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Constraints on 3- and 4-loop $β$-functions in a general four-dimensional Quantum Field TheoryJun 11 2019Aug 27 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

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

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

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

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

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

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

Scalar DemocracyFeb 19 2019We conjecture that there exists a scalar bound state for every pair of fundamental fermions at a UV (`composite') scale, $\Lambda\gg v_{\text{weak}}$. This implies a large number of universally coupled, sub-critical Higgs doublets. All but the Standard ... More

Where are the Next Higgs Bosons?Apr 08 2019Apr 16 2019Simple symmetry arguments applied to the third generation lead to a prediction: there exist new sequential Higgs doublets with masses of order $\lesssim 5 $ TeV, with approximately universal Higgs-Yukawa coupling constants, $g\sim 1$. This is calibrated ... 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

On the positive eigenvalues and eigenvectors of a non-negative matrixJun 21 2013May 04 2015The paper develops the general theory for the items in the title, assuming that the matrix is countable and cofinal.

The homoclinic and heteroclinic C*-algebras of a generalized one-dimensional solenoidSep 11 2008It is shown that the heteroclinic and homoclinic algebras of a generalized one-dimensional solenoid are simple AH-algebras of real rank zero with no dimension growth and a unique trace. In the orientable case they are AT-algebras, and in the non-orientable ... 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

KMS states, conformal measures and ends in digraphsDec 14 2016Aug 29 2018The paper develops a series of tools for the study of KMS-weights on graph C*-algebras and KMS states on their corners. The approach adopts methods and ideas from graph theory, random walks and dynamical systems.

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

Dissipative conformal measures on locally compact spacesDec 20 2013Jan 13 2014The paper introduces a general method to construct conformal measures for a local homeomorphism on a locally compact non-compact Hausdorff space, subject to mild irreducibility-like conditions. Among others the method is used to give necessary and sufficient ... More

KMS weights on groupoid and graph C*-algebrasJun 21 2013The paper contains a description of the KMS weights for the one-parameter action on the reduced C*-algebra of a second countable locally compact Hausdorff etale groupoid, arising from a continuous real valued homomorphism satisfying two conditions. The ... More

The factor type of dissipative KMS weights on graph C*-algebrasAug 29 2018We calculate the S-invariant of Connes for the von Neumann algebra factors arising from KMS-weights of a generalized gauge action on a simple graph C*-algebra when the associated measure on the infinite path space of the graph is dissipative under the ... More

Branching Rules for Specht ModulesAug 06 2004Let n be a positive integer and let Sigma_n be the symmetric group of degree n. Let S^lambda be the Specht module for Sigma_n corresponding to a partition lambda of n, defined over a field F of odd characteristic. We find the indecomposable components ... More

E-theory is a special case of KK-theorySep 09 2002Let A and B be $C^*$-algebras, A separable, and B $\sigma$-unital and stable. It is shown that there are natural isomorphisms $E(A,B)=KK(SA,Q(B))=[SA,Q(B)\otimes K]$, where $SA=C_0(0,1)\otimes A$, $[\cdot,\cdot]$ denotes the set of homotopy classes of ... More

Stellar Populations Beyond the Local Group with the NGSTJun 22 1998We present simulated J- and K-band observations of stars in the Virgo and Coma clusters of galaxies using the proposed Next Generation Space Telescope with a Near-Infrared Camera, and discuss some of the science results that might be obtained. The proposed ... More

Weighted Reed-Muller codes revisitedAug 31 2011We consider weighted Reed-Muller codes over point ensemble $S_1 \times...\times S_m$ where $S_i$ needs not be of the same size as $S_j$. For $m = 2$ we determine optimal weights and analyze in detail what is the impact of the ratio $|S_1|/|S_2|$ on the ... More

Relative K-homology and normal operatorsMay 12 2005Let $A$ be a C*-algebra, $J \subset A$ a C*-subalgebra, and let $B$ be a stable C*-algebra. Under modest assumptions we organize invertible C*-extensions of $A$ by $B$ that are trivial when restricted onto $J$ to become a group $Ext_J^{-1}(A,B)$, which ... More

Equilibrium and ground states from Cayley graphsMay 01 2017We study the KMS states and $KMS_{\infty}$ states of generalized gauge actions on the $C^*$-algebra of a pointed Cayley graph. Our results provide information for any finitely generated group, but they are only complete for nilpotent groups.

