Walks Of Length Research Articles

ON THE COMBINATORICS OF BINARY SERIES-PARALLEL GRAPHS

Binary series-parallel (BSP) graphs have applications in transportation modeling, and exhibit interesting combinatorial properties. This work is limited to the second aspect. The BSP graphs of a given size – measured in edges – are enumerated. Under a uniform probability model, we investigate the asymptotic distribution of the order (number of vertices) and the asymptotic average length of a random walk (under different strategies) of large graphs of the same size. The systematic method throughout is to define the graphs, and the features we evaluate by a structural equation (equivalent to a regular expression). The structural equation is translated into an equation for a generating function, which is then analyzed.

An AO* Based Exact Algorithm for the Canadian Traveler Problem

The Canadian traveler problem (CTP) is a simple, yet challenging, stochastic optimization problem wherein an agent is given a graph where some edges are blocked with certain probabilities and the status of these edges can be disambiguated dynamically upon reaching an incident vertex. The goal is to devise a traversal policy that results in the shortest expected walk length between a given starting vertex and a termination vertex. CTP has been shown to be intractable in many broad settings. In this paper, we introduce an optimal algorithm for the problem based on a Markov decision process formulation, which is a new improvement on AO* search that takes advantage of the special problem structure in CTP. We call our algorithm CAO*, which stands for AO* with caching. CAO* uses a caching mechanism to avoid re-expansion of previously visited states and makes use of admissible upper bounds at a node level for dynamic state-space pruning. CAO* is not polynomial time, but it can dramatically shorten the execution time needed to find an exact solution for moderately sized instances. We present computational experiments on a realistic variant of the problem involving an actual maritime minefield data set.

The Impact of a Pet, in This Case a Dog, on Physical Activity, Independence, Social Contacts, Health and Quality of Life of Elderly People

In a rural area near Munich, 52 persons aged 65 years and older were interviewed in person about health and social life circumstances. Findings: Dog owners take significantly longer walks than people who do not own dogs, averaging more than 120 minutes daily (p < 0.0001). On average, people who do not own a dog walked 38 minutes, cat owners 17 minutes. 94% of the dog owners were active daily compared to 14% of those who do not own a dog. Dog owners go to the doctor on average 5.3 times per year, people who do not own a dog 7.8 times. There was no difference between the two groups in regard to the use of medication. 80% would not move to a residential home for the elderly because of the dog, and 87% would want to take the dog along. 50% of the dog owners and 41% of those who do not own a dog had on average more than 3 contacts with other people, 6% of the dog owners and 23% of those who do not own a dog had less than one contact per day. 19% of the dog owners and 36% of those who do not own a dog would describe themselves as reserved in dealings with people. 71% stated that the dog had been very useful to help them overcome the loss of a person close to them. The W-5 [Wellbeing Five score] for dog owners was an average value of 75%, for those who did not own a dog 71%. Depression was uniformly distributed in both groups. The BMIs in both groups were similar. There was no correlation to the length of the daily walk.

The effect of walking sticks on balance in geriatric subjects.

[Purpose] Guidelines and clarity regarding the information for deciding the need for walking sticks and the suitability of these sticks is insufficient. This study aimed to evaluate the suitability of walking stick and its effects on the balance in the elderly. [Subjects and Methods] A total of 39 elderly subjects aged between 65–95 years (mean age, 76.15 ± 8.35 years) and living in the Residential Aged Care and Rehabilitation Center were included. Sociodemographic data of the individuals, the material of the walking stick, who made the decision of usage and length of walking sticks were questioned. The Berg Balance Scale (BBS) scores were used to evaluate balance. [Results] Subjects’ BBS scores while using the walking stick were higher than that without the walking stick. A significant difference was observed in BBS scores obtained with the stick and without the stick, according to body mass index parameters. Majority of the subjects also started to use walking sticks by themselves. No significant difference was observed between the ideal length and actual length of the walking stick was used. [Conclusion] Our study demonstrated that the elderly generally decide to use walking stick by themselves and chose the appropriate materials; which improves their balance.

