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Towards autonomous ocean observing systems using Miniature Underwater Gliders with UAV deployment and recovery capabilitiesFeb 08 2019This paper presents preliminary results towards the development of an autonomous ocean observing system using Miniature Underwater Gliders (MUGs) that can operate with the support of Unmanned Aerial Vehicles (UAVs) and Unmanned Surface Vessels (USVs) ... More

Test of renormalization predictions for universal finite-size scaling functionsNov 02 1999We calculate universal finite-size scaling functions for systems with an n-component order parameter and algebraically decaying interactions. Just as previously has been found for short-range interactions, this leads to a singular epsilon-expansion, where ... More

Black Hole Evaporation and ComplementarityMar 17 1995About twenty years ago Hawking made the remarkable suggestion that the black hole evaporation process will inevitably lead to a fundamental loss of quantum coherence. The mechanism by which the quantum radiation is emitted appears to be insensitive to ... More

Torsion and electron motion in Quantum Dots with crystal lattice dislocationsNov 25 1997The motion of a conducting electron in a quantum dot with one or several dislocations in the underlying crystal lattice is considered in the continuum picture, where dislocations are represented by torsion of space. The possible effects of torsion are ... More

Endomorphisms of quantized Weyl algebrasJul 15 2010Belov-Kanel and Kontsevich conjectured that the group of automorphisms of the n'th Weyl algebra and the group of polynomial symplectomorphisms of C^2 are canonically isomorphic. We discuss how this conjecture can be approached by means of (second) quantized ... More

Comment on "Geometric phases for mixed states during cyclic evolutions"Apr 30 2004Jul 08 2004It is shown that a recently suggested concept of mixed state geometric phase in cyclic evolutions [2004 {\it J. Phys. A} {\bf 37} 3699] is gauge dependent.

Isometric Embeddability of SnowflakesSep 21 2015We show that a snowflake of a metric space with positive Hausdorff dimension does not admit an isometric embedding into euclidean space.

Astrometry 1960-80: from Hamburg to HipparcosAug 08 2014Astrometry, the most ancient branch of astronomy, was facing extinction during much of the 20th century in the competition with astrophysics. The revival of astrometry came with the European astrometry satellite Hipparcos, approved by ESA in 1980 and ... More

A stabilized nonconforming finite element method for the elliptic Cauchy problemJun 17 2014In this paper we propose a nonconforming finite element method for the solution of the ill-posed elliptic Cauchy problem. We prove error estimates using continuous dependence estimates in the $L^2$-norm. The effect of perturbations in data on the estimates ... More

A Primer on Energy ConditionsApr 30 2014An energy condition, in the context of a wide class of spacetime theories (including general relativity), is, crudely speaking, a relation one demands the stress-energy tensor of matter satisfy in order to try to capture the idea that "energy should be ... More

Feynman integrals via hyperlogarithmsJun 30 2014This talk summarizes recent developments in the evaluation of Feynman integrals using hyperlogarithms. We discuss extensions of the original method, new results that were obtained with this approach and point out current problems and future directions. ... More

The Double Eulerian Polynomial and Inversion TablesJan 22 2014We show that the pair (des, ides) of statistics on the set of permu- tations has the same distribution as the pair (asc, row) of statistics on the set of inversion tables, proving a conjecture of Visontai. The common generating function of these pairs ... More

A Simple Proof of the Marker-Steinhorn Theorem for Expansions of Ordered Abelian GroupsSep 23 2013We give a short and self-contained proof of the Marker-Steinhorn Theorem for o-minimal expansions of ordered groups, based on an analysis of linear orders definable in such structures.

Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integralsMar 13 2014We provide algorithms for symbolic integration of hyperlogarithms multiplied by rational functions, which also include multiple polylogarithms when their arguments are rational functions. These algorithms are implemented in Maple and we discuss various ... More

Performance and Optimization Abstractions for Large Scale Heterogeneous Systems in the Cactus/Chemora FrameworkAug 06 2013We describe a set of lower-level abstractions to improve performance on modern large scale heterogeneous systems. These provide portable access to system- and hardware-dependent features, automatically apply dynamic optimizations at run time, and target ... More

Using Monte Carlo to optimize variable cutsDec 20 2007Dec 20 2007A Monte Carlo method to optimize cuts on variables is presented and evaluated. The method gives a much higher signal to noise ratio than does a manual choice of cuts.

