arXiv subjects

Alexei Vazquez

Publications and source records attributed to Alexei Vazquez.

At least 19 recordsLinked to original sources

arXiv2026

Absorbing phase transition in a queueing model of coupled adaptive agents

What decides whether people do things together or separately? Many activities cannot be carried out alone, and an individual must rank them against the private tasks competing for the same time. We address this within the priority-queue description of human activity by letting each agent choose the priority of a shared task rather than drawing it from a fixed distribution: the value of the joint activity, discounted by the estimated risk that the partner will not take part. Participation becomes strategic, and the model acquires a phase transition. A coupled phase, in which joint activity is sustained, is separated from an absorbing solitary phase by a saddle-node bifurcation that we obtain in closed form. The transition is discontinuous and the solitary phase is absorbing, so collapse is irreversible unless an agent persists unilaterally for of order one memory time, a cost we also compute. The heavy-tailed interevent statistics that motivate queueing models of human dynamics survive only in a narrow window at the transition, and there the exponent is fixed by the fraction of time spent coupled rather than by queue length: the universality classes of the non-strategic model do not survive the introduction of choice. On a network, attention divides as $1/(k+a)$ and fixes a critical degree beyond which no coupled state exists, so the solitary phase percolates according to the Molloy--Reed criterion with the second moment truncated at that degree --- formally an attack on hubs, with no attacker. For group activities the critical degree falls as the $(m-1)$th root, implying a maximum group size. The transition organises two quantities already measured in communication records: a finite capacity for keeping ties active, and the decay of ties whose rhythm is interrupted.

physics.soc-ph↗

arXiv2026

Local network growth: How simple rules drive network complexity

The Internet, a living cell, a circle of friends, a billion-dollar construction project: these systems share almost nothing -- yet, drawn as networks, they look astonishingly alike. Each has a few giant hubs among a multitude of sparsely connected nodes, short paths between any two parts, dense local clustering, communities, and many redundant routes. For two decades such patterns have been credited to "preferential attachment," the rich getting richer -- a rule that, taken literally, asks every newcomer to survey the whole network before it links. This book makes a simpler case, and defends it one mechanism at a time: the global regularities of real networks are not imposed from above but emerge from purely local rules, in which each new node acts only on a node it has reached and that node's immediate neighbours. A surfer following links, a friend introducing a friend, a gene copied with its connections -- none consults the network as a whole, yet each builds, in the aggregate, the full and unmistakable signature of a real complex system. Written for the curious reader as much as the specialist, with the ideas told in plain language and the mathematics set aside in boxes that can be skipped, it shows how citation graphs, the web, social ties, protein interactions, and project schedules all grow themselves from the same handful of local rules -- one local decision at a time.

physics.soc-ph↗

arXiv2026

The Ramsey community number as a renormalization-group crossing

The Ramsey community number $r_k$ is the smallest size at which a network is better described by communities than by none, under a Bayesian detection rule. On the diamond hierarchical lattice we show that $r_k$ is an exact renormalization-group crossing: the block-model sufficient statistics obey a linear map with eigenvalues $\{bs,b\}$, the degree-corrected evidence density flows to $\ln K$ at a community fixed point, and $r_k$ is the generation at which the running evidence clears the detection threshold. Degree correction advances detection by two generations. We derive $r_k(b,s;q)$ in closed form for the whole family. Finally, placing on the lattice the Reichardt--Bornholdt community Hamiltonian -- whose ground state is the partition itself -- we find an exact community-ordered phase: below the ferromagnetic critical temperature the two hubs lock into opposite communities for any resolution $\gamma>0$, a staggered order that persists as $n\to\infty$. Allowing each nested sub-community its own label, the optimal partition is a hierarchy of $q_{\rm opt}\sim\sqrt{n}$ communities, so the number of Potts states that best describes the network grows with the network. This hierarchy orders thermally level by level, through a cascade of first-order transitions whose temperatures fall as $1/\ln q$, so every stable level persists as $n\to\infty$: the emergent partition is detectable, optimal, and thermodynamically ordered.

cond-mat.stat-mech↗

arXiv2026

Community structure of the pseudofractal web

The Ramsey community number $r_\kappa$ is the smallest network size at which a graph is better described by a partition into communities than by no partition, under a prescribed detection rule. On a scale-free graph this question is confounded: a block model can split the network merely to absorb its degree distribution. I compute $r_\kappa$ analytically for the deterministic pseudofractal scale-free web of Dorogovtsev, Goltsev, and Mendes, separating genuine community structure from degree heterogeneity with two closed-form detection rules. Under a plain Bernoulli stochastic block model, the web's natural recursive bipartition is unpreferred while small and breaks at $r_\kappa=1095$ nodes, with a log-evidence growing as $(\ln 3-\tfrac{2}{3}\ln 2)n$. Under a degree-corrected model tested against the configuration-model null, the same partition survives, breaking far earlier at $r_\kappa=42$, with a log-evidence growing as $(2\ln 3-\tfrac{4}{3}\ln 2)n$ -- exactly twice the plain slope, and independent of the prior. Degree correction reverses the ordering of the candidate cuts, demoting the hub-leaf split and elevating the recursive one. Because the web is self-similar, the best description is not two communities but a nested hierarchy: the degree-corrected evidence keeps rising as the partition is refined, and is maximised at of order $\sqrt{n}$ communities of $\sim\sqrt{n}$ nodes. A purely local recursive rule thus builds true hierarchical community structure, over and above the scale-free degree sequence it also produces, in an exactly solvable setting.

