The information divergence of a probability measure P from an exponential family E over a nite set is de ned as in mum of the divergences of P from Q subject to Q ∈ E . All directional derivatives of the divergence from E are explicitly found. To this end, behaviour of the conjugate of a log-Laplace transform on the boundary of its domain is analysed. The rst order conditions for P to be a maxi...

We prove a general categorical theorem that enables us to state that under certain conditions, the range of a functor is large. As an application, we prove various results of which the following is a prototype: If every diagram, indexed by a lattice, of finite Boolean 〈∨, 0〉-semilattices with 〈∨, 0〉-embeddings, can be lifted with respect to the Conc functor on lattices, then so can every diagra...

This paper reviews the main psychological phenomena of inductive reasoning, covering 25 years of experimental and model-based research, in particular addressing four questions. First, what makes a case or event generalizable to other cases? Second, what makes a set of cases generalizable? Third, what makes a property or predicate projectable? Fourth, how do psychological models of induction add...

We present an approach of computing the intersection curve C of two rational parametric surface S1(u, s) and S2(v, t), one being projectable and hence can easily be implicitized. Plugging the parametric surface to the implicit surface yields a plane algebraic curve G(v, t) = 0. By analyzing the topology graph G of G(v, t) = 0 and the singular points on the intersection curve C we associate a sp...

How many are projectable classical linear connections with a prescribed Ricci tensor and trace of torsion on the total space fibered manifold? The questions answered in analytic case by using Cauchy-Kowalevski theorem. In C? case, we answer how 2-dimensional manifold. also deduce that any 2-form manifold at least fibres can be realized locally as connection.

Classical and quantum Friedmann-Lema\^itre-Robertson-Walker universes filled with non-interacting radiation dust fluids are considered in the framework of Ho\v{r}ava-Lifshitz gravity theory. The theory is set its projectable version without detailed balance condition. Canonical quantization performed Wheeler-DeWitt approach cosmology for a minisuperspace model light de Broglie-Bohm interpretati...

We describe some general geometric properties of the fiber product preserving bundle functors. Special attention is paid to the vertical Weil bundles. We discuss namely the flow natural maps and the functorial prolongation of connections. The main purpose of the present paper is to describe some geometric properties of the category FMm of fibered manifolds with m-dimensional bases and local fib...