Position Of Walker Research Articles

Exact Propagators of One-Dimensional Self-Interacting Random Walks.

Self-interacting random walks (SIRWs) show long-range memory effects that result from the interaction of the random walker at time t with the territory already visited at earlier times t^{'}<t. This class of non-Markovian random walks has applications in contexts as diverse as foraging theory, the behavior of living cells, and even machine learning. Despite this importance and numerous theoretical efforts, the propagator, which is the distribution of the walker's position and arguably the most fundamental quantity to characterize the process, has so far remained out of reach for all but a single class of SIRW. Here we fill this gap and provide an exact and explicit expression for the propagator of two important universality classes of SIRWs, namely, the once-reinforced random walk and the polynomially self-repelling walk. These results give access to key observables, such as the diffusion coefficient, which so far had not been determined. We also uncover an inherently non-Markovian mechanism that tends to drive the walker away from its starting point.

Parameter estimation with reluctant quantum walks: a maximum likelihood approach

The parametric maximum likelihood estimation problem is addressed in the context of quantum walk theory for quantum walks on the lattice of integers. A coin action is presented, with the real parameter θ to be estimated identified with the angular argument of an orthogonal reshuffling matrix. We provide analytic results for the probability distribution for a quantum walker to be displaced by d units from its initial position after k steps. For k large, we show that the likelihood is sharply peaked at a displacement determined by the ratio d/k which is correlated with the reshuffling parameter θ. We suggest that this ‘reluctant walker’ behaviour provides the framework for maximum likelihood estimation analysis, allowing for robust parameter estimation of θ via return probabilities of closed evolution loops and quantum measurements of the position of quantum walker with ‘reluctance index’ r = d/k.

The impact of walker height positions and their influence on triceps activity and energy conservation: a pilot study

Background/Aims Millions of adults use walkers for functional mobility. Inappropriate walker use is associated with incorrect height, forward-leaning posture, and increased energy expenditure. Few studies have investigated the impact of walker positions and their influence on triceps activity. The present study assessed walker height and baseline positioning for individuals with a 50% weight bearing restriction of the lower extremity, and implications for energy conservation. Methods A total of 38 young adults (mean age = 24.95 years; 84.2% female; 15.8% male) participated in this study with a two-wheeled walker. Participants executed five walker positions while maintaining 50% weight bearing of the lower extremity to determine the effect on triceps electromyography activity. Results Triceps electromyography activity did significantly change across the five walker positions assessed (X2 [df=37, P&lt;0.001]). This study showed that the median electromyography activity for positions B (median=0.268) and A (median=0.280) was significantly less than the median electromyography activity for position E (median=0.452; P&lt;0.001). The effect sizes for comparisons of positions B and E (r=0.49) as well as A and E were the largest (r=0.53). Conclusions These findings suggest an elbow angle of 26–35° (position B), followed by an elbow angle of 15–25° (position A), with the walker in line with the heels of the participant, to be superior in minimising exertion of the triceps.

Origin of universality in the onset of superdiffusion in Lévy walks

Superdiffusion arises when complicated, correlated, and noisy motion at the microscopic scale conspires to yield peculiar dynamics at the macroscopic scale. It ubiquitously appears in a variety of scenarios, spanning a broad range of scientific disciplines. The approach of superdiffusive systems towards their long-time, asymptotic behavior was recently studied using the Lévy walk of order 1<β<2, revealing a universal transition at the critical βc=3/2. Here, we investigate the origin of this transition and identify two crucial ingredients: a finite velocity which couples the walker's position to time and a corresponding transition in the fluctuations of the number of walks n completed by the walker at time t.Received 22 June 2020Accepted 3 August 2020DOI:https://doi.org/10.1103/PhysRevResearch.2.032042Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasAnomalous diffusionLevy flightsStatistical Physics

Quantum walks and Dirac cellular automata on a programmable trapped-ion quantum computer

The quantum walk formalism is a widely used and highly successful framework for modeling quantum systems, such as simulations of the Dirac equation, different dynamics in both the low and high energy regime, and for developing a wide range of quantum algorithms. Here we present the circuit-based implementation of a discrete-time quantum walk in position space on a five-qubit trapped-ion quantum processor. We encode the space of walker positions in particular multi-qubit states and program the system to operate with different quantum walk parameters, experimentally realizing a Dirac cellular automaton with tunable mass parameter. The quantum walk circuits and position state mapping scale favorably to a larger model and physical systems, allowing the implementation of any algorithm based on discrete-time quantum walks algorithm and the dynamics associated with the discretized version of the Dirac equation.

