $A$ be a $m\times m$ complex matrix with zero trace. Then there are $m\times m$ matrices $B$ and $C$ such that $A=[B,C]$ and $\|B\|\|C\|_2\le (\log m+O(1))^{1/2}\|A\|_2$ where $\|D\|$ is the norm of $D$ as an operator on $\ell_2^m$ and $\|D\|_2$ is ... More

The Size Distribution of Inhabited PlanetsMar 15 2015Mar 28 2016Earth-like planets are expected to provide the greatest opportunity for the detection of life beyond the Solar System. However our planet cannot be considered a fair sample, especially if intelligent life exists elsewhere. Just as a person's country of ... More

Scattering of Dark Matter and Dark EnergyJul 07 2010Oct 26 2010We demonstrate how the two dominant constituents of the Universe, dark energy and dark matter, could possess a large scattering cross-section without considerably impacting observations. Unlike models involving energy exchange between the two fluids, ... More

The longevity of habitable planets and the development of intelligent lifeJan 19 2016Aug 31 2016Why did the emergence of our species require a timescale similar to the entire habitable period of our planet? Our late appearance has previously been interpreted by Carter (2008) as evidence that observers typically require a very long development time, ... More

An Alternative Approach to Holographic Dark EnergySep 27 2006Mar 27 2007Here we consider a scenario in which dark energy is associated with the apparent area of a surface in the early universe. In order to resemble the cosmological constant at late times, this hypothetical reference scale should maintain an approximately ... More

Set-theoretical mathematics in CoqFeb 20 2004We give a brief discussion of some of the issues which have arisen in the course of formalizing some classical set-theoretical mathematics in the Coq system. This sprouts from, expands and replaces a chapter of math.HO/0311260 which will be removed in ... More

The dual boundary complex of the $SL_2$ character variety of a punctured sphereApr 21 2015Suppose $C_1,\ldots , C_k$ are generic conjugacy classes in $SL_2({\mathbb C})$. Consider the character variety of local systems on ${\mathbb P}^1-\{ y_1,\ldots , y_k\}$ whose monodromy transformations around the punctures $y_i$ are in the respective ... More

Localisation and Nonlocality in Compound Energy-Momentum EigenstatesNov 20 1995A thought experiment considering conservation of energy and momentum for a pair of free bodies together with their internal energy is used to show the existence of states that have localised position while being eigenstates of energy and momentum. These ... More

Calculating maps between n-categoriesSep 11 2000We give an explicit way of calculating the set of homotopy classes of morphisms from a Tamsamani n-category A to another one B. This calculation uses a Reedy-cofibrant cosimplicial resolution of A, using a new notion of ``free cofibration'' of n-precats. ... More

Homotopy types of strict 3-groupoidsOct 09 1998We look at strict $n$-groupoids and show that if $\Re$ is any realization functor from the category of strict $n$-groupoids to the category of spaces satisfying a minimal property of compatibility with homotopy groups, then there is no strict $n$-groupoid ... More

Beaming models and the correlations between the core dominance parameter and the core and extended powers of quasarsAug 20 1998We investigate the recent claim by Qin et al. that the observed correlations (or lack thereof) between the core dominance parameter and the core and extended powers of samples of lobe- and core-dominated quasars is in contradiction with beaming models. ... More

Effective generalized Seifert-Van Kampen: how to calculate $ΩX$Oct 07 1997Oct 19 1997Suppose $X$ is a 1-connected simplicial set with finitely many nondegenerate simplices. We give an effective algorithm to calculate a simplicial set with the $n$-type of the loop space $\Omega X$. Iterating gives an algorithm to calculate the $\pi_i(X)$, ... More

A closed model structure for $n$-categories, internal $Hom$, $n$-stacks and generalized Seifert-Van KampenApr 10 1997Mar 17 2000We define a closed model category containing the $n$-nerves defined by Tamsamani, and admitting internal $Hom$. This allows us to construct the $n+1$-category $nCAT$ by taking the internal $Hom$ for fibrant objects. We prove a generalized Seifert-Van ... More

Larc: a State Collapse Theory of Quantum MeasurementJul 17 2010This proposes a new theory of Quantum measurement; a state reduction theory in which reduction is to the elements of the number operator basis of a system, triggered by the occurrence of annihilation or creation (or lowering or raising) operators in the ... More

The topological realization of a simplicial presheafSep 03 1996The purpose of this article is to define the topological realization of a simplicial presheaf and to prove (under appropriate conditions) that it is homotopy-invariant under Illusie weak equivalence. In particular this applies to the site of schemes over ... More

Superpotentials from variational derivatives rather than Lagrangians in relativistic theories of gravityJul 19 2008The prescription of Silva to derive superpotential equations from variational derivatives rather than from Lagrangian densities is applied to theories of gravity derived from Lovelock Lagrangians in the Palatini representation. Spacetimes are without ... More

Isospin Invariance and Generalized Bose Statistics applied to Low Energy $K^{+-}K^0$ and $π^{+-}π^0$ Space SymmetriesMar 01 1999The use of isospin invariance and Generalized Bose statistics shows that the Bose-Einstein correlation (BEC) of identical bosons seen in the $K^+K^+$ and $\pi^+ \pi^+$ systems can be extended to apply to $K^+ K^o$ and $\pi^+ \pi^o$ pairs when they are ... More

Limits To Certainty in QoS Pricing and BandwidthOct 03 2001Advanced services require more reliable bandwidth than currently provided by the Internet Protocol, even with the reliability enhancements provided by TCP. More reliable bandwidth will be provided through QoS (quality of service), as currently discussed ... More

