Results for "Jason Frank"

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A detectability criterion and data assimilation for non-linear differential equationsNov 14 2017In this paper we propose a new sequential data assimilation method for non-linear ordinary differential equations with compact state space. The method is designed so that the Lyapunov exponents of the corresponding estimation error dynamics are negative, ... More
The Creation of AGB Fallback ShellsMay 12 2015Jan 22 2016The possibility that mass ejected during Asymptotic Giant Branch (AGB) stellar evolution phases falls back towards the star has been suggested in applications ranging from the formation of accretion disks to the powering of late-thermal pulses. In this ... More
How to verify computation with a rational networkJun 19 2016The present paper introduces a practical protocol for provably secure, outsourced computation. Our protocol minimizes overhead for verification by requiring solutions to withstand an interactive game between a prover and challenger. For optimization problems, ... More
The Fermi Paradox and the Aurora Effect: Exo-civilization Settlement, Expansion and Steady StatesFeb 12 2019We model the settlement of the galaxy by space-faring civilizations in order to address issues related to the Fermi Paradox. We explore the problem in a way that avoids assumptions about the intent and motivation of any exo-civilization seeking to settle ... More
Spin Seebeck devices using local on-chip heatingJan 28 2015A micro-patterned spin Seebeck device is fabricated using an on-chip heater. Current is driven through a Au heater layer electrically isolated from a bilayer consisting of Fe$_3$O$_4$ (insulating ferrimagnet) and a spin detector layer. It is shown that ... More
Energy Budget and Core-Envelope Motion in Common Envelope EvolutionDec 28 2018We analyze a 3D hydrodynamic simulation of common envelope evolution to understand how energy is transferred between various forms, leading to the partial unbinding of the envelope. We find that $13$-$14\%$ of the envelope is unbound during the simulation. ... More
Things that can be made into themselvesAug 03 2012Feb 12 2014One says that a property $P$ of sets of natural numbers can be made into itself iff there is a numbering $\alpha_0,\alpha_1,\ldots$ of all left-r.e. sets such that the index set $\{e: \alpha_e$ satisfies $P\}$ has the property $P$ as well. For example, ... More
Projected Shadowing-based Data AssimilationJul 28 2017In this article we develop algorithms for data assimilation based upon a computational time dependent stable/unstable splitting. Our particular method is based upon shadowing refinement and synchronization techniques and is motivated by work on Assimilation ... More
Derivation of Delay Equation Climate Models Using the Mori-Zwanzig FormalismFeb 08 2019Models incorporating delay have been frequently used to understand climate variability phenomena, but often the delay is introduced through an ad-hoc physical reasoning, such as the propagation time of waves. In this paper, the Mori-Zwanzig formalism ... More
Three-dimensional hydrodynamic simulations of L2 PuppisFeb 19 2016Oct 04 2016Recent observations of the L2 Puppis system suggest that this Mira-like variable may be in the early stages of forming a bipolar planetary nebula (PN). As one of nearest and brightest AGB stars, thought be a binary, L2 Puppis serves as a benchmark object ... More
Accurate Evolution of Orbiting Binary Black HolesDec 19 2005We present a detailed analysis of binary black hole evolutions in the last orbit, and demonstrate consistent and convergent results for the trajectories of the individual bodies. The gauge choice can significantly affect the overall accuracy of the evolution. ... More
A Multi-dimensional Investigation of the Effects of Publication Retraction on Scholarly ImpactFeb 29 2016Over the past few decades, the rate of publication retractions has increased dramatically in academia. In this study, we investigate retractions from a quantitative perspective, aiming to answer two fundamental questions. One, how do retractions influence ... More
Accretion in common envelope evolutionMay 09 2018Common envelope evolution (CEE) is presently a poorly understood, yet critical, process in binary stellar evolution. Characterizing the full 3D dynamics of CEE is difficult in part because simulating CEE is so computationally demanding. Numerical studies ... More
