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Shifted dual equivalence and Schur P-positivityFeb 11 2014By considering type B analogs of permutations and tableaux, we extend abstract dual equivalence to type B in two directions. In one direction, we define involutions on signed permutations and shifted tableaux that give a weak dual equivalence, thereby ... More

Shifted dual equivalence and Schur P-positivityFeb 11 2014Nov 07 2016By considering type B analogs of permutations and tableaux, we extend abstract dual equivalence to type B in two directions. In one direction, we define involutions on signed permutations and shifted tableaux that give a weak dual equivalence, thereby ... More

A generalization of Edelman--Greene insertion for Schubert polynomialsMar 14 2019Edelman and Greene generalized the Robinson--Schensted--Knuth correspondence to reduced words in order to give a bijective proof of the Schur positivity of Stanley symmetric functions. Stanley symmetric functions may be regarded as the stable limits of ... More

Schubert polynomials, slide polynomials, Stanley symmetric functions and quasi-Yamanouchi pipe dreamsMar 31 2016We introduce two new bases for polynomials that lift monomial and fundamental quasisymmetric functions to the full polynomial ring. By defining a new condition on pipe dreams, called quasi-Yamanouchi, we give a positive combinatorial rule for expanding ... More

Kohnert tableaux and a lifting of quasi-Schur functionsSep 12 2016Aug 29 2017We introduce the quasi-key basis of the polynomial ring. We prove this basis contains the quasi-Schur polynomials of of Haglund, Luoto, Mason and van Willigenburg and that stable limits of quasi-key polynomials are quasi-Schur functions, thus giving a ... More

Dual equivalence and Schur positivityJul 01 2011Jun 12 2015We define dual equivalence for any collection of combinatorial objects endowed with a descent set, and we show that giving a dual equivalence establishes the symmetry and Schur positivity of the quasi-symmetric generating function. We give an explicit ... More

Dual equivalence graphs I: A new paradigm for Schur positivityJun 11 2015We make a systematic study of a new combinatorial construction called a dual equivalence graph. We axiomatize these graphs and prove that their generating functions are symmetric and Schur positive. This provides a universal method for establishing the ... More

A combinatorial realization of Schur-Weyl duality via crystal graphs and dual equivalence graphsApr 10 2008For any polynomial representation of the special linear group, the nodes of the corresponding crystal may be indexed by semi-standard Young tableaux. Under certain conditions, the standard Young tableaux occur, and do so with weight 0. Standard Young ... More

Weak dual equivalence for polynomialsFeb 14 2017We use dual equivalence to give a short, combinatorial proof that Stanley symmetric functions are Schur positive. We introduce weak dual equivalence, and use it to give a short, combinatorial proof that Schubert polynomials are key positive. To demonstrate ... More

Approximately pi proofs that the stock market can approximate piMay 19 2013We give three derivations of Polya's approximation for the expected range of a simple random walk in one dimension. This result allows for an estimation of the volatility of a financial instrument from the difference between the high and low prices, or, ... More

A generalized Major index statisticJul 02 2008Inspired by the $k$-inversion statistic for LLT polynomials, we define a $k$-inversion number and $k$-descent set for words. Using these, we define a new statistic on words, called the $k$-major index, that interpolates between the major index and inversion ... More

Kohnert tableaux and a lifting of quasi-Schur functionsSep 12 2016We introduce the quasi-key basis of the polynomial ring. We prove this basis contains the quasi-Schur polynomials of of Haglund, Luoto, Mason and van Willigenburg and that stable limits of quasi-key polynomials are quasi-Schur functions, thus giving a ... More

Affine dual equivalence and k-Schur functionsJan 10 2012The k-Schur functions were first introduced by Lapointe, Lascoux and Morse (2003) in the hopes of refining the expansion of Macdonald polynomials into Schur functions. Recently, an alternative definition for k-Schur functions was given by Lam, Lapointe, ... More