Two-dimensional topological quantum walks in the momentum space of structured light

Quantum walks are powerful tools for quantum applications and for designing topological systems. Although they are simulated in a variety of platforms, genuine two-dimensional realizations are still challenging. Here we present an innovative approach to the photonic simulation of a quantum walk in two dimensions, where walker positions are encoded in the transverse-wavevector component of a single light beam. The desired dynamics is obtained by means of a sequence of liquid-crystal devices, which apply polarization-dependent transverse “kicks” to the photons in the beam. We engineer our quantum walk so that it realizes a periodically driven Chern insulator, and we probe its topological features by detecting the anomalous displacement of the photonic wavepacket under the effect of a constant force. Our compact, versatile platform offers exciting prospects for the photonic simulation of two-dimensional quantum dynamics and topological systems.

Directional quantum random walk induced by coherence

Quantum walk (QW), which is considered as the quantum counterpart of the classical random walk (CRW), is actually the quantum extension of CRW from the single-coin interpretation. The sequential unitary evolution engenders correlation between different steps in QW and leads to a ballistic position distribution. In this paper, we propose an alternative quantum extension of CRW from the ensemble interpretation, named quantum random walk (QRW), where the walker has many unrelated coins, modeled as two-level systems, initially prepared in the same state. We calculate the walker's position distribution in QRW for different initial coin states with the coin operator chosen as Hadamard matrix. In one-dimensional case, the walker's position is the asymmetric binomial distribution. We further demonstrate that in QRW, coherence leads the walker to perform directional movement. For an initially decoherenced coin state, the walker's position distribution is exactly the same as that of CRW. Moreover, we study QRW in 2D lattice, where the coherence plays a more diversified role in the walker's position distribution.

Parrondo games as disordered systems

Parrondo's paradox refers to the counter-intuitive situation where a winning strategy results from a suitable combination of losing ones. Simple stochastic games exhibiting this paradox have been introduced around the turn of the millennium. The common setting of these Parrondo games is that two rules, $A$ and $B$, are played at discrete time steps, following either a periodic pattern or an aperiodic one, be it deterministic or random. These games can be mapped onto 1D random walks. In capital-dependent games, the probabilities of moving right or left depend on the walker's position modulo some integer $K$. In history-dependent games, each step is correlated with the $Q$ previous ones. In both cases the gain identifies with the velocity of the walker's ballistic motion, which depends non-linearly on model parameters, allowing for the possibility of Parrondo's paradox. Calculating the gain involves products of non-commuting Markov matrices, which are somehow analogous to the transfer matrices used in the physics of 1D disordered systems. Elaborating upon this analogy, we study a paradigmatic Parrondo game of each class in the neutral situation where each rule, when played alone, is fair. The main emphasis of this systematic approach is on the dependence of the gain on the remaining parameters and, above all, on the game, i.e., the rule pattern, be it periodic or aperiodic, deterministic or random. One of the most original sides of this work is the identification of weak-contrast regimes for capital-dependent and history-dependent Parrondo games, and a detailed quantitative investigation of the gain in the latter scaling regimes.

Tracking control and identification of interaction forces for a rehabilitative training walker whose centre of gravity randomly shifts

This study investigates tracking control and the identification of interaction forces for a rehabilitative training walker whose centre of gravity randomly shifts. A stochastic model is structured to describe the motion of the walker subject to random parametric uncertainty. An observer is designed to identify the interaction forces, motion position, and motion velocity of the walker. The novelty of this approach is that the interaction forces are estimated from the reduced tracking performance rather than a conventional nonlinear function. Meanwhile, the position and velocity states are estimated based on the walker's position output. A nonlinear tracking controller is constructed to give the tracking and the estimation error systems mean-square stability both exponentially and practically. Furthermore, the mean-square errors of the interaction forces identification and the tracking motion converge to a sufficiently small neighbourhood upon tuning appropriate parameters. The results of a simulated application confirm the effectiveness of the proposed interaction forces identification and controller design method.

