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Meso-resolved simulations of shock-to-detonation transition in nitromethane with air-filled cavitiesMay 14 2019May 15 2019Two-dimensional, meso-resolved numerical simulations are performed to investigate the complete shock-to-detonation transition (SDT) process in a mixture of liquid nitromethane (NM) and air-filled, circular cavities. The shock-induced initiation behaviors ... More

Propagation of gaseous detonation waves in a spatially inhomogeneous reactive mediumMar 27 2017Detonation propagation in a compressible medium wherein the energy release has been made spatially inhomogeneous is examined via numerical simulation. The inhomogeneity is introduced via step functions in the reaction progress variable, with the local ... More

Mixing Within Patterned Vortex CoreOct 16 2009The video shows the flow dynamics within inner and outer regions of a vortex core. The observed phenomena mimic a transport process occurring within the Antarctic vortex. The video shows two distinct regions: a strongly mixed core and broad ring of weakly ... More

Supertranslations to all ordersAug 14 2009The transformation laws of the general linear superfield and chiral superfields under N=1 supertranslations are tabulated to all orders in the supertranslation parameters.

A graph-theoretic proof for Whitehead's second free-group algorithmJun 29 2017J.H.C. Whitehead's second free-group algorithm determines whether or not two given elements of a free group lie in the same orbit of the automorphism group of the free group. The algorithm involves certain connected graphs, and Whitehead used three-manifold ... More

Meso-resolved simulations of shock-to-detonation transition in nitromethane with air-filled cavitiesMay 14 2019Two-dimensional, meso-resolved numerical simulations are performed to investigate the complete shock-to-detonation transition (SDT) process in a mixture of liquid nitromethane (NM) and air-filled, circular cavities. The shock-induced initiation behaviors ... More

The decay of the Walsh coefficients of smooth functionsApr 01 2013We give upper bounds on the Walsh coefficients of functions for which the derivative of order at least one has bounded variation of fractional order. Further, we also consider the Walsh coefficients of functions in periodic and non-periodic reproducing ... More

A fast Fourier transform method for computing the weight enumerator polynomial and trigonometric degree of lattice rulesJul 23 2012A fast Fourier transform method for computing the weight enumerator polynomial and trigonometric degree of lattice rules is introduced.

Numerical integration of Hölder continuous, absolutely convergent Fourier-, Fourier cosine-, and Walsh seriesDec 04 2013Mar 12 2014We introduce quasi-Monte Carlo rules for the numerical integration of functions $f$ defined on $[0,1]^s$, $s \ge 1$, which satisfy the following properties: the Fourier-, Fourier cosine- or Walsh coefficients of $f$ are absolutely summable and $f$ satisfies ... More

Explicit constructions of quasi-Monte Carlo rules for the numerical integration of high dimensional periodic functionsApr 01 2013In this paper we give explicit constructions of point sets in the $s$ dimensional unit cube yielding quasi-Monte Carlo algorithms which achieve the optimal rate of convergence of the worst-case error for numerically integrating high dimensional periodic ... More

Hamiltonians and Green's functions which interpolate between two and three dimensionsApr 24 2002I propose to use Hamiltonians which contain two-dimensional and three-dimensional kinetic terms for the description of two-dimensional systems in physics. As a model system the evolution of three-dimensional wavefunctions in the presence of an infinitely ... More

Self-trapping of the dilatonSep 22 1995The dilaton in three dimensions does not roll. Witten's conjecture that duality between theories in three and four dimensions solves the cosmological constant problem thus may also solve the dilaton problem in string theory.

