Taylor's law in innovation processes

Taylor's law quantifies the scaling properties of the fluctuations of the number of innovations occurring in open systems. Urn-based modeling schemes have already proven to be effective in modeling this complex behaviour. Here, we present analytical estimations of Taylor's law exponents in such models, by leveraging on their representation in terms of triangular urn models. We also highlight the correspondence of these models with Poisson-Dirichlet processes and demonstrate how a non-trivial Taylor's law exponent is a kind of universal feature in systems related to human activities. We base this result on the analysis of four collections of data generated by human activity: (i) written language (from a Gutenberg corpus); (ii) an online music website (Last. fm); (iii) Twitter hashtags; (iv) an online collaborative tagging system (Del. icio. us). While Taylor's law observed in the last two datasets agrees with the plain model predictions, we need to introduce a generalization to fully characterize the behaviour of the first two datasets, where temporal correlations are possibly more relevant. We suggest that Taylor's law is a fundamental complement to Zipf's and Heaps' laws in unveiling the complex dynamical processes underlying the evolution of systems featuring innovation

Taylor's law in innovation processes

Taylor's law quantifies the scaling properties of the fluctuations of the number of innovations occurring in open systems. Urn based modelling schemes have already proven to be effective in modelling this complex behaviour. Here, we present analytical estimations of Taylor's law exponents in such models, by leveraging on their representation in terms of triangular urn models. We also highlight the correspondence of these models with Poisson-Dirichlet processes and demonstrate how a non-trivial Taylor's law exponent is a kind of universal feature in systems related to human activities. We base this result on the analysis of four collections of data generated by human activity: (i) written language (from a Gutenberg corpus); (ii) a n online music website (Last.fm); (iii) Twitter hashtags; (iv) a on-line collaborative tagging system (Del.icio.us). While Taylor's law observed in the last two datasets agrees with the plain model predictions, we need to introduce a generalization to fully characterize the behaviour of the first two datasets, where temporal correlations are possibly more relevant. We suggest that Taylor's law is a fundamental complement to Zipf's and Heaps' laws in unveiling the complex dynamical processes underlying the evolution of systems featuring innovation.Comment: 17 page

Modeling microevolution in a changing environment: The evolving quasispecies and the Diluted Champion Process

Several pathogens use evolvability as a survival strategy against acquired immunity of the host. Despite their high variability in time, some of them exhibit quite low variability within the population at any given time, a somehow paradoxical behavior often called the evolving quasispecies. In this paper we introduce a simplified model of an evolving viral population in which the effects of the acquired immunity of the host are represented by the decrease of the fitness of the corresponding viral strains, depending on the frequency of the strain in the viral population. The model exhibits evolving quasispecies behavior in a certain range of its parameters, ans suggests how punctuated evolution can be induced by a simple feedback mechanism.Comment: 15 pages, 12 figures. Figures redrawn, some additional clarifications in the text. To appear in Journal of Statistical Mechanics: Theory and Experimen

A note on the Guerra and Talagrand theorems for Mean Field Spin Glasses: the simple case of spherical models

The aim of this paper is to discuss the main ideas of the Talagrand proof of the Parisi Ansatz for the free-energy of Mean Field Spin Glasses with a physicist's approach. We consider the case of the spherical $p$-spin model, which has the following advantages: 1) the Parisi Ansatz takes the simple ``one step replica symmetry breaking form'', 2) the replica free-energy as a function of the order parameters is simple enough to allow for numerical maximization with arbitrary precision. We present the essential ideas of the proof, we stress its connections with the theory of effective potentials for glassy systems, and we reduce the technically more difficult part of the Talagrand's analysis to an explicit evaluation of the solution of a variational problem.Comment: 20 pages, 5 figures. Added references and minor language correction

Evolutionary games and quasispecies

We discuss a population of sequences subject to mutations and frequency-dependent selection, where the fitness of a sequence depends on the composition of the entire population. This type of dynamics is crucial to understand the evolution of genomic regulation. Mathematically, it takes the form of a reaction-diffusion problem that is nonlinear in the population state. In our model system, the fitness is determined by a simple mathematical game, the hawk-dove game. The stationary population distribution is found to be a quasispecies with properties different from those which hold in fixed fitness landscapes.Comment: 7 pages, 2 figures. Typos corrected, references updated. An exact solution for the hawks-dove game is provide

Small Angle X-Ray Scattering Studies of Mitochondrial Glutaminase C Reveal Extended Flexible Regions, and Link Oligomeric State with Enzyme Activity