Low Threshold Bootstrap Percolation on the Hamming TorusJul 09 2014Jun 09 2015This paper analyzes various questions pertaining to bootstrap percolation on the $d$-dimensional Hamming torus where each node is open with probability $p$ and the percolation threshold is 2. For each $d'<d$ we find the critical exponent for the event ... More

SIR dynamics in random networks with heterogeneous connectivityMay 15 2007Random networks with specified degree distributions have been proposed as realistic models of population structure, yet the problem of dynamically modeling SIR-type epidemics in random networks remains complex. I resolve this dilemma by showing how the ... More

SIR dynamics in structured populations with heterogeneous connectivityAug 22 2005Dec 20 2005Most epidemic models assume equal mixing among members of a population. An alternative approach is to model a population as random network in which individuals may have heterogeneous connectivity. This paper builds on previous research by describing the ... More

On the analytic computation of massless propagators in dimensional regularizationMay 09 2013Mar 20 2014We comment on the algorithm to compute periods using hyperlogarithms, applied to massless Feynman integrals in the parametric representation. Explicitly, we give results for all three-loop propagators with arbitrary insertions including order $\varepsilon^4$ ... More

Recursive prescription for logarithmic jet rate coefficientsMay 27 2013Feb 11 2014We derive a recursion relation for the analytic leading logarithmic coefficients of a final state gluon cascade. We demonstrate the potential of our method by analytically computing the rate coefficients for the emission of up to 80 gluons in both the ... More

Rapidity Dependence of Elliptic Flow at RHICJan 04 2006The measured elliptic flow (v2) of identified particles as a function of pT and centrality at RHIC suggests the created medium in Au+Au collisions achieves early local thermal equilibrium that is followed by hydrodynamic expansion. It is not known if ... More

Continuity in the Alexiewicz normJun 21 2006If $f$ is a Henstock--Kurzweil integrable function on the real line, the Alexiewicz norm of $f$ is $\|f\|=\sup_I|\int_I f|$ where the supremum is taken over all intervals $I\subset\R$. Define the translation $\tau_x$ by $\tau_xf(y)=f(y-x)$. Then $\|\tau_xf-f\|$ ... More

Necessary and sufficient conditions for differentiating under the integral signJan 02 2001We give necessary and sufficient conditions for differentiating under the integral sign an integral that depends on a parameter. The conditions require the equality of two iterated integrals and depend on being able to integrate every derivative. The ... More

What Is a Black Hole?Aug 04 2018Although black holes are objects of central importance across many fields of physics, there is no agreed upon definition for them, a fact that does not seem to be widely recognized. Physicists in different fields conceive of and reason about them in radically ... More

Tournament limits: Degree distributions, score functions and self-conversenessNov 29 2016Motivated by known results for finite tournaments, we define and study the score functions of tournament kernels and the degree distributions of tournament limits. Our main theorem completely characterises those distributions that appear as the degree ... More

Non-geometric backgrounds in string theoryNov 27 2018Dec 13 2018This review provides an introduction to non-geometric backgrounds in string theory. Starting from a discussion of T-duality, geometric and non-geometric torus-fibrations are reviewed, generalised geometry and its relation to non-geometric backgrounds ... More

The Asymptotic Complexity of Coded-BKW with Sieving Using Increasing Reduction FactorsJan 19 2019The Learning with Errors problem (LWE) is one of the main candidates for post-quantum cryptography. At Asiacrypt 2017, coded-BKW with sieving, an algorithm combining the Blum-Kalai-Wasserman algorithm (BKW) with lattice sieving techniques, was proposed. ... More

Some divergent trigonometric integralsJan 02 2001Some divergent trigonometric integrals have appeared in standard tables for many years, listed as converging. We give a simple proof that these integrals diverge and trace their history. The original error was made when a (startlingly) famous mathematician ... More

On invertibility preserving linear maps, simultaneous triangularization and Property LFeb 18 1997Let F be a linear unital map of a unital matrix algebra A over the complex numbers into the complex n by n matrices. Then F induces a linear unital map Fk of the k by k matrices over A into the complex nk by nk matrices by the action of F on each entry ... More

