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On the Power of Entangled Quantum ProversDec 08 2006We show that the value of a general two-prover quantum game cannot be computed by a semi-definite program ofvpolynomial size (unless P=NP), a method that has been successful in more restricted quantum games. More precisely, we show that proof of membership ... More

Parallel Repetition of Entangled GamesDec 21 2010May 11 2011We consider one-round games between a classical referee and two players. One of the main questions in this area is the parallel repetition question: Is there a way to decrease the maximum winning probability of a game without increasing the number of ... More

Robust self-testing of many-qubit statesOct 12 2016We introduce a simple two-player test which certifies that the players apply tensor products of Pauli $\sigma_X$ and $\sigma_Z$ observables on the tensor product of $n$ EPR pairs. The test has constant robustness: any strategy achieving success probability ... More

A multiprover interactive proof system for the local Hamiltonian problemAug 31 2014We give a quantum interactive proof system for the local Hamiltonian problem on n qubits in which (i) the verifier has a single round of interaction with five entangled provers, (ii) the verifier sends a classical message on O(log n) bits to each prover, ... More

Entanglement of approximate quantum strategies in XOR gamesSep 06 2016We show that for any $\varepsilon>0$ there is an XOR game $G=G(\varepsilon)$ with $\Theta(\varepsilon^{-1/5})$ inputs for one player and $\Theta(\varepsilon^{-2/5})$ inputs for the other player such that $\Omega(\varepsilon^{-1/5})$ ebits are required ... More

Privacy Amplification Against Active Quantum AdversariesAug 22 2016Privacy amplification is the task by which two cooperating parties transform a shared weak secret, about which an eavesdropper may have side information, into a uniformly random string uncorrelated from the eavesdropper. Privacy amplification against ... More

Does ignorance of the whole imply ignorance of the parts? - Large violations of non-contextuality in quantum theoryNov 30 2010May 04 2011A central question in our understanding of the physical world is how our knowledge of the whole relates to our knowledge of the individual parts. One aspect of this question is the following: to what extent does ignorance about a whole preclude knowledge ... More

More non-locality with less entanglementNov 23 2010Dec 08 2010We provide an explicit example of a Bell inequality with 3 settings and 2 outcomes per site for which the largest violation is not obtained by the maximally entangled state, even if its dimension is allowed to be arbitrarily large. This complements recent ... More

Classical zero-knowledge arguments for quantum computationsFeb 14 2019Apr 09 2019We show that every language in BQP admits a classical-verifier, quantum-prover zero-knowledge argument system which is sound against quantum polynomial-time provers and zero-knowledge for classical (and quantum) polynomial-time verifiers. The protocol ... More

Quantum ProofsOct 05 2016Quantum information and computation provide a fascinating twist on the notion of proofs in computational complexity theory. For instance, one may consider a quantum computational analogue of the complexity class \class{NP}, known as QMA, in which a quantum ... More

Fully device independent quantum key distributionOct 05 2012Nov 25 2012The laws of quantum mechanics allow unconditionally secure key distribution protocols. Nevertheless, security proofs of traditional quantum key distribution (QKD) protocols rely on a crucial assumption, the trustworthiness of the quantum devices used ... More

Unbounded entanglement in nonlocal gamesFeb 17 2014Aug 23 2015Quantum entanglement is known to provide a strong advantage in many two-party distributed tasks. We investigate the question of how much entanglement is needed to reach optimal performance. For the first time we show that there exists a purely classical ... More

Near-optimal extractors against quantum storageNov 24 2009Mar 30 2010We show that Trevisan's extractor and its variants \cite{T99,RRV99} are secure against bounded quantum storage adversaries. One instantiation gives the first such extractor to achieve an output length $\Theta(K-b)$, where $K$ is the source's entropy and ... More

A Moment Majorization principle for random matrix ensembles with applications to hardness of the noncommutative Grothendieck problemMar 17 2016We prove a moment majorization principle for matrix-valued functions with domain $\{-1,1\}^{m}$, $m\in\mathbb{N}$. The principle is an inequality between higher-order moments of a non-commutative multilinear polynomial with different random matrix ensemble ... More