MODELING AND CONTROL OF HUMAN AND WHEELED ROBOTIC WALKER COUPLED DYNAMICS

The control of assistive robotic walkers are usually designed without considering the coupled dynamics of the user and the walker. This paper proposes a coupled dynamic modeling for human walking with a wheeled robotic walker and then control of this model. The 2D linear inverted pendulum mode (LIPM) is used to model human walking. The wheeled robotic walker is modeled as a simple wheeled subsystem moving on an even ground. To simulate the human arm, a parallel linear spring and damper set is then used to indicate the interaction forces. An optimal fixed final-state controller is used to control the walking model and to keep it balanced. To check whether the LIPM model walking is balanced, the zero-moment point position is calculated and checked to be in the support polygon. The results are validated with the experimental data of human walking along with a wheeled walker for three healthy subjects. The relative positions of center of mass, the absolute positions of the human and the walker, and the velocities are considered for comparison and discussion. The results for each subject is compared with the experiments through [Formula: see text] norm of the error between human and walker positions in simulation and experiments. The proposed model can be utilized in developing controllers for robotic walkers that consider the user’s dynamics.

Quantum walker as a probe for its coin parameter

In discrete-time quantum walk (DTQW) the walker's coin space entangles with the position space after the very first step of the evolution. This phenomenon may be exploited to obtain the value of the coin parameter $\theta$ by performing measurements on the sole position space of the walker. In this paper, we evaluate the ultimate quantum limits to precision for this class of estimation protocols, and use this result to assess measurement schemes having limited access to the position space of the walker in one dimension. We find that the quantum Fisher information (QFI) of the walker's position space $H_w(\theta)$ increases with $\theta$ and with time which, in turn, may be seen as a metrological resource. We also find a difference in the QFI of {\em bounded} and {\em unbounded} DTQWs, and provide an interpretation of the different behaviors in terms of interference in the position space. Finally, we compare $H_w(\theta)$ to the full QFI $H_f(\theta)$, i.e., the QFI of the walkers position plus coin state, and find that their ratio is dependent on $\theta$, but saturates to a constant value, meaning that the walker may probe its coin parameter quite faithfully.

Percolated quantum walks with a general shift operator: From trapping to transport

We present a generalized definition of discrete-time quantum walks convenient for capturing a rather broad spectrum of walker's behavior on arbitrary graphs. It includes and covers both: the geometry of possible walker's positions with interconnecting links and the prescribed rule in which directions the walker will move at each vertex. While the former allows for the analysis of inhomogeneous quantum walks on graphs with vertices of varying degree, the latter offers us to choose, investigate, and compare quantum walks with different shift operators. The synthesis of both key ingredients constitutes a well-suited playground for analyzing percolated quantum walks on a quite general class of graphs. Analytical treatment of the asymptotic behavior of percolated quantum walks is presented and worked out in details for the Grover walk on graphs with maximal degree 3. We find, that for these walks with cyclic shift operators the existence of an edge-3-coloring of the graph allows for non-stationary asymptotic behavior of the walk. For different shift operators the general structure of localized attractors is investigated, which determines the overall efficiency of a source-to-sink quantum transport across a dynamically changing medium. As a simple nontrivial example of the theory we treat a single excitation transport on a percolated cube.

Modeling random walkers on growing random networks

We present continuum models that describe the evolution of the position of a random walker on a growing network using four different growth algorithms. Three of these involve a random element, including one in which the motility rate of the random walker controls the network topology. For motility rates in which the position of the walker can be treated as quasi-stationary, we present accurate approximations to replace pair probabilities that allow us to numerically solve an otherwise intractable system of equations.

