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Luca Ferretti

Publications and source records attributed to Luca Ferretti.

At least 19 recordsLinked to original sources
arXiv2026

Epistatic strength, modularity, and locus heterogeneity shape the number of local optima in fitness landscapes

Fitness landscapes provide a quantitative framework for understanding how natural selection shapes evolutionary trajectories. A central feature of these landscapes is their number of local optima, which determines whether fitness-increasing evolution can proceed towards a global optimum or become trapped on suboptimal peaks. Although multiple peaks are known to require reciprocal sign epistasis, the quantitative relationship between epistasis and number of peaks remains incompletely understood. Here, we show that for a broad class of unstructured fitness landscapes, i.e. isotropic Gaussian random fields, the expected number of local optima is determined by a single local measure of epistasis: the correlation of fitness effects. This provides a baseline prediction for the number of peaks in typical unstructured landscapes and links peak density directly to the amount of reciprocal sign epistasis. This baseline changes when epistatic interactions are structured. We show that clustering interactions within blocks of loci slightly increases the number of local optima. In contrast, strong heterogeneity between loci, where only a small subset of loci participate in epistatic interactions, causes the number of peaks to collapse. These results show that the number of local optima is governed not only by the overall strength of epistasis, but also by how epistatic interactions are distributed across the genotype space. Our framework therefore reconciles the central role of reciprocal sign epistasis with the observation that landscapes with similar amounts of epistasis can differ substantially in ruggedness, and provides a guide to the range of peak numbers expected in typical landscapes.

q-bio.PE↗
arXiv2026

Simple sign epistasis and evolutionary detours in fitness landscapes

In epistatic fitness landscapes, the fitness effect of a mutation depends on the genetic background and may even switch between deleterious and beneficial depending on the presence of another mutation. Epistatic interactions may cause both mutations to change the sign of each other's fitness effects (reciprocal sign epistasis) or only one mutation to do so (simple sign epistasis). Both these forms of epistasis influence evolutionary trajectories. While reciprocal sign epistasis has been associated with multi-peaked landscapes and their ruggedness, the role and relative frequency of simple sign epistasis in fitness landscapes have not been systematically investigated. Here, we prove that the presence of simple sign epistasis is associated with evolutionary detours, i.e., indirect, longer fitness-increasing paths to fitness peaks that include back-mutations. We also show that in experimentally resolved, weakly epistatic landscapes, simple sign epistasis occurs much more frequently than reciprocal sign epistasis. This result is consistent with the theoretical predictions we derive for most landscape models, with the exception of the block model and of landscapes dominated by pairwise allelic incompatibilities, such as RNA stability landscapes. Our results suggest that detours represent a general feature of evolutionary trajectories in weakly epistatic landscapes.

q-bio.PE↗
arXiv2025

Preferential attachment and power-law degree distributions in heterogeneous multilayer hypergraphs

We include complex connectivity structures and heterogeneity in models of multilayer networks or multilayer hypergraphs growing by preferential attachment. We consider the most generic connectivity structure, where the probability of acquiring a new hyperlink depends linearly on the vector of hyperdegrees of the node across all layers, as well as on the layer of the new hyperlink and the features of both linked nodes. We derive the consistency conditions that imply a power-law hyperdegree distribution for each class of nodes within each layer and of any order. For generic connectivity structures, we predict that the exponent of the power-law distribution is universal for all layers and all orders of hyperlinks, and it depends exclusively on the type of node.

cond-mat.dis-nn↗
arXiv2021

Modeling Realistic Adversarial Attacks against Network Intrusion Detection Systems