Dimensionally hybrid Green's functions and density of states for interfacesJul 12 2007Aug 30 2007The energy dependent Green's function for an interface Hamiltonian which interpolates between two and three dimensions can be calculated explicitly. This yields an expression for the density of states on the interface which interpolates continuously between ... More

The Coulomb potential in gauge theory with a dilatonJan 13 1997Feb 17 1997I calculate the potential of a pointlike particle carrying SU$(N_c)$ charge in a gauge theory with a dilaton. The solution depends on boundary conditions imposed on the dilaton: For a dilaton that vanishes at infinity the resulting potential is of the ... More

Applications of geometric discrepancy in numerical analysis and statisticsNov 15 2013In this paper we discuss various connections between geometric discrepancy measures, such as discrepancy with respect to convex sets (and convex sets with smooth boundary in particular), and applications to numerical analysis and statistics, like point ... More

Quasi-Monte Carlo numerical integration on $\mathbb{R}^s$: digital nets and worst-case errorMar 25 2010Nov 11 2010Quasi-Monte Carlo rules are equal weight quadrature rules defined over the domain $[0,1]^s$. Here we introduce quasi-Monte Carlo type rules for numerical integration of functions defined on $\mathbb{R}^s$. These rules are obtained by way of some transformation ... More

An improved proof of the Almost Stability TheoremNov 02 2018In 1989, Dicks and Dunwoody proved the Almost Stability Theorem, which has among its corollaries the Stallings-Swan theorem that groups of cohomological dimension one are free. In this article, we use a nestedness result of Bergman, Bowditch, and Dunwoody ... More

On free-group algorithms that sandwich a subgroup between free-product factorsJun 17 2013Let $F$ be a finite-rank free group and $H$ be a finite-rank subgroup of $F$. We discuss proofs of two algorithms that sandwich $H$ between an upper-layer free-product factor of $F$ that contains $H$ and a lower-layer free-product factor of $F$ that is ... More

Random weights, robust lattice rules and the geometry of the cbc$r$c algorithmSep 23 2011In this paper we study lattice rules which are cubature formulae to approximate integrands over the unit cube $[0,1]^s$ from a weighted reproducing kernel Hilbert space. We assume that the weights are independent random variables with a given mean and ... More

On two-point configurations in random setNov 09 2008Jan 27 2009We show that with high probability a random set of size $\Theta(n^{1-1/k})$ of $\{1,...,n\}$ contains two elements $a$ and $a+d^k$, where $d$ is a positive integer. As a consequence, we prove an analogue of S\'ark\"ozy-F\"urstenberg's theorem for random ... More

Graphs of groups and the Atiyah conjecture for one-relator groupsApr 25 2000Jan 17 2001Paper withdrawn because of a gap in the proof of Proposition 3 of Thomas Schick: "Integrality of L2-Betti numbers", Math. Ann. 317, 727-750 (arXiv.org/abs/math.gt/0001101). Most results of the withdrawn paper were based on this proposition.

Resistances for heat and mass transfer through a liquid-vapor interface in a binary mixtureAug 20 2010In this paper we calculate the interfacial resistances to heat and mass transfer through a liquid-vapor interface in a binary mixture. We use two methods, the direct calculation from the actual non-equilibrium solution and integral relations, derived ... More

Few-Bit CSI Acquisition for Centralized Cell-Free Massive MIMO with Spatial CorrelationFeb 19 2019The availability and accuracy of Channel State Information (CSI) play a crucial role for coherent detection in almost every communication system. Particularly in the recently proposed cell-free massive MIMO system, in which a large number of distributed ... More

Actions of the braid group, and new algebraic proofs of results of Dehornoy and LarueMay 04 2007This article surveys many standard results about the braid group with emphasis on simplifying the usual algebraic proofs. We use van der Waerden's trick to illuminate the Artin-Magnus proof of the classic presentation of the algebraic mapping-class group ... More

Optimal $\mathcal{L}_2$ discrepancy bounds for higher order digital sequences over the finite field $\mathbb{F}_2$Jul 21 2012Jun 03 2013We show that the $\mathcal{L}_2$ discrepancy of the explicitly constructed infinite sequences of points $(\boldsymbol{x}_0,\boldsymbol{x}_1, \boldsymbol{x}_2,...)$ in $[0,1)^s$ over $\mathbb{F}_2$ introduced in [J. Dick, Walsh spaces containing smooth ... More

A mnemonic for the graded-case Golod-Shafarevich inequalityAug 13 2015Apr 18 2017We draw attention to an easy-to-remember explanation for the graded-case inequality of Golod and Shafarevich. We review some of the classic material on this inequality.