Dual equivalence graphs and a combinatorial proof of LLT and Macdonald positivityMay 20 2010Oct 23 2013We make a systematic study of a new combinatorial construction called a dual equivalence graph. We axiomatize these graphs and prove that their generating functions are symmetric and Schur positive. By constructing a graph on ribbon tableaux which we ... More

A kicking basis for the two-column Garsia-Haiman modulesMay 14 2009In the early 1990s, Garsia and Haiman conjectured that the dimension of the Garsia-Haiman module is n!, and they showed that the resolution of this conjecture implies the Macdonald Positivity Conjecture. Haiman proved these conjectures in 2001 using algebraic ... More

Kohnert polynomialsNov 27 2017Aug 14 2018We associate a polynomial to any diagram of unit cells in the first quadrant of the plane using Kohnert's algorithm for moving cells down. In this way, for every weak composition one can choose a cell diagram with corresponding row-counts, with each choice ... More

A Demazure crystal construction for Schubert polynomialsMay 26 2017Sep 15 2017Stanley symmetric functions are the stable limits of Schubert polynomials. In this paper, we show that, conversely, Schubert polynomials are Demazure truncations of Stanley symmetric functions. This parallels the relationship between Schur functions and ... More

Cyclic derangementsFeb 16 2010A classic problem in enumerative combinatorics is to count the number of derangements, that is, permutations with no fixed point. Inspired by a recent generalization to facet derangements of the hypercube by Gordon and McMahon, we generalize this problem ... More

A local characterization of crystals for the quantum queer superalgebraMar 16 2018Aug 14 2018We define operators on semistandard shifted tableaux and use Stembridge's local characterization for regular graphs to prove they define a crystal structure. This gives a new proof that Schur $P$-polynomials are Schur positive. We define queer crystal ... More

Riffle shuffles of a deck with repeated cardsMay 28 2009We study the Gilbert-Shannon-Reeds model for riffle shuffles and ask 'How many times must a deck of cards be shuffled for the deck to be in close to random order?'. In 1992, Bayer and Diaconis gave a solution which gives exact and asymptotic results for ... More

A rule of thumb for riffle shufflingAug 24 2009We study how many riffle shuffles are required to mix n cards if only certain features of the deck are of interest, e.g. suits disregarded or only the colors of interest. For these features, the number of shuffles drops from 3/2 log_2(n) to log_2(n). ... More

The quantile transform of a simple walkJul 18 2013We examine a new path transform on 1-dimensional simple random walks and Brownian motion, the quantile transform. This transformation relates to identities in fluctuation theory due to Wendel, Port, Dassios and others, and to discrete and Brownian versions ... More

Riffle shuffles with biased cutsDec 12 2011The well-known Gilbert-Shannon-Reeds model for riffle shuffles assumes that the cards are initially cut 'about in half' and then riffled together. We analyze a natural variant where the initial cut is biased. Extending results of Fulman (1998), we show ... More

A combinatorial proof that Schubert vs. Schur coefficients are nonnegativeMay 11 2014We give a combinatorial proof that the product of a Schubert polynomial by a Schur polynomial is a nonnegative sum of Schubert polynomials. Our proof uses Assaf's theory of dual equivalence to show that a quasisymmetric function of Bergeron and Sottile ... More

A spectral gap precludes low-dimensional embeddingsNov 27 2016We prove that there is a universal constant $C>0$ with the following property. Suppose that $n\in \mathbb{N}$ and that $\mathsf{A}=(a_{ij})\in M_n(\mathbb{R})$ is a symmetric stochastic matrix. Denote the second-largest eigenvalue of $\mathsf{A}$ by $\lambda_2(\mathsf{A})$. ... More

Borel reducibility and symmetric modelsOct 15 2018We develop a correspondence between the study of Borel equivalence relations induced by closed subgroups of $S_\infty$, and the study of symmetric models and weak choice principles, and apply it to prove a conjecture of Hjorth-Kechris-Louveau (1998). ... More

Souslin trees at successors of regular cardinalsDec 20 2018We present a weak sufficient condition for the existence of Souslin trees at successor of regular cardinals. The result is optimal and simultaneously improves an old theorem of Gregory and a more recent theorem of the author.