On Fixation of Activated Random WalksOct 20 2009Oct 23 2009We prove that for the Activated Random Walks model on transitive unimodular graphs, if there is fixation, then every particle eventually fixates, almost surely. We deduce that the critical density is at most 1. Our methods apply for much more general ... More

Algebraic (geometric) $n$-stacksSep 17 1996We propose a generalization of Artin's definition of algebraic stack, which we call {\em geometric $n$-stack}. The main observation is that there is an inductive structure to the definition whereby the ingredients for the definition of geometric $n$-stack ... More

On the Breen-Baez-Dolan stabilization hypothesis for Tamsamani's weak n-categoriesOct 09 1998We show that if $2k\geq n$, then a k-connected weak n-category $A$ can be ``delooped'' to a k+1-connected weak n+1-category $Y$ with $Hom_Y(y,y)\cong A$. This is the essential part of the ``stabilization hypothesis'' of Baez and Dolan q-alg/9503002, math/9802029. ... More

Limits in $n$-categoriesAug 07 1997We define notions of direct and inverse limits in an $n$-category. We prove that the $n+1$-category $nCAT'$ of fibrant $n$-categories admits direct and inverse limits. At the end we speculate (without proofs) on some applications of the notion of limit, ... More

Mixed twistor structuresMay 05 1997The purpose of this paper is to introduce the notion of mixed twistor structure, a generalization of the notion of mixed Hodge structure. The utility of this notion is to make possible a theory of weights for various things surrounding arbitrary representations ... More

A relative notion of algebraic Lie group and applications to $n$-stacksJul 03 1996If $S$ is a scheme of finite type over $k=\cc $, let $\Xx /S$ denote the big etale site of schemes over $S$. We introduce {\em presentable group sheaves}, a full subcategory of the category of sheaves of groups on $\Xx /S$ which is closed under kernel, ... More

Quasars are more luminous than radio galaxies - so what?Jan 07 2003Surveys to find high-redshift radio galaxies deliberately exclude optically-bright objects, which may be distant radio-loud quasars. In order to properly determine the space density of supermassive black holes, the fraction of such objects missed must ... More

Algebraic aspects of higher nonabelian Hodge theoryFeb 10 1999Mar 02 1999We look more closely at the higher nonabelian de Rham cohomology of a smooth projective variety or family of varieties that had been defined in some previous papers. We formalize using $n$-stacks the notion of shape underlying this nonabelian cohomology. ... More

Secondary Kodaira-Spencer classes and nonabelian Dolbeault cohomologyDec 18 1997Jan 06 1998If $X$ is a smooth projective variety moving in a family, we define a secondary Kodaira-Spencer class for nonabelian Dolbeault cohomology $Hom(X_{Dol}, T)$ of $X$ with coefficients in the complexified 2-sphere $T=S^2\otimes \cc$ (which is a 3-stack on ... More

On Log Canonical Models of the Moduli Space of Stable Pointed CurvesSep 25 2007We study the log canonical models of the moduli space MBar_{0,n} of pointed stable genus zero curves with respect to the standard log canonical divisors K+aD, where D denotes the boundary. In particular we show that, as a formal consequence of a conjecture ... More

Solved and unsolved problems about abelian squaresFeb 13 2018We present and discuss a number of known results and open problems abelian squares in words on small alphabets.

Subspaces of $L_p$ that embed into $L_p(μ)$ with $μ$ finiteJan 17 2013Enflo and Rosenthal proved that $\ell_p(\aleph_1)$, $1 < p < 2$, does not (isomorphically) embed into $L_p(\mu)$ with $\mu$ a finite measure. We prove that if $X$ is a subspace of an $L_p$ space, $1< p < 2$, and $\ell_p(\aleph_1)$ does not embed into ... More

Computing p-summing norms with few vectorsSep 22 1992It is shown that the p-summing norm of any operator with n-dimensional domain can be well-aproximated using only ``few" vectors in the definition of the p-summing norm. Except for constants independent of n and log n factors, ``few" means n if 1<p<2 and ... More

Nodal-line pairing with 1D-3D coupled Fermi surfaces: a model motivated by Cr-based superconductorsJul 14 2016Motivated by the recent discovery of a new family of Chromium based superconductors, we consider a two-band model, where a band of electrons dispersing only in one direction interacts with a band of electrons dispersing in all three directions. Strong ... More

Canonical Kähler metrics on classes of Lorentzian $4$-manifoldsNov 22 2018Jan 02 2019Conditions for the existence of K\"ahler-Einstein metrics and central K\"ahler metrics along with some examples are given on classes of Lorentzian $4$-manifolds with two distinguished vector fields. The results utilize the general construction in arXiv:1711.10011 ... More

The diameter of a random Cayley graph of Z_qSep 21 2006Oct 04 2009Consider the Cayley graph of the cyclic group of prime order q with k uniformly chosen generators. For fixed k, we prove that the diameter of said graph is asymptotically (in q) of order q^(1/k). The same also holds when the generating set is taken to ... More

Transient probability currents provide upper and lower bounds on non-equilibrium steady-state currents in the Smoluchowski pictureOct 23 2018Jul 17 2019Probability currents are fundamental in characterizing the kinetics of non-equilibrium processes. Notably, the steady state current $J_{ss}$ for a source-sink process is exactly equal to the inverse of the mean-first-passage time for the process. Because ... More