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Constraints on 3- and 4-loop $β$-functions in a general four-dimensional Quantum Field TheoryJun 11 2019Jun 12 2019The $ \beta $-functions of marginal couplings are known to be closely related to the $ A $-function through Osborn's equation, derived using the local renormalization group. It is possible to derive strong constraints on the $\beta$-functions by parametrizing ... More

Constraints on 3- and 4-loop $β$-functions in a general four-dimensional Quantum Field TheoryJun 11 2019The $ \beta $-functions of marginal couplings are known to be closely related to the $ A $-function through Osborn's equation, derived using the local renormalization group. It is possible to derive strong constraints on the $\beta$-functions by parametrizing ... More

Uncovering new strong dynamics via topological interactions at the 100 TeV colliderJun 13 2017Oct 29 2017In models of composite Higgs dynamics new composite pseudoscalars can interact with the Higgs and electroweak gauge bosons via anomalous interactions, stemming from the topological sector of the underlying theory. We show that a future 100 TeV proton-proton ... More

Revealing BSM composite dynamics via topological interactions at future collidersOct 05 2017In composite Higgs models, new composite pseudoscalars can interact with the Higgs and with electroweak gauge bosons via anomalous interactions, which stem from the topological structure of the underlying theory. A future 100 TeV pp collider (FCC-pp) ... More

Raising the SUSY-breaking scale naturally in a Goldstone-Higgs modelJun 10 2016We show that by marrying the elementary-Goldstone-Higgs scenario and supersymmetry it is possible to raise the scale of supersymmetry breaking to several TeVs while keeping the relevant features of a natural supersymmetric extension of the Standard Model. ... More

Flavor Physics and Flavor Anomalies in Minimal Fundamental Partial CompositenessDec 20 2017Partial compositeness is a key ingredient of models where the electroweak symmetry is broken by a composite Higgs state. Recently, a UV completion of partial compositeness was proposed, featuring a new strongly coupled gauge interaction as well as new ... More

Minimal Fundamental Partial CompositenessApr 25 2017Dec 20 2017Building upon the fundamental partial compositeness framework we provide consistent and complete composite extensions of the standard model. These are used to determine the effective operators emerging at the electroweak scale in terms of the standard ... More

Raising the SUSY-breaking scale in a Goldstone-Higgs modelJun 10 2016Aug 28 2017We show that by combining the elementary-Goldstone-Higgs scenario and supersymmetry it is possible to raise the scale of supersymmetry breaking to several TeVs by relating it to the spontaneous-symmetry-breaking one. This is achieved by first enhancing ... More

$a$-theorem at large $N_f$Aug 01 2018Dec 18 2018We determine the Jack and Osborn a-function and related metric for gauge-fermion theories to leading order in the large number of fermions and to all orders in the gauge coupling, demonstrating that the strong a-theorem is violated for the minimal choice ... More

An Average of the Human Ear Canal: Recovering Acoustical Properties via Shape AnalysisNov 09 2018Humans are highly dependent on the ability to process audio in order to interact through conversation and navigate from sound. For this, the shape of the ear acts as a mechanical audio filter. The anatomy of the outer human ear canal to approximately ... More

Measurement of VZ production cross sections in Z -> bb decay channels in pp collisions at 8 TeVAug 21 2014We present a measurement of the WZ and ZZ production cross sections in proton-proton collisions at 8 TeV in final states where one Z boson decays to b-tagged jets, while the other gauge boson, either W or Z, is detected through its leptonic decay. The ... More

Gauge-Yukawa theories: Beta functions at large $N_f$Mar 26 2018Jul 10 2018We consider the dynamics of gauge-Yukawa theories in the presence of a large number of matter constituents. We first review the current status for the renormalization group equations of gauge-fermion theories featuring also semi-simple groups. In this ... More

Semi etale groupoids and applicationsJan 15 2009Aug 29 2009We introduce a class of locally compact Hausdorff groupoids and show how to associate C*-algebras to them in a way which generalizes the reduced C*-algebra of an 'etale groupoid. Focusing on criteria for simplicity and existence of Cartan subalgebras, ... More

The groupoid C*-algebra of a rational mapFeb 13 2012This paper contains a quite detailed description of the C*-algebra arising from the transformation groupoid of a rational map of degree at least two on the Riemann sphere. The algebra is decomposed stepwise via extensions of familiar C*-algebras whose ... More

