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
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
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
Auslander's Theorem for permutation actions on noncommutative algebrasApr 28 2017Sep 11 2018When $A = \mathbb{k}[x_1, \ldots, x_n]$ and $G$ is a small subgroup of $\operatorname{GL}_n(\mathbb{k})$, Auslander's Theorem says that the skew group algebra $A \# G$ is isomorphic to $\operatorname{End}_{A^G}(A)$ as graded algebras. We prove a generalization ... 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
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
Metropolis-Hastings Generative Adversarial NetworksNov 28 2018May 17 2019We introduce the Metropolis-Hastings generative adversarial network (MH-GAN), which combines aspects of Markov chain Monte Carlo and GANs. The MH-GAN draws samples from the distribution implicitly defined by a GAN's discriminator-generator pair, as opposed ... 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 2019May 17 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
Planetary Nebulae Shaped By Common Envelope EvolutionJul 16 2018The morphologies of planetary nebula have long been believed to be due to wind shaping processes in which a fast wind from the central star impacts a previously ejected envelope. Asymmetries assumed to exist in the slow wind envelope lead to inertial ... 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
The Formation and Evolution of Wind-Capture Disks In Binary SystemsNov 07 2012May 03 2013We study the formation, evolution and physical properties of accretion disks formed via wind capture in binary systems. Using the AMR code AstroBEAR, we have carried out high resolution 3D simulations that follow a stellar mass secondary in the co-rotating ... More
An Intriguing Failing of Convolutional Neural Networks and the CoordConv SolutionJul 09 2018Dec 03 2018Few ideas have enjoyed as large an impact on deep learning as convolution. For any problem involving pixels or spatial representations, common intuition holds that convolutional neural networks may be appropriate. In this paper we show a striking counterexample ... More
Mass Transfer and Disc Formation in AGB Binary SystemsFeb 20 2017Apr 13 2017We investigate mass transfer and the formation of disc in binary systems using a combination of numerical simulations and theory. We consider six models distinguished by binary separation, secondary mass and outflow mechanisms. Each system consists of ... More
Wind-accelerated orbital evolution in binary systems with giant starsMay 04 2017Aug 31 2017Using 3D radiation-hydrodynamic simulations and analytic theory, we study the orbital evolution of asymptotic-giant-branch (AGB) binary systems for various initial orbital separations and mass ratios, and thus different initial accretion modes. The time ... 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
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
On the discriminant of twisted tensor productsJun 09 2016Dec 21 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
Exponentially convergent data assimilation algorithm for Navier-Stokes equationsDec 23 2017The paper presents a new state estimation algorithm for a bilinear equation representing the Fourier- Galerkin (FG) approximation of the Navier-Stokes (NS) equations on a torus in R2. This state equation is subject to uncertain but bounded noise in the ... 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
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
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
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
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
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
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
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
A Minimal Subsystem of the Kari-Culik TilingsOct 06 2014Sep 29 2015The Kari-Culik tilings are formed from a set of 13 Wang tiles that tile the plane only aperiodically. They are the smallest known set of Wang tiles to do so and are not as well understood as other examples of aperiodic Wang tiles. We show that the $\mathbb{Z}^2$ ... More
The combinatorics of biased riffle shufflesDec 09 1997This paper studies biased riffle shuffles, first defined by Diaconis, Fill, and Pitman. These shuffles generalize the well-studied Gilbert-Shannon-Reeds shuffle and convolve nicely. An upper bound is given for the time for these shuffles to converge to ... More
A $2$-compact group as a spetsJun 03 2019Jun 12 2019In 1998 Malle introduced spetses which are mysterious objects with non-real Weyl groups. In algebraic topology, a $p$-compact group $\mathbf{X}$ is a space which is a homotopy-theoretic $p$-local analogue of a compact Lie group. A connected $p$-compact ... More
Asymmetric Dark MatterAug 21 2013Sep 17 2013We review the theoretical framework underlying models of asymmetric dark matter, describe astrophysical constraints which arise from observations of neutron stars, and discuss the prospects for detecting asymmetric dark matter.