Survey on Nonlocal Games and Operator Space TheoryDec 01 2015This review article is concerned with a recently uncovered connection between operator spaces, a noncommutative extension of Banach spaces, and quantum nonlocality, a striking phenomenon which underlies many of the applications of quantum mechanics to ... More

Classical zero-knowledge arguments for quantum computationsFeb 14 2019We show that every language in BQP admits a classical-verifier, quantum-prover zero-knowledge argument system which is sound against quantum polynomial-time provers and zero-knowledge for classical (and quantum) polynomial-time verifiers. The protocol ... More

Computationally-secure and composable remote state preparationApr 12 2019We introduce a protocol between a classical polynomial-time verifier and a quantum polynomial-time prover that allows the verifier to securely delegate to the prover the preparation of certain single-qubit quantum states. The protocol realizes the following ... More

Interactive proofs with approximately commuting proversOct 01 2015The class $\MIP^*$ of promise problems that can be decided through an interactive proof system with multiple entangled provers provides a complexity-theoretic framework for the exploration of the nonlocal properties of entanglement. Little is known about ... More

Constant-Soundness Interactive Proofs for Local HamiltoniansDec 07 2015$ \newcommand{\Xlin}{\mathcal{X}} \newcommand{\Zlin}{\mathcal{Z}} \newcommand{\C}{\mathbb{C}} $We give a quantum multiprover interactive proof system for the local Hamiltonian problem in which there is a constant number of provers, questions are classical ... More

A simple proof of Renner's exponential de Finetti theoremAug 17 2016Aug 20 2016We give a simple proof of the exponential de Finetti theorem due to Renner. Like Renner's proof, ours combines the post-selection de Finetti theorem, the Gentle Measurement lemma, and the Chernoff bound, but avoids virtually all calculations, including ... More

A multi-prover interactive proof for NEXP sound against entangled proversJul 03 2012Sep 26 2012We prove a strong limitation on the ability of entangled provers to collude in a multiplayer game. Our main result is the first nontrivial lower bound on the class MIP* of languages having multi-prover interactive proofs with entangled provers; namely ... More

Bounds on Dimension Reduction in the Nuclear NormJan 28 2019$ \newcommand{\schs}{\scriptstyle{\mathsf{S}}_1} $For all $n \ge 1$, we give an explicit construction of $m \times m$ matrices $A_1,\ldots,A_n$ with $m = 2^{\lfloor n/2 \rfloor}$ such that for any $d$ and $d \times d$ matrices $A'_1,\ldots,A'_n$ that ... More

Certifiable Quantum Dice - Or, testable exponential randomness expansionNov 25 2011We introduce a protocol through which a pair of quantum mechanical devices may be used to generate n bits of true randomness from a seed of O(log n) uniform bits. The bits generated are certifiably random based only on a simple statistical test that can ... More

Simple and tight device-independent security proofsJul 06 2016Proving security of device-independent (DI) cryptographic protocols has been regarded to be a complex and tedious task. In this work we show that a newly developed tool, the "entropy accumulation theorem" of Dupuis et al., can be effectively applied to ... More

A parallel repetition theorem for entangled projection gamesOct 15 2013Mar 02 2015We study the behavior of the entangled value of two-player one-round projection games under parallel repetition. We show that for any projection game $G$ of entangled value 1-eps < 1, the value of the $k$-fold repetition of G goes to zero as O((1-eps^c)^k), ... More

A simple proof of the detectability lemma and spectral gap amplificationFeb 03 2016May 23 2016The detectability lemma is a useful tool for probing the structure of gapped ground states of frustration-free Hamiltonians of lattice spin models. The lemma provides an estimate on the error incurred by approximating the ground space projector with a ... More

Trading locality for time: certifiable randomness from low-depth circuitsOct 09 2018Jan 11 2019The generation of certifiable randomness is the most fundamental information-theoretic task that meaningfully separates quantum devices from their classical counterparts. We propose a protocol for exponential certified randomness expansion using a single ... More

Optimal counterfeiting attacks and generalizations for Wiesner's quantum moneyFeb 17 2012We present an analysis of Wiesner's quantum money scheme, as well as some natural generalizations of it, based on semidefinite programming. For Wiesner's original scheme, it is determined that the optimal probability for a counterfeiter to create two ... More

