arXiv subjects

Piero Giacomelli

Publications and source records attributed to Piero Giacomelli.

13 recordsLinked to original sources

arXiv2026

Beyond the briscola advantage: a Monte Carlo dominance test for deterministic strategies in two-player Briscola Game

Briscola is a traditional Italian trick-taking card game whose simplest form is played by two players. Popular folklore credits victory almost entirely to the player who is dealt more cards of the trump suit (the so-called \emph{briscola}), so that the game would be a near-deterministic function of the deal. We test this folklore against a pre-registered alternative, namely that two deterministic rule-based refinements of the naive greedy policy -- a briscola-hoarding policy $\stratH$ and a public-information counter policy $\stratC$ -- dominate the greedy baseline $\stratG$ irrespective of trump luck. To this end we run a round-robin Monte Carlo tournament of $10^{6}$ simulated games across the nine ordered pairings of $(\stratG,\stratH,\stratC)$, retaining approximately $1.08\times 10^{5}$ non-tied games per pairing, and we analyse the resulting outcomes through Wilson confidence intervals, a Bonferroni-corrected pairwise binomial test, and a logistic regression of the game outcome on the strategy pair and on the signed briscola-count imbalance, so as to quantify the relative contribution of strategy and trump luck. We close with a reproducibility appendix that makes the simulation, the random seed and the analysis script fully deterministic.

cs.GT↗

arXiv2026

Expander Evolution Algebras

We introduce \emph{expander evolution algebras} (EEAs), a class of nonassociative algebras defined over an arbitrary field $\K$ in which the underlying undirected loopless graph of the algebra -- in the sense of Kowalski -- is an expander graph in the classical sense of Cheeger. Starting from the formal graph definition of Kowalski and the algebraic framework of Tian, we establish a dictionary between combinatorial expansion and algebraic structure: the Cheeger constant of the associated graph governs connectivity, the subalgebra lattice, the growth of the evolution sequence, and -- over $\R$ and $\C$ -- the spectral gap of the evolution operator. Over a general field $\K$ we prove that EEAs are always connected and simple (as evolution algebras), carry no proper large evolution subalgebras, and that every generator of a \emph{symmetric} EEA is algebraically persistent. Over $\C$ we obtain the sharp Alon--Boppana lower bound for the second eigenvalue of the evolution operator, leading to the definition of \emph{Ramanujan evolution algebras} as optimal expanders. We also construct families of EEAs from Cayley graphs of finite groups. We close with open problems.

math.RA↗

arXiv2026

Log-Concavity and Infinite Log-Concavity of Linear Recurrent Sequences with Linear Coefficients via Companion Matrix Methods

We study log-concavity properties of real sequences $(a_n)_{n \ge 0}$ satisfying a $d$-th order linear recurrence whose coefficients are linear functions of $n$; the so-called P-recursive (or holonomic) sequences. Writing the recurrence in companion-matrix form $\mathbf{v}_{n+1} = M_n\,\mathbf{v}_n$ with $M_n = nA + B$, we show that the log-concave operator value $\mathcal{L}(a_n) = b_n \coloneqq a_n^2 - a_{n+1}a_{n-1}$ is a quadratic form in the state vector $\mathbf{v}_n$, and identify the matrix $Q_n = Q^{(0)} + nQ^{(1)}$ whose positive semi-definiteness gives a sufficient condition for log-concavity. For the class of second-order recurrences with constant coefficients, we prove a tight (necessary and sufficient) criterion for the sequence to be $\infty$-log-concave, a consequence of the fact that $\mathcal{L}(a_n)$ is itself a geometric sequence so that $\mathcal{L}^2(a_n) = 0$ identically. We obtain analogous tight criteria for sequences fixed by $\mathcal{L}$, and for P-recursive sequences satisfying a dominant-root asymptotic behaviour. We leave some further insight in case this criteria break down in full generality.

math.CO↗

arXiv2026

The Bollob\'{a}s--Nikiforov Conjecture for Complete Multipartite Graphs and Dense $K_4$-Free Graphs

The Bollob\'as--Nikiforov conjecture asserts that for any graph $G \neq K_n$ with $m$ edges and clique number $\omega(G)$, \[ \lambda_1^2(G) + \lambda_2^2(G) \;\leq\; 2\!\left(1 - \frac{1}{\omega(G)}\right)m, \] where $\lambda_1(G) \geq \lambda_2(G) \geq \cdots \geq \lambda_n(G)$ are the adjacency eigenvalues of $G$. We prove the conjecture for all complete multipartite graphs $K_{n_1,\ldots,n_r}$ with $n_1 + \cdots + n_r > r$. The proof computes the full spectrum via a secular equation, establishes that $\lambda_2 = 0$ whenever the graph has more vertices than parts, and then applies Nikiforov's spectral Tur\'an theorem; equality holds if and only if all parts have equal size. We also prove a stability result for $K_4$-free graphs whose spectral radius is near the Tur\'an maximum: such graphs are structurally close to the balanced complete tripartite graph, and as a consequence the conjecture holds for all $K_4$-free graphs with $m = \Omega(n^2)$ when $n$ is sufficiently large. Finally, we identify the precise obstruction preventing a Hoffman-bound approach from settling the conjecture for $K_4$-free graphs with independence number $\alpha(G) \geq n/3$.

