Abstracts

Abstracts

Armando Relaño 

UCM

General theory for discrete symmetry-breaking equilibrium states in quantum systems

We derive a general theory for discrete symmetry-breaking in quantum systems, with the following highlights: (i) below the critical temperature, quantum dynamics is characterized by the existence of two non-commuting constants of motion; (ii) the resulting equilibrium ensemble predicts equilibrium states consisting in the superposition of the different symmetry-breaking branches, for example positive and negative magnetizations in the transverse-field Ising model; (iii) upon introducing a symmetry-breaking term in the Hamiltonian, one of the two constants of motion survives and stabilizes spontaneous symmetry-breaking even for quite small systems. We illustrate this result with numerical experiments.

Jorge Estrada-Álvarez

UCM

Alternative strategies to electron hydrodynamics

Viscous flow of interacting electrons in two dimensional materials [1] features a bunch of exotic  effects. A model akin the Navier-Stokes equation for classical fluids accounts for them in the so- called hydrodynamic regime. This regime occurs when electron-electron collisions are frequent  enough. We performed a detailed analysis of the hydrodynamic requirements and found three new  routes to achieve viscous electron flow [1]: favoring frequent inelastic collisions, the application  of a magnetic field or a high-frequency electric field. More reflective edges of the material further  span the range of validity of the above conditions. Our results show that the conventional  requirement of frequent electron-electron collisions is too restrictive, and, therefore, materials and  phenomena to be described using hydrodynamics are widened. We discuss recent experiments  regarding Poiseuille-like flows, superballistic conduction and negative resistances as  signatures for viscous flow onset. We conclude that these usual signatures of viscous electron  flow are achieved by following alternative meta-hydrodynamic routes. [1] Estrada-Álvarez, J. et. al. Meta-hydrodynamic routes to viscous electron flow. Preprint  https://arxiv.org/abs/2306.16210 (2023)

Antonio Rodríguez Mesas

UPM

Scaling laws in the $\alpha-$XY model

The  $\alpha-$XY  model  generalizes  the  well  known  Hamiltonian  Mean  Field    model  by introducing an interaction term  decaying with the distance among rotators as $r^{-\alpha}$, with $\alpha>0$ being the  range of interaction. In the long-range regime, $\alpha/d < 1$, $d$ being the dimension,  the  model  presents  a  quasistationary  state  (QSS)    at  a  temperature  $T_{\text{QSS}}$ before attaining the Boltzmann-Gibbs temperature. We have studied $T_{QSS}$ as well as the duration $t_{QSS}$ of the QSS,   as a function of parameters  $(N, \alpha,  d,  U)$,  with  $N$  the  number  of  rotators  and  $U$  the  total  energy  per particle, and found the scaling relations i) $t_\text{QSS}\propto N^{A(\apha/d)}e^{B(N)(\alpha/d)^2}$ [1],  ii)  $t_QSS\sim  (U_c -U)^{\xi}$  with  a  critical  exponent $\xi\simeq 5/3$ independent of $\alpha/d$ [2] and iii) $T_{\text{QSS}} -T_{\infty} \sim N ^{-\beta}$, with $T_{\infty} = 2U -1$ and the critical exponent $\beta$ decaying from 1 to 0 as $\alpha/d$ goes from 0 to 1 [3].

[1] A. Rodríguez, F. D. Nobre and C. Tsallis, Phys. Rev. E {\bf 103}, 042110 (2021)\newline [2] A. Rodríguez, F. D. Nobre and C. Tsallis, Phys. Rev. E {\bf 104}, 014144 (2021) \newline [3] A. Rodríguez, F. D. Nobre and C. Tsallis, Phys. Rev. E {\bf 105}, 044111 (2022)

Anxo Sánchez

UC3M

Emergencia de segundo orden en sistemas complejos: normas sociales y comportamiento