Parallel repetition via fortification: analytic view and the quantum caseMar 17 2016In a recent work, Moshkovitz [FOCS '14] presented a transformation on two-player games called "fortification", and gave an elementary proof of an (exponential decay) parallel repetition theorem for fortified two-player projection games. In this paper, ... More

Anchoring games for parallel repetitionSep 24 2015Two major open problems regarding the parallel repetition of games are whether an analogue of Raz's parallel-repetition theorem holds for (a) games with more than two players, and (b) games with quantum players using entanglement. We make progress on ... More

The Quantum PCP ConjectureSep 28 2013The classical PCP theorem is arguably the most important achievement of classical complexity theory in the past quarter century. In recent years, researchers in quantum computational complexity have tried to identify approaches and develop tools that ... More

QCMA hardness of ground space connectivity for commuting HamiltoniansOct 12 2016In this work we consider the ground space connectivity problem for commuting local Hamiltonians. The ground space connectivity problem asks whether it is possible to go from one (efficiently preparable) state to another by applying a polynomial length ... More

A polynomial-time algorithm for the ground state of 1D gapped local HamiltoniansJul 19 2013Computing ground states of local Hamiltonians is a fundamental problem in condensed matter physics. We give the first randomized polynomial-time algorithm for finding ground states of gapped one-dimensional Hamiltonians: it outputs an (inverse-polynomial) ... More

Non-signalling parallel repetition using de Finetti reductionsNov 06 2014In the context of multiplayer games, the parallel repetition problem can be phrased as follows: given a game $G$ with optimal winning probability $1-\alpha$ and its repeated version $G^n$ (in which $n$ games are played together, in parallel), can the ... More

Robust Randomness Amplifiers: Upper and Lower BoundsMay 28 2013Jun 23 2013A recent sequence of works, initially motivated by the study of the nonlocal properties of entanglement, demonstrate that a source of information-theoretically certified randomness can be constructed based only on two simple assumptions: the prior existence ... More

Efficient rounding for the noncommutative Grothendieck inequalityOct 29 2012The classical Grothendieck inequality has applications to the design of approximation algorithms for NP-hard optimization problems. We show that an algorithmic interpretation may also be given for a noncommutative generalization of the Grothendieck inequality ... More

A three-player coherent state embezzlement gameFeb 14 2018We introduce a three-player nonlocal game, with a finite number of classical questions and answers, such that the optimal success probability of $1$ in the game can only be achieved in the limit of strategies using arbitrarily high-dimensional entangled ... More

Rigorous RG algorithms and area laws for low energy eigenstates in 1DFeb 29 2016One of the central challenges in the study of quantum many-body systems is the complexity of simulating them on a classical computer. A recent advance of Landau et al. gave a polynomial time algorithm to actually compute a succinct classical description ... More

Using Entanglement in Quantum Multi-Prover Interactive ProofsNov 23 2007The central question in quantum multi-prover interactive proof systems is whether or not entanglement shared between provers affects the verification power of the proof system. We study for the first time positive aspects of prior entanglement and show ... More

A Quantum-Proof Non-Malleable Extractor, With Application to Privacy Amplification against Active Quantum AdversariesOct 02 2017Feb 14 2018In privacy amplification, two mutually trusted parties aim to amplify the secrecy of an initial shared secret $X$ in order to establish a shared private key $K$ by exchanging messages over an insecure communication channel. If the channel is authenticated ... More

Multiplayer XOR games and quantum communication complexity with clique-wise entanglementNov 20 2009XOR games are a simple computational model with connections to many areas of complexity theory. Perhaps the earliest use of XOR games was in the study of quantum correlations. XOR games also have an interesting connection to Grothendieck's inequality, ... More

Quantum proof systems for iterated exponential time, and beyondMay 30 2018We show that any language in nondeterministic time $\exp(\exp(\cdots \exp(n)))$, where the number of iterated exponentials is an arbitrary function $R(n)$, can be decided by a multiprover interactive proof system with a classical polynomial-time verifier ... More