math.CO↗

arXiv2025

On Log-Concave Operator Acting on Sequences and Series

In this paper, we investigate the properties of sequences and series under the action of the log-concave operator $\mathcal{L}$. We explore the relationship between the convergence of a sequence $(a_k)$ and the convergence of sequences and series derived by applying $\mathcal{L}$ iteratively. These results demonstrate the strong regularity properties of log-concave sequences and provide a framework for analyzing the convergence of sequences and series derived from the log-concave operator. The findings have implications for combinatorics, probability, optimization, and related fields, opening new avenues for further research on the behavior of log-concave sequences and their associated operators.

math.CO↗

arXiv2025

Ducci Matrices in $p$-adic Context

In this paper, we mutuate the concept of Ducci matrices to the $p$-adic setting, generalizing the classical Ducci sequences to the framework of $p$-adic numbers. The classical Ducci operator, which iteratively computes the absolute differences of neighboring elements in a sequence or matrix, is redefined using the $p$-adic absolute value $| \cdot |_p$. We investigate the dynamics of $p$-adic Ducci sequences for matrices over $\mathbb{Q}_p$, focusing on their convergence and periodicity properties.

math.NT↗

arXiv2021

$p$-adic Ducci Sequences: a short note

In this short note we formalized the definition for the Ducci operator $D$ in the context of the $p$-adic field $\mathbb{Q}_p$ as a natural extension of the classical one. Moreover we will describe the behavior of the operator and will provide some simple results as a counterpart to the classical one.

math.NT↗

arXiv2020

Implementing Suffix Array Algorithm Using Apache Big Table Data Implementation

In this paper we will describe a new approach on the well-known suffix-array algorithm using Big Table Data Technology. We will demonstrate how it is possible to refactor a well-known algorithm coupled by taking advantage of an high-performance distributed datastore, to illustrate the advantages of using datastore cloud related technology for storing large text sequences and retrieving them. A case study using DNA strings, considered one of the most difficult pattern matching problem, will be described and evaluated to demonstrate the potentiality of this implementation. Further discussion on performances and other big data related issues will be described as well as new possible lines of research in big data technology for precise medical applications.

cs.DB↗

arXiv2014

The Eve of 3D Printing in Telemedicine: State of the Art and Future Challenges

3D printing has raised a lot of attention from fields outside the manufacturing one in the last years. In this paper, we will illustrate some recent advances of 3D printing technology, applied to the field of telemedicine and remote patient care. The potentiality of this technology will be detailed without lab examples. Some crucial aspect such as the regulation of these devices and the need of some standards will also be discussed. The purpose of this paper is to present some of the most promising applications of such technology.

cs.OH↗

arXiv2012

Can an Ad-hoc ontology Beat a Medical Search Engine? The Chronious Search Engine case

Chronious is an Open, Ubiquitous and Adaptive Chronic Disease Management Platform for Chronic Obstructive Pulmonary Disease(COPD) Chronic Kidney Disease (CKD) and Renal Insufficiency. It consists of several modules: an ontology based literature search engine, a rule based decision support system, remote sensors interacting with lifestyle interfaces (PDA, monitor touch-screen) and a machine learning module. All these modules interact each other to allow the monitoring of two types of chronic diseases and to help clinician in taking decision for care purpose. This paper illustrates how the ontology search engine was created and fed and how some comparative test indicated that the ontology based approach give better results, on some estimation parameters, than the main reference web search engine.

cs.IR↗

arXiv2011

Using Soft Computer Techniques on Smart Devices for Monitoring Chronic Diseases: the CHRONIOUS case

CHRONIOUS is an Open, Ubiquitous and Adaptive Chronic Disease Management Platform for Chronic Obstructive Pulmonary Disease(COPD) Chronic Kidney Disease (CKD) and Renal Insufficiency. It consists of several modules: an ontology based literature search engine, a rule based decision support system, remote sensors interacting with lifestyle interfaces (PDA, monitor touchscreen) and a machine learning module. All these modules interact each other to allow the monitoring of two types of chronic diseases and to help clinician in taking decision for cure purpose. This paper illustrates how some machine learning algorithms and a rule based decision support system can be used in smart devices, to monitor chronic patient. We will analyse how a set of machine learning algorithms can be used in smart devices to alert the clinician in case of a patient health condition worsening trend.

cs.AI↗

arXiv2011

Log-concavity of Lucas Sequences of first kind

In these notes we address the study of the log-concave operator acting on Lucas Sequences of first kind. We will find for which initial values a generic Lucas sequence is log-concave, and using this we show when the same sequence is infinite log-concave. The main result will help to find the log-concavity of some well known recurrent sequences like Fibonacci and Mersenne. Some possible generalization for a complete classification of the log-concave operator applied to general linear recurrent sequences is proposed.

math.NT↗

arXiv2010

Wheel Random Apollonian Graphs

In this paper a subset of High-Dimensional Random Apollonian networks, that we called Wheel Random Apollonian Graphs (WRAG), is considered. We show how to generate a Wheel Random Apollonian Graph from a wheel graph. We analyse some basic graph properties like vertices and edges cardinality, some question concerning cycles and the chromaticity in such type of graphs, we suggest further work on this type of graphs.

cs.DM↗