A small molecule that walks non-directionally along a track without external intervention

Charge of the light brigade: A molecule is able to walk back and forth upon a five-foothold pentaethylenimine track without external intervention. The 1D random walk is highly processive (mean step number 530) and exchange takes place between adjacent amine groups in a stepwise fashion. The walker performs a simple task whilst walking: quenching of the fluorescence of an anthracene group sited at one end of the track. Copyright © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Distribution of the angle of rotation plane random walks

We study the probability distribution of the angle by which the tangent to the trajectory rotates in the course of a plane random walk. It is shown that the determination of this distribution function can be reduced to an integral equation, which can be rigorously transformed into a differential equation of Hill's type. We derive the asymptotic distribution for very long walks.

Not in all Walks of Life? : Social Differences in Suicide Mortality

In Finland, the suicide mortality trend has been decreasing during the last decade and a half, yet suicide was the fourth most common cause of death among both Finnish men and women aged 15 64 years in 2006. However, suicide does not occur equally among population sub-groups. Two notable social factors that position people at different risk of suicide are socioeconomic and employment status: those with low education, employed in manual occupations, having low income and those who are unemployed have been found to have an elevated suicide risk. The purpose of this study was to provide a systematic analysis of these social differences in suicide mortality in Finland. Besides studying socioeconomic trends and differences in suicide according to age and sex, different indicators for socioeconomic status were used simultaneously, taking account of their pathways and mutual associations while also paying attention to confounding and mediatory effects of living arrangements and employment status. Register data obtained from Statistics Finland were used in this study. In some analyses suicides were divided into two groups according to contributory causes of death: the first group consisted of suicide deaths that had alcohol intoxication as one of the contributory causes, and the other group is comprised of all other suicide deaths. Methods included Poisson and Cox regression models. Despite the decrease in suicide mortality trend, social differences still exist. Low occupation-based social class proved to be an important determinant of suicide risk among both men and women, but the strong independent effect of education on alcohol-associated suicide indicates that the roots of these differences are probably established in early adulthood when educational qualifications are obtained and health-behavioural patterns set. High relative suicide mortality among the unemployed during times of economic boom suggests that selective processes may be responsible for some of the employment status differences in suicide. However, long-term unemployment seems to have causal effects on suicide, which, especially among men, partly stem from low income. In conclusion, the results in this study suggest that education, occupation-based social class and employment status have causal effects on suicide risk, but to some extent selection into low education and unemployment are also involved in the explanations for excess suicide mortality among the socially deprived. It is also conceivable that alcohol use is to some extent behind social differences in suicide. In addition to those with low education, manual workers and the unemployed, young people, whose health-related behaviour is still to be adopted, would most probably benefit from suicide prevention programmes.

Path integral description of polymers using fractional Brownian walks

The statistical properties of fractional Brownian walks are used to construct a path integral representation of the conformations of polymers with different degrees of bond correlation. We specifically derive an expression for the distribution function of the chains’ end‐to‐end distance, and evaluate it by several independent methods, including direct evaluation of the discrete limit of the path integral, decomposition into normal modes, and solution of a partial differential equation. The distribution function is found to be Gaussian in the spatial coordinates of the monomer positions, as in the random walk description of the chain, but the contour variables, which specify the location of the monomer along the chain backbone, now depend on an index h, the degree of correlation of the fractional Brownian walk. The special case of h=1/2 corresponds to the random walk. In constructing the normal mode picture of the chain, we conjecture the existence of a theorem regarding the zeros of the Bessel function.

Dynamics of Fractional Brownian Walks

We investigate the dynamics of polymers whose solution configurations are represented by fractional Brownian walks. The calculation of the two dynamical quantities considered here, the longest relaxation time tau(r) and the intrinsic viscosity [eta], is formulated in terms of Langevin equations and is carried out within the continuum approach developed in an earlier paper. Our results for tau(r) and [eta] reproduce known scaling relations and provide reasonable numerical estimates of scaling amplitudes. The possible relevance of the work to the study of globular proteins and other compact polymeric phases is discussed.

Quantum Random Walks without Coin Toss

We construct a quantum random walk algorithm, based on the Dirac operator instead of the Laplacian. The algorithm explores multiple evolutionary branches by superposition of states, and does not require the coin toss instruction of classical randomised algorithms. We use this algorithm to search for a marked vertex on a hypercubic lattice in arbitrary dimensions. Our numerical and analytical results match the scaling behaviour of earlier algorithms that use a coin toss instruction.