Quantum-Proof Extractors: Optimal up to Constant FactorsMay 13 2016Aug 01 2016We give the first construction of a family of quantum-proof extractors that has optimal seed length dependence $O(\log(n/\varepsilon))$ on the input length $n$ and error $\varepsilon$. Our extractors support any min-entropy $k=\Omega(\log{n} + \log^{1+\alpha}(1/\varepsilon))$ ... More

Test for a large amount of entanglement, using few measurementsOct 03 2016Bell-inequality violations establish that two systems share some quantum entanglement. We give a simple test to certify that two systems share an asymptotically large amount of entanglement, n EPR states. The test is efficient: unlike earlier tests that ... More

Trevisan's extractor in the presence of quantum side informationDec 30 2009Jun 18 2012Randomness extraction involves the processing of purely classical information and is therefore usually studied in the framework of classical probability theory. However, such a classical treatment is generally too restrictive for applications, where side ... More

Entangled games are hard to approximateApr 23 2007Nov 21 2007We establish the first hardness results for the problem of computing the value of one-round games played by a verifier and a team of provers who can share quantum entanglement. In particular, we show that it is NP-hard to approximate within an inverse ... More

Better Gap-Hamming Lower Bounds via Better Round EliminationDec 30 2009Gap Hamming Distance is a well-studied problem in communication complexity, in which Alice and Bob have to decide whether the Hamming distance between their respective n-bit inputs is less than n/2-sqrt(n) or greater than n/2+sqrt(n). We show that every ... More

Hauteur asymptotique des points de HeegnerNov 17 2005The asymptotic behaviour of the Neron-Tate height of Heegner points on a rational elliptic curve attached to an arithmetically normalized new cusp form f of weight 2, level N and trivial character is studied in this paper. By Gross-Zagier formula, this ... More

Spectral Correlations in the Crossover Transition from a Superposition of Harmonic Oscillators to the Gaussian Unitary EnsembleJul 20 1998We compute the spectral correlation functions for the transition from a harmonic oscillator towards the Gaussian Unitary Ensemble (GUE). We use a variant of the supersymmetry method to obtain analytical results in a fast and elegant way. In contrast to ... More

Thermodynamic formalism for transport coefficients with an application to the shear modulus and shear viscosityDec 07 2016We discuss Onsager's thermodynamic formalism for transport coefficients and apply it to the calculation of the shear modulus and shear viscosity of a monodisperse system of repulsive particles. We focus on the concept of extensive "distance" and intensive ... More

On the quantifier-free dynamic complexity of ReachabilityJun 13 2013Jan 28 2015The dynamic complexity of the reachability query is studied in the dynamic complexity framework of Patnaik and Immerman, restricted to quantifier-free update formulas. It is shown that, with this restriction, the reachability query cannot be dynamically ... More

Sélection de la structure d'un perceptron multicouches pour la réduction dun modèle de simulation d'une scierieDec 05 2008Simulation is often used to evaluate the relevance of a Directing Program of Production (PDP) or to evaluate its impact on detailed sc\'enarii of scheduling. Within this framework, we propose to reduce the complexity of a model of simulation by exploiting ... More

Infinite reduced words and the Tits boundary of a Coxeter groupJan 05 2013Sep 18 2014Let (W,S) be a finite rank Coxeter system with W infinite. We prove that the limit weak order on the blocks of infinite reduced words of W is encoded by the topology of the Tits boundary of the Davis complex X of W. We consider many special cases, including ... More

An optimization principle for the computation of MHD equilibria in the solar coronaDec 21 2006AIMS: We develop an optimization principle for computing stationary MHD equilibria. METHODS: Our code for the self-consistent computation of the coronal magnetic fields and the coronal plasma uses non-force-free MHD equilibria. Previous versions of the ... More

Probabilistic Reasoning about Actions in Nonmonotonic Causal TheoriesOct 19 2012We present the language {m P}{cal C}+ for probabilistic reasoning about actions, which is a generalization of the action language {cal C}+ that allows to deal with probabilistic as well as nondeterministic effects of actions. We define a formal semantics ... More

Two-Variable Logic with Two Order RelationsOct 07 2011Mar 03 2012It is shown that the finite satisfiability problem for two-variable logic over structures with one total preorder relation, its induced successor relation, one linear order relation and some further unary relations is EXPSPACE-complete. Actually, EXPSPACE-completeness ... More

