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ADsafety: Type-Based Verification of JavaScript SandboxingJun 25 2015Web sites routinely incorporate JavaScript programs from several sources into a single page. These sources must be protected from one another, which requires robust sandboxing. The many entry-points of sandboxes and the subtleties of JavaScript demand ... More

Putting in All the Stops: Execution Control for JavaScriptFeb 08 2018Scores of compilers produce JavaScript, enabling programmers to use many languages on the Web, reuse existing code, and even use Web IDEs. Unfortunately, most compilers expose the browser's compromised execution model, so long-running programs freeze ... More

Putting in All the Stops: Execution Control for JavaScriptFeb 08 2018Apr 16 2018Scores of compilers produce JavaScript, enabling programmers to use many languages on the Web, reuse existing code, and even use Web IDEs. Unfortunately, most compilers inherit the browser's compromised execution model, so long-running programs freeze ... More

A New Slant on Lebesgue's Universal Covering ProblemJan 29 2014Feb 19 2014Lebesgue's universal covering problem is re-examined using computational methods. This leads to conjectures about the nature of the solution which if correct could provide a blueprint for a complete solution. Empirical lower bounds for the minimal area ... More

A White Hole Model of the Big BangMar 04 1998A model of the universe as a very large white hole provides a useful alternative inhomogeneous theory to pit against the homogeneous standard FLRW big bang models. The white hole would have to be sufficiently large that we can fit comfortably inside the ... More

An Acataleptic UniverseApr 24 2013John Wheeler advocated the principle that information is the foundation of physics and asked us to reformulate physics in terms of bits. The goal is to consider what we know already and work out a new mathematical theory in which space, time and matter ... More

A Generalised Stern-Brocot Tree from Regular Diophantine QuadruplesMar 06 1999Diophantine quadruples are sets of four distinct positive integers such that the product of any two is one less than a square. All known examples belong to an infinite set which can be constructed recursively. Some observations on these regular solutions ... More

Some Rational Diophantine SextuplesFeb 13 1999A famous problem posed by Diophantus was to find sets of distinct positive rational numbers such that the product of any two is one less than a rational square. Some sets of six such numbers are presented and the computational algorithm used to find them ... More

Event Loops as First-Class Values: A Case Study in Pedagogic Language DesignFeb 02 2019The World model is an existing functional input-output mechanism for event-driven programming. It is used in numerous popular textbooks and curricular settings. The World model conflates two different tasks -- the definition of an event processor and ... More

The Small Scale Structure of Space-Time: A Bibliographical ReviewJun 26 1995Jan 26 1996This essay is a tour around many of the lesser known pregeometric models of physics, as well as the mainstream approaches to quantum gravity, in search of common themes which may provide a glimpse of the final theory which must lie behind them.

Symmetry in the Topological Phase of String TheoryApr 28 1995Sep 22 1995I present arguments to the affect that the topological phase of string theory must be event-symmetric. This motivates a search for a universal string group for discrete strings in event-symmetric space-time which unifies space-time symmetry with internal ... More

The pentaquark in K-plus-d total cross section dataMay 09 2004Jun 29 2004An analysis of $K^+$-d total cross section data is undertaken to explore possible effects of the recently observed resonance in the S=+1 hadronic system with mass around 1.55 GeV. It is found that a structure corresponding to the resonance is visible ... More

The Contribution of the Light Quark Condensate to the Pion-Nucleon Sigma TermMay 08 2003There has been a discrepancy between values of the pion-nucleon sigma term extracted by two different methods for many years. Analysis of recent high precision pion-nucleon data has widened the gap between the two determinations. It is argued that the ... More

Low-energy Antiproton Interaction with HeliumMay 02 1997An ab initio potential for the interaction of the neutral helium atom with antiprotons and protons is calculated using the Born-Oppenheimer approximation. Using this potential, the annihilation cross section for antiprotons in the energy range 0.01 microvolt ... More

A law of large numbers for weighted pluralityJun 27 2011May 30 2012Consider an election between k candidates in which each voter votes randomly (but not necessarily independently) and suppose that there is a single candidate that every voter prefers (in the sense that each voter is more likely to vote for this special ... More

Breakdown of analyticity for d-bar-b and Szego kernelsJul 29 1996The CR manifold M_m = { Im z_2= Re z_1^{2m} } (m=2,3,...) is the counterexample, which has been given by M. Christ and D. Geller, to analytic hypoellipticity of d-bar-b and real analyticity of the Szego kernel. In order to give a direct interpretation ... More

