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We analyze the dynamics of room evacuation for mixed populations that include both competitive and cooperative individuals through numerical simulations using the social force model. Cooperative agents represent well-trained individuals who know how to behave in order to reduce risks within high-density crowds. We consider that competitive agents can imitate cooperative behavior when they are in close proximity to cooperators. We study the effects of the imitation of cooperative behavior on the duration and safety of evacuations, analyzing evacuation time and other quantities of interest for varying parameters such as the proportions of mixing, the aspect ratio of the room, and the parameters characterizing individual behaviors. Our main findings reveal that the addition of a relatively small number of cooperative agents into a crowd can reduce evacuation time and the density near the exit door, making the evacuation faster and safer despite an increase in the total number of agents. In particular, for long spaces such as corridors, a small number of added cooperative agents can significantly facilitate the evacuation process. We compare our results with those of systems without imitation and also study the general role of cooperation, providing further analysis for homogeneous populations. Our main conclusions emphasize the potential relevance of training people how to behave in high-density crowds

This study investigates the utilization of various mathematical models for comprehending and managing outbreaks of infectious diseases, with a specific focus on how different distributions of incubation times influence predictions regarding epidemics. Two methodologies are examined: a compartmental SEnIR ODE model, which represents an enhanced version of the mean-field SEIR model, and a stochastic agent-based complex network model. Our findings demonstrate that the selection of diverse incubation time distributions can result in noteworthy discrepancies in critical epidemic forecasts, highlighting the crucial role of precise modeling in shaping effective public health interventions. The research underscores the necessity of integrating authentic distribution patterns into epidemic modeling to increase its reliability and applicability

Networks are a convenient way to represent many interactions among different entities as they provide an efficient and clear methodology to evaluate and organize relevant data. While there are many features for characterizing networks there is a quantity that seems rather elusive: Complexity. The quantification of the complexity of networks is nowadays a fundamental problem. Here, we present a novel tool for identifying the complexity of ecological networks. We compare the behavior of two relevant indices of complexity: K-complexity and Single value decomposition (SVD) entropy. For that, we use real data and null models. Both null models consist of randomized networks built by swapping a controlled number of links of the original ones. We analyze 23 plant-pollinator and 19 host-parasite networks as case studies. Our results show interesting features in the behavior for the K-complexity and SVD entropy with clear differences between pollinator-plant and host-parasite networks, especially when the degree distribution is not preserved. Although SVD entropy has been widely used to characterize network complexity, our analyses show that K-complexity is a more reliable tool. Additionally, we show that degree distribution and density are important drivers of network complexity and should be accounted for in future studies.

Lately, concepts such as lockdown, quarantine, and social distancing have become very relevant since they have been associated with essential measures in the prevention and mitigation of COVID-19. While some conclusions about the effectiveness of these measures could be drawn from field observations, many mathematical models aimed to provide some clues. However, the reliability of these models is questioned, especially if the social structure is not included in them. In this work, we propose a mesoscopic model that allows the evaluation of the effect of measures such as social distancing and lockdown when the social topology is taken into account. The model is able to predict successive waves of infections without the need to account for reinfections, and it can qualitatively reproduce the wave patterns observed across many countries during the COVID-19 pandemic. Subsequent waves can have a higher peak of infections if the restrictiveness of the lockdown is above a certain threshold. The model is flexible and can implement various social distancing strategies by adjusting the restrictiveness and the duration of lockdown measures or specifying whether they occur once or repeatedly. It also includes the option to consider essential workers that do not isolate during a lockdown.

We consider a couple of models for the dynamics of the populations of two interacting species, inspired by Lotka-Volterra's classical equations. The novelty of this work is that the interaction terms are non local and the interaction occurs within a bounded range. These terms include the competitive intraspecific interaction among individuals and the interspecific terms for which we consider two cases: Competition and predation. The results show that not only the non-locality induces spatial structures but also allows for the survival of the species when due to predation or the competitive exclusion extinction was expected, and even promotes spatio-temporal patterns not linked to eventual temporal oscillations in the local case. In this work we also explore some interesting details about the behavior of the population dynamics that shows spatial patterns that interfere in a way that leads to non-trivial results.

The flow of grains through narrow apertures posses an extraordinary challenge: clogging. Strategies to alleviate the effect of clogging, such as the use of external vibration, are always part of the design of machinery for the handling of bulk materials. It has recently been shown that one way to reduce clogging is to use a small fraction of small particles as an additive. Besides, several works reported that self-repelling magnetic grains can flow through narrow apertures with little clogging, which suggest these are excellent candidates as "lubricating" additives for other granular materials. In this work, we study the effect of adding self-repelling magnetic particles to a sample of grains in two-dimensions. We find that, in contrast with intuition, the added magnetic grains not necessarily aid the flow of the original species.

