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A trajectory-based framework for data-driven system analysis and controlMar 26 2019Sep 04 2019The vector space of all input-output trajectories of a discrete-time linear time-invariant (LTI) system is spanned by time-shifts of a single measured trajectory, given that the respective input signal is persistently exciting. This fact, which was proven ... More

A trajectory-based framework for data-driven system analysis and controlMar 26 2019The vector space of all input-output trajectories of a discrete-time linear time-invariant (LTI) system is spanned by time-shifts of a single measured trajectory, given that the respective input signal is persistently exciting. This fact, which was proven ... More

Data-Driven Model Predictive Control with Stability and Robustness GuaranteesJun 11 2019We propose a robust data-driven model predictive control (MPC) scheme to control linear time-invariant (LTI) systems. The scheme uses an implicit model description based on behavioral systems theory and past measured trajectories. In particular, it does ... More

Robust data-driven state-feedback designSep 10 2019We consider the problem of designing robust state-feedback controllers for discrete-time linear time-invariant systems, based directly on measured data. The proposed design procedures require no model knowledge, but only a single open-loop data trajectory, ... More

Arrangement Computation for Planar Algebraic CurvesMar 24 2011We present a new certified and complete algorithm to compute arrangements of real planar algebraic curves. Our algorithm provides a geometric-topological analysis of the decomposition of the plane induced by a finite number of algebraic curves in terms ... More

The Virtuous Machine - Old Ethics for New Technology?Jun 27 2018Modern AI and robotic systems are characterized by a high and ever-increasing level of autonomy. At the same time, their applications in fields such as autonomous driving, service robotics and digital personal assistants move closer to humans. From the ... 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

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

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

Improved Parallel Construction of Wavelet Trees and Rank/Select StructuresOct 11 2016Jan 18 2017Existing 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

The choice of representative volumes in the approximation of effective properties of random materialsJul 02 2018The effective large-scale properties of materials with random heterogeneities on a small scale are typically determined by the method of representative volumes: A sample of the random material is chosen - the representative volume - and its effective ... More

Exchangeable interval hypergraphs and limits of ordered discrete structuresFeb 25 2018A hypergraph $(V,E)$ is called an interval hypergraph if there exists a linear order $l$ on $V$ such that every edge $e\in E$ is an interval w.r.t. $l$; we also assume that $\{j\}\in E$ for every $j\in V$. Our main result is a de Finetti-type representation ... More

General Erased-Word Processes: Product-Type Filtrations, Ergodic Laws and Martin BoundariesDec 01 2017Mar 26 2019We study the dynamics of erasing randomly chosen letters from words by introducing a certain class of discrete-time stochastic processes, general erased-word processes(GEWPs), and investigating three closely related topics: Representation, Martin boundary ... More

Isotropic functions revisitedMar 09 2017Jan 02 2018To a smooth and symmetric function $f$ defined on a symmetric open set $\Gamma\subset\mathbb{R}^{n}$ and a real $n$-dimensional vector space $V$ we assign an associated operator function $F$ defined on an open subset $\Omega\subset\mathcal{L}(V)$ of linear ... More

Summary of the 36th ICRC Gamma-ray Indirect sessionsAug 29 2019At the 36 th ICRC during 11 parallel Gamma-Ray Indirect sessions in total about 70 talks were presented. A few of the plenary highlight talks as well concerned mostly indirect observations of gamma rays. In addition about 140 posters on this topic have ... 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

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

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

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

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

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

The Minkowski inequality in de Sitter spaceSep 15 2019The classical Minkowski inequality in the Euclidean space provides a lower bound on the total mean curvature of a hypersurface in terms of the surface area, which is optimal on round spheres. In this paper we employ a locally constrained inverse mean ... 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

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

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

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

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

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

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

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

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

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

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

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

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 Challenge Of Data Analysis For Future CMB ObservationsMar 13 1999Ongoing observations of the Cosmic Microwave Background, such as the MAXIMA and BOOMERanG projects, are providing datasets of unprecedented quality and ever-increasing size. Exact analysis of the data they produce is a serious computational challenge, ... More