Resumen: En esta charla discuto el concepto de emergencia de segundo orden como característica clave de los sistemas complejos, en particular los sociales. La emergencia de segundo orden es la retroalimentación de los fenómenos emergentes de primer orden, que aparecen a nivel macro, sobre el nivel micro, en los agentes o componentes del sistema. Un ejemplo destacado de emergencia de segundo orden es el caso de las normas sociales. Las normas sociales surgen cuando un grupo de personas suficientemente grande comparte expectativas sobre lo que hacen las personas del grupo y lo que creen que debería hacerse. Por tanto, la norma social surge de la experiencia de los individuos y de las interacciones entre ellos. Posteriormente, las normas sociales se convierten en impulsoras del comportamiento de las personas, dando lugar así a la emergencia de segundo orden. En esta charla discuto cómo las normas sociales se forman y evolucionan en el tiempo en función de factores externos, como el riesgo de un resultado desastroso, y cómo impulsan las decisiones de la gente. Para ello desarrollamos una teoría matemática que incluye los beneficios materiales en la función de utilidad de cada individuo junto con los beneficios de cumplir la norma, de seguir las propias creencias y de ajustarse a alguna prescripción externa. La teoría se valida con experimentos y ofrece una explicación directa de cómo se produce el bucle de retroalimentación que origina el fenómeno de segundo orden. Por último, presento otro ejemplo de emergencia de segundo orden, a saber, la conformación de redes personales de relaciones por los antecedentes culturales de los individuos, mostrando cómo se relacionan al predecir la nacionalidad de un grupo de personas a partir de datos reales sobre sus redes de egos.

Miguel A. González-Casado

UC3M

The Dynamics of Signed Social Networks

In this work we develop a model able to accurately describe the dynamics of a signed social network composed by high school students, where connections represent their personal relationships. To achieve this, we analyze a dataset containing empirical data on this network to gain insights into the underlying mechanisms driving its dynamics. We identify three mechanisms: Structural Balance (driving the creation of friendships and partially the emergence of enmities), conflict (driving the dissolution of friendships and partially the formation of enmities), and reconciliation (driving the disappearance of enmities). Secondly, we construct the model that integrates these three mechanisms at a local level, taking into account the cognitive limitations of individuals, which limit the number of friendships and enmities they can maintain. The model is then calibrated using our empirical data. Our findings show that the model performs exceptionally well in describing accurately the data, including the distribution of positive and negative relationships, the abundances and dynamics of different triangle motifs and the distribution of balance within the network, among others.

Miguel Aguilar Janita

URJC

Estrés en el modelo del votante ruidoso

En esta charla presentaré un nuevo modelo para la dinámica de la formación de opiniones, el cual analizaremos bajo la aproximación de campo medio. Dicho modelo puede entenderse como una generalización del modelo del votante ruidoso, en el cual los agentes pueden cambiar entre dos opiniones disponibles bien mediante un mecanismo de copia o  bien mediante un mecanismo intrínseco, el cual está afectado por el  grado de polarización en el sistema. Además, consideramos las dos posibilidades de que el mecanismo de actualización intrínseco se vea afectado tanto positiva como negativamente bajo un incremento de la polarización. Encontramos cuatro fases del sistema, caracterizadas por la forma de la distribución de probabilidad estacionaria, y estudiamos las transiciones entre ellas. En el límite termodinámico, solo dos de estas cuatro fases sobreviven. Los resultados de nuestro estudio teórico, realizado mediante el análisis de la ecuación maestra, están en muy buen acuerdo con los resultados de nuestras simulaciones numéricas, realizadas mediante el método Gillespie. 

Luis F Seoane

CNB

Topological Communities in Complex Networks

A plethora of complex systems, from gene interactions to human communities, are captured by graphs or networks. Networks connect nodes (e.g. neurons) through edges (synapses) to summarize a system's structure. Some information is local (e.g. direct neighbors), but other is emergent and needs the complete graph to be worked out. Popular methods in network science extract distributed information from the graph -- e.g. community detection finds nodes that are significantly more connected between them than to the rest of the network. These kinds of algorithms dominate the field of network science and rely heavily on geometric proximity between nodes. Other ways of looking at complex networks have been overlooked. We introduce Topological Communities (TC), an alternative, fundamental perspective to analyze graphs. We find clusters based on topological similarity, irrespective of their geometric proximity. We thus identify nodes that play similar roles (e.g. forming disperse backbones or bridging between communities) that are missed by current techniques. In our analysis, relevant yet hidden graph structures (including some classical communities) stand out spontaneously, guiding which features should be reported about each graph. This novel method complements existing techniques and we propose that it should be a standard analysis applied to relevant networks. We illustrate topological communities, among others, in global airport connections, scientific collaboration networks, and human connectomes. We derive novel conclusions for these systems, suggesting ample applications for networks science and beyond. 

