total 973took 0.13s

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

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

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

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

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

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

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

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

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

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

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

Nonsymmetric Macdonald polynomials and a refinement of Kostka-Foulkes polynomialsMar 07 2017Mar 12 2017We study the specialization of the type A nonsymmetric Macdonald polynomials at $t=0$ based on the combinatorial formula of Haglund, Haiman, and Loehr. We prove that this specialization expands nonnegatively into the fundamental slide polynomials, introduced ... 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

Toward the Schur expansion of Macdonald polynomialsMar 21 2017We give an explicit combinatorial formula for the Schur expansion of Macdonald polynomials indexed by partitions with second part at most two. This gives a uniform formula for both hook and two column partitions. The proof comes as a corollary to the ... More

Combinatorial models for Schubert polynomialsFeb 28 2017Schubert polynomials are a basis for the polynomial ring that represent Schubert classes for the flag manifold. In this paper, we introduce and develop several new combinatorial models for Schubert polynomials that relate them to other known bases including ... More

Dual equivalence graphs II: Transformations on locally Schur positive graphsApr 24 2017Dual equivalence graphs are a powerful tool in symmetric function theory that provide a general framework for proving that a given quasisymmetric function is symmetric and Schur positive. In this paper, we study a larger family of graphs that includes ... 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

An inversion metric for reduced wordsAug 05 2018We study the graph on reduced words with edges given by the Coxeter relations for the symmetric group. We define a metric on reduced words for a given permutation, analogous to Coxeter length for permutations, for which the graph becomes ranked with unique ... More

Multiplication of a Schubert polynomial by a Stanley symmetric polynomialFeb 01 2017We prove, combinatorially, that the product of a Schubert polynomial by a Stanley symmetric polynomial is a truncated Schubert polynomial. Using Monk's rule, we derive a nonnegative combinatorial formula for the Schubert polynomial expansion of a truncated ... 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

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

Flagged $(\mathcal{P},ρ)$-partitionsApr 14 2019We introduce the theory of $(\mathcal{P},\rho)$-partitions, depending on a poset $\mathcal{P}$ and a map $\rho$ from $\mathcal{P}$ to positive integers. The generating function $\mathfrak{F}_{\mathcal{P},\rho}$ of $(\mathcal{P},\rho)$-partitions is a ... More

Demazure crystals for specialized nonsymmetric Macdonald polynomialsJan 22 2019Feb 21 2019We give an explicit, nonnegative formula for the expansion of nonsymmetric Macdonald polynomials specialized at $t=0$ in terms of Demazure characters. Our formula results from constructing Demazure crystals whose characters are the nonsymmetric Macdonald ... 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

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

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

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

Crystal graphs for shifted tableauxFeb 20 2018We define crystal operators on semistandard shifted tableaux, giving a new proof that Schur $P$-functions are Schur positive. We define a queer crystal operator to construct a connected queer crystal on semistandard shifted tableaux of a given shape, ... 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

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

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

Specht modules decompose as alternating sums of restrictions of Schur modulesSep 26 2018Schur modules give the irreducible polynomial representations of the general linear group $\mathrm{GL}_t$. Viewing the symmetric group $\mathfrak{S}_t$ as a subgroup of $\mathrm{GL}_t$, we may restrict Schur modules to $\mathfrak{S}_t$ and decompose the ... 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

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 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

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

Gaussian estimates for spatially inhomogeneous random walks on ${\mathbf{Z}}^d$Feb 27 2006It is shown in this paper that the transition kernel corresponding to a spatially inhomogeneous random walk on ${\mathbf{Z}}^d$ admits upper and lower Gaussian estimates.

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

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

Stabilization of the homotopy groups of the self equivalences of linear spheresMar 29 2019Let $G$ be a finite group. Let $U_1,U_2,\dots$ be a sequence of orthogonal representations in which any irreducible representation of $\oplus_{n \geq 1} U_n$ has infinite multiplicity. Let $V_n=\oplus_{i=1}^n U_n$ and $S(V_n)$ denote the linear sphere ... More

An average John theoremMay 03 2019We prove that the $\frac12$-snowflake of a finite-dimensional normed space $(X,\|\cdot\|_X)$ embeds into a Hilbert space with quadratic average distortion $$O\Big(\sqrt{\log \mathrm{dim}(X)}\Big).$$ We deduce from this (optimal) statement that if an $n$-vertex ... More

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

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

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.

