10 papers
A Helly-Type Theorem for two-component convex sets
Giuliamaria Menara
In any fixed dimension, consider a finite collection of sets, each consisting of exactly two disjoint, closed, convex pieces. We show that to guarantee the intersection of the whol…
Coloring semiminimal Cayley Graphs
Ignacio García-Marco, Kolja Knauer, Giuliamaria Menara
In 1978 Babai raised the question whether all semiminimal Cayley graphs have bounded chromatic number. In this paper we show that semiminimal Cayley graphs of abelian and generaliz…
Structural Properties of Non-Linear Cellular Automata: Permutivity, Surjectivity and Reversibility
Firas Ben Ramdhane, Alberto Dennunzio, Luciano Margara +1
This paper explores the algebraic conditions under which a cellular automaton with a non-linear local rule exhibits surjectivity and reversibility. We also analyze the role of perm…
Combinatorial Designs and Cellular Automata: A Survey
Luca Manzoni, Luca Mariot, Giuliamaria Menara
Cellular Automata (CA) are commonly investigated as a particular type of dynamical systems, defined by shift-invariant local rules. In this paper, we consider instead CA as algebra…
Eulerian magnitude homology: diagonality, injective words, and regular path homology
Luigi Caputi, Giuliamaria Menara
In this paper we explore the algebraic structure and combinatorial properties of eulerian magnitude homology. First, we analyze the diagonality conditions of eulerian magnitude hom…
Computing eulerian magnitude homology
Giuliamaria Menara, Luca Manzoni
In this paper tackle the problem of computing the ranks of certain eulerian magnitude homology groups of a graph G. First, we analyze the computational cost of our problem and prov…
On torsion in eulerian magnitude homology of Erdos-Renyi random graphs
Giuliamaria Menara
In this paper we investigate the regimes where an Erdos-Renyi random graph has torsion free eulerian magnitude homology groups. To this end, we start be introducing the eulerian As…
Eulerian magnitude homology: subgraph structure and random graphs
Chad Giusti, Giuliamaria Menara
In this paper we explore the connection between the ranks of the magnitude homology groups of a graph and the structure of its subgraphs. To this end, we introduce variants of magn…
Combining Genetic Programming and Particle Swarm Optimization to Simplify Rugged Landscapes Exploration
Gloria Pietropolli, Giuliamaria Menara, Mauro Castelli
Most real-world optimization problems are difficult to solve with traditional statistical techniques or with metaheuristics. The main difficulty is related to the existence of a co…
The Effect of Multi-Generational Selection in Geometric Semantic Genetic Programming
Mauro Castelli, Luca Manzoni, Luca Mariot +2
Among the evolutionary methods, one that is quite prominent is Genetic Programming, and, in recent years, a variant called Geometric Semantic Genetic Programming (GSGP) has shown t…