Optimal randomized changing dimension algorithms for infinite-dimensional integration on function spaces with ANOVA-type decompositionJun 12 2013We study the numerical integration problem for functions with infinitely many variables. The function spaces of integrands we consider are weighted reproducing kernel Hilbert spaces with norms related to the ANOVA decomposition of the integrands. The ... More

Construction of interlaced scrambled polynomial lattice rules of arbitrary high orderJan 28 2013Aug 05 2014Higher order scrambled digital nets are randomized quasi-Monte Carlo rules which have recently been introduced in [J. Dick, Ann. Statist., 39 (2011), 1372--1398] and shown to achieve the optimal rate of convergence of the root mean square error for numerical ... More

The inverse of the star-discrepancy problem and the generation of pseudo-random numbersJul 16 2014The inverse of the star-discrepancy problem asks for point sets $P_{N,s}$ of size $N$ in the $s$-dimensional unit cube $[0,1]^s$ whose star-discrepancy $D^\ast(P_{N,s})$ satisfies $$D^\ast(P_{N,s}) \le C \sqrt{s/N},$$ where $C> 0$ is a constant independent ... More

Ring coproducts embedded in power-series ringsNov 27 2012Let $R$ be a ring (associative, with 1), and let $R<< a,b>>$ denote the power-series $R$-ring in two non-commuting, $R$-centralizing variables, $a$ and $b$. Let $A$ be an $R$-subring of $R<< a>>$ and $B$ be an $R$-subring of $R<< b>>$, and let $\alpha$ ... More

The spectral measure of certain elements of the complex group ring of a wreath productJul 20 2001We use elementary methods to compute the L2-dimension of the eigenspaces of the Markov operator on the lamplighter group and of generalizations of this operator on other groups. In particular, we give a transparent explanation of the spectral measure ... More

A mnemonic for the graded-case Golod-Shafarevich inequalityAug 13 2015We draw attention to an easy-to-remember explanation for the graded-case inequality of Golod and Shafarevich. We review some of the classic material on this inequality.

Cosmological implications of a light dilatonJan 09 1998Jan 14 1998Supersymmetric Peccei-Quinn symmetry and string theory predict a complex scalar field comprising a dilaton and an axion. These fields are massless at high energies, but it is known since long that the axion is stabilized in an instanton dominated vacuum. ... More

On the least singular value of random symmetric matricesFeb 08 2011Mar 17 2011Let $F_n$ be an $n$ by $n$ symmetric matrix whose entries are bounded by $n^{\gamma}$ for some $\gamma>0$. Consider a randomly perturbed matrix $M_n=F_n+X_n$, where $X_n$ is a random symmetric matrix whose upper diagonal entries $x_{ij}$ are iid copies ... More

A new approach to an old problem of Erdos and MoserDec 04 2011Let $\eta_i, i=1,..., n$ be iid Bernoulli random variables, taking values $\pm 1$ with probability 1/2. Given a multiset $V$ of $n$ elements $v_1, ..., v_n$ of an additive group $G$, we define the \emph{concentration probability} of $V$ as $$\rho(V) := ... More

On distribution of three-term arithmetic progressions in sparse subsets of F_p^nMay 24 2009Apr 22 2010We prove a version of Szemeredi's regularity lemma for subsets of a typical random set in F_p^n. As an application, a result on the distribution of three-term arithmetic progressions in sparse sets is discussed.

