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LazyFP: Leaking FPU Register State using Microarchitectural Side-ChannelsJun 19 2018Modern processors utilize an increasingly large register set to facilitate efficient floating point and SIMD computation. This large register set is a burden for operating systems, as its content needs to be saved and restored when the operating system ... More

ZombieLoad: Cross-Privilege-Boundary Data SamplingMay 14 2019In early 2018, Meltdown first showed how to read arbitrary kernel memory from user space by exploiting side-effects from transient instructions. While this attack has been mitigated through stronger isolation boundaries between user and kernel space, ... More

A bound for orderings of Reidemeister movesNov 29 2011Dec 01 2011We provide an upper bound on the number of ordered Reidemeister moves required to pass between two diagrams of the same link. This bound is in terms of the number of unordered Reidemeister moves required.

The Definition of Mach's PrincipleJul 20 2010Two definitions of Mach's principle are proposed. Both are related to gauge theory, are universal in scope and amount to formulations of causality that take into account the relational nature of position, time, and size. One of them leads directly to ... More

In defence of negative temperatureAug 03 2015Sep 21 2015This pedagogical comment highlights three misconceptions concerning the usefulness of the concept of negative temperature; being derived from the usual, often termed Boltzmann, definition of entropy. First, both the Boltzmann and Gibbs entropies must ... More

Counting Zeros of Cosine Polynomials: On a Problem of LittlewoodOct 24 2016We show that if $A$ is a finite set of non-negative integers then the number of zeros of the function \[ f_A(\theta) = \sum_{a \in A } \cos(a\theta) , \] in $[0,2\pi]$, is at least $(\log \log \log |A|)^{1/2-\varepsilon}$. This gives the first unconditional ... More

Improved Parallel Construction of Wavelet Trees and Rank/Select StructuresOct 11 2016Existing parallel algorithms for wavelet tree construction have a work complexity of $O(n\log\sigma)$. This paper presents parallel algorithms for the problem with improved work complexity. Our first algorithm is based on parallel integer sorting and ... More

Holographic Schwinger Effect and the Geometry of EntanglementJul 25 2013Dec 23 2013In this note we point out that the recently proposed bulk dual of an entangled pair of a quark and an anti-quark corresponds to the Lorentzian continuation of the tunneling instanton describing Schwinger pair creation in the dual field theory. This observation ... More

Crossed Products by Automorphisms with the Tracial Quasi-Rokhlin PropertyJun 27 2013We introduce the tracial quasi-Rokhlin property for an automorphism alpha of a unital C*-algebra A, which is not assumed to be simple. We show that under suitable hypotheses, the associated crossed product C*-algebra C*(Z,A,alpha) is simple, and there ... More

Seesaw parametrization for n right-handed neutrinosJul 23 2012Nov 27 2012Introducing n right-handed neutrinos to the Standard Model yields, in general, massive active neutrinos. We give explicit parametrizations for the involved mixing and coupling matrices in terms of physical parameters for both the top-down and the bottom-up ... More

Synchronisation in Invertible Random Dynamical Systems on the CircleFeb 26 2015Jul 05 2015Given a composition of i.i.d. random orientation-preserving homeomorphisms or a memoryless stochastic flow of homeomorphisms on the circle, we show that provided the randomness allows for a sufficient range of possible behaviour on a finite time-scale, ... More

Analytic stability analysis of three-component self-regulatory genetic circuitAug 03 2014Aug 09 2014A self-regulatory genetic circuit, where a protein acts as a positive regulator of its own production, is known to be a simplest form of biological network with a positive feedback loop. Although at least three components, DNA, RNA, and the protein, are ... More

Pinching and asymptotical roundness for inverse curvature flows in Euclidean spaceApr 10 2014Jun 18 2015We consider inverse curvature flows in the $(n+1)$-dimensional Euclidean space, $n\geq 2,$ expanding by arbitrary negative powers of a 1-homogeneous, monotone curvature function $F$ with some concavity properties. We obtain asymptotical roundness, meaning ... More

