arXiv subjects

Fabio Martinelli

Publications and source records attributed to Fabio Martinelli.

At least 19 recordsLinked to original sources

arXiv2026

Automated Compliance Mapping in Cloud Security with Domain-Adapted Sentence Transformers

Mapping cloud security controls to technical metrics is currently a manual process. This paper proposes domain adaptation of Sentence Transformer models to automate it. We build a training corpus of 3,499 semantic pairs from five European security standards and a set of technical metrics, then expand it via back-translation and LLM-based paraphrasing to up to 13,996 samples across four scenarios. We fine-tune five architectures and evaluate their performance on two independent tasks: control-to-metric and cross-standard controls association. All fine-tuned models outperform their zero-shot baselines. On the control-to-metric task, the best model gains up to 23 nDCG@10 points, while on the cross-standard control task, \textit{multi-qa-mpnet-dot-v1} under back-translation reaches 0.870 nDCG@10. The results show that in-domain training data is a primary driver of performance for the considered case studies.

cs.CL↗

arXiv2025

Long time behaviour of one facilitated kinetically constrained models: results and open problems

Kinetically constrained models (KCMs) are interacting particle systems introduced in the '80s by physicists to have accessible stochastic models with glassy-type dynamics. The key mechanism behind the complex evolution of these otherwise simple models is the so-called dynamical facilitation, a feature embedded into the models via appropriate kinetic constraints. KCMs are reversible with respect to a Bernoulli product measure, and the analysis of their stationary evolution has witnessed significant progress in the last decade. Unfortunately, in the interesting regime when the equilibrium density of the facilitating vertices is small, many fundamental questions concerning the non-stationary evolution of even the simplest models remain unsolved. In this paper, we discuss some of these questions, along with partial new results and conjectures, for the one facilitated model and its variants, as well as for the biased annihilating branching process.

math.PR↗

arXiv2025

Cutoff for East models

We consider the East model in $\mathbb Z^d$, an example of a kinetically constrained interacting particle system with oriented constraints, together with one of its natural variant. Under any ergodic boundary condition it is known that the mixing time of the chain in a box of side $L$ is $\Theta(L)$ for any $d\ge 1$. Moreover, with minimal boundary conditions and at low temperature, i.e. low equilibrium density of the facilitating vertices, the chain exhibits cutoff around the mixing time of the $d=1$ case. Here we extend this result to high equilibrium density of the facilitating vertices. As in the low density case, the key tool is to prove that the speed of infection propagation in the $(1,1,\dots,1)$ direction is larger than $d$ $\times$ the same speed along a coordinate direction. By borrowing a technique from first passage percolation, the proof links the result to the precise value of the critical probability of oriented (bond or site) percolation in $\mathbb Z^d$.

math.PR↗

arXiv2025

Optimisation of cyber insurance coverage with selection of cost effective security controls

Nowadays, cyber threats are considered among the most dangerous risks by top management of enterprises. One way to deal with these risks is to insure them, but cyber insurance is still quite expensive. The insurance fee can be reduced if organisations improve their cyber security protection, i.e., reducing the insured risk. In other words, organisations need an investment strategy to decide the optimal amount of investments into cyber insurance and self-protection. In this work, we propose an approach to help a risk-averse organisation to distribute its cyber security investments in a cost-efficient way. What makes our approach unique is that next to defining the amount of investments in cyber insurance and self-protection, our proposal also explicitly defines how these investments should be spent by selecting the most cost-efficient security controls. Moreover, we provide an exact algorithm for the control selection problem considering several threats at the same time and compare this algorithm with other approximate algorithmic solutions.