Cascaded walks in protein sequence space: use of artificial sequences in remote homology detection between natural proteins

Over the past two decades, many ingenious efforts have been made in protein remote homology detection. Because homologous proteins often diversify extensively in sequence, it is challenging to demonstrate such relatedness through entirely sequence-driven searches. Here, we describe a computational method for the generation of `protein-like' sequences that serves to bridge gaps in protein sequence space. Sequence profile information, as embodied in a position-specific scoring matrix of multiply aligned sequences of bona fide family members, serves as the starting point in this algorithm. The observed amino acid propensity and the selection of a random number dictate the selection of a residue for each position in the sequence. In a systematic manner, and by applying a `roulette-wheel' selection approach at each position, we generate parent family-like sequences and thus facilitate an enlargement of sequence space around the family. When generated for a large number of families, we demonstrate that they expand the utility of natural intermediately related sequences in linking distant proteins. In 91% of the assessed examples, inclusion of designed sequences improved fold coverage by 5-10% over searches made in their absence. Furthermore, with several examples from proteins adopting folds such as TIM, globin, lipocalin and others, we demonstrate that the success of including designed sequences in a database positively sensitized methods such as PSI-BLAST and Cascade PSI-BLAST and is a promising opportunity for enormously improved remote homology recognition using sequence information alone.

A Robot that Walks: Emergent Behaviors from a Carefully Evolved Network

Most animals have significant behavioral expertise built in without having to explicitly learn it all from scratch. This expertise is a product of evolution of the organism; it can be viewed as a very long term form of learning which provides a structured system within which individuals might learn more specialized skills or abilities. This paper suggests one possible mechanism for analagous robot evolution by describing a carefully designed series of networks, each one being a strict augmentation of the previous one, which control a six legged walking machine capable of walking over rough terrain and following a person passively sensed in the infrared spectrum. As the completely decentralized networks are augmented, the robot's performance and behavior repertoire demonstrably improve. The rationale for such demonstrations is that they may provide a hint as to the requirements for automatically building massive networks to carry out complex sensory-motor tasks. The experiments with an actual robot ensure that an essence of reality is maintained and that no critical problems have been ignored.

Optimal foraging strategies: Lévy walks balance searching and patch exploitation under a very broad range of conditions

While evidence for optimal random search patterns, known as Lévy walks, in empirical movement data is mounting for a growing list of taxa spanning motile cells to humans, there is still much debate concerning the theoretical generality of Lévy walk optimisation. Here, using a new and robust simulation environment, we investigate in the most detailed study to date (24×10(6) simulations) the foraging and search efficiencies of 2-D Lévy walks with a range of exponents, target resource distributions and several competing models. We find strong and comprehensive support for the predictions of the Lévy flight foraging hypothesis and in particular for the optimality of inverse square distributions of move step-lengths across a much broader range of resource densities and distributions than previously realised. Further support for the evolutionary advantage of Lévy walk movement patterns is provided by an investigation into the 'feast and famine' effect, with Lévy foragers in heterogeneous environments experiencing fewer long 'famines' than other types of searchers. Therefore overall, optimal Lévy foraging results in more predictable resources in unpredictable environments.

Hierarchical random walks in trace fossils and the origin of optimal search behavior

Efficient searching is crucial for timely location of food and other resources. Recent studies show diverse living animals employ a theoretically optimal scale-free random search for sparse resources known as a Lévy walk, but little is known of the origins and evolution of foraging behaviour and the search strategies of extinct organisms. Here we show using simulations of self-avoiding trace fossil trails that randomly introduced strophotaxis (U-turns) – initiated by obstructions such as ¬¬¬self-trail avoidance or innate cueing – leads to random looping patterns with clustering across increasing scales that is consistent with the presence of Lévy walks. This predicts optimal Lévy searches can emerge from simple behaviours observed in fossil trails. We then analysed fossilized trails of benthic marine organisms using a novel path analysis technique and find the first evidence of Lévy-like search strategies in extinct animals. Our results show that simple search behaviours of extinct animals in heterogeneous environments give rise to hierarchically nested Brownian walk clusters that converge to optimal Lévy patterns. Primary productivity collapse and large-scale food scarcity characterising mass extinctions evident in the fossil record may have triggered adaptation of optimal Lévy-like searches. The findings suggest Lévy-like behaviour has been employed by foragers since at least the Eocene but may have a more ancient origin, which could explain recent widespread observations of such patterns among modern taxa.

Simulation of quantum random walks using the interference of a classical field

We suggest a theoretical scheme for the simulation of quantum random walks on a line using beam splitters, phase shifters, and photodetectors. Our model enables us to simulate a quantum random walk using of the wave nature of classical light fields. Furthermore, the proposed setup allows the analysis of the effects of decoherence. The transition from a pure mean-photon-number distribution to a classical one is studied varying the decoherence parameters.