Power Spectrum Estimators For Large CMB DatasetsDec 08 1997Dec 11 1997Forthcoming high-resolution observations of the Cosmic Microwave Background (CMB) radiation will generate datasets many orders of magnitude larger than have been obtained to date. The size and complexity of such datasets presents a very serious challenge ... More

Numerical Methods in Cosmological Global Texture SimulationsMar 03 1994Numerical simulations of the evolution of a global topological defect field have two characteristic length scales --- one macrophysical, of order the field correlation length, and the other microphysical, of order the field width. The situation currently ... More

Periods, supercongruences, and their motivic liftsAug 24 2016A period is a complex number arising as the integral of a rational function, with rational coefficients, over a rationally-defined region. Though periods are typically transcendental, the theory of motives predicts a version of Galois theory should hold ... More

Necessary and Sufficient Conditions for Stable Synchronisation in Random Dynamical SystemsAug 24 2014Feb 25 2015For a product of i.i.d. random maps or a memoryless stochastic flow on a compact space $X$, we find conditions under which the presence of locally asymptotically stable trajectories (e.g. as given by negative Lyapunov exponents) implies almost-sure mutual ... More

On vanishing criteria that control finite group structureSep 22 2015Many results have been established that show how arithmetic conditions on conjugacy class sizes affect group structure. A conjugacy class in $G$ is called vanishing if there exists some irreducible character of $G$ which evaluates to zero on the conjugacy ... More

The signed permutation group on Feynman graphsDec 08 2015Feb 23 2016The Feynman rules assign to every graph an integral which can be written as a function of a scaling parameter L. Assuming L for the process under consideration is very small, so that contributions to the renormalizaton group are small, we can expand the ... More

Non-vanishing elements in finite groupsMar 13 2016Mar 19 2016Many results have been established about determining whether or not an element evaluates to zero on an irreducible character of a group. In this note it is shown that if a group $G$ has a normal nilpotent subgroup $N$, and $P$ is a Sylow $p$-subgroup ... More

Synchronisation in Invertible Random Dynamical Systems on the CircleFeb 26 2015Aug 14 2017In this paper, we study geometric features of orientation-preserving random dynamical systems on the circle driven by memoryless noise that exhibit stable synchronisation: we consider crack points, invariant measures, and the link between synchronisation ... More

Dynamics and correlations of a Bose-Einstein condensate of photonsJul 23 2018The Tutorial reports recent experimental advances in studies of the dynamics as well as the number and phase correlations of a Bose-Einstein condensed photon gas confined in a high-finesse dye-filled microcavity. Repeated absorption-emission-processes ... More

A Hardy-Littlewood Maximal Operator Adapted to the Harmonic OscillatorDec 26 2016Dec 26 2018This paper constructs a Hardy-Littlewood type maximal operator adapted to the Schr\"{o}dinger operator $\mathcal{L} := -\Delta + |x|^{2}$ acting on $L^{2}(\mathbb{R}^{d})$. It achieves this through the use of the Gaussian grid $\Delta^{\gamma}_{0}$, constructed ... More

Interpretation of Lepton Flavor ViolationOct 24 2016Jan 30 2017The observation of a charged-lepton flavor violating process would be a definite sign for physics beyond the Standard Model, but would actually only prove that one particular linear combination of lepton numbers is violated. We categorize lepton-flavor-violating ... More

An explicit construction for neighborly centrally symmetric polytopesJun 29 2006We give an explicit construction, based on Hadamard matrices, for an infinite series of floor{sqrt{d}/2}-neighborly centrally symmetric d-dimensional polytopes with 4d vertices. This appears to be the best explicit version yet of a recent probabilistic ... More