The Ouroboros ModelMay 19 2008At the core of the Ouroboros Model lies a self-referential recursive process with alternating phases of data acquisition and evaluation. Memory entries are organized in schemata. Activation at a time of part of a schema biases the whole structure and, ... More

Is Quantum Mechanics needed to explain consciousness ?Nov 13 2007In this short comment to a recent contribution by E. Manousakis [1] it is argued that the reported agreement between the measured time evolution of conscious states during binocular rivalry and predictions derived from quantum mechanical formalisms does ... More

KMS weights on graph C*-algebrasSep 12 2014Apr 27 2016KMS weights for generalized gauge actions on graph C*-algebras are studied and a complete description of the structure is obtained for the gauge action when the graph is strongly connected and has at most countably many exits. The structure is surprisingly ... More

The C*-algebra of the exponential functionSep 23 2011The complex exponential function is a local homeomorphism and gives therefore rise to an 'etale groupoid and a C*-algebra. We determine this algebra, as well as the alge bra of the complex conjugate of the exponential function.

Flow of Activity in the Ouroboros ModelMar 29 2009The Ouroboros Model is a new conceptual proposal for an algorithmic structure for efficient data processing in living beings as well as for artificial agents. Its central feature is a general repetitive loop where one iteration cycle sets the stage for ... More

Crowded-field photometry from HST-imagingApr 29 1997We present a thorough investigation of stellar photometry based on HST imaging of crowded fields at 85 and 10 arcsec from the centre of the high-surface brightness elliptical M32. The Principal Investigators of the present archive data have elsewhere ... More

A proof of Wahl's conjecture in the symplectic caseSep 02 2010Let $X$ denote a flag variety of type $A$ or type $C$. We construct a canonical Frobenius splitting of $X \times X$ which vanishes with maximal multiplicty along the diagonal. This way we verify a conjecture by Lakshmibai, Mehta and Parameswaran in type ... More

A Dependently Typed Library for Static Information-Flow Control in IdrisFeb 18 2019Safely integrating third-party code in applications while protecting the confidentiality of information is a long-standing problem. Pure functional programming languages, like Haskell, make it possible to enforce lightweight information-flow control through ... More

The Connes-Higson construction is an isomorphismApr 28 2000Jul 19 2001Let $A$ be a separable $C^*$-algebra and $B$ a stable $C^*$-algebra containing a strictly positive element. We show that the group $\Ext(SA,B)$ of unitary equivalence classes of extensions of $SA$ by $B$, modulo the extensions which are asymptotically ... More

A new realization of the cohomology of Springer fibersNov 13 2002In this note we give a geometric realization of the cohomology of Springer fibers in type A. More precisely, we describe the cohomology by the coordinate ring of a scheme theoretic intersection of a Cartan subalgebra with a certain union of cones of nilpotent ... More

Frobenius splitting and geometry of $G$-Schubert varietiesApr 05 2007Sep 10 2008Let $X$ be an equivariant embedding of a connected reductive group $G$ over an algebraically closed field $k$ of positive characteristic. Let $B$ denote a Borel subgroup of $G$. A $G$-Schubert variety in $X$ is a subvariety of the form $\diag(G) \cdot ... More

Euler-Lagrange equations for full topology optimization of the Q-factor in leaky cavitiesApr 06 2019May 31 2019We derive Euler-Lagrange equations for the topology optimization of decay rate in 3-d lossy optical cavities. This leads to a new class of time-harmonic differential or integro-differential equations, which can be written as nonlinear Maxwell systems ... More

Modeling Music Modality with a Key-Class Invariant Pitch Chroma CNNJun 17 2019This paper presents a convolutional neural network (CNN) that uses input from a polyphonic pitch estimation system to predict perceived minor/major modality in music audio. The pitch activation input is structured to allow the first CNN layer to compute ... More

Square summability of variations and convergence of the transfer operatorDec 05 2006In this paper we study the one-sided shift operator on a state space defined by a finite alphabet. Using a scheme developed by Walters [13], we prove that the sequence of iterates of the transfer operator converges under square summability of variations ... More

