Quantum Ultra-Walks: Walks on a Line with Spatial Disorder

NASA Astrophysics Data System (ADS)

Boettcher, Stefan; Falkner, Stefan

We discuss the model of a heterogeneous discrete-time walk on a line with spatial disorder in the form of a set of ultrametric barriers. Simulations show that such an quantum ultra-walk spreads with a walk exponent dw that ranges from ballistic (dw = 1) to complete confinement (dw = ∞) for increasing separation 1 <= 1 / ɛ < ∞ in barrier heights. We develop a formalism by which the classical random walk as well as the quantum walk can be treated in parallel using a coined walk with internal degrees of freedom. For the random walk, this amounts to a 2nd -order Markov process with a stochastic coin, better know as an (anti-)persistent walk. The exact analysis, based on the real-space renormalization group (RG), reproduces the results of the well-known model of ``ultradiffusion,'' dw = 1 -log2 ɛ for 0 < ɛ <= 1 / 2 . However, while the evaluation of the RG fixed-points proceeds virtually identical, for the corresponding quantum walk with a unitary coin it fails to reproduce the numerical results. A new way to analyze the RG is indicated. Supported by NSF-DMR 1207431.

A Perron-Frobenius Type of Theorem for Quantum Operations

NASA Astrophysics Data System (ADS)

Lagro, Matthew; Yang, Wei-Shih; Xiong, Sheng

2017-10-01

We define a special class of quantum operations we call Markovian and show that it has the same spectral properties as a corresponding Markov chain. We then consider a convex combination of a quantum operation and a Markovian quantum operation and show that under a norm condition its spectrum has the same properties as in the conclusion of the Perron-Frobenius theorem if its Markovian part does. Moreover, under a compatibility condition of the two operations, we show that its limiting distribution is the same as the corresponding Markov chain. We apply our general results to partially decoherent quantum random walks with decoherence strength 0 ≤ p ≤ 1. We obtain a quantum ergodic theorem for partially decoherent processes. We show that for 0 < p ≤ 1, the limiting distribution of a partially decoherent quantum random walk is the same as the limiting distribution for the classical random walk.

Equivalence of Szegedy's and coined quantum walks

NASA Astrophysics Data System (ADS)

Wong, Thomas G.

2017-09-01

Szegedy's quantum walk is a quantization of a classical random walk or Markov chain, where the walk occurs on the edges of the bipartite double cover of the original graph. To search, one can simply quantize a Markov chain with absorbing vertices. Recently, Santos proposed two alternative search algorithms that instead utilize the sign-flip oracle in Grover's algorithm rather than absorbing vertices. In this paper, we show that these two algorithms are exactly equivalent to two algorithms involving coined quantum walks, which are walks on the vertices of the original graph with an internal degree of freedom. The first scheme is equivalent to a coined quantum walk with one walk step per query of Grover's oracle, and the second is equivalent to a coined quantum walk with two walk steps per query of Grover's oracle. These equivalences lie outside the previously known equivalence of Szegedy's quantum walk with absorbing vertices and the coined quantum walk with the negative identity operator as the coin for marked vertices, whose precise relationships we also investigate.

Efficient quantum walk on a quantum processor

PubMed Central

Qiang, Xiaogang; Loke, Thomas; Montanaro, Ashley; Aungskunsiri, Kanin; Zhou, Xiaoqi; O'Brien, Jeremy L.; Wang, Jingbo B.; Matthews, Jonathan C. F.

2016-01-01

The random walk formalism is used across a wide range of applications, from modelling share prices to predicting population genetics. Likewise, quantum walks have shown much potential as a framework for developing new quantum algorithms. Here we present explicit efficient quantum circuits for implementing continuous-time quantum walks on the circulant class of graphs. These circuits allow us to sample from the output probability distributions of quantum walks on circulant graphs efficiently. We also show that solving the same sampling problem for arbitrary circulant quantum circuits is intractable for a classical computer, assuming conjectures from computational complexity theory. This is a new link between continuous-time quantum walks and computational complexity theory and it indicates a family of tasks that could ultimately demonstrate quantum supremacy over classical computers. As a proof of principle, we experimentally implement the proposed quantum circuit on an example circulant graph using a two-qubit photonics quantum processor. PMID:27146471

Physical realizability of continuous-time quantum stochastic walks

NASA Astrophysics Data System (ADS)

Taketani, Bruno G.; Govia, Luke C. G.; Wilhelm, Frank K.

2018-05-01

Quantum walks are a promising methodology that can be used to both understand and implement quantum information processing tasks. The quantum stochastic walk is a recently developed framework that combines the concept of a quantum walk with that of a classical random walk, through open system evolution of a quantum system. Quantum stochastic walks have been shown to have applications in as far reaching fields as artificial intelligence. However, there are significant constraints on the kind of open system evolutions that can be realized in a physical experiment. In this work, we discuss the restrictions on the allowed open system evolution and the physical assumptions underpinning them. We show that general direct implementations would require the complete solution of the underlying unitary dynamics and sophisticated reservoir engineering, thus weakening the benefits of experimental implementation.

Random walk in generalized quantum theory

NASA Astrophysics Data System (ADS)

Martin, Xavier; O'Connor, Denjoe; Sorkin, Rafael D.

2005-01-01

One can view quantum mechanics as a generalization of classical probability theory that provides for pairwise interference among alternatives. Adopting this perspective, we “quantize” the classical random walk by finding, subject to a certain condition of “strong positivity”, the most general Markovian, translationally invariant “decoherence functional” with nearest neighbor transitions.

Quantum Algorithms Based on Physical Processes

DTIC Science & Technology

2013-12-03

quantum walks with hard-core bosons and the graph isomorphism problem,” American Physical Society March meeting, March 2011 Kenneth Rudinger, John...King Gamble, Mark Wellons, Mark Friesen, Dong Zhou, Eric Bach, Robert Joynt, and S.N. Coppersmith, “Quantum random walks of non-interacting bosons on...and noninteracting Bosons to distinguish nonisomorphic graphs. 1) We showed that quantum walks of two hard-core Bosons can distinguish all pairs of

Quantum Algorithms Based on Physical Processes

DTIC Science & Technology

2013-12-02

quantum walks with hard-core bosons and the graph isomorphism problem,” American Physical Society March meeting, March 2011 Kenneth Rudinger, John...King Gamble, Mark Wellons, Mark Friesen, Dong Zhou, Eric Bach, Robert Joynt, and S.N. Coppersmith, “Quantum random walks of non-interacting bosons on...and noninteracting Bosons to distinguish nonisomorphic graphs. 1) We showed that quantum walks of two hard-core Bosons can distinguish all pairs of

Open quantum random walks: Bistability on pure states and ballistically induced diffusion

NASA Astrophysics Data System (ADS)

Bauer, Michel; Bernard, Denis; Tilloy, Antoine

2013-12-01

Open quantum random walks (OQRWs) deal with quantum random motions on a line for systems with internal and orbital degrees of freedom. The internal system behaves as a quantum random gyroscope coding for the direction of the orbital moves. We reveal the existence of a transition, depending on OQRW moduli, in the internal system behaviors from simple oscillations to random flips between two unstable pure states. This induces a transition in the orbital motions from the usual diffusion to ballistically induced diffusion with a large mean free path and large effective diffusion constant at large times. We also show that mixed states of the internal system are converted into random pure states during the process. We touch upon possible experimental realizations.

History dependent quantum random walks as quantum lattice gas automata

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shakeel, Asif, E-mail: asif.shakeel@gmail.com, E-mail: dmeyer@math.ucsd.edu, E-mail: plove@haverford.edu; Love, Peter J., E-mail: asif.shakeel@gmail.com, E-mail: dmeyer@math.ucsd.edu, E-mail: plove@haverford.edu; Meyer, David A., E-mail: asif.shakeel@gmail.com, E-mail: dmeyer@math.ucsd.edu, E-mail: plove@haverford.edu

Quantum Random Walks (QRW) were first defined as one-particle sectors of Quantum Lattice Gas Automata (QLGA). Recently, they have been generalized to include history dependence, either on previous coin (internal, i.e., spin or velocity) states or on previous position states. These models have the goal of studying the transition to classicality, or more generally, changes in the performance of quantum walks in algorithmic applications. We show that several history dependent QRW can be identified as one-particle sectors of QLGA. This provides a unifying conceptual framework for these models in which the extra degrees of freedom required to store the historymore » information arise naturally as geometrical degrees of freedom on the lattice.« less

Averaging in SU(2) open quantum random walk

NASA Astrophysics Data System (ADS)

Clement, Ampadu

2014-03-01

We study the average position and the symmetry of the distribution in the SU(2) open quantum random walk (OQRW). We show that the average position in the central limit theorem (CLT) is non-uniform compared with the average position in the non-CLT. The symmetry of distribution is shown to be even in the CLT.

Synthesis of Polyferrocenylsilane Block Copolymers and their Crystallization-Driven Self-Assembly in Protic Solvents

NASA Astrophysics Data System (ADS)

Zhou, Hang

Quantum walks are the quantum mechanical analogue of classical random walks. Discrete-time quantum walks have been introduced and studied mostly on the line Z or higher dimensional space Zd but rarely defined on graphs with fractal dimensions because the coin operator depends on the position and the Fourier transform on the fractals is not defined. Inspired by its nature of classical walks, different quantum walks will be defined by choosing different shift and coin operators. When the coin operator is uniform, the results of classical walks will be obtained upon measurement at each step. Moreover, with measurement at each step, our results reveal more information about the classical random walks. In this dissertation, two graphs with fractal dimensions will be considered. The first one is Sierpinski gasket, a degree-4 regular graph with Hausdorff dimension of df = ln 3/ ln 2. The second is the Cantor graph derived like Cantor set, with Hausdorff dimension of df = ln 2/ ln 3. The definitions and amplitude functions of the quantum walks will be introduced. The main part of this dissertation is to derive a recursive formula to compute the amplitude Green function. The exiting probability will be computed and compared with the classical results. When the generation of graphs goes to infinity, the recursion of the walks will be investigated and the convergence rates will be obtained and compared with the classical counterparts.

Quantum Walk Schemes for Universal Quantum Computation

NASA Astrophysics Data System (ADS)

Underwood, Michael S.

Random walks are a powerful tool for the efficient implementation of algorithms in classical computation. Their quantum-mechanical analogues, called quantum walks, hold similar promise. Quantum walks provide a model of quantum computation that has recently been shown to be equivalent in power to the standard circuit model. As in the classical case, quantum walks take place on graphs and can undergo discrete or continuous evolution, though quantum evolution is unitary and therefore deterministic until a measurement is made. This thesis considers the usefulness of continuous-time quantum walks to quantum computation from the perspectives of both their fundamental power under various formulations, and their applicability in practical experiments. In one extant scheme, logical gates are effected by scattering processes. The results of an exhaustive search for single-qubit operations in this model are presented. It is shown that the number of distinct operations increases exponentially with the number of vertices in the scattering graph. A catalogue of all graphs on up to nine vertices that implement single-qubit unitaries at a specific set of momenta is included in an appendix. I develop a novel scheme for universal quantum computation called the discontinuous quantum walk, in which a continuous-time quantum walker takes discrete steps of evolution via perfect quantum state transfer through small 'widget' graphs. The discontinuous quantum-walk scheme requires an exponentially sized graph, as do prior discrete and continuous schemes. To eliminate the inefficient vertex resource requirement, a computation scheme based on multiple discontinuous walkers is presented. In this model, n interacting walkers inhabiting a graph with 2n vertices can implement an arbitrary quantum computation on an input of length n, an exponential savings over previous universal quantum walk schemes. This is the first quantum walk scheme that allows for the application of quantum error correction. The many-particle quantum walk can be viewed as a single quantum walk undergoing perfect state transfer on a larger weighted graph, obtained via equitable partitioning. I extend this formalism to non-simple graphs. Examples of the application of equitable partitioning to the analysis of quantum walks and many-particle quantum systems are discussed.

A Spectral Analysis of Discrete-Time Quantum Walks Related to the Birth and Death Chains

NASA Astrophysics Data System (ADS)

Ho, Choon-Lin; Ide, Yusuke; Konno, Norio; Segawa, Etsuo; Takumi, Kentaro

2018-04-01

In this paper, we consider a spectral analysis of discrete time quantum walks on the path. For isospectral coin cases, we show that the time averaged distribution and stationary distributions of the quantum walks are described by the pair of eigenvalues of the coins as well as the eigenvalues and eigenvectors of the corresponding random walks which are usually referred as the birth and death chains. As an example of the results, we derive the time averaged distribution of so-called Szegedy's walk which is related to the Ehrenfest model. It is represented by Krawtchouk polynomials which is the eigenvectors of the model and includes the arcsine law.

Lévy walks

NASA Astrophysics Data System (ADS)

Zaburdaev, V.; Denisov, S.; Klafter, J.

2015-04-01

Random walk is a fundamental concept with applications ranging from quantum physics to econometrics. Remarkably, one specific model of random walks appears to be ubiquitous across many fields as a tool to analyze transport phenomena in which the dispersal process is faster than dictated by Brownian diffusion. The Lévy-walk model combines two key features, the ability to generate anomalously fast diffusion and a finite velocity of a random walker. Recent results in optics, Hamiltonian chaos, cold atom dynamics, biophysics, and behavioral science demonstrate that this particular type of random walk provides significant insight into complex transport phenomena. This review gives a self-consistent introduction to Lévy walks, surveys their existing applications, including latest advances, and outlines further perspectives.

Quantum Walks on the Line with Phase Parameters

NASA Astrophysics Data System (ADS)

Villagra, Marcos; Nakanishi, Masaki; Yamashita, Shigeru; Nakashima, Yasuhiko

In this paper, a study on discrete-time coined quantum walks on the line is presented. Clear mathematical foundations are still lacking for this quantum walk model. As a step toward this objective, the following question is being addressed: Given a graph, what is the probability that a quantum walk arrives at a given vertex after some number of steps? This is a very natural question, and for random walks it can be answered by several different combinatorial arguments. For quantum walks this is a highly non-trivial task. Furthermore, this was only achieved before for one specific coin operator (Hadamard operator) for walks on the line. Even considering only walks on lines, generalizing these computations to a general SU(2) coin operator is a complex task. The main contribution is a closed-form formula for the amplitudes of the state of the walk (which includes the question above) for a general symmetric SU(2) operator for walks on the line. To this end, a coin operator with parameters that alters the phase of the state of the walk is defined. Then, closed-form solutions are computed by means of Fourier analysis and asymptotic approximation methods. We also present some basic properties of the walk which can be deducted using weak convergence theorems for quantum walks. In particular, the support of the induced probability distribution of the walk is calculated. Then, it is shown how changing the parameters in the coin operator affects the resulting probability distribution.

Implementing Parrondo's paradox with two-coin quantum walks

NASA Astrophysics Data System (ADS)

Rajendran, Jishnu; Benjamin, Colin

2018-02-01

Parrondo's paradox is ubiquitous in games, ratchets and random walks. The apparent paradox, devised by J. M. R. Parrondo, that two losing games A and B can produce a winning outcome has been adapted in many physical and biological systems to explain their working. However, proposals on demonstrating Parrondo's paradox using quantum walks failed for a large number of steps. In this work, we show that instead of a single coin if we consider a two-coin initial state which may or may not be entangled, we can observe a genuine Parrondo's paradox with quantum walks. Furthermore, we focus on reasons for this and pin down the asymmetry in initial two-coin state or asymmetry in shift operator, either of which is necessary for observing a genuine Parrondo's paradox. We extend our work to a three-coin initial state too with similar results. The implications of our work for observing quantum ratchet-like behaviour using quantum walks are also discussed.

Implementing Parrondo’s paradox with two-coin quantum walks

PubMed Central

Rajendran, Jishnu

2018-01-01

Parrondo’s paradox is ubiquitous in games, ratchets and random walks. The apparent paradox, devised by J. M. R. Parrondo, that two losing games A and B can produce a winning outcome has been adapted in many physical and biological systems to explain their working. However, proposals on demonstrating Parrondo’s paradox using quantum walks failed for a large number of steps. In this work, we show that instead of a single coin if we consider a two-coin initial state which may or may not be entangled, we can observe a genuine Parrondo’s paradox with quantum walks. Furthermore, we focus on reasons for this and pin down the asymmetry in initial two-coin state or asymmetry in shift operator, either of which is necessary for observing a genuine Parrondo’s paradox. We extend our work to a three-coin initial state too with similar results. The implications of our work for observing quantum ratchet-like behaviour using quantum walks are also discussed. PMID:29515873

Renormalization of the unitary evolution equation for coined quantum walks

NASA Astrophysics Data System (ADS)

Boettcher, Stefan; Li, Shanshan; Portugal, Renato

2017-03-01

We consider discrete-time evolution equations in which the stochastic operator of a classical random walk is replaced by a unitary operator. Such a problem has gained much attention as a framework for coined quantum walks that are essential for attaining the Grover limit for quantum search algorithms in physically realizable, low-dimensional geometries. In particular, we analyze the exact real-space renormalization group (RG) procedure recently introduced to study the scaling of quantum walks on fractal networks. While this procedure, when implemented numerically, was able to provide some deep insights into the relation between classical and quantum walks, its analytic basis has remained obscure. Our discussion here is laying the groundwork for a rigorous implementation of the RG for this important class of transport and algorithmic problems, although some instances remain unresolved. Specifically, we find that the RG fixed-point analysis of the classical walk, which typically focuses on the dominant Jacobian eigenvalue {λ1} , with walk dimension dw\\text{RW}={{log}2}{λ1} , needs to be extended to include the subdominant eigenvalue {λ2} , such that the dimension of the quantum walk obtains dw\\text{QW}={{log}2}\\sqrt{{λ1}{λ2}} . With that extension, we obtain analytically previously conjectured results for dw\\text{QW} of Grover walks on all but one of the fractal networks that have been considered.

Open Quantum Random Walks on the Half-Line: The Karlin-McGregor Formula, Path Counting and Foster's Theorem

NASA Astrophysics Data System (ADS)

Jacq, Thomas S.; Lardizabal, Carlos F.

2017-11-01

In this work we consider open quantum random walks on the non-negative integers. By considering orthogonal matrix polynomials we are able to describe transition probability expressions for classes of walks via a matrix version of the Karlin-McGregor formula. We focus on absorbing boundary conditions and, for simpler classes of examples, we consider path counting and the corresponding combinatorial tools. A non-commutative version of the gambler's ruin is studied by obtaining the probability of reaching a certain fortune and the mean time to reach a fortune or ruin in terms of generating functions. In the case of the Hadamard coin, a counting technique for boundary restricted paths in a lattice is also presented. We discuss an open quantum version of Foster's Theorem for the expected return time together with applications.

Faster quantum walk search on a weighted graph

NASA Astrophysics Data System (ADS)

Wong, Thomas G.

2015-09-01

A randomly walking quantum particle evolving by Schrödinger's equation searches for a unique marked vertex on the "simplex of complete graphs" in time Θ (N3 /4) . We give a weighted version of this graph that preserves vertex transitivity, and we show that the time to search on it can be reduced to nearly Θ (√{N }) . To prove this, we introduce two extensions to degenerate perturbation theory: an adjustment that distinguishes the weights of the edges and a method to determine how precisely the jumping rate of the quantum walk must be chosen.