Long monotone paths on simple 4-polytopesFeb 15 2004The Monotone Upper Bound Problem (Klee, 1965) asks if the number M(d,n) of vertices in a monotone path along edges of a d-dimensional polytope with n facets can be as large as conceivably possible: Is M(d,n) = M_{ubt}(d,n), the maximal number of vertices ... More

Between ${\cal A}$- and ${\cal B}$-setsNov 01 1998The aim of this paper is to introduce the class of ${\cal A}{\cal B}$-sets as the sets that are the intersection of an open and a semi-regular set. Several classes of well-known topological spaces are characterized via the new concept. A new decomposition ... More

Multiplications and Convolutions in L. Schwartz' Spaces of Test Functions and Distributions and their ContinuitySep 19 2012Feb 05 2013We list multiplier and convolutor spaces of the spaces occurring in L. Schwartz' "Th\'eorie des distributions". Furthermore we clarify whether the multiplications and convolutions are continuous or not.

On a Direct Description of Pseudorelativistic Nelson HamiltoniansOct 08 2018Abstract interior-boundary conditions (IBC's) allow for the direct description of the domain and the action of Hamiltonians for a certain class of ultraviolet-divergent models in Quantum Field Theory. The method was recently applied to models where nonrelativistic ... More

A general family of congruences for Bernoulli numbersJun 20 2017Nov 22 2017We prove a general family of congruences for Bernoulli numbers whose index is a polynomial function of a prime, modulo a power of that prime. Our family generalizes many known results, including the von Staudt--Clausen theorem and Kummer's congruence. ... More

Trapped modes for periodic structures in waveguidesJul 03 2002The Laplace operator is considered for waveguides perturbed by a periodic structure consisting of N congruent obstacles spanning the waveguide. Neumann boundary conditions are imposed on the periodic structure, and either Neumann or Dirichlet conditions ... More

The hyperbolic Ernst--Maxwell equations in a triangular domainNov 26 2018In a recent paper, we applied Riemann--Hilbert techniques to analyze the Goursat problem for the hyperbolic Ernst equation, which describes the interaction of two colliding gravitational plane waves. Here we generalize this approach to colliding electromagnetic ... More

Unveiling Eilenberg-type Correspondences: Birkhoff's Theorem for (finite) Algebras + DualityFeb 09 2017The purpose of the present paper is to show that: Eilenberg-type correspondences = Birkhoff's theorem for (finite) algebras + duality. We consider algebras for a monad T on a category D and we study (pseudo)varieties of T-algebras. Pseudovarieties of ... More

Generalized Selective Modal AnalysisJun 08 1999Jul 27 1999A new approach which generalizes the Selective Modal Analyis (SMA) and algorithms based upon it for solving the generalized eigenvalue problem is described. This approach allows for the systematic consideration of physical properties of the system under ... More

Exponential Patterns in Arithmetic Ramsey TheoryJul 28 2016We show that for every finite colouring of the natural numbers there exists $a,b >1$ such that the triple $\{a,b,a^b\}$ is monochromatic. We go on to show the partition regularity of a much richer class of patterns involving exponentiation. For example, ... More

A Fast Method For Bounding The CMB Power Spectrum Likelihood FunctionMar 10 1998As the Cosmic Microwave Background (CMB) radiation is observed to higher and higher angular resolution the size of the resulting datasets becomes a serious constraint on their analysis. In particular current algorithms to determine the location of, and ... More

How stable is the photon?Apr 10 2013Jul 11 2013Yes, the photon. While a nonzero photon mass has been under experimental and theoretical study for years, the possible implication of a finite photon lifetime lacks discussion. The tight experimental upper bound of the photon mass restricts the kinematically ... More

The Nature of TimeMar 20 2009A review of some basic facts of classical dynamics shows that time, or precisely duration, is redundant as a fundamental concept. Duration and the behaviour of clocks emerge from a timeless law that governs change.

