arXiv subjects

Mattia Fontana

Publications and source records attributed to Mattia Fontana.

5 recordsLinked to original sources

arXiv2026

Slice and Partition Rank Criteria for Polynomial Zero-Avoidance

We study polynomial zero-avoidance over finite vector spaces by means of slice rank and partition rank. We first make the support-entropy method effective by showing how a finite dual certificate yields an explicit entropy gap whenever the coefficient support admits no probability distribution with uniform marginals. For the quadratic elementary symmetric polynomial over fields of characteristic three, the ternary structure of the coefficient support gives a certificate with optimal normalized margin and a uniform analytic bound for the corresponding higher-degree Erdős--Ginzburg--Ziv constant, avoiding a separate optimization for each field. We then use partition rank to handle solutions in pairwise distinct variables. Equality profiles are encoded by contracted local tensors, reducing the global problem to finitely many slice-rank estimates. Applying this reduction on the multiplicative torus gives restricted-alphabet zero-sum bounds with exponential base below the alphabet size. Coordinatewise inversion and support stratification then yield, to the best of our knowledge, the first nontrivial exponential bound for the higher-degree Erdős--Ginzburg--Ziv problem over $\mathbb{F}_5^n$ associated with the fourth elementary symmetric polynomial.

math.CO↗

arXiv2026

Kinetic models of opinion-driven epidemic dynamics modulated by graphons

We introduce new kinetic equations to describe epidemics' spread while accounting for individuals' opinions on protective behaviors. Opinion exchanges occur on a social network represented by a graphon, whose choice strongly influences the dynamics and leads to the emergence of complex nonlinear phenomena, like the creation of opinion leaders or the spontaneous formation of epidemic waves. Starting from individual-based interactions, we derive a nonlinear nonlocal Fokker-Planck model involving reaction terms and degenerate drift-diffusion operators, which depend on the underlying graphon. We establish rigorous results of convergence to equilibrium in $L^1$ space, via relative entropy estimates, and in homogeneous Sobolev spaces $\dot{H}^{-s}$, $s \in \big(\frac{1}{2}, 1\big)$, using Fourier-based techniques. We then design a structure-preserving scheme for the coupled opinion-epidemiological system, highlighting graphon effects: opinion leaders supporting protective behaviors limit disease spread, whereas influenceable individuals may shift toward opposing views, worsening epidemics. At last, we introduce a time-dependent quantity analogous to the effective reproduction number, whose oscillations are linked with the formation of epidemic waves. Notably, these waves are not induced by an explicit external forcing but they naturally emerge from the interactions between agents, depending on the connectivity level prescribed by the graphon.

math.AP↗

arXiv2026

Graham conjecture on small sets in abelian groups

A famous conjecture of Graham asserts that every set $A \subseteq \mathbb{Z}_p \setminus \{0\}$ can be ordered so that all partial sums are distinct. Although this conjecture was recently proved for sufficiently large primes by Pham and Sauermann in~\cite{PM} (combined with earlier results of \cite{BBKMM}), it remains open for general abelian groups, even in the cyclic case $\mathbb{Z}_k$. In this paper, using a recursive approach, we investigate the sequenceability of subsets $A$ in generic abelian groups for small values of $|A|$. We prove that any subset $A \subseteq G\setminus\{0\}$ with $|A| \leq 20$ is sequenceable where previously it was known only for $|A|\leq 9$. This bound is improved to $|A| \leq 22$ for zero-sum subsets. Finally, regarding the related CMPP conjecture, we show that zero-sum subsets without inverse pairs are sequenceable for $|A| \leq 23$.

math.NT↗

arXiv2025

Viscophoretic particle transport

Viscosity is a fundamental property of liquids and determines the diffusivity of suspended particles. A gradient in viscosity leads to a gradient in diffusivity, yet it is unknown whether such a gradient can lead to directed transport of particles. In this work, we generate a steep, stable viscosity gradient in a microfluidic channel and image the resulting transport of suspended nanoparticles at the single-particle level using high-resolution microscopy. We observe high viscophoretic drift velocities that significantly exceed theoretical predictions. In addition, we utilize viscophoresis for a new type of particle trap. We provide a first quantification of a transport phenomenon that is of importance in any system and any application exhibiting viscosity gradients, for example in separation using membrane technology as well as in inter- and intracellular biomolecular transport.

physics.flu-dyn↗

arXiv2014

Performance of the ALICE muon trigger RPCs during LHC Run I

ALICE (A Large Ion Collider Experiment) studies the transition of nuclear matter to a deconfined phase known as Quark Gluon Plasma, in ultra-relativistic heavy-ion collisions at the LHC. ALICE is equipped with a muon spectrometer for the detection of quarkonia and heavy flavour particles. The trigger system of the spectrometer consists of 72 RPCs arranged in four detection planes, with a total area of 140 m^{2}. In the first three years of LHC operation, the muon trigger system was fully operational in data-taking in pp, Pb-Pb and p-Pb collisions. The RPC performance and stability throughout the whole data-taking period is presented and discussed, for the parameters such as the efficiency, the dark counting rate, the dark current and the cluster size.

physics.ins-det↗