Classification theorems for sumsets modulo a primeNov 09 2008Jan 27 2009Let $\Z/pZ$ be the finite field of prime order $p$ and $A$ be a subsequence of $\Z/pZ$. We prove several classification results about the following questions: (1) When can one represent zero as a sum of some elements of $A$ ? (2) When can one represent ... More

Transport of heat and mass in a two-phase mixture. From a continuous to a discontinuous descriptionJun 30 2010We present a theory which describes the transport properties of the interfacial region with respect to heat and mass transfer. Postulating the local Gibbs relation for a continuous description inside the interfacial region, we derive the description of ... More

Multivariate Time Series Classification using Dilated Convolutional Neural NetworkMay 05 2019Multivariate time series classification is a high value and well-known problem in machine learning community. Feature extraction is a main step in classification tasks. Traditional approaches employ hand-crafted features for classification while convolutional ... More

The Zieschang-McCool method for generating algebraic mapping-class groupsApr 28 2011Let g and p be non-negative integers. Let A(g,p) denote the group consisting of all those automorphisms of the free group on {t_1,...,t_p, x_1,...,x_g, y_1,...y_g} which fix the element t_1t_2...t_p[x_1,y_1]...[x_g,y_g] and permute the set of conjugacy ... More

On a projection-corrected component-by-component constructionFeb 16 2015Jun 26 2015The component-by-component construction is the standard method of finding good lattice rules or polynomial lattice rules for numerical integration. Several authors have reported that in numerical experiments the generating vector sometimes has repeated ... More

On the fast computation of the weight enumerator polynomial and the $t$ value of digital nets over finite abelian groupsOct 02 2012In this paper we introduce digital nets over finite abelian groups which contain digital nets over finite fields and certain rings as a special case. We prove a MacWilliams type identity for such digital nets. This identity can be used to compute the ... More

Infinite-Dimensional Integration in Weighted Hilbert Spaces: Anchored Decompositions, Optimal Deterministic Algorithms, and Higher Order ConvergenceOct 16 2012We study numerical integration of functions depending on an infinite number of variables. We provide lower error bounds for general deterministic linear algorithms and provide matching upper error bounds with the help of suitable multilevel algorithms ... More

The weighted star discrepancy of Korobov's $p$-setsApr 01 2014We analyze the weighted star discrepancy of so-called $p$-sets which go back to definitions due to Korobov in the 1950s and Hua and Wang in the 1970s. Since then, these sets have largely been ignored since a number of other constructions have been discovered ... More

A characterization of Sobolev spaces on the sphere and an extension of Stolarsky's invariance principle to arbitrary smoothnessMar 23 2012In this paper we study reproducing kernel Hilbert spaces of arbitrary smoothness on the sphere $\mathbb{S}^d \subset \mathbb{R}^{d+1}$. The reproducing kernel is given by an integral representation using the truncated power function $(\boldsymbol{x} \cdot ... More

Rapid laser-free ion cooling by controlled collisionDec 21 2012Feb 19 2014I propose a method to remove the axial motional excitation from an ion qubit within a few oscillation periods of a harmonic trap. The principle is to prepare another coolant ion in its motional ground state, and then apply a phonon beam splitter to swap ... More

Near invariance of the hypercubeSep 26 2014Oct 10 2014We give an almost-complete description of orthogonal matrices $M$ of order $n$ that "rotate a non-negligible fraction of the Boolean hypercube $C_n=\{-1,1\}^n$ onto itself," in the sense that $$P_{x\in C_n}(Mx\in C_n) \ge n^{-C},\mbox{ for some positive ... More

Random doubly stochastic matrices: The circular lawMay 04 2012Mar 27 2014Let $X$ be a matrix sampled uniformly from the set of doubly stochastic matrices of size $n\times n$. We show that the empirical spectral distribution of the normalized matrix $\sqrt{n}(X-{\mathbf {E}}X)$ converges almost surely to the circular law. This ... More

On the singularity of random combinatorial matricesDec 04 2011It is shown that a random $(0,1)$ matrix whose rows are independent random vectors of exactly $n/2$ zero components is non-singular with probability $1-O(n^{-C})$ for any $C>0$. The proof uses a non-standard inverse-type Littlewood-Offord result.

