## About

78

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Introduction

Additional affiliations

January 2012 - December 2015

July 1992 - present

**Università degli studi di Udine**

Position

- Professor (Associate)

Description

- Numerica Analysis, Numerical Computing, High Performance Computing, Network Analysis

July 1992 - December 2012

## Publications

Publications (78)

Cauchy-like matrices arise often as building blocks in decomposition formulas and fast algorithms for various displacement-structured matrices. A complete characterization for orthogonal Cauchy-like matrices is given here. In particular, we show that orthogonal Cauchy-like matrices correspond to eigenvector matrices of certain symmetric matrices re...

A second-order random walk on a graph or network is a random walk where transition probabilities depend not only on the present node but also on the previous one. A notable example is the non-backtracking random walk, where the walker is not allowed to revisit a node in one step. Second-order random walks can model physical diffusion phenomena in a...

We introduce a family of hypergroups, called weakly complete, generalizing the construction of complete hypergroups. Starting from a given group G, our construction prescribes the β-classes of the hypergroups and allows some hyperproducts not to be complete parts, based on a suitably defined relation over G. The commutativity degree of weakly compl...

Hypergroups can be subdivided into two large classes: those whose heart coincide with the entire hypergroup and those in which the heart is a proper sub-hypergroup. The latter class includes the family of 1-hypergroups, whose heart reduces to a singleton, and therefore is the trivial group. However, very little is known about hypergroups that are n...

A non-backtracking random walk on a graph is a random walk where, at each step, it is not allowed to return back to the node that has just been left. Non-backtracking random walks can model physical diffusion phenomena in a more realistic way than traditional random walks. However, the interest in these stochastic processes has grown only in recent...

In this paper, we show a new construction of hypergroups that, under appropriate conditions, are complete hypergroups or non-complete 1-hypergroups. Furthermore, we classify the 1-hypergroups of size 5 and 6 based on the partition induced by the fundamental relation β. Many of these hypergroups can be obtained using the aforesaid hypergroup constru...

Random graph models are a recurring tool‐of‐the‐trade for studying network structural properties and benchmarking community detection and other network algorithms. Moreover, they serve as test‐bed generators for studying diffusion and routing processes on networks. In this paper, we illustrate how to generate large random graphs having a power‐law...

This note answers in the affirmative a question raised by Sebastian Schlecht, see https://mathoverflow.net/questions/362317/orthogonalcauchylikematrix#362317.

In every hypergroup, the equivalence classes modulo the fundamental relation β are the union of hyperproducts of element pairs. Making use of this property, we introduce the notion of height of a β -class and we analyze properties of hypergroups where the height of a β -class coincides with its cardinality. As a consequence, we obtain a new charact...

The core–periphery structure is one of the key concepts in the structural analysis of complex networks. It consists of a partitioning of the node set of a given graph or network into two groups, called core and periphery, where the core nodes induce a well-connected subgraph and share connections with peripheral nodes, while the peripheral nodes ar...

The use of higher-order stochastic processes such as nonlinear Markov chains or vertex-reinforced random walks is significantly growing in recent years as they are much better at modeling high dimensional data and nonlinear dynamics in numerous application settings. In many cases of practical interest, these processes are identified with a stochast...

Being able to produce synthetic networks by means of generative random graph models and scalable algorithms is a recurring tool-of-the-trade in network analysis, as it provides a well founded basis for the statistical analysis of various properties in real-world networks. In this paper, we illustrate how to generate large random graphs having a pow...

Let R be a Krasner hyperring. In this paper, we prove a factorization theorem in the category of Krasner R-hypermodules with inclusion single-valued R-homomorphisms as its morphisms. Then, we prove various isomorphism theorems for a smaller category, i.e., the category of Krasner R-hypermodules with strong single-valued R-homomorphisms as its morph...

The tensor train (TT) decomposition is a representation technique for arbitrary tensors, which allows efficient storage and computations. For a d-dimensional tensor with d ≥ 2, that decomposition consists of two ordinary matrices and d − 2 third-order tensors. In this paper we prove that the TT decomposition of an arbitrary tensor can be computed (...

We provide explicit expressions for the eigenvalues and eigenvectors of matrices that can be written as the Hadamard product of a block partitioned matrix with constant blocks and a rank one matrix. Such matrices arise as the expected adjacency or modularity matrices in certain random graph models that are widely used as benchmarks for community de...