Accretion in Common Envelope EvolutionOct 10 2018Common envelope evolution (CEE) occurs in some binary systems involving asymptotic giant branch (AGB) or red giant branch (RGB) stars, and understanding this process is crucial for understanding the origins of various transient phenomena. CEE has been ... More
A new cohomological formula for helicity in $\R^{2k+1}$ reveals the effect of a diffeomorphism on helicityMar 08 2009Oct 26 2012The helicity of a vector field is a measure of the average linking of pairs of integral curves of the field. Computed by a six-dimensional integral, it is widely useful in the physics of fluids. For a divergence-free field tangent to the boundary of a ... More
Least-biased correction of extended dynamical systems using observational dataNov 21 2014We consider dynamical systems evolving near an equilibrium statistical state where the interest is in modelling long term behavior that is consistent with thermodynamic constraints. We adjust the distribution using an entropy-optimizing formulation that ... More
On the discriminant of twisted tensor productsJun 09 2016We provide formulas for computing the discriminant of noncommutative algebras over central subalgebras in the case of Ore extensions and skew group extensions. The formulas follow from a more general result regarding the discriminants of certain twisted ... More
Measuring and Correcting Wind-Induced Pointing Errors of the Green Bank Telescope Using an Optical Quadrant DetectorApr 08 2011Wind-induced pointing errors are a serious concern for large-aperture high-frequency radio telescopes. In this paper, we describe the implementation of an optical quadrant detector instrument that can detect and provide a correction signal for wind-induced ... More
Direct control of the small-scale energy balance in 2D fluid dynamicsDec 19 2014We explore the direct modification of the pseudo-spectral truncation of 2D, incompressible fluid dynamics to maintain a prescribed kinetic energy spectrum. The method provides a means of simulating fluid states with defined spectral properties, for the ... More
Testing the Evolutionary Link Between Submillimetre Galaxies and Quasars: CO Observations of QSOs at z~2Jun 03 2008Jul 08 2008We have used the IRAM Plateau de Bure mm interferometer and the UKIRT 1-5 um Imager Spectrometer to test the connection between the major phases of spheroid growth and nuclear accretion by mapping CO emission in nine submm-detected QSOs at z=1.7-2.6 with ... More
How powerful are integer-valued martingales?Apr 06 2010Apr 10 2010In the theory of algorithmic randomness, one of the central notions is that of computable randomness. An infinite binary sequence X is computably random if no recursive martingale (strategy) can win an infinite amount of money by betting on the values ... More
The remapped particle-mesh advection schemeJul 26 2006We describe the remapped particle-mesh method, a new mass-conserving method for solving the density equation which is suitable for combining with semi-Lagrangian methods for compressible flow applied to numerical weather prediction. In addition to the ... More
An Update on Monitoring Stellar Orbits in the Galactic CenterNov 28 2016Using 25 years of data from uninterrupted monitoring of stellar orbits in the Galactic Center, we present an update of the main results from this unique data set: A measurement of mass of and distance to SgrA*. Our progress is not only due to the eight ... More
High-Performance Distributed Multi-Model / Multi-Kernel Simulations: A Case-Study in Jungle ComputingMar 01 2012High-performance scientific applications require more and more compute power. The concurrent use of multiple distributed compute resources is vital for making scientific progress. The resulting distributed system, a so-called Jungle Computing System, ... More
Small near-Earth asteroids in the Palomar Transient Factory survey: A real-time streak-detection systemSep 26 2016Near-Earth asteroids (NEAs) in the 1-100 meter size range are estimated to be $\sim$1,000 times more numerous than the $\sim$15,000 currently-catalogued NEAs, most of which are in the 0.5-10 kilometer size range. Impacts from 10-100 meter size NEAs are ... More
Optical Monitoring of the Broad-Line Radio Galaxy 3C390.3Aug 03 2012We have undertaken a new ground-based monitoring campaign on the BLRG 3C390.3 to improve the measurement of the size of the BLR and to estimate the black hole mass. Optical spectra and g-band images were observed in 2005 using the 2.4m telescope at MDM ... More