Gradient estimates for inverse curvature flows in hyperbolic spaceOct 06 2014We prove gradient estimates for hypersurfaces in the hyperbolic space $\mathbb{H}^{n+1},$ expanding by negative powers of a certain class of homogeneous curvature functions. We obtain optimal gradient estimates for hypersurfaces evolving by certain powers ... More

Exact Partition Function Zeros of the Wako-Saito-Muñoz-Eaton Protein ModelMay 14 2013I compute exact partition function zeros of the Wako-Saito-Mu\~noz-Eaton model for various secondary structural elements and for two proteins, 1BBL and 1I6C, using both analytic and numerical methods. Two-state and barrierless downhill folding transitions ... More

Non-scale-invariant inverse curvature flows in hyperbolic spaceOct 10 2012Dec 12 2013We consider inverse curvature flows in hyperbolic space with starshaped initial hypersurface, driven by positive powers of a homogeneous curvature function. The solutions exist for all time and, after rescaling, converge to a sphere.

Analytic Partition Function Zeros of the Wako-Saito-Munoz-Eaton beta-hairpin ModelSep 26 2012Sep 28 2012An analytic formula for the density of states of Wako-Saito-Munoz-Eaton model, for a simple class of beta-hairpins, is obtained. Under certain simplifying assumptions on the structure of the native contacts and the values of local entropy, the partition ... More

Quantitative oscillation estimates for almost-umbilical closed hypersurfaces in Euclidean spaceApr 09 2014We prove $\epsilon$-closeness of hypersurfaces to a sphere in Euclidean space under the assumption that the traceless second fundamental form is $\delta$-small compared to the mean curvature. We give the explicit dependence of $\delta$ on $\epsilon$ within ... More

On universality of charge transport in AdS/CFTApr 29 2013May 17 2013We develop the holographic formulation of transport in strongly coupled two-layer systems. We identify a dc conductivity, sigma^dc, that is finite even in a translationally invariant setup, and universal for CFTs with a gravity dual. The thermoelectric ... More

Prospecies of algebras I: Basic propertiesAug 05 2016In this paper, we generalise part of the theory of hereditary algebras to the context of prospecies of algebras. Here, a prospecies is a generalisation of Gabriel's concept of species gluing algebras via projective bimodules along a quiver to obtain a ... More

Isoperimetry in supercritical bond percolation in dimensions three and higherFeb 17 2016We study the isoperimetric subgraphs of the infinite cluster $\textbf{C}_\infty$ for supercritical bond percolation on $\mathbb{Z}^d$ with $d\geq 3$. Specifically, we consider the subgraphs of $\textbf{C}_\infty \cap [-n,n]^d$ which have minimal open ... More

Lepton flavor violation with light vector bosonsFeb 11 2016May 10 2016New sub-GeV vector bosons with couplings to muons but not electrons have been discussed in order to explain the muon's magnetic moment, the gap of high-energy neutrinos in IceCube or the proton radius puzzle. If such a light Z' not only violates lepton ... More

Bond Pricing under Knightian Uncertainty: A Short Rate Model with Drift and Volatility UncertaintyAug 10 2018It is shown how to construct an arbitrage-free short rate model under uncertainty about the drift and the volatility. The uncertainty is represented by a set of priors, which naturally leads to a G-Brownian motion. Within this framework, it is shown how ... More

The Massless Nelson Hamiltonian and its DomainJan 17 2019In the theory of point interactions, one is given a formal expression for a quantum mechanical Hamiltonian. The interaction terms of the Hamiltonian are singular: they can not be rigorously defined as a perturbation (in the operator or form sense) of ... More

Prospecies of algebras I: Basic propertiesAug 05 2016Mar 06 2017In this paper, we generalise part of the theory of hereditary algebras to the context of prospecies of algebras. Here, a prospecies is a generalisation of Gabriel's concept of species gluing algebras via projective bimodules along a quiver to obtain a ... More

