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Matroid complexity and non-succinct descriptionsFeb 20 2007Sep 10 2007We investigate an approach to matroid complexity that involves describing a matroid via a list of independent sets, bases, circuits, or some other family of subsets of the ground set. The computational complexity of algorithmic problems under this scheme ... More

Science with an ngVLA: Radio Continuum Emission from Galaxies: An Accounting of Energetic ProcessesOct 15 2018Radio continuum observations have proven to be a workhorse in our understanding of the star formation process (i.e., stellar birth and death) from galaxies both in the nearby universe and out to the highest redshifts. In this article we focus on how the ... More

Closing the Blinds: Four Strategies for Protecting Smart Home Privacy from Network ObserversMay 18 2017The growing market for smart home IoT devices promises new conveniences for consumers while presenting novel challenges for preserving privacy within the home. Specifically, Internet service providers or neighborhood WiFi eavesdroppers can measure Internet ... More

A Bayesian Approach to Constraint Based Causal InferenceOct 16 2012We target the problem of accuracy and robustness in causal inference from finite data sets. Some state-of-the-art algorithms produce clear output complete with solid theoretical guarantees but are susceptible to propagating erroneous decisions, while ... More

A Logical Characterization of Constraint-Based Causal DiscoveryFeb 14 2012We present a novel approach to constraint-based causal discovery, that takes the form of straightforward logical inference, applied to a list of simple, logical statements about causal relations that are derived directly from observed (in)dependencies. ... More

A shorter proof of Lemma A.6 (arXiv:1005.0768)Jun 21 2012For the convenience of readers of the article {\em No-arbitrage pricing under systemic risk: accounting for cross-ownership} (Fischer, 2012, arXiv:1005.0768), a full proof of Lemma A.5 and a shorter proof of Lemma A.6 of that paper are provided.

Constructing Q-Fano 3-folds à la Prokhorov & ReidOct 06 2016We generalise a construction by Prokhorov & Reid of two families of Q-Fano 3-folds of index 2 to obtain five more families of Q-Fano 3-folds; four of index 2 and one of index 3. Two of the families constructed have the same Hilbert series and we study ... More

The structure theory of set addition revisitedDec 03 2012In this article we survey some of the recent developments in the structure theory of set addition.

Green's sumset problem at density one halfMar 29 2010Dec 02 2010We investigate the size of subspaces in sumsets and show two main results. First, if A is a subset of F_2^n with density at least 1/2 - o(n^{-1/2}) then A+A contains a subspace of co-dimension 1. Secondly, if A is a subset of F_2^n with density at least ... More

Three-term arithmetic progressions and sumsetsNov 10 2006Apr 01 2010Suppose that G is an abelian group and A is a finite subset of G containing no three-term arithmetic progressions. We show that |A+A| >> |A|(log |A|)^{1/3-\epsilon} for all \epsilon>0.

Additive structures in sumsetsMay 18 2006Apr 01 2010Suppose that A is a subset of the integers {1,...,N} of density a. We provide a new proof of a result of Green which shows that A+A contains an arithmetic progression of length exp(ca(log N)^{1/2}) for some absolute c>0. Furthermore we improve the length ... More

A statistical approach to covering lemmasOct 22 2016We discuss a statistical variant of Ruzsa's covering lemma and use it to show that if G is an Abelian group of bounded exponent and A in G has |A+A| < K|A| then the subgroup generated by A has size at most exp(O(K log^22K))|A|, where the constant in the ... More

An analytic approach to a weak non-Abelian Kneser-type theoremDec 03 2012We prove the following result due to Hamidoune using an analytic approach. Suppose that A is a subset of a finite group G with |AA^{-1}| \leq (2-\varepsilon)|A|. Then there is a subgroup H of G and a set X of size O_\varepsilon(1) such that A \subset ... More

Algebraicity and Asymptotics: An explosion of BPS indices from algebraic generating seriesJun 08 2016It is an observation of Kontsevich and Soibelman that generating series that produce certain (generalized) Donaldson Thomas invariants are secretly algebraic functions over the rationals. From a physical perspective this observation arises naturally for ... More