Applications of Symmetric Functions to Cycle and Increasing Subsequence Structure after Shuffles (Part 2)Mar 31 2001Apr 16 2001Using the Berele/Remmel/Kerov/Vershik variation of the Robinson-Schensted-Knuth correspondence, we study the cycle and increasing subsequence structure after various methods of shuffling. One consequence is a cycle index for shuffles like: cut a deck ... More
New Examples of Potential Theory on Bratelli DiagramsDec 17 1999We consider potential theory on Bratteli diagrams arising from Macdonald polynomials. The case of Hall-Littlewood polynomials is particularly interesting; the elements of the diagram are partitions, the branching multiplicities are integers, the combinatorial ... More
Martingales and character ratiosFeb 25 2004Some general connections between martingales and character ratios of finite groups are developed. As an application we sharpen the convergence rate in a central limit theorem for the character ratio of a random representation of the symmetric group on ... More
Stein's Method and Plancherel Measure of the Symmetric GroupMay 29 2003Nov 11 2003We initiate a Stein's method approach to the study of the Plancherel measure of the symmetric group. A new proof of Kerov's central limit theorem for character ratios of random representations of the symmetric group on transpositions is obtained; the ... More
Exact constraints on D$\leq 10$ Myers Perry black holes and the Wald ProblemSep 30 2010Jan 31 2011Exact relations on the existence of event horizons of Myers Perry black holes are obtained in $D\leq 10$ dimensions. It is further shown that naked singularities can not be produced by "spinning-up" these black holes by shooting particles into their $\lfloor\frac{D-1}{2}\rfloor$ ... More
The centered dual and the maximal injectivity radius of hyperbolic surfacesAug 27 2013Sep 05 2013We give sharp upper bounds on the maximal injectivity radius of finite-area hyperbolic surfaces and use them, for each g at least 2, to identify a constant r_{g-1,2} with the property that the set of closed genus-g hyperbolic surfaces with maximal injectivity ... More
Tessellations of hyperbolic surfacesMar 23 2011A finite subset S of a closed hyperbolic surface F canonically determines a "centered dual decomposition" of F: a cell structure with vertex set S, geodesic edges, and 2-cells that are unions of the corresponding Delaunay polygons. Unlike a Delaunay polygon, ... More
Altmetrics (Chapter from Beyond Bibliometrics: Harnessing Multidimensional Indicators of Scholarly Impact)Jul 06 2015This chapter discusses altmetrics (short for "alternative metrics"), an approach to uncovering previously-invisible traces of scholarly impact by observing activity in online tools and systems. I argue that citations, while useful, miss many important ... More
The Rogers-Ramanujan Identities, the Finite General Linear Groups, and the Hall-Littlewood PolynomialsDec 09 1997The Rogers-Ramanujan identities have been studied from the viewpoints of combinatorics, number theory, affine Lie algebras, statistical mechanics, and quantum field theory. This note connects the Rogers-Ramanujan identities with the finite general linear ... More
Moduli of PT-semistable objects IINov 29 2010May 04 2011We generalise the techniques of semistable reduction for flat families of sheaves to the setting of the derived category $D^b(X)$ of coherent sheaves on a smooth projective three-fold $X$. Then we construct the moduli of PT-semistable objects in $D^b(X)$ ... More
Denominators and Differences of Boundary Slopes for (1,1)-KnotsJan 26 2013Jul 23 2014We show that every nonzero integer occurs in the denominator of a boundary slope for infinitely many (1,1)-knots and that infinitely many (1,1)-knots have boundary slopes of arbitrarily small difference. Specifically, we prove that for any integers m, ... More
Learning Parameters for Weighted Matrix Completion via Empirical EstimationDec 31 2014Apr 02 2015Recently theoretical guarantees have been obtained for matrix completion in the non-uniform sampling regime. In particular, if the sampling distribution aligns with the underlying matrix's leverage scores, then with high probability nuclear norm minimization ... More