Node sampling using Random Centrifugal Walks

A distributed algorithm is proposed for sampling networks, so that nodes are selected by a special node (source), with a given probability distribution. We define a new class of random walks, that we call Random Centrifugal Walks (RCW). A RCW starts at the source and always moves away from it.The algorithm assumes that each node has a weight, so the nodes are selected with a probability proportional to its weight. It requires a preprocessing phase before the sampling of nodes. This preprocessing is done only once, regardless of the number of sources and the number of samples taken from the network. The length of RCW walks are bounded by the network diameter.The RCW algorithms that do not require preprocessing are proposed for grids and networks with regular concentric connectivity, for the case when the probability of selecting a node is a function of its distance to the source.

A spectral analysis of the domain decomposed Monte Carlo method for linear systems

The domain decomposed behavior of the adjoint Neumann-Ulam Monte Carlo method for solving linear systems is analyzed using the spectral properties of the linear operator. Relationships for the average length of the adjoint random walks, a measure of convergence speed and serial performance, are made with respect to the eigenvalues of the linear operator. In addition, relationships for the effective optical thickness of a domain in the decomposition are presented based on the spectral analysis and diffusion theory. Using the effective optical thickness, the Wigner rational approximation and the mean chord approximation are applied to estimate the leakage fraction of random walks from a domain in the decomposition as a measure of parallel performance and potential communication costs. The one-speed, two-dimensional neutron diffusion equation is used as a model problem in numerical experiments to test the models for symmetric operators with spectral qualities similar to light water reactor problems. In general, the derived approximations show good agreement with random walk lengths and leakage fractions computed by the numerical experiments.

DEVELOPMENT OF A PEDESTRIAN INDOOR NAVIGATION SYSTEM BASED ON MULTI-SENSOR FUSION AND FUZZY LOGIC ESTIMATION ALGORITHMS

Abstract. This paper presents a pedestrian indoor navigation system based on the multi-sensor fusion and fuzzy logic estimation algorithms. The proposed navigation system is a self-contained dead reckoning navigation that means no other outside signal is demanded. In order to achieve the self-contained capability, a portable and wearable inertial measure unit (IMU) has been developed. Its adopted sensors are the low-cost inertial sensors, accelerometer and gyroscope, based on the micro electro-mechanical system (MEMS). There are two types of the IMU modules, handheld and waist-mounted. The low-cost MEMS sensors suffer from various errors due to the results of manufacturing imperfections and other effects. Therefore, a sensor calibration procedure based on the scalar calibration and the least squares methods has been induced in this study to improve the accuracy of the inertial sensors. With the calibrated data acquired from the inertial sensors, the step length and strength of the pedestrian are estimated by multi-sensor fusion and fuzzy logic estimation algorithms. The developed multi-sensor fusion algorithm provides the amount of the walking steps and the strength of each steps in real-time. Consequently, the estimated walking amount and strength per step are taken into the proposed fuzzy logic estimation algorithm to estimates the step lengths of the user. Since the walking length and direction are both the required information of the dead reckoning navigation, the walking direction is calculated by integrating the angular rate acquired by the gyroscope of the developed IMU module. Both the walking length and direction are calculated on the IMU module and transmit to a smartphone with Bluetooth to perform the dead reckoning navigation which is run on a self-developed APP. Due to the error accumulating of dead reckoning navigation, a particle filter and a pre-loaded map of indoor environment have been applied to the APP of the proposed navigation system to extend its usability. The experiment results of the proposed navigation system demonstrate good navigation performance in indoor environment with the accurate initial location and direction.

Phase transition in random adaptive walks on correlated fitness landscapes

We study biological evolution on a random fitness landscape where correlations are introduced through a linear fitness gradient of strength c. When selection is strong and mutations rare the dynamics is a directed uphill walk that terminates at a local fitness maximum. We analytically calculate the dependence of the walk length on the genome size L. When the distribution of the random fitness component has an exponential tail, we find a phase transition of the walk length D between a phase at small c, where walks are short (D∼lnL), and a phase at large c, where walks are long (D∼L). For all other distributions only a single phase exists for any c>0. The considered process is equivalent to a zero temperature Metropolis dynamics for the random energy model in an external magnetic field, thus also providing insight into the aging dynamics of spin glasses.

Competing reaction processes on a lattice as a paradigm for catalyst deactivation.