Sampling Generative Networks: Notes on a Few Effective TechniquesSep 14 2016Sep 16 2016We introduce several techniques for sampling and visualizing the latent spaces of generative models. Replacing linear interpolation with spherical linear interpolation prevents diverging from a model's prior distribution and produces sharper samples. ... More

Scattering diagrams, Hall algebras and stability conditionsMar 01 2016Nov 11 2016To any quiver with relations we associate a consistent scattering diagram taking values in the motivic Hall algebra of its category of representations. We show that the chamber structure of this scattering diagram coincides with the natural chamber structure ... More

A new strain energy function for the hyperelastic modelling of ligaments and tendons based on fascicle microstructureOct 02 2015A new strain energy function for the hyperelastic modelling of ligaments and tendons based on the geometrical arrangement of their fibrils is derived. The distribution of the crimp angles of the fibrils is used to determine the stress-strain response ... More

Interlacements and the Wired Uniform Spanning ForestDec 28 2015Oct 18 2016We extend the Aldous-Broder algorithm to generate the wired uniform spanning forests (WUSFs) of infinite, transient graphs. We do this by replacing the simple random walk in the classical algorithm with Sznitman's random interlacement process. We then ... More

General Graph Identification By HashingDec 22 2015A method for identifying graphs using MD5 hashing is presented. This allows fast graph equality comparisons and can also be used to facilitate graph isomorphism testing. The graphs can be labeled or unlabeled. The method identifies vertices by hashing ... More

The bijection between projective indecomposable and simple modulesOct 14 2014For modules over a finite-dimensional algebra, there is a canonical one-to-one correspondence between the projective indecomposable modules and the simple modules. In this purely expository note, we take a straight-line path from the definitions to this ... More

Conformal invariance of the 3D self-avoiding walkOct 25 2013We show that if the three dimensional self-avoiding walk (SAW) is conformally invariant, then one can compute the hitting densities for the SAW in a half space and in a sphere. We test these predictions by Monte Carlo simulations and find excellent agreement, ... More

Dyck Words and Multi-Quark Primitive AmplitudesApr 29 2013I study group theory (Kleiss-Kuijf) relations between purely multi-quark primitive amplitudes at tree level, and prove that they reduce the number of independent primitives to (n-2)!/(n/2)!, where n is the number of quarks plus antiquarks, in the case ... More

Sets of beta-expansions and the Hausdorff Measure of Slices through FractalsJul 08 2013We study natural measures on sets of beta-expansions and on slices through self similar sets. In the setting of beta-expansions, these allow us to better understand the measure of maximal entropy for the random beta-transformation and to reinterpret a ... More

On the Conservativity of Some Functors in Motivic Homotopy TheoryJun 24 2015Feb 23 2016Given a 0-connective motivic spectrum $E \in SH(k)$ over a perfect field k, we determine $h_0$ of the associated motive $M E \in DM(k)$ in terms of $\pi_0 (E)$. Using this we show that if k has finite 2-\'etale cohomological dimension, then the functor ... More

The Scenery Flow for Self-Affine MeasuresMay 07 2015We describe the scaling scenery associated to Bernoulli measures supported on separated self-affine sets under the condition that certain projections of the measure are absolutely continuous.

The Generalized Slices of Hermitian K-TheoryOct 05 2016We compute the generalized slices (as defined by Spitzweck-{\O}stv{\ae}r) of the motivic spectrum KO (representing hermitian K-theory) in terms of motivic cohomology and (a version of) generalized motivic cohomology, obtaining good agreement with the ... More

Notions of Möbius inversionJan 02 2012Oct 07 2012M\"obius inversion, originally a tool in number theory, was generalized to posets for use in group theory and combinatorics. It was later generalized to categories in two different ways, both of which are useful. We provide a unifying abstract framework. ... More

Generalized Enrichment for Categories and MulticategoriesJan 29 1999In this paper we answer the question: `what kind of a structure can a general multicategory be enriched in?' The answer is, in a sense to be made precise, that a multicategory of one type can be enriched in a multicategory of the type one level up. In ... More

Basic BicategoriesOct 04 1998A concise guide to very basic bicategory theory, from the definition of a bicategory to the coherence theorem.