cs.CR↗

arXiv2022

On a front evolution problem for the multidimensional East model

We consider a natural front evolution problem the East process on $\mathbb{Z}^d, d\ge 2,$ a well studied kinetically constrained model for which the facilitation mechanism is oriented along the coordinate directions, as the equilibrium density $q$ of the facilitating vertices vanishes. Starting with a unique unconstrained vertex at the origin, let $S(t)$ consist of those vertices which became unconstrained within time $t$ and, for an arbitrary positive direction $\mathbf x,$ let $v_{\max}(\mathbf x),v_{\min}(\mathbf x )$ be the maximal/minimal velocities at which $S(t)$ grows in that direction. If $\mathbf x$ is independent of $q$, we prove that $v_{\max}(\mathbf x)= v_{\min}(\mathbf x)^{(1+o(1))}=γ(d) ^{(1+o(1))}$ as $q\to 0$, where $γ(d)$ is the spectral gap of the process on $\mathbb{Z}^d$. We also analyse the case in which some of the coordinates of $\mathbf x$ vanish as $q\to 0$. In particular, for $d=2$ we prove that if $\mathbf x$ approaches one of the two coordinate directions fast enough, then $v_{\max}(\mathbf x)= v_{\min}(\mathbf x)^{(1+o(1))}=γ(1) ^{(1+o(1))}=γ(d)^{d(1+o(1))},$ i.e. the growth of $S(t)$ close to the coordinate directions is dictated by the one dimensional process. As a result the region $S(t)$ becomes extremely elongated inside $\mathbb{Z}^d_+$. We also establish mixing time cutoff for the chain in finite boxes with minimal boundary conditions. A key ingredient of our analysis is the renormalisation technique of arXiv:1404.7257 to estimate the spectral gap of the East process. Here we extend this technique to get the main asymptotics of a suitable principal Dirichlet eigenvalue of the process.

math.PR↗

arXiv2022

Sharp threshold for the FA-2f kinetically constrained model

The Fredrickson-Andersen 2-spin facilitated model on $\mathbb{Z}^d$ (FA-2f) is a paradigmatic interacting particle system with kinetic constraints (KCM) featuring dynamical facilitation, an important mechanism in condensed matter physics. In FA-2f a site may change its state only if at least two of its nearest neighbours are empty. Although the process is reversible w.r.t. a product Bernoulli measure, it is not attractive and features degenerate jump rates and anomalous divergence of characteristic time scales as the density $q$ of empty sites tends to $0$. A natural random variable encoding the above features is $τ_0$, the first time at which the origin becomes empty for the stationary process. Our main result is the sharp threshold \[τ_0=\exp\Big(\frac{d\cdotλ(d,2)+o(1)}{q^{1/(d-1)}}\Big)\quad \text{w.h.p.}\] with $λ(d,2)$ the sharp threshold constant for 2-neighbour bootstrap percolation on $\mathbb{Z}^d$, the monotone deterministic automaton counterpart of FA-2f. This is the first sharp result for a critical KCM and it compares with Holroyd's 2003 result on bootstrap percolation and its subsequent improvements. It also settles various controversies accumulated in the physics literature over the last four decades. Furthermore, our novel techniques enable completing the recent ambitious program on the universality phenomenon for critical KCM and establishing sharp thresholds for other two-dimensional KCM.

math.PR↗

arXiv2022

Fredrickson--Andersen model in two dimensions

The present expository article overviews recent mathematical advances on the Fredrickson--Andersen kinetically constrained spin model in two dimensions. It was introduced in physics as a toy model for recovering the glassy phenomenology in supercooled liquids close to the glass transition via dynamic constraints as opposed to static interactions.

cond-mat.dis-nn↗

arXiv2021

Coalescing and branching simple symmetric exclusion process

Motivated by kinetically constrained interacting particle systems (KCM), we consider a reversible coalescing and branching simple exclusion process on a general finite graph $G=(V,E)$ dual to the biased voter model on $G$. Our main goal are tight bounds on its logarithmic Sobolev constant and relaxation time, with particular focus on the delicate slightly supercritical regime in which the equilibrium density of particles tends to zero as $|V|\rightarrow \infty$. Our results allow us to recover very directly and improve to $\ell^p$-mixing, $p\ge 2$, and to more general graphs, the mixing time results of Pillai and Smith for the Fredrickson-Andersen one spin facilitated (FA-$1$f) KCM on the discrete $d$-dimensional torus. In view of applications to the more complex FA-$j$f KCM, $j>1$, we also extend part of the analysis to an analogous process with a more general product state space.

