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Octavio Miramontes

Publications and source records attributed to Octavio Miramontes.

18 recordsLinked to original sources

Emergent dynamical phases and collective motion in termites

Termites which are able to forage in the open can be often seen, in the field or in the lab: (i) wandering around, forming no observable pattern, or (ii) clustering themselves in a dense and almost immobile pack, or (iii) milling about in a circular movement. Despite been well reported patterns, they are normally regarded as independent phenomena whose specific traits have never been properly quantified. Evidence, however, favours the hypothesis that these are interdependent patterns, arisen from self-organised interactions and movement among workers. After all, termites are a form of active matter where blind cooperative individuals are self-propelled and lack the possibility of visual cues to spatially orientate and align. It follows that their non-trivial close-contact patterns could generate motion-collision induced phase separations. This would then trigger the emergence of these three patterns (disorder, clustering, milling) as parts of the same continuum. By inspecting termite groups confined in arenas, we could quantitatively describe each one of these patterns in detail. We identified disorder, clustering and milling spatial patterns. These phases and their transitions are characterised aiming to offer refinements in the understanding of these aspects of self-propelled particles in active matter where close-range contacts and collisions are important.

q-bio.PE

Shannon entropy: an econophysical approach to cryptocurrency portfolios

Cryptocurrency markets have attracted many interest for global investors because of their novelty, wide online availability, increasing capitalization and potential profits. In the econophysics tradition we show that many of the most available cryptocurrencies have return statistics that do not follow Gaussian distributions but heavy--tailed distributions instead. Entropy measures are also applied showing that portfolio diversification is a reasonable practice for decreasing return uncertainty.

physics.soc-ph

Visibility graphs of animal foraging trajectories

The study of self-propelled particles is a fast-growing research topic where biologically inspired movement is increasingly becoming of much interest. A relevant example is the collective motion of social insects, whose variety and complexity offer fertile grounds for theoretical abstractions. It has been demonstrated that the collective motion involved in the searching behavior of termites is consistent with self-similarity, anomalous diffusion and Lévy walks. In this work, we use visibility graphs -- a method that maps time series into graphs and quantifies the signal complexity via graph topological metrics -- in the context of social insects foraging trajectories extracted from experiments. Our analysis indicates that the patterns observed for isolated termites change qualitatively when the termite density is increased, and such change cannot be explained by jamming effects only, pointing to collective effects emerging due to non-trivial foraging interactions between insects as the cause. Moreover, we find that such an onset of complexity is maximized for intermediate termite densities.

cond-mat.stat-mech

Lévy flight movements prevent extinctions and maximize population abundances in fragile Lotka Volterra systems

Multiple-scale mobility is ubiquitous in nature and has become instrumental for understanding and modeling animal foraging behavior. However, the impact of individual movements on the long-term stability of populations remains largely unexplored. We analyze deterministic and stochastic Lotka Volterra systems, where mobile predators consume scarce resources (prey) confined in patches. In fragile systems (that is, those unfavorable to species coexistence), the predator species has a maximized abundance and is resilient to degraded prey conditions when individual mobility is multiple scaled. Within the Lévy flight model, highly superdiffusive foragers rarely encounter prey patches and go extinct, whereas normally diffusing foragers tend to proliferate within patches, causing extinctions by overexploitation. Lévy flights of intermediate index allow a sustainable balance between patch exploitation and regeneration over wide ranges of demographic rates. Our analytical and simulated results can explain field observations and suggest that scale-free random movements are an important mechanism by which entire populations adapt to scarcity in fragmented ecosystems.

q-bio.PE

On a dynamical approach to some prime number sequences

In this paper we show how the cross-disciplinary transfer of techniques from Dynamical Systems Theory to Number Theory can be a fruitful avenue for research. We illustrate this idea by exploring from a nonlinear and symbolic dynamics viewpoint certain patterns emerging in some residue sequences generated from the prime number sequence. We show that the sequence formed by the residues of the primes modulo $k$ are maximally chaotic and, while lacking forbidden patterns, display a non-trivial spectrum of Renyi entropies which suggest that every block of size $m>1$, while admissible, occurs with different probability. This non-uniform distribution of blocks for $m>1$ contrasts Dirichlet's theorem that guarantees equiprobability for $m=1$. We then explore in a similar fashion the sequence of prime gap residues. This sequence is again chaotic (positivity of Kolmogorov-Sinai entropy), however chaos is weaker as we find forbidden patterns for every block of size $m>1$. We relate the onset of these forbidden patterns with the divisibility properties of integers, and estimate the densities of gap block residues via Hardy-Littlewood $k$-tuple conjecture. We use this estimation to argue that the amount of admissible blocks is non-uniformly distributed, what supports the fact that the spectrum of Renyi entropies is again non-trivial in this case. We complete our analysis by applying the Chaos Game to these symbolic sequences, and comparing the IFS attractors found for the experimental sequences with appropriate null models.