General Operads and MulticategoriesOct 08 1998Notions of `operad' and `multicategory' abound. This work provides a single framework in which many of these various notions can be expressed. Explicitly: given a monad * on a category S, we define the term `(S,*)-multicategory', subject to certain conditions ... More

Stability conditions on a non-compact Calabi-Yau threefoldSep 02 2005Feb 28 2006We study the space of stability conditions $\Stab(X)$ on the non-compact Calabi-Yau threefold $X$ which is the total space of the canonical bundle of $\PP^2$. We give a combinatorial description of an open subset of $\Stab(X)$ and state a conjecture relating ... More

Flops and derived categoriesSep 06 2000This paper contains some applications of Fourier-Mukai techniques to the birational geometry of threefolds. In particular, we prove that birational Calabi-Yau threefolds have equivalent derived categories. To do this we show how flops arise naturally ... More

Algebraic and Affine Pattern AvoidanceMar 15 2013We investigate various connections between the 0-Hecke monoid, Catalan monoid, and pattern avoidance in permutations, providing new tools for approaching pattern avoidance in an algebraic framework. In particular, we characterize containment of a class ... More

Hall algebras and curve-counting invariantsFeb 23 2010We use Joyce's theory of motivic Hall algebras to prove that reduced Donaldson-Thomas curve-counting invariants on Calabi-Yau threefolds coincide with stable pair invariants, and that the generating functions for these invariants are Laurent expansions ... More

Monte Carlo Tests of SLE Predictions for the 2D Self-Avoiding WalkDec 21 2001The conjecture that the scaling limit of the two-dimensional self-avoiding walk (SAW) in a half plane is given by the stochastic Loewner evolution (SLE) with $\kappa=8/3$ leads to explicit predictions about the SAW. A remarkable feature of these predictions ... More

Spaces of stability conditionsNov 16 2006Stability conditions are a mathematical way to understand $\Pi$-stability for D-branes in string theory. Spaces of stability conditions seem to be related to moduli spaces of conformal field theories. This is a survey article describing what is currently ... More

Regularity and nearness theorems for families of local Lie groupsJun 14 2012In this work, we prove three types of results with the strategy that, together, the author believes these should imply the local version of Hilbert's Fifth problem. In a separate development, we construct a nontrivial topology for rings of map germs on ... More

Testing the Boundary Conditions of General Relativity Near the Earth-Sun Saddle PointJun 07 1998Jun 03 1999We suggest that a satellite with a stable atomic clock on board be sent through the Earth-Sun gravitational saddle point to experimentally determine whether Nature prefers static solutions of the field equations of General Relativity, such as the standard ... More

Conformal invariance predictions for the three-dimensional self-avoiding walkAug 20 2014Dec 23 2014If the three dimensional self-avoiding walk (SAW) is conformally invariant, then one can compute the hitting densities for the SAW in a half-space and in a sphere. The ensembles of SAW's used to define these hitting densities involve walks of arbitrary ... More

Speech Coding, Speech Interfaces and IoT - Opportunities and ChallengesNov 14 2018Recent speech and audio coding standards such as 3GPP Enhanced Voice Services match the foreseeable needs and requirements in transmission of speech and audio, when using current transmission infrastructure and applications. Trends in Internet-of-Things ... More

Locality of the critical probability for transitive graphs of exponential growthAug 27 2018Around 2008, Schramm conjectured that the critical probabilities for Bernoulli bond percolation satisfy the following continuity property: If $(G_n)_{n\geq 1}$ is a sequence of transitive graphs converging locally to a transitive graph $G$ and $\limsup_{n\to\infty} ... More

Using weighting algorithms to refine source direction determinations in all-sky gravitational wave burst searches with two-detector networksMay 03 2018I explore the possibility of resurrecting an old, non-Bayesian computational approach for inferring the source direction of a gravitational wave from the output of a two-detector network. The method gives the beam pattern response functions and time delay, ... More

Affine Grassmannians in A^1-algebraic topologyJan 25 2018Mar 25 2019Let k be a field. Denote by Spc(k)_* the unstable, pointed motivic homotopy category and by Omega_Gm: Spc(k)_* \to Spc(k)_* the Gm-loops functor. For a k-group G, denote by Gr_G the affine Grassmannian of G. If G is isotropic reductive, we provide a canonical ... More