Transforming Rectangles into Squares, with Applications to Strong ColoringsMar 15 2011It is proved that every singular cardinal $\lambda$ admits a function $RTS:[\lambda^+]^2\rightarrow[\lambda^+]^2$ that transforms rectangles into squares. Namely, for every cofinal subsets $A,B$ of $\lambda^+$, there exists a cofinal subset $C$ of $lambda^+$, ... More

A Compositional Approach to Network AlgorithmsMay 19 2018We present elements of a typing theory for flow networks, where "types", "typings", and "type inference" are formulated in terms of familiar notions from polyhedral analysis and convex optimization. Based on this typing theory, we develop an alternative ... More

The normaliser decomposition for p-local finite groupsApr 22 2009We construct an analogue of the normaliser decomposition for p-local finite groups (S,F,L) with respect to collections of F-centric subgroups and collections of elementary abelian subgroups of S. This enables us to describe the classifying space of a ... More

The Ostaszewski square, and homogenous Souslin treesMay 15 2011Assume GCH and let $\lambda$ denote an uncountable cardinal. We prove that if $\square_\lambda$ holds, then this may be witnessed by a coherent sequence $< C_\alpha | \alpha < \lambda^+ >$ with the following remarkable guessing property: For every sequence ... More

L_1 embeddings of the Heisenberg group and fast estimation of graph isoperimetryMar 22 2010We survey connections between the theory of bi-Lipschitz embeddings and the Sparsest Cut Problem in combinatorial optimization. The story of the Sparsest Cut Problem is a striking example of the deep interplay between analysis, geometry, and probability ... More

Discrete Riesz transforms and sharp metric $X_p$ inequalitiesJan 13 2016$ \renewcommand{\subset}{\subseteq} \newcommand{\N}{\mathbb N} $For $p\in [2,\infty)$ the metric $X_p$ inequality with sharp scaling parameter is proven here to hold true in $L_p$. The geometric consequences of this result include the following sharp ... More

Jensen's diamond principle and its relativesNov 11 2009Jun 22 2010We survey some recent results on the validity of Jensen's diamond principle at successor cardinals. We also discuss weakening of this principle such as club guessing, and anti-diamond principles such as uniformization. A collection of open problems is ... More

Mathematical Logic in Computer ScienceFeb 07 2018The article retraces major events and milestones in the mutual influences between mathematical logic and computer science since the 1950s.

Antichains in partially ordered sets of singular cofinalityJun 01 2006Dec 17 2006In their paper from 1981, Milner and Sauer conjectured that for any poset P, if cf(P)=lambda>cf(lambda)=kappa, then P must contain an antichain of size kappa. We prove that for lambda>cf(lambda)=kappa, if there exists a cardinal mu<lambda such that cov(lambda,mu,kappa,2)=lambda, ... More

Cohomology Developed Matrices - constructing weighing matrices from their automorphismsMar 01 2019The aim of this work is to construct families of weighing matrices via automorphisms and cohomology. We study some well known families such as Payley's conference and Hadamard matrices and Projective Space weighing matrices, and put them in the context ... More

A primer on problems and prospects of dark energyApr 22 2009Sep 26 2009This review on dark energy is intended for a wider audience, beginners as well as experts. It contains important notes on various aspects of dark energy and its alternatives. The section on Newtonian cosmology followed by heuristic arguments to capture ... More

A Pieri rule for skew shapesAug 03 2009Apr 26 2010The Pieri rule expresses the product of a Schur function and a single row Schur function in terms of Schur functions. We extend the classical Pieri rule by expressing the product of a skew Schur function and a single row Schur function in terms of skew ... More

A pedagogical explanation for the non-renormalizability of gravitySep 22 2007Dec 03 2007We present a short and intuitive argument explaining why gravity is non-renormalizable. The argument is based on black-hole domination of the high energy spectrum of gravity and not on the standard perturbative irrelevance of the gravitational coupling. ... More