Dipaths of length at least double the minimum outdegreeAug 10 2016Aug 12 2016A special case of a conjecture by Thomass\'e is that any oriented graph with minimum outdegree k contains a dipath of length 2k. For the sake of proving whether or not a counterexample exists, we present reductions and establish bounds on both connectivity ... More

Latent heat of the large N finite temperature phase transitionJul 04 2005Reduced large N gauge theories have a phase with unbroken center symmetry and phases in which that symmetry is broken for Polyakov loops in one or more lattice directions. The phase with unbroken symmetry is associated with the zero temperature, infinite ... More

Absence of Physical Walls in Hot Gauge TheoriesOct 18 1995This paper shows that there are no {\em physical} walls in the deconfined, high-temperature phase of $Z(2)$ lattice gauge theory. In a Hamiltonian formulation, the interface in the Wilson lines is not physical. The line interface and its energy are interpreted ... More

Klein's Fundamental 2-Form of Second Kind for the $C_{ab}$ CurvesJan 04 2017Mar 17 2017In this paper, we derive the exact formula of Klein's fundamental 2-form of second kind for the so-called $C_{ab}$ curves. The problem was initially solved by Klein in the 19th century for the hyper-elliptic curves, but little progress had been seen for ... More

A Generalization of the Chow-Liu Algorithm and its Application to Statistical LearningFeb 10 2010We extend the Chow-Liu algorithm for general random variables while the previous versions only considered finite cases. In particular, this paper applies the generalization to Suzuki's learning algorithm that generates from data forests rather than trees ... More

Miura: Divisor Class Group ArithmeticDec 25 2015The Package Miura contains functions that compute divisor class group arithmetic for nonsingular curves. The package reduces computation in a divisor class group to that in the ideal class group via the isomorphism. The underlying quotient ring should ... More

Zassenhaus Conjecture for Integral Group Rings of Simple Linear GroupsDec 01 2015We prove that the Zassenhaus conjecture is true for $PSL(2,8)$ and $PSL(2,17)$. This is a continuation of research initiated by W. Kimmerle, M. Hertweck and C. H\"ofert.

Noncommutative Network ModelsApr 19 2018May 25 2018Network models, which abstractly are given by lax symmetric monoidal functors, are used to construct operads for modeling and designing complex networks. Many common types of networks can be modeled with simple graphs with edges weighted by a monoid. ... More

Connecting neutral current $B$ anomalies with the heaviness of the third familyMay 15 2019It is possible, and for several reasons attractive, to explain a collection of recent anomalies involving $b\rightarrow s\mu\mu$ processes with a $Z^{\prime}$ gauge boson coupled only to the third family in the weak eigenbasis. From this premise, requiring ... More

String Partons and Multiple QuantisationSep 16 1996I consider an algebraic construction of creation and annihilation operators for superstring and p-brane parton models. The result can be interpreted as a realisation of multiple quantisation and suggests a relationship between quantisation and dimension. ... More

Asymptotic Properties of Random Voronoi Cells with Arbitrary Underlying DensityNov 28 2018Dec 31 2018We consider the Voronoi diagram generated by $n$ i.i.d. $\mathbb{R}^{d}$-valued random variables with an arbitrary underlying probability density function $f$ on $\mathbb{R}^{d}$, and analyse the asymptotic behaviours of certain geometric properties, ... More

Asymptotic expansion of the Bergman kernel for weakly pseudoconvex tube domains in C^2Oct 10 1996In this paper we give an asymptotic expansion of the Bergman kernel for certain weakly pseudoconvex tube domains of finite type in C^2. Our asymptotic formula asserts that the singularity of the Bergman kernel at weakly pseudoconvex points is essentially ... More

CP and T violation in long baseline experiments with low energy neutrinoJun 13 2000Stimulated by the idea of PRISM, a very high intensity muon ring with rather low energy, we consider possibilities of observing CP-violation effects in neutrino oscillation experiments. Destructive sum of matter effect and CP-violation effect can be avoided ... More

A Theoretical Analysis of the BDeu Scores in Bayesian Network Structure LearningJul 15 2016Dec 02 2016In Bayesian network structure learning (BNSL), we need the prior probability over structures and parameters. If the former is the uniform distribution, the latter determines the correctness of BNSL. In this paper, we compare BDeu (Bayesian Dirichlet equivalent ... More