Knot types of generalized Kirchhoff rodsAug 30 2017Kirchhoff energy is a classical functional on the space of arclength-parameterized framed curves whose critical points approximate configurations of springy elastic rods. We introduce a generalized functional on the space of framed curves of arbitrary ... More

Long time thermal asymptotics of nonlinear Luttinger liquid from inverse scatteringAug 07 2017I derive a Fredholm determinant for the thermal correlator of vertex operators with a conformally invariant density matrix and nonlinear time evolution. Using the method of nonlinear steepest descent I find the long time asymptotics at finite temperature. ... More

Measuring technological complexity - Current approaches and a new measure of structural complexityAug 24 2017Mar 09 2018The paper reviews two prominent approaches for the measurement of technological complexity: the method of reflection and the assessment of technologies' combinatorial difficulty. It discusses their central underlying assumptions and identifies potential ... More

Rigidity in etale motivic stable homotopy theoryOct 18 2018For a scheme X, denote by SH(X_et^hyp) the stabilization of the hypercompletion of its etale infty-topos, and by SH_et(X) the localization of the stable motivic homotopy category SH(X) at the (desuspensions of) etale hypercovers. For a stable infty-category ... More

Bornological modifications of hyperspace topologiesApr 09 2013The bornological convergence structures that have been studied recently as generalizations of Attouch-Wets convergence define pretopologies on hyperspaces. In this paper we characterize the topological reflections of these pretopologies and translate ... More

Minimal elements of stopping time $σ$-algebrasDec 12 2011Jun 19 2012We show how minimal elements of a stopping time $\sigma$-algebra can be expressed in terms of the minimal elements of the $\sigma$-algebra of the underlying filtration. This facilitates an intuitive interpretation of stopping time $\sigma$-algebras. An ... More

Stopping times are hitting times: a natural representationDec 07 2011Jun 19 2012There exists a simple, didactically useful one-to-one relationship between stopping times and adapted c\`agl\`ad (LCRL) processes that are non-increasing and take the values 0 and 1 only. As a consequence, stopping times are always hitting times.

On Multiple and Polynomial Recurrent extensions of infinite measure preserving transformationsMar 30 2007Mar 11 2009We prove that multiple-recurrence and polynomial-recurrence of invertible infinite measure preserving transformations are both properties which pass to extensions.

A Fast Algorithm for Simulating the Chordal Schramm-Loewner EvolutionJul 29 2005Apr 24 2007The Schramm-Loewner evolution (SLE) can be simulated by dividing the time interval into N subintervals and approximating the random conformal map of the SLE by the composition of N random, but relatively simple, conformal maps. In the usual implementation ... More

A primer on reflexivity and price dynamics under systemic riskJan 27 2013A simple quantitative example of a reflexive feedback process and the resulting price dynamics after an exogenous price shock to a financial network is presented. Furthermore, an outline of a theory that connects financial reflexivity, which stems from ... More

No-arbitrage pricing under cross-ownershipMay 05 2010We generalize Merton's asset valuation approach to systems of multiple financial firms where cross-ownership of equities and liabilities is present. The liabilities, which may include debts and derivatives, can be of differing seniority. We derive equations ... More

Reflectionless discrete Schrödinger operators are spectrally atypicalMar 06 2017Dec 14 2017We prove that, if an isospectral torus contains a discrete Schr\"odinger operator with nonconstant potential, the shift dynamics on that torus cannot be minimal. Consequently, we specify a generic sense in which finite unions of nondegenerate closed intervals ... More

Clifford correspondences and irreducible restrictions of charactersJun 09 2018For a finite group $G$ and complex character $\chi\in\mathrm{Irr}(G)$ that restricts irreducibly to a normal subgroup $N\vartriangleleft G,$ we prove a theorem about Clifford correspondences between the characters of subgroups of $G$ that induce $\chi.$ ... More

Uniformizable and realcompact bornological universesSep 28 2009Bornological universes were introduced some time ago by Hu and obtained renewed interest in recent articles on convergence in hyperspaces and function spaces and optimization theory. One of Hu's results gives us a necessary and sufficient condition for ... More

