We present a two-level parameterized Model Order Reduction (pMOR) technique for the linear hyperbolic Partial Differential Equation (PDE) of time-domain elastodynamics. In order to approximate frequency-domain PDE, we take advantage Port-Reduced Reduced-Basis Component (PR-RBC) method develop (in offline stage) reduced bases subdomains; latter are then assembled online form global domains inter...

We study the computational problem of checking whether a logical sentence is true in a finite abelian group. We prove that model checking first-order sentences on finite abelian groups is fixed-parameter tractable, when parameterized by the size of the sentence. We also prove that model checking monadic second-order sentences on finite abelian groups finitely presented by integer matrices is no...

A logical framework is a meta-language for the formalization of deductive systems. We provide a brief introduction to logical frameworks and their methodology, concentrating on LF. We use first-order logic as the running example to illustrate the representations of syntax, natural deductions, and proof transformations. We also sketch a recent formulation of LF centered on the notion of canonica...

I explain a method to learn to achieve goals in games. In very complex games, such as the game of Go, a search intensive approach is intractable. A knowledge intensive approach is best suited. I represent knowledge using the combinatorial game theory and first order logic. I give a method to learn to predict the consequences of some moves. Each rule is learned using a single example, by explain...

for some λ ∈ C, x ∈ I = [a, b], and y ∈ C2(I). It was first introduced in a 1837 publication [7] by the eminent French mathematicians Joseph Liouville (1809 1882) and Jacques Charles François Sturm (1803 1855). At this point, our initial questions might be: why is this problem important? What can we say about the structure of this equation? How about the solutions? We will tackle a few basic re...

Let K be a set of n non-intersecting objects in 3-space. A depth order of K, if exists, is a linear order < of the objects in K such that if K; L 2 K and K lies vertically below L then K < L. We present a new technique for computing depth orders, and apply it to several special classes of objects. Our results include: (i) If K is a set of n triangles whose xy-projections are alìfat', then a dep...

BIP is a component-based framework for system design built on three pillars: behavior, interaction, and priority. In this paper, we introduce first-order interaction logic (FOIL) that extends BIP without priorities to systems parameterized in the number of components. We show that FOIL captures classical parameterized architectures such as token-passing rings, cliques of identical components co...

Context-aware development has been an emergent subject of many research works in ubiquitous computing. Few of them propose Model Driven Development as a standard on context-aware development. Many focus on context capture and adaptation by the use of legacy architectures and others artifacts to input context into application logic. This work proposes Model Driven Development to promote reuse, a...

In this paper we study the problem of finding an induced subgraph of size at most k with minimum degree at least d for a given graph G, from the parameterized complexity perspective. We call this problem Minimum Subgraph of Minimum Degree ≥d (MSMDd). For d = 2 it corresponds to finding a shortest cycle of the graph. Our main motivation to study this problem is its strong relation to Dense k-Sub...