Shape theory and extensions of C*-algebrasJul 09 2010Let $A$, $A'$ be separable $C^*$-algebras, $B$ a stable $\sigma$-unital $C^*$-algebra. Our main result is the construction of the pairing $[[A',A]]\times\operatorname{Ext}^{-1/2}(A,B)\to\operatorname{Ext}^{-1/2}(A',B)$, where $[[A',A]]$ denotes the set ... 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

On the lack of inverses to C*-extensions related to property T groupsJan 24 2005Using ideas of S. Wassermann on non-exact $C^*$-algebras and property T groups, we show that one of his examples of non-invertible C*-extensions is not semi-invertible. To prove this, we show that a certain element vanishes in the asymptotic tensor product. ... More

Euler-Lagrange equations for full topology optimization of the Q-factor in leaky cavitiesApr 06 2019We derive Euler-Lagrange equations for ``the full topology optimization'' of the decay rate of eigenoscillations in 3d lossy optical cavities. The approach is based on the notion of Pareto optimal frontier and on the multi-parameter perturbation theory ... More

Gradient-flowed thermal correlators: how much flow is too much?Feb 13 2018Gradient flow has been proposed in the lattice community as a tool to reduce the sensitivity of operator correlation functions to noisy UV fluctuations. We test perturbatively under what conditions doing so may contaminate the results. To do so, we compute ... More

Extensions of the reduced group C*-algebra of a free product of amenable groupsFeb 19 2009Jun 09 2009We prove that the unitary equivalence classes of extensions of C*_r(G) by any sigma-unital stable C"-algebra, taken modulo extensions which split via an asymptotic homomorphism, form a group which can be calculated from the universal coefficient theorem ... More

Weyl Consistency Conditions and $γ_{5}$Jan 09 2019Jul 01 2019The treatment of $\gamma_{5}$ in Dimensional Regularization leads to ambiguities in field-theoretic calculations, of which one example is the coefficient of a particular term in the four-loop gauge $\beta$-functions of the Standard Model. Using Weyl Consistency ... More

The structure of a the C*-algebra of a locally injective surjectionNov 02 2010We obtain a description of the C*-algebras which can occur as a simple quotient of the C*-algebra of a locally injective surjection on a compact metric space of finite covering dimension.

Probing the faint end of the Galaxy luminosity function at z=3 with Ly-alpha emissionMay 23 2001We present spectroscopic observations obtained with the ESO Very Large Telecope (VLT) of seven candidate Ly-alpha emitting galaxies in the field of the radio quiet Q1205-30 at z=3.04 previously detected with deep narrow band imaging. Based on equivalent ... More

Ly-alpha Emission from a Lyman Limit Absorber at z=3.036Nov 09 1999Deep, 17.8 hours, narrow band imaging obtained at the ESO 3.5m New Technology Telescope has revealed extended (galaxy sized) Ly-alpha emission from a high redshift Lyman limit absorber. The absorber is a z(abs) approx. z(em) Lyman limit absorber seen ... More

Heat Transport in Confined Strongly Coupled 2D Dust ClustersApr 16 2013Dusty plasmas are a model system for studying strong correlation. The dust grains' size of a few micro-meters and their characteristic oscillation frequency of a few hertz allows for an investigation of many particle effects on an atomic level. In this ... More

The C*-algebra of an affine map on the 3-torusApr 01 2012We study the C*-algebra of an affine map on a compact abelian group and give necessary and sufficient conditions for strong transitivity when the group is a torus. The structure of the C*-algebra is completely determined for all strongly transitive affine ... 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

Thermal Quarkonium Mass Shift from Euclidean CorrelatorsMar 19 2019Jun 03 2019Brambilla, Escobedo, Soto, and Vairo have derived an effective description of quarkonium with two parameters; a momentum diffusion term and a real self-energy term. We point out that the real self-energy term can be expressed directly in terms of Euclidean ... 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

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.