Saúl Ares

CNB

Feedback control of organ size precision in the Drosophila eye

Biological processes are intrinsically noisy and yet, the result of development, like the species-specific size and shape of organs, is usually remarkably precise. This precision suggests the existence of mechanisms of feedback control that ensure that deviations from a target size are minimized. Still, we have very limited understanding of how these mechanisms operate. Here, we investigate the problem of organ size precision using the Drosophila eye. The size of the adult eye depends on the rates at which eye progenitor cells grow and differentiate. We first find that the progenitor net growth rate results from the balance between their proliferation and apoptosis, with this latter contributing to determining both final eye size and its variability. In turn, apoptosis of progenitor cells is hampered by Dpp, a BMP2/4 signaling molecule transiently produced by early differentiating retinal cells. Our genetic experiments show how the status of retinal differentiation is communicated to progenitors through the differentiation-dependent production of Dpp. By adjusting the rate of apoptosis, Dpp concentration exerts a feedback control over the net growth of progenitors to reduce final eye size variability. To dissect the dynamics of eye growth and differentiation, we have devised a theoretical model that captures the essential biological processes involved. This model is defined by three key variables: the width of the progenitor cell region (G), the width of the differentiated retinal cell region (R), and an intermediary strip of recently differentiated retinal cells (Rn) that produce Dpp. These variables collectively encapsulate the transformative stages of cellular development in the eye. The dynamics of these variables are governed by the interplay of progenitor cell proliferation, apoptosis, and cellular differentiation, with transitions from progenitor cells to newly differentiated cells (G -> Rn) and from newly differentiated to fully differentiated retinal cells (Rn -> R). To account for the intrinsic stochasticity in biological systems, we have incorporated this interplay into a set of three Langevin equations. These equations, with noise terms modeling the fluctuations related to each of the basic processes in play, effectively capture the fluctuations inherent in the biological processes. Our model faithfully reproduces the observed dynamics of eye growth and differentiation in experimental settings. Moreover, it provides a means to investigate the contribution of each process’ fluctuations to the asymmetry typically seen between the two eyes of a single fly. Through linear stability analysis, we further demonstrate the stabilizing role of apoptosis in arresting eye growth. Consequently, our model not only captures the dynamics of eye development but also provides a framework for exploring the complex interplay of the constituent processes and their roles in developmental robustness. Reference: Navarro, T., Iannini, A., Neto, M., Campoy-Lopez, A., Muñoz-García, J., Pereira, P.S., Ares, S.* and Casares F.*, 2023. Feedback control of organ size precision is mediated by BMP2-regulated apoptosis in the Drosophila eye. PLoS Biology (under review). 

Pablo Catalán

UC3M

De biólogo a matemático... Y vuelta a biólogo

Donde compartiré mi reciente vuelta al mundo experimental junto a Saúl Ares en el CNB, tras años alejado de las pipetas. Hablaremos de bacterias, resistencia a antibióticos y terapias secuenciales.

Juan Pablo Miranda López

UCM

Self-organized states of solutions of active ring polymers in bulk and under confinement

In the presented work we study, by means of numerical simulations, the behaviour of a suspension of active ring polymers in the bulk and under lateral confinement. When changing the separation between the confining planes and the polymers' density, we detect the emergence of a self-organised dynamical state, characterised by the coexistence of slowly diffusing clusters of rotating disks and faster rings moving in between them. This system represents a peculiar case at the crossing point between polymer, liquid crystals and active matter physics, where the interplay between activity, topology and confinement leads to a spontaneous segregation of a one component solution. 

Horacio Serna

UCM

Collective motion of self-propelled particles in periodic heterogeneous media

We study systems of swarming self-propelled particles when in contact with periodic arrays of circular obstacles in 2D. The particles motion is described by the original Vicsek model with angular noise. The obstacles are arranged in a square lattice and elastic collisions between the particles and the obstacles are considered. The parameters of the model are set to obtain a big swarm of particles with a preferred direction in bulk. We observe that by increasing the radius of the obstacles a transition from super-diffusive to diffusive-like behaviour can be induced. This change in the system’s dynamic behaviour is reflected in structural properties: the super diffusive behaviour corresponds to one big cluster moving in a preferred direction as in bulk, whereas the diffusive-like behaviour corresponds to many small clusters moving in different directions. We also observed that the separation between the obstacles plays a role in the system’s behaviour by shifting the packing fraction of obstacles at which the transition occurs. Finally, we give some perspectives on the study of active agents in complex environments and their potential use in technological applications.

