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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 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

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 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

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

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

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

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

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

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

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

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

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

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

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

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

Shorting in Speculative MarketsMay 16 2017Jul 29 2019We propose a continuous-time model of trading with heterogeneous beliefs. Risk-neutral agents face quadratic costs-of-carry on positions and thus their marginal valuations decrease with the size of their position, as it would be the case for risk-averse ... 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

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

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

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

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

Convergence to the Mean Field Game Limit: A Case StudyJun 03 2018May 28 2019We 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

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

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

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

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

Proof Tree Preserving InterpolationMay 15 2017Craig interpolation in SMT is difficult because, e. g., theory combination and integer cuts introduce mixed literals, i. e., literals containing local symbols from both input formulae. In this paper, we present a scheme to compute Craig interpolants in ... 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 properties of Dirichlet forms on discrete spacesJan 17 2012Sep 02 2016We provide an introduction to Dirichlet forms on discrete spaces and study their global properties such as recurrence, stochastic completeness and regularity of the Neumann form. In this setting we compare the notion of a recurrent Dirichlet form and ... More

Exponential Decay and Ionization Thresholds in Non-Relativistic Quantum ElectrodynamicsJun 17 2002Jun 27 2003Spatial localization of the electrons of an atom or molecule is studied in models of non-relativistic matter coupled to quantized radiation. We give two definitions of the ionization threshold. One in terms of spectral data of cluster Hamiltonians, and ... 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

On the $S_2$-fication of Some Toric VarietiesSep 15 2006Some results on the Cohen-Macaulayness of the canonical module. We study the $S_2$-fication of rings which are quotients by lattices ideals. Given a simplicial lattice ideal of codimension two $I,$ its Macaulayfication is given explicitly from a system ... 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

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

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

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

Low growth equational complexityJul 25 2016The equational complexity function $\beta_\mathscr{V}:\mathbb{N}\to\mathbb{N}$ of an equational class of algebras $\mathscr{V}$ bounds the size of equation required to determine membership of $n$-element algebras in $\mathscr{V}$. Known examples of finitely ... 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

Absence of eigenvalues of non-selfadjoint Schrödinger operators on the boundary of their numerical rangeAug 05 2011Jun 12 2012We use a classical result of Hildebrandt to establish simple conditions for the absence of eigenvalues of non-selfadjoint discrete and continuous Schr\"odinger operators on the boundary of their numerical range.

Gompertz and Verhulst frameworks for growth and decay descriptionAug 25 2011Feb 03 2013Verhulst logistic curve either grows OR decays, depending on the {\it growth rate} parameter value. A similar situation is found in the Gompertz law about human mortality. However, growth can neither be infinite nor reach a finite steady state at an infinite ... 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

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

Segre embeddings, Hilbert series and Newcomb's problemJun 28 2013Jan 16 2014Monomial ideals and toric rings are closely related. By consider a Grobner basis we can always associated to any ideal $I$ in a polynomial ring a monomial ideal ${\rm in}_\prec I$, in some special situations the monomial ideal ${\rm in}_\prec I$ is square ... 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

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

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

Semiclassical approach to universality in quantum chaotic transportNov 22 2011May 08 2012The statistics of quantum transport through chaotic cavities with two leads is encoded in transport moments $M_m={\rm Tr}[(t^\dag t)^m]$, where $t$ is the transmission matrix, which have a known universal expression for systems without time-reversal symmetry. ... More

Variation of discrete spectra for non-selfadjoint perturbations of selfadjoint operatorsFeb 06 2012Apr 08 2013Let B=A+K where A is a bounded selfadjoint operator and K is an element of the von Neumann-Schatten ideal S_p with p>1. Let {\lambda_n} denote an enumeration of the discrete spectrum of B. We show that $\sum_n \dist(\lambda_n, \sigma(A))^p$ is bounded ... 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

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

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

Non-relativistic Matter and Quantized RadiationOct 12 2004This is a didactic review of spectral and dynamical properties of atoms and molecules at energies below the ionization threshold, the focus being on recent work in which the author was involved. As far as possible, the results are described using a simple ... 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

Tight embedding of modular lattices into partition lattices: progress and programApr 12 2017Jun 25 2018Representing lattices L by equivalence relations amounts to embed them into the lattice Part(V) of all partitions of a set V, and has a long history. Here we are concerned with MODULAR lattices L and aim for sets V as small as possible, i.e. |V| = d(L)+1 ... 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

Cayley graphs of diameter two with order greater than 0.684 of the Moore bound for any degreeNov 11 2015May 22 2016It is known that the number of vertices of a graph of diameter two cannot exceed $d^2+1$. In this contribution we give a new lower bound for orders of Cayley graphs of diameter two in the form $C(d,2)>0.684d^2$ valid for all degrees $d\geq 360756$. The ... More

Coherent measures of the impact of co-authors in peer review journals and in proceedings publicationsJun 17 2015This paper focuses on the coauthor effect in different types of publications, usually not equally respected in measuring research impact. {\it A priori} unexpected relationships are found between the total coauthor core value, $m_a$, of a leading investigator ... 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

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

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

Perturbation determinants in Banach spaces - with an application to eigenvalue estimates for perturbed operatorsJul 24 2015Oct 29 2015In the first part of this paper we provide a self-contained introduction to (regularized) perturbation determinants for operators in Banach spaces. In the second part, we use these determinants to derive new bounds on the discrete eigenvalues of compactly ... More

Assessing the true role of coauthors in the h-index measure of an author scientific impactJan 10 2015A method based on the classical principal component analysis leads to demonstrate that the role of co-authors should give a h-index measure to a group leader higher than usually accepted. The method rather easily gives what is usually searched for, i.e. ... More

A biased view of a few possible components when reflecting on the present decade financial and economic crisisNov 29 2014Is the present economic and financial crisis similar to some previous one? It would be so nice to prove that universality laws exist for predicting such rare events under a minimum set of realistic hypotheses. First, I briefly recall whether patterns, ... More