We consider the class of 0-semigroups (H, ⋆) that are obtained by adding a zero element to a group (G, ·) so that for all x, y ∈ G it holds x ⋆ y ≠ 0 ⇒ x ⋆ y = xy. These semigroups are called 0-extensions of (G, ·). We introduce a merging operation that constructs a 0-semihypergroup from a 0-extension of (G, ·) by a suitable superposition of the pr...

In a graph or complex network, communities and anti-communities are node sets whose modularity attains extremely large values, positive and negative, respectively. We consider the simultaneous detection of communities and anti-communities, by looking at spectral methods based on various matrix-based definitions of the modularity of a vertex set. In...

Nodal theorems for generalized modularity matrices ensure that the cluster located by the positive entries of the leading eigenvector of various modularity matrices induces a connected subgraph. In this paper we obtain lower bounds for the modularity of that set of nodes showing that, under certain conditions, the nodal domains induced by eigenvect...

Nodal theorems for generalized modularity matrices ensure that the cluster located by the positive entries of the leading eigenvector of various modularity matrices induces a connected subgraph. In this paper we obtain lower bounds for the modularity of that subgraph showing that, under certain conditions, the nodal domains induced by eigenvectors...

The Total Least Squares solution of an overdetermined, approximate linear equation \(Ax \approx b\) minimizes a nonlinear function which characterizes the backward error. We devise a variant of the Gauss–Newton iteration with guaranteed convergence to that solution, under classical well-posedness hypotheses. At each iteration, the proposed method r...

We propose a new localization result for the leading eigenvalue and eigenvector of a symmetric matrix A. The result exploits the Frobenius inner product between A and a given rank-one landmark matrix X. Different choices for X may be used, depending upon the problem under investigation. In particular, we show that the choice where X is the all-ones...

For any integer n ≥ 2, let R0(n + 1) be the class of 0-semihypergroups H of size n + 1 such that {y} ⊆ xy ⊆ {0, y} for all x, y ∈ H - {0}, all subsemihypergroups K ⊆ H are 0-simple and, when |K| ≥ 3, the fundamental relation βK is not transitive. We determine a transversal of isomorphism classes of semihypergroups in R0(n + 1) and we prove that its...

Various modularity matrices appeared in the recent literature on network analysis and alge-braic graph theory. Their purpose is to allow writing as quadratic forms certain combinatorial functions appearing in the framework of graph clustering problems. In this paper we put in evidence certain common traits of various modularity matrices and shed li...

Fully simple semihypergroups have been introduced in [9], motivated by the study of the transitivity of the fundamental relation β in semihypergroups. Here, we determine a transversal of isomorphism classes of fully simple semihypergroups with a right absorbing element. The structure of that transversal can be described by means of certain transiti...

One of the most relevant tasks in network analysis is the detection of
community structures, or clustering. Most popular techniques for community
detection are based on the maximization of a quality function called
modularity, which in turn is based upon particular quadratic forms associated
to a real symmetric modularity matrix $M$, defined in ter...

Slides for a talk delivered at VDM60, see http://bugs.unica.it/VDM60

Let G(n) denote the class of hypergroups of type U on the right of size n with bilateral scalar identity. In this paper we consider the hypergroups (H, o). G(7) which own a proper and non- trivial subhypergroup h. For these hypergroups we prove that h is closed if and only if ( H - h) o (H - h) = h. Moreover we consider the set G(7) of hypergroups...

Among hyperstructures of type U on the right having small size, the order 6 is a relevant case. Indeed, only if the order is ≥ 6 there exist proper semihypergrops and hypergroups of type U on the right whose right scalar identity is not also left identity. In the present paper we show a construction of hypergroups of type U on the right whose right...

We propose a family of Markov chain-based models for the link analysis of scientific publications. The PageRank-style model and the dummy paper model discussed in [Electron. Trans. Numer. Anal., 33 (2008), pp. 1–16] can be obtained by a particular choice of its parameters. Since scientific publications can be ordered by the date of publication it i...

We consider the fundamental relations β and γ in simple and 0-simple semihypergroups, especially in connection with certain minimal cardinality questions. In particular, we enumerate and exhibit all simple and 0-simple semihypergroups having order 3 where β is not transitive, apart of isomorphisms. Moreover, we show that the least order for which t...