Discrete-time Quantum Walks via Interchange Framework and Memory in Quantum Evolution

NASA Astrophysics Data System (ADS)

Dimcovic, Zlatko

One of the newer and rapidly developing approaches in quantum computing is based on "quantum walks," which are quantum processes on discrete space that evolve in either discrete or continuous time and are characterized by mixing of components at each step. The idea emerged in analogy with the classical random walks and stochastic techniques, but these unitary processes are very different even as they have intriguing similarities. This thesis is concerned with study of discrete-time quantum walks. The original motivation from classical Markov chains required for discrete-time quantum walks that one adds an auxiliary Hilbert space, unrelated to the one in which the system evolves, in order to be able to mix components in that space and then take the evolution steps accordingly (based on the state in that space). This additional, "coin," space is very often an internal degree of freedom like spin. We have introduced a general framework for construction of discrete-time quantum walks in a close analogy with the classical random walks with memory that is rather different from the standard "coin" approach. In this method there is no need to bring in a different degree of freedom, while the full state of the system is still described in the direct product of spaces (of states). The state can be thought of as an arrow pointing from the previous to the current site in the evolution, representing the one-step memory. The next step is then controlled by a single local operator assigned to each site in the space, acting quite like a scattering operator. This allows us to probe and solve some problems of interest that have not had successful approaches with "coined" walks. We construct and solve a walk on the binary tree, a structure of great interest but until our result without an explicit discrete time quantum walk, due to difficulties in managing coin spaces necessary in the standard approach. Beyond algorithmic interests, the model based on memory allows one to explore effects of history on the quantum evolution and the subtle emergence of classical features as "memory" is explicitly kept for additional steps. We construct and solve a walk with an additional correlation step, finding interesting new features. On the other hand, the fact that the evolution is driven entirely by a local operator, not involving additional spaces, enables us to choose the Fourier transform as an operator completely controlling the evolution. This in turn allows us to combine the quantum walk approach with Fourier transform based techniques, something decidedly not possible in classical computational physics. We are developing a formalism for building networks manageable by walks constructed with this framework, based on the surprising efficiency of our framework in discovering internals of a simple network that we so far solved. Finally, in line with our expectation that the field of quantum walks can take cues from the rich history of development of the classical stochastic techniques, we establish starting points for the work on non-Abelian quantum walks, with a particular quantum-walk analog of the classical "card shuffling," the walk on the permutation group. In summary, this thesis presents a new framework for construction of discrete time quantum walks, employing and exploring memoried nature of unitary evolution. It is applied to fully solving the problems of: A walk on the binary tree and exploration of the quantum-to-classical transition with increased correlation length (history). It is then used for simple network discovery, and to lay the groundwork for analysis of complex networks, based on combined power of efficient exploration of the Hilbert space (as a walk mixing components) and Fourier transformation (since we can choose this for the evolution operator). We hope to establish this as a general technique as its power would be unmatched by any approaches available in the classical computing. We also looked at the promising and challenging prospect of walks on non-Abelian structures by setting up the problem of "quantum card shuffling," a quantum walk on the permutation group. Relation to other work is thoroughly discussed throughout, along with examination of the context of our work and overviews of our current and future work.

Continuous time quantum random walks in free space

NASA Astrophysics Data System (ADS)

Eichelkraut, Toni; Vetter, Christian; Perez-Leija, Armando; Christodoulides, Demetrios; Szameit, Alexander

2014-05-01

We show theoretically and experimentally that two-dimensional continuous time coherent random walks are possible in free space, that is, in the absence of any external potential, by properly tailoring the associated initial wave function. These effects are experimentally demonstrated using classical paraxial light. Evidently, the usage of classical beams to explore the dynamics of point-like quantum particles is possible since both phenomena are mathematically equivalent. This in turn makes our approach suitable for the realization of random walks using different quantum particles, including electrons and photons. To study the spatial evolution of a wavefunction theoretically, we consider the one-dimensional paraxial wave equation (i∂z +1/2 ∂x2) Ψ = 0 . Starting with the initially localized wavefunction Ψ (x , 0) = exp [ -x2 / 2σ2 ] J0 (αx) , one can show that the evolution of such Gaussian-apodized Bessel envelopes within a region of validity resembles the probability pattern of a quantum walker traversing a uniform lattice. In order to generate the desired input-field in our experimental setting we shape the amplitude and phase of a collimated light beam originating from a classical HeNe-Laser (633 nm) utilizing a spatial light modulator.

Connectivity is a Poor Indicator of Fast Quantum Search

NASA Astrophysics Data System (ADS)

Meyer, David A.; Wong, Thomas G.

2015-03-01

A randomly walking quantum particle evolving by Schrödinger's equation searches on d -dimensional cubic lattices in O (√{N }) time when d ≥5 , and with progressively slower runtime as d decreases. This suggests that graph connectivity (including vertex, edge, algebraic, and normalized algebraic connectivities) is an indicator of fast quantum search, a belief supported by fast quantum search on complete graphs, strongly regular graphs, and hypercubes, all of which are highly connected. In this Letter, we show this intuition to be false by giving two examples of graphs for which the opposite holds true: one with low connectivity but fast search, and one with high connectivity but slow search. The second example is a novel two-stage quantum walk algorithm in which the walking rate must be adjusted to yield high search probability.

Novel pseudo-random number generator based on quantum random walks.

PubMed

Yang, Yu-Guang; Zhao, Qian-Qian

2016-02-04

In this paper, we investigate the potential application of quantum computation for constructing pseudo-random number generators (PRNGs) and further construct a novel PRNG based on quantum random walks (QRWs), a famous quantum computation model. The PRNG merely relies on the equations used in the QRWs, and thus the generation algorithm is simple and the computation speed is fast. The proposed PRNG is subjected to statistical tests such as NIST and successfully passed the test. Compared with the representative PRNG based on quantum chaotic maps (QCM), the present QRWs-based PRNG has some advantages such as better statistical complexity and recurrence. For example, the normalized Shannon entropy and the statistical complexity of the QRWs-based PRNG are 0.999699456771172 and 1.799961178212329e-04 respectively given the number of 8 bits-words, say, 16Mbits. By contrast, the corresponding values of the QCM-based PRNG are 0.999448131481064 and 3.701210794388818e-04 respectively. Thus the statistical complexity and the normalized entropy of the QRWs-based PRNG are closer to 0 and 1 respectively than those of the QCM-based PRNG when the number of words of the analyzed sequence increases. It provides a new clue to construct PRNGs and also extends the applications of quantum computation.

Novel pseudo-random number generator based on quantum random walks

PubMed Central

Yang, Yu-Guang; Zhao, Qian-Qian

2016-01-01

In this paper, we investigate the potential application of quantum computation for constructing pseudo-random number generators (PRNGs) and further construct a novel PRNG based on quantum random walks (QRWs), a famous quantum computation model. The PRNG merely relies on the equations used in the QRWs, and thus the generation algorithm is simple and the computation speed is fast. The proposed PRNG is subjected to statistical tests such as NIST and successfully passed the test. Compared with the representative PRNG based on quantum chaotic maps (QCM), the present QRWs-based PRNG has some advantages such as better statistical complexity and recurrence. For example, the normalized Shannon entropy and the statistical complexity of the QRWs-based PRNG are 0.999699456771172 and 1.799961178212329e-04 respectively given the number of 8 bits-words, say, 16Mbits. By contrast, the corresponding values of the QCM-based PRNG are 0.999448131481064 and 3.701210794388818e-04 respectively. Thus the statistical complexity and the normalized entropy of the QRWs-based PRNG are closer to 0 and 1 respectively than those of the QCM-based PRNG when the number of words of the analyzed sequence increases. It provides a new clue to construct PRNGs and also extends the applications of quantum computation. PMID:26842402

Quantum Hash function and its application to privacy amplification in quantum key distribution, pseudo-random number generation and image encryption

NASA Astrophysics Data System (ADS)

Yang, Yu-Guang; Xu, Peng; Yang, Rui; Zhou, Yi-Hua; Shi, Wei-Min

2016-01-01

Quantum information and quantum computation have achieved a huge success during the last years. In this paper, we investigate the capability of quantum Hash function, which can be constructed by subtly modifying quantum walks, a famous quantum computation model. It is found that quantum Hash function can act as a hash function for the privacy amplification process of quantum key distribution systems with higher security. As a byproduct, quantum Hash function can also be used for pseudo-random number generation due to its inherent chaotic dynamics. Further we discuss the application of quantum Hash function to image encryption and propose a novel image encryption algorithm. Numerical simulations and performance comparisons show that quantum Hash function is eligible for privacy amplification in quantum key distribution, pseudo-random number generation and image encryption in terms of various hash tests and randomness tests. It extends the scope of application of quantum computation and quantum information.

Quantum Hash function and its application to privacy amplification in quantum key distribution, pseudo-random number generation and image encryption

PubMed Central

Yang, Yu-Guang; Xu, Peng; Yang, Rui; Zhou, Yi-Hua; Shi, Wei-Min

2016-01-01

Quantum information and quantum computation have achieved a huge success during the last years. In this paper, we investigate the capability of quantum Hash function, which can be constructed by subtly modifying quantum walks, a famous quantum computation model. It is found that quantum Hash function can act as a hash function for the privacy amplification process of quantum key distribution systems with higher security. As a byproduct, quantum Hash function can also be used for pseudo-random number generation due to its inherent chaotic dynamics. Further we discuss the application of quantum Hash function to image encryption and propose a novel image encryption algorithm. Numerical simulations and performance comparisons show that quantum Hash function is eligible for privacy amplification in quantum key distribution, pseudo-random number generation and image encryption in terms of various hash tests and randomness tests. It extends the scope of application of quantum computation and quantum information. PMID:26823196

Quantum Hash function and its application to privacy amplification in quantum key distribution, pseudo-random number generation and image encryption.

PubMed

Yang, Yu-Guang; Xu, Peng; Yang, Rui; Zhou, Yi-Hua; Shi, Wei-Min

2016-01-29

Quantum information and quantum computation have achieved a huge success during the last years. In this paper, we investigate the capability of quantum Hash function, which can be constructed by subtly modifying quantum walks, a famous quantum computation model. It is found that quantum Hash function can act as a hash function for the privacy amplification process of quantum key distribution systems with higher security. As a byproduct, quantum Hash function can also be used for pseudo-random number generation due to its inherent chaotic dynamics. Further we discuss the application of quantum Hash function to image encryption and propose a novel image encryption algorithm. Numerical simulations and performance comparisons show that quantum Hash function is eligible for privacy amplification in quantum key distribution, pseudo-random number generation and image encryption in terms of various hash tests and randomness tests. It extends the scope of application of quantum computation and quantum information.

The open quantum Brownian motions

NASA Astrophysics Data System (ADS)

Bauer, Michel; Bernard, Denis; Tilloy, Antoine

2014-09-01

Using quantum parallelism on random walks as the original seed, we introduce new quantum stochastic processes, the open quantum Brownian motions. They describe the behaviors of quantum walkers—with internal degrees of freedom which serve as random gyroscopes—interacting with a series of probes which serve as quantum coins. These processes may also be viewed as the scaling limit of open quantum random walks and we develop this approach along three different lines: the quantum trajectory, the quantum dynamical map and the quantum stochastic differential equation. We also present a study of the simplest case, with a two level system as an internal gyroscope, illustrating the interplay between the ballistic and diffusive behaviors at work in these processes. Notation H_z : orbital (walker) Hilbert space, {C}^{{Z}} in the discrete, L^2({R}) in the continuum H_c : internal spin (or gyroscope) Hilbert space H_sys=H_z\\otimesH_c : system Hilbert space H_p : probe (or quantum coin) Hilbert space, H_p={C}^2 \\rho^tot_t : density matrix for the total system (walker + internal spin + quantum coins) \\bar \\rho_t : reduced density matrix on H_sys : \\bar\\rho_t=\\int dxdy\\, \\bar\\rho_t(x,y)\\otimes | x \\rangle _z\\langle y | \\hat \\rho_t : system density matrix in a quantum trajectory: \\hat\\rho_t=\\int dxdy\\, \\hat\\rho_t(x,y)\\otimes | x \\rangle _z\\langle y | . If diagonal and localized in position: \\hat \\rho_t=\\rho_t\\otimes| X_t \\rangle _z\\langle X_t | ρt: internal density matrix in a simple quantum trajectory Xt: walker position in a simple quantum trajectory Bt: normalized Brownian motion ξt, \\xi_t^\\dagger : quantum noises

Analysis of coined quantum walks with renormalization

NASA Astrophysics Data System (ADS)

Boettcher, Stefan; Li, Shanshan

2018-01-01

We introduce a framework to analyze quantum algorithms with the renormalization group (RG). To this end, we present a detailed analysis of the real-space RG for discrete-time quantum walks on fractal networks and show how deep insights into the analytic structure as well as generic results about the long-time behavior can be extracted. The RG flow for such a walk on a dual Sierpinski gasket and a Migdal-Kadanoff hierarchical network is obtained explicitly from elementary algebraic manipulations, after transforming the unitary evolution equation into Laplace space. Unlike for classical random walks, we find that the long-time asymptotics for the quantum walk requires consideration of a diverging number of Laplace poles, which we demonstrate exactly for the closed-form solution available for the walk on a one-dimensional loop. In particular, we calculate the probability of the walk to overlap with its starting position, which oscillates with a period that scales as NdwQ/df with system size N . While the largest Jacobian eigenvalue λ1 of the RG flow merely reproduces the fractal dimension, df=log2λ1 , the asymptotic analysis shows that the second Jacobian eigenvalue λ2 becomes essential to determine the dimension of the quantum walk via dwQ=log2√{λ1λ2 } . We trace this fact to delicate cancellations caused by unitarity. We obtain identical relations for other networks, although the details of the RG analysis may exhibit surprisingly distinct features. Thus, our conclusions—which trivially reproduce those for regular lattices with translational invariance with df=d and dwQ=1 —appear to be quite general and likely apply to networks beyond those studied here.

Generalized teleportation by quantum walks

NASA Astrophysics Data System (ADS)

Wang, Yu; Shang, Yun; Xue, Peng

2017-09-01

We develop a generalized teleportation scheme based on quantum walks with two coins. For an unknown qubit state, we use two-step quantum walks on the line and quantum walks on the cycle with four vertices for teleportation. For any d-dimensional states, quantum walks on complete graphs and quantum walks on d-regular graphs can be used for implementing teleportation. Compared with existing d-dimensional states teleportation, prior entangled state is not required and the necessary maximal entanglement resource is generated by the first step of quantum walk. Moreover, two projective measurements with d elements are needed by quantum walks on the complete graph, rather than one joint measurement with d^2 basis states. Quantum walks have many applications in quantum computation and quantum simulations. This is the first scheme of realizing communicating protocol with quantum walks, thus opening wider applications.

Spatial Search by Quantum Walk is Optimal for Almost all Graphs.

PubMed

Chakraborty, Shantanav; Novo, Leonardo; Ambainis, Andris; Omar, Yasser

2016-03-11

The problem of finding a marked node in a graph can be solved by the spatial search algorithm based on continuous-time quantum walks (CTQW). However, this algorithm is known to run in optimal time only for a handful of graphs. In this work, we prove that for Erdös-Renyi random graphs, i.e., graphs of n vertices where each edge exists with probability p, search by CTQW is almost surely optimal as long as p≥log^{3/2}(n)/n. Consequently, we show that quantum spatial search is in fact optimal for almost all graphs, meaning that the fraction of graphs of n vertices for which this optimality holds tends to one in the asymptotic limit. We obtain this result by proving that search is optimal on graphs where the ratio between the second largest and the largest eigenvalue is bounded by a constant smaller than 1. Finally, we show that we can extend our results on search to establish high fidelity quantum communication between two arbitrary nodes of a random network of interacting qubits, namely, to perform quantum state transfer, as well as entanglement generation. Our work shows that quantum information tasks typically designed for structured systems retain performance in very disordered structures.

Quantum dynamics of nuclear spins and spin relaxation in organic semiconductors

NASA Astrophysics Data System (ADS)

Mkhitaryan, V. V.; Dobrovitski, V. V.

2017-06-01

We investigate the role of the nuclear-spin quantum dynamics in hyperfine-induced spin relaxation of hopping carriers in organic semiconductors. The fast-hopping regime, when the carrier spin does not rotate much between subsequent hops, is typical for organic semiconductors possessing long spin coherence times. We consider this regime and focus on a carrier random-walk diffusion in one dimension, where the effect of the nuclear-spin dynamics is expected to be the strongest. Exact numerical simulations of spin systems with up to 25 nuclear spins are performed using the Suzuki-Trotter decomposition of the evolution operator. Larger nuclear-spin systems are modeled utilizing the spin-coherent state P -representation approach developed earlier. We find that the nuclear-spin dynamics strongly influences the carrier spin relaxation at long times. If the random walk is restricted to a small area, it leads to the quenching of carrier spin polarization at a nonzero value at long times. If the random walk is unrestricted, the carrier spin polarization acquires a long-time tail, decaying as 1 /√{t } . Based on the numerical results, we devise a simple formula describing the effect quantitatively.

Quantum speedup of Monte Carlo methods.

PubMed

Montanaro, Ashley

2015-09-08

Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition functions. In this work, we describe a quantum algorithm which can accelerate Monte Carlo methods in a very general setting. The algorithm estimates the expected output value of an arbitrary randomized or quantum subroutine with bounded variance, achieving a near-quadratic speedup over the best possible classical algorithm. Combining the algorithm with the use of quantum walks gives a quantum speedup of the fastest known classical algorithms with rigorous performance bounds for computing partition functions, which use multiple-stage Markov chain Monte Carlo techniques. The quantum algorithm can also be used to estimate the total variation distance between probability distributions efficiently.

Quantum speedup of Monte Carlo methods

PubMed Central

Montanaro, Ashley

2015-01-01

Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition functions. In this work, we describe a quantum algorithm which can accelerate Monte Carlo methods in a very general setting. The algorithm estimates the expected output value of an arbitrary randomized or quantum subroutine with bounded variance, achieving a near-quadratic speedup over the best possible classical algorithm. Combining the algorithm with the use of quantum walks gives a quantum speedup of the fastest known classical algorithms with rigorous performance bounds for computing partition functions, which use multiple-stage Markov chain Monte Carlo techniques. The quantum algorithm can also be used to estimate the total variation distance between probability distributions efficiently. PMID:26528079

Trapping photons on the line: controllable dynamics of a quantum walk

NASA Astrophysics Data System (ADS)

Xue, Peng; Qin, Hao; Tang, Bao

2014-04-01

Optical interferometers comprising birefringent-crystal beam displacers, wave plates, and phase shifters serve as stable devices for simulating quantum information processes such as heralded coined quantum walks. Quantum walks are important for quantum algorithms, universal quantum computing circuits, quantum transport in complex systems, and demonstrating intriguing nonlinear dynamical quantum phenomena. We introduce fully controllable polarization-independent phase shifters in optical pathes in order to realize site-dependent phase defects. The effectiveness of our interferometer is demonstrated through realizing single-photon quantum-walk dynamics in one dimension. By applying site-dependent phase defects, the translational symmetry of an ideal standard quantum walk is broken resulting in localization effect in a quantum walk architecture. The walk is realized for different site-dependent phase defects and coin settings, indicating the strength of localization signature depends on the level of phase due to site-dependent phase defects and coin settings and opening the way for the implementation of a quantum-walk-based algorithm.

