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Random G-expectationsSep 11 2010Sep 05 2013We construct a time-consistent sublinear expectation in the setting of volatility uncertainty. This mapping extends Peng's G-expectation by allowing the range of the volatility uncertainty to be stochastic. Our construction is purely probabilistic and ... More

Robust Superhedging with Jumps and DiffusionJul 07 2014Jul 17 2015We establish a nondominated version of the optional decomposition theorem in a setting that includes jump processes with nonvanishing diffusion as well as general continuous processes. This result is used to derive a robust superhedging duality and the ... More

A Mean Field Game of Optimal StoppingMay 30 2016We formulate a stochastic game of mean field type where the agents solve optimal stopping problems and interact through the proportion of players that have already stopped. Working with a continuum of agents, typical equilibria become functions of the ... More

The Opportunity Process for Optimal Consumption and Investment with Power UtilityDec 09 2009Jun 03 2010We study the utility maximization problem for power utility random fields in a semimartingale financial market, with and without intermediate consumption. The notion of an opportunity process is introduced as a reduced form of the value process of the ... More

Risk Aversion Asymptotics for Power Utility MaximizationMar 18 2010We consider the economic problem of optimal consumption and investment with power utility. We study the optimal strategy as the relative risk aversion tends to infinity or to one. The convergence of the optimal consumption is obtained for general semimartingale ... More

A Quasi-Sure Approach to the Control of Non-Markovian Stochastic Differential EquationsJun 16 2011May 07 2012We study stochastic differential equations (SDEs) whose drift and diffusion coefficients are path-dependent and controlled. We construct a value process on the canonical path space, considered simultaneously under a family of singular measures, rather ... More

Power Utility Maximization in Constrained Exponential Lévy ModelsDec 09 2009Sep 07 2010We study power utility maximization for exponential L\'evy models with portfolio constraints, where utility is obtained from consumption and/or terminal wealth. For convex constraints, an explicit solution in terms of the L\'evy triplet is constructed ... More

The Bellman equation for power utility maximization with semimartingalesDec 09 2009Mar 08 2012We study utility maximization for power utility random fields with and without intermediate consumption in a general semimartingale model with closed portfolio constraints. We show that any optimal strategy leads to a solution of the corresponding Bellman ... More

Pathwise Construction of Stochastic IntegralsAug 15 2011Jun 20 2012We propose a method to construct the stochastic integral simultaneously under a non-dominated family of probability measures. Path-by-path, and without referring to a probability measure, we construct a sequence of Lebesgue-Stieltjes integrals whose medial ... More

A Mean Field Game of Optimal StoppingMay 30 2016Nov 30 2017We formulate a stochastic game of mean field type where the agents solve optimal stopping problems and interact through the proportion of players that have already stopped. Working with a continuum of agents, typical equilibria become functions of the ... More

Utility Maximization under Model Uncertainty in Discrete TimeJul 13 2013We give a general formulation of the utility maximization problem under nondominated model uncertainty in discrete time and show that an optimal portfolio exists for any utility function that is bounded from above. In the unbounded case, integrability ... More

Superreplication under Model Uncertainty in Discrete TimeJan 15 2013Feb 14 2014We study the superreplication of contingent claims under model uncertainty in discrete time. We show that optimal superreplicating strategies exist in a general measure-theoretic setting; moreover, we characterize the minimal superreplication price as ... More

Canonical Supermartingale CouplingsSep 09 2016Nov 26 2017Two probability distributions $\mu$ and $\nu$ in second stochastic order can be coupled by a supermartingale, and in fact by many. Is there a canonical choice? We construct and investigate two couplings which arise as optimizers for constrained Monge-Kantorovich ... More

A Mean Field CompetitionAug 03 2017We introduce a mean field game with rank-based reward: competing agents optimize their effort to achieve a goal, are ranked according to their completion time, and paid a reward based on their relative rank. First, we propose a tractable Poissonian model ... More

Robust Utility Maximization with Lévy ProcessesFeb 20 2015Mar 22 2016We study a robust portfolio optimization problem under model uncertainty for an investor with logarithmic or power utility. The uncertainty is specified by a set of possible L\'evy triplets; that is, possible instantaneous drift, volatility and jump characteristics ... More