Intrinsic Time Quantum GravityMar 15 2016Correct identification of the true gauge symmetry of General Relativity being 3d spatial diffeomorphism invariant(3dDI) (not the conventional infinite tensor product group with principle fibre bundle structure), together with intrinsic time extracted ... More

Inverse Littlewood-Offord problems and The Singularity of Random Symmetric MatricesJan 16 2011Dec 31 2012Let $M_n$ denote a random symmetric $n$ by $n$ matrix, whose upper diagonal entries are iid Bernoulli random variables (which take value -1 and 1 with probability 1/2). Improving the earlier result by Costello, Tao and Vu, we show that $M_n$ is non-singular ... More

Can $μ$--$e$ Conversion in Nuclei be a Good Probe for Lepton-Number Violating Higgs Couplings ?Aug 27 1993Motivated by the improving sensitivity, $R$, of experiments on $\mu~Ti \rightarrow e~Ti$ and the enhanced Higgs nucleon interaction, we study this lepton number violating process induced by Higgs exchange. Taking the possible sensitivity, $R \simeq 10^{-16}$, ... More

Characterization of Strongly Equivalent Logic Programs in Intermediate LogicsJun 03 2002The non-classical, nonmonotonic inference relation associated with the answer set semantics for logic programs gives rise to a relationship of 'strong equivalence' between logical programs that can be verified in 3-valued Goedel logic, G3, the strongest ... More

Coupling of fermionic fields with mass dimensions one to the O'Raifeartaigh modelAug 23 2012The objective of this article is to discuss the coupling of fermionic fields with mass dimension one to the O'Raifeartaigh model to study supersymmetry breaking for fermionic fields with mass dimension one. We find that the coupled model has two distinct ... More

On subgroups of Coxeter groupsNov 30 2007A right-angled Coxeter group is a group with a given set of generators of order two, subject only to the relations that certain pairs of the generators commute. Various papers have shown how homological properties of the Coxeter group are related to homological ... More

Gamma ray signals of the annihilation of Higgs-portal singlet dark matterApr 15 2016Jun 05 2016This article is an exploration of gamma ray signals of annihilating Higgs-portal singlet scalar and vector dark matter. Gamma ray signals are considered in the context of contributions from annihilations of singlets in the galactic halo to the Isotropic ... More

Retracts of vertex sets of trees and the almost stability theoremOct 07 2005Sep 19 2006Let G be a group, let T be an (oriented) G-tree with finite edge stabilizers, and let VT denote the vertex set of T. We show that, for each G-retract V' of the G-set VT, there exists a G-tree whose edge stabilizers are finite and whose vertex set is V'. ... More

A Supersymmetric Lagrangian for Fermionic Fields with Mass Dimension OneOct 05 2010Oct 31 2010We present the derivation of a supersymmetric model for fermionic fields with integer valued mass dimension based on a general superfield with one free spinor index. First, we demonstrate that it is impossible to formulate such a model based on a general ... More

On the intersection of free subgroups in free products of groupsFeb 13 2007Let (G_i | i in I) be a family of groups, let F be a free group, and let G = F *(*I G_i), the free product of F and all the G_i. Let FF denote the set of all finitely generated subgroups H of G which have the property that, for each g in G and each i ... More

Isomorphisms of Brin-Higman-Thompson groupsDec 07 2011Sep 10 2012Let $m, m', r, r',t, t'$ be positive integers with $r, r' \ge 2$. Let $L_r$ denote the ring that is universal with an invertible $1 \times r$ matrix. Let $M_m(L_r^{\otimes t})$ denote the ring of $m \times m$ matrices over the tensor product of $t$ copies ... More

A simple Proof of Stolarsky's Invariance PrincipleJan 24 2011Stolarsky [Proc. Amer. Math. Soc. 41 (1973), 575--582] showed a beautiful relation that balances the sums of distances of points on the unit sphere and their spherical cap $\mathbb{L}_2$-discrepancy to give the distance integral of the uniform measure ... More