The search for more realistic models for interacting species has produced many adaptations of the original Lotka-Volterra equations, such as the inclusion of the Allee effect and the different Holling's types of functional response. In the present work we show that a correct implementation of both ideas together requires a careful formulation. We focus our work in the fact that a density dependent carrying capacity, combined with the Allee effect, can lead to meaningless effects. We illustrate the difficulties in predator-prey and two-species competition models, together with our proposed solution of the careful inclusion of the corresponding cubic terms.

In this work we analyze an evolutionary game that incorporates the ideas presented by Cipolla in his work \textit{The fundamental laws of human stupidity}. The game considers four strategies, three of them are inherent to the player behavior and can evolve via an imitation dynamics, while the fourth one is associated to an eventual behavior that can be adopted by any player at any time with certain probability. This fourth strategy corresponds to what Cipolla calls a stupid person. The probability of behaving stupidly acts as a parameter that induces a phase transition in the steady the distribution of strategies among the population.

In this work we present an evolutionary game inspired by the work of Carlo Cipolla entitled The basic laws of human stupidity. The game expands the classical scheme of two archetypical strategies, collaborators and defectors, by including two additional strategies. One of these strategies is associated to a stupid player that according to Cipolla is the most dangerous one as it undermines the global wealth of the population. By considering a spatial evolutionary game and imitation dynamics that go beyond the paradigm of a rational player we explore the impact of Cipolla' s ideas and analyze the extent of the damage that the stupid players inflict on the population

Apis mellifera plays a crucial role as pollinator of the majority of crops linked to food production and thus its presence is currently fundamental to our health and survival. The composition and configuration of the landscape in which Apis mellifera lives will likely determine the well-being of the hives and the pollination service that their members can provide to the crops. Here we present a spatially explicit model that predicts the spatial distribution of visits by Apis mellifera to crops, by simulating daily trips of honey bees, the demographical dynamic of each hive and their honey production. This model goes beyond existing approaches by including 1) a flower resource affected by the feedback interaction between nectar extraction, pollination, blossoming and repeated visits, 2) a pollinators dynamic that allows competition through short term resource depletion, 3) a probabilistic approach of the foraging behavior, modeling the fact that the pollinators have only partial knowledge of the resource on their surroundings, and 4) the specific and systematic foraging behavior and strategies of Apis mellifera at the moment of choosing foraging sites, as opposed to those adopted by solitary and wild pollinators. With a balance between simplicity and realism we show the importance of keeping a minimal fraction of natural habitat in an agricultural landscape. We also evaluate the effects of the landscape's structure on pollination, and demonstrate that there exists an optimal size of natural habitat patches that maximizes the pollination service for a fixed fraction of natural habitat., Comment: To appear in Ecological modelling

We present a study on the rock art of Northern Patagonia based on network analysis and communities detection. We unveil a significant aggregation of archaeological sites, linked by common rock art motifs that turn out to be consistent with their geographical distribution and archaeological background of hunter-gatherer stages of regional peopling and land use. This exploratory study will allow us to approach more accurately some social strategies of visual communication entailed by rock art motif distribution, in space and time.

We develop a mathematical model of extinction and coexistence in a generic predator-prey ecosystem composed of two herbivores in asymmetrical competition and a hunter exerting a predatory pressure on both species. With the aim of representing the satiety of hunters when preys are overabundant, we introduce for the predation behavior a dependence on preys density. Specifically, predation is modeled as growing proportionally to the presence of herbivores at low density, and saturating when the total population of prey is sufficiently large. The model predicts the existence of different regimes depending on the parameters considered: survival of a single species, coexistence of two species and extinction of the third one, and coexistence of the three species. But more interestingly, in some regions parameters space the solutions oscillate in time, both as a transient phenomena and as persistent oscillations of constant amplitude. The phenomenon is not present for the more idealized linear predation model, suggesting that it can be the source of real ecosystems oscillations.

The present work analyses a particular scenario of consensus formation, where the individuals navigate across an underlying network defining the topology of the walks. The consensus, associated to a given opinion coded as a simple messages, is generated by interactions during the agent's walk and manifest itself in the collapse of the various opinions into a single one. We analyze how the topology of the underlying networks and the rules of interaction between the agents promote or inhibit the emergence of this consensus. We find that non-linear interaction rules are required to form consensus and that consensus is more easily achieved in networks whose degree distribution is narrower.