Elagage d'un perceptron multicouches : utilisation de l'analyse de la variance de la sensibilité des paramètresDec 04 2008The stucture determination of a neural network for the modelisation of a system remain the core of the problem. Within this framework, we propose a pruning algorithm of the network based on the use of the analysis of the sensitivity of the variance of ... More

On the boundedness of an iteration involving points on the hypersphereJan 11 2010Oct 05 2010For a finite set of points $X$ on the unit hypersphere in $\mathbb{R}^d$ we consider the iteration $u_{i+1}=u_i+\chi_i$, where $\chi_i$ is the point of $X$ farthest from $u_i$. Restricting to the case where the origin is contained in the convex hull of ... More

Nef reduction and anticanonical bundlesOct 31 2003We investigate the structure of smooth projective 3-folds X with -K_X nef and K_X^3=0.

Causes and Explanations in the Structural-Model Approach: Tractable CasesDec 12 2012In this paper, we continue our research on the algorithmic aspects of Halpern and Pearl's causes and explanations in the structural-model approach. To this end, we present new characterizations of weak causes for certain classes of causal models, which ... More

Dynamic Conjunctive QueriesApr 05 2017The article investigates classes of queries maintainable by conjunctive queries (CQs) and their extensions and restrictions in the dynamic complexity framework of Patnaik and Immerman. Starting from the basic language of quantifier-free conjunctions of ... More

How deals with discrete data for the reduction of simulation models using neural networkJun 10 2009Simulation is useful for the evaluation of a Master Production/distribution Schedule (MPS). Also, the goal of this paper is the study of the design of a simulation model by reducing its complexity. According to theory of constraints, we want to build ... More

kdecopula: An R Package for the Kernel Estimation of Copula DensitiesMar 14 2016May 14 2016We describe the R package kdecopula, which provides fast implementations of various kernel estimators for the copula density. Due to its several plotting options it is particularly useful for the exploratory analysis of dependence structures. It can be ... More

Geometric compactification of moduli spaces of half-translation structures on surfacesFeb 03 2016In this paper, we give an equivariant compactification of the space PFlat(S) of homothety classes of half-translation structures on a compact, connected, orientable surface S. We introduce the space PMix(S) of homothety classes of mixed structures on ... More

Matrix product purifications for canonical ensembles and quantum number distributionsJul 06 2016Matrix product purifications (MPP) are a very efficient tool for the simulation of strongly correlated quantum many-body systems at finite temperatures. When a system features symmetries, these can be used to reduce computation costs substantially. It ... More

Compressed Sensing with Nonlinear Observations and Related Nonlinear Optimisation ProblemsMay 08 2012Non-convex constraints have recently proven a valuable tool in many optimisation problems. In particular sparsity constraints have had a significant impact on sampling theory, where they are used in Compressed Sensing and allow structured signals to be ... More

Does the wavefunction of the universe exist?Apr 07 2004Jun 02 2004The overwhelming majority of scientists still takes it for granted that classical mechanics (ClM) is nothing but a limiting case of quantum mechanics (QM). Although some physicists restrict this belief to a generalized QM as represented, e. g., by the ... More

Asymptotics of robust utility maximizationMar 06 2012For a stochastic factor model we maximize the long-term growth rate of robust expected power utility with parameter $\lambda\in(0,1)$. Using duality methods the problem is reformulated as an infinite time horizon, risk-sensitive control problem. Our results ... More

On the concept of (homo)morphism : a key notion in the learning of abstract algebraMar 28 2013This article is dedicated to the investigation of difficulties involved in the understanding of the homomorphism concept. It doesn't restrict to group-theory but on the contrary raises the issue of developing teaching strategies aiming at gaining access ... More

Hessian corrections to the Metropolis Adjusted Langevin AlgorithmJul 22 2015A natural method for the introduction of second-order derivatives of the log likelihood into MCMC algorithms is introduced, based on Taylor expansion of the Langevin equation followed by exact solution of the truncated system.