math.PR↗

arXiv2020

alurity, a toolbox for robot cybersecurity

The reuse of technologies and inherent complexity of most robotic systems is increasingly leading to robots with wide attack surfaces and a variety of potential vulnerabilities. Given their growing presence in public environments, security research is increasingly becoming more important than in any other area, specially due to the safety implications that robot vulnerabilities could cause on humans. We argue that security triage in robotics is still immature and that new tools must be developed to accelerate the testing-triage-exploitation cycle, necessary for prioritizing and accelerating the mitigation of flaws. The present work tackles the current lack of offensive cybersecurity research in robotics by presenting a toolbox and the results obtained with it through several use cases conducted over a year period. We propose a modular and composable toolbox for robot cybersecurity: alurity. By ensuring that both roboticists and security researchers working on a project have a common, consistent and easily reproducible development environment, alurity aims to facilitate the cybersecurity research and the collaboration across teams.

cs.RO↗

arXiv2020

Universality for critical KCM: finite number of stable directions

In this paper we consider kinetically constrained models (KCM) on $\mathbb Z^2$ with general update families $\mathcal U$. For $\mathcal U$ belonging to the so-called "critical class" our focus is on the divergence of the infection time of the origin for the equilibrium process as the density of the facilitating sites vanishes. In a recent paper Marêché and two of the present authors proved that if $\mathcal U$ has an infinite number of "stable directions", then on a doubly logarithmic scale the above divergence is twice the one in the corresponding $\mathcal U$-bootstrap percolation. Here we prove instead that, contrary to previous conjectures, in the complementary case the two divergences are the same. In particular, we establish the full universality partition for critical $\mathcal U$. The main novel contribution is the identification of the leading mechanism governing the motion of infected critical droplets. It consists of a peculiar hierarchical combination of mesoscopic East-like motions.

math.PR↗

arXiv2019

Diffusive scaling of the Kob-Andersen model in $\mathbb{Z}^d$

We consider the Kob-Andersen model, a cooperative lattice gas with kinetic constraints which has been widely analyzed in the physics literature in connection with the study of the liquid/glass transition. We consider the model in a finite box of linear size $L$ with sources at the boundary. Our result, which holds in any dimension and significantly improves upon previous ones, establishes for any positive vacancy density $q$ a purely diffusive scaling of the relaxation time $T_{\rm rel}$ of the system. Furthermore, as $q\downarrow 0$ we prove upper and lower bounds on $L^{-2} T_{\rm rel} (q,L)$ which agree with the physicists belief that the dominant equilibration mechanism is a cooperative motion of rare large droplets of vacancies. The main tools combine a recent set of ideas and techniques developed to establish universality results for kinetically constrained spin models, with methods from bootstrap percolation, oriented percolation and canonical flows for Markov chains.

math.PR↗

arXiv2019

On the Effectiveness of System API-Related Information for Android Ransomware Detection

Ransomware constitutes a significant threat to the Android operating system. It can either lock or encrypt the target devices, and victims are forced to pay ransoms to restore their data. Hence, the prompt detection of such attacks has a priority in comparison to other malicious threats. Previous works on Android malware detection mainly focused on Machine Learning-oriented approaches that were tailored to identifying malware families, without a clear focus on ransomware. More specifically, such approaches resorted to complex information types such as permissions, user-implemented API calls, and native calls. However, this led to significant drawbacks concerning complexity, resilience against obfuscation, and explainability. To overcome these issues, in this paper, we propose and discuss learning-based detection strategies that rely on System API information. These techniques leverage the fact that ransomware attacks heavily resort to System API to perform their actions, and allow distinguishing between generic malware, ransomware and goodware. We tested three different ways of employing System API information, i.e., through packages, classes, and methods, and we compared their performances to other, more complex state-of-the-art approaches. The attained results showed that systems based on System API could detect ransomware and generic malware with very good accuracy, comparable to systems that employed more complex information. Moreover, the proposed systems could accurately detect novel samples in the wild and showed resilience against static obfuscation attempts. Finally, to guarantee early on-device detection, we developed and released on the Android platform a complete ransomware and malware detector (R-PackDroid) that employed one of the methodologies proposed in this paper.