We consider a boundary identification problem arising in nondestructive testing of materials. The problem is to recover a part Gamma(1) subset of partial derivative Omega of the boundary of a bounded, planar domain Omega from one Cauchy data pair (u, partial derivative u/partial derivative v) of a harmonic potential u in Omega collected on an acces...

A thin conducting plate has an inaccessible side in contact with aggressive external agents. On the other side, we are able to heat the plate and take temperature maps in laboratory conditions. Detecting and evaluating damage on the inaccessible side from thermal data requires the solution of a nonlinear inverse problem for the heat equation in the...

Singular Spectrum Analysis is a quite recent technique for the analysis of experimental time series, based on the singular value decomposition of certain Hankel matrices. However, the mathematical and physical interpretation of the singular values in this kind of application is not fully clarified. In this paper, using asymptotic properties of the...

We analyze the componentwise and normwise sensitivity of inverses of Cauchy, Vandermonde, and Cauchy-Vandermonde matrices,
with respect to relative componentwise perturbations in the nodes defining these matrices. We obtain a priori, easily computable upper bounds for these condition numbers. In particular, we improve known estimates for Vandermond...

By means of a blend of theoretical arguments and computer algebra techniques, we prove that the number of isomorphism classes of hypergroups of type U on the right of order five, having a scalar (bilateral) identity, is 14751. In this way, we complete the classification of hypergroups of type U on the right of order five, started in our preceding p...

We study existence and possible uniqueness of special semihypergroups of type U on the right. In particular, we prove that there exists a unique proper semihypergroup of this kind having order 6, apart
of isomorphisms; the least order for a hypergroup of type U on the right to have a stable part which is not a subhypergroup is 9; and the minimal ca...

It is known that any symmetric matrix can be transformed by an explicitly computable orthogonal transformation into diagonal-plus-semiseparable
form, with prescribed diagonal term. In this paper, we present perturbation bounds for such transformations, under the condition
that the diagonal term is close to (part of) the spectrum of the given matrix...

From the nucleus, histone deacetylase 4 (HDAC4) regulates a variety of cellular processes, including growth, differentiation, and survival, by orchestrating transcriptional changes. Extracellular signals control its repressive influence mostly through regulating its nuclear-cytoplasmic shuttling. In particular, specific posttranslational modificati...

We generalize the classical definition of hypergroups of type U on the right to semihypergroups, and we prove some properties of their subsemihypergroups and subhypergroups. In particular, we obtain that a finite proper semihypergroup of type U on the right can exist only if its order is at least 6. We prove that one such semihypergroup of order 6...

The connection between Gauss quadrature rules and the algebraic eigenvalue problem for a Jacobi matrix was first exploited
in the now classical paper by Golub and Welsch (Math. Comput. 23(106), 221–230, 1969). From then on many computational problems arising in the construction of (polynomial) Gauss quadrature formulas have been
reduced to solving...

Nondestructive evaluation of hidden surface damage by means of stationary thermographic methods requires the construction of approximated solutions of a boundary identification problem for an elliptic equation. In this paper, we describe and test a regularized reconstruction algorithm based on the linearization of this class of inverse problems. Th...

Stationary thermography can be used for investigating the functional form of a nonlinear cooling law that describes heat exchanges through an inaccessible part of the boundary of a conductor. In this paper, we obtain a logarithmic stability estimate for the associated nonlinear inverse problem. This stability estimate is obtained from the convergen...

Stationary thermography can be used for investigating the functional form of a nonlinear cooling law that describes heat exchanges through an inaccessible part of the boundary of a conductor. In this paper, we obtain a logarithmic stability estimate for the associated nonlinear inverse problem. This stability estimate is obtained from the convergen...

A thin plate Ω has an inaccessible side in contact with aggressive external agents. On the other side we are able to heat the plate and take temperature maps (thermal data) in laboratory conditions. Detecting and evaluating damages on the inaccessible side from thermal data requires the solution of a nonlinear inverse problem for the heat equation....

We consider a thin metallic plate whose top side is inaccessible and in contact with a corroding fluid. Heat exchange between
metal and fluid follows linear Newton's cooling law as long as the inaccessible side is not damaged. We assume that the effects
of corrosion are modelled by means of a nonlinear perturbation in the exchange law. On the other...

