The results in this paper involve two different topics in the descriptive theory of Polish group actions. The book Becker-Kechris [6] is an introduction to that theory. Our two topics—and two collections of theorems—are rather unrelated, but the proofs for both topics are essentially the same. Locally compact Polish groups, i.e., second countable locally compact groups, are the traditional obje...

In its current state of early development, the field of knowledge management (KM) is increasingly characterized by a small number of recurrent dichotomies. Chief among these is the distinction between tacit and explicit knowledge that Nonaka and others seem to have borrowed from Polanyi’s educational theory. The reverence this dichotomy is now accorded is considerable, and nearly every work wri...

This paper proposes a novel inference task for probabilistic databases: the most probable database (MPD) problem. The MPD is the most probable deterministic database where a given query or constraint is true. We highlight two distinctive applications, in database repair of key and dependency constraints, and in finding most probable explanations in statistical relational learning. The MPD probl...

We prove a complexity dichotomy theorem for all non-negative weighted counting Constraint Satisfaction Problems (CSP). This caps a long series of important results on counting problems including unweighted and weighted graph homomorphisms [19, 8, 18, 12] and the celebrated dichotomy theorem for unweighted #CSP [6, 4, 21, 22]. Our dichotomy theorem gives a succinct criterion for tractability. If...

Finite valued constraint satisfaction problems are a formalism for describing many natural optimization problems, where constraints on the values that variables can take come with rational weights and the aim is to find an assignment of minimal cost. Thapper and Živný have recently established a complexity dichotomy for finite valued constraint languages. They show that each such language eithe...

A topological model is presented for complex data sets in which the attributes can be cast into a dichotomy. It is shown that the relative dominance of the two parts in such a dichotomy can be measured by the corresponding areas in its star plot. An optimization model is proposed to maximize the resolution of such a measure by choice of configuration of the attributes, as well as the angles amo...

We investigate data-enriched models, like Petri nets with data, where executability of a transition is conditioned by a relation between data values involved. Decidability status of various decision problems in such models may depend on the structure of data domain. According to the WQO Dichotomy Conjecture, if a data domain is homogeneous then it either exhibits a well quasi-order (in which ca...

Word W is said to encounter word V provided there is a homomorphism φ mapping letters to nonempty words so that φ(V) is a substring of W. For example, taking φ such that φ(h) = c and φ(u) = ien, we see that " science " encounters " huh " since cienc = φ(huh). The density of V in W , δ(V, W), is the proportion of substrings of W that are homomorphic images of V. So the density of " huh " in " sc...

We derive new estimates of the spectral dichotomy for matrices and matrix pencils which are based upon estimates of the restrictions of Green functions associated with the spectrum dichotomy problem onto the stable and unstable invariant subspaces and estimates of angles between these subspaces. De nouvelles estimations pour la dichotomie spectrale R esum e : Nous etablissons de nouvelles estim...

Given a preference profile, a social dichotomy function partitions the set of alternatives into a set of approved alternatives and a set of disapproved alternatives. The Borda mean rule approves all alternatives with above-average Borda score, and disapproves alternatives with below-average Borda score. We show that the Borda mean rule is the unique social dichotomy function satisfying neutrali...