A Parallel/Recursive AlgorithmDec 23 2003Jun 17 2004An algorithm is discussed for converting a class of recursive processes to a parallel system. It is argued that this algorithm can be superior to certain methods currently found in the literature for an important subset of problems. The cases of homogeneous ... More

Covariant Energy-Momentum Conservation In General RelativityJan 08 1997Jan 17 1997A covariant formula for conserved currents of energy, momentum and angular-momentum is derived from a general form of Noethers theorem applied directly to the Einstein-Hilbert action of classical general relativity. Energy conservation in a closed big-bang ... More

Event Symmetric Open String Field TheoryMay 26 1994Field Theory on Event Symmetric space-time is constructed using the gauge group of discrete open strings. Models with invariant actions can be viewed as natural extensions of Matrix Models. The objective is to find a fundamental non-perturbative pre-theory ... More

Is the Universe Uniquely Determined by Invariance Under Quantisation?Mar 25 1996In this sequel to my previous paper, "Is String Theory in Knots?" I explore ways of constructing symmetries through an algebraic stepping process using knotted graphs. The hope is that this may lead to an algebraic formulation of string theory. In the ... More

Possible Candidates for SUSY E$_6$ GUT with an Intermediate ScaleFeb 02 1996We study the possibility of an intermediate scale existing in supersymmetric E$_6$ grand unified theories. The intermediate scale is demanded to be around $10^{12}$ GeV so that neutrinos can obtain masses suitable for explaining the experimental data ... More

The CMB in a Causal Set UniverseNov 19 2007We discuss Cosmic Microwave Background constraints on the causal set theory of quantum gravity, which has made testable predictions about the nature of dark energy. We flesh out previously discussed heuristic constraints by showing how the power spectrum ... More

Forest Learning from Data and its Universal CodingAug 01 2018Aug 03 2018This paper considers structure learning from data with $n$ samples of $p$ variables, assuming that the structure is a forest, using the Chow-Liu algorithm. Specifically, for incomplete data, we construct two model selection algorithms that complete in ... More

Nonparametric Estimation and On-Line Prediction for General Stationary Ergodic SourcesFeb 24 2010Jun 26 2010We proposed a learning algorithm for nonparametric estimation and on-line prediction for general stationary ergodic sources. We prepare histograms each of which estimates the probability as a finite distribution, and mixture them with weights to construct ... More

Complexifications of Morse functions and the directed Donaldson-Fukaya categoryAug 04 2008Sep 15 2009Let N be a closed four dimensional manifold which admits a self-indexing Morse function f with only 3 critical values 0,2,4, and a unique maximum and minimum. Let g be a Riemannian metric on N such that (f,g) is Morse-Smale. We construct from (N,f,g) ... More

Spectral projections and resolvent bounds for partially elliptic quadratic differential operatorsJun 17 2012Mar 04 2013We study resolvents and spectral projections for quadratic differential operators under an assumption of partial ellipticity. We establish exponential-type resolvent bounds for these operators, including Kramers-Fokker-Planck operators with quadratic ... More

Resolvent estimates for non-selfadjoint operators with double characteristicsOct 14 2009Sep 23 2011We study resolvent estimates for non-selfadjoint semiclassical pseudodifferential operators with double characteristics. Assuming that the quadratic approximation along the double characteristics is elliptic, we obtain polynomial upper bounds on the resolvent ... More

Minimal Problems for the Calibrated Trifocal VarietyNov 18 2016We determine the algebraic degree of minimal problems for the calibrated trifocal variety in computer vision. We rely on numerical algebraic geometry and the homotopy continuation software Bertini.

Neutrino Oscillation and CP ViolationAug 07 2000Sep 20 2000We reconsider the meaning of observing CP violation in neutrino oscillation.

A SUSY SO(10) GUT with an Intermediate ScaleAug 09 1995Aug 29 1995We examine a superpotential for an SO(10) GUT and show that if the parameters of the superpotential are in a certain region, the SO(10) GUT has an intermediate symmetry ${\rm SU(2)}_L \otimes {\rm SU(2)}_R \otimes {\rm SU(3)}_C \otimes {\rm U(1)}_{B-L}$ ... More

Monoenergetic Neutrino Beam for Long Baseline ExperimentsMar 15 2005Mar 21 2005In an electron capture process by a nucleus, emitted neutrinos are monoenergetic. By making use of it, we study how to get a completely monoenergetic neutrino beam in a long baseline experiment.