Arbitrage and duality in nondominated discrete-time modelsMay 26 2013Mar 16 2015We consider a nondominated model of a discrete-time financial market where stocks are traded dynamically, and options are available for static hedging. In a general measure-theoretic setting, we show that absence of arbitrage in a quasi-sure sense is ... More

Weak Dynamic Programming for Generalized State ConstraintsMay 04 2011Oct 19 2012We provide a dynamic programming principle for stochastic optimal control problems with expectation constraints. A weak formulation, using test functions and a probabilistic relaxation of the constraint, avoids restrictions related to a measurable selection ... More

Martingale Inequalities and Deterministic CounterpartsJan 19 2014Oct 18 2014We study martingale inequalities from an analytic point of view and show that a general martingale inequality can be reduced to a pair of deterministic inequalities in a small number of variables. More precisely, the optimal bound in the martingale inequality ... More

Canonical Supermartingale CouplingsSep 09 2016Two probability distributions $\mu$ and $\nu$ in second stochastic order can be coupled by a supermartingale, and in fact by many. Is there a canonical choice? We construct and investigate two couplings which arise as optimizers for constrained Monge-Kantorovich ... More

Stochastic Target Games and Dynamic Programming via Regularized Viscosity SolutionsJul 22 2013Jan 31 2015We study a class of stochastic target games where one player tries to find a strategy such that the state process almost-surely reaches a given target, no matter which action is chosen by the opponent. Our main result is a geometric dynamic programming ... More

Optimal stopping under adverse nonlinear expectation and related gamesDec 10 2012Sep 09 2015We study the existence of optimal actions in a zero-sum game $\inf_{\tau}\sup_PE^P[X_{\tau}]$ between a stopper and a controller choosing a probability measure. This includes the optimal stopping problem $\inf_{\tau}\mathcal{E}(X_{\tau})$ for a class ... More

Nonlinear Lévy Processes and their CharacteristicsJan 28 2014Jan 11 2015We develop a general construction for nonlinear L\'evy processes with given characteristics. More precisely, given a set $\Theta$ of L\'evy triplets, we construct a sublinear expectation on Skorohod space under which the canonical process has stationary ... More

Superreplication under Volatility Uncertainty for Measurable ClaimsAug 31 2012Apr 14 2013We establish the duality-formula for the superreplication price in a setting of volatility uncertainty which includes the example of "random G-expectation." In contrast to previous results, the contingent claim is not assumed to be quasi-continuous.

Conditional Optimal Stopping: A Time-Inconsistent OptimizationJan 17 2019Inspired by recent work of P.-L. Lions on conditional optimal control, we introduce a problem of optimal stopping under bounded rationality: the objective is the expected payoff at the time of stopping, conditioned on another event. For instance, an agent ... More

Measurability of Semimartingale Characteristics with Respect to the Probability LawDec 05 2013Jul 07 2014Given a c\`adl\`ag process $X$ on a filtered measurable space, we construct a version of its semimartingale characteristics which is measurable with respect to the underlying probability law. More precisely, let $\mathfrak{P}_{sem}$ be the set of all ... More

Consistent Price Systems under Model UncertaintyAug 23 2014We develop a version of the fundamental theorem of asset pricing for discrete-time markets with proportional transaction costs and model uncertainty. A robust notion of no-arbitrage of the second kind is defined and shown to be equivalent to the existence ... More

Superhedging and Dynamic Risk Measures under Volatility UncertaintyNov 12 2010Jun 12 2012We consider dynamic sublinear expectations (i.e., time-consistent coherent risk measures) whose scenario sets consist of singular measures corresponding to a general form of volatility uncertainty. We derive a c\`adl\`ag nonlinear martingale which is ... More

Supply and Shorting in Speculative MarketsMay 16 2017Aug 18 2017We propose a continuous-time model of trading among risk-neutral agents with heterogeneous beliefs. Agents face quadratic costs-of-carry on their positions and as a consequence, their marginal valuation of the asset decreases when the magnitude of their ... More

Small-Time Asymptotics of Option Prices and First Absolute MomentsJun 11 2010Jun 16 2011We study the leading term in the small-time asymptotics of at-the-money call option prices when the stock price process $S$ follows a general martingale. This is equivalent to studying the first centered absolute moment of $S$. We show that if $S$ has ... More