Atom laser coherence and its control via feedbackFeb 05 2002Jun 18 2002We present a quantum-mechanical treatment of the coherence properties of a single-mode atom laser. Specifically, we focus on the quantum phase noise of the atomic field as expressed by the first-order coherence function, for which we derive analytical ... More

Reducing the linewidth of an atom laser by feedbackJan 23 2001Feb 05 2002A continuous atom laser will almost certainly have a linewidth dominated by the effect of the atomic interaction energy, which turns fluctuations in the condensate atom number into fluctuations in the condensate frequency. These correlated fluctuations ... More

Effects of twin-beam squashed light on a three-level atomApr 09 2001Feb 05 2002An electro-optical feedback loop can make in-loop light (squashed light) which produces a photocurrent with noise below the standard quantum limit (such as squeezed light). We investigate the effect of squashed light interacting with a three-level atom ... More

Selective self-excitation of higher vibrational modes of graphene nano-ribbons and carbon nanotubes through magnetomotive instabilityDec 05 2011We demonstrate theoretically the feasibility of selective self-excitation of higher-mode flexural vibrations of graphene nano-ribbons and carbon nanotubes by the means of magnetomotive instability. Apart from the mechanical resonator, the device consists ... More

Metric spaces and SDGOct 31 2016Nov 01 2016We explore how the synthetic theory of metric spaces (Busemann) can coexist with synthetic differential geometry in the sense based on nilpotent elements in the number line.

Selfoscillations of Suspended Carbon Nanotubes with a Deflection Sensitive Resistance under Voltage BiasJul 07 2010We theoretically investigate the electro-mechanics of a Suspended Carbon Nanotube with a Deflection Sensitive Resistance subjected to a homogeneous Magnetic Field and a constant Voltage Bias. We show that, (with the exception of a singular case), for ... More

Extracting the neutron-neutron scattering length -- recent developmentsApr 17 2009The experimental and theoretical issues and challenges for extracting the neutron-neutron scattering length are discussed. Particular emphasis is placed on recent results and their impact on the field. Comments are made regarding current experimental ... More

Estimating the Degree of Entanglement of Unknown Gaussian StatesOct 31 2006We give an introduction to Gaussian states and operations. A discussion of the entanglement properties of bipartite Gaussian states in terms of its covariance matrix follows. It is explained how entanglement can be witnessed using feasible measurements, ... More

Characterization of large price variations in financial marketsOct 25 2002Statistics of drawdowns (loss from the last local maximum to the next local minimum) plays an important role in risk assessment of investment strategies. As they incorporate higher ($>$ two) order correlations, they offer a better measure of real market ... More

Comment on A.-L. Barabasi, Nature 435 207-211 (2005)Feb 04 2006The purpose of this communication is twofold. First, it clarifies the origin of the power law obtained in the computer simulations presented in A.-L. Barabasi, Nature 435 207-211 (2005) as well as presenting a statistically more sound analysis of the ... More

Comment on recent claims by Sornette and ZhouFeb 07 2003Comment on recent claims by Sornette and Zhou: D. Sornette and W. Zhou, Quantitative Finance 2 (6), 468-481 (2002); Evidence of a Worldwide Stock Market Log-Periodic Anti-Bubble Since Mid-2000, cond-mat/0212010; Renormalization Group Analysis of the 2000-2002 ... More

Spikes as regularizersNov 18 2016We present a confidence-based single-layer feed-forward learning algorithm SPIRAL (Spike Regularized Adaptive Learning) relying on an encoding of activation spikes. We adaptively update a weight vector relying on confidence estimates and activation offsets ... More

Subword counting and the incidence algebraFeb 10 2015Mar 11 2015The Pascal matrix, $P$, is an upper diagonal matrix whose entries are the binomial coefficients. In 1993 Call and Velleman demonstrated that it satisfies the beautiful relation $P=\exp(H)$ in which $H$ has the numbers 1, 2, 3, etc. on its superdiagonal ... More

Tempo-Invariant Processing of Rhythm with Convolutional Neural NetworksApr 22 2018Apr 28 2018Rhythm patterns can be performed with a wide variation of tempi. This presents a challenge for many music information retrieval (MIR) systems; ideally, perceptually similar rhythms should be represented and processed similarly, regardless of the specific ... More