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 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

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

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.

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.

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

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

A new perspective on the dynamics of fragmented populationsDec 03 2008Understanding the time evolution of fragmented animal populations and their habitats, connected by migration, is a problem of both theoretical and practical interest. This paper presents a method for calculating the time evolution of the habitats' population ... 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

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

Remarks on reply to Johansen's commentJun 25 2002Remarks on reply (cond-mat/0206368) to Johansen's comment (cond-mat/0205249)

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

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

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

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

Multiadaptive Galerkin Methods for ODEs III: A Priori Error EstimatesMay 14 2012The multiadaptive continuous/discontinuous Galerkin methods mcG(q) and mdG(q) for the numerical solution of initial value problems for ordinary differential equations are based on piecewise polynomial approximation of degree q on partitions in time with ... More

Random walks, arrangements, cell complexes, greedoids, and self-organizing librariesMay 01 2008The starting point is the known fact that some much-studied random walks on permutations, such as the Tsetlin library, arise from walks on real hyperplane arrangements. This paper explores similar walks on complex hyperplane arrangements. This is achieved ... 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

Realizability and Internal Model Control on NetworksDec 19 2018Mar 30 2019It is proved that network realizability of controllers can be enforced without conservatism using convex constraints on the closed loop transfer function. Once a network realizable closed loop transfer matrix has been found, a corresponding controller ... 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

Integration of 1-forms and connectionsFeb 28 2019We give a combinatorial/geometric argument of the classical result that an affine connection, which is both torsion free and curvature free, is locally an affine space.

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

First-passage percolation on Cartesian power graphsJun 29 2015We consider first-passage percolation with standard exponential edge weights on the class of "high-dimensional" graphs that can be written as an iterated Cartesian product $G\square G \square \dots \square G$ of some base graph $G$ as the number of factors ... 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

Comment on "Are financial crashes predictable?"May 13 2002May 15 2002Comment on "Are financial crashes predictable?", L. Laloux, M. Potters, R. Cont, J.P Aguilar and J.-P. Bouchaud, Europhys. Lett. 45, 1-5 (1999)

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

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

The random strategy in Maker-Breaker graph minor gamesJul 10 2019In a $(1:b)$ biased Maker-Breaker game, how good a strategy is for a player can be measured by the bias range for which its rival can win, choosing an appropriate counterstrategy. Bednarska and {\L}uczak proved that, in the $H$-subgraph game, the uniformly ... 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

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

Non-commutative residue of projections in Boutet de Monvel's calculusSep 21 2007Using results by Melo, Nest, Schick, and Schrohe on the K-theory of Boutet de Monvel's calculus of boundary value problems, we show that the non-commutative residue introduced by Fedosov, Golse, Leichtnam, and Schrohe vanishes on projections in the calculus. ... 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

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

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

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

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

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

Energetics of the brain and AIFeb 12 2016Does the energy requirements for the human brain give energy constraints that give reason to doubt the feasibility of artificial intelligence? This report will review some relevant estimates of brain bioenergetics and analyze some of the methods of estimating ... More

Chiral squaring and KLT relationsJan 12 2016Jan 29 2016We demonstrate that amplitudes based on matter supermultiplets can be combined to provide amplitudes of vector supermultiplets by means of KLT relations. In practice we do this by developing a procedure for removing supersymmetry supercharges from super ... More

Empirical Gaussian priors for cross-lingual transfer learningJan 09 2016Sequence model learning algorithms typically maximize log-likelihood minus the norm of the model (or minimize Hamming loss + norm). In cross-lingual part-of-speech (POS) tagging, our target language training data consists of sequences of sentences with ... 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.

Entropy in the Kuramoto model and its implications for the stability of partially synchronized statesOct 10 2014Nov 04 2014We discuss the concept of entropy applied to the infinite-N Kuramoto model and derive an expression for its time derivative. The time derivative of the entropy functional is shown to depend on the synchronization order parameter in a very simple way and, ... 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

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

Polyphonic Pitch Tracking with Deep Layered LearningApr 09 2018Mar 18 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