Constructing Sublinear Expectations on Path SpaceMay 11 2012Apr 11 2013We provide a general construction of time-consistent sublinear expectations on the space of continuous paths. It yields the existence of the conditional G-expectation of a Borel-measurable (rather than quasi-continuous) random variable, a generalization ... More

A Risk-Neutral Equilibrium Leading to Uncertain Volatility PricingDec 29 2016Jan 03 2018We study the formation of derivative prices in equilibrium between risk-neutral agents with heterogeneous beliefs about the dynamics of the underlying. Under the condition that the derivative cannot be shorted, we prove the existence of a unique equilibrium ... More

Fine Properties of the Optimal Skorokhod Embedding ProblemMar 09 2019We study the problem of stopping a Brownian motion at a given distribution $\nu$ while optimizing a reward function that depends on the (possibly randomized) stopping time and the Brownian motion. Our first result establishes that the set $\mathcal{T}(\nu)$ ... More

Complete Duality for Martingale Optimal Transport on the LineJul 02 2015Jun 12 2016We study the optimal transport between two probability measures on the real line, where the transport plans are laws of one-step martingales. A quasi-sure formulation of the dual problem is introduced and shown to yield a complete duality theory for general ... More

Multiperiod Martingale TransportMar 30 2017May 18 2019Consider a multiperiod optimal transport problem where distributions $\mu_{0},\dots,\mu_{n}$ are prescribed and a transport corresponds to a scalar martingale $X$ with marginals $X_{t}\sim\mu_{t}$. We introduce particular couplings called left-monotone ... More

Stochastic target games with controlled lossJun 27 2012Apr 28 2014We study a stochastic game where one player tries to find a strategy such that the state process reaches a target of controlled-loss-type, no matter which action is chosen by the other player. We provide, in a general setup, a relaxed geometric dynamic ... More

Bounds for VIX Futures given S&P 500 SmilesSep 19 2016Jun 22 2017We derive sharp bounds for the prices of VIX futures using the full information of S&P 500 smiles. To that end, we formulate the model-free sub/superreplication of the VIX by trading in the S&P 500 and its vanilla options as well as the forward-starting ... More

Bounds for VIX Futures given S&P 500 SmilesSep 19 2016We derive sharp bounds for the prices of VIX futures using the full information of S&P 500 smiles. To that end, we formulate the model-free sub/superreplication of the VIX by trading in the S&P 500 and its vanilla options as well as the forward-starting ... More

Weak Approximation of G-ExpectationsMar 02 2011We introduce a notion of volatility uncertainty in discrete time and define the corresponding analogue of Peng's G-expectation. In the continuous-time limit, the resulting sublinear expectation converges weakly to the G-expectation. This can be seen as ... More

Asset Pricing with Heterogeneous Beliefs and IlliquidityMay 14 2019This paper studies the equilibrium price of an asset that is traded in continuous time between N agents who have heterogeneous beliefs about the state process underlying the asset's payoff. We propose a tractable model where agents maximize expected returns ... More

Multiperiod Martingale TransportMar 30 2017Consider a multiperiod optimal transport problem where distributions $\mu_{0},\dots,\mu_{n}$ are prescribed and a transport corresponds to a scalar martingale $X$ with marginals $X_{t}\sim\mu_{t}$. We introduce particular couplings called left-monotone ... More

Convergence to the Mean Field Game Limit: A Case StudyJun 03 2018We study the convergence of Nash equilibria in a game of optimal stopping. If the associated mean field game has a unique equilibrium, any sequence of $n$-player equilibria converges to it as $n\to\infty$. However, both the finite and infinite player ... More

Robust Fundamental Theorem for Continuous ProcessesOct 18 2014Jul 18 2015We study a continuous-time financial market with continuous price processes under model uncertainty, modeled via a family $\mathcal{P}$ of possible physical measures. A robust notion ${\rm NA}_{1}(\mathcal{P})$ of no-arbitrage of the first kind is introduced; ... More

ALLSAT compressed with wildcards. Part 2: All k-models of a BDDMar 24 2017Aug 23 2017If f is a Boolean function given by a BDD then it is well known how to calculate the number of models (i.e. bitstrings x with f(x)=1). Let |x| be the number of 1's in x. How to calculate the number of k-models x (i.e. having |x|=k) is lesser known; we ... More

