13 citations · 39 across the 14 of their papers we have counts for
18 papers
Adversarial Robustness in Deep Learning: Attacks on Fragile Neurons
Chandresh Pravin, Ivan Martino, Giuseppe Nicosia +1
We identify fragile and robust neurons of deep learning architectures using nodal dropouts of the first convolutional layer. Using an adversarial targeting algorithm, we correlate…
Cooperative games on simplicial complexes
Ivan Martino
In this work, we define cooperative games on simplicial complexes, generalizing the study of probabilistic values of Weber and quasi-probabilistic values of Bilbao, Driessen, Jimén…
Efficiency Axioms for simplicial complexes
Ivan Martino
We study the notion of efficiency for cooperative games on simplicial complexes. In such games, the grand coalition may be forbidden, and, thus, it is a non-trivial problem t…
Probabilistic values for simplicial complexes
Ivan Martino
In this manuscript, we define and study probabilistic values for cooperative games on simplicial complexes. Inspired by the work of Weber "Probabilistic values for games", we estab…
Set of independencies and Tutte polynomial of matroids over a domain
Alessio Borzì, Ivan Martino
In this work, we study matroids over a domain and several classical combinatorial and algebraic invariants related. We define their Grothendieck-Tutte polynomial $T_{\mathcal{M}}(x…
On the codimension of Noether-Lefshetz loci for toric threefolds
Valeriano Lanza, Ivan Martino
In this manuscript we sharpen the lower bound on the codimension of the irreducible components of the Noether-Lefschetz locus of surfaces in projective toric threefolds given in [B…
Finite Groups Generated in Low Real Codimension
Ivan Martino, Rahul Singh
We study the intersection lattice of the arrangement of subspaces fixed by subgroups of a finite linear group . When is a reflection group, this arrangement…
Cohen-Macaulay Property of pinched Veronese Rings
Ornella Greco, Ivan Martino
In this work, we study the Betti numbers of pinched Veronese rings, by means of the reduced homology of squarefree divisor complexes. We characterize when these rings are Cohen-Mac…
Face module for realizable Z-matroids
Ivan Martino
In this work, we define the face module for a realizable matroid over Z. Its Hilbert series is, indeed, the expected specialization of the Grothendieck - Tutte polynomial defined b…
Motivic classes of classifying stacks of some semi-direct products
Ivan Martino, Federico Scavia
Let k be a field, let G be a finite group and let T be a split k-torus on which G acts multiplicatively, and for every m greater than 1 denote by T[m] the m-torsion subgroup of T.…
Syzygies of the Veronese modules
Ornella Greco, Ivan Martino
We study the minimal free resolution of the Veronese modules of the polynomial ring in n variables, by giving a formula for the Betti numbers in terms of the reduced homology of so…
Introduction to the Ekedahl Invariants
Ivan Martino
In 2009 T. Ekedahl introduced certain cohomological invariants for finite groups. In this work we introduce these invariants and we show some of their properties. We also give an e…
The Ekedahl Invariants for finite groups
Ivan Martino
In 2009 Ekedahl introduced certain cohomological invariants of finite groups which are naturally related to the Noether Problem. We show that these invariants are trivial for every…
On the variety of linear recurrences and numerical semigroups
Ivan Martino, Luca Martino
In this work, we prove the existence of linear recurrences of order M with a non-trivial solution vanishing exactly on the set of gaps (or a subset) of a numerical semigroup S fini…
Regular sequences of power sums and complete symmetric polynomials
Neeraj Kumar, Ivan Martino
In this article, we carry out the investigation for regular sequences of symmetric polynomials in the polynomial ring in three and four variable. Any two power sum element in $\mat…
Vertex Collapsing and Cut Ideals
Ivan Martino
In this work we study how some elementary graph operations (like the disjoint union) and the collapse of two vertices modify the cut ideal of a graph. They pave the way for reducin…
Systematic Discovery of Runge-Kutta Methods through Algebraic Varieties
Ivan Martino, Giuseppe Nicosia
This work presents a new evolutionary optimization algorithm in theoretical mathematics with important applications in scientific computing. The use of the evolutionary algorithm i…
An Algebraic Proof for the Identities for Degree of Syzygies in Numerical Semigroup
Ivan Martino, Neeraj Kumar
In a recent paper by L. Fel two new identities for the degree of syzygies are given. We present an algebraic proof of them, using only basic homological algebra tools. We also exte…