Twisted filtrations of Soergel bimodules and linear Rouquier complexesJan 03 2016We consider twisted standard filtrations of Soergel bimodules associated to arbitrary Coxeter groups and show that the graded multiplicities in these filtrations can be interpreted as structure constants in the Hecke algebra. This corresponds to the positivity ... More

Yangian Superalgebras in Conformal Field TheoryNov 30 2010Dec 07 2010Quantum Yangian symmetry in several sigma models with supergroup or supercoset as target is established. Starting with a two-dimensional conformal field theory that has current symmetry of a Lie superalgebra with vanishing Killing form we construct non-local ... More

Precise evaluation of thermal response functions by optimized density matrix renormalization group schemesJan 10 2013Jul 17 2013This paper provides a study and discussion of earlier as well as novel more efficient schemes for the precise evaluation of finite-temperature response functions of strongly correlated quantum systems in the framework of the time-dependent density matrix ... More

Numerical study of a three-dimensional generalized stadium billiardSep 17 1999May 04 2000We study a generalized three-dimensional stadium billiard and present strong numerical evidence that this system is completely chaotic. In this convex billiard chaos is generated by the defocusing mechanism. The construction of this billiard uses cylindrical ... More

Lyapunov exponents and Kolmogorov-Sinai entropy for a high-dimensional convex billiardSep 06 1999We compute the Lyapunov exponents and the Kolmogorov-Sinai (KS) entropy for a self-bound N-body system that is realized as a convex billiard. This system exhibits truly high-dimensional chaos, and 2N-4 Lyapunov exponents are found to be positive. The ... More

Universal solutions for interacting bosons in one-dimensional harmonic trapsAug 28 2001We consider systems of interacting bosons confined to one-dimensional harmonic traps. In the limit of perturbatively weak two-body interactions the system exhibits several universal states that are exact solutions for a large class of two-body interactions. ... More

Target-Superspace in 2d Dilatonic SupergravityJun 29 1999The N=1 supersymmetric version of generalized 2d dilaton gravity can be cast into the form of a Poisson Sigma Model, where the target space and its Poisson bracket are graded. The target space consists of a 1+1 superspace and the dilaton, which is the ... More

High energy scattering amplitudes in matrix string theoryMay 12 1999Mar 15 2000High energy fixed angle scattering is studied in matrix string theory. The saddle point world sheet configurations, which give the dominant contributions to the string theory amplitude, are taken as classical backgrounds in matrix string theory. A one ... More

Towards a Mori theory on compact Kaehler threefolds,IIFeb 04 1998We prove the existence of a Mori contraction on a compact Kaehler threefold whose canonical bundle is (analytically) not nef if the threefold can be approximated by projective threefolds or if the algebraic dimension is 2.

Non-Central Multivariate Chi-Square and Gamma DistributionsApr 23 2016Jul 05 2016A (p-1)-variate integral representation is given for the cumulative distribution function of the general p-variate non-central gamma distribution with a non-centrality matrix of any admissible rank. The real part of products of well known analytical functions ... More

Algebraic K-Theory of infinity-OperadsMar 09 2013Sep 03 2014The theory of dendroidal sets has been developed to serve as a combinatorial model for homotopy coherent operads by Moerdijk and Weiss. An infinity-operad is a dendroidal set D satisfying certain lifting conditions. In this paper we give a definition ... More

A multidimensional continued fraction generalization of Stern's diatomic sequenceJun 28 2012Sep 10 2013Continued fractions are linked to Stern's diatomic sequence 0,1,1,2,1,3,2,3,1,4,... (given by the recursion relation a_2n=a_n and a_{2n+1} = a_n + a_{n+1}, where a_0=0 and a_1=1), which has long been known. Using a particular multidimensional continued ... More

Measuring Information TransferJan 19 2000An information theoretic measure is derived that quantifies the statistical coherence between systems evolving in time. The standard time delayed mutual information fails to distinguish information that is actually exchanged from shared information due ... More

Predicting trend reversals using market instantaneous stateOct 30 2013Mar 03 2014Collective behaviours taking place in financial markets reveal strongly correlated states especially during a crisis period. A natural hypothesis is that trend reversals are also driven by mutual influences between the different stock exchanges. Using ... More

Effective Theory for Heavy QuarksJun 11 1996In this series of lectures the basic ideas of the $1/m_Q$ expansion in QCD ($m_Q$ is the mass of a heavy quark) are outlined. Applications to exclusive and inclusive decays are given.