Concentrating entanglement by local actions---beyond mean valuesJul 20 1997Jul 08 1999Suppose two distant observers Alice and Bob share a pure bipartite quantum state. By applying local operations and communicating with each other using a classical channel, Alice and Bob can manipulate it into some other states. Previous investigations ... More

New commutation relations for quantum gravityJan 15 2016A new set of fundamental commutation relations for quantum gravity is presented. The basic variables are the eight components of the unimodular part of the spatial dreibein and eight SU(3) generators which correspond to Klauder's momentric variables. ... More

L^2-Betti numbers of one-relator groupsAug 19 2005Sep 19 2006We determine the L^2-Betti numbers of all one-relator groups and all surface-plus-one-relation groups (surface-plus-one-relation groups were introduced by Hempel who called them one-relator surface groups). In particular we show that for all such groups ... More

Quasi-Monte Carlo rules for numerical integration over the unit sphere $\mathbb{S}^2$Jan 28 2011Jul 29 2011We study numerical integration on the unit sphere $\mathbb{S}^2 \subset \mathbb{R}^3$ using equal weight quadrature rules, where the weights are such that constant functions are integrated exactly. The quadrature points are constructed by lifting a $(0,m,2)$-net ... More

Random matrices: Law of the determinantDec 04 2011Jan 13 2014Let $A_n$ be an $n$ by $n$ random matrix whose entries are independent real random variables with mean zero, variance one and with subexponential tail. We show that the logarithm of $|\det A_n|$ satisfies a central limit theorem. More precisely, \begin{eqnarray*}\sup_{x\in ... More

A discrete mean value of the derivative of the Riemann zeta functionJun 12 2007In this article we compute a discrete mean value of the derivative of the Riemann zeta function. This mean value will be important for several applications concerning the size of $\zeta'(\rho)$ where $\zeta(s)$ is the Riemann zeta function and $\rho$ ... More

Extreme values of zeta prime rhoJun 12 2007In this article we exhibit small and large values of $\zeta'(\rho)$ by applying Soundararajan's resonance method. Our results assume the Riemann hypothesis.

The fourth moment of ζ^{'}(ρ)Oct 23 2003Discrete moments of the Riemann zeta function were studied by Gonek and Hejhal in the 1980's. They independently formulated a conjecture concerning the size of these moments. In 1999, Hughes, Keating, and O'Connell, by employing a random matrix model, ... More

General Relativity without paradigm of space-time covariance, and resolution of the problem of timeJan 16 2012Feb 07 2014The framework of a theory of gravity from the quantum to the classical regime is presented. The paradigm shift from full spacetime covariance to spatial diffeomorphism invariance, together with clean decomposition of the canonical structure, yield transparent ... More

What can we learn from the measurement $R_b \equiv Γ(Z\to b \overline{b}) / Γ(Z\to {\rm hadrons})$?Mar 15 1995We examine the effect of new physics on the $R_b \equiv \Gamma(Z\rightarrow \bar{b}b)/\Gamma(Z\rightarrow {\rm hadrons})$. Conditions for large contributions are derived.

Production of scalar particles in expanding spacetimeMay 26 2005Jun 07 2005In this paper, we investigate cosmological particle production using quantum field theory (QFT). We will consider how production of scalar particles can occur in an expanding universe. By introducing a time-dependent energy parameter representing the ... More

The sixth moment of the Riemann zeta function and ternary additive divisor sumsOct 17 2016Hardy and Littlewood initiated the study of the $2k$-th moments of the Riemann zeta function on the critical line. In 1918 Hardy and Littlewood established an asymptotic formula for the second moment and in 1926 Ingham established an asymptotic formula ... More

Knot and braid invariants from contact homology IFeb 10 2003Jan 29 2005We introduce topological invariants of knots and braid conjugacy classes, in the form of differential graded algebras, and present an explicit combinatorial formulation for these invariants. The algebras conjecturally give the relative contact homology ... More

Knot and braid invariants from contact homology II, with an appendix written jointly with Siddhartha GadgilMar 27 2003Sep 01 2005We present a topological interpretation of knot and braid contact homology in degree zero, in terms of cords and skein relations. This interpretation allows us to extend the knot invariant to embedded graphs and higher-dimensional knots. We calculate ... More

A characterization of torsion theories in the cluster category of Dynkin type A_{\infty}May 24 2010Let D be the cluster category of Dynkin type A_{\infty}. This paper provides a bijection between torsion theories in D and certain configurations of arcs connecting non-neighbouring integers.