Deep Layered Learning in MIRApr 18 2018Dec 10 2018Deep learning has boosted the performance of many music information retrieval (MIR) systems in recent years. Yet, the complex hierarchical arrangement of music makes end-to-end learning hard for some MIR tasks - a very deep and flexible processing chain ... More

The Ground State Energy of a Dilute Bose Gas in Dimension n >3Jan 23 2014Mar 24 2014We consider a Bose gas in spatial dimension $n>3$ with a repulsive, radially symmetric two-body potential $V$. In the limit of low density $\rho$, the ground state energy per particle in the thermodynamic limit is shown to be $(n-2)|\mathbb S^{n-1}|a^{n-2}\rho$, ... More

Theory of characteristics for first order partial differential equationsNov 25 2010We use the method of synthetic differential geometry to revisit the geometric reasoning employed by Lie, Klein and others in their study of partial differential equations.

Commutation StructuresNov 02 2005For a fixed object X in a monoidal category, an X-commutation structure on an object A is just a map from XA to AX. We study aspects of such structure in case A has a dual.

Calculus of extensive quantitiesMay 17 2011We show how a commutative monad gives rise to a theory of extensive quantities, including (under suitable further conditions) a differential calculus of such. The relationship to Schwartz distributions is dicussed. The paper is a companion to the author's ... More

First neighbourhood of the diagonal, and geometric distributionsJun 07 2002We describe the geometric notion of distribution in synthetic terms, utilizing the notion of "first neighbourhood of the diagonal" from algebraic geometry. We characterize involutive distributions in combinatorial terms.

A $q$-analogue of the FKG inequality and some applicationsJun 07 2009Aug 21 2009Let $L$ be a finite distributive lattice and $\mu : L \to {\mathbb R}^{+}$ a log-supermodular function. For functions $k: L \to {\mathbb R}^{+}$ let $$E_{\mu} (k; q) \defeq \sum_{x\in L} k(x) \mu (x) q^{{\mathrm rank}(x)} \in {\mathbb R}^{+}[q].$$ We ... More

On the invariants of the splitting algebraMay 23 2011For a given monic polynomial $p(t)$ of degree $n$ over a commutative ring $k$, the splitting algebra is the universal $k$-algebra in which $p(t)$ has $n$ roots, or, more precisely, over which $p(t)$ factors, $p(t)=(t-\xi_1)...(t-\xi_n)$. The symmetric ... More

Accessibility percolation and first-passage site percolation on the unoriented binary hypercubeJan 09 2015Inspired by biological evolution, we consider the following so-called accessibility percolation problem: The vertices of the unoriented $n$-dimensional binary hypercube are assigned independent $U(0, 1)$ weights, referred to as fitnesses. A path is considered ... More

Multi-Adaptive Galerkin Methods for ODEs IMay 12 2012We present multi-adaptive versions of the standard continuous and discontinuous Galerkin methods for ODEs. Taking adaptivity one step further, we allow for individual time-steps, order and quadrature, so that in particular each individual component has ... More

Pregroupoids and their enveloping groupoidsFeb 03 2005We prove that the forgetful functor from groupoids to pregroupoids has a left adjoint, with the front adjunction injective. Thus we get an enveloping groupoid for any pregroupoid. We prove that the category of torsors is equivalent to that of pregroupoids. ... More

On a common carrier hypothesis for the 6613.6 and 6196.0 Å diffuse interstellar bandsNov 30 2016We explore via spectroscopic modeling whether the highly correlated diffuse interstellar bands at 6613.6 and 6196.0 {\AA} might originate from a single molecule. Efforts were made to simulate the band contours of the DIBs along the three lines-of-sight, ... More

The 2PI coupling expansion revisitedNov 01 2005Recently, out-of-equilibrium field theory has been studied using approximations based on truncations of the 2PI effective action. Although results are promising, the convergence of subsequent orders of the approximation is difficult to get a handle on, ... More

Response time of internautsMar 01 2001A new experiment measuring the dynamical response of the Internet population to a ``point-like'' perturbation has been performed. The nature of the perturbation was that of an announcement, specifically a web-interview on stock market crashes, which contained ... More

Polyphonic Pitch Tracking with Deep Layered LearningApr 09 2018Jan 10 2019This paper presents a polyphonic pitch tracking system able to extract both framewise and note-based estimates from audio. The system uses several artificial neural networks in a deep layered learning setup. First, cascading networks are applied to a ... More

The Dirichlet problem for p-harmonic functions on the topologist's combApr 05 2013In this paper we study the Perron method for solving the p-harmonic Dirichlet problem on the topologist's comb. For functions which are bounded and continuous at the accessible points, we obtain invariance of the Perron solutions under arbitrary perturbations ... More

Metric spaces and SDGOct 31 2016Feb 22 2017We explore how the synthetic theory of metric spaces (Busemann) can coexist with synthetic differential geometry in the sense based on nilpotent elements in the number line.