Driven topological systems in the classical limit

NASA Astrophysics Data System (ADS)

Duncan, Callum W.; Öhberg, Patrik; Valiente, Manuel

2017-03-01

Periodically driven quantum systems can exhibit topologically nontrivial behavior, even when their quasienergy bands have zero Chern numbers. Much work has been conducted on noninteracting quantum-mechanical models where this kind of behavior is present. However, the inclusion of interactions in out-of-equilibrium quantum systems can prove to be quite challenging. On the other hand, the classical counterpart of hard-core interactions can be simulated efficiently via constrained random walks. The noninteracting model, proposed by Rudner et al. [Phys. Rev. X 3, 031005 (2013), 10.1103/PhysRevX.3.031005], has a special point for which the system is equivalent to a classical random walk. We consider the classical counterpart of this model, which is exact at a special point even when hard-core interactions are present, and show how these quantitatively affect the edge currents in a strip geometry. We find that the interacting classical system is well described by a mean-field theory. Using this we simulate the dynamics of the classical system, which show that the interactions play the role of Markovian, or time-dependent disorder. By comparing the evolution of classical and quantum edge currents in small lattices, we find regimes where the classical limit considered gives good insight into the quantum problem.

Continuous-time quantum walks on star graphs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Salimi, S.

2009-06-15

In this paper, we investigate continuous-time quantum walk on star graphs. It is shown that quantum central limit theorem for a continuous-time quantum walk on star graphs for N-fold star power graph, which are invariant under the quantum component of adjacency matrix, converges to continuous-time quantum walk on K{sub 2} graphs (complete graph with two vertices) and the probability of observing walk tends to the uniform distribution.

A Local-Realistic Model of Quantum Mechanics Based on a Discrete Spacetime

NASA Astrophysics Data System (ADS)

Sciarretta, Antonio

2018-01-01

This paper presents a realistic, stochastic, and local model that reproduces nonrelativistic quantum mechanics (QM) results without using its mathematical formulation. The proposed model only uses integer-valued quantities and operations on probabilities, in particular assuming a discrete spacetime under the form of a Euclidean lattice. Individual (spinless) particle trajectories are described as random walks. Transition probabilities are simple functions of a few quantities that are either randomly associated to the particles during their preparation, or stored in the lattice nodes they visit during the walk. QM predictions are retrieved as probability distributions of similarly-prepared ensembles of particles. The scenarios considered to assess the model comprise of free particle, constant external force, harmonic oscillator, particle in a box, the Delta potential, particle on a ring, particle on a sphere and include quantization of energy levels and angular momentum, as well as momentum entanglement.

Local Random Quantum Circuits are Approximate Polynomial-Designs

NASA Astrophysics Data System (ADS)

Brandão, Fernando G. S. L.; Harrow, Aram W.; Horodecki, Michał

2016-09-01

We prove that local random quantum circuits acting on n qubits composed of O( t 10 n 2) many nearest neighbor two-qubit gates form an approximate unitary t-design. Previously it was unknown whether random quantum circuits were a t-design for any t > 3. The proof is based on an interplay of techniques from quantum many-body theory, representation theory, and the theory of Markov chains. In particular we employ a result of Nachtergaele for lower bounding the spectral gap of frustration-free quantum local Hamiltonians; a quasi-orthogonality property of permutation matrices; a result of Oliveira which extends to the unitary group the path-coupling method for bounding the mixing time of random walks; and a result of Bourgain and Gamburd showing that dense subgroups of the special unitary group, composed of elements with algebraic entries, are ∞-copy tensor-product expanders. We also consider pseudo-randomness properties of local random quantum circuits of small depth and prove that circuits of depth O( t 10 n) constitute a quantum t-copy tensor-product expander. The proof also rests on techniques from quantum many-body theory, in particular on the detectability lemma of Aharonov, Arad, Landau, and Vazirani. We give applications of the results to cryptography, equilibration of closed quantum dynamics, and the generation of topological order. In particular we show the following pseudo-randomness property of generic quantum circuits: Almost every circuit U of size O( n k ) on n qubits cannot be distinguished from a Haar uniform unitary by circuits of size O( n ( k-9)/11) that are given oracle access to U.

A simple method for finding the scattering coefficients of quantum graphs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cottrell, Seth S.

2015-09-15

Quantum walks are roughly analogous to classical random walks, and similar to classical walks they have been used to find new (quantum) algorithms. When studying the behavior of large graphs or combinations of graphs, it is useful to find the response of a subgraph to signals of different frequencies. In doing so, we can replace an entire subgraph with a single vertex with variable scattering coefficients. In this paper, a simple technique for quickly finding the scattering coefficients of any discrete-time quantum graph will be presented. These scattering coefficients can be expressed entirely in terms of the characteristic polynomial ofmore » the graph’s time step operator. This is a marked improvement over previous techniques which have traditionally required finding eigenstates for a given eigenvalue, which is far more computationally costly. With the scattering coefficients we can easily derive the “impulse response” which is the key to predicting the response of a graph to any signal. This gives us a powerful set of tools for rapidly understanding the behavior of graphs or for reducing a large graph into its constituent subgraphs regardless of how they are connected.« less

Dissipative quantum computing with open quantum walks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sinayskiy, Ilya; Petruccione, Francesco

An open quantum walk approach to the implementation of a dissipative quantum computing scheme is presented. The formalism is demonstrated for the example of an open quantum walk implementation of a 3 qubit quantum circuit consisting of 10 gates.

Quantum walks with an anisotropic coin II: scattering theory

NASA Astrophysics Data System (ADS)

Richard, S.; Suzuki, A.; de Aldecoa, R. Tiedra

2018-05-01

We perform the scattering analysis of the evolution operator of quantum walks with an anisotropic coin, and we prove a weak limit theorem for their asymptotic velocity. The quantum walks that we consider include one-defect models, two-phase quantum walks, and topological phase quantum walks as special cases. Our analysis is based on an abstract framework for the scattering theory of unitary operators in a two-Hilbert spaces setting, which is of independent interest.

Quantum walks of interacting fermions on a cycle graph

PubMed Central

Melnikov, Alexey A.; Fedichkin, Leonid E.

2016-01-01

Quantum walks have been employed widely to develop new tools for quantum information processing recently. A natural quantum walk dynamics of interacting particles can be used to implement efficiently the universal quantum computation. In this work quantum walks of electrons on a graph are studied. The graph is composed of semiconductor quantum dots arranged in a circle. Electrons can tunnel between adjacent dots and interact via Coulomb repulsion, which leads to entanglement. Fermionic entanglement dynamics is obtained and evaluated. PMID:27681057

Experimental two-dimensional quantum walk on a photonic chip

PubMed Central

Lin, Xiao-Feng; Feng, Zhen; Chen, Jing-Yuan; Gao, Jun; Sun, Ke; Wang, Chao-Yue; Lai, Peng-Cheng; Xu, Xiao-Yun; Wang, Yao; Qiao, Lu-Feng; Yang, Ai-Lin

2018-01-01

Quantum walks, in virtue of the coherent superposition and quantum interference, have exponential superiority over their classical counterpart in applications of quantum searching and quantum simulation. The quantum-enhanced power is highly related to the state space of quantum walks, which can be expanded by enlarging the photon number and/or the dimensions of the evolution network, but the former is considerably challenging due to probabilistic generation of single photons and multiplicative loss. We demonstrate a two-dimensional continuous-time quantum walk by using the external geometry of photonic waveguide arrays, rather than the inner degree of freedoms of photons. Using femtosecond laser direct writing, we construct a large-scale three-dimensional structure that forms a two-dimensional lattice with up to 49 × 49 nodes on a photonic chip. We demonstrate spatial two-dimensional quantum walks using heralded single photons and single photon–level imaging. We analyze the quantum transport properties via observing the ballistic evolution pattern and the variance profile, which agree well with simulation results. We further reveal the transient nature that is the unique feature for quantum walks of beyond one dimension. An architecture that allows a quantum walk to freely evolve in all directions and at a large scale, combining with defect and disorder control, may bring up powerful and versatile quantum walk machines for classically intractable problems. PMID:29756040

Experimental two-dimensional quantum walk on a photonic chip.

PubMed

Tang, Hao; Lin, Xiao-Feng; Feng, Zhen; Chen, Jing-Yuan; Gao, Jun; Sun, Ke; Wang, Chao-Yue; Lai, Peng-Cheng; Xu, Xiao-Yun; Wang, Yao; Qiao, Lu-Feng; Yang, Ai-Lin; Jin, Xian-Min

2018-05-01

Quantum walks, in virtue of the coherent superposition and quantum interference, have exponential superiority over their classical counterpart in applications of quantum searching and quantum simulation. The quantum-enhanced power is highly related to the state space of quantum walks, which can be expanded by enlarging the photon number and/or the dimensions of the evolution network, but the former is considerably challenging due to probabilistic generation of single photons and multiplicative loss. We demonstrate a two-dimensional continuous-time quantum walk by using the external geometry of photonic waveguide arrays, rather than the inner degree of freedoms of photons. Using femtosecond laser direct writing, we construct a large-scale three-dimensional structure that forms a two-dimensional lattice with up to 49 × 49 nodes on a photonic chip. We demonstrate spatial two-dimensional quantum walks using heralded single photons and single photon-level imaging. We analyze the quantum transport properties via observing the ballistic evolution pattern and the variance profile, which agree well with simulation results. We further reveal the transient nature that is the unique feature for quantum walks of beyond one dimension. An architecture that allows a quantum walk to freely evolve in all directions and at a large scale, combining with defect and disorder control, may bring up powerful and versatile quantum walk machines for classically intractable problems.

Discrete-time quantum walk with nitrogen-vacancy centers in diamond coupled to a superconducting flux qubit

NASA Astrophysics Data System (ADS)

Hardal, Ali Ü. C.; Xue, Peng; Shikano, Yutaka; Müstecaplıoğlu, Özgür E.; Sanders, Barry C.

2013-08-01

We propose a quantum-electrodynamics scheme for implementing the discrete-time, coined quantum walk with the walker corresponding to the phase degree of freedom for a quasimagnon field realized in an ensemble of nitrogen-vacancy centers in diamond. The coin is realized as a superconducting flux qubit. Our scheme improves on an existing proposal for implementing quantum walks in cavity quantum electrodynamics by removing the cumbersome requirement of varying drive-pulse durations according to mean quasiparticle number. Our improvement is relevant to all indirect-coin-flip cavity quantum-electrodynamics realizations of quantum walks. Our numerical analysis shows that this scheme can realize a discrete quantum walk under realistic conditions.

Discrete spacetime, quantum walks, and relativistic wave equations

NASA Astrophysics Data System (ADS)

Mlodinow, Leonard; Brun, Todd A.

2018-04-01

It has been observed that quantum walks on regular lattices can give rise to wave equations for relativistic particles in the continuum limit. In this paper, we define the three-dimensional discrete-time walk as a product of three coined one-dimensional walks. The factor corresponding to each one-dimensional walk involves two projection operators that act on an internal coin space; each projector is associated with either the "forward" or "backward" direction in that physical dimension. We show that the simple requirement that there is no preferred axis or direction along an axis—that is, that the walk be symmetric under parity transformations and steps along different axes of the cubic lattice be uncorrelated—leads, in the case of the simplest solution, to the requirement that the continuum limit of the walk is fully Lorentz-invariant. We show further that, in the case of a massive particle, this symmetry requirement necessitates the use of a four-dimensional internal space (as in the Dirac equation). The "coin flip" operation is generated by the parity transformation on the internal coin space, while the differences of the projection operators associated with each dimension must all anticommute. Finally, we discuss the leading correction to the continuum limit, and the possibility of distinguishing through experiment between the discrete random walk and the continuum-based Dirac equation as a description of fermion dynamics.

Coined quantum walks on weighted graphs

NASA Astrophysics Data System (ADS)

Wong, Thomas G.

2017-11-01

We define a discrete-time, coined quantum walk on weighted graphs that is inspired by Szegedy’s quantum walk. Using this, we prove that many lackadaisical quantum walks, where each vertex has l integer self-loops, can be generalized to a quantum walk where each vertex has a single self-loop of real-valued weight l. We apply this real-valued lackadaisical quantum walk to two problems. First, we analyze it on the line or one-dimensional lattice, showing that it is exactly equivalent to a continuous deformation of the three-state Grover walk with faster ballistic dispersion. Second, we generalize Grover’s algorithm, or search on the complete graph, to have a weighted self-loop at each vertex, yielding an improved success probability when l < 3 + 2\\sqrt{2} ≈ 5.828 .

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xu, Xin-Ping, E-mail: xuxp@mail.ihep.ac.cn; Ide, Yusuke

In the literature, there are numerous studies of one-dimensional discrete-time quantum walks (DTQWs) using a moving shift operator. However, there is no exact solution for the limiting probability distributions of DTQWs on cycles using a general coin or swapping shift operator. In this paper, we derive exact solutions for the limiting probability distribution of quantum walks using a general coin and swapping shift operator on cycles for the first time. Based on the exact solutions, we show how to generate symmetric quantum walks and determine the condition under which a symmetric quantum walk appears. Our results suggest that choosing various coinmore » and initial state parameters can achieve a symmetric quantum walk. By defining a quantity to measure the variation of symmetry, deviation and mixing time of symmetric quantum walks are also investigated.« less

Simulation of quantum dynamics with integrated photonics

NASA Astrophysics Data System (ADS)

Sansoni, Linda; Sciarrino, Fabio; Mataloni, Paolo; Crespi, Andrea; Ramponi, Roberta; Osellame, Roberto

2012-12-01

In recent years, quantum walks have been proposed as promising resources for the simulation of physical quantum systems. In fact it is widely adopted to simulate quantum dynamics. Up to now single particle quantum walks have been experimentally demonstrated by different approaches, while only few experiments involving many-particle quantum walks have been realized. Here we simulate the 2-particle dynamics on a discrete time quantum walk, built on an array of integrated waveguide beam splitters. The polarization independence of the quantum walk circuit allowed us to exploit the polarization entanglement to encode the symmetry of the two-photon wavefunction, thus the bunching-antibunching behavior of non interacting bosons and fermions has been simulated. We have also characterized the possible distinguishability and decoherence effects arising in such a structure. This study is necessary in view of the realization of a quantum simulator based on an integrated optical array built on a large number of beam splitters.

Group velocity of discrete-time quantum walks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kempf, A.; Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1; Portugal, R.

2009-05-15

We show that certain types of quantum walks can be modeled as waves that propagate in a medium with phase and group velocities that are explicitly calculable. Since the group and phase velocities indicate how fast wave packets can propagate causally, we propose the use of these wave velocities in our definition for the hitting time of quantum walks. Our definition of hitting time has the advantage that it requires neither the specification of a walker's initial condition nor of an arrival probability threshold. We give full details for the case of quantum walks on the Cayley graphs of Abelianmore » groups. This includes the special cases of quantum walks on the line and on hypercubes.« less

Quantum snake walk on graphs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rosmanis, Ansis

2011-02-15

I introduce a continuous-time quantum walk on graphs called the quantum snake walk, the basis states of which are fixed-length paths (snakes) in the underlying graph. First, I analyze the quantum snake walk on the line, and I show that, even though most states stay localized throughout the evolution, there are specific states that most likely move on the line as wave packets with momentum inversely proportional to the length of the snake. Next, I discuss how an algorithm based on the quantum snake walk might potentially be able to solve an extended version of the glued trees problem, whichmore » asks to find a path connecting both roots of the glued trees graph. To the best of my knowledge, no efficient quantum algorithm solving this problem is known yet.« less

An uncertainty principle for unimodular quantum groups

DOE Office of Scientific and Technical Information (OSTI.GOV)

Crann, Jason; Université Lille 1 - Sciences et Technologies, UFR de Mathématiques, Laboratoire de Mathématiques Paul Painlevé - UMR CNRS 8524, 59655 Villeneuve d'Ascq Cédex; Kalantar, Mehrdad, E-mail: jason-crann@carleton.ca, E-mail: mkalanta@math.carleton.ca

2014-08-15

We present a generalization of Hirschman's entropic uncertainty principle for locally compact Abelian groups to unimodular locally compact quantum groups. As a corollary, we strengthen a well-known uncertainty principle for compact groups, and generalize the relation to compact quantum groups of Kac type. We also establish the complementarity of finite-dimensional quantum group algebras. In the non-unimodular setting, we obtain an uncertainty relation for arbitrary locally compact groups using the relative entropy with respect to the Haar weight as the measure of uncertainty. We also show that when restricted to q-traces of discrete quantum groups, the relative entropy with respect tomore » the Haar weight reduces to the canonical entropy of the random walk generated by the state.« less

Irreconcilable difference between quantum walks and adiabatic quantum computing

NASA Astrophysics Data System (ADS)

Wong, Thomas G.; Meyer, David A.

2016-06-01

Continuous-time quantum walks and adiabatic quantum evolution are two general techniques for quantum computing, both of which are described by Hamiltonians that govern their evolutions by Schrödinger's equation. In the former, the Hamiltonian is fixed, while in the latter, the Hamiltonian varies with time. As a result, their formulations of Grover's algorithm evolve differently through Hilbert space. We show that this difference is fundamental; they cannot be made to evolve along each other's path without introducing structure more powerful than the standard oracle for unstructured search. For an adiabatic quantum evolution to evolve like the quantum walk search algorithm, it must interpolate between three fixed Hamiltonians, one of which is complex and introduces structure that is stronger than the oracle for unstructured search. Conversely, for a quantum walk to evolve along the path of the adiabatic search algorithm, it must be a chiral quantum walk on a weighted, directed star graph with structure that is also stronger than the oracle for unstructured search. Thus, the two techniques, although similar in being described by Hamiltonians that govern their evolution, compute by fundamentally irreconcilable means.

Quantum walks in brain microtubules--a biomolecular basis for quantum cognition?

PubMed

Hameroff, Stuart

2014-01-01

Cognitive decisions are best described by quantum mathematics. Do quantum information devices operate in the brain? What would they look like? Fuss and Navarro () describe quantum lattice registers in which quantum superpositioned pathways interact (compute/integrate) as 'quantum walks' akin to Feynman's path integral in a lattice (e.g. the 'Feynman quantum chessboard'). Simultaneous alternate pathways eventually reduce (collapse), selecting one particular pathway in a cognitive decision, or choice. This paper describes how quantum walks in a Feynman chessboard are conceptually identical to 'topological qubits' in brain neuronal microtubules, as described in the Penrose-Hameroff 'Orch OR' theory of consciousness. Copyright © 2013 Cognitive Science Society, Inc.

pyCTQW: A continuous-time quantum walk simulator on distributed memory computers

NASA Astrophysics Data System (ADS)

Izaac, Josh A.; Wang, Jingbo B.

2015-01-01

In the general field of quantum information and computation, quantum walks are playing an increasingly important role in constructing physical models and quantum algorithms. We have recently developed a distributed memory software package pyCTQW, with an object-oriented Python interface, that allows efficient simulation of large multi-particle CTQW (continuous-time quantum walk)-based systems. In this paper, we present an introduction to the Python and Fortran interfaces of pyCTQW, discuss various numerical methods of calculating the matrix exponential, and demonstrate the performance behavior of pyCTQW on a distributed memory cluster. In particular, the Chebyshev and Krylov-subspace methods for calculating the quantum walk propagation are provided, as well as methods for visualization and data analysis.

Path-sum solution of the Weyl quantum walk in 3 + 1 dimensions

NASA Astrophysics Data System (ADS)

D'Ariano, G. M.; Mosco, N.; Perinotti, P.; Tosini, A.