Assume that a Robin boundary condition models the presence of defects in the thermal (or electric) insulation of the top side of the open rectangular domain Ω R 2. The temperature (or electrostatic potential, respectively) in Ω satisfies the Laplace's equation. Here we study the inverse problem of recovering the heat exchange coefficient γ in the R...

We prove that the unitary factor appearing in the QR factorization of a suitably defined rational Krylov matrix transforms a Hermitian matrix having pairwise distinct eigenvalues into a diagonal-plus-semiseparable form with prescribed diagonal term. This transformation is essentially uniquely defined by its first column. Furthermore, we prove that...

This paper deals with the construction of effective heuristic methods for investigating the effect of corrosion on the inaccessible side of a thin metallic plate. In particular, we derive explicit formulas for the thin plate approximation of the positive functions γ and θ that, appearing in the Robin boundary condition u n x , a - a θ ( x )+aγ(x)ux...

This paper deals with the construction of effective heuristic methods for investigating the effect of corrosion on the inaccessible side of a thin metallic plate. In particular, we derive explicit formulas for the Thin Plate Approximation of the positive functions γ and θ that, in our model, describe energy dispersion and material loss respectively...

Thermographic inspection consists of the application of a heat flux to an object and subsequent temperature measurements on a portion of its surface. Lamps or laser devices are used for active heating, while temperature maps are collected by means of infrared cameras. In this framework, we assume that some damage (possibly due to corrosion) is expe...

We describe rank structures in generalized inverses of possibly rectangular banded matrices. In particular, we show that various
kinds of generalized inverses of rectangular banded matrices have submatrices whose rank depends on the bandwidth and on the
nullity of the matrix. Moreover, we give an explicit representation formula for some generalized...

The linear space of all proper rational functions with prescribed poles is considered. Given a set of points z i in the complex plane and the weights w i we define the discrete inner product 〈ϕ,ψ〉:=∑ i=0 n |w i | 2 ϕ(z i ) ¯ψ(z i )· We derive a method to compute the coefficients of a recurrence relation generating a set of orthonormal rational basi...

In this paper we study both direct and inverse eigenvalue problems for diagonal-plus-semiseparable (dpss) matrices. In particular, we show that the computation of the eigenvalues of a symmetric dpss matrix can be reduced by a congruence transformation to solving a generalized symmetric definite tridiagonal eigenproblem. Using this reduction, we dev...

We review some classical results on the zero distribution of orthogonal polynomials on the light of spectral theory for Toeplitz matrix sequences. In particular, we discuss some recent results by A. Kuijlaars and W. Van Assche on ortogonal polynomials with asymptotically periodic and discontinuously varying recurrence coefficients.

We present a fast algorithm for computing the QR factorization of Cauchy-like matrices with real nodes. The algorithm is based on the existence of certain generalized recurrences among the columns of Q and R T , does not require squaring the matrix, and fully exploits the displacement structure of Cauchy-like matrices. Moreover, we describe a class...

The space of all proper rational functions with prescribed real poles is considered. Given a set of points zi on the real line and the weights wi, we define the discrete inner product (formula in paper). In this paper we derive an efficient method to compute the coefficients of a recurrence relation generating a set of orthonormal rational basis fu...

We describe a stable algorithm, having linear complexity, for the solution of banded-plus-semiseparable linear systems. The
algorithm exploits the structural properties of the inverse of a semiseparable matrix. Stability is achieved by combining
these properties with partial pivoting techniques. Several numerical experiments are shown to confirm th...

Mixed and componentwise condition numbers are useful in understanding stability properties of algorithms for solving structured
linear systems. The DFT (discrete Fourier transform) is an essential building block of these algorithms. We obtain estimates
of mixed and componentwise condition numbers of the DFT. To this end, we explicitly compute certa...

We present a fast algorithm for computing the QR factorization of Cauchy matrices with real nodes. The algorithm works for almost any input matrix, does not require squaring the matrix, and fully exploits the displacement structure of Cauchy matrices. We prove that, if the determinant of a certain semiseparable matrix is non-zero, a three term recu...

We consider the problem of approximating a nonnegative function from the knowledge of its first Fourier coefficients. Here, we analyze a method introduced heuristically in a paper by Borwein and Huang (SIAM J. Opt. 5 (1995) 68–99), where it is shown how to construct cheaply a trigonometric or algebraic polynomial whose exponential is close in some...