Green function for the diffusion limit of one-dimensional continuous time random walks

It is shown how the fractional probability density diffusion equation for the diffusion limit of one-dimensional continuous time random walks may be derived from a generalized Markovian Chapman-Kolmogorov equation. The non-Markovian behaviour is incorporated into the Markovian Chapman-Kolmogorov equation by postulating a Levy like distribution of waiting times as a kernel. The Chapman-Kolmogorov equation so generalised then takes on the form of a convolution integral. The dependence on the initial conditions typical of a non-Markovian process is treated by adding a time dependent term involving the survival probability to the convolution integral. In the diffusion limit these two assumptions about the past history of the process are sufficient to reproduce anomalous diffusion and relaxation behaviour of the Cole-Cole type. The Green function in the diffusion limit is calculated using the fact that the characteristic function is the Mittag-Leffler function. Fourier inversion of the characteristic function yields the Green function in terms of a Wright function. The moments of the distribution function are evaluated from the Mittag-Leffler function using the properties of characteristic functions and a relation between the powers of the second moment and higher order even moments is derived. (C) 2004 Elsevier B.V. All rights reserved.

How do grazers achieve their distribution? A continuum of models from random diffusion to the ideal free distribution using biased random walks

A conceptual model is described for generating distributions of grazing animals, according to their searching behavior, to investigate the mechanisms animals may use to achieve their distributions. The model simulates behaviors ranging from random diffusion, through taxis and cognitively aided navigation (i.e., using memory), to the optimization extreme of the Ideal Free Distribution. These behaviors are generated from simulation of biased diffusion that operates at multiple scales simultaneously, formalizing ideas of multiple-scale foraging behavior. It uses probabilistic bias to represent decisions, allowing multiple search goals to be combined (e.g., foraging and social goals) and the representation of suboptimal behavior. By allowing bias to arise at multiple scales within the environment, each weighted relative to the others, the model can represent different scales of simultaneous decision-making and scale-dependent behavior. The model also allows different constraints to be applied to the animal's ability (e.g., applying food-patch accessibility and information limits). Simulations show that foraging-decision randomness and spatial scale of decision bias have potentially profound effects on both animal intake rate and the distribution of resources in the environment. Spatial variograms show that foraging strategies can differentially change the spatial pattern of resource abundance in the environment to one characteristic of the foraging strategy.</

Localizationlike effect in two-dimensional alternate quantum walks with periodic coin operations

Exploiting multidimensional quantum walks as feasible platforms for quantum computation and quantum simulation attracts constantly growing attention from a broad experimental physics community. Here, we propose a two-dimensional quantum walk scheme with a single-qubit coin that presents, in the considered regimes, a strong localizationlike effect on the walker. The result could provide new possible directions for the implementation of quantum algorithms or from the point of view of quantum simulation. We characterize the localizationlike effect in terms of the parameters of a step-dependent qubit operation that acts on the coin space after any standard coin operation, showing that a proper choice can guarantee a nonnegligible probability of finding the walker in the origin even for large times. We finally discuss the robustness to imperfections, a qualitative relation with coherences behavior, and possible experimental realizations of this model with the current state-of-the-art settings.

Geographical Applications for Sound Walks

Geography has long been a predominantly visual discipline, but recent work in geography has sought to explore the multisensory, embodied, emotional and affective dimensions of people’s relations with places. One way to engage this type of exploration is through the use of sound walks: walks along a specified route accompanied by a soundtrack (on headphones or stationary speakers) that conveys information, enacts a story, produces an ambience or atmosphere, or illuminates certain aspects of the environment through which the listener is walking. This thesis aims to show how geographers can benefit from using sound walks as thinking tools, representational tools and teaching tools. Drawing on my own experiences producing sound walks, I first examine the ways that sound walk production processes help generate productive geographical thinking for those producing sound walks (Chapter Two). The various stages of producing a sound walk require different skill sets, pose different challenges, and require different sorts of environmental awareness, and therefore present novel opportunities for developing geographical insights about specific places or spatial relations. Second, I focus on four experientially-oriented aspects of sound walks – using multiple senses, walking, contingency, and moments of interaction – to argue that sound walks can be useful representational tools for geographers, whether those creating sound walks subscribe to a representational or non-representational theory of knowledge (Chapter Three). The value of sound walks as representational tools is in the experience of ‘doing’ them. That is, audiences discover for themselves through interaction what is being represented, rather than having it delivered to them. The experiential elements of ‘doing’ sound walks recommend them as potentially helpful representational tools for geographers. Third, by examining the work of a small sample of fourth year “Advanced Geography of Music” students, I develop the argument that sound walks can be effective tools for teaching students and for creating circumstances for students to learn independently (Chapter Four). Sound walks have potential to be effective pedagogical tools because they are commensurate with several key pedagogical schools of thought that emphasise the importance of requiring students to engage actively with their environment using a combination of senses. The thesis demonstrates that sound walks are a worthwhile resource for geographers to use theoretically, representationally and pedagogically in their work. The next step is for geographers to put them into practice and realize this potential.