arXiv subjects

Alexei Vazquez

Publications and source records attributed to Alexei Vazquez.

At least 37 records · Page 2Linked to original sources

arXiv2023

Complex hypergraphs

Providing an abstract representation of natural and human complex structures is a challenging problem. Accounting for the system heterogenous components while allowing for analytical tractability is a difficult balance. Here I introduce complex hypergraphs (chygraphs), bringing together concepts from hypergraphs, multi-layer networks, simplicial complexes and hyperstructures. To illustrate the applicability of this combinatorial structure I calculate the component sizes statistics and identify the transition to a giant component. To this end I introduce a vectorization technique that tackles the multi-level nature of chygraphs. I conclude that chygraphs are a unifying representation of complex systems allowing for analytical insight.

physics.soc-ph↗

arXiv2022

From subexponential distributions to black swan dominance

The shape of empirical distributions with heavy tails is a recurrent matter of debate. There are claims of a power laws and the associated scale invariance. There are plenty of challengers as well, the lognormal and stretched exponential among others. Here I point out that, with regard to summation invariance, all what matters is they are subexponential distributions. I provide numerical examples highlighting the key properties of subexponential distributions. The summation invariance and the black swan dominance: the sum is dominated by the maximum. Finally, I illustrate the use of these properties to tackle problems in random networks, infectious dynamics and project delays.

physics.soc-ph↗

arXiv2022

Tropical approximation to finish time of activity networks

We breakdown complex projects into activities and their logical dependencies. We estimate the project finish time based on the activity durations and relations. However, adverse events trigger delay cascades shifting the finish time. Here I derive a tropical algebraic equation for the finish time of activity networks, encapsulating the principle of linear superposition of exogenous perturbations in the tropical sense. From the tropical algebraic equation I derive the finish time distribution with explicit reference to the distribution of exogenous delays and the network topology and geometry.

physics.soc-ph↗

arXiv2022

Growth principles of natural hypergraphs

Several systems can be represented by hypergraphs, an extension of graphs with associations between any number of vertices. These natural hypergraphs doe not appear at once. They are generated by some dynamical process of hypergraph evolution. Here I investigate what are the minimal growth principles of natural hypergraphs. I postulate edge duplication and vertex addition at edge duplications as the key principles of hypergraph growth. The implementation of these two principles induce the emergence of preferential attachment, power law degree distribution, the small-world property, high clustering coefficient and the founder effect. This work clarifies the distinction between principles, emergent properties and context specific details in the context of hypergraph growth dynamics.

physics.soc-ph↗

arXiv2022

Activity networks determine project performance

Projects are characterised by activity networks with a critical path, a sequence of activities from start to end, that must be finished on time to complete the project on time. Watching over the critical path is the project manager's strategy to ensure timely project completion. This intense focus on a single path contrasts the broader complex structure of the activity network, and is due to our poor understanding on how that structure influences this critical path. Here, we use a generative model and detailed data from 77 real world projects (plus 10 billion dollars total budget) to demonstrate how this network structure forces us to look beyond the critical path. We introduce a duplication-split model of project schedules that yields (i) identical power-law in- and-out degree distributions and (ii) a vanishing fraction of critical path activities with schedule size. These predictions are corroborated in real projects. We demonstrate that the incidence of delayed activities in real projects is consistent with the expectation from percolation theory in complex networks. We conclude that delay propagation in project schedules is a network property and it is not confined to the critical path.

physics.soc-ph↗

arXiv2020

Zero forcing number of graphs with a power law degree distribution

The zero forcing number is the minimum number of black vertices that can turn a white graph black following a single neighbour colour forcing rule. The zero forcing number provides topological information about linear algebra on graphs, with applications to the controllability of linear dynamical systems and quantum walks on graphs among other problems. Here, I investigate the zero forcing number of undirected simple graphs with a power law degree distribution $p_k\sim k^{-γ}$. For graphs generated by the preferential attachment model, with a diameter scaling logarithmically with the graph size, the zero forcing number approaches the graph size when $γ\rightarrow2$. In contrast, for graphs generated by the deactivation model, with a diameter scaling linearly with the graph size, the zero forcing number is smaller than the graph size independently of $γ$. Therefore the scaling of the graph diameter with the graph size is another factor determining the controllability of dynamical systems.

math.CO↗

arXiv2020

The colon-pile

Bacteria populate the colon where they replicate and migrate in response to nutrient availability. Here I model the colon bacterial population as a sandpile model, the colon-pile. Sand addition mimics bacterial replication and grains toppling represents bacterial migration coupled to high population density. The numerical simulations reveal a behaviour similar to non-conservative sandpile models, approaching a critical state with system wide avalanches when the death rate becomes negligible. The critical exponents estimation indicates that the colon-pile belongs to a new universality class. This work suggest that the colon microbiome is in a self-organised critical state, where small perturbations can trigger large scale rearrangements, covering an area comparable to the system size and characterised by a 1/f noise spectra

q-bio.PE↗

arXiv2019

Cell population heterogeneity driven by stochastic partition and growth optimality

