Shannon Entropy: An Econophysical Approach to Cryptocurrency Portfolios.

Cryptocurrency markets have attracted many interest for global investors because of their novelty, wide on-line 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, instead following heavy-tailed distributions. Entropy measures are applied, showing that portfolio diversification is a reasonable practice for decreasing return uncertainty.

Scale-free movement patterns in termites emerge from social interactions and preferential attachments.

As the number or density of interacting individuals in a social group increases, a transition can develop from uncorrelated and disordered behavior of the individuals to a collective coherent pattern. We expand this observation by exploring the fine details of termite movement patterns to demonstrate that the value of the scaling exponent µ of a power law describing the Lévy walk of an individual is modified collectively as the density of animals in the group changes. This effect is absent when termites interact with inert obstacles. We also show that the network of encounters and interactions among specific individuals is selective, resembling a preferential attachment mechanism that is important for social networking. Our data strongly suggest that preferential attachments, a phenomenon not reported previously, and favorite interactions with a limited number of acquaintances are responsible for the generation of Lévy movement patterns in these social insects.

Lévy foraging patterns of rural humans.

Movement patterns resembling Lévy walks, often attributed to the execution of an advantageous probabilistic searching strategy, are found in a wide variety of organisms, from cells to human hunter-gatherers. It has been suggested that such movement patterns may be fundamental to how humans interact and experience the world and that they may have arisen early in our genus with the evolution of a hunting and gathering lifestyle. Here we show that Lévy walks are evident in the Me'Phaa of Mexico, in Brazilian Cariri farmers and in Amazonian farmers when gathering firewood, wild fruit and nuts. Around 50% of the search patterns resemble Lévy walks and these are characterized by Lévy exponents close to 1.7. The other search patterns more closely resemble bi-phasic walks. We suggest potential generative mechanisms for the occurrence of these ubiquitous Lévy walks which can be used to guide future studies on human mobility. We show that frequent excursions and meanderings from pre-existing trails can account for our observations.

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.

On a Dynamical Approach to Some Prime Number Sequences.

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, unexpectedly 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. We numerically find that this sequence is again chaotic (positivity of Kolmogorov-Sinai entropy), however chaos is weaker as forbidden patterns emerge 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 Iterated Function System (IFS) attractors found for the experimental sequences with appropriate null models.

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.

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 (Uria lomvia). However, Poissonian detection statistics is not observed in long-range seabirds such as the wandering albatross (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.

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

In this Letter 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.

Individual basis for collective behaviour in the termite, Cornitermes cumulans.

Interactions among individuals in social groups lead to the emergence of collective behaviour at large scales by means of multiplicative non-linear effects. Group foraging, nest building and task allocation are just some well-known examples present in social insects. However the precise mechanisms at the individual level that trigger and amplify social phenomena are not fully understood. Here we show evidence of complex dynamics in groups of the termite, Cornitermes cumulans (Kollar) (Isoptera: Termitidae), of different sizes and qualitatively compare the behaviour observed with that exhibited by agent-based computer models. It is then concluded that certain aspects of social behaviour in insects have a universal basis common to interconnected systems and that this may be useful for understanding the temporal dynamics of systems displaying social behaviour in general.

Phase transition in a stochastic prime-number generator.

We introduce a stochastic algorithm that acts as a prime-number generator. The dynamics of this 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.

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 individual primates 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 field observations of 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.

Commercial gouache as a dye for termites in laboratory assays

Estudos foram conduzidos para avaliar a adequabilidade de um corante barato, prontamente disponível e aplicável topicamente, como marcador para operários de Cornitermes cumulans (Insecta: Isoptera) em ensaios de laboratório. Os padrões de sobrevivência dos cupins marcados não se distinguem daqueles apresentados pelos cupins sem marcação, cerca de 300 minutos desde o início do experimento. Após esse limiar, a mortalidade dos cupins marcados é acelerada quando comparada com cupins não marcados. Tal mortalidade, entretanto, não difere entre cupins marcados com duas cores diferentes da mesma marca comercial de guache. Concluiu-se que o guache comercial é adequado como marcador de operários de C. cumulans, desde que (i) experimentos não investiguem hipóteses explicitamente dependentes de tempos de sobrevivência maiores do que 300 min., ou então que (ii) experimentos incluam um grupo "controle" composto de cupins corados com um pigmento diferente da cor usada no grupo "tratamento".

The colour of noise in short ecological time series data.

The statistical properties of ecological time series data and general trends therein have historically been of great interest to ecologists. In recent years, there has been a focus on establishing the relative importance of 'memory' in these data. The classic study by Pimm & Redfearn (1988 Nature, 334, 613-614) has been extremely important in establishing within the ecological community the idea that population time series are generally 'red-shifted' (dominated by long-term trends). This conclusion was reached by exploring the relationship between observed variability and census length in ecological data and comparing them with those for artificially generated data. Here, we highlight some subtle problems with this approach and suggest possible alternative methods of analysis, especially when the time series of interest are short.

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 to random field models. This picture differs from the common knowledge (supported by equilibrium results) that ferromagnetic shortcut connections favor order and uniformity. We briefly discuss some implications of these results regarding the dynamics of social changes.