Exo-Jupiters and Saturns from two Gaia-like missionsAug 19 2014Detection and orbit determination for thousands of planets with periods up to about 40 years would be obtained by astrometry from two Gaia-like missions, results which cannot be obtained by any other mission, planned or proposed. A billion stars of all ... More

A Constructive Examination of a Russell-style Ramified Type TheoryApr 22 2017In this paper we examine the natural interpretation of a ramified type hierarchy into Martin-L\"of type theory with an infinite sequence of universes. It is shown that under this predicative interpretation some useful special cases of Russell's reducibility ... More

On Young tableau involutions and patterns in permutationsAug 01 2009This thesis deals with three different aspects of the combinatorics of permutations. In the first two papers, two flavours of pattern avoiding permutations are examined; and in the third paper Young tableaux, which are closely related to permutations ... More

Finite von Neumann algebra factors with property GammaOct 13 2000Oct 14 2000Techniques introduced by G. Pisier in his proof that finite von Neumann factors with property gamma have length at most 5 are modified to prove that the length is 3. It is proved that if such a factor is a complemented subspace of some larger C*-algebra ... More

Bootstrap percolation on the Hamming torus with threshold 2Jul 09 2014Nov 01 2017This paper analyzes various questions pertaining to bootstrap percolation on the $d$-dimensional Hamming torus where each node is open with probability $p$ and the percolation threshold is 2. For each $d'<d$ we find the critical exponent for the event ... More

Principally polarized abelian surfaces with surjective galois representations on l-torsionDec 14 2012Nov 15 2013Given a rational variety $V$ defined over $K$, we consider a principally polarized abelian variety $A$ of dimension $g$ defined over $V$. For each prime l we then consider the galois representation on the $l$-torsion of $A_t$, where $t$ is a $K$-rational ... More

Classification of pairs of rotations in finite-dimensional Euclidean spaceFeb 20 2008A rotation in a Euclidean space V is an orthogonal map on V which acts locally as a plane rotation with some fixed angle. We give a classification of all pairs of rotations in finite-dimensional Euclidean space, up to simultaneous conjugation with orthogonal ... More

Local Moufang setsJun 15 2017All known Moufang sets arise, in some way or another, from an algebraic structure which can be called `division' in some way. In this PhD dissertation, I made an attempt to develop a theory of local Moufang sets, which generalize Moufang sets in a way ... More

On weakly D-differentiable operatorsMar 29 2013Mar 11 2015For an unbounded self-adjoint operator D on a Hilbert space H and a bounded operator a on H we say that a is weakly D-differentiable if for any pair of vectors x, y in H the function <exp(itD) a exp(-itD)x, y> is differentiable at t =0. We find several ... More

Hall-Littlewood polynomials and vector bundles on the Hilbert schemeDec 28 2012Let $E$ be the bundle defined by applying a polynomial representation of $GL_n$ to the tautological bundle on the Hilbert scheme of $n$ points in the complex plane. By a result of Haiman, the Cech cohomology groups $H^i(E)$ vanish for all $i>0$. It follows ... More

The regulated primitive integralNov 15 2009A function on the real line is called regulated if it has a left limit and a right limit at each point. If $f$ is a Schwartz distribution on the real line such that $f=F'$ (distributional or weak derivative) for a regulated function $F$ then the regulated ... More

Localization and free energy asymptotics in disordered statistical mechanics and random growth modelsJun 18 2019This dissertation develops, for several families of statistical mechanical and random growth models, techniques for analyzing infinite-volume asymptotics. In the statistical mechanical setting, we focus on the low-temperature phases of spin glasses and ... More

Generalized integrands and bond portfolios: Pitfalls and counter examplesSep 12 2009Jan 05 2011We construct Zero-Coupon Bond markets driven by a cylindrical Brownian motion in which the notion of generalized portfolio has important flaws: There exist bounded smooth random variables with generalized hedging portfolios for which the price of their ... More

Detection of a Hypercharge Axion in ATLASMay 28 2001This Master of Science thesis treats the hypercharge axion, which is a hypothetical pseudo-scalar particle with electroweak interactions. First, the theoretical context and the motivations for this study are discussed. In short, the hypercharge axion ... More

Tomography of random social networksSep 15 2005We study the statistical properties of large random networks with specified degree distributions. New techniques are presented for analyzing the structure of social networks. Specifically, we address the question of how many nodes exist at a distance ... More