Iterative Hard Thresholding for Weighted Sparse ApproximationDec 12 2013Jan 07 2015Recent work by Rauhut and Ward developed a notion of weighted sparsity and a corresponding notion of Restricted Isometry Property for the space of weighted sparse signals. Using these notions, we pose a best weighted sparse approximation problem, i.e. ... More
The exponential of the spin representation of the Lorentz algebraJan 29 2012As discussed in a previous article, any (real) Lorentz algebra element possess a unique orthogonal decomposition as a sum of two mutually annihilating decomposable Lorentz algebra elements. In this article, this concept is extended to the spin representation ... More
The loop-erased random walk and the uniform spanning tree on the four-dimensional discrete torusFeb 23 2006Jul 29 2007Let x and y be points chosen uniformly at random from $\Z_n^4$, the four-dimensional discrete torus with side length n. We show that the length of the loop-erased random walk from x to y is of order $n^2 (\log n)^{1/6}$, resolving a conjecture of Benjamini ... More
T-structures on elliptic fibrationsSep 10 2015We consider t-structures that naturally arise on elliptic fibrations. By filtering the category of coherent sheaves on an elliptic fibration using the torsion pairs corresponding to these t-structures, we prove results describing equivalences of t-structures ... More
A Polynomial Bound on the Regularity of an Ideal in Terms of Half of the SyzygiesDec 01 2011Let K be a field and let S = K[x_1, ..., x_n] be a polynomial ring. Consider a homogenous ideal I in S. Let t_i denote reg(Tor_i (S/I, K)), the maximal degree of an ith syzygy of S/I. We prove bounds on the numbers t_i for i > n/2 purely in terms of the ... More
The minimum rank problem over finite fieldsJan 18 2008The structure of all graphs having minimum rank at most k over a finite field with q elements is characterized for any possible k and q. A strong connection between this characterization and polarities of projective geometries is explained. Using this ... More
Stillman's Question for Exterior Algebras and Herzog's Conjecture on Betti Numbers of Syzygy ModulesJul 30 2013Jan 24 2018Let K be a field of characteristic 0 and consider exterior algebras of finite dimensional K-vector spaces. In this short paper we exhibit principal quadric ideals in a family whose Castelnuovo-Mumford regularity is unbounded. This negatively answers the ... More
Rigorous results for a population model with selection II: genealogy of the populationJul 01 2015We consider a model of a population of fixed size $N$ undergoing selection. Each individual acquires beneficial mutations at rate $\mu_N$, and each beneficial mutation increases the individual's fitness by $s_N$. Each individual dies at rate one, and ... More
The number of small blocks in exchangeable random partitionsNov 09 2009Jul 12 2010Suppose $\Pi$ is an exchangeable random partition of the positive integers and $\Pi_n$ is its restriction to $\{1, ..., n\}$. Let $K_n$ denote the number of blocks of $\Pi_n$, and let $K_{n,r}$ denote the number of blocks of $\Pi_n$ containing $r$ integers. ... More
Generalized equivariant homology on simplicial complexesMar 08 2011A careful account is given of generalized equivariant homology theories on the category of topological pairs acted on by a group. In particular, upon restriction to the category of equivariant simplicial complexes, the equivalence of equivariant simplicial ... More
Free Diffusions and Property AOJul 07 2009We consider von Neumann algebras generated by the stationary laws of free stochastic differential equations of the form $dX_t = dS_t -1/2 DV(X_t)$ for a suitably convex multivariate noncommutative polynomial $V$. Using techniques of Guionnet and Shlyakhtenko, ... More
Stability and Fourier-Mukai transforms on elliptic fibrationsJun 19 2012Jan 17 2014We systematically develop Bridgeland's and Bridgeland-Maciocia's techniques for studying elliptic fibrations, and identify criteria that ensure 2-term complexes are mapped to torsion-free sheaves under a Fourier-Mukai transform. As an application, we ... More
The Kodaira dimension of spaces of rational curves on low degree hypersurfacesMay 29 2003For a hypersurface in complex projective space $X\subset \PP^n$, we investigate the singularities and Kodaira dimension of the Kontsevich moduli spaces $\Kbm{0,0}{X,e}$ parametrizing rational curves of degree $e$ on $X$. If $d+e \leq n$ and $X$ is a general ... More