Global analytic solutions of the semiconductor Boltzmann-Dirac-Benney equation with relaxation time approximationMar 01 2018The global existence of a solution of the semiconductor Boltzmann-Dirac-Benney equation \[ \partial_t f + \nabla\epsilon(p)\cdot\nabla_x f - \nabla \rho_f(x,t)\cdot\nabla_p f = \frac{\mathcal F_\lambda(p)-f}\tau, \quad x\in\mathbb{R}^d,\ p\in B, \ t>0 ... More

Eigenvalues of compactly perturbed operators via entropy numbersOct 04 2017Jan 25 2018We derive new estimates for the number of discrete eigenvalues of compactly perturbed operators on Banach spaces, assuming that the perturbing operator is an element of a weak entropy number ideal. Our results improve upon earlier results by the author ... More

The Relation between Subfactors arising from Conformal Nets and the Realization of Quantum DoublesNov 28 2015We give a precise definition for when a subfactor arises from a conformal net which can be motivated by classification of defects. We show that a subfactor $N \subset M$ arises from a conformal net if there is a conformal net whose representation category ... More

Quotients of spectra of almost factorial domains and Mori dream spacesAug 03 2015We prove that a GIT chamber quotient of an affine variety $X=Spec(A)$ by a reductive group $G$, where $A$ is an almost factorial domain, is a Mori dream space if it is projective, regardless of the codimension of the unstable locus. This includes an explicit ... More

Some remarks on upper bounds for Weierstrass primary factors and their application in spectral theoryApr 06 2017May 15 2017We study upper bounds on Weierstrass primary factors and discuss their application in spectral theory. One of the main aims of this note is to draw attention to works of Blumenthal and Denjoy from 1910, but we also provide some new results and some numerical ... More

Zipf-Mandelbrot-Pareto model for co-authorship popularityApr 01 2014Each co-author (CA) of any scientist can be given a rank ($r$) of importance according to the number ($J$) of joint publications which the authors have together. In this paper, the Zipf-Mandelbrot-Pareto law, i.e. $ J \propto 1/(\nu+r)^{\zeta}$ is shown ... More

Binary Scientific Star Coauthors Core SizeJan 15 2014It is examined whether the relationship $ J \propto A/r^{\alpha}$, and the subsequent coauthor core notion (Ausloos 2013), between the number ($J$) of joint publications (JP) by a "main scientist" (LI) with her/his coauthors (CAs) can be extended to a ... More

Expansion of polynomial Lie group integrals in terms of certain maps on surfaces, and factorizations of permutationsJan 29 2016Feb 07 2016Using the diagrammatic approach to integrals over Gaussian random matrices, we find a representation for polynomial Lie group integrals as infinite sums over certain maps on surfaces. The maps involved satisfy a specific condition: they have some marked ... More

Large Networks of Diameter Two Based on Cayley GraphsSep 02 2015Apr 20 2017In this contribution we present a construction of large networks of diameter two and of order $\frac{1}{2}d^2$ for every degree $d\geq 8$, based on Cayley graphs with surprisingly simple underlying groups. For several small degrees we construct Cayley ... More

France new regions planning? Better order or more disorder ?Aug 10 2015This paper grounds the critique of the 'reduction of regions in a country' not only in its geographical and social context but also in its entropic space. The various recent plans leading to the reduction of the number of regions in metropolitan France ... More

Statistics of time delay and scattering correlation functions in chaotic systems II. Semiclassical ApproximationJul 20 2015We consider $S$-matrix correlation functions for a chaotic cavity having $M$ open channels, in the absence of time-reversal invariance. Relying on a semiclassical approximation, we compute the average over $E$ of the quantities ${\rm Tr}[S^\dag(E-\epsilon)S(E+\epsilon)]^n$, ... More

Dodgson polynomial identitiesOct 15 2018Dodgson polynomials appear in Schwinger parametric Feynman integrals and are closely related to the well known Kirchhoff (or first Symanzik) polynomial. In this article a new combinatorial interpretation and a generalisation of Dodgson polynomials are ... More

Extending the Particle ESBGK Method to Diatomic Molecules including Quantized Vibrational EnergiesSep 01 2018The particle-based ellipsoidal statistical Bhatnagar-Gross-Krook (ESBGK) model is extended to diatomic molecules and compared with the Direct Simulation Monte Carlo (DSMC) method. For this an efficient method is developed that optionally allows the handling ... More