Deficiency Symmetries of Surgeries in $S^3$Apr 01 2013We examine certain symmetries in the deficiencies of a rational surgery on a knot in $S^3$ by comparing the $\text{Spin}^c$-structures on the rational surgery with those on a related integral surgery. We then provide an application of these symmetries ... More

A generalisation of Nash's theorem with higher-order functionalsJan 21 2013The recent theory of sequential games and selection functions by Mar- tin Escardo and Paulo Oliva is extended to games in which players move simultaneously. The Nash existence theorem for mixed-strategy equilibria of finite games is generalised to games ... More

Low temperature behavior of finite-size one-dimensional Ising model and the partition function zerosJul 25 2014Jul 29 2014In contrast to the infinite chain, the low-temperature expansion of a one-dimensional free-field Ising model has a strong dependence on boundary conditions. I derive explicit formula for the leading term of the expansion both under open and periodic boundary ... More

Growing spin model in deterministic and stochastic treesJul 07 2014We solve the growing asymmetric Ising model [Phys. Rev. E 89, 012105 (2014)] in the topologies of deterministic and stochastic (random) scale-free trees predicting its non-monotonous behavior for external fields smaller than the coupling constant $J$. ... More

Phase diagram of the Wako-Saito-Munoz-Eaton beta-hairpin Model obtained with partition function zerosJul 21 2014I study the partition function zeros of the Wako-Saito-Munoz-Eaton (WSME) beta hairpin model in the complex temperature plane. For various values of the entropy cost of disordering a bond, the zeros show clear locus corresponding to the folding transition. ... More

Regression with Distance MatricesMar 15 2013Aug 28 2013Data types that lie in metric spaces but not in vector spaces are difficult to use within the usual regression setting, either as the response and/or a predictor. We represent the information in these variables using distance matrices which requires only ... More

Shape Dynamics. An IntroductionMay 01 2011Shape dynamics is a completely background-independent universal framework of dynamical theories from which all absolute elements have been eliminated. For particles, only the variables that describe the shapes of the instantaneous particle configurations ... More

Solitonic fermions in the confining phase of SU(2) Yang-Mills theoryJan 21 2009We consider spatial coarse-graining in statistical ensembles of non-selfintersecting and one-fold selfintersecting center-vortex loops as they emerge in the confining phase of SU(2) Yang-Mills thermodynamics. This coarse-graining is due to a noisy environment ... More

Interpretation of Lepton Flavor ViolationOct 24 2016The 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

Leptogenesis with Lepton-Number-Violating Dirac NeutrinosJul 08 2013Oct 08 2013Dirac neutrinos with lepton-number-violating interactions can give rise to a new leptogenesis mechanism. In its simplest renormalizable realization, based on a gauged B-L symmetry spontaneously broken by four units, the decay of a new scalar creates an ... More

Mirror OptionsJul 26 2001In this work we present a new family of options (mirror options) specially crafted to satisfy the necessities of aggressive speculators. The main ideas behind mirror options are: 1) A product that can be adjusted by the holder to agree with his/her market ... More

Homogeneous and locally homogeneous solutions to symplectic curvature flowFeb 07 2012J. Streets and G. Tian recently introduced symplectic curvature flow, a geometric flow on almost K\"ahler manifolds generalising K\"ahler-Ricci flow. The present article gives examples of explicit solutions to this flow of non-K\"ahler structures on several ... More

Recognising Abelian Sylow Subgroups in Finite GroupsJul 16 2014Let p be a prime. We prove that if a finite group G has non-abelian Sylow p-subgroups, and the class size of every p-element in G is coprime to p; then G contains a simple group as a subquotient which exhibits the same property. In addition we provide ... More

An answer to a question of PyrihOct 30 1998Nov 07 1998We answer a recent question of Pyrih by proving that a topological space $(X,\tau)$ is open-normal if and only if it is extremally disconnected.