2017-10-01

We consider the Weyl quantum walk in 3+1 dimensions, that is a discrete-time walk describing a particle with two internal degrees of freedom moving on a Cayley graph of the group , which in an appropriate regime evolves according to Weyl's equation. The Weyl quantum walk was recently derived as the unique unitary evolution on a Cayley graph of that is homogeneous and isotropic. The general solution of the quantum walk evolution is provided here in the position representation, by the analytical expression of the propagator, i.e. transition amplitude from a node of the graph to another node in a finite number of steps. The quantum nature of the walk manifests itself in the interference of the paths on the graph joining the given nodes. The solution is based on the binary encoding of the admissible paths on the graph and on the semigroup structure of the walk transition matrices. This article is part of the themed issue `Second quantum revolution: foundational questions'.

Quantum walks and wavepacket dynamics on a lattice with twisted photons.

PubMed

Cardano, Filippo; Massa, Francesco; Qassim, Hammam; Karimi, Ebrahim; Slussarenko, Sergei; Paparo, Domenico; de Lisio, Corrado; Sciarrino, Fabio; Santamato, Enrico; Boyd, Robert W; Marrucci, Lorenzo

2015-03-01

The "quantum walk" has emerged recently as a paradigmatic process for the dynamic simulation of complex quantum systems, entanglement production and quantum computation. Hitherto, photonic implementations of quantum walks have mainly been based on multipath interferometric schemes in real space. We report the experimental realization of a discrete quantum walk taking place in the orbital angular momentum space of light, both for a single photon and for two simultaneous photons. In contrast to previous implementations, the whole process develops in a single light beam, with no need of interferometers; it requires optical resources scaling linearly with the number of steps; and it allows flexible control of input and output superposition states. Exploiting the latter property, we explored the system band structure in momentum space and the associated spin-orbit topological features by simulating the quantum dynamics of Gaussian wavepackets. Our demonstration introduces a novel versatile photonic platform for quantum simulations.

Quantum walks with an anisotropic coin I: spectral theory

NASA Astrophysics Data System (ADS)

Richard, S.; Suzuki, A.; Tiedra de Aldecoa, R.

2018-02-01

We perform the spectral analysis of the evolution operator U of quantum walks with an anisotropic coin, which include one-defect models, two-phase quantum walks, and topological phase quantum walks as special cases. In particular, we determine the essential spectrum of U, we show the existence of locally U-smooth operators, we prove the discreteness of the eigenvalues of U outside the thresholds, and we prove the absence of singular continuous spectrum for U. Our analysis is based on new commutator methods for unitary operators in a two-Hilbert spaces setting, which are of independent interest.

Optimal Quantum Spatial Search on Random Temporal Networks

NASA Astrophysics Data System (ADS)

Chakraborty, Shantanav; Novo, Leonardo; Di Giorgio, Serena; Omar, Yasser

2017-12-01

To investigate the performance of quantum information tasks on networks whose topology changes in time, we study the spatial search algorithm by continuous time quantum walk to find a marked node on a random temporal network. We consider a network of n nodes constituted by a time-ordered sequence of Erdös-Rényi random graphs G (n ,p ), where p is the probability that any two given nodes are connected: After every time interval τ , a new graph G (n ,p ) replaces the previous one. We prove analytically that, for any given p , there is always a range of values of τ for which the running time of the algorithm is optimal, i.e., O (√{n }), even when search on the individual static graphs constituting the temporal network is suboptimal. On the other hand, there are regimes of τ where the algorithm is suboptimal even when each of the underlying static graphs are sufficiently connected to perform optimal search on them. From this first study of quantum spatial search on a time-dependent network, it emerges that the nontrivial interplay between temporality and connectivity is key to the algorithmic performance. Moreover, our work can be extended to establish high-fidelity qubit transfer between any two nodes of the network. Overall, our findings show that one can exploit temporality to achieve optimal quantum information tasks on dynamical random networks.

Quantum simulation of a quantum stochastic walk

NASA Astrophysics Data System (ADS)

Govia, Luke C. G.; Taketani, Bruno G.; Schuhmacher, Peter K.; Wilhelm, Frank K.

2017-03-01

The study of quantum walks has been shown to have a wide range of applications in areas such as artificial intelligence, the study of biological processes, and quantum transport. The quantum stochastic walk (QSW), which allows for incoherent movement of the walker, and therefore, directionality, is a generalization on the fully coherent quantum walk. While a QSW can always be described in Lindblad formalism, this does not mean that it can be microscopically derived in the standard weak-coupling limit under the Born-Markov approximation. This restricts the class of QSWs that can be experimentally realized in a simple manner. To circumvent this restriction, we introduce a technique to simulate open system evolution on a fully coherent quantum computer, using a quantum trajectories style approach. We apply this technique to a broad class of QSWs, and show that they can be simulated with minimal experimental resources. Our work opens the path towards the experimental realization of QSWs on large graphs with existing quantum technologies.

Quantum logic using correlated one-dimensional quantum walks

NASA Astrophysics Data System (ADS)

Lahini, Yoav; Steinbrecher, Gregory R.; Bookatz, Adam D.; Englund, Dirk

2018-01-01

Quantum Walks are unitary processes describing the evolution of an initially localized wavefunction on a lattice potential. The complexity of the dynamics increases significantly when several indistinguishable quantum walkers propagate on the same lattice simultaneously, as these develop non-trivial spatial correlations that depend on the particle's quantum statistics, mutual interactions, initial positions, and the lattice potential. We show that even in the simplest case of a quantum walk on a one dimensional graph, these correlations can be shaped to yield a complete set of compact quantum logic operations. We provide detailed recipes for implementing quantum logic on one-dimensional quantum walks in two general cases. For non-interacting bosons—such as photons in waveguide lattices—we find high-fidelity probabilistic quantum gates that could be integrated into linear optics quantum computation schemes. For interacting quantum-walkers on a one-dimensional lattice—a situation that has recently been demonstrated using ultra-cold atoms—we find deterministic logic operations that are universal for quantum information processing. The suggested implementation requires minimal resources and a level of control that is within reach using recently demonstrated techniques. Further work is required to address error-correction.

Measuring graph similarity through continuous-time quantum walks and the quantum Jensen-Shannon divergence.

PubMed

Rossi, Luca; Torsello, Andrea; Hancock, Edwin R

2015-02-01

In this paper we propose a quantum algorithm to measure the similarity between a pair of unattributed graphs. We design an experiment where the two graphs are merged by establishing a complete set of connections between their nodes and the resulting structure is probed through the evolution of continuous-time quantum walks. In order to analyze the behavior of the walks without causing wave function collapse, we base our analysis on the recently introduced quantum Jensen-Shannon divergence. In particular, we show that the divergence between the evolution of two suitably initialized quantum walks over this structure is maximum when the original pair of graphs is isomorphic. We also prove that under special conditions the divergence is minimum when the sets of eigenvalues of the Hamiltonians associated with the two original graphs have an empty intersection.

Freezing Coherent Field Growth in a Cavity by the Quantum Zeno Effect

NASA Astrophysics Data System (ADS)

Bernu, J.; Deléglise, S.; Sayrin, C.; Kuhr, S.; Dotsenko, I.; Brune, M.; Raimond, J. M.; Haroche, S.

2008-10-01

We have frozen the coherent evolution of a field in a cavity by repeated measurements of its photon number. We use circular Rydberg atoms dispersively coupled to the cavity mode for an absorption-free photon counting. These measurements inhibit the growth of a field injected in the cavity by a classical source. This manifestation of the quantum Zeno effect illustrates the backaction of the photon number determination onto the field phase. The residual growth of the field can be seen as a random walk of its amplitude in the two-dimensional phase space. This experiment sheds light onto the measurement process and opens perspectives for active quantum feedback.

On-chip generation of Einstein-Podolsky-Rosen states with arbitrary symmetry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gräfe, Markus; Heilmann, René; Nolte, Stefan

We experimentally demonstrate a method for integrated-optical generation of two-photon Einstein-Podolsky-Rosen states featuring arbitrary symmetries. In our setting, we employ detuned directional couplers to impose a freely tailorable phase between the two modes of the state. Our results allow to mimic the quantum random walk statistics of bosons, fermions, and anyons, particles with fractional exchange statistics.

Observation of quasiperiodic dynamics in a one-dimensional quantum walk of single photons in space

NASA Astrophysics Data System (ADS)

Xue, Peng; Qin, Hao; Tang, Bao; Sanders, Barry C.

2014-05-01

We realize the quasi-periodic dynamics of a quantum walker over 2.5 quasi-periods by realizing the walker as a single photon passing through a quantum-walk optical-interferometer network. We introduce fully controllable polarization-independent phase shifters in each optical path to realize arbitrary site-dependent phase shifts, and employ large clear-aperture beam displacers, while maintaining high-visibility interference, to enable 10 quantum-walk steps to be reached. By varying the half-wave-plate setting, we control the quantum-coin bias thereby observing a transition from quasi-periodic dynamics to ballistic diffusion.

Generation of Nonclassical Biphoton States through Cascaded Quantum Walks on a Nonlinear Chip

NASA Astrophysics Data System (ADS)

Solntsev, Alexander S.; Setzpfandt, Frank; Clark, Alex S.; Wu, Che Wen; Collins, Matthew J.; Xiong, Chunle; Schreiber, Andreas; Katzschmann, Fabian; Eilenberger, Falk; Schiek, Roland; Sohler, Wolfgang; Mitchell, Arnan; Silberhorn, Christine; Eggleton, Benjamin J.; Pertsch, Thomas; Sukhorukov, Andrey A.; Neshev, Dragomir N.; Kivshar, Yuri S.

2014-07-01

We demonstrate a nonlinear optical chip that generates photons with reconfigurable nonclassical spatial correlations. We employ a quadratic nonlinear waveguide array, where photon pairs are generated through spontaneous parametric down-conversion and simultaneously spread through quantum walks between the waveguides. Because of the quantum interference of these cascaded quantum walks, the emerging photons can become entangled over multiple waveguide positions. We experimentally observe highly nonclassical photon-pair correlations, confirming the high fidelity of on-chip quantum interference. Furthermore, we demonstrate biphoton-state tunability by spatial shaping and frequency tuning of the classical pump beam.

One-Dimensional Quantum Walks with One Defect

NASA Astrophysics Data System (ADS)

Cantero, M. J.; Grünbaum, F. A.; Moral, L.; Velázquez, L.

The CGMV method allows for the general discussion of localization properties for the states of a one-dimensional quantum walk, both in the case of the integers and in the case of the nonnegative integers. Using this method we classify, according to such localization properties, all the quantum walks with one defect at the origin, providing explicit expressions for the asymptotic return probabilities to the origin.

Möbius quantum walk

NASA Astrophysics Data System (ADS)

Moradi, Majid; Annabestani, Mostafa

2017-12-01

By adding an extra Hilbert space to the Hadamard quantum walk on cycle (QWC), we present a new type of QWC, the Möbius quantum walk (MQW). The new space configuration enables the particle to rotate around the axis of movement. We define the factor α as the Möbius factor, which is the number of rotations per cycle. So, by α=0 we have a normal QWC, while α \

The rate constant of a quantum-diffusion-controlled bimolecular reaction

NASA Astrophysics Data System (ADS)

Bondarev, B. V.

1986-04-01

A quantum-mechanical equation is derived in the tight-bond approximation which describes the motion and chemical interaction of a pair of species A and B when their displacement in the matrix is caused by tunnelling. Within the framework of the discrete model of random walks, definitions are given of the probability and rate constant of a reaction A + B → P (products) proceeding in a condensed medium. A method is suggested for calculating the rate constant of a quantum-diffusion-controlled bimolecular reaction. By this method, an expression is obtained for the rate constant in the stationary spherically symmetrical case. An equation for the density matrix is also proposed which describes the motion and chemical interaction of a pair of species when the quantum and classical diffusion are competitive.

History dependent quantum walk on the cycle with an unbalanced coin

NASA Astrophysics Data System (ADS)

Krawec, Walter O.

2015-06-01

Recently, a new model of quantum walk, utilizing recycled coins, was introduced; however little is yet known about its properties. In this paper, we study its behavior on the cycle graph. In particular, we will consider its time averaged distribution and how it is affected by the walk's "memory parameter"-a real parameter, between zero and eight, which affects the walk's coin flip operator. Despite an infinite number of different parameters, our analysis provides evidence that only a few produce non-uniform behavior. Our analysis also shows that the initial state, and cycle size modulo four all affect the behavior of this walk. We also prove an interesting relationship between the recycled coin model and a different memory-based quantum walk recently proposed.

Experimental Quantum-Walk Revival with a Time-Dependent Coin

NASA Astrophysics Data System (ADS)

Xue, P.; Zhang, R.; Qin, H.; Zhan, X.; Bian, Z. H.; Li, J.; Sanders, Barry C.

2015-04-01

We demonstrate a quantum walk with time-dependent coin bias. With this technique we realize an experimental single-photon one-dimensional quantum walk with a linearly ramped time-dependent coin flip operation and thereby demonstrate two periodic revivals of the walker distribution. In our beam-displacer interferometer, the walk corresponds to movement between discretely separated transverse modes of the field serving as lattice sites, and the time-dependent coin flip is effected by implementing a different angle between the optical axis of half-wave plate and the light propagation at each step. Each of the quantum-walk steps required to realize a revival comprises two sequential orthogonal coin-flip operators, with one coin having constant bias and the other coin having a time-dependent ramped coin bias, followed by a conditional translation of the walker.

Parrondo's game using a discrete-time quantum walk

NASA Astrophysics Data System (ADS)

Chandrashekar, C. M.; Banerjee, Subhashish

2011-04-01

We present a new form of a Parrondo game using discrete-time quantum walk on a line. The two players A and B with different quantum coins operators, individually losing the game can develop a strategy to emerge as joint winners by using their coins alternatively, or in combination for each step of the quantum walk evolution. We also present a strategy for a player A ( B) to have a winning probability more than player B ( A). Significance of the game strategy in information theory and physical applications are also discussed.

Discrete-Time Quantum Walk with Phase Disorder: Localization and Entanglement Entropy.

PubMed

Zeng, Meng; Yong, Ee Hou

2017-09-20

Quantum Walk (QW) has very different transport properties to its classical counterpart due to interference effects. Here we study the discrete-time quantum walk (DTQW) with on-site static/dynamic phase disorder following either binary or uniform distribution in both one and two dimensions. For one dimension, we consider the Hadamard coin; for two dimensions, we consider either a 2-level Hadamard coin (Hadamard walk) or a 4-level Grover coin (Grover walk) for the rotation in coin-space. We study the transport properties e.g. inverse participation ratio (IPR) and the standard deviation of the density function (σ) as well as the coin-position entanglement entropy (EE), due to the two types of phase disorders and the two types of coins. Our numerical simulations show that the dimensionality, the type of coins, and whether the disorder is static or dynamic play a pivotal role and lead to interesting behaviors of the DTQW. The distribution of the phase disorder has very minor effects on the quantum walk.

Mixing times in quantum walks on two-dimensional grids

DOE Office of Scientific and Technical Information (OSTI.GOV)

Marquezino, F. L.; Portugal, R.; Abal, G.

2010-10-15

Mixing properties of discrete-time quantum walks on two-dimensional grids with toruslike boundary conditions are analyzed, focusing on their connection to the complexity of the corresponding abstract search algorithm. In particular, an exact expression for the stationary distribution of the coherent walk over odd-sided lattices is obtained after solving the eigenproblem for the evolution operator for this particular graph. The limiting distribution and mixing time of a quantum walk with a coin operator modified as in the abstract search algorithm are obtained numerically. On the basis of these results, the relation between the mixing time of the modified walk and themore » running time of the corresponding abstract search algorithm is discussed.« less

Mixing times in quantum walks on two-dimensional grids

NASA Astrophysics Data System (ADS)

Marquezino, F. L.; Portugal, R.; Abal, G.

2010-10-01

Mixing properties of discrete-time quantum walks on two-dimensional grids with toruslike boundary conditions are analyzed, focusing on their connection to the complexity of the corresponding abstract search algorithm. In particular, an exact expression for the stationary distribution of the coherent walk over odd-sided lattices is obtained after solving the eigenproblem for the evolution operator for this particular graph. The limiting distribution and mixing time of a quantum walk with a coin operator modified as in the abstract search algorithm are obtained numerically. On the basis of these results, the relation between the mixing time of the modified walk and the running time of the corresponding abstract search algorithm is discussed.

Improving the efficiency of quantum hash function by dense coding of coin operators in discrete-time quantum walk

NASA Astrophysics Data System (ADS)

Yang, YuGuang; Zhang, YuChen; Xu, Gang; Chen, XiuBo; Zhou, Yi-Hua; Shi, WeiMin

2018-03-01

Li et al. first proposed a quantum hash function (QHF) in a quantum-walk architecture. In their scheme, two two-particle interactions, i.e., I interaction and π-phase interaction are introduced and the choice of I or π-phase interactions at each iteration depends on a message bit. In this paper, we propose an efficient QHF by dense coding of coin operators in discrete-time quantum walk. Compared with existing QHFs, our protocol has the following advantages: the efficiency of the QHF can be doubled and even more; only one particle is enough and two-particle interactions are unnecessary so that quantum resources are saved. It is a clue to apply the dense coding technique to quantum cryptographic protocols, especially to the applications with restricted quantum resources.

Quantum Markov chains

NASA Astrophysics Data System (ADS)

Gudder, Stanley

2008-07-01

A new approach to quantum Markov chains is presented. We first define a transition operation matrix (TOM) as a matrix whose entries are completely positive maps whose column sums form a quantum operation. A quantum Markov chain is defined to be a pair (G,E) where G is a directed graph and E =[Eij] is a TOM whose entry Eij labels the edge from vertex j to vertex i. We think of the vertices of G as sites that a quantum system can occupy and Eij is the transition operation from site j to site i in one time step. The discrete dynamics of the system is obtained by iterating the TOM E. We next consider a special type of TOM called a transition effect matrix. In this case, there are two types of dynamics, a state dynamics and an operator dynamics. Although these two types are not identical, they are statistically equivalent. We next give examples that illustrate various properties of quantum Markov chains. We conclude by showing that our formalism generalizes the usual framework for quantum random walks.

Two-walker discrete-time quantum walks on the line with percolation

NASA Astrophysics Data System (ADS)

Rigovacca, L.; di Franco, C.

2016-02-01

One goal in the quantum-walk research is the exploitation of the intrinsic quantum nature of multiple walkers, in order to achieve the full computational power of the model. Here we study the behaviour of two non-interacting particles performing a quantum walk on the line when the possibility of lattice imperfections, in the form of missing links, is considered. We investigate two regimes, statical and dynamical percolation, that correspond to different time scales for the imperfections evolution with respect to the quantum-walk one. By studying the qualitative behaviour of three two-particle quantities for different probabilities of having missing bonds, we argue that the chosen symmetry under particle-exchange of the input state strongly affects the output of the walk, even in noisy and highly non-ideal regimes. We provide evidence against the possibility of gathering information about the walkers indistinguishability from the observation of bunching phenomena in the output distribution, in all those situations that require a comparison between averaged quantities. Although the spread of the walk is not substantially changed by the addition of a second particle, we show that the presence of multiple walkers can be beneficial for a procedure to estimate the probability of having a broken link.

