# Maurizio PartonUniversità degli Studi G. d'Annunzio Chieti e Pescara | UNICH · Department of Economics

Maurizio Parton

PhD in mathematics

Working in differential geometry and machine learning

## About

60

Publications

5,859

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664

Citations

Introduction

**Skills and Expertise**

Additional affiliations

November 2002 - present

## Publications

Publications (60)

This paper presents the second-place methodology in the Volvo Discovery Challenge at ECML-PKDD 2024, where we used Long Short-Term Memory networks and pseudo-labeling to predict maintenance needs for a component of Volvo trucks. We processed the training data to mirror the test set structure and applied a base LSTM model to label the test data iter...

A coverage assumption is critical with policy gradient methods, because while the objective function is insensitive to updates in unlikely states, the agent may need improvements in those states to reach a nearly optimal payoff. However, this assumption can be unfeasible in certain environments, for instance in online learning, or when restarts are...

Portfolio allocation represents a significant challenge within financial markets, traditionally relying on correlation or covariance matrices to delineate relationships among stocks. However, these methodologies assume time stationarity and only capture linear relationships among stocks. In this study, we propose to substitute the conventional Pear...

In 2021, Adam Zsolt Wagner proposed an approach to disprove conjectures in graph theory using Reinforcement Learning (RL). Wagner's idea can be framed as follows: consider a conjecture, such as a certain quantity f(G) < 0 for every graph G; one can then play a single-player graph-building game, where at each turn the player decides whether to add a...

This paper summarizes the activities regarding the development of Artificial Intelligence (AI) for Sustainability conducted by the members of the AIIS (Artificial Intelligence and Intelligent Systems) node of the University "G. d'Annunzio" of Chieti-Pescara (Ud'A).

Portfolio allocation represents a significant challenge within financial markets, traditionally relying on correlation or covariance matrices to delineate relationships among stocks. However, these methodologies assume time stationarity and only capture linear relationships among stocks.
In this study, we propose to substitute the conventional Pear...

Deep learning architectures suffer from depth-related performance degradation, limiting the effective depth of neural networks. Approaches like ResNet are able to mitigate this, but they do not completely eliminate the problem. We introduce Global Neural Networks (GloNet), a novel architecture overcoming depth-related issues, designed to be superim...

We use Graph Neural Networks on signature-augmented graphs derived from time series for Predictive Maintenance. With this technique, we propose a solution to the Intelligent Data Analysis Industrial Challenge 2024 on the newly released SCANIA Component X dataset. We describe an Exploratory Data Analysis and preprocessing of the dataset, proposing i...

Community detection for time series without prior knowledge poses an open challenge within complex networks theory. Traditional approaches begin by assessing time series correlations and maximizing modularity under diverse null models. These methods suffer from assuming temporal stationarity and are influenced by the granularity of observation inte...

The Consumer Financial Protection Bureau defines the notion of payoff amount as the amount that has to be payed at a particular time in order to completely pay off the debt, in case the lender intends to pay off the loan early, way before the last installment is due (CFPB 2020). This amount is well-understood for loans at compound interest, but muc...

Computational units in artificial neural networks follow a simplified model of biological neurons. In the biological model, the output signal of a neuron runs down the axon, splits following the many branches at its end, and passes identically to all the downward neurons of the network. Each of the downward neurons will use their copy of this signa...

This paper aims to investigate the possibility of using artificial intelligence (AI) to resolve the legal issues raised by the Covid-19 emergency about the fate of continuing execution contracts, or those with deferred or periodic execution, as well as, more generally, to deal with exceptional events and contingencies. We first study whether the It...

AlphaGo, AlphaGo Zero, and all of their derivatives can play with superhuman strength because they are able to predict the win-lose outcome with great accuracy. However, Go as a game is decided by a final score difference, and in final positions AlphaGo plays suboptimal moves: this is not surprising, since AlphaGo is completely unaware of the final...

The paper is part of an attempt of understanding non-Kähler threefolds. We start by looking at compact complex non-Kähler threefolds with algebraic dimension two and admitting lcK metrics. Under certain assumptions, we prove that they are blown-up quasi-bundles over a projective surface.

Having access to an exploring restart distribution (the so-called wide coverage assumption) is critical with policy gradient methods. This is due to the fact that, while the objective function is insensitive to updates in unlikely states, the agent may still need improvements in those states in order to reach a nearly optimal payoff. For this reaso...

A Pseudo-Random Number Generator (PRNG) is any algorithm generating a sequence of numbers approximating properties of random numbers. These numbers are widely employed in mid-level cryptography and in software applications. Test suites are used to evaluate the quality of PRNGs by checking statistical properties of the generated sequences. These seq...

A Pseudo-Random Number Generator (PRNG) is any algorithm generating a sequence of numbers approximating properties of random numbers. These numbers are widely employed in mid-level cryptography and in software applications. Test suites are used to evaluate PRNGs quality by checking statistical properties of the generated sequences. These sequences...