Stein's Method and Non-Reversible Markov ChainsDec 09 1997Aug 17 2004Let W be either the number of descents or inversions of a permutation. Stein's method is applied to show that W satisfies a central limit theorem with error rate n^(-1/2). The construction of an exchangeable pair (W,W') used in Stein's method is non-trivial ... More
Descent algebras, hyperplane arrangements, and shuffling cardsJan 20 1998Jul 15 1999Two notions of riffle shuffling on finite Coxeter groups are given: one using Solomon's descent algebra and another using random walk on chambers of hyperplane arrangements. These coincide for types $A$,$B$,$C$, $H_3$, and rank two groups. Both notions ... More
On the maximal graded shifts of ideals and modulesJan 24 2018We generalize a result of Eisenbud-Huneke-Ulrich on the maximal graded shifts of a module with prescribed annihilator and prove a linear regularity bound for ideals in a polynomial ring depending only on the first $p - c$ steps in the resolution, where ... More
Relations among conditional probabilitiesAug 08 2008We describe a Groebner basis of relations among conditional probabilities in a discrete probability space, with any set of conditioned-upon events. They may be specialized to the partially-observed random variable case, the purely conditional case, and ... More
Jørgensen Number and ArithmeticityMay 08 2009A J{\o}rgensen group is a non-elementary Kleinian group that can be generated by two elements for which equality holds in J{\o}rgensen's Inequality. This paper shows that the only torsion-free J{\o}rgensen group is the figure-eight knot group, identifies ... More
Fourier-Mukai transforms of slope stable torsion-free sheaves on a product elliptic threefoldOct 09 2017On the product elliptic threefold $X = C \times S$ where $C$ is an elliptic curve and $S$ is a K3 surface of Picard rank 1, we define a notion of limit tilt stability, which satisfies the Harder-Narasimhan property. We show that under the Fourier-Mukai ... More
On some moduli of complexes on K3 surfacesMar 07 2012We consider moduli stacks of Bridgeland semistable objects that previously had only set-theoretic identifications with Uhlenbeck compactification spaces. On a K3 surface $X$, we give examples where such a moduli stack is isomorphic to a moduli stack of ... More
The Delaunay tessellation in hyperbolic spaceAug 22 2013Aug 05 2016The Delaunay tessellation of a locally finite subset of hyperbolic space is constructed using convex hulls in Euclidean space of one higher dimension. For finite and lattice-invariant sets it is proven to be a polyhedral decomposition, and versions (necessarily ... More
Affine shuffles, shuffles with cuts, the Whitehouse module, and patience sortingOct 18 1999May 12 2000Type A affine shuffles are compared with riffle shuffles followed by a cut. Although these probability measures on the symmetric group S_n are different, they both satisfy a convolution property. Strong evidence is given that when the underlying parameter ... More
Applications of Symmetric Functions to Cycle and Subsequence Structure after ShufflesFeb 22 2001Jan 29 2002Using symmetric function theory, we study the cycle structure and increasing subsequence structure of permutations after various shuffling methods, emphasizing the role of Cauchy type identities and the Robinson-Schensted-Knuth correspondence. One consequence ... More
Random matrix theory over finite fields: a surveyMar 28 2000Mar 27 2001First we survey generating function methods for obtaining useful probability estimates about random matrices in the finite classical groups. Then we describe a probabilistic picture of conjugacy classes which is coherent and beautiful. Connections are ... More
Bijective Proofs for "Enumerative Properties of Ferrers Graphs"Dec 15 2003Recently, Ehrenborg and Van Willenburg defined a class of bipartite graphs that correspond naturally to Ferrers diagrams, and proved several results about them. We give bijective proofs for the (already known) expressions for the number of spanning trees ... More
Multiplier Ideals of Sufficiently General PolynomialsMar 17 2003It is well known that the multiplier ideal $\multr{I}$ of an ideal $I$ determines in a straightforward way the multiplier ideal $\multr{f}$ of a sufficiently general element $f$ of $I$. We give an explicit condition on a polynomial $f \in \CC[x_1,...,x_n]$ ... More
Multiplier Ideals of Monomial IdealsMar 31 2000In this note we calculate the multiplier ideal associated to an arbitrary monomial ideal in C^n. We discuss applications to the calculation of log canonical thresholds.