Glutaminase C is a key metabolic enzyme, which is unregulated in many cancer systems and believed to play a central role in the Warburg effect, whereby cancer cells undergo changes to an altered metabolic profile. A long-standing hypothesis links enzymatic activity to the protein oligomeric state, hence the study of the solution behavior in general and the oligomer state in particular of glutaminase C is important for the understanding of the mechanism of protein activation and inhibition. In this report, this is extensively investigated in correlation to enzyme concentration or phosphate level, using a high-throughput microfluidic-mixing chip for the SAXS data collection, and we confirm that the oligomeric state correlates with activity. The in-depth solution behavior analysis further reveals the structural behavior of flexible regions of the protein in the dimeric, tetrameric and octameric state and investigates the C-terminal influence on the enzyme solution behavior. Our data enable SAXS-based rigid body modeling of the full-length tetramer states, thereby presenting the first ever experimentally derived structural model of mitochondrial glutaminase C including the N- and C-termini of the enzyme

Canalization of the evolutionary trajectory of the human influenza virus

Since its emergence in 1968, influenza A (H3N2) has evolved extensively in genotype and antigenic phenotype. Antigenic evolution occurs in the context of a two-dimensional 'antigenic map', while genetic evolution shows a characteristic ladder-like genealogical tree. Here, we use a large-scale individual-based model to show that evolution in a Euclidean antigenic space provides a remarkable correspondence between model behavior and the epidemiological, antigenic, genealogical and geographic patterns observed in influenza virus. We find that evolution away from existing human immunity results in rapid population turnover in the influenza virus and that this population turnover occurs primarily along a single antigenic axis. Thus, selective dynamics induce a canalized evolutionary trajectory, in which the evolutionary fate of the influenza population is surprisingly repeatable and hence, in theory, predictable.Comment: 29 pages, 5 figures, 10 supporting figure

Inference algorithms for gene networks: a statistical mechanics analysis

The inference of gene regulatory networks from high throughput gene expression data is one of the major challenges in systems biology. This paper aims at analysing and comparing two different algorithmic approaches. The first approach uses pairwise correlations between regulated and regulating genes; the second one uses message-passing techniques for inferring activating and inhibiting regulatory interactions. The performance of these two algorithms can be analysed theoretically on well-defined test sets, using tools from the statistical physics of disordered systems like the replica method. We find that the second algorithm outperforms the first one since it takes into account collective effects of multiple regulators

Replicated Transfer Matrix Analysis of Ising Spin Models on `Small World' Lattices

We calculate equilibrium solutions for Ising spin models on `small world' lattices, which are constructed by super-imposing random and sparse Poissonian graphs with finite average connectivity c onto a one-dimensional ring. The nearest neighbour bonds along the ring are ferromagnetic, whereas those corresponding to the Poisonnian graph are allowed to be random. Our models thus generally contain quenched connectivity and bond disorder. Within the replica formalism, calculating the disorder-averaged free energy requires the diagonalization of replicated transfer matrices. In addition to developing the general replica symmetric theory, we derive phase diagrams and calculate effective field distributions for two specific cases: that of uniform sparse long-range bonds (i.e. `small world' magnets), and that of (+J/-J) random sparse long-range bonds (i.e. `small world' spin-glasses).Comment: 22 pages, LaTeX, IOP macros, eps figure

Procedure in sala dialisi durante l’emergenza Covid-19

Scopo Scopo del presente documento \ue8 definire modalit\ue0 omogenee di gestione del paziente dializzato a partire dalla comparsa di casi accertati nella popolazione italiana di infezione da nuovo Coronavirus 2019-nCoV (Covid-19). Applicabilit\ue0 Il presente documento si applica alle attivit\ue0 di sala dialitica di seguito descritte. Il documento \ue8 attualmente in applicazione presso i due presidi ospedalieri dell\u2019ASST Santi Paolo e Carlo e relativi CAL Mompiani e Rozzano. Descrizione Questo documento espone le misure di prevenzione e di controllo della diffusione dell\u2019infezione da nuovo Coronavirus, attuate dal giorno 24/02/2020 dal personale dell\u2019unit\ue0 operativa dialisi al fine di limitare la trasmissione da persona a persona. Le indicazioni che seguono hanno quindi l\u2019obiettivo di garantire l\u2019uniformit\ue0 di comportamento degli operatori sanitari nel confronto dei pazienti afferenti al centro, al fine di identificare e gestire i casi sospetti, probabili e confermati da infezione da Coronavirus. Tutti i pazienti che giungono in ospedale per eseguire la seduta emodialitica vengono considerati \u201cpotenzialmente\u201d infetti da Covid-19 e, pertanto, tutti gli operatori e tutti i pazienti devono seguire le indicazioni del protocollo sui dispositivi di protezione individuale (DPI): l\u2019igiene delle mani, l\u2019utilizzo della cuffia, mascherina chirurgica occhiali o visiera, guanti e camice come da procedure