math.NT

Fruitful symbioses between termites and computers

The living-together of distinct organisms in a single termite nest along with the termite builder colony, is emblematic in its ecological and evolutionary significance. On top of preserving biodiversity, these interspecific and intraspecific symbioses provide useful examples of interindividual associations thought to underly transitions in organic evolution. Being interindividual in nature, such processes may involve emergent phenomena and hence call for analytical solutions provided by computing tools and modelling, as opposed to classical biological methods of analysis. Here we provide selected examples of such solutions, showing that termite studies may profit from a symbiotic-like link with computing science to open up wide and new research avenues in ecology and evolution.

q-bio.PE

Lévy flights and self-similar exploratory behaviour of termite workers: beyond model fitting

Animal movements have been related to optimal foraging strategies where self-similar trajectories are central. Most of the experimental studies done so far have focused mainly on fitting statistical models to data in order to test for movement patterns described by power-laws. Here we show by analyzing over half a million movement displacements that isolated termite workers actually exhibit a range of very interesting dynamical properties --including Lévy flights-- in their exploratory behaviour. Going beyond the current trend of statistical model fitting alone, our study analyses anomalous diffusion and structure functions to estimate values of the scaling exponents describing displacement statistics. We evince the fractal nature of the movement patterns and show how the scaling exponents describing termite space exploration intriguingly comply with mathematical relations found in the physics of transport phenomena. By doing this, we rescue a rich variety of physical and biological phenomenology that can be potentially important and meaningful for the study of complex animal behavior and, in particular, for the study of how patterns of exploratory behaviour of individual social insects may impact not only their feeding demands but also nestmate encounter patterns and, hence, their dynamics at the social scale.

q-bio.PE

Social Evolution: New Horizons

Cooperation is a widespread natural phenomenon yet current evolutionary thinking is dominated by the paradigm of selfish competition. Recent advanced in many fronts of Biology and Non-linear Physics are helping to bring cooperation to its proper place. In this contribution, the most important controversies and open research avenues in the field of social evolution are reviewed. It is argued that a novel theory of social evolution must integrate the concepts of the science of Complex Systems with those of the Darwinian tradition. Current gene-centric approaches should be reviewed and com- plemented with evidence from multilevel phenomena (group selection), the constrains given by the non-linear nature of biological dynamical systems and the emergent nature of dissipative phenomena.

q-bio.PE

The effects of spatially heterogeneous prey distributions on detection patterns in foraging seabirds

Many attempts to relate animal foraging patterns to landscape heterogeneity are focused on the analysis of foragers movements. Resource detection patterns in space and time are not commonly studied, yet they are tightly coupled to landscape properties and add relevant information on foraging behavior. By exploring simple foraging models in unpredictable environments we show that the distribution of intervals between detected prey (detection statistics)is mostly determined by the spatial structure of the prey field and essentially distinct from predator displacement statistics. Detections are expected to be Poissonian in uniform random environments for markedly different foraging movements (e.g. Lévy and ballistic). This prediction is supported by data on the time intervals between diving events on short-range foraging seabirds such as the thick-billed murre ({\it Uria lomvia}). However, Poissonian detection statistics is not observed in long-range seabirds such as the wandering albatross ({\it Diomedea exulans}) due to the fractal nature of the prey field, covering a wide range of spatial scales. For this scenario, models of fractal prey fields induce non-Poissonian patterns of detection in good agreement with two albatross data sets. We find that the specific shape of the distribution of time intervals between prey detection is mainly driven by meso and submeso-scale landscape structures and depends little on the forager strategy or behavioral responses.

q-bio.PE

Non-Lévy mobility patterns of Mexican Me'Phaa peasants searching for fuelwood

We measured mobility patterns that describe walking trajectories of individual Me'Phaa peasants searching and collecting fuelwood in the forests of "La Montaña de Guerrero" in Mexico. These one-day excursions typically follow a mixed pattern of nearly-constant steps when individuals displace from their homes towards potential collecting sites and a mixed pattern of steps of different lengths when actually searching for fallen wood in the forest. Displacements in the searching phase seem not to be compatible with Lévy flights described by power-laws with optimal scaling exponents. These findings however can be interpreted in the light of deterministic searching on heavily degraded landscapes where the interaction of the individuals with their scarce environment produces alternative searching strategies than the expected Lévy flights. These results have important implications for future management and restoration of degraded forests and the improvement of the ecological services they may provide to their inhabitants.

q-bio.PE

Number theoretic example of scale-free topology inducing self-organized criticality

In this work we present a general mechanism by which simple dynamics running on networks become self-organized critical for scale free topologies. We illustrate this mechanism with a simple arithmetic model of division between integers, the division model. This is the simplest self-organized critical model advanced so far, and in this sense it may help to elucidate the mechanism of self-organization to criticality. Its simplicity allows analytical tractability, characterizing several scaling relations. Furthermore, its mathematical nature brings about interesting connections between statistical physics and number theoretical concepts. We show how this model can be understood as a self-organized stochastic process embedded on a network, where the onset of criticality is induced by the topology.