Duality for generic algebrasDec 20 2014We prove that double dualization into the generic algebra for an algebraic theory has some Gelfand- or Stone- duality properties

A Lipschitz metric for conservative solutions of the two-component Hunter--Saxton systemFeb 26 2015We establish the existence of conservative solutions of the initial value problem of the two-component Hunter--Saxton system on the line. Furthermore we investigate the stability of these solutions by constructing a Lipschitz metric.

Not served on a silver platter! Access to online mathematics information in AfricaMay 18 2009This paper argues that, contrary to the beliefs of many, the amount of mathematics information available for African researchers, including electronic scientific journals and databases, is indeed substantial. However, whereas information resources are ... More

Estimating the Electromagnetic Chiral Lagrangian CoefficientsJun 09 2004In the low energy region chiral perturbation theory including virtual photons is used to derive the structure of the generating functional. The work we do is performed within the three flavor framework and reaches up to next-to-leading order. An Euclidian ... More

Experiments on Internet ResponseSep 01 2005This paper suggests a generalized distribution of response times to new information $\sim t^{-b}$ for human populations in the absence of deadlines. This has important implications for psychological and social studies as well the study of dynamical networks ... More

2PI simulations in expanding backgrounds: Doing it anyway!Oct 16 2008I set out the 2PI formalism for quantum fields in a Friedmann-Robertson-Walker Universe. I show how one can solve self-consistently for the quantum field evolution and the evolution of the cosmological scale factor, using a renormalised semi-classical ... More

Most edge-orderings of $K_n$ have maximal altitudeMay 23 2016Suppose the edges of the complete graph on $n$ vertices are assigned a uniformly chosen random ordering. Let $X$ denote the corresponding number of Hamiltonian paths that are increasing in this ordering. It was shown in a recent paper by Lavrov and Loh ... More

Standard Model CP-violation and Cold Electroweak BaryogenesisSep 13 2010Jun 30 2011Using large scale real-time lattice simulations, we calculate the baryon asymmetry generated at a fast, cold electroweak symmetry breaking transition. CP-violation is provided by the leading effective bosonic term resulting from integrating out the fermions ... More

Charge symmetry breaking and the d d -> alpha pi0 reaction -- recent theoretical developmentsSep 13 2004The status of the theoretical effort to calculate charge-symmetry-breaking pion production reactions will be presented. The main emphasis will be on the d d -> alpha pi0 reaction, especially in relation to the recent IUCF experiment. Suggestions for future ... More

Threshold Production of the HypertritonJun 28 1996The cross section for threshold production of the hypertriton in the reaction pd->^3_\Lambda H K^+ is calculated in a two-step model and compared to the break-up process pd -> d\LambdaK^+. The latter process is shown to be dominant already at 2 MeV above ... More

Control Synthesis with Localizability and Passivity ConstraintsDec 19 2018A compact formulation of the most central idea in system level synthesis is given, namely that controller localizability can be enforced using convex constraints on the closed loop. Moreover, it is noted that for passive open loop systems, a passivity ... More

Fibrations as Eilenberg-Moore algebrasDec 05 2013We give an elementary exposition of some fundamental facts about fibered (or rather opfibered) categories, in terms of monads and 2-categories. The account avoids any mention of category-valued functors and pseudofunctors.