Categories of contextsJul 02 2014Morphisms between (formal) contexts are certain pairs of maps, one between objects and one between attributes of the contexts in question. We study several classes of such morphisms and the connections between them. Among other things, we show that the ... More

ALLSAT compressed with wildcards: All k-models of a BDDMar 24 2017Mar 11 2019Given a Binary Decision Diagram of a Boolean function \phi in variables, all N many k-ones models of \phi can be enumerated in time polynomial in n and N. Although this only guarantees enumeraton one-by-one, in practise compression (using wildcards) is ... More

ALLSAT compressed with wildcards. Part 1: Converting CNF's to orthogonal DNF'sAug 30 2016Mar 17 2017For most branching algorithms in Boolean logic "branching" means "variable-wise branching". We present the apparently novel technique of clause-wise branching, which is used to solve the ALLSAT problem for arbitrary Boolean functions in CNF format. Specifically, ... More

Inclusion-exclusion enhanced by nerve stimulationSep 26 2013Aug 05 2018When evaluating the lengthy inclusion-exclusion expansion many of its terms may turn out to be zero, and hence should be discarded beforehand. Often this can be done. The main idea is that the index sets of nonzero terms constitute a set ideal (called ... More

Models in Boundary Quantum Field Theory Associated with Lattices and Loop Group ModelsAug 24 2011Aug 17 2012In this article we give new examples of models in boundary quantum field theory, i.e. local time-translation covariant nets of von Neumann algebras, using a recent construction of Longo and Witten, which uses a local conformal net A on the real line together ... More

Simplicial ideals, 2-linear ideals and arithmetical rankFeb 22 2007In the first part of this paper we study scrollers and linearly joined varieties. A particular class of varieties, of important interest in classical Geometry are Cohen--Macaulay varieties of minimal degree. They appear naturally studying the fiber cone ... More

Splitting of separatrices in the resonances of nearly integrable Hamiltonian Systems of one and a half degrees of freedomApr 12 2012In this paper we consider general nearly integrable analytic Hamiltonian systems of one and a half degrees of freedom which are a trigonometric polynomial in the angular state variable. In the resonances of these systems generically appear hyperbolic ... More

A remark on the constructibility of real root representations of quivers using universal extension functorsFeb 21 2008Jul 20 2008In this paper we consider the following question: Is it possible to construct all real root representations of a given quiver Q by using universal extension functors, starting with a real Schur representation? We give a concrete example answering this ... More

Exact uncertainty principle and quantization: implications for the gravitational fieldJan 10 2005The quantization of the gravitational field is discussed within the exact uncertainty approach. The method may be described as a Hamilton-Jacobi quantization of gravity. It differs from previous approaches that take the classical Hamilton-Jacobi equation ... More

Statistical Physics in MeteorologyJan 13 2004Various aspects of modern statistical physics and meteorology can be tied together. The historical importance of the University of Wroclaw in the field of meteorology is first pointed out. Next, some basic difference about time and space scales between ... More

Statistics of quantum transport in chaotic cavities with broken time-reversal symmetryMay 29 2008Aug 04 2008The statistical properties of quantum transport through a chaotic cavity are encoded in the traces $\T={\rm Tr}(tt^\dag)^n$, where $t$ is the transmission matrix. Within the Random Matrix Theory approach, these traces are random variables whose probability ... More

SiLC simulation status reportJan 29 2008The SiLC - Silicon for the Linear Collider - collaboration aims to develop silicon detector technology for tracking in the international linear collider experiments. The R & D programme involves a substantial effort in simulation of the response of detector ... More

UV Finite Field Theories on Noncommutative Spacetimes: the Quantum Wick Product and Time Independent Perturbation TheoryDec 12 2006In this article an energy correction is calculated in the time independent perturbation setup using a regularised ultraviolet finite Hamiltonian on the noncommutative Minkowski space. The correction to the energy is invariant under rotation and translation ... More

Econophysics of Stock and Foreign Currency Exchange MarketsJun 01 2006Econophysics is a science in its infancy, born about ten years ago at this time of writing, at the crossing roads of physics, mathematics, computing and of course economics and finance. It also covers human sciences, because all economics is ultimately ... More

Counting or producing all fixed cardinality transversalsJun 01 2011Nov 22 2012An algorith to count, or alternatively generate, all k-element transversals of a set system is presented and compared with three known methods. For special cases it works in output-linear time.