We mobilize both a generating function approach and the theory of finite Markov processes to compute the probability of irreversible absorption of a randomly diffusing species on a lattice with competing reaction centers. We consider an N-site lattice populated by a single deep trap, and N-1 partially absorbing traps (absorption probability 0<s<1). The influence of competing reaction centers on the probability of reaction at a target site (the deep trap) and the mean walk length of the random walker before localization (a measure of the reaction efficiency) are computed for different geometries. Both analytic expressions and numerical results are given for reactive processes on two-dimensional surfaces of Euler characteristic Ω=0 and Ω=2. The results obtained allow a characterization of catalyst deactivation processes on planar surfaces and on catalyst pellets where only a single catalytic site remains fully active (deep trap), the other sites being only partially active as a result of surface poisoning. The central result of our study is that the predicted dependence of the reaction efficiency on system size N and on s is in qualitative accord with previously reported experimental results, notably catalysts exhibiting selective poisoning due to surface sites that have different affinities for chemisorption of the poisoning agent (e.g., acid zeolite catalysts). Deviations from the efficiency of a catalyst with identical sites are quantified, and we find that such deviations display a significant dependence on the topological details of the surface (for fixed values of N and s we find markedly different results for, say, a planar surface and for the polyhedral surface of a catalyst pellet). Our results highlight the importance of surface topology for the efficiency of catalytic conversion processes on inhomogeneous substrates, and in particular for those aimed at industrial applications. From our exact analysis we extract results for the two limiting cases s≈1 and s≈0, corresponding respectively to weak and strong catalyst poisoning (decreasing s leads to a monotonic decrease in the efficiency of catalytic conversion). The results for the s≈0 case are relevant for the dual problem of light-energy conversion via trapping of excitations in the chlorophyll antenna network. Here, decreasing the probability of excitation trapping s at sites other than the target molecule does not result in a decrease of the efficiency as in the catalyst case, but rather in enhanced efficiency of light-energy conversion, which we characterize in terms of N and s. The one-dimensional case and its connection with a modified version of the gambler's ruin problem are discussed. Finally, generalizations of our model are described briefly.

On the expected distance of a random walk

This paper investigates the Euclidean length of a random walk though n coplanar points. The length of which has multiple applications including spanning trees, Steiner trees, and certain forms of the travelling salesman problem. To estimate this distance, we partition an area A into m equivalent squares and then add the expected Euclidean distances travelled between each of the m squares with the expected Euclidean distances travelled within each of the m squares. The end result is a closed form model for the expected length of a random walk through n coplanar points. Some avenues of future research are also included.

Walking for Transportation and Leisure Among U.S. Adults--National Health Interview Survey 2010.

Walking, the most commonly reported physical activity among U.S. adults, is undertaken in various domains, including transportation and leisure. This study examined prevalence, bout length, and mean amount of walking in the last week for transportation and leisure, by selected characteristics. Self-reported data from the 2010 National Health Interview Survey (N = 24,017) were analyzed. Prevalence of transportation walking was 29.4% (95% CI: 28.6%-30.3%) and of leisure walking was 50.0% (95% CI: 49.1%-51.0%). Prevalence of transportation walking was higher among men; prevalence of leisure walking was higher among women. Most (52.4%) transportation walking bouts were 10 to 15 minutes; leisure walking bouts were distributed more evenly (28.0%, 10-15 minutes; 17.1%, 41-60 minutes). Mean time spent in transportation walking was higher among men, decreased with increasing BMI, and varied by race/ethnicity and region of residence. Mean time spent leisure walking increased with increasing age and with decreasing BMI. Demographic correlates and patterns of walking differ by domain. Interventions focusing on either leisure or transportation walking should consider correlates for the specific walking domain. Assessing prevalence, bout length, and mean time of walking for transportation and leisure separately allows for more comprehensive surveillance of walking.

Correlation between the Quality of Attention and Cognitive Competence with Motor Action in Stroke Patients.