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

Discrete harmonic functions in Lipschitz domainsJan 03 2019We prove the existence and uniqueness of a discrete nonnegative harmonic function for a random walk satisfying finite range, centering and ellipticity conditions, killed when leaving a globally Lipschitz domain in $\mathbb{Z}^d$. Our method is based on ... More

Vainshtein mechanism in Gauss-Bonnet gravity and Galileon aetherJul 10 2011Dec 19 2011We derive field equations of Gauss-Bonnet gravity in 4 dimensions after dimensional reduction of the action and demonstrate that in this scenario Vainshtein mechanism operates in the flat spherically symmetric background. We show that inside this Vainshtein ... More

Properties of Galaxies and Groups: Nature versus NurtureSep 08 2011Due to the inherently nonlinear nature of gravity cosmological N-body simulations have become an invaluable tool when the growth of structure is being studied and modelled closer to the present epoch. Large simulations with high dynamical range have made ... More

Dynamical friction in an isentropic gasMar 03 2012When a gravitating object moves across a given mass distribution, it creates an overdense wake behind it. Here, we performed an analytical study of the structure of the flow far from object when the flow is isentropic and the object moves subsonically ... More

On the origin of the HI holes in the interstellar medium of dwarf irregular galaxiesFeb 25 2004May 03 2005We suggest that large HI holes observed in the interstellar medium (ISM) of galaxies such as the Large Magellanic Cloud (LMC) and Holmberg II (Ho II, DDO 50, UGC 4305) can form as the combined result of turbulence coupled to thermal and gravitational ... More

Lower bounds for distributed markov chain problemsOct 29 2008We study the worst-case communication complexity of distributed algorithms computing a path problem based on stationary distributions of random walks in a network $G$ with the caveat that $G$ is also the communication network. The problem is a natural ... More

Non-Gaussianity in Curvaton Models with Nearly Quadratic PotentialAug 26 2005Sep 06 2005We consider curvaton models with potentials that depart slightly from the quadratic form. We show that although such a small departure does not modify significantly the Gaussian part of the curvature perturbation, it can have a pronounced effect on the ... More

A note on superposition of two unknown states using Deutsch CTC modelMay 17 2016Sep 05 2016In a recent work, authors prove a yet another no-go theorem that forbids the existence of a universal probabilistic quantum protocol producing a superposition of two unknown quantum states. In this short note, we show that in the presence of closed time ... More

New Development in RF Pulse CompressionAug 20 2000Oct 01 2000Several pulse compression systems have been proposed for future linear collider. Most of these systems require hundreds of kilometers of low-loss waveguide runs. To reduce the waveguide length and improve the efficiency of these systems, components for ... More

A unified approach to scaling solutions in a general cosmological backgroundSep 21 2004Oct 18 2004Our ignorance about the source of cosmic acceleration has stimulated study of a wide range of models and modifications to gravity. Cosmological scaling solutions in any of these theories are privileged because they represent natural backgrounds relevant ... More

A Viable Cosmology with a Scalar Field Coupled to the Trace of the Stress-TensorDec 27 2002Feb 20 2003We study the cosmological evolution of a scalar field that couples to the trace $T=T^{a}_a$ of energy momentum tensor of all the fields (including itself). In the case of a shallow exponential potential, the presence of coupling to the trace $T$ in the ... More

Conceptual Design Of An Ideal Variable Coupler For Superconducting Radiofrequency 1.3GHz CavitiesJun 27 2014Inspired by the development of over-moded RF component as an undulator, we explored another over-moded structure that could serve the variable coupling for SRF purpose. This application is to fulfill variation of S11 from 0 to -20db with CW power of 7 ... More

Backlog and Delay Reasoning in HARQ SystemsJun 04 2015Recently, hybrid-automatic-repeat-request (HARQ) systems have been favored in particular state-of-the-art communications systems since they provide the practicality of error detections and corrections aligned with repeat-requests when needed at receivers. ... More

Electronic Structure and Bonding of Icosahedral Core-Shell Gold-Silver Nanoalloy Clusters Au_(144-x)Ag_x(SR)_60Aug 26 2011Atomically precise thiolate-stabilized gold nanoclusters are currently of interest for many cross-disciplinary applications in chemistry, physics and molecular biology. Very recently, synthesis and electronic properties of "nanoalloy" clusters Au_(144-x)Ag_x(SR)_60 ... More

Dark matter from gravitational particle production at reheatingDec 22 2015Jul 26 2016We show that curvature induced particle production at reheating generates adiabatic dark matter if there are non-minimally coupled spectator scalars weakly coupled to visible matter. The observed dark matter abundance implies an upper bound on spectator ... More