Isotropic quantum walks on lattices and the Weyl equation

NASA Astrophysics Data System (ADS)

D'Ariano, Giacomo Mauro; Erba, Marco; Perinotti, Paolo

2017-12-01

We present a thorough classification of the isotropic quantum walks on lattices of dimension d =1 ,2 ,3 with a coin system of dimension s =2 . For d =3 there exist two isotropic walks, namely, the Weyl quantum walks presented in the work of D'Ariano and Perinotti [G. M. D'Ariano and P. Perinotti, Phys. Rev. A 90, 062106 (2014), 10.1103/PhysRevA.90.062106], resulting in the derivation of the Weyl equation from informational principles. The present analysis, via a crucial use of isotropy, is significantly shorter and avoids a superfluous technical assumption, making the result completely general.

Quantum walks and wavepacket dynamics on a lattice with twisted photons

PubMed Central

Cardano, Filippo; Massa, Francesco; Qassim, Hammam; Karimi, Ebrahim; Slussarenko, Sergei; Paparo, Domenico; de Lisio, Corrado; Sciarrino, Fabio; Santamato, Enrico; Boyd, Robert W.; Marrucci, Lorenzo

2015-01-01

The “quantum walk” has emerged recently as a paradigmatic process for the dynamic simulation of complex quantum systems, entanglement production and quantum computation. Hitherto, photonic implementations of quantum walks have mainly been based on multipath interferometric schemes in real space. We report the experimental realization of a discrete quantum walk taking place in the orbital angular momentum space of light, both for a single photon and for two simultaneous photons. In contrast to previous implementations, the whole process develops in a single light beam, with no need of interferometers; it requires optical resources scaling linearly with the number of steps; and it allows flexible control of input and output superposition states. Exploiting the latter property, we explored the system band structure in momentum space and the associated spin-orbit topological features by simulating the quantum dynamics of Gaussian wavepackets. Our demonstration introduces a novel versatile photonic platform for quantum simulations. PMID:26601157

Two-photon quantum walk in a multimode fiber

PubMed Central

Defienne, Hugo; Barbieri, Marco; Walmsley, Ian A.; Smith, Brian J.; Gigan, Sylvain

2016-01-01

Multiphoton propagation in connected structures—a quantum walk—offers the potential of simulating complex physical systems and provides a route to universal quantum computation. Increasing the complexity of quantum photonic networks where the walk occurs is essential for many applications. We implement a quantum walk of indistinguishable photon pairs in a multimode fiber supporting 380 modes. Using wavefront shaping, we control the propagation of the two-photon state through the fiber in which all modes are coupled. Excitation of arbitrary output modes of the system is realized by controlling classical and quantum interferences. This report demonstrates a highly multimode platform for multiphoton interference experiments and provides a powerful method to program a general high-dimensional multiport optical circuit. This work paves the way for the next generation of photonic devices for quantum simulation, computing, and communication. PMID:27152325

Parametric Quantum Search Algorithm as Quantum Walk: A Quantum Simulation

NASA Astrophysics Data System (ADS)

Ellinas, Demosthenes; Konstandakis, Christos

2016-02-01

Parametric quantum search algorithm (PQSA) is a form of quantum search that results by relaxing the unitarity of the original algorithm. PQSA can naturally be cast in the form of quantum walk, by means of the formalism of oracle algebra. This is due to the fact that the completely positive trace preserving search map used by PQSA, admits a unitarization (unitary dilation) a la quantum walk, at the expense of introducing auxiliary quantum coin-qubit space. The ensuing QW describes a process of spiral motion, chosen to be driven by two unitary Kraus generators, generating planar rotations of Bloch vector around an axis. The quadratic acceleration of quantum search translates into an equivalent quadratic saving of the number of coin qubits in the QW analogue. The associated to QW model Hamiltonian operator is obtained and is shown to represent a multi-particle long-range interacting quantum system that simulates parametric search. Finally, the relation of PQSA-QW simulator to the QW search algorithm is elucidated.

Fractional quantum mechanics on networks: Long-range dynamics and quantum transport

NASA Astrophysics Data System (ADS)

Riascos, A. P.; Mateos, José L.

2015-11-01

In this paper we study the quantum transport on networks with a temporal evolution governed by the fractional Schrödinger equation. We generalize the dynamics based on continuous-time quantum walks, with transitions to nearest neighbors on the network, to the fractional case that allows long-range displacements. By using the fractional Laplacian matrix of a network, we establish a formalism that combines a long-range dynamics with the quantum superposition of states; this general approach applies to any type of connected undirected networks, including regular, random, and complex networks, and can be implemented from the spectral properties of the Laplacian matrix. We study the fractional dynamics and its capacity to explore the network by means of the transition probability, the average probability of return, and global quantities that characterize the efficiency of this quantum process. As a particular case, we explore analytically these quantities for circulant networks such as rings, interacting cycles, and complete graphs.

Fractional quantum mechanics on networks: Long-range dynamics and quantum transport.

PubMed

Riascos, A P; Mateos, José L

2015-11-01

In this paper we study the quantum transport on networks with a temporal evolution governed by the fractional Schrödinger equation. We generalize the dynamics based on continuous-time quantum walks, with transitions to nearest neighbors on the network, to the fractional case that allows long-range displacements. By using the fractional Laplacian matrix of a network, we establish a formalism that combines a long-range dynamics with the quantum superposition of states; this general approach applies to any type of connected undirected networks, including regular, random, and complex networks, and can be implemented from the spectral properties of the Laplacian matrix. We study the fractional dynamics and its capacity to explore the network by means of the transition probability, the average probability of return, and global quantities that characterize the efficiency of this quantum process. As a particular case, we explore analytically these quantities for circulant networks such as rings, interacting cycles, and complete graphs.

A Rout to Protect Quantum Gates constructed via quantum walks from Noises.

PubMed

Du, Yi-Mu; Lu, Li-Hua; Li, You-Quan

2018-05-08

The continuous-time quantum walk on a one-dimensional graph of odd number of sites with an on-site potential at the center is studied. We show that such a quantum-walk system can construct an X-gate of a single qubit as well as a control gate for two qubits, when the potential is much larger than the hopping strength. We investigate the decoherence effect and find that the coherence time can be enhanced by either increasing the number of sites on the graph or the ratio of the potential to the hopping strength, which is expected to motivate the design of the quantum gate with long coherence time. We also suggest several experimental proposals to realize such a system.

Repelling, binding, and oscillating of two-particle discrete-time quantum walks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Qinghao; Li, Zhi-Jian, E-mail: zjli@sxu.edu.cn

In this paper, we investigate the effects of particle–particle interaction and static force on the propagation of probability distribution in two-particle discrete-time quantum walk, where the interaction and static force are expressed as a collision phase and a linear position-dependent phase, respectively. It is found that the interaction can lead to boson repelling and fermion binding. The static force also induces Bloch oscillation and results in a continuous transition from boson bunching to fermion anti-bunching. The interplays of particle–particle interaction, quantum interference, and Bloch oscillation provide a versatile framework to study and simulate many-particle physics via quantum walks.

Quantum search algorithms on a regular lattice

NASA Astrophysics Data System (ADS)

Hein, Birgit; Tanner, Gregor

2010-07-01

Quantum algorithms for searching for one or more marked items on a d-dimensional lattice provide an extension of Grover’s search algorithm including a spatial component. We demonstrate that these lattice search algorithms can be viewed in terms of the level dynamics near an avoided crossing of a one-parameter family of quantum random walks. We give approximations for both the level splitting at the avoided crossing and the effectively two-dimensional subspace of the full Hilbert space spanning the level crossing. This makes it possible to give the leading order behavior for the search time and the localization probability in the limit of large lattice size including the leading order coefficients. For d=2 and d=3, these coefficients are calculated explicitly. Closed form expressions are given for higher dimensions.

Quantum-enhanced deliberation of learning agents using trapped ions

NASA Astrophysics Data System (ADS)

Dunjko, V.; Friis, N.; Briegel, H. J.

2015-02-01

A scheme that successfully employs quantum mechanics in the design of autonomous learning agents has recently been reported in the context of the projective simulation (PS) model for artificial intelligence. In that approach, the key feature of a PS agent, a specific type of memory which is explored via random walks, was shown to be amenable to quantization, allowing for a speed-up. In this work we propose an implementation of such classical and quantum agents in systems of trapped ions. We employ a generic construction by which the classical agents are ‘upgraded’ to their quantum counterparts by a nested process of adding coherent control, and we outline how this construction can be realized in ion traps. Our results provide a flexible modular architecture for the design of PS agents. Furthermore, we present numerical simulations of simple PS agents which analyze the robustness of our proposal under certain noise models.

Weak limit of the three-state quantum walk on the line

NASA Astrophysics Data System (ADS)

Falkner, Stefan; Boettcher, Stefan

2014-07-01

We revisit the one-dimensional discrete time quantum walk with three states and the Grover coin, the simplest model that exhibits localization in a quantum walk. We derive analytic expressions for the localization and a long-time approximation for the entire probability density function (PDF). We find the possibility for asymmetric localization to the extreme that it vanishes completely on one site of the initial conditions. We also connect the time-averaged approximation of the PDF found by Inui et al. [Phys. Rev. E 72, 056112 (2005), 10.1103/PhysRevE.72.056112] to a spatial average of the walk. We show that this smoothed approximation predicts moments of the real PDF accurately.

Random walks and diffusion on networks

NASA Astrophysics Data System (ADS)

Masuda, Naoki; Porter, Mason A.; Lambiotte, Renaud

2017-11-01

Random walks are ubiquitous in the sciences, and they are interesting from both theoretical and practical perspectives. They are one of the most fundamental types of stochastic processes; can be used to model numerous phenomena, including diffusion, interactions, and opinions among humans and animals; and can be used to extract information about important entities or dense groups of entities in a network. Random walks have been studied for many decades on both regular lattices and (especially in the last couple of decades) on networks with a variety of structures. In the present article, we survey the theory and applications of random walks on networks, restricting ourselves to simple cases of single and non-adaptive random walkers. We distinguish three main types of random walks: discrete-time random walks, node-centric continuous-time random walks, and edge-centric continuous-time random walks. We first briefly survey random walks on a line, and then we consider random walks on various types of networks. We extensively discuss applications of random walks, including ranking of nodes (e.g., PageRank), community detection, respondent-driven sampling, and opinion models such as voter models.

Quantum Dynamics of Helium Clusters

DTIC Science & Technology

1993-03-01

the structure of both these and the HeN clusters in the body fixed frame by computing principal moments of inertia, thereby avoiding the...8217 of helium clusters, with the modification that we subtract 0.96 K from the computed values so that lor sufficiently large clusters we recover the...phonon spectrum of liquid He. To get a picture of these spectra one needs to compute the structure functions 51. Monte Carlo random walk simulations

Coin state properties in quantum walks

PubMed Central

Andrade, R. F. S.

2013-01-01

Recent experimental advances have measured individual coin components in discrete time quantum walks, which have not received the due attention in most theoretical studies on the theme. Here is presented a detailed investigation of the properties of M, the difference between square modulus of coin states of discrete quantum walks on a linear chain. Local expectation values are obtained in terms of real and imaginary parts of the Fourier transformed wave function. A simple expression is found for the average difference between coin states in terms of an angle θ gauging the coin operator and its initial state. These results are corroborated by numerical integration of dynamical equations in real space. The local dependence is characterized both by large and short period modulations. The richness of revealed patterns suggests that the amount of information stored and retrieved from quantum walks is significantly enhanced if M is taken into account. PMID:23756358

Statistical model of exotic rotational correlations in emergent space-time

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hogan, Craig; Kwon, Ohkyung; Richardson, Jonathan

2017-06-06

A statistical model is formulated to compute exotic rotational correlations that arise as inertial frames and causal structure emerge on large scales from entangled Planck scale quantum systems. Noncommutative quantum dynamics are represented by random transverse displacements that respect causal symmetry. Entanglement is represented by covariance of these displacements in Planck scale intervals defined by future null cones of events on an observer's world line. Light that propagates in a nonradial direction inherits a projected component of the exotic rotational correlation that accumulates as a random walk in phase. A calculation of the projection and accumulation leads to exact predictionsmore » for statistical properties of exotic Planck scale correlations in an interferometer of any configuration. The cross-covariance for two nearly co-located interferometers is shown to depart only slightly from the autocovariance. Specific examples are computed for configurations that approximate realistic experiments, and show that the model can be rigorously tested.« less

Deterministic realization of collective measurements via photonic quantum walks.

PubMed

Hou, Zhibo; Tang, Jun-Feng; Shang, Jiangwei; Zhu, Huangjun; Li, Jian; Yuan, Yuan; Wu, Kang-Da; Xiang, Guo-Yong; Li, Chuan-Feng; Guo, Guang-Can

2018-04-12

Collective measurements on identically prepared quantum systems can extract more information than local measurements, thereby enhancing information-processing efficiency. Although this nonclassical phenomenon has been known for two decades, it has remained a challenging task to demonstrate the advantage of collective measurements in experiments. Here, we introduce a general recipe for performing deterministic collective measurements on two identically prepared qubits based on quantum walks. Using photonic quantum walks, we realize experimentally an optimized collective measurement with fidelity 0.9946 without post selection. As an application, we achieve the highest tomographic efficiency in qubit state tomography to date. Our work offers an effective recipe for beating the precision limit of local measurements in quantum state tomography and metrology. In addition, our study opens an avenue for harvesting the power of collective measurements in quantum information-processing and for exploring the intriguing physics behind this power.

Zeno subspace in quantum-walk dynamics

NASA Astrophysics Data System (ADS)

Chandrashekar, C. M.

2010-11-01

We investigate discrete-time quantum-walk evolution under the influence of periodic measurements in position subspace. The undisturbed survival probability of the particle at the position subspace P(0,t) is compared with the survival probability after frequent (n) measurements at interval τ=t/n, P(0,τ)n. We show that P(0,τ)n>P(0,t) leads to the quantum Zeno effect in position subspace when a parameter θ in the quantum coin operations and frequency of measurements is greater than the critical value, θ>θc and n>nc. This Zeno effect in the subspace preserves the dynamics in coin Hilbert space of the walk dynamics and has the potential to play a significant role in quantum tasks such as preserving the quantum state of the particle at any particular position, and to understand the Zeno dynamics in a multidimensional system that is highly transient in nature.

How measurement reversal could erroneously suggest the capability to discriminate the preparation basis of a quantum ensemble

NASA Astrophysics Data System (ADS)

Goyal, Sandeep K.; Singh, Rajeev; Ghosh, Sibasish

2016-01-01

Mixed states of a quantum system, represented by density operators, can be decomposed as a statistical mixture of pure states in a number of ways where each decomposition can be viewed as a different preparation recipe. However the fact that the density matrix contains full information about the ensemble makes it impossible to estimate the preparation basis for the quantum system. Here we present a measurement scheme to (seemingly) improve the performance of unsharp measurements. We argue that in some situations this scheme is capable of providing statistics from a single copy of the quantum system, thus making it possible to perform state tomography from a single copy. One of the by-products of the scheme is a way to distinguish between different preparation methods used to prepare the state of the quantum system. However, our numerical simulations disagree with our intuitive predictions. We show that a counterintuitive property of a biased classical random walk is responsible for the proposed mechanism not working.

Quantum transport with long-range steps on Watts-Strogatz networks

NASA Astrophysics Data System (ADS)

Wang, Yan; Xu, Xin-Jian

2016-07-01

We study transport dynamics of quantum systems with long-range steps on the Watts-Strogatz network (WSN) which is generated by rewiring links of the regular ring. First, we probe physical systems modeled by the discrete nonlinear schrödinger (DNLS) equation. Using the localized initial condition, we compute the time-averaged occupation probability of the initial site, which is related to the nonlinearity, the long-range steps and rewiring links. Self-trapping transitions occur at large (small) nonlinear parameters for coupling ɛ=-1 (1), as long-range interactions are intensified. The structure disorder induced by random rewiring, however, has dual effects for ɛ=-1 and inhibits the self-trapping behavior for ɛ=1. Second, we investigate continuous-time quantum walks (CTQW) on the regular ring ruled by the discrete linear schrödinger (DLS) equation. It is found that only the presence of the long-range steps does not affect the efficiency of the coherent exciton transport, while only the allowance of random rewiring enhances the partial localization. If both factors are considered simultaneously, localization is greatly strengthened, and the transport becomes worse.

Quantum walks of correlated photon pairs in two-dimensional waveguide arrays.

PubMed

Poulios, Konstantinos; Keil, Robert; Fry, Daniel; Meinecke, Jasmin D A; Matthews, Jonathan C F; Politi, Alberto; Lobino, Mirko; Gräfe, Markus; Heinrich, Matthias; Nolte, Stefan; Szameit, Alexander; O'Brien, Jeremy L

2014-04-11

We demonstrate quantum walks of correlated photons in a two-dimensional network of directly laser written waveguides coupled in a "swiss cross" arrangement. The correlated detection events show high-visibility quantum interference and unique composite behavior: strong correlation and independence of the quantum walkers, between and within the planes of the cross. Violations of a classically defined inequality, for photons injected in the same plane and in orthogonal planes, reveal nonclassical behavior in a nonplanar structure.

Evaluation of parameters for particles acceleration by the zero-point field of quantum electrodynamics

NASA Technical Reports Server (NTRS)

Rueda, A.

1985-01-01

That particles may be accelerated by vacuum effects in quantum field theory has been repeatedly proposed in the last few years. A natural upshot of this is a mechanism for cosmic rays (CR) primaries acceleration. A mechanism for acceleration by the zero-point field (ZPE) when the ZPE is taken in a realistic sense (in opposition to a virtual field) was considered. Originally the idea was developed within a semiclassical context. The classical Einstein-Hopf model (EHM) was used to show that free isolated electromagnrtically interacting particles performed a random walk in phase space and more importantly in momentum space when submitted to the perennial action of the so called classical electromagnrtic ZPE.

Area law violations and quantum phase transitions in modified Motzkin walk spin chains

NASA Astrophysics Data System (ADS)

Sugino, Fumihiko; Padmanabhan, Pramod

2018-01-01

Area law violations for entanglement entropy in the form of a square root have recently been studied for one-dimensional frustration-free quantum systems based on the Motzkin walks and their variations. Here we consider a Motzkin walk with a different Hilbert space on each step of the walk spanned by the elements of a symmetric inverse semigroup with the direction of each step governed by its algebraic structure. This change alters the number of paths allowed in the Motzkin walk and introduces a ground state degeneracy that is sensitive to boundary perturbations. We study the frustration-free spin chains based on three symmetric inverse semigroups, \

Quantum-like Viewpoint on the Complexity and Randomness of the Financial Market

NASA Astrophysics Data System (ADS)

Choustova, Olga

In economics and financial theory, analysts use random walk and more general martingale techniques to model behavior of asset prices, in particular share prices on stock markets, currency exchange rates and commodity prices. This practice has its basis in the presumption that investors act rationally and without bias, and that at any moment they estimate the value of an asset based on future expectations. Under these conditions, all existing information affects the price, which changes only when new information comes out. By definition, new information appears randomly and influences the asset price randomly. Corresponding continuous time models are based on stochastic processes (this approach was initiated in the thesis of [4]), see, e.g., the books of [33] and [37] for historical and mathematical details.

Linear Optical Quantum Metrology with Single Photons: Exploiting Spontaneously Generated Entanglement to Beat the Shot-Noise Limit

NASA Astrophysics Data System (ADS)

Motes, Keith R.; Olson, Jonathan P.; Rabeaux, Evan J.; Dowling, Jonathan P.; Olson, S. Jay; Rohde, Peter P.