Testing galaxy formation scenarios with a new mass estimatorNov 30 2009We present the recently derived Wolf et al. (2009) mass estimator, which is applicable for spherical pressure-supported stellar systems spanning over ten orders of magnitude in luminosity, as a tool to test galaxy formation theories. We show that all ... More

Anti-holomorphic twistor and Symplectic structureMay 26 2000Jul 06 2000It is well known that the twisters, section of twister space, classify the almost complex structure on even dimensional Riemannian manifold $X$. In this paper, it will be proved that a harmonic and anti-holomorphic twister is equivalent ti a symplectic ... More

The Picard-Lefschetz theory of complexified Morse functionsJun 08 2009Given a closed manifold N and a self-indexing Morse function f: N --> R with up to four distinct Morse indices, we construct a symplectic Lefschetz fibration pi: E --> C which models the complexification of f on the disk cotangent bundle, f_C : D(T*N) ... More

On the index of harmonic maps from surfaces to complex projective spacesJan 31 2019We shall find the dimension of the spaces of holomorphic sections and holomorphic differentials of certain line bundles to give improved lower bounds on the index of complex isotropic harmonic maps from the sphere and torus to complex projective spaces. ... More

Universal Bayesian Measures and Universal Histogram SequencesMay 23 2014Consider universal data compression: the length $l(x^n)$ of sequence $x^n\in A^n$ with finite alphabet $A$ and length $n$ satisfies Kraft's inequality over $A^n$, and $-\frac{1}{n}\log \frac{P^n(x^n)}{Q^n(x^n)}$ almost surely converges to zero as $n$ ... More

A Construction of Bayesian Networks from Databases Based on an MDL PrincipleMar 06 2013This paper addresses learning stochastic rules especially on an inter-attribute relation based on a Minimum Description Length (MDL) principle with a finite number of examples, assuming an application to the design of intelligent relational database systems. ... More

The elliptic evolution of non-self-adjoint degree-2 HamiltoniansJan 03 2017We study the relationship between the classical Hamilton flow and the quantum Schr\"odinger evolution where the Hamiltonian is a degree-2 complex-valued polynomial. When the flow obeys a strict positivity condition equivalent to compactness of the evolution ... More

Two-Pion Exchange in Proton-Proton ScatteringJun 21 2006The contribution of the box and crossed two-pion-exchange diagrams to proton-proton scattering at 90$^{\circ}_{c.m.}$ is calculated in the laboratory momentum range up to 12 GeV/c. Relativistic form factors related to the nucleon and pion size and representing ... More

Two-Pion Exchange in proton-proton ScatteringAug 15 2001We present calculations of the two-pion-exchange contribution to proton-proton scattering at 90 degrees using form factors appropriate for representing the distribution of the constituent partons of the nucleon. Talk given at MENU2001, George Washington ... More

CP and T violation test in neutrino oscillationJan 16 1997I examine how large violation of CP and T is allowed in long base line neutrino experiments. When we attribute both the atmospheric neutrino anomaly and the solar neutrino deficit to neutrino oscillation we may have a sizable T violation effect proportional ... More

Absence of Physical Walls in Hot Gauge TheoriesAug 15 1996This paper shows that there are no physical walls in the deconfined, high-temperature phase of Z(2) lattice gauge theory. In a Hamiltonian formulation, the interface in the Wilson lines is not physical. The line interface and its energy are interpreted ... More

Singularities of the Bergman kernel for certain weakly pseudoconvex domainsJun 26 1996Consider the Bergman kernel $K^B(z)$ of the domain $\ellip = \{z \in \Comp^n ; \sum_{j=1}^n |z_j|^{2m_j}<1 \}$, where $m=(m_1,\ldots,m_n) \in \Natl^n$ and $m_n \neq 1$. Let $z^0 \in \partial \ellip$ be any weakly pseudoconvex point, $k \in \Natl$ the ... More

Quantum contextuality from a simple principle?Oct 22 2012Oct 24 2012In a recent article entitled "A simple explanation of the quantum violation of a fundamental inequality," Cabello proposes a condition on a class of probabilistic models that, he claims, gives the same bound on contextuality for the KCBS inequality as ... More

A Theoretical Analysis of the BDeu Scores in Bayesian Network Structure LearningJul 15 2016Jul 18 2016In Bayesian network structure learning (BNSL), we need the prior probability over structures and parameters. If the former is the uniform distribution, the latter determines the correctness of BNSL. In this paper, we compare BDeu (Bayesian Dirichlet equivalent ... More

