Discrete-time quantum walk dispersion control through long-range correlations.

We investigate the evolution dynamics of inhomogeneous discrete-time one-dimensional quantum walks displaying long-range correlations in both space and time. The associated quantum coin operators of internal states are built to exhibit random inhomogeneity distribution of long-range correlations embedded in the time evolution protocol through a fractional Brownian motion with spectrum following a power-law behavior, S(k)∼1/k^{ν}. From extensive numerical simulations with averages over a large number of independent realizations of the phases of quantum coins, the power-law correlated disorder encoded in the coin phases is shown to give rise to a wide variety of spreading patterns of the qubit states, from localized to subdiffusive, diffusive, and superdiffusive (including ballistic) behavior, depending on the relative strength of the parameters driving the correlation degree. Dispersion control is possible in one-dimensional discrete-time quantum walks by tuning the long-range correlation properties assigned to the inhomogeneous quantum coin operator.

Lévy walkers inside spherical shells with absorbing boundaries: Towards settling the optimal Lévy walk strategy for random searches.

The Lévy flight foraging hypothesis states that organisms must have evolved adaptations to exploit Lévy walk search strategies. Indeed, it is widely accepted that inverse square Lévy walks optimize the search efficiency in foraging with unrestricted revisits (also known as nondestructive foraging). However, a mathematically rigorous demonstration of this for dimensions D≥2 is still lacking. Here we study the very closely related problem of a Lévy walker inside annuli or spherical shells with absorbing boundaries. In the limit that corresponds to the foraging with unrestricted revisits, we show that inverse square Lévy walks optimize the search. This constitutes the strongest formal result to date supporting the optimality of inverse square Lévy walks search strategies.

Effect of the search space dimensionality for finding close and faraway targets in random searches.

We investigate the dependence on the search space dimension of statistical properties of random searches with Lévy α-stable and power-law distributions of step lengths. We find that the probabilities to return to the last target found (P_{0}) and to encounter faraway targets (P_{L}), as well as the associated Shannon entropy S, behave as a function of α quite differently in one (1D) and two (2D) dimensions, a somewhat surprising result not reported until now. While in 1D one always has P_{0}≥P_{L}, an interesting crossover takes place in 2D that separates the search regimes with P_{0}>P_{L} for higher α and P_{0}

Photonics bridges between turbulence and spin glass phenomena in the 2021 Nobel Prize in Physics.

A photonic connection between turbulence and spin glasses has been recently established both theoretically and experimentally using a random fiber laser as a photonic platform. Besides unveiling this interplay, it links the works of two 2021 Nobel laureates in Physics.

Landscape-scaled strategies can outperform Lévy random searches.

Information on the relevant global scales of the search space, even if partial, should conceivably enhance the performance of random searches. Here we show numerically and analytically that the paradigmatic uninformed optimal Lévy searches can be outperformed by informed multiple-scale random searches in one (1D) and two (2D) dimensions, even when the knowledge about the relevant landscape scales is incomplete. We show in the low-density nondestructive regime that the optimal efficiency of biexponential searches that incorporate all key scales of the 1D landscape of size L decays asymptotically as η_{opt}∼1/sqrt[L], overcoming the result η_{opt}∼1/(sqrt[L]lnL) of optimal Lévy searches. We further characterize the level of limited information the searcher can have on these scales. We obtain the phase diagram of bi- and triexponential searches in 1D and 2D. Remarkably, even for a certain degree of lack of information, partially informed searches can still outperform optimal Lévy searches. We discuss our results in connection with the foraging problem.

Transient dynamics in a nonequilibrium superdiffusive reaction-diffusion process: Nonequilibrium random search as a case study.

Transient regimes, often difficult to characterize, can be fundamental in establishing final steady states features of reaction-diffusion phenomena. This is particularly true in ecological problems. Here, through both numerical simulations and an analytic approximation, we analyze the transient of a nonequilibrium superdiffusive random search when the targets are created at a certain rate and annihilated upon encounters (a key dynamics, e.g., in biological foraging). The steady state is achieved when the number of targets stabilizes to a constant value. Our results unveil how key features of the steady state are closely associated to the particularities of the initial evolution. The searching efficiency variation in time is also obtained. It presents a rather surprising universal behavior at the asymptotic limit. These analyses shed some light into the general relevance of transients in reaction-diffusion systems.