2015-05-01

Quantum number-path entanglement is a resource for supersensitive quantum metrology and in particular provides for sub-shot-noise or even Heisenberg-limited sensitivity. However, such number-path entanglement has been thought to be resource intensive to create in the first place—typically requiring either very strong nonlinearities, or nondeterministic preparation schemes with feedforward, which are difficult to implement. Very recently, arising from the study of quantum random walks with multiphoton walkers, as well as the study of the computational complexity of passive linear optical interferometers fed with single-photon inputs, it has been shown that such passive linear optical devices generate a superexponentially large amount of number-path entanglement. A logical question to ask is whether this entanglement may be exploited for quantum metrology. We answer that question here in the affirmative by showing that a simple, passive, linear-optical interferometer—fed with only uncorrelated, single-photon inputs, coupled with simple, single-mode, disjoint photodetection—is capable of significantly beating the shot-noise limit. Our result implies a pathway forward to practical quantum metrology with readily available technology.

Linear optical quantum metrology with single photons: exploiting spontaneously generated entanglement to beat the shot-noise limit.

PubMed

Motes, Keith R; Olson, Jonathan P; Rabeaux, Evan J; Dowling, Jonathan P; Olson, S Jay; Rohde, Peter P

2015-05-01

Quantum number-path entanglement is a resource for supersensitive quantum metrology and in particular provides for sub-shot-noise or even Heisenberg-limited sensitivity. However, such number-path entanglement has been thought to be resource intensive to create in the first place--typically requiring either very strong nonlinearities, or nondeterministic preparation schemes with feedforward, which are difficult to implement. Very recently, arising from the study of quantum random walks with multiphoton walkers, as well as the study of the computational complexity of passive linear optical interferometers fed with single-photon inputs, it has been shown that such passive linear optical devices generate a superexponentially large amount of number-path entanglement. A logical question to ask is whether this entanglement may be exploited for quantum metrology. We answer that question here in the affirmative by showing that a simple, passive, linear-optical interferometer--fed with only uncorrelated, single-photon inputs, coupled with simple, single-mode, disjoint photodetection--is capable of significantly beating the shot-noise limit. Our result implies a pathway forward to practical quantum metrology with readily available technology.

Partition-based discrete-time quantum walks

NASA Astrophysics Data System (ADS)

Konno, Norio; Portugal, Renato; Sato, Iwao; Segawa, Etsuo

2018-04-01

We introduce a family of discrete-time quantum walks, called two-partition model, based on two equivalence-class partitions of the computational basis, which establish the notion of local dynamics. This family encompasses most versions of unitary discrete-time quantum walks driven by two local operators studied in literature, such as the coined model, Szegedy's model, and the 2-tessellable staggered model. We also analyze the connection of those models with the two-step coined model, which is driven by the square of the evolution operator of the standard discrete-time coined walk. We prove formally that the two-step coined model, an extension of Szegedy model for multigraphs, and the two-tessellable staggered model are unitarily equivalent. Then, selecting one specific model among those families is a matter of taste not generality.

Physical realization of topological quantum walks on IBM-Q and beyond

NASA Astrophysics Data System (ADS)

Balu, Radhakrishnan; Castillo, Daniel; Siopsis, George

2018-07-01

We discuss an efficient physical realization of topological quantum walks on a one-dimensional finite lattice with periodic boundary conditions (circle). The N-point lattice is realized with {log}}2N qubits, and the quantum circuit utilizes a number of quantum gates that are polynomial in the number of qubits. In a certain scaling limit, we show that a large number of steps are implemented with a number of quantum gates which are independent of the number of steps. We ran the quantum algorithm on the IBM-Q five-qubit quantum computer, thus experimentally demonstrating topological features, such as boundary bound states, on a one-dimensional lattice with N = 4 points.

Novel Image Encryption based on Quantum Walks

PubMed Central

Yang, Yu-Guang; Pan, Qing-Xiang; Sun, Si-Jia; Xu, Peng

2015-01-01

Quantum computation has achieved a tremendous success during the last decades. In this paper, we investigate the potential application of a famous quantum computation model, i.e., quantum walks (QW) in image encryption. It is found that QW can serve as an excellent key generator thanks to its inherent nonlinear chaotic dynamic behavior. Furthermore, we construct a novel QW-based image encryption algorithm. Simulations and performance comparisons show that the proposal is secure enough for image encryption and outperforms prior works. It also opens the door towards introducing quantum computation into image encryption and promotes the convergence between quantum computation and image processing. PMID:25586889

Record statistics of a strongly correlated time series: random walks and Lévy flights

NASA Astrophysics Data System (ADS)

Godrèche, Claude; Majumdar, Satya N.; Schehr, Grégory

2017-08-01

We review recent advances on the record statistics of strongly correlated time series, whose entries denote the positions of a random walk or a Lévy flight on a line. After a brief survey of the theory of records for independent and identically distributed random variables, we focus on random walks. During the last few years, it was indeed realized that random walks are a very useful ‘laboratory’ to test the effects of correlations on the record statistics. We start with the simple one-dimensional random walk with symmetric jumps (both continuous and discrete) and discuss in detail the statistics of the number of records, as well as of the ages of the records, i.e. the lapses of time between two successive record breaking events. Then we review the results that were obtained for a wide variety of random walk models, including random walks with a linear drift, continuous time random walks, constrained random walks (like the random walk bridge) and the case of multiple independent random walkers. Finally, we discuss further observables related to records, like the record increments, as well as some questions raised by physical applications of record statistics, like the effects of measurement error and noise.

Experimental realization of generalized qubit measurements based on quantum walks

NASA Astrophysics Data System (ADS)

Zhao, Yuan-yuan; Yu, Neng-kun; Kurzyński, Paweł; Xiang, Guo-yong; Li, Chuan-Feng; Guo, Guang-Can

2015-04-01

We report an experimental implementation of a single-qubit generalized measurement scenario, the positive-operator valued measure (POVM), based on a quantum walk model. The qubit is encoded in a single-photon polarization. The photon performs a quantum walk on an array of optical elements, where the polarization-dependent translation is performed via birefringent beam displacers and a change of the polarization is implemented with the help of wave plates. We implement: (i) trine POVM, i.e., the POVM elements uniformly distributed on an equatorial plane of the Bloch sphere; (ii) symmetric-informationally-complete (SIC) POVM; and (iii) unambiguous discrimination of two nonorthogonal qubit states.

Faster search by lackadaisical quantum walk

NASA Astrophysics Data System (ADS)

Wong, Thomas G.

2018-03-01

In the typical model, a discrete-time coined quantum walk searching the 2D grid for a marked vertex achieves a success probability of O(1/log N) in O(√{N log N}) steps, which with amplitude amplification yields an overall runtime of O(√{N} log N). We show that making the quantum walk lackadaisical or lazy by adding a self-loop of weight 4 / N to each vertex speeds up the search, causing the success probability to reach a constant near 1 in O(√{N log N}) steps, thus yielding an O(√{log N}) improvement over the typical, loopless algorithm. This improved runtime matches the best known quantum algorithms for this search problem. Our results are based on numerical simulations since the algorithm is not an instance of the abstract search algorithm.

A simulator for discrete quantum walks on lattices

NASA Astrophysics Data System (ADS)

Rodrigues, J.; Paunković, N.; Mateus, P.

In this paper, we present a simulator for two-particle quantum walks on the line and one-particle on a two-dimensional squared lattice. It can be used to investigate the equivalence between the two cases (one- and two-particle walks) for various boundary conditions (open, circular, reflecting, absorbing and their combinations). For the case of a single walker on a two-dimensional lattice, the simulator can also implement the Möbius strip. Furthermore, other topologies for the walker are also simulated by the proposed tool, like certain types of planar graphs with degree up to 4, by considering missing links over the lattice. The main purpose of the simulator is to study the genuinely quantum effects on the global properties of the two-particle joint probability distribution on the entanglement between the walkers/axis. For that purpose, the simulator is designed to compute various quantities such as: the entanglement and classical correlations, (classical and quantum) mutual information, the average distance between the two walkers, different hitting times and quantum discord. These quantities are of vital importance in designing possible algorithmic applications of quantum walks, namely in search, 3-SAT problems, etc. The simulator can also implement the static partial measurements of particle(s) positions and dynamic breaking of the links between certain nodes, both of which can be used to investigate the effects of decoherence on the walker(s). Finally, the simulator can be used to investigate the dynamic Anderson-like particle localization by varying the coin operators of certain nodes on the line/lattice. We also present some illustrative and relevant examples of one- and two-particle quantum walks in various scenarios. The tool was implemented in C and is available on-line at http://qwsim.weebly.com/.

Quantum walks of two interacting particles on percolation graphs

NASA Astrophysics Data System (ADS)

Siloi, Ilaria; Benedetti, Claudia; Piccinini, Enrico; Paris, Matteo G. A.; Bordone, Paolo

2017-10-01

We address the dynamics of two indistinguishable interacting particles moving on a dynamical percolation graph, i.e., a graph where the edges are independent random telegraph processes whose values jump between 0 and 1, thus mimicking percolation. The interplay between the particle interaction strength, initial state and the percolation rate determine different dynamical regimes for the walkers. We show that, whenever the walkers are initially localised within the interaction range, fast noise enhances the particle spread compared to the noiseless case.

Real-time monitoring of Lévy flights in a single quantum system

NASA Astrophysics Data System (ADS)

Issler, M.; Höller, J.; Imamoǧlu, A.

2016-02-01

Lévy flights are random walks where the dynamics is dominated by rare events. Even though they have been studied in vastly different physical systems, their observation in a single quantum system has remained elusive. Here we analyze a periodically driven open central spin system and demonstrate theoretically that the dynamics of the spin environment exhibits Lévy flights. For the particular realization in a single-electron charged quantum dot driven by periodic resonant laser pulses, we use Monte Carlo simulations to confirm that the long waiting times between successive nuclear spin-flip events are governed by a power-law distribution; the corresponding exponent η =-3 /2 can be directly measured in real time by observing the waiting time distribution of successive photon emission events. Remarkably, the dominant intrinsic limitation of the scheme arising from nuclear quadrupole coupling can be minimized by adjusting the magnetic field or by implementing spin echo.

Open Quantum Walks with Noncommuting Jump Operators

NASA Astrophysics Data System (ADS)

Caballar, Roland Cristopher; Petruccione, Francesco; Sinayskiy, Ilya

2014-03-01

We examine homogeneous open quantum walks along a line, wherein each forward step is due to one quantum jump operator, and each backward step due to another quantum jump operator. We assume that these two quantum jump operators do not commute with each other. We show that if the system has N internal degrees of freedom, for particular forms of these quantum jump operators, we can obtain exact probability distributions which fall into two distinct classes, namely Gaussian distributions and solitonic distributions. We also show that it is possible for a maximum of 2 solitonic distributions to be present simultaneously in the system. Finally, we consider applications of these classes of jump operators in quantum state preparation and quantum information. We acknowledge support from the National Institute for Theoretical Physics (NITheP).

Open Quantum Walks and Dissipative Quantum Computing

NASA Astrophysics Data System (ADS)

Petruccione, Francesco

2012-02-01

Open Quantum Walks (OQWs) have been recently introduced as quantum Markov chains on graphs [S. Attal, F. Petruccione, C. Sabot, and I. Sinayskiy, E-print: http://hal.archives-ouvertes.fr/hal-00581553/fr/]. The formulation of the OQWs is exclusively based upon the non-unitary dynamics induced by the environment. It will be shown that OQWs are a very useful tool for the formulation of dissipative quantum computing and quantum state preparation. In particular, it will be shown how to implement single qubit gates and the CNOT gate as OQWs on fully connected graphs. Also, OQWS make possible the dissipative quantum state preparation of arbitrary single qubit states and of all two-qubit Bell states. Finally, it will be shown how to reformulate efficiently a discrete time version of dissipative quantum computing in the language of OQWs.

Movement patterns of Tenebrio beetles demonstrate empirically that correlated-random-walks have similitude with a Lévy walk.

PubMed

Reynolds, Andy M; Leprêtre, Lisa; Bohan, David A

2013-11-07

Correlated random walks are the dominant conceptual framework for modelling and interpreting organism movement patterns. Recent years have witnessed a stream of high profile publications reporting that many organisms perform Lévy walks; movement patterns that seemingly stand apart from the correlated random walk paradigm because they are discrete and scale-free rather than continuous and scale-finite. Our new study of the movement patterns of Tenebrio molitor beetles in unchanging, featureless arenas provides the first empirical support for a remarkable and deep theoretical synthesis that unites correlated random walks and Lévy walks. It demonstrates that the two models are complementary rather than competing descriptions of movement pattern data and shows that correlated random walks are a part of the Lévy walk family. It follows from this that vast numbers of Lévy walkers could be hiding in plain sight.

Counting statistics of many-particle quantum walks

NASA Astrophysics Data System (ADS)

Mayer, Klaus; Tichy, Malte C.; Mintert, Florian; Konrad, Thomas; Buchleitner, Andreas

2011-06-01

We study quantum walks of many noninteracting particles on a beam splitter array as a paradigmatic testing ground for the competition of single- and many-particle interference in a multimode system. We derive a general expression for multimode particle-number correlation functions, valid for bosons and fermions, and infer pronounced signatures of many-particle interferences in the counting statistics.

Distribution of chirality in the quantum walk: Markov process and entanglement

DOE Office of Scientific and Technical Information (OSTI.GOV)

Romanelli, Alejandro

The asymptotic behavior of the quantum walk on the line is investigated, focusing on the probability distribution of chirality independently of position. It is shown analytically that this distribution has a longtime limit that is stationary and depends on the initial conditions. This result is unexpected in the context of the unitary evolution of the quantum walk as it is usually linked to a Markovian process. The asymptotic value of the entanglement between the coin and the position is determined by the chirality distribution. For given asymptotic values of both the entanglement and the chirality distribution, it is possible tomore » find the corresponding initial conditions within a particular class of spatially extended Gaussian distributions.« less

Interferometers as probes of Planckian quantum geometry

NASA Astrophysics Data System (ADS)

Hogan, Craig J.

2012-03-01

A theory of position of massive bodies is proposed that results in an observable quantum behavior of geometry at the Planck scale, tP. Departures from classical world lines in flat spacetime are described by Planckian noncommuting operators for position in different directions, as defined by interactions with null waves. The resulting evolution of position wave functions in two dimensions displays a new kind of directionally coherent quantum noise of transverse position. The amplitude of the effect in physical units is predicted with no parameters, by equating the number of degrees of freedom of position wave functions on a 2D space-like surface with the entropy density of a black hole event horizon of the same area. In a region of size L, the effect resembles spatially and directionally coherent random transverse shear deformations on time scale ≈L/c with typical amplitude ≈ctPL. This quantum-geometrical “holographic noise” in position is not describable as fluctuations of a quantized metric, or as any kind of fluctuation, dispersion or propagation effect in quantum fields. In a Michelson interferometer the effect appears as noise that resembles a random Planckian walk of the beam splitter for durations up to the light-crossing time. Signal spectra and correlation functions in interferometers are derived, and predicted to be comparable with the sensitivities of current and planned experiments. It is proposed that nearly colocated Michelson interferometers of laboratory scale, cross-correlated at high frequency, can test the Planckian noise prediction with current technology.

On Convergent Probability of a Random Walk

ERIC Educational Resources Information Center

Lee, Y.-F.; Ching, W.-K.

2006-01-01

This note introduces an interesting random walk on a straight path with cards of random numbers. The method of recurrent relations is used to obtain the convergent probability of the random walk with different initial positions.

Scaling Limit of Symmetric Random Walk in High-Contrast Periodic Environment

NASA Astrophysics Data System (ADS)

Piatnitski, A.; Zhizhina, E.

2017-11-01

The paper deals with the asymptotic properties of a symmetric random walk in a high contrast periodic medium in Z^d, d≥1. From the existing homogenization results it follows that under diffusive scaling the limit behaviour of this random walk need not be Markovian. The goal of this work is to show that if in addition to the coordinate of the random walk in Z^d we introduce an extra variable that characterizes the position of the random walk inside the period then the limit dynamics of this two-component process is Markov. We describe the limit process and observe that the components of the limit process are coupled. We also prove the convergence in the path space for the said random walk.

Quantum walks: The first detected passage time problem

NASA Astrophysics Data System (ADS)

Friedman, H.; Kessler, D. A.; Barkai, E.

2017-03-01

Even after decades of research, the problem of first passage time statistics for quantum dynamics remains a challenging topic of fundamental and practical importance. Using a projective measurement approach, with a sampling time τ , we obtain the statistics of first detection events for quantum dynamics on a lattice, with the detector located at the origin. A quantum renewal equation for a first detection wave function, in terms of which the first detection probability can be calculated, is derived. This formula gives the relation between first detection statistics and the solution of the corresponding Schrödinger equation in the absence of measurement. We illustrate our results with tight-binding quantum walk models. We examine a closed system, i.e., a ring, and reveal the intricate influence of the sampling time τ on the statistics of detection, discussing the quantum Zeno effect, half dark states, revivals, and optimal detection. The initial condition modifies the statistics of a quantum walk on a finite ring in surprising ways. In some cases, the average detection time is independent of the sampling time while in others the average exhibits multiple divergences as the sampling time is modified. For an unbounded one-dimensional quantum walk, the probability of first detection decays like (time)(-3 ) with superimposed oscillations, with exceptional behavior when the sampling period τ times the tunneling rate γ is a multiple of π /2 . The amplitude of the power-law decay is suppressed as τ →0 due to the Zeno effect. Our work, an extended version of our previously published paper, predicts rich physical behaviors compared with classical Brownian motion, for which the first passage probability density decays monotonically like (time)-3 /2, as elucidated by Schrödinger in 1915.

Graphic matching based on shape contexts and reweighted random walks

NASA Astrophysics Data System (ADS)

Zhang, Mingxuan; Niu, Dongmei; Zhao, Xiuyang; Liu, Mingjun

2018-04-01

Graphic matching is a very critical issue in all aspects of computer vision. In this paper, a new graphics matching algorithm combining shape contexts and reweighted random walks was proposed. On the basis of the local descriptor, shape contexts, the reweighted random walks algorithm was modified to possess stronger robustness and correctness in the final result. Our main process is to use the descriptor of the shape contexts for the random walk on the iteration, of which purpose is to control the random walk probability matrix. We calculate bias matrix by using descriptors and then in the iteration we use it to enhance random walks' and random jumps' accuracy, finally we get the one-to-one registration result by discretization of the matrix. The algorithm not only preserves the noise robustness of reweighted random walks but also possesses the rotation, translation, scale invariance of shape contexts. Through extensive experiments, based on real images and random synthetic point sets, and comparisons with other algorithms, it is confirmed that this new method can produce excellent results in graphic matching.

Quantum state engineering using one-dimensional discrete-time quantum walks

NASA Astrophysics Data System (ADS)

Innocenti, Luca; Majury, Helena; Giordani, Taira; Spagnolo, Nicolò; Sciarrino, Fabio; Paternostro, Mauro; Ferraro, Alessandro

2017-12-01

Quantum state preparation in high-dimensional systems is an essential requirement for many quantum-technology applications. The engineering of an arbitrary quantum state is, however, typically strongly dependent on the experimental platform chosen for implementation, and a general framework is still missing. Here we show that coined quantum walks on a line, which represent a framework general enough to encompass a variety of different platforms, can be used for quantum state engineering of arbitrary superpositions of the walker's sites. We achieve this goal by identifying a set of conditions that fully characterize the reachable states in the space comprising walker and coin and providing a method to efficiently compute the corresponding set of coin parameters. We assess the feasibility of our proposal by identifying a linear optics experiment based on photonic orbital angular momentum technology.

