1 citations · 1 across the 12 of their papers we have counts for
15 papers
A universal dichotomy for concentration in randomly colored graphs
Nicola Apollonio
Let be Euclidean norm of the degree sequence of a graph normalized by the graph size. We prove that when the vertices of a graph are randomly colored with colors such that…
The Critical Patch Size Problem in Random Graphs
Nicola Apollonio, Veronica Tora, Davide Vergni
The problem of {\it critical patch size} -- a threshold condition for population persistence -- is investigated in the context of discrete habitats, modeled as graphs with a distin…
Posterior Bayesian Neural Networks with Dependent Weights
Nicola Apollonio, Giovanni Franzina, Giovanni Luca Torrisi
We consider fully connected and feedforward deep neural networks with dependent and possibly heavy-tailed weights, as introduced in [26], to address limitations of the standard Gau…
Functions that are uniquely maximized by sparse quasi-star graphs, and uniquely minimized by quasi-complete graphs
Nicola Apollonio
We show that for a certain class of convex functions , including the exponential functions with a real number, and all the powers , $x\geq…
Cantelli's bounds for generalized tail inequalities in Euclidean spaces
Nicola Apollonio
Let be a centered random vector in a finite dimensional real inner product space . For a subset of the ambient vector space of and $x,\,y\in…
Normal approximation of Random Gaussian Neural Networks
Nicola Apollonio, Daniela De Canditiis, Giovanni Franzina +2
In this paper we provide explicit upper bounds on some distances between the (law of the) output of a random Gaussian NN and (the law of) a random Gaussian vector. Our results conc…
Second-order moments of the size of randomly induced subgraphs of given order
Nicola Apollonio
For a graph and a positive integer , let be the size of a subgraph of induced by a randomly sampled subset of vertices. Second-order moments of enc…
Network homophily via tail inequalities
Nicola Apollonio, Paolo G. Franciosa, Daniele Santoni
Homophily is the principle whereby "similarity breeds connections". We give a quantitative formulation of this principle within networks. Given a network and a labeled partition of…
Two New Characterizations of Path Graphs
Nicola Apollonio, Lorenzo Balzotti
Path graphs are intersection graphs of paths in a tree. We start from the characterization of path graphs by Monma and Wei [C.L.~Monma,~and~V.K.~Wei, Intersection Graphs of Paths i…
A novel method for assessing and measuring homophily in networks through second-order statistics
Nicola Apollonio, Paolo Giulio Franciosa, Daniele Santoni
We present a new method for assessing and measuring homophily in networks whose nodes have categorical attributes, namely when the nodes of networks come partitioned into classes (…
A New Characterization of Path Graphs
Nicola Apollonio, Lorenzo Balzotti
Path graphs are intersection graphs of paths in a tree.~In this paper we give a "6\ good characterization" of path graphs, namely, we prove that path graph membership is in $NP\cap…
A tight relation between series-parallel graphs and Bipartite Distance Hereditary graphs
Nicola Apollonio, Massimiliano Caramia, Paolo Giulio Franciosa +1
Bandelt and Mulder's structural characterization of Bipartite Distance Hereditary graphs asserts that such graphs can be built inductively starting from a single vertex and by repe…
On Computing the Galois Lattice of Bipartite Distance Hereditary Graphs
Nicola Apollonio, Paolo Giulio Franciosa
The class of Bipartite Distance Hereditary (BDH) graphs is the intersection between bipartite domino-free and chordal bipartite graphs.\ Graphs in both the latter classes have line…
Minimally unbalanced diamond-free graphs and Dyck-paths
N. Apollonio, A. Galluccio
A -matrix is balanced if it does not contain a submatrix of odd order having exactly two 1's per row and per column. A graph is balanced if its clique-matrix…
On the Galois Lattice of Bipartite Distance Hereditary Graphs
Nicola Apollonio, Massimiliano Caramia, Paolo Giulio Franciosa
We give a complete characterization of bipartite graphs having tree-like Galois lattices. We prove that the poset obtained by deleting bottom and top elements from the Galois latti…