We study a model of seed dispersal that considers the inclusion of an animal disperser moving diffusively, feeding on fruits and transporting the seeds, which are later deposited and capable of germination. The dynamics depends on several population parameters of growth, decay, harvesting, transport, digestion and germination. In particular, the deposition of transported seeds at places away from their collection sites produces a delay in the dynamics, whose effects are the focus of this work. Analytical and numerical solutions of different simplified scenarios show the existence of travelling waves. The effect of zoochory is apparent in the increase of the velocity of these waves. The results support the hypothesis of the relevance of animal mediated seed dispersion when trying to understand the origin of the high rates of vegetable invasion observed in real systems., Comment: Accepted in Journal of Theoretical Biology

In this work we present a model for the evacuation of pedestrians from an enclosure considering a continuous space substrate and discrete time. We analyze the influence of behavioral features that affect the use of the empty space, that can be linked to the attitudes or characters of the pedestrians. We study how the interaction of different behavioral profiles affects the needed time to evacuate completely a room and the occurrence of clogging. We find that neither fully egotistic nor fully cooperative attitudes are optimal from the point of view of the crowd. In contrast, intermediate behaviors provide lower evacuation times. This lead us to identify some phenomena closely analogous to the {\em faster-is-slower} effect. The proposed model enables for the introduction of Game Theory elements to solve conflicts between pedestrians which try to occupy the same space. Moreover, it allows for distinguishing between the role of the attitudes in the search for empty space and the attitudes in the conflicts. In the present version we only focus on the first of these instances.

We propose an evolutionary coordination game to formalize a simplified model of the evolution of strategies during human courtship. The dynamics, derived from the consideration of experimental observations on human social behavior driven by self-esteem, turns out to be non-payoff monotonic. This property gives rise to nontrivial evolution in the players' strategies, which we study both numerically and analytically.

We study a mechanistic mathematical model of extinction and coexistence in a generic hunter-prey ecosystem. The model represents typical scenarios of human invasion and environmental change, characteristic of the late Pleistocene, concomitant with the extinction of fauna in many regions of the world. As a first approach we focus on a small trophic web of three species, including two herbivores in asymmetric competition, in order to characterize the generic behaviors. Specifically, we use a stochastic dynamical system, allowing the study of the role of fluctuations and spatial correlations. We show that the presence of hunters drives the superior herbivore to extinction even in habitats that would allow coexistence, and even when the pressure of hunting is lower than on the inferior one. The role of system size and fluctuating populations is addressed, showing an ecological meltdown in small systems in the presence of humans. The time to extinction as a function of the system size, as calculated with the model, shows a good agreement with paleontological data. Other findings show the intricate play of the anthropic and environmental factors that may have caused the extinction of megafauna., Comment: Quaternary International (2015, in press)

We present a model for a random walk with memory, phenomenologically inspired in a biological system. The walker has the capacity to remember the time of the last visit to each site and the step taken from there. This memory affects the behavior of the walker each time it reaches an already visited site modulating the probability of repeating previous moves. This probability increases with the time elapsed from the last visit. A biological analog of the walker is a frugivore, with the lattice sites representing plants. The memory effect can be associated with the time needed by plants to recover its fruit load. We propose two different strategies, conservative and explorative, as well as intermediate cases, leading to non intuitive interesting results, such as the emergence of cycles., Comment: To appear in Phys. Rev. E

We study a simple model of a forager as a walk that modifies a relaxing substrate. Within it simplicity, this provides an insight on a number of relevant and non-intuitive facts. Even without memory of the good places to feed and no explicit cost of moving, we observe the emergence of a finite home range. We characterize the walks and the use of resources in several statistical ways, involving the behavior of the average used fraction of the system, the length of the cycles followed by the walkers, and the frequency of visits to plants. Preliminary results on population effects are explored by means of a system of two non directly interacting animals. Properties of the overlap of home ranges show the existence of a set of parameters that provides the best utilization of the shared resource.

Since its first formulations almost a century ago, mathematical models for disease spreading contributed to understand, evaluate and control the epidemic processes.They promoted a dramatic change in how epidemiologists thought of the propagation of infectious diseases.In the last decade, when the traditional epidemiological models seemed to be exhausted, new types of models were developed.These new models incorporated concepts from graph theory to describe and model the underlying social structure.Many of these works merely produced a more detailed extension of the previous results, but some others triggered a completely new paradigm in the mathematical study of epidemic processes. In this review, we will introduce the basic concepts of epidemiology, epidemic modeling and networks, to finally provide a brief description of the most relevant results in the field., Comment: 17 pages, 13 figures

We study a model of associative memory based on a neural network with small-world structure. The efficacy of the network to retrieve one of the stored patterns exhibits a phase transition at a finite value of the disorder. The more ordered networks are unable to recover the patterns, and are always attracted to mixture states. Besides, for a range of the number of stored patterns, the efficacy has a maximum at an intermediate value of the disorder. We also give a statistical characterization of the attractors for all values of the disorder of the network., Comment: 5 pages, 4 figures (eps)