Computation of Ground-State Properties in Molecular Systems: Back-Propagation with Auxiliary-Field Quantum Monte Carlo.

PubMed

Motta, Mario; Zhang, Shiwei

2017-11-14

We address the computation of ground-state properties of chemical systems and realistic materials within the auxiliary-field quantum Monte Carlo method. The phase constraint to control the Fermion phase problem requires the random walks in Slater determinant space to be open-ended with branching. This in turn makes it necessary to use back-propagation (BP) to compute averages and correlation functions of operators that do not commute with the Hamiltonian. Several BP schemes are investigated, and their optimization with respect to the phaseless constraint is considered. We propose a modified BP method for the computation of observables in electronic systems, discuss its numerical stability and computational complexity, and assess its performance by computing ground-state properties in several molecular systems, including small organic molecules.

Calendar effects in quantum mechanics in view of interactive holography

NASA Astrophysics Data System (ADS)

Berkovich, Simon

2013-04-01

Quantum mechanics in terms of interactive holography appears as `normal' science [1]. With the holography quantum behavior is determined by the interplay of material formations and their conjugate images. To begin with, this effortlessly elucidates the nonlocality in quantum entanglements. Then, it has been shown that Schr"odinger's dynamics for a single particle arises from Bi-Fragmental random walks of the particle itself and its holographic image. For many particles this picture blurs with fragments merging as bosons or fermions. In biomolecules, swapping of particles and their holographic placeholders leads to self-replication of the living matter. Because of broad interpretations of quantum formalism direct experiments attributing it to holography may not be very compelling. The holographic mechanism better reveals as an absolute frame of reference. A number of physical and biological events exhibit annual variations when Earth orbital position changes with respect to the universal holographic mechanism. The well established calendar variations of heart attacks can be regarded as a positive outcome of a generalization of the Michelson experiment, where holography is interferometry and ailing hearts are detectors of pathologically replicated proteins. Also, there have been already observed calendar changes in radioactive decay rates. The same could be expected for various fine quantum experiences, like, e.g., Josephson tunneling. In other words, Quantum Mechanics (February) Quantum Mechanics (August). [1] S. Berkovich, ``A comprehensive explanation of quantum mechanics,'' www.cs.gwu.edu/research/technical-report/170 .

Efficient sampling of complex network with modified random walk strategies

NASA Astrophysics Data System (ADS)

Xie, Yunya; Chang, Shuhua; Zhang, Zhipeng; Zhang, Mi; Yang, Lei

2018-02-01

We present two novel random walk strategies, choosing seed node (CSN) random walk and no-retracing (NR) random walk. Different from the classical random walk sampling, the CSN and NR strategies focus on the influences of the seed node choice and path overlap, respectively. Three random walk samplings are applied in the Erdös-Rényi (ER), Barabási-Albert (BA), Watts-Strogatz (WS), and the weighted USAir networks, respectively. Then, the major properties of sampled subnets, such as sampling efficiency, degree distributions, average degree and average clustering coefficient, are studied. The similar conclusions can be reached with these three random walk strategies. Firstly, the networks with small scales and simple structures are conducive to the sampling. Secondly, the average degree and the average clustering coefficient of the sampled subnet tend to the corresponding values of original networks with limited steps. And thirdly, all the degree distributions of the subnets are slightly biased to the high degree side. However, the NR strategy performs better for the average clustering coefficient of the subnet. In the real weighted USAir networks, some obvious characters like the larger clustering coefficient and the fluctuation of degree distribution are reproduced well by these random walk strategies.

Continuous-time quantum walks on multilayer dendrimer networks

NASA Astrophysics Data System (ADS)

Galiceanu, Mircea; Strunz, Walter T.

2016-08-01

We consider continuous-time quantum walks (CTQWs) on multilayer dendrimer networks (MDs) and their application to quantum transport. A detailed study of properties of CTQWs is presented and transport efficiency is determined in terms of the exact and average return probabilities. The latter depends only on the eigenvalues of the connectivity matrix, which even for very large structures allows a complete analytical solution for this particular choice of network. In the case of MDs we observe an interplay between strong localization effects, due to the dendrimer topology, and good efficiency from the linear segments. We show that quantum transport is enhanced by interconnecting more layers of dendrimers.

Approximate Locality for Quantum Systems on Graphs

NASA Astrophysics Data System (ADS)

Osborne, Tobias J.

2008-10-01

In this Letter we make progress on a long-standing open problem of Aaronson and Ambainis [Theory Comput. 1, 47 (2005)1557-2862]: we show that if U is a sparse unitary operator with a gap Δ in its spectrum, then there exists an approximate logarithm H of U which is also sparse. The sparsity pattern of H gets more dense as 1/Δ increases. This result can be interpreted as a way to convert between local continuous-time and local discrete-time quantum processes. As an example we show that the discrete-time coined quantum walk can be realized stroboscopically from an approximately local continuous-time quantum walk.

Stationary states in quantum walk search

NASA Astrophysics Data System (ADS)

PrÅ«sis, Krišjānis; Vihrovs, Jevgěnijs; Wong, Thomas G.

2016-09-01

When classically searching a database, having additional correct answers makes the search easier. For a discrete-time quantum walk searching a graph for a marked vertex, however, additional marked vertices can make the search harder by causing the system to approximately begin in a stationary state, so the system fails to evolve. In this paper, we completely characterize the stationary states, or 1-eigenvectors, of the quantum walk search operator for general graphs and configurations of marked vertices by decomposing their amplitudes into uniform and flip states. This infinitely expands the number of known stationary states and gives an optimization procedure to find the stationary state closest to the initial uniform state of the walk. We further prove theorems on the existence of stationary states, with them conditionally existing if the marked vertices form a bipartite connected component and always existing if nonbipartite. These results utilize the standard oracle in Grover's algorithm, but we show that a different type of oracle prevents stationary states from interfering with the search algorithm.

Limitations of discrete-time quantum walk on a one-dimensional infinite chain

NASA Astrophysics Data System (ADS)

Lin, Jia-Yi; Zhu, Xuanmin; Wu, Shengjun

2018-04-01

How well can we manipulate the state of a particle via a discrete-time quantum walk? We show that the discrete-time quantum walk on a one-dimensional infinite chain with coin operators that are independent of the position can only realize product operators of the form eiξ A ⊗1p, which cannot change the position state of the walker. We present a scheme to construct all possible realizations of all the product operators of the form eiξ A ⊗1p. When the coin operators are dependent on the position, we show that the translation operators on the position can not be realized via a DTQW with coin operators that are either the identity operator 1 or the Pauli operator σx.

Supercritical entanglement in local systems: Counterexample to the area law for quantum matter.

PubMed

Movassagh, Ramis; Shor, Peter W

2016-11-22

Quantum entanglement is the most surprising feature of quantum mechanics. Entanglement is simultaneously responsible for the difficulty of simulating quantum matter on a classical computer and the exponential speedups afforded by quantum computers. Ground states of quantum many-body systems typically satisfy an "area law": The amount of entanglement between a subsystem and the rest of the system is proportional to the area of the boundary. A system that obeys an area law has less entanglement and can be simulated more efficiently than a generic quantum state whose entanglement could be proportional to the total system's size. Moreover, an area law provides useful information about the low-energy physics of the system. It is widely believed that for physically reasonable quantum systems, the area law cannot be violated by more than a logarithmic factor in the system's size. We introduce a class of exactly solvable one-dimensional physical models which we can prove have exponentially more entanglement than suggested by the area law, and violate the area law by a square-root factor. This work suggests that simple quantum matter is richer and can provide much more quantum resources (i.e., entanglement) than expected. In addition to using recent advances in quantum information and condensed matter theory, we have drawn upon various branches of mathematics such as combinatorics of random walks, Brownian excursions, and fractional matching theory. We hope that the techniques developed herein may be useful for other problems in physics as well.

Supercritical entanglement in local systems: Counterexample to the area law for quantum matter

PubMed Central

Movassagh, Ramis; Shor, Peter W.

2016-01-01

Quantum entanglement is the most surprising feature of quantum mechanics. Entanglement is simultaneously responsible for the difficulty of simulating quantum matter on a classical computer and the exponential speedups afforded by quantum computers. Ground states of quantum many-body systems typically satisfy an “area law”: The amount of entanglement between a subsystem and the rest of the system is proportional to the area of the boundary. A system that obeys an area law has less entanglement and can be simulated more efficiently than a generic quantum state whose entanglement could be proportional to the total system’s size. Moreover, an area law provides useful information about the low-energy physics of the system. It is widely believed that for physically reasonable quantum systems, the area law cannot be violated by more than a logarithmic factor in the system’s size. We introduce a class of exactly solvable one-dimensional physical models which we can prove have exponentially more entanglement than suggested by the area law, and violate the area law by a square-root factor. This work suggests that simple quantum matter is richer and can provide much more quantum resources (i.e., entanglement) than expected. In addition to using recent advances in quantum information and condensed matter theory, we have drawn upon various branches of mathematics such as combinatorics of random walks, Brownian excursions, and fractional matching theory. We hope that the techniques developed herein may be useful for other problems in physics as well. PMID:27821725

Random walks on combs

NASA Astrophysics Data System (ADS)

Durhuus, Bergfinnur; Jonsson, Thordur; Wheater, John F.

2006-02-01

We develop techniques to obtain rigorous bounds on the behaviour of random walks on combs. Using these bounds, we calculate exactly the spectral dimension of random combs with infinite teeth at random positions or teeth with random but finite length. We also calculate exactly the spectral dimension of some fixed non-translationally invariant combs. We relate the spectral dimension to the critical exponent of the mass of the two-point function for random walks on random combs, and compute mean displacements as a function of walk duration. We prove that the mean first passage time is generally infinite for combs with anomalous spectral dimension.

Coupled continuous time-random walks in quenched random environment

NASA Astrophysics Data System (ADS)

Magdziarz, M.; Szczotka, W.

2018-02-01

We introduce a coupled continuous-time random walk with coupling which is characteristic for Lévy walks. Additionally we assume that the walker moves in a quenched random environment, i.e. the site disorder at each lattice point is fixed in time. We analyze the scaling limit of such a random walk. We show that for large times the behaviour of the analyzed process is exactly the same as in the case of uncoupled quenched trap model for Lévy flights.

Towards non-classical walks with bright laser pulses

NASA Astrophysics Data System (ADS)

Sephton, B.; Dudley, A.; Forbes, A.

2017-08-01

In the avid search for means to increase computational power in comparison to that which is currently available, quantum walks (QWs) have become a promising option with derived quantum algorithms providing an associated speed up compared to what is currently used for implementation in classical computers. It has additionally been shown that the physical implementation of QWs will provide a successful computational basis for a quantum computer. It follows that considerable drive for finding such means has been occurring over the 20+ years since its introduction with phenomena such as electrons and photons being employed. Principal problems encountered with such quantum systems involve the vulnerability to environmental influence as well as scalability of the systems. Here we outline how to perform the QW due to interference characteristics inherent in the phenomenon, to mitigate these challenges. We utilize the properties of vector beams to physically implement such a walk in orbital angular momentum space by manipulating polarization and exploiting the non-separability of such beams.

Recurrence of random walks with long-range steps generated by fractional Laplacian matrices on regular networks and simple cubic lattices

NASA Astrophysics Data System (ADS)

Michelitsch, T. M.; Collet, B. A.; Riascos, A. P.; Nowakowski, A. F.; Nicolleau, F. C. G. A.

2017-12-01

We analyze a Markovian random walk strategy on undirected regular networks involving power matrix functions of the type L\\frac{α{2}} where L indicates a ‘simple’ Laplacian matrix. We refer to such walks as ‘fractional random walks’ with admissible interval 0<α ≤slant 2 . We deduce probability-generating functions (network Green’s functions) for the fractional random walk. From these analytical results we establish a generalization of Polya’s recurrence theorem for fractional random walks on d-dimensional infinite lattices: The fractional random walk is transient for dimensions d > α (recurrent for d≤slantα ) of the lattice. As a consequence, for 0<α< 1 the fractional random walk is transient for all lattice dimensions d=1, 2, .. and in the range 1≤slantα < 2 for dimensions d≥slant 2 . Finally, for α=2 , Polya’s classical recurrence theorem is recovered, namely the walk is transient only for lattice dimensions d≥slant 3 . The generalization of Polya’s recurrence theorem remains valid for the class of random walks with Lévy flight asymptotics for long-range steps. We also analyze the mean first passage probabilities, mean residence times, mean first passage times and global mean first passage times (Kemeny constant) for the fractional random walk. For an infinite 1D lattice (infinite ring) we obtain for the transient regime 0<α<1 closed form expressions for the fractional lattice Green’s function matrix containing the escape and ever passage probabilities. The ever passage probabilities (fractional lattice Green’s functions) in the transient regime fulfil Riesz potential power law decay asymptotic behavior for nodes far from the departure node. The non-locality of the fractional random walk is generated by the non-diagonality of the fractional Laplacian matrix with Lévy-type heavy tailed inverse power law decay for the probability of long-range moves. This non-local and asymptotic behavior of the fractional random walk introduces small-world properties with the emergence of Lévy flights on large (infinite) lattices.

Search for Directed Networks by Different Random Walk Strategies

NASA Astrophysics Data System (ADS)

Zhu, Zi-Qi; Jin, Xiao-Ling; Huang, Zhi-Long

2012-03-01

A comparative study is carried out on the efficiency of five different random walk strategies searching on directed networks constructed based on several typical complex networks. Due to the difference in search efficiency of the strategies rooted in network clustering, the clustering coefficient in a random walker's eye on directed networks is defined and computed to be half of the corresponding undirected networks. The search processes are performed on the directed networks based on Erdös—Rényi model, Watts—Strogatz model, Barabási—Albert model and clustered scale-free network model. It is found that self-avoiding random walk strategy is the best search strategy for such directed networks. Compared to unrestricted random walk strategy, path-iteration-avoiding random walks can also make the search process much more efficient. However, no-triangle-loop and no-quadrangle-loop random walks do not improve the search efficiency as expected, which is different from those on undirected networks since the clustering coefficient of directed networks are smaller than that of undirected networks.

Projective simulation for artificial intelligence

NASA Astrophysics Data System (ADS)

Briegel, Hans J.; de Las Cuevas, Gemma

2012-05-01

We propose a model of a learning agent whose interaction with the environment is governed by a simulation-based projection, which allows the agent to project itself into future situations before it takes real action. Projective simulation is based on a random walk through a network of clips, which are elementary patches of episodic memory. The network of clips changes dynamically, both due to new perceptual input and due to certain compositional principles of the simulation process. During simulation, the clips are screened for specific features which trigger factual action of the agent. The scheme is different from other, computational, notions of simulation, and it provides a new element in an embodied cognitive science approach to intelligent action and learning. Our model provides a natural route for generalization to quantum-mechanical operation and connects the fields of reinforcement learning and quantum computation.

Projective simulation for artificial intelligence

PubMed Central

Briegel, Hans J.; De las Cuevas, Gemma

2012-01-01

We propose a model of a learning agent whose interaction with the environment is governed by a simulation-based projection, which allows the agent to project itself into future situations before it takes real action. Projective simulation is based on a random walk through a network of clips, which are elementary patches of episodic memory. The network of clips changes dynamically, both due to new perceptual input and due to certain compositional principles of the simulation process. During simulation, the clips are screened for specific features which trigger factual action of the agent. The scheme is different from other, computational, notions of simulation, and it provides a new element in an embodied cognitive science approach to intelligent action and learning. Our model provides a natural route for generalization to quantum-mechanical operation and connects the fields of reinforcement learning and quantum computation. PMID:22590690

JOURNAL SCOPE GUIDELINES: Paper classification scheme

NASA Astrophysics Data System (ADS)

2005-06-01

This scheme is used to clarify the journal's scope and enable authors and readers to more easily locate the appropriate section for their work. For each of the sections listed in the scope statement we suggest some more detailed subject areas which help define that subject area. These lists are by no means exhaustive and are intended only as a guide to the type of papers we envisage appearing in each section. We acknowledge that no classification scheme can be perfect and that there are some papers which might be placed in more than one section. We are happy to provide further advice on paper classification to authors upon request (please email jphysa@iop.org). 1. Statistical physics numerical and computational methods statistical mechanics, phase transitions and critical phenomena quantum condensed matter theory Bose-Einstein condensation strongly correlated electron systems exactly solvable models in statistical mechanics lattice models, random walks and combinatorics field-theoretical models in statistical mechanics disordered systems, spin glasses and neural networks nonequilibrium systems network theory 2. Chaotic and complex systems nonlinear dynamics and classical chaos fractals and multifractals quantum chaos classical and quantum transport cellular automata granular systems and self-organization pattern formation biophysical models 3. Mathematical physics combinatorics algebraic structures and number theory matrix theory classical and quantum groups, symmetry and representation theory Lie algebras, special functions and orthogonal polynomials ordinary and partial differential equations difference and functional equations integrable systems soliton theory functional analysis and operator theory inverse problems geometry, differential geometry and topology numerical approximation and analysis geometric integration computational methods 4. Quantum mechanics and quantum information theory coherent states eigenvalue problems supersymmetric quantum mechanics scattering theory relativistic quantum mechanics semiclassical approximations foundations of quantum mechanics and measurement theory entanglement and quantum nonlocality geometric phases and quantum tomography quantum tunnelling decoherence and open systems quantum cryptography, communication and computation theoretical quantum optics 5. Classical and quantum field theory quantum field theory gauge and conformal field theory quantum electrodynamics and quantum chromodynamics Casimir effect integrable field theory random matrix theory applications in field theory string theory and its developments classical field theory and electromagnetism metamaterials 6. Fluid and plasma theory turbulence fundamental plasma physics kinetic theory magnetohydrodynamics and multifluid descriptions strongly coupled plasmas one-component plasmas non-neutral plasmas astrophysical and dusty plasmas

A discrete random walk on the hypercube

NASA Astrophysics Data System (ADS)

Zhang, Jingyuan; Xiang, Yonghong; Sun, Weigang

2018-03-01

In this paper, we study the scaling for mean first-passage time (MFPT) of random walks on the hypercube and obtain a closed-form formula for the MFPT over all node pairs. We also determine the exponent of scaling efficiency characterizing the random walks and compare it with those of the existing networks. Finally we study the random walks on the hypercube with a located trap and provide a solution of the Kirchhoff index of the hypercube.

Statistical moments of quantum-walk dynamics reveal topological quantum transitions.

PubMed

Cardano, Filippo; Maffei, Maria; Massa, Francesco; Piccirillo, Bruno; de Lisio, Corrado; De Filippis, Giulio; Cataudella, Vittorio; Santamato, Enrico; Marrucci, Lorenzo

2016-04-22

Many phenomena in solid-state physics can be understood in terms of their topological properties. Recently, controlled protocols of quantum walk (QW) are proving to be effective simulators of such phenomena. Here we report the realization of a photonic QW showing both the trivial and the non-trivial topologies associated with chiral symmetry in one-dimensional (1D) periodic systems. We find that the probability distribution moments of the walker position after many steps can be used as direct indicators of the topological quantum transition: while varying a control parameter that defines the system phase, these moments exhibit a slope discontinuity at the transition point. Numerical simulations strongly support the conjecture that these features are general of 1D topological systems. Extending this approach to higher dimensions, different topological classes, and other typologies of quantum phases may offer general instruments for investigating and experimentally detecting quantum transitions in such complex systems.