It is considered that cognitive function and attention could affect walking, motion control, and proper conduct during the walk. To determine whether there is a difference in the quality of attention and cognitive ability in stroke patients and patients without neurological damage of similar age and education and to determine whether the connection of attention and cognition affects motor skills, the sample consisted of 50 stroke patients tested with hemiparesis, involved in the process of rehabilitation, and 50 persons, randomly chosen, without neurological damage. The survey used the following tests: Trail Making (TMT A B) test for assessing the flexibility of attention; Mini-Mental State Examination (MMSE) for cognitive status; Functional Ambulation Category (FAC) test to assess the functional status and parameters of walk: speed, frequency, and length of stride; STEP test for assessing the precision of movement and balance. With stroke patients, relationship between age and performance on the MMSE test was marginally significant. The ratio of performance to TMT A B test and years does not indicate statistical significance, while statistical significance between the MMSE test performance and education exists. In stroke patients, performance on MMSE test is correlated with the frequency and length of stride walk. The quality of cognitive function and attention is associated with motor skills but differs in stroke patients and people without neurological damage of similar age. The significance of this correlation can supplement research in neurorehabilitation, improve the quality of medical rehabilitation, and contribute to efficient recovery of these patients.

Chemotactic Traveling Waves by Metric of Food

The meaningful distance to biological organisms is not necessarily one measured by the Euclidean metric but possibly one by a metric that counts the amount of resources such as food. It is assumed in this paper that the distance for biological organisms is measured by the amount of food between two places. A new chemotaxis model is introduced as an application of this “metric of food.” It is shown that, if the walk length of a random walk system is given by such a metric, the well-known chemotactic traveling wave phenomena can be obtained without the typical assumption that microscopic scale bacteria may sense the macroscopic scale gradient of a chemical concentration. The uniqueness and the existence of a traveling wave solution are obtained.

Signatures of Lévy flights with annealed disorder.

We present theoretical and experimental results of Lévy flights of light originating from a random walk of photons in a hot atomic vapor. In contrast to systems with quenched disorder, this system does not present any correlations between the position and the step length of the random walk. In an analytical model based on microscopic first principles including Doppler broadening we find anomalous Lévy-type superdiffusion corresponding to a single-step size distribution P(x)∝x^{-(1+α)}, with α≈1. We show that this step size distribution leads to a violation of Ohm's law [T_{diff}∝L^{-α/2}≠L^{-1}], as expected for a Lévy walk of independent steps. Furthermore, the spatial profile of the transmitted light develops power-law tails [T_{diff}(r)∝r^{-3-α}]. In an experiment using a slab geometry with hot Rb vapor, we measured the total diffuse transmission T_{diff} and the spatial profile of the transmitted light T_{diff}(r). We obtained the microscopic Lévy parameter α under macroscopic multiple scattering conditions paving the way to investigation of Lévy flights in different atomic physics and astrophysics systems.

Length of adaptive walk on uncorrelated and correlated fitness landscapes.

We consider the adaptation dynamics of an asexual population that walks uphill on a rugged fitness landscape which is endowed with a large number of local fitness peaks. We work in a parameter regime where only those mutants that are a single mutation away are accessible, as a result of which the population eventually gets trapped at a local fitness maximum and the adaptive walk terminates. We study how the number of adaptive steps taken by the population before reaching a local fitness peak depends on the initial fitness of the population, the extreme value distribution of the beneficial mutations, and correlations among the fitnesses. Assuming that the relative fitness difference between successive steps is small, we analytically calculate the average walk length for both uncorrelated and correlated fitnesses in all extreme value domains for a given initial fitness. We present numerical results for the model where the fitness differences can be large and find that the walk length behavior differs from that in the former model in the Fréchet domain of extreme value theory. We also discuss the relevance of our results to microbial experiments.

The effect of knee orthoses on gait parameters in medial knee compartment osteoarthritis

Knee osteoarthritis is a musculoskeletal condition which is most prevalent in the medial compartment. This injury causes considerable pain, disability, and negative changes in kinetic and kinematic parameters. The efficiency of unloader valgus brace as a conservative treatment for medial knee osteoarthritis is not well documented. The aim of this study was to review the previous research regarding the biomechanical effects of knee valgus braces on walking in medial compartment knee osteoarthritis patients. Literature review According to the population intervention comparison outcome measure methods and based on selected keywords, 12 studies were chosen according to (met) the inclusion criteria. The results indicated that treatment with knee braces was effective in decreasing pain, improving function, ameliorating improvement in range of motion, and increasing speed of walking and step length in conjunction with a reduction in the adduction moment applied to the knee. Osteoarthritis knee braces may be considered for improvement of walking and treatment of medial compartment knee osteoarthritis. Knee braces are an orthotic intervention that could potentially be significant in assisting in improving the walking parameters and treatment of medial compartment knee osteoarthritis.