A classical result of structured numerical linear algebra states that the inverse of a nonsingular semiseparable matrix is a tridiagonal matrix. Such a property of a semiseparable matrix has been proved to be useful for devising linear complexity solvers, for establishing recurrence relations among its columns or rows and, moreover, for efficiently...

New algorithms to reduce a diagonal plus a symmetric semiseparable matrix to a symmetric tridiagonal one and an algorithm to reduce a diagonal plus an unsymmetric semiseparable matrix to a bidiagonal one are considered. The algorithms are fast and stable, requiring a computational cost of O(N2), where N is the order of the considered matrix.

Let P be a symmetric positive de nite Pick matrix of order n. The following facts will be proven here: 1. P is the Gram matrix of a set of rational functions, with respect to a inner product de ned in terms of a generating function" associated to P ; 2. Its condition number is lower-bounded by a function growing exponentially in n. 3. P can be eect...

In this paper a technique based on isospectral flows is introduced to compute the eigenvalues of displacement structured matrices. The matrix structures dealt with are defined by means of singular displacement operators, and include, for example, Toeplitz, Toeplitz-plus-Hankel, and symmetric Loewner matrices. The flow starting from a matrix with a...

By means of recent results concerning spectral distributions of Toeplitz matrices, we show that the singular values of a sequence of block p-level Hankel matrices , generated by a p-variate, matrix-valued measure μ whose singular part is finitely supported, are always clustered at zero, thus extending a result known when p=1 and μ is real valued an...

We consider the problem of detecting corrosion damage on an inaccessible part of a metallic specimen. Electrostatic data are collected on an accessible part of the boundary. The adoption of a simplified model of corrosion appearance reduces our problem to recovering a functional coefficient in a Robin boundary condition for Laplace's equation. We r...

This paper is concerned with eigenvalue computations with displacement structured matrices, for example, Toeplitz or Toeplitz-plus-Hankel. A technique using isospectral flows is introduced. The flow is enforced to preserve the displacement structure of the originary matrix by means of a suitable constraint added in its formulation. In order to fulf...

Let u be harmonic in the interior of a rectangle Ω and satisfy the third-kind boundary condition un + γu = Φ where Φ ≥ 0, γ ≥ 0 with supports included in the bottom and in the top side of Ω, respectively. Recovering γ from a knowledge of Φ and of the trace of u on the bottom of Ω is a nonlinear inverse problem of interest in the field of nondestruc...

We consider the set of solutions A of the matrix equation A=zPAP * where |z|=1 and P * =P -1 =P k-1 for some integer k. In particular, we exhibit a suitable canonical form and some algebraic properties owned by all matrices in this set.

We study asymptotic and uniform properties of eigenvalues of a large class of real symmetric matrices that can be decomposed
into the sum of a Toeplitz matrix and a Hankel matrix. In particular, we show that their properties are essentially driven
by those of the Toeplitz part. A special subclass of structured matrices arising in an approximation p...

The present paper deals with the reconstruction of an unknown probability density u in [0,1] from a finite number of moments and some additional local a priori information (location and type of singularities of u or du dx). If the additional information may be represented by means of a density w, it is natural to select our estimator of u by minimi...

After proving that any Hankel matrix generated by moments of positive functions is conditioned essentially the same as the Hilbert matrix of the same size, we show a preconditioning technique, i.e., a congruence transform of the original Hankel matrix that drastically reduces its ill-conditioning. Applications of this result to classical orthogonal...

Let Vn,m be a rectangular n×m Vandermonde matrix with real nodes and let the number m of nodes be greater than the number n of powers;
in this paper we find, under mild restrictions on the nodes, that the behavior of the spectral conditioning of Vn,m for m→∞ is essentially the square root of the conditioning of the Hilbert matrix of order n.

By using suitable bordering and modification techniques, spectral properties of some classes of pentadiagonal symmetric matrices
are found.

## Projects

Projects (5)

The online journal "Symmetry" announces a special issue on "Symmetry in Numerical Linear and Multilinear Algebra", whose guest editor... it's me. See here for more details: http://www.mdpi.com/journal/symmetry/special_issues/Numerical_Linear_Multilinear_Algebra