Limit points of the iterative scaling procedureJul 23 2012The iterative scaling procedure (ISP) is an algorithm which computes a sequence of matrices, starting from some given matrix. The objective is to find a matrix 'proportional' to the given matrix, having given row and column sums. In many cases, for example ... More

Path correlations in a randomly oriented complete bipartite graphFeb 08 2011In a randomly oriented graph containing vertices $x$ and $y$, denote by $\{x\to y\}$ the event that there is a directed path from $x$ to $y$. We study the correlation between the events $\{x\to y\}$ and $\{y\to z\}$ for a (large) oriented complete bipartite ... More

Laplacian Growth, Elliptic Growth, and Singularities of the Schwarz PotentialSep 27 2010The Schwarz function has played an elegant role in understanding and in generating new examples of exact solutions to the Laplacian growth (or "Hele- Shaw") problem in the plane. The guiding principle in this connection is the fact that "non-physical" ... More

Characterizing the Set of Coherent Lower Previsions with a Finite Number of Constraints or VerticesMar 15 2012The standard coherence criterion for lower previsions is expressed using an infinite number of linear constraints. For lower previsions that are essentially defined on some finite set of gambles on a finite possibility space, we present a reformulation ... More

Outbursts of WZ Sge stars/TOADs: a phenomenological comparison with soft X-ray transientsDec 01 1998The outbursts of WZ Sge stars (or TOADs), are compared to those seen in the (soft) X-ray transients. Both types of outbursts exhibit strong similarities: large amplitudes, long recurrence times, occurrence of superhumps, and of rebrightenings or reflares ... More

Towards 4U 1630-47: a black-hole soft X-ray transient odysseyJul 27 1998Aug 12 19984U 1630-47 is a black-hole X-ray transient with one of the shortest recurrence times. Despite its regular outburst behaviour little is known about this source. Only recently has attention to this system increased. I discuss there the basic known (X-ray) ... More

Askey-Wilson polynomials and the quantum SU(2) group: survey and applicationsJul 25 1994Generalised matrix elements of the irreducible representations of the quantum $SU(2)$ group are defined using certain orthonormal bases of the representation space. The generalised matrix elements are relatively infinitesimal invariant with respect to ... More

One-parameter orthogonality relations for basic hypergeometric seriesMay 27 2003The second order hypergeometric q-difference operator is studied for the value c=-q. For certain parameter regimes the corresponding recurrence relation can be related to a symmetric operator on the Hilbert space l^2(Z). The operator has deficiency indices ... More

The observers' view of (very) long X-ray bursts: they are super!Oct 15 2003In many X-ray point sources on the sky, the X-ray emission arises because hydrogen and/or helium is accreted onto a neutron star from a nearby donor star. When this matter settles on the neutron star surface, it will undergo nuclear fusion. For a large ... More

Bootstrap percolation on the Hamming torus with threshold 2Jul 09 2014Oct 15 2016This paper analyzes various questions pertaining to bootstrap percolation on the $d$-dimensional Hamming torus where each node is open with probability $p$ and the percolation threshold is 2. For each $d'<d$ we find the critical exponent for the event ... More

A decomposition of the Schur block product on matrices of operatorsNov 08 2018Given two $m \times n $ matrices $A = (a_{ij})$ and $B=(b_{ij}) $ with entries in $B(H)$ for some Hilbert space $H,$ the Schur block product is the $m \times n$ matrix $ A\square B := (a_{ij}b_{ij}).$ There exists an $m \times n$ matrix $S = (s_{ij})$ ... More

Quantal interferometry with dissipative internal motionJun 02 2004Nov 16 2004In presence of dissipation, quantal states may acquire complex-valued phase effects. We suggest a notion of dissipative interferometry that accommodates this complex-valued structure and that may serve as a tool for analyzing the effect of certain kinds ... More

TASEP in any Weyl GroupApr 08 2014We investigate a Markov chain defined by Thomas Lam, which generalizes the multi-type TASEP on a ring to any Weyl group. For groups of type C we define an analogue of the multiline queues of Ferrari and Martin (which compute the stationary distribution ... More

Using real algebraic geometry to solve combinatorial problems with symmetriesAug 05 2014Nov 10 2014Many combinatorial problems can be formulated as a polynomial optimization problem that can be solved by state-of-the-art methods in real algebraic geometry. In this paper we explain many important methods from real algebraic geometry, we review several ... More