We present an ongoing effort to implement Universal Algebra in the UniMath system. Our aim is to develop a general framework for formalizing and studying Universal Algebra in a proof assistant. By constituting a formal system for isolating the invariants of the theory we are interested in -- that is, general algebraic structures modulo isomorphism...

The paper is part of an attempt of understanding non-K\"ahler threefolds. We start by looking at compact complex threefolds with algebraic dimension two and admitting locally conformally K\"ahler metrics. Under mild assumptions, we prove that they are blown-up quasi-bundles over a projective curve.

Pseudo-Random Numbers Generators (PRNGs) are algorithms produced to generate long sequences of statistically uncorrelated numbers, i.e. Pseudo-Random Numbers (PRNs). These numbers are widely employed in mid-level cryptography and in software applications. Test suites are used to evaluate PRNGs quality by checking statistical properties of the gener...

Pseudo-Random Numbers Generators (PRNGs) are algorithms produced to generate long sequences of statistically uncorrelated numbers, i.e. Pseudo-Random Numbers (PRNs). These numbers are widely employed in mid-level cryptography and in software applications. Test suites are used to evaluate PRNGs quality by checking statistical properties of the gener...

We develop a new model that can be applied to any perfect information two-player zero-sum game to target a high score, and thus a perfect play. We integrate this model into the Monte Carlo tree search-policy iteration learning pipeline introduced by Google DeepMind with AlphaGo. Training this model on 9x9 Go produces a superhuman Go player, thus pr...

A classical theorem of Kervaire states that products of spheres are parallelizable if and only if at least one of the factors has odd dimension. Two explicit parallelizations on such products seem to be quite natural, and have been previously studied by the erst named author in [32]. The present paper is devoted to the three choices G = G , Spin(7)...

Starting from the 2001 Thomas Friedrich’s work on Spin ( 9 ) , we review some interactions between Spin ( 9 ) and geometries related to octonions. Several topics are discussed in this respect: explicit descriptions of the Spin ( 9 ) canonical 8-form and its analogies with quaternionic geometry as well as the role of Spin ( 9 ) both in the classical...

Starting from Thomas Friedrich’s work “Weak Spin(9) structures on 16-dimensional Riemannian manifolds”, we review several interactions between Spin(9) and geometries related to octonions. Several topics are discussed in this respect: explicit descriptions of the Spin(9) canonical 8-form and its analogies with quaternionic geometry, the role of Spin...

We propose a multiple-komi modification of the AlphaGo Zero/Leela Zero paradigm. The winrate as a function of the komi is modeled with a two-parameters sigmoid function, so that the neural network must predict just one more variable to assess the winrate for all komi values. A second novel feature is that training is based on self-play games that o...

We give an algorithm to enumerate all primitive abundant numbers (briefly, PANs) with a fixed $\Omega$ (the number of prime factors counted with their multiplicity), and explicitly find all PANs up to $\Omega=6$, count all PANs and square-free PANs up to $\Omega=7$ and count all odd PANs and odd square-free PANs up to $\Omega=8$. We find primitive...

In this paper we review the well-known fact that the only spheres admitting an almost complex structure are S^2 and S^6. The proof described here uses characteristic classes and the Bott periodicity theorem in topological K-theory. This paper originates from the talk "Almost Complex Structures on Spheres" given by the second author at the MAM1 work...

We obtain structure results for locally conformally symplectic Lie algebras. We classify locally conformally symplectic structures on four-dimensional Lie algebras and construct locally conformally symplectic structures on compact quotients of all four-dimensional connected and simply connected solvable Lie groups.

We prove that any line bundle on Oeljeklaus-Toma manifolds of simple type is flat. As a corollary, we get that Oeljeklaus-Toma manifolds of simple type are rigid.

In this paper we study some structure properties of primitive weird numbers in terms of their factorization. We give sufficient conditions to ensure that a positive integer is weird. Two algorithms for generating weird numbers having a given number of distinct prime factors are presented. These algorithms yield primitive weird numbers of the form m...

We give an inductive construction for irreducible Clifford systems on
Euclidean vector spaces. We then discuss how this notion can be adapted to
Riemannian manifolds, and outline some developments in octonionic geometry.

TheHermitian symmetric spaceM = EIII appears in the classification of complete simply connected
Riemannian manifolds carrying a parallel even Clifford structure [19]. This means the existence of a real oriented
Euclidean vector bundle E over it together with an algebra bundle morphism φ : Cl0(E) → End(TM)
mapping Ʌ2E into skew-symmetric endomorphis...

The Hermitian symmetric space M = EIII appears in the classification of complete simply connected Riemannian manifolds carrying a parallel even Clifford structure [19]. This means the existence of a real oriented Euclidean vector bundle E over it together with an algebra bundle morphism φ : Cl⁰(E) → End(TM) mapping Δ²E into skew-symmetric endomorph...