Modeling mass independent of anisotropySep 01 2010By manipulating the spherical Jeans equation, Wolf et al. (2010) show that the mass enclosed within the 3D deprojected half-light radius r_1/2 can be determined with only mild assumptions about the spatial variation of the stellar velocity dispersion ... More

Etale homotopy theory of non-archimedean analytic spacesAug 11 2017We review the shape theory of $\infty$-topoi, and relate it with the usual cohomology of locally constant sheaves. Additionally, a new localization of profinite spaces is defined which allows us to extend the \'etale realization functor of Isaksen. We ... More

Dirac brushes (or, the fractional Fourier transform of Dirac combs)Dec 13 2018In analogy with the Poisson summation formula, we identify when the fractional Fourier transform, applied to a Dirac comb in dimension one, gives a discretely supported measure. We describe the resulting series of complex multiples of delta functions, ... More

Non-elliptic quadratic forms and semiclassical estimates for non-selfadjoint operatorsSep 23 2011We consider a class of pseudodifferential operators with a doubly characteristic point, where the quadratic part of the symbol fails to be elliptic but obeys an averaging assumption. Under suitable additional assumptions, semiclassical resolvent estimates ... More

Partial-wave analysis of $K^+$ nucleon scatteringNov 27 2006Feb 06 2007We have performed a partial-wave analysis of K$^+$-nucleon scattering in the momentum range from 0 to 1.5 GeV/c addressing the uncertainties of the results and comparing them with several previous analyses. It is found that the treatment of the reaction ... More

Accountable Anonymous Group MessagingApr 18 2010Users often wish to participate in online groups anonymously, but misbehaving users may abuse this anonymity to spam or disrupt the group. Messaging protocols such as Mix-nets and DC-nets leave online groups vulnerable to denial-of-service and Sybil attacks, ... More

K$^+$-nucleon interactionMay 19 2008The Born approximation to the quark-gluon-exchange mechanism for K$^+$N scattering is used as a starting point to generate a potential for this system. The valence quark wave function of the nucleon is generalized from a single Gaussian to a sum of Gaussians ... More

Final State Interactions in Pion Production from NucleiAug 16 2002We have calculated the effect of the inclusion of final state interactions on pion production from nuclei with incident pion beams. We find that the effect of absorption, along with geometric considerations, explains much of the enhancement at low invariant ... More

The Lebesgue Universal Covering ProblemFeb 04 2015Sep 19 2015In 1914 Lebesgue defined a "universal covering" to be a convex subset of the plane that contains an isometric copy of any subset of diameter 1. His challenge of finding a universal covering with the least possible area has been addressed by various mathematicians: ... More

Equivariant mirrors and the Virasoro conjecture for flag manifoldsOct 24 2002We found an explicit description of all $GL(n,\RR)$-Whittaker functions as oscillatory integrals and thus constructed equivariant mirrors of flag manifolds. As a consequence we proved the Virasoro conjecture for flag manifolds.

Parameter spaces for curves on surfaces and enumeration of rational curvesAug 22 1996We answer some enumerative questions about irreducible rational curves on Hirzebruch surfaces, by combining an idea of Kontsevich with the study of the geometry of certain natural parameter spaces. Our formulas generalize Kontsevich's formula for rational ... More

Lepton Flavor Violation in a Long Baseline ExperimentOct 29 2004Feb 16 2005We evaluate the size of a coupling for a lepton flavor violating interaction with neutrinos (nLFV) in the minimal supersymmetric standard model with right-handed neutrinos (MSSMRN). It is expected that the nLFV interactions are detected in a long baseline ... More

R-Parity Violation in a SUSY GUT Model and Radiative Neutrino MassesMay 26 2003Jul 11 2003Within the framework of an SU(5) SUSY GUT model, a mechanism which effectively induces R-parity-violating terms below the unification energy scale M_X is proposed. The model has matter fields \bar{5}_{L(+)}+10_{L(-)} and Higgs fields H_{(-)} and \bar{H}_{(+)} ... More

CP- and T-Violation Effects in Long Baseline Neutrino Oscillation ExperimentsJul 01 1997Aug 03 1999We examine how large CP- and T-violation effects are allowed in long baseline neutrino experiments with three generations of neutrinos, considering both the solar neutrino deficit and the atmospheric neutrino anomaly. We considerd two cases: When we attribute ... More