cs.CR↗

arXiv2018

Towards a universality picture for the relaxation to equilibrium of kinetically constrained models

Recent years have seen a great deal of progress in our understanding of bootstrap percolation models, a particular class of monotone cellular automata. In the two dimensional lattice there is now a quite satisfactory understanding of their evolution starting from a random initial condition, with a strikingly beautiful universality picture for their critical behaviour. Much less is known for their non-monotone stochastic counterpart, namely kinetically constrained models (KCM). In KCM each vertex is resampled (independently) at rate one by tossing a p-coin iff it can be infected in the next step by the bootstrap model. In particular infection can also heal, hence the non-monotonicity. Besides the connection with bootstrap percolation, KCM have an interest in their own as they feature some of the most striking features of the liquid/glass transition, a major and still largely open problem in condensed matter physics. In this paper we pave the way towards proving universality results for KCM similar to those for bootstrap percolation. Our novel and general approach establishes a close connection between the critical scaling of characteristic time scales for KCM and the scaling of the critical length in critical bootstrap models. Although the full proof of universality for KCM is deferred to a forthcoming paper, here we apply our general method to the Friedrickson-Andersen k-facilitated models, amongst the most studied KCM, and to the Gravner-Griffeath model. In both cases our results are close to optimal.

math.PR↗

arXiv2018

Exact asymptotics for Duarte and supercritical rooted kinetically constrained models

Kinetically constrained models (KCM) are reversible interacting particle systems on $\mathbb Z^d$ with continuous time Markov dynamics of Glauber type, which represent a natural stochastic (and non-monotone) counterpart of the family of cellular automata known as $\mathcal U$-bootstrap percolation. Furthermore, KCM have an interest in their own since they display some of the most striking features of the liquid-glass transition, a major and longstanding open problem in condensed matter physics. A key issue for KCM is to identify the scaling of the characteristic time scales when the equilibrium density of empty sites, $q$, goes to zero. In [19,20] a general scheme was devised to determine a sharp upper bound for these time scales. Our paper is devoted to developing a (very different) technique which allows to prove matching lower bounds. We analyse the class of two-dimensional supercritical rooted KCM and the Duarte KCM, the most studied critical $1$-rooted model. We prove that the relaxation time and the mean infection time diverge for supercritical rooted KCM as $e^{Θ((\log q)^2)}$ and for Duarte KCM as $e^{Θ((\log q)^4/q^2)}$ when $q\downarrow 0$. These results prove the conjectures put forward in [20,22], and establish that the time scales for these KCM diverge much faster than for the corresponding $\mathcal U$-bootstrap processes, the main reason being the occurrence of energy barriers which determine the dominant behaviour for KCM, but which do not matter for the bootstrap dynamics.

math.PR↗

arXiv2018

Practical Location Validation in Participatory Sensing Through Mobile WiFi Hotspots