Mario Castro

UPC

Apología de la vaca esférica: modelos sencillos para sistemas complejos

El éxito de la Ciencia de la Complejidad se debe, fundamentalmente, a su capacidad de explicar comportamientos emergentes y universales a partir de modelos relativamente sencillos. Por contra, en áreas afines como la Biología matemática o la Ecología, existe una tendencia creciente hacia la formulación de modelos detallados que tratan de capturar matemática decenas de mecanismos microscópicos y que dan lugar a una multitud de parámetros libres. Muchos de estos parámetros no se pueden medir experimentalmente y, en el mejor de los casos, los valores estimados divergen en un uno o dos órdenes de magnitud. En esta charla trataré de argumentar que el concepto de vaca esférica (es decir un modelo simple, pero no demasiado) no es solo una manera conveniente de atacar problemas complejos sino que, en muchos casos, es la única manera honesta pero a la vez constructiva de avanzar en esas disciplinas afines. Avances recientes en conceptos metodológicos como la identificabilidad o los llamados modelos sloppy" permiten construir, de una manera sistemática y basada en datos, modelos sencillos que capturan los ingredientes esenciales de modelos más sofisticados pero imposibles de falsificar experimentalmente. Utilizando ejemplos tomados de la Inmunología de sistemas , la Epidemiología o la Ecología, mostraré algunos problemas comunes en su modelado y varias posibles soluciones complementarias: la construcción de modelos top-down, la reducción sistemática de modelos, y el modelado de nuestra ignorancia mediante el uso de distribuciones de probabilidad. En definitiva, mi intención es resolver la tensión entre la complejidad que imponen las ciencias afines y la sorprendente eficacia de los modelos sencillos. 

Carla Alejandre Villalobos

CAB

Modeling a primordial, non-enzymatic RNA replication in the early Earth

Carla Alejandre1, Adrián Aguirre-Tamaral2, Carlos Briones1 and Jacobo Aguirre1,3 1Centro de Astrobiología (CAB), CSIC-INTA, Madrid, Spain 2Centro de Biotecnoloía y Genómica de Plantas (CBGP), UPM-INIA, Madrid, Spain 3Grupo Interdisciplinar de Sistemas Complejos (GISC), Madrid, Spain

Life appeared on Earth around 3.800 million years ago, not long after our planet became habitable. The hypothesis of the primordial soup describes a very young planet in which prebiotic chemistry could have progressively increased the available molecular complexity in several out-of-equilibrium environments such as surface lakes, seacoasts, water-mineral interfaces, oceanic hydrothermal vents, etc. In some of those scenarios, the accumulation of organic compounds and the availability of energetic sources laid the foundations for the emergence of life. One of the widely accepted hypotheses related to the origin of life, widely supported by experimental data, is the RNA world. It suggests that life was originated in an environment in which informational and functional RNA molecules were able to self-replicate (through the activity of RNA ribozymes). Later evolution of these primordial RNA populations would give rise to the decoupling of genotype and phenotype in the RNA/protein and DNA/RNA/protein worlds [1]. However, the sophisticated machinery associated with current RNA polymerase enzymes could not emerge randomly from those initial organic compounds that were available in the stage of prebiotic chemistry. Instead, a step-wise, ligation-based modular evolution of short RNA sequences seems a more plausible pathway for the appearance of the first RNA molecules with enzymatic properties [2]. Nevertheless, even modular evolution of RNA requires the presence of an up-to-now unknown replicative mechanism to guarantee the availability of copies of specific RNA sequences (oligoribonucleotides) in which selection can act. In this work we describe the development of a theoretical and computational model to simulate the polymerization of single ribonucleotides and a subsequent non-enzymatic, template-dependent replication mechanism for the primordial RNA molecules. These processes would have arisen in a confined space such as the interphase between an aqueous solution and the interlayers of clay minerals, an environment known to favor RNA polymerization [3, 4].  In our simulations, two RNA polymerization processes are described: (i) surface-dependent, random polymerization of ribonucleotides, and (ii) template-dependent polymerization thanks to RNA complementary base pairing (RNA replication). This conceptually simple in silico model allows us to test how environmental conditions can affect the length and fidelity of RNA copies, as well as to study how the efficiency of the RNA replicative phenomenology depends on the parameters of the system, such as the amount of available ribonucleotides, size of genetic alphabet, the strength of chemical bonds or environmental fluctuations. Our theoretical and numerical results point towards oscillatory environments as necessary requirements for the formation of efficient copies of long enough RNA sequences, in agreement with recent works in the field that suggest that fluctuating environments where necessary for life to emerge [5].  [1] K. Ruiz-Mirazo, C. Briones, and A. de la Escosura, Prebiotic systems chemistry: New perspectives for the origins of life, Chemical Reviews 114, 285-366 (2014). [2] C. Briones, M. Stich, and SC. Manrubia, The dawn of the RNA World: toward functional complexity through ligation of random RNA oligomers, RNA 15, 743749 (2009). [3] W. Huang, and J.P. Ferris, One-step, regioselective synthesis of up to 50-mers of RNA oligomers by montmorillonite catalysis, J. Am. Chem. Soc. 128, 89148919 (2006). [4] H. Kaddour, S. Gerislioglu, P. Dalai, T. Miyoshi, C. Wesdemiotis, and N. Sahai, Nonenzymatic RNA oligomerization at the mineral-water Interface: An insight into the adsorption-polymerization relationship, J. Phys. Chem. C 122, 29386-29397 (2018). [5] H. Boigenzahn, and J. Yin, Glycine to oligoglycine via sequential trimetaphosphate activation steps in drying environments, Origins of Life and Evolution of Biospheres 52, 249261 (2022). 