A way to crosscheck $μ$-$e$ conversion in the case of no signals of $μ\to e γ$ and $μ\to 3e$Sep 05 2014We consider the case that $\mu$-$e$ conversion signal is discovered but other charged lepton flavor violating (cLFV) processes will never be found. In such a case, we need other approaches to confirm the $\mu$-$e$ conversion and its underlying physics ... More

Yet another correlation in the analysis of CP violation using a neutrino oscillation experimentNov 07 2002We investigate the effect induced by variations in the density profile of the Earth's interior using a long-baseline neutrino oscillation experiment. At first, we point out two facts. (i) The most essential part of the matter profile is the first Fourier ... More

Duality of a Supersymmetric Standard Model without R parityNov 23 1995Recently one of the authors proposed a dual theory of a Supersymmetric Standard Model (SSM), in which it is naturally understood that at least one quark (the top quark) should be heavy, i.e., almost the same order as the weak scale, and the supersymmetric ... More

Computation of the string tension in four-dimensional Yang-Mills theory using large N reductionAug 11 2009Oct 23 2009Continuum reduction and Monte Carlo simulation are used to calculate the heavy quark potential and the string tension in large N Yang-Mills theory in four dimensions. The potential is calculated out to a separation of nine lattice units on a lattice with ... More

Standard(-like) Model from an SO(12) Grand Unified Theory in six-dimensions with $S_2$ extra-spaceOct 06 2008Mar 09 2009We analyze a gauge-Higgs unification model which is based on a gauge theory defined on a six-dimensional spacetime with an $S^2$ extra-space. We impose a symmetry condition for a gauge field and non-trivial boundary conditions of the $S^2$. We provide ... More

The Acceleration of Thermal Protons at Parallel Collisionless Shocks: Three-dimensional Hybrid SimulationsMar 21 2013Jul 08 2013We present three-dimensional hybrid simulations of collisionless shocks that propagate parallel to the background magnetic field to study the acceleration of protons that forms a high-energy tail on the distribution. We focus on the initial acceleration ... More

Operations that preserve the covering property of the lifting regionOct 06 2014Jul 02 2015We contribute to the theory for minimal liftings of cut-generating functions. In particular, we give three operations that preserve the so-called covering property of certain structured cut-generating functions. This has the consequence of vastly expanding ... More

Concentration inequalities for a removal-driven thinning processAug 09 2016Apr 27 2017We prove exponential concentration estimates and a strong law of large numbers for a particle system that is the simplest representative of a general class of models for 2D grain boundary coarsening. The system consists of $n$ particles in $(0,\infty)$ ... More

Log-decay $F$-isocrystals on higher dimensional varietiesFeb 13 2019Let $k$ be a perfect field of positive characteristic and let $X$ be a smooth irreducible quasi-compact scheme over $k$. The Drinfeld-Kedlaya theorem states that for an irreducible $F$-isocrystal on $X$, the gap between consecutive generic slopes is bounded ... More

On the topology of algebraic surfaces and reduction modulo pApr 05 2002May 08 2002We observe that the oriented homeomorphism type of a simply- connected smooth projective surface is determined by its algebraic structure modulo an odd prime of good reduction.

The moving particle lemma for the exclusion process on a weighted graphJun 05 2016Jun 07 2017We prove a version of the moving particle lemma for the exclusion process on any finite weighted graph, based on the octopus inequality of Caputo, Liggett, and Richthammer. In light of their proof of Aldous' spectral gap conjecture, we conjecture that ... More

Noise Stability and Correlation with Half SpacesMar 06 2016Benjamini, Kalai and Schramm showed that a monotone function $f : \{-1,1\}^n \to \{-1,1\}$ is noise stable if and only if it is correlated with a half-space (a set of the form $\{x: \langle x, a\rangle \le b\}$). We study noise stability in terms of correlation ... More

An extension of heat hierarchyJan 19 2014We propose a formally completely integrable extension of heat hierarchy based on the space of symmetries isomorphic to the Weyl algebra $\mathfrak{A}_1$. The extended heat hierarchy will be the basic model for the analysis of the extension property of ... More

Free resolutions of algebrasOct 19 2012Given an algebra A, presented by generators and relations, i.e. as a quotient of a tensor algebra by an ideal, we construct a free algebra resolution of A, i.e. a differential graded algebra which is quasi-isomorphic to A and which is itself a tensor ... More