The reliability of information in participatory sensing (PS) systems largely depends on the accuracy of the location of the participating users. However, existing PS applications are not able to efficiently validate the position of users in large-scale outdoor environments. In this paper, we present an efficient and scalable Location Validation System (LVS) to secure PS systems from location-spoofing attacks. In particular, the user location is verified with the help of mobile WiFi hot spots (MHSs), which are users activating the WiFi hotspot capability of their smartphones and accepting connections from nearby users, thereby validating their position inside the sensing area. The system also comprises a novel verification technique called Chains of Sight, which tackles collusion-based attacks effectively. LVS also includes a reputation-based algorithm that rules out sensing reports of location-spoofing users. The feasibility and efficiency of the WiFi-based approach of LVS is demonstrated by a set of indoor and outdoor experiments conducted using off-the-shelf smartphones, while the energy-efficiency of LVS is demonstrated by experiments using the Power Monitor energy tool. Finally, the security properties of LVS are analyzed by simulation experiments. Results indicate that the proposed LVS system is energy-efficient, applicable to most of the practical PS scenarios, and efficiently secures existing PS systems from location-spoofing attacks.

cs.NI↗

arXiv2018

Universality results for kinetically constrained spin models in two dimensions

Kinetically constrained models (KCM) are reversible interacting particle systems on $\mathbb Z^d$ with continuous time Markov dynamics of Glauber type, which represent a natural stochastic (and non-monotone) counterpart of the family of cellular automata known as $\mathcal U$-bootstrap percolation. KCM also display some of the peculiar features of the so-called "glassy dynamics", and as such they are extensively used in the physics literature to model the liquid-glass transition, a major and longstanding open problem in condensed matter physics. We consider two-dimensional KCM with update rule $\mathcal U$, and focus on proving universality results for the mean infection time of the origin, in the same spirit as those recently established in the setting of $\mathcal U$-bootstrap percolation. We first identify what we believe are the correct universality classes, which turn out to be different from those of $\mathcal U$-bootstrap percolation. We then prove universal upper bounds on the mean infection time within each class, which we conjecture to be sharp up to logarithmic corrections. In certain cases, including all supercritical models, and the well-known Duarte model, our conjecture has recently been confirmed in [MMT]. In fact, in these cases our upper bound is sharp up to a constant factor in the exponent. For certain classes of update rules, it turns out that the infection time of the KCM diverges much faster than for the corresponding $\mathcal U$-bootstrap process when the equilibrium density of infected sites goes to zero. This is due to the occurrence of energy barriers which determine the dominant behaviour for KCM, but which do not matter for the monotone bootstrap dynamics.

math.PR↗

arXiv2017

Entropic repulsion in $|\nabla ϕ|^p$ surfaces: a large deviation bound for all $p\geq 1$

We consider the $(2+1)$-dimensional generalized solid-on-solid (SOS) model, that is the random discrete surface with a gradient potential of the form $|\nablaϕ|^{p}$, where $p\in [1,+\infty]$. We show that at low temperature, for a square region $Λ$ with side $L$, both under the infinite volume measure and under the measure with zero boundary conditions around $Λ$, the probability that the surface is nonnegative in $Λ$ behaves like $\exp(-4βτ_{p,β} L H_p(L) )$, where $β$ is the inverse temperature, $τ_{p,β}$ is the surface tension at zero tilt, or step free energy, and $H_p(L)$ is the entropic repulsion height, that is the typical height of the field when a positivity constraint is imposed. This generalizes recent results obtained in \cite{CMT} for the standard SOS model ($p=1$).

math.PR↗

arXiv2016

Upper triangular matrix walk: Cutoff for finitely many columns

We consider random walk on the group of uni-upper triangular matrices with entries in $\mathbb{F}_2$ which forms an important example of a nilpotent group. Peres and Sly (2013) proved tight bounds on the mixing time of this walk up to constants. It is well known that the single column projection of this chain is the one dimensional East process. In this article, we complement the Peres-Sly result by proving a cutoff result for the mixing of finitely many columns in the upper triangular matrix walk at the same location as the East process of the same dimension. Moreover, we also show that the spectral gaps of the matrix walk and the East process are equal. The proof of the cutoff result is based on a recursive argument which uses a local version of a dual process appearing in Peres and Sly (2013), various combinatorial consequences of mixing and concentration results for the movement of the front in the one dimensional East process.

math.PR↗