Sward structure and ingestive behavior of cows in tropical pastures managed under different forage allowances / Estrutura do dossel forrageiro e comportamento ingestivo de vacas em pastos tropicais manejados sob diferentes ofertas de forragem

This study evaluated how changing the structure of Brachiaria brizantha cv. Marandu pasture under different forage allowances (FA) of 4, 7, 10 and 13kg DM/100kg BW (body weight) affected animal behavior over a two-year evaluation period. The experiment was conducted as a randomized block design with three replications (paddock). Sward height, total forage, and stem mass were lower for pastures managed with lower FA. Lower leaf mass was observed for lower FA in the second year. In hand-plucked samples, leaf and stem percentages remained unchanged in the morning but leaf percentage increased while stems decreased in the afternoon. Permanence time decreased linearly with increasing FA. In turn, a quadratic effect was observed for displacement rate. The bite rate was similar among different FAs. The results demonstrate that FA varying between 7 and 10kg DM/100kg BW are more suitable to balance the amounts of leaves and stems in the sward. The studied FA levels do not limit forage availability. Permanence time decreases and displacement rate increases as FA increases.(AU)

O objetivo foi avaliar como mudanças na estrutura de pastos de Brachiaria brizantha cv. Marandu, sob diferentes ofertas de forragem (OF) de 4, 7, 10 e 13kg MS/100kg PC, afetam o comportamento animal durante um período de avaliação de dois anos. O delineamento utilizado foi em blocos ao acaso, com três repetições (piquetes). A altura do dossel, a massa de forragem total e de colmos foram menores em pastos manejados com menores OF. A menor massa de folhas foi observada na menor OF no segundo ano. Nas amostras de pastejo simulado, as porcentagens de folhas e colmos não diferiram pela manhã, mas a porcentagem de folhas aumentou, enquanto a de colmos diminuiu à tarde. O tempo de permanência dos animais diminuiu linearmente com o aumento das OF. Efeito quadrático foi observado para taxa de deslocamento. A taxa de bocados foi similar entre as OF. Os resultados demonstram que variar as OF entre 7 e 10kg MS/100kg PC é mais adequado para balancear as quantidades de folhas e colmos no dossel forrageiro. Os níveis de OF estudados não limitam a forragem disponível. O tempo de permanência diminuí e a taxa de deslocamento aumenta com o aumento das OF.(AU)

Why Lévy α-stable distributions lack general closed-form expressions for arbitrary α.

The ubiquitous Lévy α-stable distributions lack general closed-form expressions in terms of elementary functions-Gaussian and Cauchy cases being notable exceptions. To better understand this 80-year-old conundrum, we study the complex analytic continuation p_{α}(z), z∈C, of the symmetric Lévy α-stable distribution family p_{α}(x), x∈R, parametrized by 0<α≤2. We first extend known but obscure results, and give a new proof that p_{α}(z) is holomorphic on the entire complex plane for 1<α≤2, whereas p_{α}(z) is not even meromorphic on C for 0<α<1. Next, we unveil the complete complex analytic structure of p_{α}(z) using domain coloring. Finally, motivated by these insights, we argue that there cannot be closed-form expressions in terms of elementary functions for p_{α}(x) for general α.

First-passage times in multiscale random walks: The impact of movement scales on search efficiency.

An efficient searcher needs to balance properly the trade-off between the exploration of new spatial areas and the exploitation of nearby resources, an idea which is at the core of scale-free Lévy search strategies. Here we study multiscale random walks as an approximation to the scale-free case and derive the exact expressions for their mean-first-passage times in a one-dimensional finite domain. This allows us to provide a complete analytical description of the dynamics driving the situation in which both nearby and faraway targets are available to the searcher, so the exploration-exploitation trade-off does not have a trivial solution. For this situation, we prove that the combination of only two movement scales is able to outperform both ballistic and Lévy strategies. This two-scale strategy involves an optimal discrimination between the nearby and faraway targets which is only possible by adjusting the range of values of the two movement scales to the typical distances between encounters. So, this optimization necessarily requires some prior information (albeit crude) about target distances or distributions. Furthermore, we found that the incorporation of additional (three, four, …) movement scales and its adjustment to target distances does not improve further the search efficiency. This allows us to claim that optimal random search strategies arise through the informed combination of only two walk scales (related to the exploitative and the explorative scales, respectively), expanding on the well-known result that optimal strategies in strictly uninformed scenarios are achieved through Lévy paths (or, equivalently, through a hierarchical combination of multiple scales).