A fundamental question in biology is how cell populations evolve into different subtypes based on homogeneous processes at the single cell level. Here we show that population bimodality can emerge even when biological processes are homogenous at the cell level and the environment is kept constant. Our model is based on the stochastic partitioning of a cell component with an optimal copy number. We show that the existence of unimodal or bimodal distributions depends on the variance of partition errors and the growth rate tolerance around the optimal copy number. In particular, our theory provides a consistent explanation for the maintenance of aneuploid states in a population. The proposed model can also be relevant for other cell components such as mitochondria and plasmids, whose abundances affect the growth rate and are subject to stochastic partition at cell division.

q-bio.MN↗

arXiv2011

Spreading Dynamics Following Bursty Human Activity Patterns

We study the susceptible-infected model with power-law waiting time distributions $P(τ)\sim τ^{-α}$, as a model of spreading dynamics under heterogeneous human activity patterns. We found that the average number of new infections $n(t)$ at time $t$ decays as a power law in the long time limit, $n(t) \sim t^{-β}$, leading to extremely slow revalence decay.We also found that the exponent in the spreading dynamics, $β$, is related to that in the waiting time distribution, $α$, in a way depending on the interactions between agents but is insensitive to the network topology. These observations are well supported by both the theoretical predictions and the long prevalence decay time in real social spreading phenomena. Our results unify individual activity patterns with macroscopic collective dynamics at the network level.

physics.data-an↗

arXiv2010

Higher Order Boolean networks as models of cell state dynamics

The regulation of the cell state is a complex process involving several components. These complex dynamics can be modeled using Boolean networks, allowing us to explain the existence of different cell states and the transition between them. Boolean models have been introduced both as specific examples and as ensemble or distribution network models. However, current ensemble Boolean network models do not make a systematic distinction between different cell components such as epigenetic factors, gene and transcription factors. Consequently, we still do not understand their relative contributions in controlling the cell fate. In this work we introduce and study higher order Boolean networks, which feature an explicit distinction between the different cell components and the types of interactions between them. We show that the stability of the cell state dynamics can be determined solving the eigenvalue problem of a matrix representing the regulatory interactions and their strengths. The qualitative analysis of this problem indicates that, in addition to the classification into stable and chaotic regimes, the cell state can be simple or complex depending on whether it can be deduced from the independent study of its components or not. Finally, we illustrate how the model can be expanded considering higher levels and higher order dynamics.

q-bio.MN↗

arXiv2009

Optimal cytoplasmatic density and flux balance model under macromolecular crowding effects

Macromolecules occupy between 34 and 44% of the cell cytoplasm, about half the maximum pack- ing density of spheres in three dimension. Yet, there is no clear understanding of what is special about this value. To address this fundamental question we investigate the effect of macromolecular crowding on cell metabolism. We develop a cell scale flux balance model capturing the main features of cell metabolism at different nutrient uptakes and macromolecular densities. Using this model we show there are two metabolic regimes at low and high nutrient uptakes. The latter regime is charac- terized by an optimal cytoplasmatic density where the increase of reaction rates by confinement and the decrease by diffusion slow-down balance. More important, the predicted optimal density is in the range of the experimentally determined density of E. coli. We conclude that cells have evolved to a cytoplasmatic density resulting in the maximum metabolic rate given the nutrient availability and macromolecular crowding effects and report a flux balance model accounting for its effect.

q-bio.MN↗

arXiv2008

Bayesian approach to clustering real value, categorical and network data: solution via variational methods

Data clustering, including problems such as finding network communities, can be put into a systematic framework by means of a Bayesian approach. The application of Bayesian approaches to real problems can be, however, quite challenging. In most cases the solution is explored via Monte Carlo sampling or variational methods. Here we work further on the application of variational methods to clustering problems. We introduce generative models based on a hidden group structure and prior distributions. We extend previous attends by Jaynes, and derive the prior distributions based on symmetry arguments. As a case study we address the problems of two-sides clustering real value data and clustering data represented by a hypergraph or bipartite graph. From the variational calculations, and depending on the starting statistical model for the data, we derive a variational Bayes algorithm, a generalized version of the expectation maximization algorithm with a built in penalization for model complexity or bias. We demonstrate the good performance of the variational Bayes algorithm using test examples.