WIMPless Dark Matter: Models and SignaturesDec 01 2010We consider experimental signatures of WIMPless dark matter. We focus on models where the WIMPless dark matter candidate is a Majorana fermion, and dark matter scattering is predominantly spin-dependent. These models can be probed by IceCube/DeepCore, ... More
Construction of Regular Non-Atomic Strictly-Positive Measures in Second-Countable Locally Compact Non-Atomic Hausdorff SpacesJul 14 2018Feb 21 2019This paper presents a constructive proof of the existence of a regular non-atomic strictly-positive measure on any second-countable locally compact non-atomic Hausdorff space. This construction involves a sequence of finitely-additive set functions defined ... More
Improving on bold play when the gambler is restrictedDec 18 2004Suppose a gambler starts with a fortune in (0,1) and wishes to attain a fortune of 1 by making a sequence of bets. Assume thay whenever the gambler stakes the amount s, the gambler's fortune increases by s with probability w and decreases by s with probability ... More
When does randomness come from randomness?Aug 20 2015Mar 08 2016A result of Shen says that if $F\colon2^{\mathbb{N}}\rightarrow2^{\mathbb{N}}$ is an almost-everywhere computable, measure-preserving transformation, and $y\in2^{\mathbb{N}}$ is Martin-L\"of random, then there is a Martin-L\"of random $x\in2^{\mathbb{N}}$ ... 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
Totally geodesic surfaces and homologyJan 23 2006Apr 23 2009We construct examples of hyperbolic rational homology spheres and hyperbolic knot complements in rational homology spheres containing closed embedded totally geodesic surfaces.
A note on the Brown--Erdős--Sós conjecture in groupsFeb 20 2019Apr 09 2019We show that a dense subset of a sufficiently large group multiplication table contains either a large part of the addition table of the integers modulo some $k$, or the entire multiplication table of a certain large abelian group, as a subgrid. As a ... 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
The classification of compact simply connected biquotients in dimension 6 and 7Mar 24 2014Aug 23 2016We classify all compact simply connected biquotients of dimension 6 and 7. For each $6$-dimensional biquotient, all pairs of groups $(G,H)$ and homomorphisms $H\rightarrow G\times G$ giving rise to it are classified.
Rationally $4$-periodic biquotientsMay 25 2016Aug 22 2017An $n$-dimensional manifold $M$ is said to be rationally $4$-periodic if there is an element $e\in H^4(M;\mathbb{Q})$ with the property that cupping with $e$, $\cdot \cup e:H^\ast(M;\mathbb{Q})\rightarrow H^{\ast + 4}(M;\mathbb{Q})$ is injective for $0< ... More
The Doorways Problem and Sturmian WordsMay 01 2017The doorways problem considers adjacent parallel hallways of unit width each with a single doorway (aligned with integer lattice points) of unit width. It then asks, what are the properties of lines that pass through each doorway? Configurations of doorways ... 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
A relation between higher-rank PT stable objects and quotients of coherent sheavesOct 02 2018On a smooth projective threefold, we construct an essentially surjective functor $\mathcal{F}$ from a category of two-term complexes to a category of quotients of coherent sheaves, and describe the fibers of this functor. Under a coprime assumption on ... 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
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
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
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
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
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
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
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
Purification and characterization of a novel archaeo-eukaryotic primase from MimivirusAug 29 2016Oct 04 2016DNA replication is a process which is common to all domains of life yet different replication mechanisms are seen among different organisms. The mechanism of replication on such a structure is not yet understood. With this bigger picture in mind, we have ... More
Monopole Quantum Numbers in the Staggered Flux Spin LiquidApr 04 2008Apr 17 2008Algebraic spin liquids, which are exotic gapless spin states preserving all microscopic symmetries, have been widely studied due to potential realizations in frustrated quantum magnets and the cuprates. At low energies, such putative phases are described ... More
The local maxima of maximal injectivity radius among hyperbolic surfacesJun 26 2015The function on the Teichmueller space of complete, orientable, finite-area hyperbolic surfaces of a fixed topological type that assigns to a hyperbolic surface its maximal injectivity radius has no local maxima that are not global maxima.