Comparison of metric spectral gapsAug 13 2013Oct 21 2013Let $A=(a_{ij})\in M_n(\R)$ be an $n$ by $n$ symmetric stochastic matrix. For $p\in [1,\infty)$ and a metric space $(X,d_X)$, let $\gamma(A,d_X^p)$ be the infimum over those $\gamma\in (0,\infty]$ for which every $x_1,...,x_n\in X$ satisfy $$ \frac{1}{n^2} ... More

Hedetniemi's conjecture for uncountable graphsJul 25 2013It is proved that in Godel's constructible universe, for every infinite successor cardinal k, there exist graphs G and H of size and chromatic number k, for which the tensor product graph (G x H) is countably chromatic.

Quantum Space-Time and Noncommutative Gauge Field TheoriesSep 09 2009Sep 17 2009The three original publications in this thesis encompass various aspects in the still developing area of noncommutative quantum field theory, ranging from fundamental concepts to model building. One of the key features of noncommutative space-time is ... More

Kinetically Constrained Models with Random ConstraintsDec 03 2018We study two kinetically constrained models in a quenched random environment. The first model is a mixed threshold Fredrickson-Andersen model on $\mathbb{Z}^{2}$, where the update threshold is either $1$ or $2$. The second is a mixture of the Fredrickson-Andersen ... More

The evolution of the core mass function by gas accretionJul 20 2012We show how the mass function of dense cores (CMF) which results from the gravoturbulent fragmentation of a molecular cloud evolves in time under the effect of gas accretion. Accretion onto the cores leads to the formation of larger numbers of massive ... More

Implementing Power Law Inflation with Tachyon Rolling on the BraneMay 15 2002Jul 09 2002We study a minimally coupled tachyon field rolling down to its ground state on the FRW brane. We construct tacyonic potential which can implements power law inflation in the brane world cosmology. The potential turns out to be ${V_0 \phi^{-1}}$ on the ... More

Exact Inflationary Solution On The BraneMay 15 2001Jul 31 2001We study the evolution of universe with a single scalar field of constant potential minimally coupled to gravity in the brane world cosmology.We find an exact inflationary solution which is not in slow roll.We discuss the limiting cases of the solution.We ... More

A Note on the Cosmological Dynamics in Finite-Range GravityOct 28 2002Dec 25 2002In this note we consider the homogeneous and isotropic cosmology in the finite-range gravity theory recently proposed by Babak and Grishchuk. In this scenario the universe undergoes late time accelerated expansion if both the massive gravitons present ... More

Kahler potentials for the MSSM inflation and the spectral indexOct 08 2007Nov 10 2007Recently it has been argued that some of the fine-tuning problems of the MSSM inflation associated with the existence of a saddle point along a flat direction may be solved naturally in a class of supergravity models. Here we extend the analysis and show ... More

On general properties of Lorentz invariant formulation of noncommutative quantum field theoryApr 21 2008Aug 19 2008We study general properties of certain Lorentz invariant noncommutative quantum field theories proposed in the literature. We show that causality in those theories does not hold, in contrast to the canonical noncommutative field theory with the light-wedge ... More

Feedback Regulated Star Formation: From Star Clusters to GalaxiesJul 05 2011This paper summarises results from semi-analytical modelling of star formation in protocluster clumps of different metallicities. In this model, gravitationally bound cores form uniformly in the clump following a prescribed core formation efficiency per ... More

Feedback Regulated Star Formation: Implications for the Kennicutt-Schmidt LawJun 16 2011Jul 07 2011We derive a metallicity dependent relation between the surface density of the star formation rate (Sigma_{SFR}) and the gas surface density (Sigma_{g}) in a feedback regulated model of star formation in galactic disks. In this model, star formation occurs ... More