Angle-action estimation in a general axisymmetric potentialAug 14 2012The usefulness of angle-action variables in galaxy dynamics is well known, but their use is limited due to the difficulty of their calculation in realistic galaxy potentials. Here we present a method for estimating angle-action variables in a realistic ... More
Algorithmic detection and description of hyperbolic structures on closed 3-manifolds with solvable word problemFeb 19 2001Jan 23 2002We outline a rigorous algorithm, first suggested by Casson, for determining whether a closed orientable 3-manifold M is hyperbolic, and to compute the hyperbolic structure, if one exists. The algorithm requires that a procedure has been given to solve ... More
Fluctuations of the empirical quantiles of independent Brownian motionsDec 22 2008Aug 18 2010We consider $n$ independent, identically distributed one-dimensional Brownian motions, $B_j(t)$, where $B_j(0)$ has a rapidly decreasing, smooth density function $f$. The empirical quantiles, or pointwise order statistics, are denoted by $B_{j:n}(t)$, ... More
Semisimple orbits of Lie algebras and card shuffling measures on Coxeter groupsDec 09 1997Jan 17 1998Solomon's descent algebra is used to define a family of signed measures M(W,x) for a finite Coxeter group W and non-zero x. The measures corresponding to W of types A and B are known to arise from the theory of card shuffling and to be related to the ... More
Machine Learning With Feature Selection Using Principal Component Analysis for Malware Detection: A Case StudyFeb 10 2019Cyber security threats have been growing significantly in both volume and sophistication over the past decade. This poses great challenges to malware detection without considerable automation. In this paper, we have proposed a novel approach by extending ... More
Fully-projected subsetsFeb 12 2017Let $k$ and $i_1,\ldots,i_n$ be natural numbers. Place $k$ balls into a multidimensional box of $i_1\times\cdots \times i_n$ cells, no more than one ball to each cell, such that the projections to each of the coordinate axes have cardinalities $i_1,\ldots,i_n$, ... More
Cycle indices for the finite classical groupsDec 09 1997This paper defines and develops cycle indices for the finite classical groups. These tools are then applied to study properties of a random matrix chosen uniformly from one of these groups. Properties studied by this technique will include semisimplicity, ... More
Variations of the solution to a stochastic heat equationDec 31 2005Nov 22 2007We consider the solution to a stochastic heat equation. This solution is a random function of time and space. For a fixed point in space, the resulting random function of time, $F(t)$, has a nontrivial quartic variation. This process, therefore, has infinite ... More
A Polynomial Invariant Of Twisted Graph DiagramsJun 19 2007Twisted graph diagrams are virtual graph diagrams with bars on edges. A bijection between abstract graph diagrams and twisted graph diagrams is constructed. Then a polynomial invariant of Yamada-type is developed which provides a lower bound for the virtual ... More
Dialog-based Language LearningApr 20 2016Aug 23 2016A long-term goal of machine learning research is to build an intelligent dialog agent. Most research in natural language understanding has focused on learning from fixed training sets of labeled data, with supervision either at the word level (tagging, ... More
The geometry of cyclic hyperbolic polygonsJan 25 2011Jun 30 2015A hyperbolic polygon is defined to be cyclic, horocyclic, or equidistant if its vertices lie on a metric circle, horocycle, or a component of the equidistant locus to a hyperbolic geodesic, respectively. Convex such $n$-gons are parametrized by the subspaces ... More
A sharp analysis of the mixing time for random walk on rooted treesAug 08 2009We define an analog of Plancherel measure for the set of rooted unlabeled trees on n vertices, and a Markov chain which has this measure as its stationary distribution. Using the combinatorics of commutation relations, we show that order n^2 steps are ... More
Commutation relations and Markov chainsDec 09 2007Jan 20 2008It is shown that the combinatorics of commutation relations is well suited for analyzing the convergence rate of certain Markov chains. Examples studied include random walk on irreducible representations, a local random walk on partitions whose stationary ... More