Enumeration of monochromatic three term arithmetic progressions in two-colorings of cyclic groupsAug 05 2014Nov 10 2014One of the toughest problems in Ramsey theory is to determine the existence of monochromatic arithmetic progressions in groups whose elements have been colored. We study the harder problem to not only determine the existence of monochromatic arithmetic ... More

On hyperlogarithms and Feynman integrals with divergences and many scalesJan 17 2014Mar 31 2014It was observed that hyperlogarithms provide a tool to carry out Feynman integrals. So far, this method has been applied successfully to finite single-scale processes. However, it can be employed in more general situations. We give examples of integrations ... More

Decomposition of tournament limitsApr 14 2016The theory of tournament limits and tournament kernels (often called graphons) is developed by extending common notions for finite tournaments to this setting; in particular we study transitivity and irreducibility of limits and kernels. We prove that ... More

Semi device independence of the BB84 protocolDec 10 2015May 24 2016The BB84 quantum key distribution protocol is semi device independent in the sense that it can be shown to be secure if just one of the users' devices is restricted to a qubit Hilbert space. Here, we derive an analytic lower bound on the asymptotic secret ... More

On the Topology of Metric Spaces definable in o-minimal expansions of fieldsOct 25 2015Nov 11 2015We study the topology of metric spaces which are definable in o-minimal expansions of ordered fields. We show that a definable metric space either contains an infinite definable discrete set or is definably homeomorphic to a definable set equipped with ... More

The Astrometric Foundation of AstrophysicsAug 09 2014Dec 04 2014Astrophysical studies require a knowledge of very accurate positions, motions and distances of stars. A brief overview is given of the significance and development of astrometry by ESA's two astrometric satellites, Hipparcos and Gaia, launched in respectively ... More

If Metrical Structure Were Not Dynamical, Counterfactuals in General Relativity Would Be EasySep 13 2015General relativity poses serious problems for counterfactual propositions peculiar to it as a physical theory. Because these problems arise solely from the dynamical nature of spacetime geometry, they are shared by all schools of thought on how counterfactuals ... More

Measure, Topology and Probabilistic Reasoning in CosmologySep 07 2015I explain the difficulty of making various concepts of and relating to probability precise, rigorous and physically significant when attempting to apply them in reasoning about objects (e.g., spacetimes) living in infinite-dimensional spaces, working ... More

Estimates of Henstock--Kurzweil Poisson integralsJun 18 2004If $f$ is a real-valued function on $[-\pi,\pi]$ that is Henstock--Kurzweil integrable, let $u_r(\theta)$ be its Poisson integral. It is shown that $\|u_r\|_p=o(1/(1-r))$ as $r\to 1$ and this estimate is sharp for $1\leq p\leq\infty$. If $\mu$ is a finite ... More

Hölder estimates for viscosity solutions of equations of fractional $p$-Laplace typeMay 26 2014Jun 24 2014We prove H\"older estimates for viscosity solutions of a class of possibly degenerate and singular equations modelled by the fractional $p$-Laplace equation $$ \text{PV} \int_{\mathbb{R}^n}\frac{|u(x)-u(x+y)|^{p-2}(u(x)-u(x+y))}{|y|^{n+sp}}\, dy =0, $$ ... More

Static overscreening and nonlinear response in the Hubbard ModelMay 29 2001We investigate the static charge response for the Hubbard model. Using the Slave-Boson method in the saddle-point approximation we calculate the charge susceptibility. We find that RPA works quite well close to half-filling, breaking, of course, down ... More

Jigsaw Percolation on Erdos-Renyi Random GraphsMar 21 2015Mar 28 2015We extend the jigsaw percolation model to analyze graphs where both underlying people and puzzle graphs are Erd\H{o}s-R\'enyi random graphs. Let $p_{\text{ppl}}$ and $p_{\text{puz}}$ denote the probability that an edge exists in the respective people ... More

Block matching algorithm based on Harmony Search optimization for motion estimationJun 17 2014Motion estimation is one of the major problems in developing video coding applications. Among all motion estimation approaches, Block-matching (BM) algorithms are the most popular methods due to their effectiveness and simplicity for both software and ... More

