We introduce a family of modal expansions of Belnap-Dunn four-valued logic and related systems, and interpret them in many-valued Kripke structures. Using algebraic logic techniques and topological duality for modal algebras, and generalizing the so-called twist-structure representation, we axiomatize by means of Hilbert-style calculi the least modal logic over the four-element Belnap lattice a...

We consider the general problem of learning an unknown functional dependency, f : X !→ Y, between a structured input space X and a structured output space Y, from labeled and unlabeled examples. We formulate this problem in terms of data-dependent regularization in Vector-valued Reproducing Kernel Hilbert Spaces (Micchelli & Pontil, 2005) which elegantly extend familiar scalarvalued kernel meth...

The quantum theories we want to understand are describing phenomena which take place in Euclidean space E. Among other things, such a theory is supposed to have an associated Hilbert space H, whose vectors represent the possible “states” of the system. You are perhaps already familiar with one simple example of a quantum theory, namely quantum Maxwell theory, which describes the dynamics of the...

Keywords: Local mean decomposition Data fusion Complex signal analysis Time–frequency analysis Signal nonlinearity Spike identification a b s t r a c t The local mean decomposition (LMD) has been recently developed for the analysis of time series which have nonlinearity and nonstationarity. The smoothed local mean of the LMD surpasses the cubic spline method used by the empirical mode decomposi...

The main purpose of this paper is providing a systematic study and classification of non-scalar kernels for Reproducing Kernel Hilbert Spaces (RKHS), to be used in the analysis of deformation in shape spaces endowed with metrics induced by the action of groups of diffeomorphisms. After providing an introduction to matrix-valued kernels and their relevant differential properties, we explore exte...

Let X and Y be two Hilbert spaces, and L(X, Y ) the space of bounded linear transformations from X into Y . Let {An} ⊂ L(X, Y ) be a weakly periodic sequence of period T . Spectral theory of weakly periodic sequences in a Hilbert space is studied by H. L. Hurd and V. Mandrekar (1991). In this work we proceed further to characterize {An} by a positive measure μ and a number T of L(X, X)-valued f...

We dispense with semimartingale (and Dirichlet process) assumptions while investigating arbitrary-order stochastic semi-linear parabolic equations. The emergence of fractional L evy processes in pressing applications like communication networks and mathematical nance highlights the need for studying stochastic evolutionary equations under general noise conditions. Our principle result states th...

We propose a combination of Bochvar’s strict three-valued logic, McCarthy’s sequential three-valued logic, and process algebra via the conditional guard construct. This combination entails the introduction of a new constant meaningless in process algebra. We present an operational semantics in SOS-style, and a completeness result for ACP with conditional guard construct and the proposed logic.

We dispense with semimartingale (and Dirichlet process) assumptions while investigating arbitrary-order stochastic semi-linear parabolic equations. The emergence of fractional L evy processes in pressing applications like communication networks and mathematical nance highlights the need for studying stochastic evolutionary equations under general noise conditions. Our principle result states th...