An Inductive Proof of the Berry-Esseen Theorem for Character RatiosMar 11 2005Aug 08 2006Bolthausen used a variation of Stein's method to give an inductive proof of the Berry-Esseen theorem for sums of independent, identically distributed random variables. We modify this technique to prove a Berry-Esseen theorem for character ratios of a ... More
Stein's Method and Minimum Parsimony Distance after ShufflesOct 29 2004Motivated by Bourque and Pevzner's simulation study of the parsimony method for studying genome rearrangement, Berestycki and Durrett used techniques from random graph theory to prove that the minimum parsimony distance after iterating the random transposition ... More
A New Bound for Kloosterman SumsMay 22 2001Jun 21 2001We give generating functions for Gauss sums for finite general linear and unitary groups. For the general linear case only our method of proof is new, but we deduce a bound on Kloosterman sums which is sometimes sharper than Deligne's bound from algebraic ... More
Applications of the Brauer complex: card shuffling, permutation statistics, and dynamical systemsFeb 14 2001May 09 2001By algebraic group theory, there is a map from the semisimple conjugacy classes of a finite group of Lie type to the conjugacy classes of the Weyl group. Picking a semisimple class uniformly at random yields a probability measure on conjugacy classes ... More
A Probabilistic Proof of the Rogers Ramanujan IdentitiesJan 13 2000Nov 21 2000The asymptotic probability theory of conjugacy classes of the finite general linear and unitary groups leads to a probability measure on the set of all partitions of natural numbers. A simple method of understanding these measures in terms of Markov chains ... More
Stein's method, heat kernel, and traces of powers of elements of compact Lie groupsMay 07 2010Combining Stein's method with heat kernel techniques, we show that the trace of the jth power of an element of U(n,C), USp(n,C) or SO(n,R) has a normal limit with error term of order j/n. In contrast to previous works, here j may be growing with n. The ... More
Bounding the area of a centered dual two-cell below, given lower bounds on its side lengthsAug 31 2015Suppose $C$ is a compact, $n$-edged two-cell of the centered dual decomposition of a locally finite set in the hyperbolic plane, a coarsening of the Delaunay tessellation which was introduced in the author's prior work. We describe an effectively computable ... More
Determining the velocity dispersion of the thick discMay 24 2012Jul 23 2012We attempt to recover the mean vertical velocity and vertical velocity dispersion as a function of the Galactic height for a sample drawn from a realistic Galaxy distribution function by following the method presented in Moni Bidin et al. (2012). We find ... More
Enhanced $thj$ signal at the LHC with $h\rightarrow γγ$ decay and $\mathcal{CP}$-violating top-Higgs couplingOct 10 2014Apr 03 2015We study the observability of non-standard top Yukawa couplings in the $pp\rightarrow t(\rightarrow \ell \nu_\ell b ) h(\rightarrow \gamma\gamma)j$ channel at 14 TeV high-luminosity LHC (HL-LHC). The small diphoton branching ratio is enhanced when the ... More
Efficient Normal-Form Parsing for Combinatory Categorial GrammarJun 02 1996Under categorial grammars that have powerful rules like composition, a simple n-word sentence can have exponentially many parses. Generating all parses is inefficient and obscures whatever true semantic ambiguities are in the input. This paper addresses ... More
The radial defocusing nonlinear Schrödinger equation in three space dimensionsJan 20 2014We study the defocusing nonlinear Schr\"odinger equation in three space dimensions. We prove that any radial solution that remains bounded in the critical Sobolev space must be global and scatter. In the energy-supercritical setting, we employ a space-localized ... More
Speculative Parallel Evaluation Of Classification Trees On GPGPU Compute EnginesNov 06 2011We examine the problem of optimizing classification tree evaluation for on-line and real-time applications by using GPUs. Looking at trees with continuous attributes often used in image segmentation, we first put the existing algorithms for serial and ... More
Stillman's Question for Exterior AlgebrasJul 30 2013Let K be any field and consider exterior algebras of a finite dimensional K-vector space. In this very short paper we exhibit principal quadric ideals in a family whose Castelnuovo Mumford regularity is unbounded.