Astrometry for DynamicsAug 14 2014In May 2013, I responded with the present paper to ESA's call for White Papers for the definition of Large missions. This was half a year before the launch of ESA's large astrometry mission Gaia. The present proposal for a Gaia successor mission is similar ... More

Estimates of the remainder in Taylor's theorem using the Henstock--Kurzweil integralJun 18 2004When a real-valued function of one variable is approximated by its $n^{th}$ degree Taylor polynomial, the remainder is estimated using the Alexiewicz and Lebesgue $p$-norms in cases where $f^{(n)}$ or $f^{(n+1)}$ are Henstock--Kurzweil integrable. When ... More

Bounds on the Mordell--Weil rank of elliptic curves over imaginary quadratic number fields with class number 1Nov 19 2018We generalize the lemmas of Thomas Kretschmer to arbitrary number fields, and apply them with a 2-descent argument to obtain bounds for families of elliptic curves over certain imaginary quadratic number fields with class number 1. One such family occurs ... More

On work and heat in time-dependent strong couplingMay 22 2017This paper revisits the classical problem of representing a thermal bath interacting with a system as a large collection of harmonic oscillators initially in thermal equilibrium. As is well known the system then obeys an equation, which in the bulk and ... More

Normal forms for the G_2-action on the real symmetric 7x7-matrices by conjugationMar 12 2007Jun 08 2007The exceptional Lie group G_2 acts on the set of real symmetric 7x7-matrices by conjugation. We solve the normal form problem for this group action. In view of earlier results, this gives rise to a classification of all finite-dimensional real flexible ... More

Equity Allocation and Portfolio Selection in Insurance: A simplified Portfolio ModelJul 22 1999A quadratic discrete time probabilistic model, for optimal portfolio selection in (re-)insurance is studied. For positive values of underwriting levels, the expected value of the accumulated result is optimized, under constraints on its variance and on ... More

Isotopes of Hurwitz algebrasDec 08 2010Aug 10 2018We study the class of all algebras that are isotopic to a Hurwitz algebra. Isomorphism classes of such algebras are shown to correspond to orbits of a certain group action. A complete, geometrically intuitive description of the category of isotopes of ... More

Fourier series with the continuous primitive integralMay 27 2011Fourier series are considered on the one-dimensional torus for the space of periodic distributions that are the distributional derivative of a continuous function. This space of distributions is denoted $\alext$ and is a Banach space under the Alexiewicz ... More

Rapidly growing Fourier integralsJan 02 2001The Riemann-Lebesgue Lemma says that the Fourier transform of an absolutely integrable function on the real line tends to zero as the transform parameter tends to infinity. When the integral is allowed to converge conditionally, the transform can have ... More

Higher Weak Derivatives and Reflexive Algebras of OperatorsApr 14 2015Jul 09 2015Let D be a self-adjoint operator on a Hilbert space H and x a bounded operator on H. We say that x is n-times weakly D-differentiable, if for any pair of vectors a, b from H the function < exp(itD)x exp(-itD) a, b> is n-times differentiable. We give several ... More

Robust error estimates for stabilized finite element approximations of the two dimensional Navier-Stokes equations with application to implicit large eddy simulationMar 08 2013Apr 12 2013We consider error estimates in weak parametrised norms for stabilized finite element approximations of the two-dimensional Navier-Stokes' equations. These weak norms can be related to the norms of certain filtered quantities, where the parameter of the ... More

Error estimates for shock capturing finite element approximations of the one dimensional Burgers' equationNov 04 2011May 07 2014We propose an error analysis in weak norms of a shock capturing finite element method for the Burgers' equation. The estimates can be related to estimates of certain filtered quantities and are robust in the inviscid limit. Using a total variation apriori ... More

Constructivist and Structuralist Foundations: Bishop's and Lawvere's Theories of SetsJan 30 2012Bishop's informal set theory is briefly discussed and compared to Lawvere's Elementary Theory of the Category of Sets (ETCS). We then present a constructive and predicative version of ETCS, whose standard model is based on the constructive type theory ... More

The Asymptotic Complexity of Coded-BKW with Sieving Using Increasing Reduction FactorsJan 19 2019May 17 2019The Learning with Errors problem (LWE) is one of the main candidates for post-quantum cryptography. At Asiacrypt 2017, coded-BKW with sieving, an algorithm combining the Blum-Kalai-Wasserman algorithm (BKW) with lattice sieving techniques, was proposed. ... More