The monodromy of $F$-isocrystals with log-decayDec 04 2016Let U be a smooth geometrically connected affine curve over $\mathbb{F}_p$ with compactification X. Following Dwork and Katz, a $p$-adic representation $\rho$ of $\pi_1(U)$ corresponds to an \'etale $F$-isocrystal. By work of Tsuzuki and Crew an $F$-isocrystal ... More

Rational curves on hypersurfaces of low degree, IIJul 27 2002This is a continuation of "Rational curves on hypersurfaces of low degree", math.AG/0203088. We prove that if d^2+d+1 < n and d > 2, then for a general hypersurface X_d in P^n of degree d, for each degree e the space of rational curves of degree e on ... More

Small-scale Gradients of Charged Particles in the Heliospheric Magnetic FieldJul 16 2013Oct 31 2013Using numerical simulations of charged-particles propagating in the heliospheric magnetic field, we study small-scale gradients, or "dropouts", in the intensity of solar energetic particles seen at 1 AU. We use two turbulence models, the foot-point random ... More

The Acceleration of Electrons at Perpendicular Shocks and its Implication for Solar Energetic Particle eventsJul 27 2012We present a study of the acceleration of electrons at a perpendicular shock that propagates through a turbulent magnetic field. The energization process of electrons is investigated by utilizing a combination of hybrid (kinetic ions and fluid electron) ... More

Formal Killing fields for minimal Lagrangian surfaces in complex space formsNov 11 2013Sep 03 2014The differential system for minimal Lagrangian surfaces in a $2_{\mathbb{C}}$-dimensional, non-flat, complex space form is an elliptic system defined on the bundle of oriented Lagrangian planes. This is a 6-symmetric space associated with the Lie group ... More

On weak and strong solution operators for evolution equations coming from quadratic operatorsSep 03 2014Jul 12 2016We identify, through a change of variables, solution operators for evolution equations with generators given by certain simple first-order differential operators acting on Fock spaces. This analysis applies, through unitary equivalence, to a broad class ... More

The subalgebras of $A_2$Sep 03 2015A classification of the semisimple subalgebras of the Lie algebra of traceless $3\times 3$ matrices with complex entries, denoted $A_2$, is well-known. We classify its nonsemisimple subalgebras, thus completing the classification of the subalgebras of ... More

Monoidal Grothendieck ConstructionSep 03 2018Feb 18 2019We lift the standard equivalence between fibrations and indexed categories to an equivalence between monoidal fibrations and monoidal indexed categories, namely weak monoidal pseudofunctors to the 2-category of categories. In doing so, we investigate ... More

Approximating (Unweighted) Tree Augmentation via Lift-and-Project (Part 0: $1.8+ε$ approximation for (Unweighted) TAP)Apr 04 2016We study the unweighted Tree Augmentation Problem (TAP) via the Lasserre (Sum of Squares) system. We prove an approximation guarantee of ($1.8+\epsilon$) relative to an SDP relaxation, which matches the combinatorial approximation guarantee of Even, Feldman, ... More

Approximating (Unweighted) Tree Augmentation via Lift-and-Project, Part I: Stemless TAPAug 29 2015In Part I, we study a special case of the unweighted Tree Augmentation Problem (TAP) via the Lasserre (Sum of Squares) system. In the special case, we forbid so-called stems; these are a particular type of subtree configuration. For stemless TAP, we prove ... More

Local ergodicity in the exclusion process on an infinite weighted graphMay 29 2017Aug 23 2017We establish an abstract local ergodic theorem, under suitable space-time scaling, for the (boundary-driven) symmetric exclusion process on an increasing sequence of balls covering an infinite weighted graph. The proofs are based on 1-block and 2-blocks ... More

The monodromy of unit-root $F$-isocrystals with geometric originDec 06 2018Jan 09 2019Let $C$ be a smooth curve over a finite field in characteristic $p$ and let $M$ be an overconvergent $F$-isocrystal over $C$. After replacing $C$ with a dense open subset $M$ obtains a slope filtration, whose steps interpolate the Frobenius eigenvalues ... More

Riposte: An Anonymous Messaging System Handling Millions of UsersMar 20 2015Oct 30 2016This paper presents Riposte, a new system for anonymous broadcast messaging. Riposte is the first such system, to our knowledge, that simultaneously protects against traffic-analysis attacks, prevents anonymous denial-of-service by malicious clients, ... More