Why is Universe so dark ?Jan 06 2014In this presentation prepared for a general audience, we briefly mention the shortcomings of standard model of universe. We then focus on the late time inconsistency of the model dubbed age crisis whose resolution requires the presence of a repulsive ... More

Dark energy and possible alternativesJan 07 2009We present a brief review of various approaches to late time acceleration of universe. The cosmological relevance of scaling solutions is emphasized in case of scalar field models of dark energy. The underlying features of a variety of scalar field models ... More

Restricted invertibility revisitedJan 05 2016Nov 25 2016Suppose that $m,n\in \mathbb{N}$ and that $A:\mathbb{R}^m\to \mathbb{R}^n$ is a linear operator. It is shown here that if $k,r\in \mathbb{N}$ satisfy $k<r\le \mathrm{\bf rank(A)}$ then there exists a subset $\sigma\subseteq \{1,\ldots,m\}$ with $|\sigma|=k$ ... More

Time Distribution for Persistent Viral InfectionFeb 24 2019We study the early stages of viral infection, and the distribution of times to obtain a persistent infection. The virus population proliferates by entering and reproducing inside a target cell until a sufficient number of new virus particles are released ... More

Minimal types in super-dependent theoriesNov 01 2007We give necessary and sufficient geometric conditions for a theory definable in an o-minimal structure to interpret a real closed field. The proof goes through an analysis of thorn-minimal types in super-rosy dependent theories of finite rank. We prove ... More

Scale-oblivious metric fragmentation and the nonlinear Dvoretzky theoremMar 21 2010We introduce a randomized iterative fragmentation procedure for finite metric spaces, which is guaranteed to result in a polynomially large subset that is $D$-equivalent to an ultrametric, where $D\in (2,\infty)$ is a prescribed target distortion. Since ... More

Recovering convex boundaries from blurred and noisy observationsAug 01 2006We consider the problem of estimating convex boundaries from blurred and noisy observations. In our model, the convolution of an intensity function $f$ is observed with additive Gaussian white noise. The function $f$ is assumed to have convex support ... More

Completeness of algebraic CPS simulationsJul 31 2012The algebraic lambda calculus and the linear algebraic lambda calculus are two extensions of the classical lambda calculus with linear combinations of terms. They arise independently in distinct contexts: the former is a fragment of the differential lambda ... More

Explaining the Energetic AGN Outburst of MS0735+7421 with Massive Slow JetsApr 22 2009May 29 2009By conducting axisymmetrical hydrodynamical numerical simulations (2.5 dimensional code) we show that slow, massive, wide jets can reproduce the morphology of the huge X-ray deficient bubble pair in the cluster of galaxies MS0735+7421. The total energy ... More

Sound Waves Excitation by Jet-Inflated Bubbles in Clusters of GalaxiesAug 17 2008We show that repeated sound waves in the intracluster medium (ICM) can be excited by a single inflation episode of an opposite bubble pair. To reproduce this behavior in numerical simulations the bubbles should be inflated by jets, rather than being injected ... More

Spectral theory of metastability and extinction in a branching-annihilation reactionDec 06 2006Apr 01 2007We apply the spectral method, recently developed by the authors, to calculate the statistics of a reaction-limited multi-step birth-death process, or chemical reaction, that includes as elementary steps branching A->2A and annihilation 2A->0. The spectral ... More

Spectral formulation and WKB approximation for rare-event statistics in reaction systemsJun 08 2006Sep 23 2006We develop a spectral formulation and a stationary WKB approximation for calculating the probabilities of rare events (large deviations from the mean) in systems of reacting particles with infinite-range interaction, describable by a master equation. ... More

Parametric Autoresonance in Faraday wavesJun 03 2005We develop a theory of parametric excitation of weakly nonlinear standing gravity waves in a tank, which is under vertical vibrations with a slowly time-dependent ("chirped") vibration frequency. We show that, by using a negative chirp, one can excite ... More