The incremental diffusion of machine learning algorithms in supporting cybersecurity is creating novel defensive opportunities but also new types of risks. Multiple researches have shown that machine learning methods are vulnerable to adversarial attacks that create tiny perturbations aimed at decreasing the effectiveness of detecting threats. We observe that existing literature assumes threat models that are inappropriate for realistic cybersecurity scenarios because they consider opponents with complete knowledge about the cyber detector or that can freely interact with the target systems. By focusing on Network Intrusion Detection Systems based on machine learning, we identify and model the real capabilities and circumstances required by attackers to carry out feasible and successful adversarial attacks. We then apply our model to several adversarial attacks proposed in literature and highlight the limits and merits that can result in actual adversarial attacks. The contributions of this paper can help hardening defensive systems by letting cyber defenders address the most critical and real issues, and can benefit researchers by allowing them to devise novel forms of adversarial attacks based on realistic threat models.

cs.CR↗
arXiv2018

Universality classes of interaction structures for NK fitness landscapes

Kauffman's NK-model is a paradigmatic example of a class of stochastic models of genotypic fitness landscapes that aim to capture generic features of epistatic interactions in multilocus systems. Genotypes are represented as sequences of $L$ binary loci. The fitness assigned to a genotype is a sum of contributions, each of which is a random function defined on a subset of $k \le L$ loci. These subsets or neighborhoods determine the genetic interactions of the model. Whereas earlier work on the NK model suggested that most of its properties are robust with regard to the choice of neighborhoods, recent work has revealed an important and sometimes counter-intuitive influence of the interaction structure on the properties of NK fitness landscapes. Here we review these developments and present new results concerning the number of local fitness maxima and the statistics of selectively accessible (that is, fitness-monotonic) mutational pathways. In particular, we develop a unified framework for computing the exponential growth rate of the expected number of local fitness maxima as a function of $L$, and identify two different universality classes of interaction structures that display different asymptotics of this quantity for large $k$. Moreover, we show that the probability that the fitness landscape can be traversed along an accessible path decreases exponentially in $L$ for a large class of interaction structures that we characterize as locally bounded. Finally, we discuss the impact of the NK interaction structures on the dynamics of evolution using adaptive walk models.

q-bio.PE↗
arXiv2017

Decomposing the site frequency spectrum: the impact of tree topology on neutrality tests

We investigate the dependence of the site frequency spectrum (SFS) on the topological structure of genealogical trees. We show that basic population genetic statistics - for instance estimators of $θ$ or neutrality tests such as Tajima's $D$ - can be decomposed into components of waiting times between coalescent events and of tree topology. Our results clarify the relative impact of the two components on these statistics. We provide a rigorous interpretation of positive or negative values of an important class of neutrality tests in terms of the underlying tree shape. In particular, we show that values of Tajima's $D$ and Fay and Wu's $H$ depend in a direct way on a peculiar measure of tree balance which is mostly determined by the root balance of the tree. We present a new test for selection in the same class as Fay and Wu's $H$ and discuss its interpretation and power. Finally, we determine the trees corresponding to extreme expected values of these neutrality tests and present formulae for these extreme values as a function of sample size and number of segregating sites.

q-bio.PE↗
arXiv2017

The expected neutral frequency spectrum of linked sites

We present an exact, closed expression for the expected neutral Site Frequency Spectrum for two neutral sites, 2-SFS, without recombination. This spectrum is the immediate extension of the well known single site $θ/f$ neutral SFS. Similar formulae are also provided for the case of the expected SFS of sites that are linked to a focal neutral mutation of known frequency. Formulae for finite samples are obtained by coalescent methods and remarkably simple expressions are derived for the SFS of a large population, which are also solutions of the multi-allelic Kolmogorov equations. Besides the general interest of these new spectra, they relate to interesting biological cases such as structural variants and introgressions. As an example, we present the expected neutral frequency spectrum of regions with a chromosomal inversion.

q-bio.PE↗
arXiv2015

Watterson estimators for Next Generation Sequencing: from trios to autopolyploids

Several variations of the Watterson estimator of variability for Next Generation Sequencing (NGS) data have been proposed in the literature. We present a unified framework for generalized Watterson estimators based on Maximum Composite Likelihood, which encompasses most of the existing estimators. We propose this class of unbiased estimators as generalized Watterson estimators for a large class of NGS data, including pools and trios. We also discuss the relation with the estimators that have been proposed in the literature and show that they admit two equivalent but seemingly different forms, deriving a set of combinatorial identities as a byproduct. Finally, we give a detailed treatment of Watterson estimators for single or multiple autopolyploid individuals.

