I aim to give the flavour of a selection of topics based around Fräıssé’s notion of homogeneous structure. This is an area connecting ideas from model theory, permutation group theory, combinatorics, descriptive set theory, complexity theory, and other subjects. I will touch superficially a number of these subjects, with little in depth. The background assumed will be basic first order logic (l...

Local sentences and the formal languages they define were introduced by Ressayre in [Res88]. We prove that locally finite ω-languages and effective analytic sets have the same topological complexity: the Borel and Wadge hierarchies of the class of locally finite ω-languages are equal to the Borel and Wadge hierarchies of the class of effective analytic sets. In particular, for each non-null rec...

Classical structure of rough set theory was first formulated by Z. Pawlak in [6]. The foundation of its object classification is an equivalence binary relation and equivalence classes. The upper and lower approximation operations are two core notions in rough set theory. They can also be seenas a closure operator and an interior operator of the topology induced by an equivalence relation on a u...

background: endometriosis is a common chronic inflammation which leads to infertility and chronic pelvic pain in affected women. secretory phospholipase a2 type iia (spla2iia) is an acute phase reactant that is markedly increased in inflammatory disorders. objective: to assess the effects of ω-3 and ω-6 polyunsaturated fatty acids (pufas) administration in endometrial cells culture on spla2iia ...

and Applied Analysis 3 We denote by ∧l ∧l R the space of l-covectors in R and the direct sum ∧ R n ⊕ l 0 ∧l R 2.1 is a graded algebra with respect to the wedge product ∧. We will make use of the exterior derivative: d : C∞ ( Ω,∧l ) −→ C∞ ( Ω,∧l 1 ) 2.2 and its formal adjoint operator d∗ −1 nl 1 ∗ d∗ : C∞ ( Ω,∧l 1 ) −→ C∞ ( Ω,∧l ) , 2.3 known as the Hodge codifferential, where the symbol ∗ denot...

A generalized cusp C is diffeomorphic to [0,∞) times a closed Euclidean manifold. Geometrically C is the quotient of a properly convex domain by a lattice, Γ, in one of a family of affine groups G(ψ), parameterized by a point ψ in the (dual closed) Weyl chamber for SL(n+1,R), and Γ determines the cusp up to equivalence. These affine groups correspond to certain fibered geometries, each of which...

In addition to sparseness, there is much interest in penalties that encourage smoothness, especially in the context of functional data analysis. We show how the GPMF can be used with smooth penalties and propose a generalized gradient descent method to solve for these smooth GPMF factors. Many have proposed to obtain smoothness in the factors by using a quadratic penalty. Rice and Silverman (19...