Enhanced shot noise in asymmetric interacting two level systemsAug 30 2011Feb 01 2012We study a model of two interacting levels that are attached to two electronic leads, where one of the levels is attached very weakly to the leads. We use rate equations method to calculate the average current and the noise of electrons transmitted through ... More

Random Martingales and localization of maximal inequalitiesDec 06 2009Dec 09 2009Let $(X,d,\mu)$ be a metric measure space. For $\emptyset\neq R\subseteq (0,\infty)$ consider the Hardy-Littlewood maximal operator $$ M_R f(x) \stackrel{\mathrm{def}}{=} \sup_{r \in R} \frac{1}{\mu(B(x,r))} \int_{B(x,r)} |f| d\mu.$$ We show that if there ... More

Reducts of Hrushovski's constructions of a higher geometrical aritySep 21 2017Sep 18 2018Let $\mathbb{M}_n$ denote the structure obtained from Hrushovski's (non collapsed) construction with an n-ary relation and $PG(\mathbb{M}_n)$ its associated pre-geometry. It was shown by Evans and Ferreira that $PG(\mathbb{M}_3)\not\cong PG(\mathbb{M}_4)$. ... More

On reducts of Hrushovski's construction - the non-collapsed caseMay 09 2013We show that the rank {\omega} structure obtained by the non-collapsed version of Hrushovski's amalgamation construction has a proper reduct. We show that this reduct is the Fra\"iss\'e-Hrushovski limit of its own age with respect to a pre-dimension function ... More

Towards a Calculus for Non-Linear Spectral Gaps [Extended Abstract]Oct 11 2009Given a finite regular graph G=(V,E) and a metric space (X,d_X), let $gamma_+(G,X) denote the smallest constant $\gamma_+>0$ such that for all f,g:V\to X we have: \frac{1}{|V|^2}\sum_{x,y\in V} d_X(f(x),g(y))^2\le \frac{\gamma_+}{|E|} \sum_{xy\in E} d_X(f(x),g(y))^2. ... More

Encounter time of two loci governed by polymer de-condensation and local chromatin interactionJul 10 2017The time for a DNA sequence to find its homologous depends on a long random search process inside the cell nucleus. Using polymer models, we model and compute here the mean first encounter time (MFET) between two sites located on two different polymer ... More

X-ray Absorption of High Redshift QuasarsJul 08 2013Soft X-ray photoelectric absorption of high-z quasars has been known for two decades, but has no unambiguous astro-physical context. We construct the largest sample to date of 58 high redshift quasars (z > 0.45) selected from the XMM-Newton archive based ... More

Heat flow and quantitative differentiationAug 05 2016For every Banach space $(Y,\|\cdot\|_Y)$ that admits an equivalent uniformly convex norm we prove that there exists $c=c(Y)\in (0,\infty)$ with the following property. Suppose that $n\in \mathbb{N}$ and that $X$ is an $n$-dimensional normed space with ... More

On Lipschitz extension from finite subsetsJun 14 2015We prove that for every $n\in \mathbb{N}$ there exists a metric space $(X,d_X)$, an $n$-point subset $S\subseteq X$, a Banach space $(Z,\|\cdot\|_Z)$ and a $1$-Lipschitz function $f:S\to Z$ such that the Lipschitz constant of every function $F:X\to Z$ ... More

Poincaré inequalities, embeddings, and wild groupsMay 21 2010Jan 23 2011We present geometric conditions on a metric space $(Y,d_Y)$ ensuring that almost surely, any isometric action on $Y$ by Gromov's expander-based random group has a common fixed point. These geometric conditions involve uniform convexity and the validity ... More

Markov convexity and local rigidity of distorted metricsMar 12 2008Jul 26 2010It is shown that a Banach space admits an equivalent norm whose modulus of uniform convexity has power-type p if and only if it is Markov p-convex. Counterexamples are constructed to natural questions related to isomorphic uniform convexity of metric ... More