A novel type of branch and bound for maximum independent setJan 28 2009Feb 12 2010Several algorithms are presented. The standard algorithm generates all N anticliques of a graph with v vertices in time O(N^v2). It can e.g. be adapted to calculate the independence polynomial of G, to generate all maximum cardinality anticliques, or ... More

Revisiting the enumeration of all models of a Boolean 2-CNFAug 13 2012Feb 19 2016An O(Nn^2 + n^2) time algorithm to enumerate all N models of a Boolean 2-CNF with n variables is presented. Using don't care symbols the models are output in clusters rather than one by one. Computer experiments confirm the high efficiency of the method. ... More

Output polynomial enumeration of all fixed-cardinality ideals of a poset, respectively all fixed-cardinality subtrees of a treeAug 10 2012Apr 04 2013The N cardinality k ideals of any w-element poset (w, k variable) can be enumerated in time O(Nw^3). The corresponding bound for k-element subtrees of a w-element tree is O(Nw^5). An algorithm is described that by the use of wildcards displays all order ... More

Quiver representations of maximal rank type and an application to representations of a quiver with three verticesFeb 20 2008We introduce the notion of ''maximal rank type'' for representations of quivers, which requires certain collections of maps involved in the representation to be of maximal rank. We show that real root representations of quivers are of maximal rank type. ... More

Some basics of $su(1,1)$Jul 13 2004A basic introduction to the $su(1,1)$ algebra is presented, in which we discuss the relation with canonical transformations, the realization in terms of quantized radiation field modes and coherent states. Instead of going into details of these topics, ... More

The Structure of Cold Dark Matter Halos: Recent Insights from High Resolution SimulationsSep 23 2009We review results from recent high resolution cosmological structure formation simulations, namely the Via Lactea I & II and GHALO projects. These simulations study the formation of Milky Way sized objects within a cosmological framework. We discuss the ... More

A particle mechanism for the index of refractionSep 11 2007We propose to go away from the electromagnetic wave description of light and to explain through a purely corpuscular and neutral approach, the phenomenon of the slowing down of light in a transparent medium. The quantum predictions and ours are compared ... More

Energy-dependent correlations in the $S$-matrix of chaotic systemsJul 11 2016The $M$-dimensional unitary matrix $S(E)$, which describes scattering of waves is in general a strongly fluctuating function of the energy, specially for complex systems such as ballistic cavities whose geometry induces chaotic ray dynamics. Its statistical ... More

Detector Optimization for SiD using PFAFeb 18 2009A summary of the optimization of the SiD detector is given. To optimize its performance in terms of Particle Flow Algorithms (PFA), five basic detector parameters have been varied and the impact on the obtained energy resolution using Particle Flow Algorithms ... More

CALICE Si/W electromagnetic CalorimeterFeb 18 2009The CALICE prototype for a Si/W electromagnetic calorimeter has been tested in large scale test beams. Several million events with electrons and hadrons of different energies and impact angles have been recorded. The energy resolution has been measured ... More

On the span of lattice points in a parallelepipedJun 08 2015We find a good characterization for the following problem: Given an integral row vector $c=(c_{1}\ldots,c_{n})$ where each $c_{i}\in\{-1,0,1\}$ and a lattice $\Lambda\subset\mathbf{R}^{n}$ which contains the integer lattice $\mathbf{Z}^{n}$, do all lattice ... More

Compressed representation of learning spacesJul 22 2014Dec 16 2015Learning Spaces are certain set systems that are applied in the mathematical modeling of education. We propose a suitable compression (without loss of information) of such set systems to facilitate their logical and statistical analysis. Under certain ... More

A note on the automorphism group of the root lattice of the U-dual modular groupSep 30 2010We study the inclusion system of the quantum deformed 2 dimensional Yang- Mills root module to the graded root module of the U-dual modular group. The irreducible representation of the U-dual modular group is the quantum deformed black brane throat. We ... More

Finding or counting all shellings of a simplicial complexNov 28 2018The shellability status of previously investigated simplicial complexes with up to 24 facets is settled. In case of shellability the exact number of shellings is determined. Our algorithm merely relies on the facets, and not on additional information ... More

Computing the output distribution and selection probabilities of a stack filter from the DNF of its positive Boolean functionJan 14 2010Aug 27 2012Many nonlinear filters used in practise are stack filters. An algorithm is presented which calculates the output distribution of an arbitrary stack filter S from the disjunctive normal form (DNF) of its underlying positive Boolean function. The so called ... More