Connecting Atomistic and Continuous Models of ElastodynamicsJun 06 2016Jun 29 2016We prove long-time existence of solutions for the equations of atomistic elastodynamics on a bounded domain with time-dependent boundary values as well as their convergence to a solution of continuum nonlinear elastodynamics as the interatomic distances ... More

Quantitative normal approximation for sums of random variables with multilevel local dependence structureMay 24 2019We establish a quantitative normal approximation result for sums of random variables with multilevel local dependencies. As a corollary, we obtain a quantitative normal approximation result for linear functionals of random fields which may be approximated ... More

The Kato Square Root Problem for Divergence Form Operators with PotentialDec 26 2018Jan 13 2019The Kato square root problem for divergence form elliptic operators with potential $V:\mathbb{R}^{n} \rightarrow \mathbb{C}$ is the equivalence statement $\left\Vert \left( \mathcal{L}_{A}^{V} \right)^{\frac{1}{2}}u \right\Vert \simeq \left\Vert \nabla ... More

The derivation of Markov processes that violate detailed balanceAug 01 2017Feb 22 2018Time-reversal symmetry of microscopic laws dictates that the equilibrium distribution of a stochastic process must obey the detailed balance. On the other hand, cyclic Markov processes that do not admit equilibrium distributions with detailed balance, ... More

The Hull-White Model under Knightian Uncertainty about the VolatilityAug 10 2018May 09 2019We construct an arbitrage-free short rate model under Knightian uncertainty about the volatility. The uncertainty is represented by a set of priors, which naturally leads to a G-Brownian motion. Within this framework, it is shown how to characterize the ... More

Majorons as cold light dark matterSep 25 2018Majorons are the Goldstone bosons of spontaneously broken lepton number and hence intimately connected to Majorana neutrino masses. Since all majoron couplings are heavily suppressed by the seesaw scale they are interesting candidates for long-lived dark ... More

Finite F-inveres covers do existAug 15 2018We show that every finite inverse monoid has an idempotent-separating cover by a finite F-inverse monoid. This provides a positive answer to a conjecture of Henckell and Rhodes.

AI Researchers, Video Games Are Your Friends!Dec 06 2016If you are an artificial intelligence researcher, you should look to video games as ideal testbeds for the work you do. If you are a video game developer, you should look to AI for the technology that makes completely new types of games possible. This ... More

Timelike twisted geometriesNov 02 2016Jan 11 2017Within the twistorial parametrization of Loop Quantum Gravity we investigate the consequences of choosing a spacelike normal vector in the linear simplicity constraints. The amplitudes for the $SU(2)$ boundary states of Loop Quantum Gravity, given by ... More

Monochromatic Solutions to Systems of Exponential EquationsJul 30 2016Let $n\in \mathbb{N}$, $R$ be a binary relation on $[n]$, and $C_1(i,j),\ldots,C_n(i,j) \in \mathbb{Z}$, for $i,j \in [n]$. We define the exponential system of equations $\mathcal{E}(R,(C_k(i,j)_{i,j,k})$ to be the system \[ X_i^{Y_1^{C_1(i,j)} \cdots ... More

Phenomenology of MajoronsSep 22 2017Majorons are the Goldstone bosons associated to lepton number and thus closely connected to Majorana neutrino masses. Couplings to charged fermions arise at one-loop level, including lepton-flavor-violating ones that lead to decays $\ell\to \ell' J$, ... More

Intrinsic isoperimetry of the giant component of supercritical bond percolation in dimension twoNov 01 2016We study the isoperimetric subgraphs of the giant component $\textbf{C}_n$ of supercritical bond percolation on the square lattice. These are subgraphs of $\textbf{C}_n$ having minimal edge boundary to volume ratio. In contrast to the work of Biskup, ... More

Kalai's squeezed 3-spheres are polytopalOct 22 2001In 1988, Kalai extended a construction of Billera and Lee to produce many triangulated (d-1)-spheres. In fact, in view of upper bounds on the number of simplicial d-polytopes by Goodman and Pollack, he derived that for every dimension d>=5, most of these ... More