Iker Atienza Diez

CNB

SARS-CoV-2 Virus Transition to Neutrality

Genotype networks are powerful representations of great aid in the interpretation of evolutionary processes, especially for highly heterogeneous molecular populations. These networks can be constructed at different scales, for instance by deep-sequencing evolving in-vitro populations or through geographically extended data of a circulating pathogen. In this contribution, we present the SARSCoV-2 (SARS2) genotype network (GN) reconstructed from genomic data spanning from December 2019 to March 2023, with Wuhan-Hu-1 strain (GenBank: MN908947.3) as wildtype (WT) reference sequence.   SARS2 genome is about 30,000 base-pairs long. The reconstruction of the network using whole genomes is computationally unfeasible, so we have selected the Receptor Binding Domain (RBD) section of the viral Spike protein. The RBD contains 223 amino acids (S:319-541) involved in the recognition of the human ACE2 receptor, and thus in cell entry of the virus. A haplotype is any sequence that differs from the WT. After curating the original dataset, we analyse 5, 799, 310 complete genomes to extract the set of different haplotypes in the RBD section of interest; we identify 28, 686 unique haplotypes with an abundance ranging from 1 to 1, 915, 492 sequences. Each identified haplotype is a node in our GN, and two nodes are connected through an edge if their sequences differ by a single mutation: SARS2 GN has 27, 634 nodes and 56, 122 edges. Our analysis of the topological properties of this GN reveals that it is weakly disassortative and has an average degree ⟨k⟩ ≃ 4.   Since genomes in the dataset are labelled according to the variant they belong to, an analysis using the subset of haplotypes in each variant is possible. Since our study is limited to the RBD, there is some degeneracy in this classification, with 916 (3.31%) multi-variant haplotypes, that is, sequences that can be classified in two or more variants. All variants of concern, except Omicron, are relatively close to the WT (< 5 mutations). Omicron-labelled haplotypes are more diverse in terms of mutations, suggesting that this variant has explored a larger region of genotype space. Our analysis supports as well that the fitness landscape around this variant is flatter, since its associated subnetwork has a significantly larger number of nodes with high degree, consistently leading to a less disassortative pattern than that of previous variants. Interestingly, the SARS2 GN contains a large number of cycles, pointing at a non-uniqueness of evolutionary pathways linking different haplotypes within and between variants.   We have also explored the temporal appearance of different haplotypes and found, first, a burst of haplotype diver sity (12/2021-01/2022) associated to the emergence of Omicron and, second, a waxing and waning pattern in haplotype abundance caused by the sequential emergence of new successful variants. We observe that some early-explored, but not fixed, haplotypes re-emerge when Omicron arises, pos sibly due to other accompanying mutations out of the RBD region.

Aniello Lamp

UC3M

Sparse species interactions reproduce abundance correlation patterns in microbial communities

During the last decades macroecology has identified broad-scale patterns of abundances and diversity of microbial communities and put forward some potential explanations for them. However, these advances are not paralleled by a full understanding of the dynamical processes behind them. In particular, abundance fluctuations of different species are found to be correlated, both across time and across communities in metagenomic samples. Reproducing such correlations through appropriate population models remains an open challenge. The present paper tackles this problem and points to sparse species interactions as a necessary mechanism to account for them. Specifically, we discuss several possibilities to include interactions in population models and recognize Lotka-Volterra constants as a successful ansatz. For this, we design a Bayesian inference algorithm to extract sets of interaction constants able to reproduce empirical probability distributions of pairwise correlations for diverse biomes. Importantly, the inferred models still reproduce well-known single-species macroecological patterns concerning abundance fluctuations across both species and communities. Endorsed by the agreement with the empirically observed phenomenology, our analyses provide insights on the properties of the networks of microbial interactions, revealing that sparsity is a crucial feature.