An efficient data structure for counting all linear extensions of a poset, calculating its jump number, and the likesApr 25 2017Achieving the goals in the title (and others) relies on a cardinality-wise scanning of the ideals of the poset. Specifically, the relevant numbers attached to the k+1 element ideals are inferred from the corresponding numbers of the k-element (order) ... More

Compressed representation of Learning SpacesJul 22 2014Dec 02 2016Learning Spaces are certain set systems that are applied in the mathematical modeling of education. We propose a suitable compression (without loss of information) of such set systems to facilitate their logical and statistical analysis. Under certain ... More

The asymptotic number of binary codes and binary matroidsAug 04 2004The asyptotic number of nonequivalent binary n-codes is determined. This is also the asymptotic number of nonisomorphic binary n-matroids. The connection to a result of Lefmann, Roedl, Phelps is explored. The latter states that almost all binary n-codes ... More

The Nash problem on arcs for surface singularitiesSep 22 2006Let $(X,O)$ be a germ of a normal surface singularity, $\pi : \tilde X\longrightarrow X$ be the minimal resolution of singularities and let $A=(a_{i,j})$ be the $n\times n$ symmetrical intersection matrix of the exceptional set of $\tilde X$. In an old ... More

Precision Electroweak MeasurementsNov 23 1996Recent electroweak precision measurements from e+e- and pbarp colliders are presented. Some emphasis is placed on the recent developments in the heavy flavor sector. The measurements are compared to predictions from the Standard Model of electroweak interactions. ... More

Electroweak Measurements from Hadron CollidersSep 08 1997A review of recent electroweak results from hadron colliders is given. Properties of the W and Z gauge bosons using final states containing electrons and muons based on large integrated luminosities are presented. The emphasis is placed on the measurement ... More

Super-sharp resonances in chaotic wave scatteringJan 16 2012Wave scattering in chaotic systems can be characterized by its spectrum of resonances, $z_n=E_n-i\frac{\Gamma_n}{2}$, where $E_n$ is related to the energy and $\Gamma_n$ is the decay rate or width of the resonance. If the corresponding ray dynamics is ... More

A Remark on CFT Realization of Quantum Doubles of Subfactors. Case Index < 4Jun 08 2015It is well-known that the quantum double $D(N\subset M)$ of a finite depth subfactor $N\subset M$, or equivalently the Drinfeld center of the even part fusion category, is a unitary modular tensor category. Thus should arise in conformal field theory. ... More

Statistics of time delay in quantum chaotic transportAug 07 2014Jul 22 2015We study the statistical properties of the time delay matrix $Q$ in the context of quantum transport through a chaotic cavity, in the absence of time-reversal invariance. First, we approach the problem from the point of view of random matrix theory, and ... More

Pre-big bang scenario and the WZW modelJan 10 2014Jun 09 2015Extensive studies of pre-big bang scenarios for Bianchi-I type universe have been made, at various approximation levels. Knowing the solution of the equations for the post-big bang universe, the symmetries of the equations (time reversal and scale dual ... More

Resonances in open quantum mapsNov 30 2012We review recent studies about the resonance spectrum of quantum scattering systems, in the semiclassical limit and assuming chaotic classical dynamics. Stationary quantum properties are related to fractal structures in the classical phase space. We focus ... More

A remark about the anomalies of cyclic holomorphic permutation orbifoldsDec 31 2018Using a result of Longo and Xu, we show that the anomaly arising from a cyclic permutation orbifold of order 3 of a holomorphic conformal net $\mathcal A$ with central charge $c=8k$ depends on the "gravitational anomaly" $k\pmod 3$. In particular, the ... More

Hierarchical Bipartite Graph Convolution NetworksNov 17 2018Dec 13 2018Recently, graph neural networks have been adopted in a wide variety of applications ranging from relational representations to modeling irregular data domains such as point clouds and social graphs. However, the space of graph neural network architectures ... More

Generalized Orbifold Construction for Conformal NetsJul 31 2016Let $\mathcal{B}$ be a conformal net. We give the notion of a proper action of a finite hypergroup acting by vacuum preserving unital completely positive (so-called stochastic) maps, which generalizes the proper actions of finite groups. Taking fixed ... More