MADCAP - The Microwave Anisotropy Dataset Computational Analysis PackageNov 19 1999Realizing the extraordinary scientific potential of the CMB requires precise measurements of its tiny anisotropies over a significant fraction of the sky at very high resolution. The analysis of the resulting datasets is a serious computational challenge. ... More

On The Absence Of Open Strings In A Lattice-Free Simulation Of Cosmic String FormationNov 10 1995May 02 1996Lattice-based string formation algorithms can, at least in principle, be reduced to the study of the statistics of the corresponding aperiodic random walk. Since in three or more dimensions such walks are transient this approach necessarily generates ... More

Self-Sealing Shells: Blowouts and Blisters on the Surfaces of Leaky Wind-Blown-Bubbles and Supernova RemnantsAug 15 2013Blowouts can occur when a dense shell confining hot, high pressure, gas ruptures. The venting gas inflates a blister on the surface of the shell. Here we examine the growth of such blisters on the surfaces of wind-blown-bubbles (WBBs) and supernova remnants ... More

Convergence to the equilibria for self-stabilizing processes in double-well landscapeMay 24 2013We investigate the convergence of McKean-Vlasov diffusions in a nonconvex landscape. These processes are linked to nonlinear partial differential equations. According to our previous results, there are at least three stationary measures under simple assumptions. ... More

Measurements of $Δm_d$, $Δm_s$, and $\sin 2 β$ with LHCbDec 18 2012We present measurements of the oscillation frequencies $\Delta m_d$ and $\Delta m_s$ of $B$ meson mixing as well as a measurement of the time-dependent CP-asymmetry in decays of $B^0\to J/\psi K_{\text{S}}^0$ based on $1.0\,\text{fb}^{-1}$ of data collected ... More

Mach's Principle: A Response to Mashhoon and Wesson's Paper arXiv: 1106.6036Aug 15 2011In their recent "Mach's principle and higher-dimensional dynamics", Mashhoon and Wesson argue that Mach's principle is not properly incorporated into general relativity and that in Einstein's theory "the origin of inertia remains essentially the same ... More

Microcanonical analysis of a nonequilibrium phase transitionJun 25 2015Jul 06 2015Microcanonical analysis is a powerful method for studying phase transitions of finite-size systems. This method has been used so far only for studying phase transitions of equilibrium systems, which can be described by microcanonical entropy. I show that ... More

The electroweak matter sector from an effective theory perspectiveAug 07 2002The object of this thesis is the study of some open problems in the electroweak matter sector from an effective theory perspective. The topics studied include: General aspects of dynamical symmetry breaking models, studying what traces these mechanisms ... More

Lepton Number Violation with and without Majorana NeutrinosMar 26 2015We discuss the various incarnations of a gauged B-L symmetry: 1) unbroken, it features Dirac neutrinos, neutrinogenesis to create the baryon asymmetry of our Universe, and a potentially light Z' boson; 2) broken by two units, we obtain the standard case ... More

Unbroken B-L SymmetryAug 28 2014Nov 10 2014The difference between baryon number B and lepton number L is the only anomaly-free global symmetry of the Standard Model, easily promoted to a local symmetry by introducing three right-handed neutrinos, which automatically make neutrinos massive. The ... More

Parallel Wavelet Tree ConstructionJul 30 2014Apr 01 2015We present parallel algorithms for wavelet tree construction with polylogarithmic depth, improving upon the linear depth of the recent parallel algorithms by Fuentes-Sepulveda et al. We experimentally show on a 40-core machine with two-way hyper-threading ... More

Multiple harmonic sums and Wolstenholme's theoremFeb 01 2013We give a family of congruences for the binomial coefficients ${kp-1\choose p-1}$ in terms of multiple harmonic sums, a generalization of the harmonic numbers. Each congruence in this family (which depends on an additional parameter $n$) involves a linear ... More