Fluctuations for the Ginzburg-Landau $\nabla φ$ Interface Model on a Bounded DomainFeb 02 2010Jun 08 2010We study the massless field on $D_n = D \cap \tfrac{1}{n} \Z^2$, where $D \subseteq \R^2$ is a bounded domain with smooth boundary, with Hamiltonian $\CH(h) = \sum_{x \sim y} \CV(h(x) - h(y))$. The interaction $\CV$ is assumed to be symmetric and uniformly ... More
Rationality and the Jordan-Gatti-Viniberghi decompositionJan 19 2012Sep 14 2012We verify the conjecture of [10] and use it to prove that the semisimple parts of the rational Jordan-Kac-Vinberg decompositions of a rational vector all lie in a single rational orbit.
Semisimple orbits of Lie algebras and card shuffling on Coxeter groupsMar 02 1999Aug 26 1999Random walk on the chambers of hyperplanes arrangements is used to define a family of card shuffling measures $H_{W,x}$ for a finite Coxeter group W and real $x \neq 0$. By algebraic group theory, there is a map from the semisimple orbits of the adjoint ... More
A probabilistic approach toward the finite general linear and unitary groupsDec 09 1997Probabilistic algorithms are applied to prove theorems about the finite general linear and unitary groups which are typically proved by techniques such as character theory and Moebius inversion. Among the theorems studied are Steinberg's count of unipotent ... More
New Electrochemical Characterization Methods for Nanocomposite Supercapacitor ElectrodesJun 02 2014Apr 19 2016Supercapacitor electrodes fabricated from a nanocomposite consisting of multiwall carbon nanotubes and titanium oxide nanoparticles were characterized electrochemically. Conventional electrochemical characterizations cyclic voltammetry and galvanostatic ... More
The distribution of r-free numbers in arithmetic progressionsFeb 25 2013A positive integer n is called r-free if n is not divisible by the r-th power of a prime. Generalizing earlier work of Orr, we provide an upper bound of Bombieri-Vinogradov type for the r-free numbers in arithmetic progressions.
Dynamics of the evolving Bolthausen-Sznitman coalescentDec 12 2011Consider a population of fixed size that evolves over time. At each time, the genealogical structure of the population can be described by a coalescent tree whose branches are traced back to the most recent common ancestor of the population. As time goes ... More
Rigorous results for a population model with selection I: evolution of the fitness distributionJul 01 2015We consider a model of a population of fixed size $N$ undergoing selection. Each individual acquires beneficial mutations at rate $\mu_N$, and each beneficial mutation increases the individual's fitness by $s_N$. Each individual dies at rate one, and ... More
New directions in the pursuit of Majorana fermions in solid state systemsFeb 06 2012The 1937 theoretical discovery of Majorana fermions--whose defining property is that they are their own anti-particles--has since impacted diverse problems ranging from neutrino physics and dark matter searches to the fractional quantum Hall effect and ... More