Empire by Invitation: William Walker and Manifest Destiny in Central America by Michel Gobat

Reviewed by: Empire by Invitation: William Walker and Manifest Destiny in Central America by Michel Gobat Matthew J. Clavin Empire by Invitation: William Walker and Manifest Destiny in Central America. By Michel Gobat. (Cambridge, Mass., and London: Harvard University Press, 2018. Pp. [x], 367. $39.95, ISBN 978-0-674-73749-5.) Though contemporaries of slave owners, slave traders, and secessionists, filibusters still stand out for their negative portrayal in the historiography of antebellum America. Dedicated to spreading slavery beyond the borders of the U.S. South, they waged violent wars against foreign people and nations, [End Page 442] imperiled freedom throughout the Americas, and brought the United States to the brink of civil war. The reputation is hard to refute. But in this important study, Michel Gobat shows that in the case of William Walker's infamous conquest of Nicaragua in the 1850s, Central Americans invited filibusters to their shores and then assisted the invaders in toppling the government. According to Gobat, whose first book on the United States' occupation of Nicaragua in the early twentieth century similarly exploited Spanish and English sources to great effect, William Walker and the filibusters he commanded were "liberal imperialists" fighting to bring American business and technology, along with a free and democratic political system, to a region in desperate need of assistance (p. 156). With northern Free Soilers, free black emigrationists, and European revolutionaries composing a portion of Walker's army, it is no surprise that native Nicaraguans—from elite white landowners to dark-skinned farmers, shopkeepers, and soldiers—saw in these filibusters an opportunity to remake their young nation into a miniature version of the United States. The experiment was, for a brief moment, successful. After disembarking on Nicaragua's west coast in the summer of 1855, Walker and his followers brought peace to a war-torn nation and instituted a series of reforms that resulted in the creation of a fully functioning nation-state. In collaboration with countless native Nicaraguans, including lowly peasants, powerful property owners, and Catholic priests, Walker and his filibusters established a court and tax-collection system, an all-volunteer army, a customhouse, and a post office. The objective at all times was clear: "Americanization" (p. 5). More than a brief chapter in the long history of manifest destiny, Walker's Nicaraguan conquest, according to Gobat, was a pivotal moment in the history of the Americas. Building on an idea he first articulated in the American Historical Review, Gobat considers the episode crucial in the "invention of Latin America" ("The Invention of Latin America: A Transnational History of Anti-Imperialism, Democracy, and Race," American Historical Review, 118 [December 2013], pp. 1345-75). After several months of Walker's rule, Central Americans united in an armed revolt against the filibusters and expelled them from the region. "The idea of Latin America," Gobat boldly contends in this book, "was the most enduring outcome of the anti-U.S. moment" (p. 96). Desperate to reclaim his position of power, Walker returned to the United States. While northerners had grown suspicious of his enterprise and withdrew their support, white southerners who were hell-bent on spreading their peculiar institution to the tropics continued to rally behind his cause. By insisting that Walker's proslavery position emerged only at this moment, Gobat takes his biggest swing at the conventional wisdom regarding filibusterism. In so doing, he erroneously paints the adventurer—who in 1856 infamously re-legalized slavery in Nicaragua—as an antislavery activist. With freedom and slavery often serving as two sides of the same coin, Walker ultimately strove to spread both—far beyond the United States' southern border. That being said, Gobat should be commended. He has produced an outstanding transnational history that, because of its originality and style, will appeal to scholars and students alike. [End Page 443] Matthew J. Clavin University of Houston Copyright © 2019 Southern Historical Association

Quantum walks over a square lattice

Quantum random walk finds application in efficient quantum algorithms as well as in quantum network theory. Here we study the mixing time of a discrete quantum walk over a square lattice in the presence of dynamic percolation and decoherence. We consider bit-flip and phase damping noise, and evaluate the instantaneous mixing time for both the cases. Using numerical analysis we show that, in the case of phase damping noise, the probability distribution of walker's position is sufficiently close to the uniform distribution after infinite time. However, during the action of bit-flip noise, even after infinite time the total variational distance between the two probability distributions is large enough.

Quantum walk on a toral phase space

A quantum walk on a toral phase space involving translations in position and its conjugate momentum is studied in the simple context of a coined walker in discrete time. The resultant walk, with a family of coins parametrized by an angle is such that its spectrum is exactly solvable with eigenangles for odd parity lattices being equally spaced, a feature that is remarkably independent of the coin. The eigenvectors are naturally specified in terms using the q-Pochhammer symbol, but can also be written in terms of elementary functions, and their entanglement can be analytically found. While the phase-space walker shares many features in common with the well-studied case of a coined walker in discrete time and space, such as ballistic growth of the walker position, it also presents novel features such as exact periodicity, and formation of cat-states in phase space. The participation ratio (PR), a measure of delocalization in walker space, is studied in the context of both kinds of quantum walks; while the classical PR increases as there is a time interval during which the quantum walks display a power-law growth ∼t0.825. Studying the evolution of coherent states in phase space under the walk enables us to identify an Ehrenfest time after which the coin-walker entanglement saturates.