Assouad's theorem with dimension independent of the snowflakingDec 10 2010It is shown that for every $K>0$ and $\e\in (0,1/2)$ there exist $N=N(K)\in \N$ and $D=D(K,\e)\in (1,\infty)$ with the following properties. For every separable metric space $(X,d)$ with doubling constant at most $K$, the metric space $(X,d^{1-\e})$ admits ... More

$L_p$ compression, traveling salesmen, and stable walksApr 30 2009We show that if $H$ is a group of polynomial growth whose growth rate is at least quadratic then the $L_p$ compression of the wreath product $\Z\bwr H$ equals $\max{\frac{1}{p},{1/2}}$. We also show that the $L_p$ compression of $\Z\bwr \Z$ equals $\max{\frac{p}{2p-1},\frac23}$ ... More

Ramsey partitions and proximity data structuresNov 23 2005May 10 2006This paper addresses two problems lying at the intersection of geometric analysis and theoretical computer science: The non-linear isomorphic Dvoretzky theorem and the design of good approximate distance oracles for large distortion. We introduce the ... More

Weak square and stationary reflectionNov 16 2017It is well-known that the square principle $\square_\lambda$ entails the existence of a non-reflecting stationary subset of $\lambda^+$, whereas the weak square principle $\square^*_\lambda$ does not. Here we show that if $\mu^{\mathrm{cf}(\lambda)} < ... More

Improved bounds in the scaled Enflo type inequality for Banach spacesApr 23 2010It is shown that if (X,||.||_X) is a Banach space with Rademacher type p \ge 1, then for every integer n there exists an even integer m < Cn^{2-1/p}log n (C is an absolute constant), such that for every f:Z_m^n --> X, \Avg_{x,\e}[||f(x+ m\e/2)-f(x)}||_X^p] ... More

On the Gravitational Boundedness of Small Scale Structures in Molecular CloudsDec 21 2006We investigate, in a set of 3D numerical simulations of driven, magnetized, isothermal, and self-gravitating molecular clouds (MCs), the statistical correlations between the energy ratios (thermal/gravity, and kinetic/gravity) of clumps and cores (CCs) ... More

Intertwining operator associated to the complex Dunkl operator of type $G(m,1,N)$Nov 10 2013In this work, we consider the Dunkl complex reflection operators related to the group $G(m,1,N)$ in the complex plane \begin{align*} T_i=\frac{\partial}{\partial z_i}+k_0\sum_{j\neq i}\sum_{r=0}^{m-1}\frac{1-s_i^{-r}(i,j)s_i^r} {z_i-\varepsilon^r z_j}+\sum_{j=1}^{m-1}k_j\sum_{r=0}^{m-1}\frac{\varepsilon^{-rj}s_i^r}{z_i}, ... More

String-inspired cosmology: Late time transition from scaling matter era to dark energy universe caused by a Gauss-Bonnet couplingAug 25 2006Dec 18 2006The Gauss-Bonnet (GB) curvature invariant coupled to a scalar field $\phi$ can lead to an exit from a scaling matter-dominated epoch to a late-time accelerated expansion, which is attractive to alleviate the coincident problem of dark energy. We derive ... More

Submillimeter corrections to gravity and the metastability of white dwarf and neutron starsMar 20 2006The string inspired higher dimensional theories suggest modification of Newton's law at submillimeter length scales. Inter-particle distances in white dwarf and neutron stars are $10^{-10} cms$ and $10^{-13} cms$ respectively, and therefore, the effects ... More

Manybody treatment of white dwarf and neutron stars on the braneFeb 07 2005Jul 15 2005Brane-World models suggest modification of Newton's law of gravity on the 3-brane at submillimeter scales. The brane-world induced corrections are in higher powers of inverse distance and appear as additional terms with the Newtonian potential. The average ... More

Unifying Brane World Inflation with QuintessenceMay 03 2004Sep 15 2004We review the recent attempts of unifying inflation with quintessence. It appears natural to join the two ends in the framework of brane world cosmology. The models of quintessential inflation belong to the class of {\it non-oscillatory} models for which ... More