physics.soc-ph↗

arXiv2026

The ring wants to be broken

The Ramsey community number $r_\kappa$ is the minimum network size at which a graph's connectivity is better described by a partition into communities than by no partition, under a prescribed community-detection rule. It was introduced through numerical simulations of networks grown by local rules, which suggested that community structure can emerge without any node heterogeneity. Here I compute $r_\kappa$ analytically for the simplest homogeneous, locally wired graph: the circulant ring lattice $C_n(1,\dots,c)$. Using a Bernoulli stochastic block model with symmetric $\mathrm{Beta}$ priors as the detection rule, the Bayesian evidence for a balanced two-community partition and for the unpartitioned network are both obtained in closed form, so the transition between them can be located exactly. The result is a sharp dependence on the interaction range: the plain cycle ($c=1$) is never partitioned, its two-community posterior decaying as $n^{-(2\alpha+3)}$, so $r_\kappa=\infty$; but the next-nearest-neighbour ring ($c=2$) acquires a finite $r_\kappa\simeq 35$ nodes, above which the partition is preferred with a log-evidence growing as $(\ln 2)\,n$. This provides an exactly solvable instance of community emergence in a network with no built-in communities, and shows that a minimal amount of local connectivity is enough to break the ring.

physics.soc-ph↗

arXiv2026

Local network evolution rules drive shortest path multiplicity

The shortest path multiplicity, here denoted by $\mu$, is an important metric of complex networks. For real networks $\mu$ is high and it correlates with the network community structure. Since local network evolution induces network communities, it is possible that a high shortest path multiplicity is the natural expectation of local evolution rules. Here I demonstrate, by means of numerical simulations, that this is indeed the case. For random graphs with arbitrary degree distributions $p_k$, $\langle\mu\rangle\sim \langle k(k-1)\rangle / (\langle k\rangle e)$, growing with the network size when $p_k\sim k^{-\gamma}$ and $\gamma\leq3$. For networks generated by local rules, $\langle\mu\rangle$ increases with the network size and it does so faster than what is observed in their randomized versions. Furthermore, the number of communities increases with the network size and the correlation with $\langle \mu\rangle$ follows.

physics.soc-ph↗

arXiv2025

Emergence of network communities driven by local rules

Natural systems are modeled by networks with nodes and links. Often the nodes are segregated into communities with different connectivity patterns. Node heterogeneity such as political affiliation in social networks or biological function in gene networks are highlighted as key factors driving the segregation of nodes into communities. Here, by means of numerical simulations, I show that node heterogeneity is not a necessary requirement. To this end I introduce the Ramsey community number, $r_ \kappa$, the minimum graph size that warranties the emergence of network communities with almost certainty. Using the stochastic block model and Infomap methods for community detection, I show that networks generated by local rules have finite $r_ \kappa$ values while their randomized versions do not have emergent communities. I conjecture that network communities are an emergent property of networks evolving with local rules.

physics.soc-ph↗

arXiv2024

Deduction of the Bromilow's time-cost model from the fractal nature of activity networks

In 1969 Bromilow observed that the time $T$ to execute a construction project follows a power law scaling with the project cost $C$, $T\sim C^B$ [Bromilow 1969]. While the Bromilow's time-cost model has been extensively tested using data for different countries and project types, there is no theoretical explanation for the algebraic scaling. Here I mathematically deduce the Bromilow's time-cost model from the fractal nature of activity networks. The Bromislow's exponent is $B=1-\alpha$, where $1-\alpha$ is the scaling exponent between the number of activities in the critical path $L$ and the number of activities $N$, $L\sim N^{1-\alpha}$ with $0\leq\alpha<1$ [Vazquez et al 2023]. I provide empirical data showing that projects with low serial/parallel (SP)% have lower $B$ values than those with higher SP%. I conclude that the Bromilow's time-cost model is a law of activity networks, the Bromilow's exponent is a network property and forecasting project duration from cost should be limited to projects with high SP%.

physics.soc-ph↗

arXiv2024

Selective advantage of aerobic glycolysis over oxidative phosphorylation

The utilization of glycolysis in aerobic conditions have been a subject of debate for more than a century. A hypothesis supported by previous data is that glycolysis has a higher rate of ATP production per protein mass and per occupied volume than oxidative phosphorylation (OxPhos). However, a recent work by Shen et al14 challenges previous estimates, reporting that OxPhos has a higher rate of ATP production per protein mass than glycolysis. Here I show that Shen et al14 make a key assumption that is a subject of debate: that the proteomic cost of OxPhos is limited to proteins in enzymes of OxPhos and the TCA cycle. I argue that an intact mitochondria is required for functional OxPhos and therefore the whole mitochondrial protein content should be included for the cost estimate of OxPhos. After doing so, glycolysis is the most efficient pathway per protein mass or per volume fraction.