Diffusions in random environment and ballistic behaviorSep 23 2005Sep 26 2005This article is accepted for publication in the "Annals I.H.P. Prob. & Stat.". We investigate the ballistic behavior of diffusions in random environment. We introduce conditions in the spirit of (T) and (T') of the discrete setting, cf. Sznitman \cite{szn01}, ... More

Pole-free solutions of the first Painlevé hierarchy and non-generic critical behavior for the KdV equationJul 01 2011We establish the existence of real pole-free solutions to all even members of the Painlev\'e I hierarchy. We also obtain asymptotics for those solutions and describe their relevance in the description of critical asymptotic behavior of solutions to the ... More

On the Crepant Resolution Conjecture in the Local CaseOct 13 2008In this paper we analyze four examples of birational transformations between local Calabi-Yau 3-folds: two crepant resolutions, a crepant partial resolution, and a flop. We study the effect of these transformations on genus-zero Gromov-Witten invariants, ... More

Tail Invariant Measures of the Dyck ShiftJun 02 2004Nov 07 2007We show that the one-sided Dyck shift has a unique tail invariant topologically $\sigma$-finite measure (up to scaling). This invariant measure of the one sided Dyck turns out to be a shift-invariant probability. Furthermore, it is one of the two ergodic ... More

Explicit moduli spaces for congruences of elliptic curvesApr 26 2018We determine explicit birational models over Q for the modular surfaces parametrising pairs of N-congruent elliptic curves in all cases where this surface is an elliptic surface. In each case we also determine the rank of the Mordell-Weil lattice and ... More

The Hessian of a genus one curveOct 12 2006Nov 30 2010We continue our development of the invariant theory of genus one curves with the aim of computing certain twists of the universal family of elliptic curves parametrised by the modular curve X(n) for n = 2,3,4,5. Our construction makes use of a covariant ... More

The invariants of a genus one curveOct 10 2006It was first pointed out by Weil that we can use classical invariant theory to compute the Jacobian of a genus one curve. The invariants required for curves of degree n = 2,3,4 were already known to the nineteenth centuary invariant theorists. We have ... More

The Euler characteristic of a categoryOct 08 2006The Euler characteristic of a finite category is defined and shown to be compatible with Euler characteristics of other types of object, including orbifolds. A formula for the cardinality of the colimit of a diagram of sets is proved, generalizing the ... More

A general theory of self-similarity II: recognitionNov 15 2004This paper concerns the self-similarity of topological spaces, in the sense defined in math.DS/0411344. I show how to recognize self-similar spaces, or more precisely, universal solutions of self-similarity systems. Examples include the standard simplices ... More

Topology and Higher-Dimensional Category Theory: the Rough IdeaJun 27 2001Higher-dimensional category theory is the study of n-categories, operads, braided monoidal categories, and other such exotic structures. Although it can be treated purely as an algebraic subject, it is inherently topological in nature: the higher-dimensional ... More

General self-similarity: an overviewNov 15 2004Informal seminar notes explaining the ideas in math.DS/0411344 and math.DS/0411345.

Scattering diagrams, Hall algebras and stability conditionsMar 01 2016To any quiver with relations we associate a consistent scattering diagram taking values in the motivic Hall algebra of its category of representations. We show that the chamber structure of this scattering diagram coincides with the natural chamber structure ... More

Stability conditions on K3 surfacesJul 11 2003Nov 16 2006This paper contains a description of one connected component of the space of stability conditions on the bounded derived category of coherent sheaves on a complex algebraic K3 surface.