Modificações na estrutura vertical de pastos de capim-xaraés sob lotação intermitente por bovinos / Changes in the vertical structure of xaraés palisadegrass pastures under intermittent stocking by cattle

O objetivo deste trabalho foi avaliar os efeitos dos índices de área foliar residual (IAFr), dos anos de avaliação e dos ciclos de pastejo sobre as modificações na estrutura vertical do dossle, bem como a proporção de componentes morfológicos de pastos capim-xaraés submetidos a intensidades de pastejo, durante dois verões. O experimento foi conduzido na Faculdade de Ciências Agrárias e Veterinária da Unesp, Câmpus de Jaboticabal, SP, e as intensidades de pastejos foram definidas por IAFr: 0,8; 1,3; 1,8 e 2,3. Quando o dossel interceptou 95% da luz incidente, os animais foram colocados no piquete para o pastejo e permaneceram até o IAFr alvo ser alcançado. Os pastejos foram realizados por vacas da raça Holandesa (Bos taurus taurus L.) não lactantes, com peso corporal médio de 450kg±50kg, utilizando-se a técnica de mob-stocking. Foram avaliadas a proporção de componentes morfológicos dos pastos e a estrutura vertical do dossel pelo aparelho de ponto inclinado. Índices de área foliar residual de 1,3 a 1,8 são os que melhores respostas apresentam em relação à estrutura vertical do dossel e à proporção dos componentes morfológicos de pastos de capim-xaraés submetidos a intensidades de pastejo.

The aim of this study was to evaluate the effects of residual leaf area index (rLAI), years of evaluation and grazing cycles in the vertical structure of the canopy and the proportion of morphological components of xaraés palisadegrass pastures submitted to grazing intensities in two summers. The experiment was carried out at the Faculdade de Ciências Agrárias e Veterinária of Unesp, Campus of Jaboticabal, SP and the intensities of grazing were defined by four rLAI: 0.8, 1.3, 1.8 and 2.3. When the canopy intercepted 95% of incident light, the animals were placed on the pasture for grazing and kept until the rLAI target had been reached. Pastures were grazed by non-lactating Holstein cows (Bos taurus taurus L.) using the mob-stocking technique. the proportion of the morphological components of the pasture and the vertical structure of the canopy by the inclined point device was evaluated. Residual leaf area index from 1.3 to 1.8 are the best in relation to the vertical structure of the canopy and proportion of the morphological components of the pasture submitted to grazing intensities.

Inferring Lévy walks from curved trajectories: A rescaling method.

An important problem in the study of anomalous diffusion and transport concerns the proper analysis of trajectory data. The analysis and inference of Lévy walk patterns from empirical or simulated trajectories of particles in two and three-dimensional spaces (2D and 3D) is much more difficult than in 1D because path curvature is nonexistent in 1D but quite common in higher dimensions. Recently, a new method for detecting Lévy walks, which considers 1D projections of 2D or 3D trajectory data, has been proposed by Humphries et al. The key new idea is to exploit the fact that the 1D projection of a high-dimensional Lévy walk is itself a Lévy walk. Here, we ask whether or not this projection method is powerful enough to cleanly distinguish 2D Lévy walk with added curvature from a simple Markovian correlated random walk. We study the especially challenging case in which both 2D walks have exactly identical probability density functions (pdf) of step sizes as well as of turning angles between successive steps. Our approach extends the original projection method by introducing a rescaling of the projected data. Upon projection and coarse-graining, the renormalized pdf for the travel distances between successive turnings is seen to possess a fat tail when there is an underlying Lévy process. We exploit this effect to infer a Lévy walk process in the original high-dimensional curved trajectory. In contrast, no fat tail appears when a (Markovian) correlated random walk is analyzed in this way. We show that this procedure works extremely well in clearly identifying a Lévy walk even when there is noise from curvature. The present protocol may be useful in realistic contexts involving ongoing debates on the presence (or not) of Lévy walks related to animal movement on land (2D) and in air and oceans (3D).

Robustness of optimal random searches in fragmented environments.

The random search problem is a challenging and interdisciplinary topic of research in statistical physics. Realistic searches usually take place in nonuniform heterogeneous distributions of targets, e.g., patchy environments and fragmented habitats in ecological systems. Here we present a comprehensive numerical study of search efficiency in arbitrarily fragmented landscapes with unlimited visits to targets that can only be found within patches. We assume a random walker selecting uniformly distributed turning angles and step lengths from an inverse power-law tailed distribution with exponent µ. Our main finding is that for a large class of fragmented environments the optimal strategy corresponds approximately to the same value µ(opt)≈2. Moreover, this exponent is indistinguishable from the well-known exact optimal value µ(opt)=2 for the low-density limit of homogeneously distributed revisitable targets. Surprisingly, the best search strategies do not depend (or depend only weakly) on the specific details of the fragmentation. Finally, we discuss the mechanisms behind this observed robustness and comment on the relevance of our results to both the random search theory in general, as well as specifically to the foraging problem in the biological context.

Efficient search of multiple types of targets.