q-bio.PE↗
arXiv2015

Epistasis and constraints in fitness landscapes

Genotypic fitness landscapes are constructed by assessing the fitness of all possible combinations of a given number of mutations. In the last years, several experimental fitness landscapes have been completely resolved. As fitness landscapes are high-dimensional, their characterization relies on simple measures of their structure, which can be used as statistics in empirical applications. Here we propose two new sets of measures that explicitly capture two relevant features of fitness landscapes: epistasis and constraints. The first set contains new measures for epistasis based on the correlation of fitness effects of mutations. They have a natural interpretation, capture well the interaction between mutations, can be obtained analytically for most landscape models and can therefore be used to discriminate between different models. The second set contains measures of evolutionary constraints based on "chains" of forced mutations along fitness-increasing paths. Some of these measures are non-monotonic in the amount of epistatic interactions, but have instead a maximum for intermediate values. We further characterize the relationships of these measures to the ones that were previous proposed (e.g. number of peaks, roughness/slope, fraction of non-additive components, etc). Finally, we show how these measures can help uncovering the amount and the nature of epistatic interactions in two experimental landscapes.

q-bio.PE↗
arXiv2014

A simple model for the distribution of plasmid lengths

Plasmids are major players in Horizontal Gene Transfer mechanisms, hence they are highly variable in their gene content and length. We propose a model for the fitness of a plasmid as a function of its length, which predicts diminishing returns. We infer the distribution of plasmid lengths by a simple evolutionary model and we show that there is a positive correlation between the presence and efficiency of the conjugation machinery and the length of the plasmid. The model predicts an "insertion load" on plasmids, which could explain also the fact that plasmids are widespread in bacterial populations but rarely established. Finally we discuss how the typical length of plasmids increases with the amount of stress in the environment, focusing on the recent human-driven increase in antibiotic concentrations.

q-bio.PE↗
arXiv2014

Condensation and topological phase transitions in a dynamical network model with rewiring of the links

Growing network models with both heterogeneity of the nodes and topological constraints can give rise to a rich phase structure. We present a simple model based on preferential attachment with rewiring of the links. Rewiring probabilities are modulated by the negative fitness of the nodes and by the constraint for the network to be a simple graph. At low temperatures and high rewiring rates, this constraint induces a Bose-Einstein condensation of paths of length 2, i.e. a new phase transition with an extended condensate of links. The phase space of the model includes further transitions in the scaling of the connected component and the degeneracy of the network.

cond-mat.dis-nn↗
arXiv2014

Duality between preferential attachment and static random networks on hyperbolic spaces

There is a complex relation between the mechanism of preferential attachment, scale-free degree distributions and hyperbolicity in complex networks. In fact, both preferential attachment and hidden hyperbolic spaces often generate scale-free networks. We show that there is actually a duality between a class of growing spatial networks based on preferential attachment on the sphere and a class of static random networks on the hyperbolic plane. Both classes of networks have the same scale-free degree distribution as the Barabasi-Albert model. As a limit of this correspondence, the Barabasi-Albert model is equivalent to a static random network on an hyperbolic space with infinite curvature.

cond-mat.dis-nn↗
arXiv2012

Phase diagram of the Bose-Hubbard Model on Complex Networks

Critical phenomena can show unusual phase diagrams when defined in complex network topologies. The case of classical phase transitions such as the classical Ising model and the percolation transition has been studied extensively in the last decade. Here we show that the phase diagram of the Bose-Hubbard model, an exclusively quantum mechanical phase transition, also changes significantly when defined on random scale-free networks. We present a mean-field calculation of the model in annealed networks and we show that when the second moment of the average degree diverges the Mott-insulator phase disappears in the thermodynamic limit. Moreover we study the model on quenched networks and we show that the Mott-insulator phase disappears in the thermodynamic limit as long as the maximal eigenvalue of the adjacency matrix diverges. Finally we study the phase diagram of the model on Apollonian scale-free networks that can be embedded in 2 dimensions showing the extension of the results also to this case.

