Rosetta is a systems level design language that allows algebraic specification of systems through facets. The usual approach to formally describe a specification is to define an algebra that satisfies the specification. Although it is possible to formally describe Rosetta facets with the use of algebras, we choose to use the dual of algebra, i.e. coalgebra, to do so. Coalgebras are particularly...

The goal of the present document is to support the taxonomy for bidirectional model synchronization developed in [1] with a formal semantics. The taxonomy is 3D so that each synchronization type is characterized by a triple of coordinates (x, y, z), in which x classifies the organizational symmetry of the case, y is for the informational symmetry, and z is for incrementality of the update propa...

Taking a Fiedler’s result [1] on the spectrum of a matrix formed from two symmetric matrices as a motivation, a more general result is deduced and applied to the determination of adjacency and Laplacian spectra of graphs obtained by a generalized join graph operation on families of graphs (regular in the case of adjacency spectra and arbitrary in the case of Laplacian spectra). Some additional ...

A generalized star-triangle transformation and a concept of triangle-duality have been introduced recently in the physics literature to predict exact percolation threshold values of several lattices. We investigate the mathematical conditions for the solution of bond percolation models, and identify an infinite class of lattice graphs for which exact bond percolation thresholds may be rigorousl...

With coalgebras usually being defined in terms of an endofunctor T on sets, this paper shows that modal logics for T -coalgebras can be naturally described as functors L on boolean algebras. Building on this idea, we study soundness, completeness and expressiveness of coalgebraic logics from the perspective of duality theory. That is, given a logic L for coalgebras of an endofunctor T , we cons...

following the categorical approach to universal algebra through algebraic theories, proposed by f.~w.~lawvere in his phd thesis, this paper aims at introducing a similar setting for general topology. the cornerstone of the new framework is the notion of emph{categorically-algebraic} (emph{catalg}) emph{topological theory}, whose models induce a category of topological structures. we introduce t...

In this paper we investigate some dual algebraic-geometric codes associated with the Giulietti–Korchmáros maximal curve. We compute minimum distance and weight codewords of such generalized Hamming weights codes.

We present a characterization, in terms of projective biduality, for the hypersurfaces appearing in the boundary of the convex hull of a compact real algebraic variety. 1. Formula for the Algebraic Boundary Convex algebraic geometry is concerned with the algebraic study of convex sets that arise in polynomial optimization. One topic of recent interest is the convex hull conv(C) of a compact alg...