Random searches often take place in fragmented landscapes. Also, in many instances like animal foraging, significant benefits to the searcher arise from visits to a large diversity of patches with a well-balanced distribution of targets found. Up to date, such aspects have been widely ignored in the usual single-objective analysis of search efficiency, in which one seeks to maximize just the number of targets found per distance traversed. Here we address the problem of determining the best strategies for the random search when these multiple-objective factors play a key role in the process. We consider a figure of merit (efficiency function), which properly "scores" the mentioned tasks. By considering random walk searchers with a power-law asymptotic Lévy distribution of step lengths, p(ℓ)∼ℓ(-µ), with 1<µ≤3, we show that the standard optimal strategy with µ(opt)≈2 no longer holds universally. Instead, optimal searches with enhanced superdiffusivity emerge, including values as low as µ(opt)≈1.3 (i.e., tending to the ballistic limit). For the general theory of random search optimization, our findings emphasize the necessity to correctly characterize the multitude of aims in any concrete metric to compare among possible candidates to efficient strategies. In the context of animal foraging, our results might explain some empirical data pointing to stronger superdiffusion (µ<2) in the search behavior of different animal species, conceivably associated to multiple goals to be achieved in fragmented landscapes.

Improving trauma documentation in the emergency department.

Adequate and complete trauma documentation continues to be a struggle for many health care institutions. A recently accredited Pennsylvania trauma center shared its struggles and successes in the improvement of trauma documentation in the emergency department. Such interventions included education for new nurses and ongoing education, a user-friendly trauma flow sheet, and a peer review process. Fewer documentation deficiencies were seen after the implementation of such interventions. Variables found to have a positive impact on these results were recognition of patients with low severity injuries, the peer review process, and emergency department administrative involvement.

Unveiling a mechanism for species decline in fragmented habitats: fragmentation induced reduction in encounter rates.

Several studies have reported that fragmentation (e.g. of anthropogenic origin) of habitats often leads to a decrease in the number of species in the region. An important mechanism causing this adverse ecological impact is the change in the encounter rates (i.e. the rates at which individuals meet other organisms of the same or different species). Yet, how fragmentation can change encounter rates is poorly understood. To gain insight into the problem, here we ask how landscape fragmentation affects encounter rates when all other relevant variables remain fixed. We present strong numerical evidence that fragmentation decreases search efficiencies thus encounter rates. What is surprising is that it falls even when the global average densities of interacting organisms are held constant. In other words, fragmentation per se can reduce encounter rates. As encounter rates are fundamental for biological interactions, it can explain part of the observed diminishing in animal biodiversity. Neglecting this effect may underestimate the negative outcomes of fragmentation. Partial deforestation and roads that cut through forests, for instance, might be responsible for far greater damage than thought. Preservation policies should take into account this previously overlooked scientific fact.

Conditions under which a superdiffusive random-search strategy is necessary.

Intuitively, lower target densities and lower detection capabilities should demand more sophisticated search strategies for a random search reasonable outcome. In contrast, when targets are easily found, a simple Brownian random walk strategy is enough. But where is the threshold between these two scenarios and when is optimization really necessary? We address this considering the interplay between two essential scales in random search, the average distance between neighbor targets l(0) and the detection capability r(v). In the limit cases the ratio ß=r(v)/l(0) suffices to characterize the problem. For low (high) ß a superdiffusive behavior is (is not) crucial for the process optimization. However, there is a crossover range, which is a nontrivial function of r(v) and l(0), separating the two regimes. We analyze this intermediate region, common in nature, and discuss the often overlooked important trade between resources availability and the searcher location power. Our results highlight contexts where efficient random search is a key factor for survival, such as in animal foraging.

Dissipative Lévy random searches: universal behavior at low target density.

We investigate the problem of survival at the very low target-density limit and report on a second-order phase transition for one-dimensional random searches in which the energy cost of locomotion is a function of the distance traveled by the searcher. Surprisingly, from analytical calculations (also tested numerically) we find identical critical exponents for arbitrary energy cost functions. We conclude that there is a single universality class that describes this process.

How landscape heterogeneity frames optimal diffusivity in searching processes.

Theoretical and empirical investigations of search strategies typically have failed to distinguish the distinct roles played by density versus patchiness of resources. It is well known that motility and diffusivity of organisms often increase in environments with low density of resources, but thus far there has been little progress in understanding the specific role of landscape heterogeneity and disorder on random, non-oriented motility. Here we address the general question of how the landscape heterogeneity affects the efficiency of encounter interactions under global constant density of scarce resources. We unveil the key mechanism coupling the landscape structure with optimal search diffusivity. In particular, our main result leads to an empirically testable prediction: enhanced diffusivity (including superdiffusive searches), with shift in the diffusion exponent, favors the success of target encounters in heterogeneous landscapes.