Research on Pedestrian Navigation Algorithm Based on MEMS Inertial Devices

Pedestrian navigation system (PNS) is also known as the walker navigation system, which is mainly used to track and posit real-time position of walker, to provide walk speed and position of walker, and also be applied to military, science, sport, rescue, the blind navigation, electronic product, etc. GPS signal is unreliable and difficult to provide accurate location information in most environments such as indoor, urban streets and canyons. At this point, the autonomous navigation system based on the proposed algorithm is a good solution. This article mainly analyzes the MEMS inertial device in the actual engineering practice, the application of the low precision of MEMS inertial device used in personal navigation correction algorithm, and combines the MEMS inertial sensors and GPS receiver, satisfies the requirement of pedestrian positioning. Using the complementary filter to fuse sensor data, we can obtain information of high precision orientation.

Doubling the success of quantum walk search using internal-state measurements

In typical discrete-time quantum walk algorithms, one measures the position of the walker while ignoring its internal spin/coin state. Rather than neglecting the information in this internal state, we show that additionally measuring it doubles the success probability of many quantum spatial search algorithms. For example, this allows Grover's unstructured search problem to be solved with certainty, rather than with probability 1/2 if only the walker's position is measured, so the additional measurement yields a search algorithm that is twice as fast as without it, on average. Thus the internal state of discrete-time quantum walks holds valuable information that can be utilized to improve algorithms. Furthermore, we determine conditions for which spatial search problems on regular graphs are amenable to this doubling of the success probability, and this involves diagrammatically analyzing search using degenerate perturbation theory and deriving a useful formula for how the quantum walk acts in its reduced subspace.

Solvable continuous-time random walk model of the motion of tracer particles through porous media.

We consider the continuous-time random walk (CTRW) model of tracer motion in porous medium flows based on the experimentally determined distributions of pore velocity and pore size reported by Holzner etal. [M. Holzner et al., Phys. Rev. E 92, 013015 (2015)PLEEE81539-375510.1103/PhysRevE.92.013015]. The particle's passing through one channel is modeled as one step of the walk. The step (channel) length is random and the walker's velocity at consecutive steps of the walk is conserved with finite probability, mimicking that at the turning point there could be no abrupt change of velocity. We provide the Laplace transform of the characteristic function of the walker's position and reductions for different cases of independence of the CTRW's step duration τ, length l, and velocity v. We solve our model with independent l and v. The model incorporates different forms of the tail of the probability density of small velocities that vary with the model parameter α. Depending on that parameter, all types of anomalous diffusion can hold, from super- to subdiffusion. In a finite interval of α, ballistic behavior with logarithmic corrections holds, which was observed in a previously introduced CTRW model with independent l and τ. Universality of tracer diffusion in the porous medium is considered.

Scaling analysis of random walks with persistence lengths: Application to self-avoiding walks.

We develop an approach for performing scaling analysis of N-step random walks (RWs). The mean square end-to-end distance, 〈R[over ⃗]_{N}^{2}〉, is written in terms of inner persistence lengths (IPLs), which we define by the ensemble averages of dot products between the walker's position and displacement vectors, at the jth step. For RW models statistically invariant under orthogonal transformations, we analytically introduce a relation between 〈R[over ⃗]_{N}^{2}〉 and the persistence length, λ_{N}, which is defined as the mean end-to-end vector projection in the first step direction. For self-avoiding walks (SAWs) on 2D and 3D lattices we introduce a series expansion for λ_{N}, and by Monte Carlo simulations we find that λ_{∞} is equal to a constant; the scaling corrections for λ_{N} can be second- and higher-order corrections to scaling for 〈R[over ⃗]_{N}^{2}〉. Building SAWs with typically 100 steps, we estimate the exponents ν_{0} and Δ_{1} from the IPL behavior as function of j. The obtained results are in excellent agreement with those in the literature. This shows that only an ensemble of paths with the same length is sufficient for determining the scaling behavior of 〈R[over ⃗]_{N}^{2}〉, being that the whole information needed is contained in the inner part of the paths.