For a fairly general reductive group G/Qp , we explicitly compute the space of locally algebraic vectors in the Breuil–Herzig construction (ρ)ord , for a potentially semistableBorel-valued representationρ ofGal(Q̄p/Qp). The point beingwedealwith thewhole representation, not just its socle—and we go beyond GLn(Qp). In the case of GL2(Qp), this relation is one of the key properties of the p-adic l...

We examine the collective behaviour of coupled Duffing Hamiltonian systems (HS) and show the existence of measure synchronization (MS) in the quasi-periodic (QP) and -chaotic states. We show that the dynamics of coupled Duffing Hamiltonians exhibit a transition to coherent invariant measure, their orbits sharing the same phase space as the coupling strength is increased. Transitions from QP mea...

Remark. Apropos of reduction mod p: If V is a Qp-vector space and G ⊂ GL(V ) is a compact subgroup, then there exists a G-fixed lattice in V for the following reason. Pick any lattice L ⊂ V . Then the G-stabilizer of L is open and of finite index. So Λ = ∑ g∈G gL ⊂ V is also a lattice, and it is definitely G-stable. The same works with coefficients in any finite extension of Qp, or even in Qp (...

Given a compact p-adic Lie group G over a finite unramified extension L/Qp let GL/Qp be the product over all Galois conjugates of G. We construct an exact and faithful functor from admissible G-Banach space representations to admissible locally L-analytic GL/Qp -representations that coincides with passage to analytic vectors in case L = Qp. On the other hand, we study the functor ”passage to an...

We introduce a new method for data clustering based on a particular Gaussian mixture model (GMM). Each cluster of data, modeled as a GMM into an input space, is interpreted as a hyperplane in a high dimensional mapping space where the underlying coefficients are found by solving a quadratic programming (QP) problem. The main contributions of this work are (1) an original probabilistic framework...

1. Pointwise. Each point in the dest is determined from the corresponding point in the src. We start with 3 points specifying the initial coordinate space and the 3 corresponding points that specify the transformed coordinate space, and transform an entire image pointwise by the transformation (1). 2. Sequential. The entire image is successively transformed by a sequence of shear, scale and tra...

We study irregularity properties of generic Peano functions; we apply these results to the determination of the pointwise smoothness of a Peano function introduced by Lebesgue and of some related functions, showing that they are either monohölder or multifractal functions. We test on these examples several numerical variants of the multifractal formalism, and we show how a change of topology on...