Signatures of hit and run collisionsOct 13 2018Terrestrial planets grew in a series of similar-sized collisions that swept up most of the next-largest bodies. Theia was accreted by the Earth to form the Moon according to the theory. Planetesimals likewise may have finished their accretion in a sequence ... More

A simplified characteristic functions of quantum heatApr 06 2019This paper presents a simplified structure of the characteristic function of the distribution of energy changes in a bosonic environment interacting linearly with a quantum system. This characteristic function of quantum heat can be expressed using the ... More

Upper and Lower Bounds on Zero-Sum Generalized Schur NumbersAug 11 2018Let $S_{\mathfrak{z}}(k,r)$ be the least positive integer such that for any $r$-coloring $\chi : \{1,2,\dots,S_{\mathfrak{z}}(k,r)\} \longrightarrow \{1, 2, \dots, r\}$, there is a sequence $x_1, x_2, \dots, x_k$ such that $\sum_{i=1}^{k-1} x_i = x_k$, ... More

Understanding AI Data Repositories with Automatic Query GenerationApr 20 2018We describe a set of techniques to generate queries automatically based on one or more ingested, input corpuses. These queries require no a priori domain knowledge, and hence no human domain experts. Thus, these auto-generated queries help address the ... More

A unified picture of strong coupling stochastic thermodynamics and time reversalsDec 21 2017Jan 02 2018Strong-coupling statistical thermodynamics is formulated as Hamiltonian dynamics of an observed system interacting with another unobserved system (a bath). It is shown that the entropy production functional of stochastic thermodynamics, defined as the ... More

Categories with families and first-order logic with dependent sortsMay 05 2016Jul 07 2019First-order logic with dependent sorts, such as Makkai's first-order logic with dependent sorts (FOLDS), or Aczel's and Belo's dependently typed (intuitionistic) first-order logic (DFOL), may be regarded as logic enriched dependent type theories. Categories ... More

Del Pezzo Surfaces in Weighted Projective SpacesJan 23 2013Nov 15 2016We study singular del Pezzo surfaces that are quasi-smooth and well-formed weighted hypersurfaces. We give an algorithm how to classify all of them.

Addition formula for 2-parameter family of Askey-Wilson polynomialsDec 07 1994For a two parameter family of Askey-Wilson polynomials, that can be regarded as basic analogues of the Legendre polynomials, an addition formula is derived. The addition formula is a two-parameter extension of Koornwinder's addition formula for the little ... More

A global view of quantum computation with noisy componentsJun 30 2016The operation of a quantum computer is considered as a general quantum operation on a mixed state on many qubits followed by a measurement. The general quantum operation is further represented as a Feynman-Vernon double path integral over the histories ... More

On RG-flow and the Cosmological ConstantDec 07 1999Dec 13 1999The AdS/CFT correspondence implies that the effective action of certain strongly coupled large $N$ gauge theories satisfy the Hamilton-Jacobi equation of 5d gravity. Using an analogy with the relativistic point particle, I construct a low energy effective ... More

Global Aspects of Electric-Magnetic DualityJun 01 1995Jun 06 1995We show that the partition function of free Maxwell theory on a generic Euclidean four-manifold transforms in a non-trivial way under electric-magnetic duality. The classical part of the partition sum can be mapped onto the genus-one partition function ... More

Ordinary differential equations with only entire solutionsJun 06 1997We prove necessary and sufficient conditions for a system $\dot z_i=z_ip_i(z)$ ($p_i$ a polynomial) to have only entire analytic functions as solutions.

A quantum cloning bound and application to quantum key distributionMar 20 2013Aug 14 2013We introduce a quantum cloning bound which we apply to a straightforward and relatively direct security proof of the prepare-and-measure Bennett-Brassard 1984 (BB84) quantum key distribution (QKD) protocol against collective attacks. The approach we propose ... More

On geometric phases for quantum trajectoriesAug 30 2006A sequence of completely positive maps can be decomposed into quantum trajectories. The geometric phase or holonomy of such a trajectory is delineated. For nonpure initial states, it is shown that well-defined holonomies can be assigned by using Uhlmann's ... More