Conditions implying the uniqueness of the weak*-topology on certain group algebras

We investigate possible preduals of the measure algebra M(G) of a locally compact group and the Fourier algebra A(G) of a separable compact group. Both of these algebras are canonically dual spaces and the canonical preduals make the multiplication separately weak*-continuous so that these algebras are dual Banach algebras. In this paper we find additional conditions under which the preduals C0(G) of M(G) and C*(G) of A(G) are uniquely determined. In both cases we consider a natural comultiplication and show that the canonical predual gives rise to the unique weak*-topology making both the multiplication separately weak*-continuous and the comultiplication weak*-continuous. In particular, dual cohomological properties of these algebras are well defined with this additional structure

Preduals of semigroup algebras

For a locally compact group G, the measure convolution algebra M(G) carries a natural coproduct. In previous work, we showed that the canonical predual C 0(G) of M(G) is the unique predual which makes both the product and the coproduct on M(G) weak*-continuous. Given a discrete semigroup S, the convolution algebra ℓ 1(S) also carries a coproduct. In this paper we examine preduals for ℓ 1(S) making both the product and the coproduct weak*-continuous. Under certain conditions on S, we show that ℓ 1(S) has a unique such predual. Such S include the free semigroup on finitely many generators. In general, however, this need not be the case even for quite simple semigroups and we construct uncountably many such preduals on ℓ 1(S) when S is either ℤ+×ℤ or (ℕ,⋅)

Shift invariant preduals of ℓ₁(ℤ)

The Banach space ℓ<sub>1</sub>(ℤ) admits many non-isomorphic preduals, for example, C(K) for any compact countable space K, along with many more exotic Banach spaces. In this paper, we impose an extra condition: the predual must make the bilateral shift on ℓ<sub>1</sub>(ℤ) weak<sup>*</sup>-continuous. This is equivalent to making the natural convolution multiplication on ℓ<sub>1</sub>(ℤ) separately weak*-continuous and so turning ℓ<sub>1</sub>(ℤ) into a dual Banach algebra. We call such preduals <i>shift-invariant</i>. It is known that the only shift-invariant predual arising from the standard duality between C<sub>0</sub>(K) (for countable locally compact K) and ℓ<sub>1</sub>(ℤ) is c<sub>0</sub>(ℤ). We provide an explicit construction of an uncountable family of distinct preduals which do make the bilateral shift weak<sup>*</sup>-continuous. Using Szlenk index arguments, we show that merely as Banach spaces, these are all isomorphic to c<sub>0</sub>. We then build some theory to study such preduals, showing that they arise from certain semigroup compactifications of ℤ. This allows us to produce a large number of other examples, including non-isometric preduals, and preduals which are not Banach space isomorphic to c<sub>0</sub>

{VeSTA} : a Tool to Verify the Correct Integration of a Component in a Composite Timed System

International audienceVesta is a push-button tool for checking the correct integration of a component in an environment, for component-based timed systems. By correct integration, we mean that the local properties of the component are preserved when this component is merged into an environment. This correctness is checked by means of a so-called divergencesensitive and stability-respecting timed tau-simulation, ensuring the preservation of all linear timed properties expressed in the logical formalism Mitl (Metric Interval Temporal Logic), as well as strong non-zenoness and deadlock-freedom. The development of the tool was guided by the architecture of the Open-Kronos tool. This allows, as additional feature, an easy connection of the models considered in Vesta to the Open- Caesar verification platform, and to the Open-Kronos tool

Spontaneous alloying in binary metal microclusters - A molecular dynamics study -

Microcanonical molecular dynamics study of the spontaneous alloying(SA), which is a manifestation of fast atomic diffusion in a nano-sized metal cluster, is done in terms of a simple two dimensional binary Morse model. Important features observed by Yasuda and Mori are well reproduced in our simulation. The temperature dependence and size dependence of the SA phenomena are extensively explored by examining long time dynamics. The dominant role of negative heat of solution in completing the SA is also discussed. We point out that a presence of melting surface induces the diffusion of core atoms even if they are solid-like. In other words, the {\it surface melting} at substantially low temperature plays a key role in attaining the SA.Comment: 15 pages, 12 fgures, Submitted to Phys.Rev.

LTL Parameter Synthesis of Parametric Timed Automata

The parameter synthesis problem for parametric timed automata is undecidable in general even for very simple reachability properties. In this paper we introduce restrictions on parameter valuations under which the parameter synthesis problem is decidable for LTL properties. The investigated bounded integer parameter synthesis problem could be solved using an explicit enumeration of all possible parameter valuations. We propose an alternative symbolic zone-based method for this problem which results in a faster computation. Our technique extends the ideas of the automata-based approach to LTL model checking of timed automata. To justify the usefulness of our approach, we provide experimental evaluation and compare our method with explicit enumeration technique.Comment: 23 pages, extended versio

Efficient Emptiness Check for Timed B\"uchi Automata (Extended version)

The B\"uchi non-emptiness problem for timed automata refers to deciding if a given automaton has an infinite non-Zeno run satisfying the B\"uchi accepting condition. The standard solution to this problem involves adding an auxiliary clock to take care of the non-Zenoness. In this paper, it is shown that this simple transformation may sometimes result in an exponential blowup. A construction avoiding this blowup is proposed. It is also shown that in many cases, non-Zenoness can be ascertained without extra construction. An on-the-fly algorithm for the non-emptiness problem, using non-Zenoness construction only when required, is proposed. Experiments carried out with a prototype implementation of the algorithm are reported.Comment: Published in the Special Issue on Computer Aided Verification - CAV 2010; Formal Methods in System Design, 201

Parameter-Independent Strategies for pMDPs via POMDPs

Markov Decision Processes (MDPs) are a popular class of models suitable for solving control decision problems in probabilistic reactive systems. We consider parametric MDPs (pMDPs) that include parameters in some of the transition probabilities to account for stochastic uncertainties of the environment such as noise or input disturbances. We study pMDPs with reachability objectives where the parameter values are unknown and impossible to measure directly during execution, but there is a probability distribution known over the parameter values. We study for the first time computing parameter-independent strategies that are expectation optimal, i.e., optimize the expected reachability probability under the probability distribution over the parameters. We present an encoding of our problem to partially observable MDPs (POMDPs), i.e., a reduction of our problem to computing optimal strategies in POMDPs. We evaluate our method experimentally on several benchmarks: a motivating (repeated) learner model; a series of benchmarks of varying configurations of a robot moving on a grid; and a consensus protocol.Comment: Extended version of a QEST 2018 pape

Noncommutative Figa-Talamanca-Herz algebras for Schur multipliers

We introduce a noncommutative analogue of the Fig\'a-Talamanca-Herz algebra $A_p(G)$ on the natural predual of the operator space $\frak{M}_{p,cb}$ of completely bounded Schur multipliers on Schatten space $S_p$. We determine the isometric Schur multipliers and prove that the space $\frak{M}_{p}$ of bounded Schur multipliers on Schatten space $S_p$ is the closure in the weak operator topology of the span of isometric multipliers.Comment: 24 pages; corrected typo