Stability conditions on triangulated categoriesDec 17 2002Feb 08 2006This paper introduces the notion of a stability condition on a triangulated category. The motivation comes from the study of Dirichlet branes in string theory, and especially from M.R. Douglas's notion of $\Pi$-stability. From a mathematical point of ... More

The Globular Cluster Luminosity Function: New Progress in Understanding an Old Distance IndicatorApr 16 2003I review the Globular Cluster Luminosity Function (GCLF) with emphasis on recent observational data and theoretical progress. As is well known, the turn-over magnitude (TOM) is a good distance indicator for early-type galaxies within the limits set by ... More

Numerical simulations of the intergalactic mediumSep 05 2002The intergalactic medium at redshifts 2--6 can be studied observationally through the absorption features it produces in the spectra of background quasars. Most of the UV-absorption lines arise in mildly overdense regions, which can be simulated reliably ... More

Phase separation in the neutral Falicov-Kimball modelMay 30 1997The Falicov-Kimball model consists of spinless electrons and classical particles (ions) on a lattice. The electrons hop between nearest neighbor sites while the ions do not. We consider the model with equal numbers of ions and electrons and with a large ... More

Motivic and Real Etale Stable Homotopy TheoryAug 31 2016Let X be a Noetherian scheme of finite dimension and denote by rho the (additive inverse of the) morphism in SH(X) from S to Gm corresponding to the unit -1. Here SH(X) denotes the motivic stable homotopy category. We show that the category obtained by ... More

Numerical Evaluation of Two-Loop Integrals in FDRDec 15 2015Feb 05 2016We present a method to numerically evaluate infrared-finite one- and two-loop integrals within the Four-Dimensional Regularization/Renormalization approach, in which a small mass serves as regulator. Typical integrals exhibit a logarithmic dependence ... More

A new strain energy function for modelling ligaments and tendons whose fascicles have a helical arrangement of fibrilsAug 17 2015A new strain energy function for the hyperelastic modelling of ligaments and tendons whose fascicles have a helical arrangement of fibrils is derived. The stress-strain response of a single fascicle whose fibrils exhibit varying levels of crimp throughout ... More

Wired Cycle-Breaking Dynamics for Uniform Spanning ForestsApr 15 2015We prove that every component of the wired uniform spanning forest (WUSF) is one-ended almost surely in every transient reversible random graph, removing the bounded degree hypothesis required by earlier results. We deduce that every component of the ... More

Constraints on Axion Inflation from the Weak Gravity ConjectureMar 03 2015Sep 08 2015We derive constraints facing models of axion inflation based on decay constant alignment from a string-theoretic and quantum gravitational perspective. In particular, we investigate the prospects for alignment and `anti-alignment' of $C_4$ axion decay ... More

A Note on the Kullback-Leibler Divergence for the von Mises-Fisher distributionFeb 25 2015We present a derivation of the Kullback Leibler (KL)-Divergence (also known as Relative Entropy) for the von Mises Fisher (VMF) Distribution in $d$-dimensions.

Anonymized e-mail interviews with R package maintainers active on CRAN and GitHubJun 17 2016This technical report accompanies a research article that empirically studies the problems related to inter-repository package dependencies in the R ecosystem of statistical computing, with a focus on R packages hosted on CRAN and GitHub. The current ... More

The size of maximal systems of brick islandsOct 21 2010For integers $m_1,...,m_d>0$ and a cuboid $M=[0,m_1]\times ... \times [0,m_d]\subset \mathbb{R}^d$, a brick of $M$ is a closed cuboid whose vertices have integer coordinates. A set $H$ of bricks in $M$ is a system of brick islands if for each pair of ... More

Divisorial Extractions from Singular Curves in Smooth 3-Folds, IMar 29 2014Consider a singular curve $\Gamma$ contained in a smooth 3-fold $X$. Assuming the general elephant conjecture, the general hypersurface section $\Gamma\subset S\subset X$ is Du Val. Under that assumption, this paper describes the construction of a divisorial ... More

Hall algebras and Donaldson-Thomas invariantsNov 11 2016This is a survey article on Hall algebras and their applications to the study of motivic invariants of moduli spaces of coherent sheaves on Calabi-Yau threefolds. It is a write-up of my talks at the 2015 Salt Lake City AMS Summer Research Institute and ... More

Codensity and the Giry monadOct 16 2014The Giry monad on the category of measurable spaces sends a space to a space of all probability measures on it. There is also a finitely additive Giry monad in which probability measures are replaced by finitely additive probability measures. We give ... More

On certain other sets of integersJul 30 2010Jan 31 2011We show that if A is a subset of {1,...,N} containing no non-trivial three-term arithmetic progressions then |A|=O(N/ log^{3/4-o(1)} N).