The Minimum Tollbooth Problem in Atomic Network Congestion Games with Unsplittable FlowsJun 24 2019This work analyzes the minimum tollbooth problem in atomic network congestion games with unsplittable flows. The goal is to place tolls on edges, such that there exists a pure Nash equilibrium in the tolled game that is a social optimum in the untolled ... More

Boundary behavior of solutions of a class of genuinely nonlinear hyperbolic systemsMar 12 2007Sep 16 2007For a certain class of genuinely nonlinear two-by-two planar hyperbolic systems we show that any classical solution on a smoothly bounded domain has nontangential boundary limits except on a set whose Hausdorff dimension is bounded by some system-dependent ... More

Values of symmetric polynomials and a truncated analogue of the Riemann zeta functionJul 09 2014Jan 12 2015For each positive integer n, we determine the set of symmetric functions f for which the congruence f(p/1,p/2,...,p/(p-1)) \equiv 0 mod p^n holds for all sufficiently large primes p. Our determination is conditional on a conjecture regarding the modulo ... More

Auslander-Reiten theory of Frobenius-Lusztig kernelsJan 25 2012In this paper we show that the tree class of a component of the stable Auslander-Reiten quiver of a Frobenius-Lusztig kernel is one of the three infinite Dynkin diagrams. For the special case of the small quantum group we show that the periodic components ... More

Orthocompactness and semi-stratifiability in the density topologySep 12 1998The density topology $\cal T$ is a topology on the real line, finer than the usual topology, having as its open sets the measurable subsets of ${\mathbb R}$, which are of density 1 at each of their points. The aim of this paper is to determine which subsets ... More

Asymptotics to all orders of the Euler--Darboux equation in a triangleJun 08 2018Nov 26 2018In Einstein's theory of relativity, the interaction of two collinearly polarized plane gravitational waves can be described by a Goursat problem for the Euler--Darboux equation in a triangular domain. In this paper, using a representation of the solution ... More

Inverse curvature flows in Riemannian warped productsDec 27 2017Jan 24 2018The long-time existence and umbilicity estimates for compact, graphical solutions to expanding curvature flows are deduced in Riemannian warped products of a real interval with a compact fibre. Notably we do not assume the ambient manifold to be rotationally ... More

Isoperimetry in supercritical bond percolation in dimensions three and higherFeb 17 2016Oct 27 2017We study the isoperimetric subgraphs of the infinite cluster $\textbf{C}_\infty$ for supercritical bond percolation on $\mathbb{Z}^d$ with $d\geq 3$. Specifically, we consider the subgraphs of $\textbf{C}_\infty \cap [-n,n]^d$ which have minimal open ... More

Timelike twisted geometriesNov 02 2016Within the twistorial parametrization of Loop Quantum Gravity we investigate the consequences of choosing a spacelike normal vector in the linear simplicity constraints. The amplitudes for the $SU(2)$ boundary states of Loop Quantum Gravity, given by ... More

Mesh-free free-form lensing I: Methodology and application to mass reconstructionDec 16 2014Jun 10 2016Many applications and algorithms in the field of gravitational lensing make use of meshes with a finite number of nodes to analyze and manipulate data. Specific examples in lensing are astronomical CCD images in general, the reconstruction of density ... More

The inverse mean curvature flow in warped cylinders of non-positive radial curvatureDec 19 2013Oct 06 2016We consider the inverse mean curvature flow in smooth Riemannian manifolds of the form $([R_{0},\infty)\times S^n,\bar{g})$ with metric $\bar{g}=dr^2+{\vartheta}^2(r){\sigma}$ and non-positive radial sectional curvature. We prove, that for initial mean-convex ... More

Smallness and Comparison Properties for Minimal Dynamical SystemsJun 27 2013We introduce the dynamic comparison property for minimal dynamical systems which has applications to the study of crossed product C*-algebras. We demonstrate that this property holds for a large class of systems which includes all examples where the underlying ... More