Evaluating sliding and sticky target policies by measuring temporal drift in acyclic walks through a web archive

When viewing an archived page using the archive's user interface (UI), the user selects a datetime to view from a list. The archived web page, if available, is then displayed. From this display, the web archive UI attempts to simulate the web browsing experience by smoothly transitioning between archived pages. During this process, the target datetime changes with each link followed, potentially drifting away from the datetime originally selected. For sparsely archived resources, this almost transparent drift can be many years in just a few clicks. We conducted 200,000 acyclic walks of archived pages, following up to 50 links per walk, comparing the results of two target datetime policies. The Sliding Target policy allows the target datetime to change as it does in archive UIs such as the Internet Archive's Wayback Machine. The Sticky Target policy, represented by the Memento API, keeps the target datetime the same throughout the walk. We found that the Sliding Target policy drift increases with the number of walk steps, number of domains visited, and choice (number of links available). However, the Sticky Target policy controls temporal drift, holding it to $$<$$<30 days on average regardless of walk length or number of domains visited. The Sticky Target policy shows some increase as choice increases, but this may be caused by other factors. We conclude that based on walk length, the Sticky Target policy generally produces at least 30 days less drift than the Sliding Target policy.

Quasi‐cyclic low‐density parity‐check codes based on finite set systems

A finite set system (FSS) is a pair (V, ℬ) where V is a finite set whose members are called points, equipped with a finite collection of its subsets ℬ whose members are called blocks. In this paper, FSSs are used to define a class of quasi-cyclic low-density parity-check (LDPC) codes, called FSS codes, such that the constructed codes possess large girth and arbitrary column-weight distributions. Especially, the constructed column weight-2 FSS codes have higher rates than the column weight-2 geometric and cylinder-type codes with the same girths. To find the maximum girth of FSS codes based on (V, ℬ), inevitable walks are defined in ℬ such that the maximum girth is determined by the smallest length of the inevitable walks in ℬ. Simulation results show that the constructed FSS codes have very good performance over the additive white Gaussian noise channel with iterative decoding and achieve significantly large coding gains compared with the random-like LDPC codes of the same lengths and rates.

Transfer Effects of Fall Training on Balance Performance and Spatiotemporal Gait Parameters in Healthy Community-Dwelling Older Adults: A Pilot Study

This study examined transfer effects of fall training on fear of falling (Falls Efficacy Scale—International [FES–I]), balance performance, and spatiotemporal gait characteristics in older adults. Eighteen community-dwelling older adults (ages 65–85) were randomly assigned to an intervention or control group. The intervention group completed 12 training sessions (60 min, 6 weeks). During pre- and posttesting, we measured FES–I, balance performance (double limb, closed eyes; single limb, open eyes; double limb, open eyes with motor-interfered task), and gait parameters (e.g., velocity; cadence; stride time, stride width, and stride length; variability of stride time and stride length) under single- and motor-interfered tasks. Dual tasks were applied to appraise improvements of cognitive processing during balance and gait. FES–I (p = .33) and postural sway did not significantly change (0.36 < p < .79). Trends toward significant interaction effects were found for step width during normal walking and stride length variability during the motor dual task (p = .05, ηp2 = .22). Fall training did not sufficiently improve fear of falling, balance, or gait performance under single- or dual-task conditions in healthy older adults.

SOME PROPERTIES OF BINARY SERIES-PARALLEL GRAPHS

We introduce an incremental growth model for directed binary series-parallel (SP) graphs. The vertices of a directed binary SP graphs can only have outdgrees 1 or 2. We show that the number of vertices of outdegree 1 have a normal distribution (so, necessarily, the vertices of outdegree 2 have a normal distribution, too). Furthermore, we study the average length of a random walk between the poles of the graph. The asymptotic equivalent of the latter property includes the golden ratio. Pólya urns will systematically provide a coding method to initiate the studies.