Vibrational assignments and line shapes in inelastic tunnelling spectroscopy: H on Cu(100)Apr 21 2006We have carried out a computational study of the inelastic electron tunneling spectrum (IETS) of the two vibrational modes of a single hydrogen atom on a Cu(100) surface in a scanning tunneling microscopy (STM) junction. This study addresses key issues ... More

Phantom Field and the Fate of UniverseDec 01 2003Dec 05 2003In this paper we analyze the cosmological dynamics of phantom field in a variety of potentials unbounded from above. We demonstrate that the nature of future evolution generically depends upon the steepness of the phantom potential and discuss the fate ... More

Approximate kernel clusteringJul 29 2008Dec 09 2008In the kernel clustering problem we are given a large $n\times n$ positive semi-definite matrix $A=(a_{ij})$ with $\sum_{i,j=1}^na_{ij}=0$ and a small $k\times k$ positive semi-definite matrix $B=(b_{ij})$. The goal is to find a partition $S_1,...,S_k$ ... More

Nonlinear spectral calculus and super-expandersJul 19 2012Mar 20 2013Nonlinear spectral gaps with respect to uniformly convex normed spaces are shown to satisfy a spectral calculus inequality that establishes their decay along Cesaro averages. Nonlinear spectral gaps of graphs are also shown to behave sub-multiplicatively ... More

A note on dichotomies for metric transformsFeb 09 2011We show that for every nondecreasing concave function w:R+ --> R+ with w(0)=0, either every finite metric space embeds with distortion arbitrarily close to 1 into a metric space of the form (X,w o d) for some metric d on X, or there exists a=a(w)>0 and ... More

Ultrametric skeletonsDec 15 2011Dec 17 2011We prove that for every $\epsilon\in (0,1)$ there exists $C_\epsilon\in (0,\infty)$ with the following property. If $(X,d)$ is a compact metric space and $\mu$ is a Borel probability measure on $X$ then there exists a compact subset $S\subseteq X$ that ... More

Planar Earthmover is not in $L_1$Sep 26 2005We show that any $L_1$ embedding of the transportation cost (a.k.a. Earthmover) metric on probability measures supported on the grid $\{0,1,...,n\}^2\subseteq \R^2$ incurs distortion $\Omega(\sqrt{\log n})$. We also use Fourier analytic techniques to ... More

Interference of diffusing photons and level crossing spectroscopyOct 17 2006We show that a new interference effect appears in the intensity fluctuations of photons multiply scattered by an atomic gas of large optical depth b. This interference occurs only for scattering atoms that are Zeeman degenerate and it leads to a deviation ... More

Exercices de style: a homotopy theory for set theory, IFeb 28 2011Apr 27 2012We construct a model category (in the sense of Quillen) for set theory, starting from two arbitrary, but natural, conventions. It is the simplest category satisfying our conventions and modelling the notions of finiteness, countability and infinite equi-cardinality. ... More

The Hough transform estimatorMar 29 2005This article pursues a statistical study of the Hough transform, the celebrated computer vision algorithm used to detect the presence of lines in a noisy image. We first study asymptotic properties of the Hough transform estimator, whose objective is ... More

Validity of heavy traffic steady-state approximations in generalized Jackson NetworksOct 04 2004Mar 09 2006We consider a single class open queueing network, also known as a generalized Jackson network (GJN). A classical result in heavy-traffic theory asserts that the sequence of normalized queue length processes of the GJN converge weakly to a reflected Brownian ... More

A-infinity monads and completionMay 20 2008Apr 02 2010Given an operad A of topological spaces, we consider A-monads in a topological category C . When A is an A-infinity-operad, any A-monad K : C -> C can be thought of as a monad up to coherent homotopies. We define the completion functor with respect to ... More

A simplicial $A_\infty$-operad acting on $R$-resolutionsJan 07 2009We construct a combinatorial model of an A-infinity-operad which acts simplicially on the cobar resolution (not just its total space) of a simplicial set with respect to a ring R.