physics.data-an↗

arXiv2007

Population stratification using a statistical model on hypergraphs

Population stratification is a problem encountered in several areas of biology and public health. We tackle this problem by mapping a population and its elements attributes into a hypergraph, a natural extension of the concept of graph or network to encode associations among any number of elements. On this hypergraph, we construct a statistical model reflecting our intuition about how the elements attributes can emerge from a postulated population structure. Finally, we introduce the concept of stratification representativeness as a mean to identify the simplest stratification already containing most of the information about the population structure. We demonstrate the power of this framework stratifying an animal and a human population based on phenotypic and genotypic properties, respectively.

q-bio.PE↗

arXiv2007

Impact of non-Poisson activity patterns on spreading processes

Halting a computer or biological virus outbreak requires a detailed understanding of the timing of the interactions between susceptible and infected individuals. While current spreading models assume that users interact uniformly in time, following a Poisson process, a series of recent measurements indicate that the inter-contact time distribution is heavy tailed, corresponding to a temporally inhomogeneous bursty contact process. Here we show that the non-Poisson nature of the contact dynamics results in prevalence decay times significantly larger than predicted by the standard Poisson process based models. Our predictions are in agreement with the detailed time resolved prevalence data of computer viruses, which, according to virus bulletins, show a decay time close to a year, in contrast with the one day decay predicted by the standard Poisson process based models.

physics.data-an↗

arXiv2006

Spreading dynamics on small-world networks with connectivity fluctuations and correlations

Infectious diseases and computer malwares spread among humans and computers through the network of contacts among them. These networks are characterized by wide connectivity fluctuations, connectivity correlations and the small-world property. In a previous work [A. Vazquez, Phys. Rev. Lett. 96, 038702 (2006)] I have shown that the connectivity fluctuations together with the small-world property lead to a novel spreading law, characterized by an initial power law growth with an exponent determined by the average node distance on the network. Here I extend these results to consider the influence of connectivity correlations which are generally observed in real networks. I show that assortative and disassortative connectivity correlations enhance and diminish, respectively, the range of validity of this spreading law. As a corollary I obtain the region of connectivity fluctuations and degree correlations characterized by the absence of an epidemic threshold. These results are relevant for the spreading of infectious diseases, rumors, and information among humans and the spreading of computer viruses, email worms and hoaxes among computer users.

q-bio.PE↗

arXiv2006

Epidemic outbreaks on structured populations

Our chances to halt epidemic outbreaks rely on how accurately we represent the population structure underlying the disease spread. When analyzing global epidemics this force us to consider metapopulation models taking into account intra- and inter-community interactions. Recently Watts et al introduced a metapopulation model which accounts for several features observed in real outbreaks [Watts et al, PNAS 102, 11157 (2005)]. In this work I provide an analytical solution to this model, enhancing our understanding of the model and the epidemic outbreaks it represents. First, I demonstrate that depending on the intra-community expected outbreak size and the fraction of social bridges the epidemic outbreaks die out or there is a finite probability to observe a global epidemics. Second, I show that the global scenario is characterized by resurgent epidemics, their number increasing with increasing the intra-community average distance between individuals. Finally, I present empirical data for the AIDS epidemics supporting the model predictions.

q-bio.PE↗

arXiv2006

Spreading of infectious diseases on heterogeneous populations: multi-type network approach

I study the spreading of infectious diseases on heterogeneous populations. I represent the population structure by a contact-graph where vertices represent agents and edges represent disease transmission channels among them. The population heterogeneity is taken into account by the agent's subdivision in types and the mixing matrix among them. I introduce a type-network representation for the mixing matrix allowing an intuitive understanding of the mixing patterns and the analytical calculations. Using an iterative approach I obtain recursive equations for the probability distribution of the outbreak size as a function of time. I demonstrate that the expected outbreak size and its progression in time are determined by the largest eigenvalue of the reproductive number matrix and the characteristic distance between agents on the contact-graph. Finally, I discuss the impact of intervention strategies to halt epidemic outbreaks. This work provides both a qualitative understanding and tools to obtain quantitative predictions for the spreading dynamics on heterogeneous populations.

q-bio.PE↗

arXiv2006

Impact of memory on human dynamics

Our experience of web access slowing down is a consequence of the aggregated web access pattern of web users. This is just one example among several human oriented services which are strongly affected by human activity patterns. Recent empirical evidence is indicating that human activity patterns are characterized by power law distributions of inter-event times, where large fluctuations rather than regularity is the common case. I show that this temporal heterogeneity can be explained by two mechanisms: (i) humans have some perception of their past activity rate and (ii) based on that they react by accelerating or reducing their activity rate. Using these two mechanisms I explain the inter-event time statistics of Darwin's and Einstein's correspondence and the email activity within an university environment. Moreover, they are typical examples of the the accelerating and reducing class, respectively. These results are relevant to the system design of human oriented services.

physics.soc-ph↗