Multi-outcome and Multidimensional Market Scoring RulesFeb 08 2012Hanson's market scoring rules allow us to design a prediction market that still gives useful information even if we have an illiquid market with a limited number of budget-constrained agents. Each agent can "move" the current price of a market towards ... More

A Fractional Power for Dunkl Transforms in $ L^{2}(\R^{N}, ω_{k}(x)dx)$Oct 30 2013A new fractional version of the Dunkl transform for real order $\alpha$ is obtained. An integral representation, a Bochner type identity and a Master formula for this transform are derived.

Quintessential Inflation on the Brane and the Relic Gravity Wave BackgroundFeb 11 2004Sep 11 2004Quintessential inflation describes a scenario in which both inflation and dark energy (quintessence) are described by the same scalar field. In conventional braneworld models of quintessential inflation gravitational particle production is used to reheat ... More

Spectral action beyond the standard modelSep 17 2001We rehabilitate the M_1(C)+ M_2(C)+ M_3(C) model of electro-magnetic, weak and strong forces as an almost commutative geometry in the setting of the spectral action.

Integral Geometric Dual Distributions of Multilinear ModelsNov 22 2018We propose an integral geometric approach for computing dual distributions for the parameter distributions of multilinear models. The dual distributions can be computed from, for example, the parameter distributions of conics, multiple view tensors, homographies, ... More

WKB theory of large deviations in stochastic populationsDec 05 2016Stochasticity can play an important role in the dynamics of biologically relevant populations. These span a broad range of scales: from intra-cellular populations of molecules to population of cells and then to groups of plants, animals and people. Large ... 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

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

Magneto-thermal condensation modes including the effects of charged dust particlesJun 15 2008Feb 03 2009We study thermal instability in a magnetized and partially ionized plasma with charged dust particles. Our linear analysis shows that the growth rate of the unstable modes in the presence of dust particles strongly depends on the ratio of the cooling ... More

A classical field theory formulation for the numerical solution of time harmonic electromagnetic fieldsFeb 05 2019Finite element representations of Maxwell's equations pose unusual challenges inherent to the variational representation of the `curl-curl' equation for the fields. We present a variational formulation based on classical field theory. Borrowing from QED, ... More

A classical field theory formulation for the numerical solution of time harmonic electromagnetic fieldsFeb 05 2019Apr 01 2019Finite element representations of Maxwell's equations pose unusual challenges inherent to the variational representation of the `curl-curl' equation for the fields. We present a variational formulation based on classical field theory. Borrowing from QED, ... More

Backstepping feedback control of open channel flowOct 29 2014We derive a feedback control law for the control of the downstream flow in a 1-D open channel by manipulating the water flow at an upstream location. We use backstepping for controller design and Lyapunov techniques for stability analysis. Finally, the ... More

Control Variables, Discrete Instruments, and Identification of Structural FunctionsSep 15 2018Control variables provide an important means of controlling for endogeneity in econometric models with nonseparable and/or multidimensional heterogeneity. We allow for discrete instruments, giving identification results under a variety of restrictions ... 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

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

Moments of the distance between independent random vectorsMay 03 2019We derive various sharp bounds on moments of the distance between two independent random vectors taking values in a Banach space.

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

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

Scaled Enflo type is equivalent to Rademacher typeJun 11 2005We introduce the notion of scaled Enflo type of a metric space, and show that for Banach spaces, scaled Enflo type p is equivalent to Rademacher type p.

Nonembeddability theorems via Fourier analysisOct 26 2005Various new nonembeddability results (mainly into $L_1$) are proved via Fourier analysis. In particular, it is shown that the Edit Distance on $\{0,1\}^d$ has $L_1$ distortion $(\log d)^{\frac12-o(1)}$. We also give new lower bounds on the $L_1$ distortion ... More

Metric CotypeJun 10 2005Feb 08 2011We introduce the notion of cotype of a metric space, and prove that for Banach spaces it coincides with the classical notion of Rademacher cotype. This yields a concrete version of Ribe's theorem, settling a long standing open problem in the nonlinear ... More

Cross-Validation for Correlated DataApr 04 2019May 12 2019K-fold cross-validation (CV) with squared error loss is widely used for evaluating predictive models, especially when strong distributional data assumptions cannot be taken. However, CV with squared error loss is not free from distributional assumptions, ... More