Tilting Saturn without tilting Jupiter: Constraints on giant planet migrationSep 23 2015The migration and encounter histories of the giant planets in our Solar System can be constrained by the obliquities of Jupiter and Saturn. We have performed secular simulations with imposed migration and N-body simulations with planetesimals to study ... More

A characterization of incomplete sequences in $F_p^d$Dec 04 2011A sequence $A$ of elements an additive group $G$ is {\it incomplete} if there exists a group element that {\it can not} be expressed as a sum of elements from $A$. The study of incomplete sequences is a popular topic in combinatorial number theory. However, ... More

Large gaps between the zeros of the Riemann zeta functionOct 25 2005We show that the generalized Riemann hypothesis implies that there are infinitely many consecutive zeros of the Riemann zeta function whose spacing is 2.9125 times larger than the average spacing. This is deduced from the calculation of the second moment ... More

QCD renormalization for the top-quark mass in a mass geometrical mean hierarchyApr 13 1992$QCD$ renormalization for the top-quark mass is calculated in a mass geometrical mean hierarchy, $m_d m_b = m_s^2$ and $m_u m_t = m_c^2$. The physical mass, $m_t(m_t) = 160 {\pm} 50 GeV$ is obtained, which agrees very well with electroweak precision measurement. ... More

A note on Majorana neutrinos, leptonic CKM and electron electric dipole momentOct 16 1995The electric dipole moment of the electron, $d_e$, is known to vanish up to thre e-loops in the standard model with massless neutrinos. However, if neutrinos are massive Majorana particles, we obtain the result that $d_e$ induced by leptonic CKM mechanism ... More

Muon Number Violating Processes in Single Particle Extensions of the Standard ModelApr 07 1994We study the one-loop induced muon number processes when the standard model is minimally extended to include a $\rm SU(2)$ singlet of a charged scalar $h^+$ and a neutral fermion $N$. We find that $\mu \rightarrow e \gamma$ is more sensitive for the former ... More

Point sets on the sphere $\mathbb{S}^2$ with small spherical cap discrepancySep 15 2011In this paper we study the geometric discrepancy of explicit constructions of uniformly distributed points on the two-dimensional unit sphere. We show that the spherical cap discrepancy of random point sets, of spherical digital nets and of spherical ... More

Non-orientable surface-plus-one-relation groupsOct 15 2008Recently Dicks-Linnell determined the $L^2$-Betti numbers of the orientable surface-plus-one-relation groups, and their arguments involved some results that were obtained topologically by Hempel and Howie. Using algebraic arguments, we now extend all ... More

A weighted Discrepancy Bound of quasi-Monte Carlo Importance SamplingJan 21 2019Importance sampling Monte-Carlo methods are widely used for the approximation of expectations with respect to partially known probability measures. In this paper we study a deterministic version of such an estimator based on quasi-Monte Carlo. We obtain ... More

Security proof of a three-state quantum key distribution protocol without rotational symmetryJul 08 2006Sep 20 2006Standard security proofs of quantum key distribution (QKD) protocols often rely on symmetry arguments. In this paper, we prove the security of a three-state protocol that does not possess rotational symmetry. The three-state QKD protocol we consider involves ... More

Left relatively convex subgroupsMar 05 2015Let G be a group and H be a subgroup of G. We say that H is left relatively convex in G if the left G-set G/H has at least one G-invariant order; when G is left orderable, this holds if and only if H is convex in G under some left ordering of G. We give ... More