Microcanonical Origin of the Maximum Entropy Principle for Open SystemsJun 26 2012The canonical ensemble describes an open system in equilibrium with a heat bath of fixed temperature. The probability distribution of such a system, the Boltzmann distribution, is derived from the uniform probability distribution of the closed universe ... More

Biserial algebras via subalgebras and the path algebra of D_4Apr 22 2010We give two new criteria for a basic algebra to be biserial. The first one states that an algebra is biserial iff all subalgebras of the form eAe where e is supported by at most 4 vertices are biserial. The second one gives some condition on modules that ... More

A Rotating Holographic SuperconductorMar 03 2009Mar 31 2009In this paper we initiate the study of SSB in 3+1 dimensional rotating, charged, asymptotically AdS black holes. The theory living on their boundary, R x S^2, has the interpretation of a 2+1 dimensional rotating holographic superconductor. We study the ... More

A Criterion for $\mathcal{Z}$-Stability with Applications to Crossed ProductsJul 27 2015Aug 31 2016Building on an argument by Toms and Winter, we show that if $A$ is a simple, separable, unital, $\mathcal{Z}$-stable C*-algebra, then the crossed product of $C(X,A)$ by an automorphism is also Z-stable, provided that the automorphism induces a minimal ... More

The set of infinite valence values of an analytic functionAug 21 2015It is shown (Theorem A and its corollary) that if g is any nonconstant nonunivalent analytic function on a half-plane H and if D is either a half-plane or a smoothly bounded Jordan domain, then there is a function f on D for which f'(D) subset g'(H) such ... More

Evolution of a Subsumption Architecture NeurocontrollerMay 06 2004An approach to robotics called layered evolution and merging features from the subsumption architecture into evolutionary robotics is presented, and its advantages are discussed. This approach is used to construct a layered controller for a simulated ... More

A more "complete" version of the Pi-theorem: DRAFTJul 22 2011The traditional Pi-theorem tells us that for any dimensionally invariant relation there exists a full set of independent dimensionless "Pi groups" which can be used to nondimensionalise the relation. In this paper, we seek to understand better the structure ... More

Arrows of time in unconfined systemsFeb 25 2016Entropy and the second law of thermodynamcs were discovered through study of the behaviour of gases in confined spaces. The related techniques developed in the kinetic theory of gases have failed to resolve the apparent conflict between the time-reversal ... More

Synchronisation of almost all trajectories of a random dynamical systemNov 27 2015Jan 09 2016It has been shown by Le Jan that, given a memoryless-noise random dynamical system together with an ergodic distribution for the associated Markov transition probabilities, if the support of the ergodic distribution admits locally asymptotically stable ... More

Next Generation Multicuts for Semi-Planar GraphsNov 06 2015We study the problem of multicut segmentation. We introduce modified versions of the Semi-PlanarCC based on bounding Lagrange multipliers. We apply our work to natural image segmentation.

Gale duality bounds for roots of polynomials with nonnegative coefficientsJul 20 2007Nov 16 2009We bound the location of roots of polynomials that have nonnegative coefficients with respect to a fixed but arbitrary basis of the vector space of polynomials of degree at most $d$. For this, we interpret the basis polynomials as vector fields in the ... More

The MHS algebra and supercongruencesAug 24 2016Jun 20 2017A supercongruence is a congruence between rational numbers modulo a power of a prime. In this paper, we give a technique for finding and algorithmically proving supercongruences by expressing terms as infinite series involving certain generalizations ... More

Perturbed redshifts from N-body simulationsAug 24 2017Jan 31 2018In order to keep pace with the increasing data quality of astronomical surveys the observed source redshift has to be modeled beyond the well-known Doppler contribution. In this letter I want to examine the gauge issue that is often glossed over when ... More