Weak Gibbs property and systems of numeration parÉric OLIVIER et Alain THOMAS Résumé. Nousétudions les propriétés d'autosimilarité et la nature gibbsienne de certaines mesures definies sur l'espace produit Ω r := {0, 1,. .. , r−1} N. Cet espace peutêtre identifiéà l'intervalle [0, 1] au moyen de la numération en base r. Le dernier paragraphe concerne la convolution de Bernoulli en base β = 1+ √...

In the adversarial-perturbation problem of neural networks, an adversary starts with a neural network model F and a point x that F classifies correctly, and applies a small perturbation to x to produce another point x′ that F classifies incorrectly. In this paper, we propose taking into account the inherent confidence information produced by models when studying adversarial perturbations, where...

Weak states on posets are defined which are in some analogy to states on orthomodular posets used in axiomatic quantum mechanics. It is shown how certain properties of the set of weak states characterize certain properties of the underlying poset. Orthomodular posets serve as algebraic models for logics in axiomatic quantum mechanics. States on them are considered which reflect the properties o...

We continue to study nitary abstract elementary classes, de ned in [7]. We introduce a concept of weak κ -categoricity and an f-primary model in a א0 -stable simple nitary AEC with the extension property, and gain the following theorem: Let (K,4K) be a simple nitary AEC, weakly categorical in some uncountable κ . Then (K,4K) is weakly categorical in each λ ≥ min{κ,i(2א0 )+} . We have that if th...

We study the genericity of the first weak inverse shadowing property and the second weak inverse shadowing property in the space of homeomorphisms on a compact metric space, and show that every shift homeomorphism does not have the first weak inverse shadowing property but it has the second weak inverse shadowing property.

We study nonlinear m-term approximation with regard to a redundant dictionary D in a Hilbert space H. It is known that the Pure Greedy Algorithm (or, more generally, the Weak Greedy Algorithm) provides for each f ∈ H and any dictionary D an expansion into a series f = ∞ X j=1 cj(f)φj(f), φj(f) ∈ D, j = 1, 2, . . . with the Parseval property: ‖f‖2 = j |cj(f)|. Following the paper of A. Lutoborsk...

This report contains a novel approach to observation equivalence for coalgebras. We describe how to define weak homomorphisms, weak bisimulation, and investigate the connection between these notions as well as the relation to the known theory of bisimulation for coalgebras. The ultimate result of the paper is the correctness-proof for a weak coinduction proof principle.

We study nonlinear m-term approximation with regard to a redundant dictionary D in a Banach space. It is known that in the case of Hilbert space H the pure greedy algorithm (or, more generally, the weak greedy algorithm) provides for each f ∈ H and any dictionaryD an expansion into a series f = ∞ ∑ j=1 cj (f ) j (f ), j (f ) ∈ D, j = 1, 2, . . . with the Parseval property: ‖f ‖2 = ∑j |cj (f )|2...