Proof Techniques in Quasi-Monte Carlo TheoryMar 28 2014Sep 02 2014In this survey paper we discuss some tools and methods which are of use in quasi-Monte Carlo (QMC) theory. We group them in chapters on Numerical Analysis, Harmonic Analysis, Algebra and Number Theory, and Probability Theory. We do not provide a comprehensive ... More

Spatial low-discrepancy sequences, spherical cone discrepancy, and applications in financial modelingAug 20 2014In this paper we introduce a reproducing kernel Hilbert space defined on $\mathbb{R}^{d+1}$ as the tensor product of a reproducing kernel defined on the unit sphere $\mathbb{S}^{d}$ in $\mathbb{R}^{d+1}$ and a reproducing kernel defined on $[0,\infty)$. ... More

New formulation of Horava-Lifshitz quantum gravity as a master constraint theoryJul 09 2010Jun 01 2011Both projectable and non-projectable versions of Horava-Lifshitz gravity face serious challenges. In the non-projectable version, the constraint algebra is seemingly inconsistent. The projectable version lacks a local Hamiltonian constraint, thus allowing ... More

A proposal for a scalable universal bosonic simulator using individually trapped ionsMay 08 2012We describe a possible architecture to implement a universal bosonic simulator (UBS) using trapped ions. Single ions are confined in individual traps, and their motional states represent the bosonic modes. Single-mode linear operators, nonlinear phase-shifts, ... More

Universal Quantum Computing with Arbitrary Continuous-Variable EncodingMay 30 2016Implementing a qubit quantum computer in continuous-variable systems conventionally requires the engineering of specific interactions according to the encoding basis states. In this work, we present a unified formalism to conduct universal quantum computation ... More

Random matrices: tail bounds for gaps between eigenvaluesApr 01 2015May 02 2015Gaps (or spacings) between consecutive eigenvalues are a central topic in random matrix theory. The goal of this paper is to study the tail distribution of these gaps in various random matrix models. We give the first repulsion bound for random matrices ... More

Random integral matrices: universality of surjectivity and the cokernelJun 02 2018For a random matrix of entries sampled independently from a fairly general distribution in Z we study the probability that the cokernel is isomorphic to a given finite abelian group, or when it is cyclic. This includes the probability that the linear ... More

Active Sensing of Social NetworksJan 21 2016This paper develops an active sensing method to estimate the relative weight (or trust) agents place on their neighbors' information in a social network. The model used for the regression is based on the steady state equation in the linear DeGroot model ... More

$8π$-periodic dissipationless ac Josephson effect on a quantum spin-Hall edge via a Quantum magnetic impuritySep 09 2016Time-reversal invariance places strong constraints on the properties of the quantum spin Hall edge. One such restriction is the inevitability of dissipation in a Josephson junction between two superconductors formed on such an edge without the presence ... More

Experimental quantum key distribution with active phase randomizationNov 06 2006Phase randomization is an important assumption made in many security proofs of practical quantum key distribution (QKD) systems. Here, we present the first experimental demonstration of QKD with reliable active phase randomization. One key contribution ... More

Why quantum bit commitment and ideal quantum coin tossing are impossibleMay 16 1996Aug 22 1996There had been well known claims of ``provably unbreakable'' quantum protocols for bit commitment and coin tossing. However, we, and independently Mayers, showed that all proposed quantum bit commitment (and therefore coin tossing) schemes are, in principle, ... More

Pre-fixed Threshold Real Time Selection Method in Free-space Quantum Key DistributionDec 24 2017Free-space Quantum key distribution (QKD) allows two parties to share a random key with unconditional security, between ground stations, between mobile platforms, and even in satellite-ground quantum communications. Atmospheric turbulence causes fluctuations ... More

Experimental demonstration of phase-remapping attack in a practical quantum key distribution systemMay 13 2010Unconditional security proofs of various quantum key distribution (QKD) protocols are built on idealized assumptions. One key assumption is: the sender (Alice) can prepare the required quantum states without errors. However, such an assumption may be ... More