We propose a new technique combining dynamic and static analysis of programs to find linear invariants. We use a statistical tool, called simple component analysis, to analyze partial execution traces of a given program. We get a new coordinate system in the vector space of program variables, which is used to specialize numerical abstract domains....

We deal with Riemannian properties of the octonionic Hopf fibration
S^{15}-->S^8, in terms of the structure given by its symmetry group Spin(9). In
particular, we show that any vertical vector field has at least one zero, thus
reproving the non-existence of S^1 subfibrations. We then discuss
Spin(9)-structures from a conformal viewpoint and determi...

A locally conformally K\"ahler (LCK) manifold is a complex manifold covered
by a K\"ahler manifold, with the covering group acting by homotheties. We show
that if such a compact manifold X admits a holomorphic submersion with positive
dimensional fibers at least one of which is of K\"ahler type, then X is
globally conformally K\"ahler or biholomorp...

We give an interpretation of the maximal number of linearly independent
vector fields on spheres in terms of the Spin(9) representation on R^16. This
casts an insight on the role of Spin(9) as a subgroup of SO(16) on the
existence of vector fields on spheres, parallel to the one played by complex,
quaternionic and octonionic structures on R^2, R^4...

For a Spin(9)-structure on a Riemannian manifold M
16 we write explicitly the matrix ψ of its Kähler 2-forms and the canonical 8-form ΦSpin(9). We then prove that ΦSpin(9) coincides up to a constant with the fourth coefficient of the characteristic polynomial of ψ. This is inspired by lower dimensional situations, related to Hopf fibrations and to...

We present a tool which performs abstract interpretation based static analysis of numerical variables. The novelty is that
the analysis is parametric, and parameters are chosen by applying a variant of principal component analysis to partial execution
traces of programs.

We propose a new technique for developing ad-hoc numerical abstract domains by means of statistical analysis. We apply Principal
Component Analysis to partial execution traces of programs, to find out a “best basis” in the vector space of program variables.
This basis may be used to specialize numerical abstract domains, in order to enhance the pre...

We consider locally conformal Kähler geometry as an equivariant, homothetic Kähler geometry (K, Γ). We show that the de Rham class of the Lee form can be naturally identified with the homomorphism projecting Γ to its dilation factors, thus completing the description of locally conformal Kähler geometry in this equivariant setting. The rank rM
of a...

We consider locally conformal Kähler geometry as an equivariant (homothetic) Kähler geometry: a locally conformal Kähler manifold is, up to equivalence, a pair (K,Γ), where K is a Kähler manifold and Γ is a discrete Lie group of biholomorphic homotheties acting freely and properly discontinuously. We define a new invariant of a locally conformal Kä...

We characterize compact locally conformal parallel G2 (respectively, Spin(7)) manifolds as fiber bundles over S1 with compact nearly Kähler (respectively, compact nearly parallel G2) fiber. A more specific characterization is provided when the local parallel structures are flat.

We characterize compact locally conformal parallel $G_2$ (respectively, $Spin(7)$) manifolds as fiber bundles over $S^1$ with compact nearly K\"ahler (respectively, compact nearly parallel $G_2$) fiber. A more specific characterization is provided when the local parallel structures are flat.

A classical theorem of Kervaire states that products of spheres are parallelizable if and only if at least one of the fac-tors has odd dimension. We give explicit parallelizations. We show that the Calabi-Eckmann Hermitian structures on products of two odd-dimensional spheres are invariant with respect to these parallelizations.

We define reduction of locally conformal Kähler manifolds, considered as conformal Hermitian manifolds, and we show its equivalence with an unpublished construction given by Biquard and Gauduchon. We show the compatibility between this reduction and Kähler reduction of the universal cover. By a recent result of Kamishima and the second author, in t...

This paper classifies Hermitian structures on 6-dimensional nilmanifolds M=Gamma\G for which the fundamental 2-form is partial derivative(partial derivative) over bar -closed, a condition that is shown to depend only on the underlying complex structure J of M. The space of such J is described when G is the complex Heisenberg group, and explicit sol...

The aim of this paper is to write an explicit orthonormal parallelization for all parallelizable products of spheres, using an explicit isomorphism with a trivial vector bundle.

We describe a family of locally conformal Kaehler metrics on class 1
Hopf surfaces H containing some recent metrics constructed by P.
Gauduchon and L. ornea. We study some canonical foliations associated to
these metrics, in particular a 2-dimensional foliation E that is shown
to be independent of the metric. We elementary prove that E has compact...

In this paper we describe a family of locally conformal Kähler metrics on class 1 Hopf surfaces H
α,β containing some recent metrics constructed in [GO98]. We study some canonical foliations associated to these metrics, in particular a 2-dimensional foliation ℰα,β that is shown to be independent of the metric. We prove with elementary tools that ℰα...

## Questions

Question (1)

I'm looking for examples of finite subgroups of Spin(9), acting freely on S^{15}. Any idea?