The isomorphism problem for quantum affine spaces, homogenized quantized Weyl algebras, and quantum matrix algebrasMay 27 2016Bell and Zhang have shown that if $A$ and $B$ are two connected graded algebras finitely generated in degree one that are isomorphic as ungraded algebras, then they are isomorphic as graded algebras. We exploit their result to solve the isomorphism problem ... More
Dimension of the SLE light cone, the SLE fan, and SLE$_κ(ρ)$ for $κ\in (0,4)$ and $ρ\in [\tfracκ{2}-4,-2)$Jun 22 2016Suppose that $h$ is a Gaussian free field (GFF) on a planar domain. Fix $\kappa \in (0,4)$. The SLE$_\kappa$ light cone ${\mathbf L}(\theta)$ of $h$ with opening angle $\theta \in [0,\pi]$ is the set of points reachable from a given boundary point by ... More
Moduli of PT-Semistable Objects INov 25 2010We show boundedness for PT-semistable objects of any Chern classes on a smooth projective three-fold $X$. Then we show that the stack of objects in the heart $\langle \Coh_{\leq 1}(X), \Coh_{\geq 2}(X)[1] \rangle$ satisfies a version of the valuative ... 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
Quasi-stationary Random Overlap Structures and the Continuous CascadesJun 11 2008Jun 18 2009A random overlap structure (ROSt) is a measure on pairs (X,Q) where X is a locally finite sequence in the real line with a maximum and Q a positive semidefinite matrix of overlaps intrinsic to the particles X. Such a measure is said to be quasi-stationary ... More
Three new almost positively curved manifoldsApr 01 2015Oct 23 2018A Riemannian manifold is called almost positively curved if the set of points for which all $2$-planes have positive sectional curvature is open and dense. We find three new examples of almost positively curved manifolds: $Sp(3)/Sp(1)^2$, and two circle ... 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
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
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
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
Estimation of the r-th derivative of a density function by the tilted kernel estimatorOct 27 2015We consider the problem of estimating the s-th derivative of a density function f by the tilted Kernel estimator introduced in Hall and Doosti (2012). Then we further show this estimator achieves the same convergence rate, in probability, the wavelet ... More
Novel Dark Matter Models and Detection StrategiesOct 11 2012We consider the impact of relaxing some typical assumptions about dark matter interactions, including isospin-invariance, elastic scattering and contact interactions. We show that detection strategies with neutrino detectors, gamma-ray searches, new direct ... More
A Brief Comment on Instanton-like Singularities and Cosmological HorizonsApr 15 2002Apr 27 2002We argue that in the presence of instanton-like singularities, the existence of cosmological horizons can become frame-dependent, ie. a horizon which appears in Einstein frame may not appear in string frame. We speculate on the relation between instanton-like ... 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
Deformation Theory of Asymptotically Conical Coassociative 4-foldsNov 05 2004Oct 26 2009We study coassociative 4-folds N in R^7 which are asymptotically conical to a cone C with rate lambda<1. If lambda is in the interval [-2,1) and generic, we show that the moduli space of coassociative deformations of N which are also asymptotically conical ... 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
On the close interaction between algorithmic randomness and constructive/computable measure theoryDec 08 2018Mar 16 2019This is a survey of constructive and computable measure theory with an emphasis on the close connections with algorithmic randomness. We give a brief history of constructive measure theory from Brouwer to the present, emphasizing how Schnorr randomness ... 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.
Covariant bandlimitation from Generalized Uncertainty PrinciplesMar 28 2019It is widely believed that combining the uncertainty principle with gravity will lead to an effective minimum length scale. A particular challenge is to specify this scale in a coordinate-independent manner so that covariance is not broken. Here we examine ... More
Probing the flavor dependence of proton's light-quark sea in the SeaQuest experimentJul 31 2019Surprisingly large flavor asymmetry of the light-quark sea in the proton was reported in deep-inelastic scattering and Drell-Yan experiments. The Bjorken-$x$ dependence of the $\bar{d}/\bar{u}$ ratio extracted from the Fermilab E866 experiment also revealed ... More
Torsion pairs and filtrations in abelian categories with tilting objectsFeb 13 2013Given a noetherian abelian category $\mathcal Z$ of homological dimension two with a tilting object $T$, the abelian category $\mathcal Z$ and the abelian category of modules over $\text{End} (T)^{\textit{op}}$ are related by a sequence of two tilts; ... More
Global existence for semilinear wave equations exterior to nontrapping obstaclesOct 16 2002Feb 21 2003In this paper, we show global existence, in spatial dimensions greater than or equal to four, for semilinear wave equations with quadratic nonlinearities exterior to a nontrapping obstacle. This extends the previous work of Shibata-Tsutsumi and Hayashi. ... More
Global Strichartz Estimates for Solutions to the Wave Equation Exterior to a Convex ObstacleOct 15 2002Jul 20 2004In this paper, we show that certain local Strichartz estimates for solutions of the wave equation exterior to a convex obstacle can be extended to estimates that are global in both space and time. This extends the work that was done previously by H. Smith ... More
Polynomial Bridgeland Stable Objects and Reflexive SheavesDec 19 2011Aug 01 2012On a smooth projective threefold, we show that there are only two isomorphism types for the moduli of stable objects with respect to Bayer's standard polynomial Bridgeland stability - the moduli of Gieseker-stable sheaves and the moduli of PT-stable objects ... More
A Survey of Exoplanetary Detection TechniquesMay 07 2018Exoplanets, or planets outside our own solar system, have long been of interest to astronomers; however, only in the past two decades have scientists had the technology to characterize and study planets so far away from us. With advanced telescopes and ... More
Isomorphisms of some quantum spacesOct 31 2012May 16 2013We consider a series of questions that grew out of determining when two quantum planes are isomorphic. In particular, we consider a similar question for quantum matrix algebras and certain ambiskew polynomial rings. Additionally, we modify a result by ... More
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
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
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