Properties of Intercalated 2H-NbSe2, 4Hb-TaS2 and 1T-TaS2

The layered compounds 2H-NbSe, 24Hb-TaS, 2and 1T-TaS2 have been intercalated with organic molecules; and the resulting crystal structure, heat capacity, conductivity, and superconductivity have been studied. The coordination in the disulfide layers was found to be unchanged in the product phase. Resistance minima appear and the superconducting transition temperature is reduced in the NbSe2 complex. Conversely, superconductivity is induced in the 4Hb-TaS2 complex. Corresponding evidence of a large change of the density of states, negative for 2H-NbSe2 and positive for 4Hb-TaS2, was also observed upon intercalation. The transport properties of all the intercalation complexes show a pronounced dependence upon the coordination of the transition metal

Monoids, Embedding Functors and Quantum Groups

We show that the left regular representation \pi_l of a discrete quantum group (A,\Delta) has the absorbing property and forms a monoid (\pi_l,\tilde{m},\tilde{\eta}) in the representation category Rep(A,\Delta). Next we show that an absorbing monoid in an abstract tensor *-category C gives rise to an embedding functor E:C->Vect_C, and we identify conditions on the monoid, satisfied by (\pi_l,\tilde{m},\tilde{\eta}), implying that E is *-preserving. As is well-known, from an embedding functor E: C->\mathrm{Hilb} the generalized Tannaka theorem produces a discrete quantum group (A,\Delta) such that C is equivalent to Rep_f(A,\Delta). Thus, for a C^*-tensor category C with conjugates and irreducible unit the following are equivalent: (1) C is equivalent to the representation category of a discrete quantum group (A,\Delta), (2) C admits an absorbing monoid, (3) there exists a *-preserving embedding functor E: C->\mathrm{Hilb}.Comment: Final version, to appear in Int. Journ. Math. (Added some references and Subsection 1.2.) Latex2e, 21 page

Twisting algebras using non-commutative torsors

Non-commutative torsors (equivalently, two-cocycles) for a Hopf algebra can be used to twist comodule algebras. After surveying and extending the literature on the subject, we prove a theorem that affords a presentation by generators and relations for the algebras obtained by such twisting. We give a number of examples, including new constructions of the quantum affine spaces and the quantum tori.Comment: 27 pages. Masuoka is a new coauthor. Introduction was revised. Sections 1 and 2 were thoroughly restructured. The presentation theorem in Section 3 is now put in a more general framework and has a more general formulation. Section 4 was shortened. All examples (quantum affine spaces and tori, twisting of SL(2), twisting of the enveloping algebra of sl(2)) are left unchange

The K-theory of free quantum groups

In this paper we study the K -theory of free quantum groups in the sense of Wang and Van Daele, more precisely, of free products of free unitary and free orthogonal quantum groups. We show that these quantum groups are K -amenable and establish an analogue of the Pimsner–Voiculescu exact sequence. As a consequence, we obtain in particular an explicit computation of the K -theory of free quantum groups. Our approach relies on a generalization of methods from the Baum–Connes conjecture to the framework of discrete quantum groups. This is based on the categorical reformulation of the Baum–Connes conjecture developed by Meyer and Nest. As a main result we show that free quantum groups have a γ -element and that γ=1 . As an important ingredient in the proof we adapt the Dirac-dual Dirac method for groups acting on trees to the quantum case. We use this to extend some permanence properties of the Baum–Connes conjecture to our setting

Twisting and Rieffel's deformation of locally compact quantum groups. Deformation of the Haar measure

We develop the twisting construction for locally compact quantum groups. A new feature, in contrast to the previous work of M. Enock and the second author, is a non-trivial deformation of the Haar measure. Then we construct Rieffel's deformation of locally compact quantum groups and show that it is dual to the twisting. This allows to give new interesting concrete examples of locally compact quantum groups, in particular, deformations of the classical $az+b$ group and of the Woronowicz' quantum $az+b$ group

N-complexes as functors, amplitude cohomology and fusion rules

We consider N-complexes as functors over an appropriate linear category in order to show first that the Krull-Schmidt Theorem holds, then to prove that amplitude cohomology only vanishes on injective functors providing a well defined functor on the stable category. For left truncated N-complexes, we show that amplitude cohomology discriminates the isomorphism class up to a projective functor summand. Moreover amplitude cohomology of positive N-complexes is proved to be isomorphic to an Ext functor of an indecomposable N-complex inside the abelian functor category. Finally we show that for the monoidal structure of N-complexes a Clebsch-Gordan formula holds, in other words the fusion rules for N-complexes can be determined.Comment: Final versio

Quantum Isometries of the finite noncommutative geometry of the Standard Model

We compute the quantum isometry group of the finite noncommutative geometry F describing the internal degrees of freedom in the Standard Model of particle physics. We show that this provides genuine quantum symmetries of the spectral triple corresponding to M x F where M is a compact spin manifold. We also prove that the bosonic and fermionic part of the spectral action are preserved by these symmetries.Comment: 29 pages, no figures v3: minor change

Sequential design of computer experiments for the estimation of a probability of failure

This paper deals with the problem of estimating the volume of the excursion set of a function $f:\mathbb{R}^d \to \mathbb{R}$ above a given threshold, under a probability measure on $\mathbb{R}^d$ that is assumed to be known. In the industrial world, this corresponds to the problem of estimating a probability of failure of a system. When only an expensive-to-simulate model of the system is available, the budget for simulations is usually severely limited and therefore classical Monte Carlo methods ought to be avoided. One of the main contributions of this article is to derive SUR (stepwise uncertainty reduction) strategies from a Bayesian-theoretic formulation of the problem of estimating a probability of failure. These sequential strategies use a Gaussian process model of $f$ and aim at performing evaluations of $f$ as efficiently as possible to infer the value of the probability of failure. We compare these strategies to other strategies also based on a Gaussian process model for estimating a probability of failure.Comment: This is an author-generated postprint version. The published version is available at http://www.springerlink.co

On Bayesian Search for the Feasible Space Under Computationally Expensive Constraints

We are often interested in identifying the feasible subset of a decision space under multiple constraints to permit effective design exploration. If determining feasibility required computationally expensive simulations, the cost of exploration would be prohibitive. Bayesian search is data-efficient for such problems: starting from a small dataset, the central concept is to use Bayesian models of constraints with an acquisition function to locate promising solutions that may improve predictions of feasibility when the dataset is augmented. At the end of this sequential active learning approach with a limited number of expensive evaluations, the models can accurately predict the feasibility of any solution obviating the need for full simulations. In this paper, we propose a novel acquisition function that combines the probability that a solution lies at the boundary between feasible and infeasible spaces (representing exploitation) and the entropy in predictions (representing exploration). Experiments confirmed the efficacy of the proposed function