Review of Heavy Quark Effective TheoryNov 25 1996A short review of a few selected topics in Heavy Quark Effective Theory is given. Applications to exclusive decays are discussed.

Weak Decays of Heavy-Quark SystemsMay 23 1994The recent theoretical progress in the description of semileptonic decays in the framework of the heavy mass expansion is summarized. Both inclusive and exclusive decays are considered.

An arbitrarily distortable Banach spaceApr 03 1991In this work we construct a ``Tsirelson like Banach space'' which is arbitrarily distortable.

The Grothendieck-Teichmüller group action on differential forms and formality morphism of chainsAug 28 2013Jan 14 2014It is known that one can associate a Kontsevich-type formality morphism to every Drinfeld associator. We show that this morphism may be extended to a Kontsevich-Shoikhet formality morphism of cochains and chains, by describing the action of the Grothendieck-Teichm\"uller ... More

Stable cohomology of polyvector fieldsOct 17 2011Dec 03 2014We show that the stable cohomology of the algebraic polyvector fields on $\mathbb{R}^n$, with values in the adjoint representation is the symmetric product space on the cohomology of M. Kontsevich's graph complex, up to some known classes.

CP-stability and the local lifting propertyJul 14 2015The purpose of this note is to discuss the local lifting property in terms of an equivalent approximation-type property, CP-stability, which was formulated by the author and Isaac Goldbring for the purposes of studying the continuous model theory of C$^*$-algebras ... More

Three-dimensional analytical magnetohydrostatic equilibria of rigidly rotating magnetospheres in cylindrical geometryJun 04 2009We present three-dimensional solutions of the magnetohydrostatic equations in the co-rotating frame of reference outside a magnetized rigidly rotating cylinder. We make no symmetry assumption for the magnetic field, but to be able to make analytical progress ... More

Particle Correlations at LEPJan 30 2002Particle correlations are extensively studied to obtain information about the dynamics of hadron production. From 1989 to 2000 the four LEP collaborations recorded more than 16 million hadronic Z0 decays and several thousand W+W- events. In Z0 decays, ... More

Anthropomorphic Quantum Darwinism as an explanation for ClassicalityJun 15 2009According to the so-called ``Quantum Darwinist'' approach, the emergence of ``classical islands'' from a quantum background is assumed to obey a (selection) principle of maximal information. We illustrate this idea by considering the coupling of two particles ... More

Comment on ``A local hidden variable model of quantum correlations exploiting the detection loophole''Jul 20 1999We study in this short comment the analogies and the differences that exist between several local hidden variable models.

A new expression for mutually unbiased bases in prime power dimensionsSep 15 2004Nov 26 2004Mutually unbiased bases generalize the X, Y and Z qubit bases. They possess numerous applications in quantum information science. It is well-known that in prime power dimensions N=p^m (with p prime and m a positive integer) there exists a maximal set ... More

Mapping the vacuum structure of gauged maximal supergravities: an application of high-performance symbolic algebraMay 20 2003The analysis of the extremal structure of the scalar potentials of gauged maximally extended supergravity models in five, four, and three dimensions, and hence the determination of possible vacuum states of these models is a computationally challenging ... More

Introducing LambdaTensor1.0 - A package for explicit symbolic and numeric Lie algebra and Lie group calculationsAug 29 2002Mar 26 2003Due to the occurrence of large exceptional Lie groups in supergravity, calculations involving explicit Lie algebra and Lie group element manipulations easily become very complicated and hence also error-prone if done by hand. Research on the extremal ... More

Some stationary points of gauged N=16 D=3 supergravityJan 05 2002Five nontrivial stationary points are found for maximal gauged N=16 supergravity in three dimensions with gauge group $SO(8)\times SO(8)$ by restricting the potential to a submanifold of the space of $SU(3)\subset(SO(8)\times SO(8))_{\rm diag}$ singlets. ... More

The many vacua of gauged extended supergravitiesNov 12 2008A novel method is presented which employs advanced numerical techniques used in the engineering sciences to find and study the properties of nontrivial vacua of gauged extended supergravity models. While this method only produces approximate numerical ... More