q-bio.BM↗

arXiv2023

Emerge of scaling in project schedules

A project schedule contains a network of activities, the activity durations, the early and late finish dates for each activity, and the associated total float or slack times, the difference between the late and early dates. Here I show that the distribution of activity durations and total floats of construction project schedules exhibit a power law scaling. The power law scaling of the activity durations is explained by a historical process of specialization fragmenting old activities into new activities with shorter duration. In contrast, the power law scaling of the total floats distribution across activities is determined by the activity network. I demonstrate that the power law scaling of the activity duration distribution is essential to obtain a good estimate of the project delay distribution, while the actual total float distribution is less relevant. Finally, using extreme value theory and scaling arguments, I provide a mathematical proof for reference class forecasting for the project delay distribution. The project delay cumulative distribution function is $G(z) = \exp( - (z_c/z)^{1/s})$, where $s>0$ and $z_c>0$ are shape and scale parameters. Furthermore, if activity delays follow a lognormal distribution, as the empirical data suggests, then $s=1$ and $z_c \sim N^{0.20}d_{\max}^{1+0.20(1-\gamma_d)}$, where $N$ is the number of activities, $d_{\max}$ the maximum activity duration in units of days and $\gamma_d$ the power law exponent of the activity duration distribution. These results offer new insights about project schedules, reference class forecasting and delay risk analysis.

physics.soc-ph↗

arXiv2023

Manageable to unmanageable transition in a fractal model of project networks

Project networks are characterized by power law degree distributions, a property that is known to promote spreading. In contrast, the longest path length of project networks scales algebraically with the network size, which improves the impact of random interventions. Using the duplication-split model of project networks, I provide convincing evidence that project networks are fractal networks. The average distance between nodes scales as $\langle d\rangle \sim N^{\beta}$ with $0<\beta<1$. The average number of nodes $\langle N\rangle_d$ within a distance $d$ scales as $\langle N\rangle_d\sim d^{D_f}$, with a fractal dimension $D_f=1/\beta>1$. Furthermore, I demonstrate that the duplication-split networks are fragile for duplication rates $q q_c$, in spite the mean out-degree diverges with increasing the network size. I conclude the project networks generated by the duplication-split model are manageable for $q<q_c$ and unmanageable otherwise.

physics.soc-ph↗

arXiv2023

Robustness and complexity of directed and weighted metabolic hypergraphs

Metabolic networks are probably among the most challenging and important biological networks. Their study provides insight into how biological pathways work and how robust a specific organism is against an environment or therapy. Here we propose a directed hypergraph with edge-dependent vertex weight as a novel framework to represent metabolic networks. This hypergraph-based representation captures higher-order interactions among metabolites and reactions, as well as the directionalities of reactions and stoichiometric weights, preserving all essential information. Within this framework, we propose the communicability and the search information as metrics to quantify the robustness and complexity of directed hypergraphs. We explore the implications of network directionality on these measures and illustrate a practical example by applying them to the small-scale e\_coli\_core model. Additionally, we compare the robustness and the complexity of 30 different models of metabolism, connecting structural and biological properties. Our findings show that antibiotic resistance is associated with high structural robustness, while the complexity can distinguish between eukaryotic and prokaryotic organisms.

physics.soc-ph↗

arXiv2023

Percolation in higher order networks via mapping to chygraphs

Percolation theory investigates systems of interconnected units, their resilience to damage and their propensity to propagation. For random networks we can solve the percolation problems analytically using the generating function formalism. Yet, with the introduction of higher order networks, the generating function calculations are becoming difficult to perform and harder to validate. Here, I illustrate the mapping of percolation in higher order networks to percolation in chygraphs. Chygraphs are defined as a set of complexes where complexes are hypergraphs with vertex sets in the set of complexes. In a previous work I reported the generating function formalism to percolation in chygraphs and obtained an analytical equation for the order parameter. Taking advantage of this result, I recapitulate analytical results for percolation problems in higher order networks and report extensions to more complex scenarios using symbolic calculations. The code for symbolic calculations can be found at https://github.com/av2atgh/chygraph.

cond-mat.dis-nn↗

arXiv2023

Activity delay patterns in project networks

Delays in activities completion drive human projects to schedule and cost overruns. It is believed activity delays are the consequence of multiple idiosyncrasies without specific patterns or rules. Here we show that is not the case. Using data for 180 construction project schedules, we demonstrate that activity delays satisfy a universal model that we call the law of activity delays. After we correct for delay risk factors, what remains follows a log-normal distribution.

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

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

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↗