On a non-abelian Balog-Szemeredi-type lemmaDec 02 2009Oct 14 2010We show that if G is a group and A is a finite subset of G with |A^2| < K|A|, then for all k there is a symmetric neighbourhood of the identity S with S^k a subset of A^2A^{-2} and |S| > exp(-K^{O(k)})|A|.

On a theorem of ShkredovJul 31 2008Jan 26 2011We show that if A is a finite subset of an abelian group with additive energy at least c|A|^3 then there is a subset L of A with |L|=O(c^{-1}\log |A|) such that |A \cap Span(L)| >> c^{1/3}|A|.

Bounds in the idempotent theoremOct 22 2016We show that if G is a finite Abelian group and f is an integer-valued map on G with algebra norm at most M then there is some L < \exp(M^{4+o(1)}), cosets of (possibly different) subgroups W_1,...,W_L, and s_1,...,s_L \in {-1,1} such that f=\sum_i{s_i1_{W_i}}. ... More

Solving xz=yy in certain subsets of finite groupsNov 17 2016We show that if G is a finite group and A is a subset of G with no non-trivial solutions to xz=yy then |A| < |G|/(log log |G|)^c.

Learning to Learn Neural NetworksOct 19 2016Meta-learning consists in learning learning algorithms. We use a Long Short Term Memory (LSTM) based network to learn to compute on-line updates of the parameters of another neural network. These parameters are stored in the cell state of the LSTM. Our ... More

Radiative Balance between Photon Emission from Surface and in VolumeDec 02 2016An expression is derived which links the probability of photon reabsorption (recycling) in a material with other optical parameters. We discuss the application of this relation in several typical situations which are relevant in the operation of devices ... More

No-Arbitrage Prices of Cash Flows and Forward Contracts as Choquet RepresentationsJun 05 2015Jun 27 2015In a market of deterministic cash flows, given as an additive, symmetric relation of exchangeability on the finite signed Borel measures on the non-negative real time axis, it is shown that the only arbitrage-free price functional that fulfills some additional ... More

Combinatorial cost: a coarse settingNov 01 2017Dec 14 2017The main inspiration for this paper is a paper by Elek where he introduces combinatorial cost for graph sequences. We show that having cost equal to 1 and hyperfiniteness are coarse invariants. We also show `cost-1' for box spaces behaves multiplicatively ... More

Overlap-Add Windows with Maximum Energy Concentration for Speech and Audio ProcessingFeb 04 2019Processing of speech and audio signals with time-frequency representations require windowing methods which allow perfect reconstruction of the original signal and where processing artifacts have a predictable behavior. The most common approach for this ... More

Schur's colouring theorem for non-commuting pairsJan 07 2019For G a finite non-Abelian group we write c(G) for the probability that two randomly chosen elements commute and k(G) for the largest integer such that any k(G)-colouring of G is guaranteed to contain a monochromatic quadruple (x,y,xy,yx) with xy not ... More

The coset and stability ringsOct 24 2018Feb 05 2019We show that if $G$ is a discrete Abelian group and $A \subset G$ has $\|1_A\|_{B(G)} \leq M$ then $A$ is $O(\exp(\pi M))$-stable in the sense of Terry and Wolf.

Koszul duality for toric varietiesAug 22 2003Jul 13 2006We show that certain categories of perverse sheaves on a pair of affine toric varieties defined by dual cones are Koszul dual in the sense of Beilinson, Ginzburg and Soergel. The functor expressing this duality is constructed explicitly using a combinatorial ... More

Fredholm modules over certain group C*-algebrasJan 23 2001Dec 20 2001Motivated by the search for new examples of "noncommutative manifolds", we study the noncommutative geometry of the group C*-algebras of various discrete groups. The examples we consier are the infinite dihedral group ${\bf Z} \times_{\sigma} {\bf Z}_2$ ... More

The noncommutative geometry of the discrete Heisenberg groupJan 10 2002Motivated by the search for new examples of ``noncommutative manifolds'', we study the noncommutative geometry (in the sense of Connes) of the group C*-algebra of the three dimensional discrete Heisenberg group. We present a unified treatment of the K-homology, ... More