Monads and extensive quantitiesMar 30 2011If T is a commutative monad on a cartesian closed category, then there exists a natural T-bilinear pairing from T(X) times the space of T(1)-valued functions on X ("integration"), as well as a natural T-bilinear action on T(X) by the space of these functions. ... More

Volume form as volume of infinitesimal simplicesJun 02 2000In the context of Synthetic Differential Geometry, we describe the square volume of a ``second-infinitesimal simplex'', in terms of square-distance between its vertices. The square-volume function thus described is symmetric in the vertices. The square-volume ... More

Projective lines as groupoids with projection structureOct 20 2013The coordinate projective line over a field is seen as a groupoid with a further `projection' structure. We investigate conversely to what extent such an, abstractly given, groupoid may be coordinatized by a suitable field constructed out of the geometry. ... More

Some matrices with nilpotent entries, and their determinantsDec 15 2006We study algebraic properties of matrices whose rows are mutual neighbours, and are also neigbours of 0 ("neighbour" in the sense of a certain nilpotency condition). The intended application is in synthetic differential geometry. For a square matrix of ... More

Stochastic and deterministic molecular dynamics derived from the time-independent Schrödinger equationDec 23 2008Jan 12 2010Ehrenfest, Born-Oppenheimer, Langevin and Smoluchowski dynamics are shown to be accurate approximations of time-independent Schr\"odinger observables for a molecular system avoiding caustics, in the limit of large ratio of nuclei and electron masses, ... More

A comparison theorem for $f$-vectors of simplicial polytopesMay 12 2006Nov 07 2006Let $f_i(P)$ denote the number of $i$-dimensional faces of a convex polytope $P$. Furthermore, let $S(n,d)$ and $C(n,d)$ denote, respectively, the stacked and the cyclic $d$-dimensional polytopes on $n$ vertices. Our main result is that for every simplicial ... More

A linear threshold for uniqueness of solutions to random jigsaw puzzlesJan 17 2017Aug 15 2018We consider a problem introduced by Mossel and Ross [Shotgun assembly of labeled graphs, arXiv:1504.07682]. Suppose a random $n\times n$ jigsaw puzzle is constructed by independently and uniformly choosing the shape of each "jig" from $q$ possibilities. ... More

On the uniform equidistribution of closed horospheres in hyperbolic manifoldsMar 17 2011We prove asymptotic equidistribution results for pieces of large closed horospheres in cofinite hyperbolic manifolds of arbitrary dimension. This extends earlier results by Hejhal and Str\"ombergsson in dimension 2. Our proofs use spectral methods, and ... More

On the value distribution of the Epstein zeta function in the critical stripMay 13 2011We study the value distribution of the Epstein zeta function $E_n(L,s)$ for $0<s<\frac{n}{2}$ and a random lattice $L$ of large dimension $n$. For any fixed $c\in(1/4,1/2)$ and $n\to\infty$, we prove that the random variable $V_n^{-2c}E_n(\cdot,cn)$ has ... More

On the value distribution and moments of the Epstein zeta function to the right of the critical stripJun 09 2010Sep 08 2010We study the Epstein zeta function $E_n(L,s)$ for $s>\frac{n}{2}$ and determine for fixed $c>\frac{1}{2}$ the value distribution and moments of $E_n(\cdot,cn)$ (suitably normalized) as $n\to\infty$. We further discuss the random function $c\mapsto E_n(\cdot,cn)$ ... More

Origin of Crashes in 3 US stock markets: Shocks and BubblesJan 13 2004This paper presents an exclusive classification of the largest crashes in Dow Jones Industrial Average (DJIA), SP500 and NASDAQ in the past century. Crashes are objectively defined as the top-rank filtered drawdowns (loss from the last local maximum to ... More

Quantum mechanics as "space-time statistical mechanics"?Jan 24 2005In this paper we discuss and analyse the idea of trying to see (non-relativistic) quantum mechanics as a ``space-time statistical mechanics'', by using the classical statistical mechanical method on objective microscopic space-time configurations. It ... More

SUSY Flat Direction Decay - the prospect of particle production and preheating investigated in the unitary gaugeJan 04 2008Apr 22 2010We look at the possibility of non-perturbative particle production after inflation from SUSY flat directions produced by rotating eigenstates thereby avoiding the standard adiabaticity conditions. This might lead to preheating and prevent the delay of ... More

Local positivity of line bundles on smooth toric varieties and Cayley polytopesJul 11 2013For any non-negative integer $k$ the $k$-th osculating dimension at a given point $x$ of a variety $X$ embedded in projective space gives a measure of the local positivity of order $k$ at that point. In this paper we show that a smooth toric embedding ... More