nlin.AO

Evidence for biological Lévy flights stands

Edwards et al. [Nature 449, 1044-1048 (2007)] revisited well-known studies reporting power-laws in the frequency distribution of flight duration of wandering albatrosses, and concluded that no Lévy process could model recent observations with higher resolution. Here we show that this re-analysis suffers from a conceptual misunderstanding, and that the new albatross data remain consistent with a biological Lévy flight.

q-bio.PE

Phase transition and computational complexity in a stochastic prime number generator

We introduce a prime number generator in the form of a stochastic algorithm. The character of such algorithm gives rise to a continuous phase transition which distinguishes a phase where the algorithm is able to reduce the whole system of numbers into primes and a phase where the system reaches a frozen state with low prime density. In this paper we firstly pretend to give a broad characterization of this phase transition, both in terms of analytical and numerical analysis. Critical exponents are calculated, and data collapse is provided. Further on we redefine the model as a search problem, fitting it in the hallmark of computational complexity theory. We suggest that the system belongs to the class NP. The computational cost is maximal around the threshold, as common in many algorithmic phase transitions, revealing the presence of an easy-hard-easy pattern. We finally relate the nature of the phase transition to an average-case classification of the problem.

cs.CC

Phase transition in a stochastic prime number generator

We introduce a stochastic algorithm that acts as a prime number generator. The dynamics of such algorithm gives rise to a continuous phase transition which separates a phase where the algorithm is able to reduce a whole set of integers into primes and a phase where the system reaches a frozen state with low prime density. We present both numerical simulations and an analytical approach in terms of an annealed approximation, by means of which the data are collapsed. A critical slowing down phenomenon is also outlined.

physics.comp-ph

Scale-free foraging by primates emerges from their interaction with a complex environment

Scale-free foraging patterns are widespread among animals. These may be the outcome of an optimal searching strategy to find scarce randomly distributed resources, but a less explored alternative is that this behaviour may result from the interaction of foraging animals with a particular distribution of resources. We introduce a simple foraging model where individuals follow mental maps and choose their displacements according to a maximum efficiency criterion, in a spatially disordered environment containing many trees with a heterogeneous size distribution. We show that a particular tree size frequency distribution induces non-Gaussian movement patterns with multiple spatial scales (Lévy walks). These results are consistent with tree size variation and Spider monkey (Ateles geoffroyi) foraging patterns. We discuss the consequences that our results may have for the patterns of seed dispersal by foraging primates.

q-bio.PE

Unexpected trends in termite survival

Survival in groups of termites is known to be socially facilitated since individual longevity is increased together with the size of the group. Here we report on experimental evidence that survival as a function of group size in {\textit Cornitermes cumulans} (Kollar) does not increase asysmptotically but it peaks in a group size range at which individual longevity is maximal. Strinkly, this same effect in other social insects was noted more than fifty years ago, but it was regarded as ``aberrant'' since it has been generally assumed that individual survival should increase with the size of the group. We also provide evidence that individual activity --measured as mobility-- is maximal at approximately the same group-size range as the observed survival

physics.bio-ph

Interface Motion and Pinning in Small World Networks

We show that the nonequilibrium dynamics of systems with many interacting elements located on a small-world network can be much slower than on regular networks. As an example, we study the phase ordering dynamics of the Ising model on a Watts-Strogatz network, after a quench in the ferromagnetic phase at zero temperature. In one and two dimensions, small-world features produce dynamically frozen configurations, disordered at large length scales, analogous of random field models. This picture differs from the common knowledge (supported by equilibrium results) that ferromagnetic short-cuts connections favor order and uniformity. We briefly discuss some implications of these results regarding the dynamics of social changes.

cond-mat.dis-nn

Levy walk patterns in the foraging movements of spider monkeys (Ateles geoffroyi)

Scale invariant patterns have been found in different biological systems, in many cases resembling what physicists have found in other nonbiological systems. Here we describe the foraging patterns of free-ranging spider monkeys (Ateles geoffroyi) in the forest of the Yucatan Peninsula, Mexico and find that these patterns resemble what physicists know as Levy walks. First, the length of a trajectory s constituent steps, or continuous moves in the same direction, is best described by a power-law distribution in which the frequency of ever larger steps decreases as a negative power function of their length. The rate of this decrease is very close to that predicted by a previous analytical Levy walk model to be an optimal strategy to search for scarce resources distributed at random Viswanathan et al 1999). Second, the frequency distribution of the duration of stops or waiting times also approximates a power-law function. Finally, the mean square displacement during the monkeys first foraging trip increases more rapidly than would be expected from a random walk with constant step length, but within the range predicted for Levy walks. In view of these results, we analyze the different exponents characterizing the trajectories described by females and males, and by monkeys on their own or when part of a subgroup. We discuss the origin of these patterns and their implications for the foraging ecology of spider monkeys.

physics.bio-ph