Survey on preopen setsOct 30 1998The aim of this survey article is to cover most of the recent research on preopen sets. I try to present majority of the results on preopen sets that I am aware of.

Logics and Games for True ConcurrencyNov 04 2010We study the underlying mathematical properties of various partial order models of concurrency based on transition systems, Petri nets, and event structures, and show that the concurrent behaviour of these systems can be captured in a uniform way by two ... More

Representation type of Frobenius-Lusztig kernelsAug 21 2011Sep 23 2011In this article we show that almost all blocks of all Frobenius-Lusztig kernels are of wild representation type extending results of Feldvoss andWitherspoon, who proved this result for the principal block of the zeroth Frobenius-Lusztig kernel. Furthermore ... More

Asymptotic relations for weighted finite multiple zeta valuesSep 04 2013Feb 13 2014Multiple zeta values are real numbers defined by an infinite series generalizing values of the Riemann zeta function at positive integers. Finite truncations of this series are called multiple harmonic sums and are known to have interesting arithmetic ... More

In the bocs seat: Quasi-hereditary algebras and representation typeJan 15 2016This paper surveys bocses, quasi-hereditary algebras and their relationship which was established in a recent result by Koenig, Ovsienko, and the author. Particular emphasis is placed on applications of this result to the representation type of the category ... More

Almost-Orthogonality of Restricted Haar-FunctionsJul 27 2018We consider the Haar functions $h_I$ on dyadic intervals. We show that if $p>\frac23$ and $E\subset[0,1]$ then the set of all functions $\|h_I1_E\|_2^{-1}h_I1_E$ with $|I\cap E|\geq p|I|$ is a Riesz sequence. For $p\leq\frac23$ we provide a counterexample. ... More

Sequential periods of the crystalline FrobeniusMay 04 2018There is a notion of $p$-adic period coming from the crystalline Frobenius automorphism of the de Rham cohomology of an algebraic variety. In this paper, we consider sequences of $p$-adic periods, one for each prime. We study the sequences using motivic ... More

The completed finite period map and Galois theory of supercongruencesMar 13 2017Jun 20 2017A period is a complex number arising as the integral of a rational function with algebraic number coefficients over a rationally-defined region. Although periods are typically transcendental numbers, there is a conjectural Galois theory of periods coming ... More

Weak-strong uniqueness of solutions to entropy-dissipating reaction-diffusion equationsMar 02 2017We establish a weak-strong uniqueness principle for solutions to entropy-dissipating reaction-diffusion equations: As long as a strong solution to the reaction-diffusion equation exists, any weak solution and even any renormalized solution must coincide ... More

Central intersections of element centralisersFeb 01 2017In 1970 R. Schmidt gave a structural classification for CA-groups. In this paper we consider a condition upon the intersection of element centralisers which turns out to be equivalent to the definition of a CA-group. We then weaken which centralisers ... More

Exponential Patterns in Arithmetic Ramsey TheoryJul 28 2016Oct 20 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 note on the "conditional triviality" property for regular conditional distributionsNov 28 2015We make the simple, and yet deep, observation that a regular conditional distribution (rcd) almost surely trivialises the conditioning $\sigma$-algebra if and only if there exists a "measurable selection" of regular conditional distributions for almost ... More

On the resonances of the Laplacian on waveguidesSep 21 2001The resonances for the Dirichlet and Neumann Laplacian are studied on compactly perturbed waveguides. An upper bound on the number of resonances near the physical plane is proven. In the absence of resonances, an upper bound is proven for the localised ... More

Counting Zeros of Cosine Polynomials: On a Problem of LittlewoodOct 24 2016Feb 05 2019We 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

Optimizing Communication by Compression for Multi-GPU Scalable Breadth-First SearchesApr 03 2017The Breadth First Search (BFS) algorithm is the foundation and building block of many higher graph-based operations such as spanning trees, shortest paths and betweenness centrality. The importance of this algorithm increases each day due to it is a key ... 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