cond-mat.dis-nn↗
arXiv2012

Features and heterogeneities in growing network models

Many complex networks from the World-Wide-Web to biological networks are growing taking into account the heterogeneous features of the nodes. The feature of a node might be a discrete quantity such as a classification of a URL document as personal page, thematic website, news, blog, search engine, social network, ect. or the classification of a gene in a functional module. Moreover the feature of a node can be a continuous variable such as the position of a node in the embedding space. In order to account for these properties, in this paper we provide a generalization of growing network models with preferential attachment that includes the effect of heterogeneous features of the nodes. The main effect of heterogeneity is the emergence of an "effective fitness" for each class of nodes, determining the rate at which nodes acquire new links. The degree distribution exhibits a multiscaling behaviour analogous to the the fitness model. This property is robust with respect to variations in the model, as long as links are assigned through effective preferential attachment. Beyond the degree distribution, in this paper we give a full characterization of the other relevant properties of the model. We evaluate the clustering coefficient and show that it disappears for large network size, a property shared with the Barabási-Albert model. Negative degree correlations are also present in the studied class of models, along with non-trivial mixing patterns among features. We therefore conclude that both small clustering coefficients and disassortative mixing are outcomes of the preferential attachment mechanism in general growing networks.

physics.soc-ph↗
arXiv2011

Preferential attachment in growing spatial networks

We obtain the degree distribution for a class of growing network models on flat and curved spaces. These models evolve by preferential attachment weighted by a function of the distance between nodes. The degree distribution of these models is similar to the one of the fitness model of Bianconi and Barabasi, with a fitness distribution dependent on the metric and the density of nodes. We show that curvature singularities in these spaces can give rise to asymptotic Bose-Einstein condensation, but transient condensation can be observed also in smooth hyperbolic spaces with strong curvature. We provide numerical results for spaces of constant curvature (sphere, flat and hyperbolic space) and we discuss the conditions for the breakdown of this approach and the critical points of the transition to distance-dominated attachment. Finally we discuss the distribution of link lengths.

cond-mat.dis-nn↗
arXiv2010

Properties of neutrality tests based on allele frequency spectrum

One of the main necessities for population geneticists is the availability of statistical tools that enable to accept or reject the neutral Wright-Fisher model with high power. A number of statistical tests have been developed to detect specific deviations from the null frequency spectrum in different directions (i.e., Tajima's D, Fu and Li's F and D test, Fay and Wu's H). Recently, a general framework was proposed to generate all neutrality tests that are linear functions of the frequency spectrum. In this framework, a family of optimal tests was developed to have almost maximum power against a specific alternative evolutionary scenario. Following these developments, in this paper we provide a thorough discussion of linear and nonlinear neutrality tests. First, we present the general framework for linear tests and emphasize the importance of the property of scalability with the sample size (that is, the results of the tests should not depend on the sample size), which, if missing, can guide to errors in data interpretation. The motivation and structure of linear optimal tests are discussed. In a further generalization, we develop a general framework for nonlinear neutrality tests and we derive nonlinear optimal tests for polynomials of any degree in the frequency spectrum.

q-bio.QM↗
arXiv2009

Dynamics of condensation in growing complex networks

A condensation transition was predicted for growing technological networks evolving by preferential attachment and competing quality of their nodes, as described by the fitness model. When this condensation occurs a node acquires a finite fraction of all the links of the network. Earlier studies based on steady state degree distribution and on the mapping to Bose-Einstein condensation, were able to identify the critical point. Here we characterize the dynamics of condensation and we present evidence that below the condensation temperature there is a slow down of the dynamics and that a single node (not necessarily the best node in the network) emerges as the winner for very long times. The characteristic time t* at which this phenomenon occurs diverges both at the critical point and at $T -> 0$ when new links are attached deterministically to the highest quality node of the network.

cond-mat.stat-mech↗