Thermal state entanglement in harmonic latticesMar 07 2008Jun 18 2008We investigate the entanglement properties of thermal states of the harmonic lattice in one, two and three dimensions. We establish the value of the critical temperature for entanglement between neighbouring sites and give physical reasons. Further sites ... More

A classification of smooth convex 3-polytopes with at most 16 lattice pointsJun 21 2012We provide a complete classification up to isomorphism of all smooth convex lattice 3-polytopes with at most 16 lattice points. There exist in total 103 different polytopes meeting these criteria. Of these, 99 are strict Cayley polytopes and the remaining ... More

Completeness of the ring of polynomialsDec 19 2013Let $k$ be an uncountable field. We prove that the polynomial ring $R:=k[X_1,\dots,X_n]$ in $n\ge 2$ variables over $k$ is complete in its adic topology. In addition we prove that also the localization $R_{\goth m}$ at a maximal ideal $\goth m\subset ... More

Algebra of Principal Fibre Bundles, and ConnectionsMay 12 2000We put together some of the efforts by several people of making aspects of fibre bundle theory into algebra. The initiator of these efforts was Charles Ehresmann, who put the notion of groupoid and groupoid action in the focus of fibre bundle theory in ... More

Bundle functors and fibrationsMay 10 2015We give an account, in terms of fibered categories and their fibrewise duals, of aspects of the theory of bundle functors and star-bundle functors in differential geometry.

Langevin molecular dynamics derived from Ehrenfest dynamicsDec 21 2007Mar 30 2011Stochastic Langevin molecular dynamics for nuclei is derived from the Ehrenfest Hamiltonian system (also called quantum classical molecular dynamics) in a Kac-Zwanzig setting, with the initial data for the electrons stochastically perturbed from the ground ... More

Infinitesimal aspects of the Laplace operatorJun 23 2000In the context of synthetic differential geometry, we study the Laplace operator an a Riemannian manifold. The main new aspect is a neighbourhood of the diagonal, smaller than the second neighbourhood usually required as support for second order differential ... More

Commutative monads as a theory of distributionsAug 30 2011The theory of commutative monads on cartesian closed categories provides a framework where aspects of the theory of distributions and other extensive quantities can be formulated and some results proved. We make explicit a link between our theory and ... More

Exploring light supersymmetry with GAMBITMay 24 2019I summarize a recent study by the GAMBIT Collaboration in which we investigated the combined collider constraints on the chargino and neutralino sector of the Minimal Supersymmetric Standard Model. Through a large fit using GAMBIT we found that current ... More

A geometric theory of harmonic and semi-conformal mapsJun 12 2003We describe for any Riemannian manifold a certain infinitesimal neighbourhood of the diagonal. Semi-conformal maps are analyzed as those that preserve such neighbourhoods; harmonic maps are analyzed as those that preserve mirror image formation for pairs ... More

Unoriented first-passage percolation on the n-cubeFeb 12 2014Jun 05 2014The $n$-dimensional binary hypercube is the graph whose vertices are the binary $n$-tuples $\{0, 1\}^n$ and where two vertices are connected by an edge if they differ at exactly one coordinate. We prove that if the edges are assigned independent mean ... More

A computation of Poisson kernels for some standard weighted biharmonic operators in the unit discJul 03 2007We compute Poisson kernels for integer weight parameter standard weighted biharmonic operators in the unit disc with Dirichlet boundary conditions. The computations performed extend the supply of explicit examples of such kernels and suggest similar formulas ... More

Elements of a metric spectral theoryApr 02 2019This paper discusses a general method for spectral type theorems using metric spaces instead of vector spaces. Advantages of this approach are that it applies to genuinely non-linear situations and also to random versions. Metric analogs of operator norm, ... More

Partial Realization Theory and System Identification ReduxJun 17 2017Some twenty years ago we introduced a nonstandard matrix Riccati equation to solve the partial stochastic realization problem. In this paper we provide a new derivation of this equation in the context of system identification. This allows us to show that ... More

Probing Human Response TimesMay 05 2003Jan 14 2004In a recent preprint \cite{eck}, the temporal dynamics of an e-mail network has been investigated by J.P. Eckmann, E. Moses and D. Sergi. Specifically, the time period between an e-mail message and its reply were recorded. It will be shown here that their ... More