Statistical moments of quantum-walk dynamics reveal topological quantum transitions

PubMed Central

Cardano, Filippo; Maffei, Maria; Massa, Francesco; Piccirillo, Bruno; de Lisio, Corrado; De Filippis, Giulio; Cataudella, Vittorio; Santamato, Enrico; Marrucci, Lorenzo

2016-01-01

Many phenomena in solid-state physics can be understood in terms of their topological properties. Recently, controlled protocols of quantum walk (QW) are proving to be effective simulators of such phenomena. Here we report the realization of a photonic QW showing both the trivial and the non-trivial topologies associated with chiral symmetry in one-dimensional (1D) periodic systems. We find that the probability distribution moments of the walker position after many steps can be used as direct indicators of the topological quantum transition: while varying a control parameter that defines the system phase, these moments exhibit a slope discontinuity at the transition point. Numerical simulations strongly support the conjecture that these features are general of 1D topological systems. Extending this approach to higher dimensions, different topological classes, and other typologies of quantum phases may offer general instruments for investigating and experimentally detecting quantum transitions in such complex systems. PMID:27102945

Sensitivity of quantum walks to a boundary of two-dimensional lattices: approaches based on the CGMV method and topological phases

NASA Astrophysics Data System (ADS)

Endo, Takako; Konno, Norio; Obuse, Hideaki; Segawa, Etsuo

2017-11-01

In this paper, we treat quantum walks in a two-dimensional lattice with cutting edges along a straight boundary introduced by Asboth and Edge (2015 Phys. Rev. A 91 022324) in order to study one-dimensional edge states originating from topological phases of matter and to obtain collateral evidence of how a quantum walker reacts to the boundary. Firstly, we connect this model to the CMV matrix, which provides a 5-term recursion relation of the Laurent polynomial associated with spectral measure on the unit circle. Secondly, we explicitly derive the spectra of bulk and edge states of the quantum walk with the boundary using spectral analysis of the CMV matrix. Thirdly, while topological numbers of the model studied so far are well-defined only when gaps in the bulk spectrum exist, we find a new topological number defined only when there are no gaps in the bulk spectrum. We confirm that the existence of the spectrum for edge states derived from the CMV matrix is consistent with the prediction from a bulk-edge correspondence using topological numbers calculated in the cases where gaps in the bulk spectrum do or do not exist. Finally, we show how the edge states contribute to the asymptotic behavior of the quantum walk through limit theorems of the finding probability. Conversely, we also propose a differential equation using this limit distribution whose solution is the underlying edge state.

Dirac Cellular Automaton from Split-step Quantum Walk

PubMed Central

Mallick, Arindam; Chandrashekar, C. M.

2016-01-01

Simulations of one quantum system by an other has an implication in realization of quantum machine that can imitate any quantum system and solve problems that are not accessible to classical computers. One of the approach to engineer quantum simulations is to discretize the space-time degree of freedom in quantum dynamics and define the quantum cellular automata (QCA), a local unitary update rule on a lattice. Different models of QCA are constructed using set of conditions which are not unique and are not always in implementable configuration on any other system. Dirac Cellular Automata (DCA) is one such model constructed for Dirac Hamiltonian (DH) in free quantum field theory. Here, starting from a split-step discrete-time quantum walk (QW) which is uniquely defined for experimental implementation, we recover the DCA along with all the fine oscillations in position space and bridge the missing connection between DH-DCA-QW. We will present the contribution of the parameters resulting in the fine oscillations on the Zitterbewegung frequency and entanglement. The tuneability of the evolution parameters demonstrated in experimental implementation of QW will establish it as an efficient tool to design quantum simulator and approach quantum field theory from principles of quantum information theory. PMID:27184159

Influence of the random walk finite step on the first-passage probability

NASA Astrophysics Data System (ADS)

Klimenkova, Olga; Menshutin, Anton; Shchur, Lev

2018-01-01

A well known connection between first-passage probability of random walk and distribution of electrical potential described by Laplace equation is studied. We simulate random walk in the plane numerically as a discrete time process with fixed step length. We measure first-passage probability to touch the absorbing sphere of radius R in 2D. We found a regular deviation of the first-passage probability from the exact function, which we attribute to the finiteness of the random walk step.

Hybrid intelligent methodology to design translation invariant morphological operators for Brazilian stock market prediction.

PubMed

Araújo, Ricardo de A

2010-12-01

This paper presents a hybrid intelligent methodology to design increasing translation invariant morphological operators applied to Brazilian stock market prediction (overcoming the random walk dilemma). The proposed Translation Invariant Morphological Robust Automatic phase-Adjustment (TIMRAA) method consists of a hybrid intelligent model composed of a Modular Morphological Neural Network (MMNN) with a Quantum-Inspired Evolutionary Algorithm (QIEA), which searches for the best time lags to reconstruct the phase space of the time series generator phenomenon and determines the initial (sub-optimal) parameters of the MMNN. Each individual of the QIEA population is further trained by the Back Propagation (BP) algorithm to improve the MMNN parameters supplied by the QIEA. Also, for each prediction model generated, it uses a behavioral statistical test and a phase fix procedure to adjust time phase distortions observed in stock market time series. Furthermore, an experimental analysis is conducted with the proposed method through four Brazilian stock market time series, and the achieved results are discussed and compared to results found with random walk models and the previously introduced Time-delay Added Evolutionary Forecasting (TAEF) and Morphological-Rank-Linear Time-lag Added Evolutionary Forecasting (MRLTAEF) methods. Copyright © 2010 Elsevier Ltd. All rights reserved.

Quantum walks, deformed relativity and Hopf algebra symmetries

PubMed Central

2016-01-01

We show how the Weyl quantum walk derived from principles in D'Ariano & Perinotti (D'Ariano & Perinotti 2014 Phys. Rev. A 90, 062106. (doi:10.1103/PhysRevA.90.062106)), enjoying a nonlinear Lorentz symmetry of dynamics, allows one to introduce Hopf algebras for position and momentum of the emerging particle. We focus on two special models of Hopf algebras–the usual Poincaré and the κ-Poincaré algebras. PMID:27091171

Alzheimer random walk

NASA Astrophysics Data System (ADS)

Odagaki, Takashi; Kasuya, Keisuke

2017-09-01

Using the Monte Carlo simulation, we investigate a memory-impaired self-avoiding walk on a square lattice in which a random walker marks each of sites visited with a given probability p and makes a random walk avoiding the marked sites. Namely, p = 0 and p = 1 correspond to the simple random walk and the self-avoiding walk, respectively. When p> 0, there is a finite probability that the walker is trapped. We show that the trap time distribution can well be fitted by Stacy's Weibull distribution b(a/b){a+1}/{b}[Γ({a+1}/{b})]-1x^a\\exp(-a/bx^b)} where a and b are fitting parameters depending on p. We also find that the mean trap time diverges at p = 0 as p- α with α = 1.89. In order to produce sufficient number of long walks, we exploit the pivot algorithm and obtain the mean square displacement and its Flory exponent ν(p) as functions of p. We find that the exponent determined for 1000 step walks interpolates both limits ν(0) for the simple random walk and ν(1) for the self-avoiding walk as [ ν(p) - ν(0) ] / [ ν(1) - ν(0) ] = pβ with β = 0.388 when p ≪ 0.1 and β = 0.0822 when p ≫ 0.1. Contribution to the Topical Issue "Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.

A New Random Walk for Replica Detection in WSNs.

PubMed

Aalsalem, Mohammed Y; Khan, Wazir Zada; Saad, N M; Hossain, Md Shohrab; Atiquzzaman, Mohammed; Khan, Muhammad Khurram

2016-01-01

Wireless Sensor Networks (WSNs) are vulnerable to Node Replication attacks or Clone attacks. Among all the existing clone detection protocols in WSNs, RAWL shows the most promising results by employing Simple Random Walk (SRW). More recently, RAND outperforms RAWL by incorporating Network Division with SRW. Both RAND and RAWL have used SRW for random selection of witness nodes which is problematic because of frequently revisiting the previously passed nodes that leads to longer delays, high expenditures of energy with lower probability that witness nodes intersect. To circumvent this problem, we propose to employ a new kind of constrained random walk, namely Single Stage Memory Random Walk and present a distributed technique called SSRWND (Single Stage Memory Random Walk with Network Division). In SSRWND, single stage memory random walk is combined with network division aiming to decrease the communication and memory costs while keeping the detection probability higher. Through intensive simulations it is verified that SSRWND guarantees higher witness node security with moderate communication and memory overheads. SSRWND is expedient for security oriented application fields of WSNs like military and medical.

A New Random Walk for Replica Detection in WSNs

PubMed Central

Aalsalem, Mohammed Y.; Saad, N. M.; Hossain, Md. Shohrab; Atiquzzaman, Mohammed; Khan, Muhammad Khurram

2016-01-01

Wireless Sensor Networks (WSNs) are vulnerable to Node Replication attacks or Clone attacks. Among all the existing clone detection protocols in WSNs, RAWL shows the most promising results by employing Simple Random Walk (SRW). More recently, RAND outperforms RAWL by incorporating Network Division with SRW. Both RAND and RAWL have used SRW for random selection of witness nodes which is problematic because of frequently revisiting the previously passed nodes that leads to longer delays, high expenditures of energy with lower probability that witness nodes intersect. To circumvent this problem, we propose to employ a new kind of constrained random walk, namely Single Stage Memory Random Walk and present a distributed technique called SSRWND (Single Stage Memory Random Walk with Network Division). In SSRWND, single stage memory random walk is combined with network division aiming to decrease the communication and memory costs while keeping the detection probability higher. Through intensive simulations it is verified that SSRWND guarantees higher witness node security with moderate communication and memory overheads. SSRWND is expedient for security oriented application fields of WSNs like military and medical. PMID:27409082

A proposal for the experimental detection of CSL induced random walk

PubMed Central

Bera, Sayantani; Motwani, Bhawna; Singh, Tejinder P.; Ulbricht, Hendrik

2015-01-01

Continuous Spontaneous Localization (CSL) is one possible explanation for dynamically induced collapse of the wave-function during a quantum measurement. The collapse is mediated by a stochastic non-linear modification of the Schrödinger equation. A consequence of the CSL mechanism is an extremely tiny violation of energy-momentum conservation, which can, in principle, be detected in the laboratory via the random diffusion of a particle induced by the stochastic collapse mechanism. In a paper in 2003, Collett and Pearle investigated the translational CSL diffusion of a sphere, and the rotational CSL diffusion of a disc, and showed that this effect dominates over the ambient environmental noise at low temperatures and extremely low pressures (about ten-thousandth of a pico-Torr). In the present paper, we revisit their analysis and argue that this stringent condition on pressure can be relaxed, and that the CSL effect can be seen at the pressure of about a pico-Torr. A similar analysis is provided for diffusion produced by gravity-induced decoherence, where the effect is typically much weaker than CSL. We also discuss the CSL induced random displacement of a quantum oscillator. Lastly, we propose possible experimental set-ups justifying that CSL diffusion is indeed measurable with the current technology. PMID:25563619

Random walks of colloidal probes in viscoelastic materials

NASA Astrophysics Data System (ADS)

Khan, Manas; Mason, Thomas G.

2014-04-01

To overcome limitations of using a single fixed time step in random walk simulations, such as those that rely on the classic Wiener approach, we have developed an algorithm for exploring random walks based on random temporal steps that are uniformly distributed in logarithmic time. This improvement enables us to generate random-walk trajectories of probe particles that span a highly extended dynamic range in time, thereby facilitating the exploration of probe motion in soft viscoelastic materials. By combining this faster approach with a Maxwell-Voigt model (MVM) of linear viscoelasticity, based on a slowly diffusing harmonically bound Brownian particle, we rapidly create trajectories of spherical probes in soft viscoelastic materials over more than 12 orders of magnitude in time. Appropriate windowing of these trajectories over different time intervals demonstrates that random walk for the MVM is neither self-similar nor self-affine, even if the viscoelastic material is isotropic. We extend this approach to spatially anisotropic viscoelastic materials, using binning to calculate the anisotropic mean square displacements and creep compliances along different orthogonal directions. The elimination of a fixed time step in simulations of random processes, including random walks, opens up interesting possibilities for modeling dynamics and response over a highly extended temporal dynamic range.

The Shark Random Swim - (Lévy Flight with Memory)

NASA Astrophysics Data System (ADS)

Businger, Silvia

2018-05-01

The Elephant Random Walk (ERW), first introduced by Schütz and Trimper (Phys Rev E 70:045101, 2004), is a one-dimensional simple random walk on Z having a memory about the whole past. We study the Shark Random Swim, a random walk with memory about the whole past, whose steps are α -stable distributed with α \\in (0,2] . Our aim in this work is to study the impact of the heavy tailed step distributions on the asymptotic behavior of the random walk. We shall see that, as for the ERW, the asymptotic behavior of the Shark Random Swim depends on its memory parameter p, and that a phase transition can be observed at the critical value p=1/α.

Record statistics of financial time series and geometric random walks

NASA Astrophysics Data System (ADS)

Sabir, Behlool; Santhanam, M. S.

2014-09-01

The study of record statistics of correlated series in physics, such as random walks, is gaining momentum, and several analytical results have been obtained in the past few years. In this work, we study the record statistics of correlated empirical data for which random walk models have relevance. We obtain results for the records statistics of select stock market data and the geometric random walk, primarily through simulations. We show that the distribution of the age of records is a power law with the exponent α lying in the range 1.5≤α≤1.8. Further, the longest record ages follow the Fréchet distribution of extreme value theory. The records statistics of geometric random walk series is in good agreement with that obtained from empirical stock data.

Index Theory of One Dimensional Quantum Walks and Cellular Automata

NASA Astrophysics Data System (ADS)

Gross, D.; Nesme, V.; Vogts, H.; Werner, R. F.

2012-03-01

If a one-dimensional quantum lattice system is subject to one step of a reversible discrete-time dynamics, it is intuitive that as much "quantum information" as moves into any given block of cells from the left, has to exit that block to the right. For two types of such systems — namely quantum walks and cellular automata — we make this intuition precise by defining an index, a quantity that measures the "net flow of quantum information" through the system. The index supplies a complete characterization of two properties of the discrete dynamics. First, two systems S 1, S 2 can be "pieced together", in the sense that there is a system S which acts like S 1 in one region and like S 2 in some other region, if and only if S 1 and S 2 have the same index. Second, the index labels connected components of such systems: equality of the index is necessary and sufficient for the existence of a continuous deformation of S 1 into S 2. In the case of quantum walks, the index is integer-valued, whereas for cellular automata, it takes values in the group of positive rationals. In both cases, the map {S mapsto ind S} is a group homomorphism if composition of the discrete dynamics is taken as the group law of the quantum systems. Systems with trivial index are precisely those which can be realized by partitioned unitaries, and the prototypes of systems with non-trivial index are shifts.

Quantum walks, deformed relativity and Hopf algebra symmetries.

PubMed

Bisio, Alessandro; D'Ariano, Giacomo Mauro; Perinotti, Paolo

2016-05-28

We show how the Weyl quantum walk derived from principles in D'Ariano & Perinotti (D'Ariano & Perinotti 2014Phys. Rev. A90, 062106. (doi:10.1103/PhysRevA.90.062106)), enjoying a nonlinear Lorentz symmetry of dynamics, allows one to introduce Hopf algebras for position and momentum of the emerging particle. We focus on two special models of Hopf algebras-the usual Poincaré and theκ-Poincaré algebras. © 2016 The Author(s).

New Quantum Diffusion Monte Carlo Method for strong field time dependent problems

NASA Astrophysics Data System (ADS)

Kalinski, Matt

2017-04-01

We have recently formulated the Quantum Diffusion Quantum Monte Carlo (QDMC) method for the solution of the time-dependent Schrödinger equation when it is equivalent to the reaction-diffusion system coupled by the highly nonlinear potentials of the type of Shay. Here we formulate a new Time Dependent QDMC method free of the nonlinearities described by the constant stochastic process of the coupled diffusion with transmutation. As before two kinds of diffusing particles (color walkers) are considered but which can further also transmute one into the other. Each of the species undergoes the hypothetical Einstein random walk progression with transmutation. The progressed particles transmute into the particles of the other kind before contributing to or annihilating the other particles density. This fully emulates the Time Dependent Schrödinger equation for any number of quantum particles. The negative sign of the real and the imaginary parts of the wave function is handled by the ``spinor'' densities carrying the sign as the degree of freedom. We apply the method for the exact time-dependent observation of our discovered two-electron Langmuir configurations in the magnetic and circularly polarized fields.

QCCM Center for Quantum Algorithms

DTIC Science & Technology

2008-10-17

algorithms (e.g., quantum walks and adiabatic computing ), as well as theoretical advances relating algorithms to physical implementations (e.g...Park, NC 27709-2211 15. SUBJECT TERMS Quantum algorithms, quantum computing , fault-tolerant error correction Richard Cleve MITACS East Academic...0511200 Algebraic results on quantum automata A. Ambainis, M. Beaudry, M. Golovkins, A. Kikusts, M. Mercer, D. Thrien Theory of Computing Systems 39(2006

Phenomenological picture of fluctuations in branching random walks

NASA Astrophysics Data System (ADS)

Mueller, A. H.; Munier, S.

2014-10-01

We propose a picture of the fluctuations in branching random walks, which leads to predictions for the distribution of a random variable that characterizes the position of the bulk of the particles. We also interpret the 1 /√{t } correction to the average position of the rightmost particle of a branching random walk for large times t ≫1 , computed by Ebert and Van Saarloos, as fluctuations on top of the mean-field approximation of this process with a Brunet-Derrida cutoff at the tip that simulates discreteness. Our analytical formulas successfully compare to numerical simulations of a particular model of a branching random walk.

Covering Ground: Movement Patterns and Random Walk Behavior in Aquilonastra anomala Sea Stars.

PubMed

Lohmann, Amanda C; Evangelista, Dennis; Waldrop, Lindsay D; Mah, Christopher L; Hedrick, Tyson L

2016-10-01

The paths animals take while moving through their environments affect their likelihood of encountering food and other resources; thus, models of foraging behavior abound. To collect movement data appropriate for comparison with these models, we used time-lapse photography to track movements of a small, hardy, and easy-to-obtain organism, Aquilonastra anomala sea stars. We recorded the sea stars in a tank over many hours, with and without a food cue. With food present, they covered less distance, as predicted by theory; this strategy would allow them to remain near food. We then compared the paths of the sea stars to three common models of animal movement: Brownian motion, Lévy walks, and correlated random walks; we found that the sea stars' movements most closely resembled a correlated random walk. Additionally, we compared the search performance of models of Brownian motion, a Lévy walk, and a correlated random walk to that of a model based on the sea stars' movements. We found that the behavior of the modeled sea star walk was similar to that of the modeled correlated random walk and the Brownian motion model, but that the sea star walk was slightly more likely than the other walks to find targets at intermediate distances. While organisms are unlikely to follow an idealized random walk in all details, our data suggest that comparing the effectiveness of an organism's paths to those from theory can give insight into the organism's actual movement strategy. Finally, automated optical tracking of invertebrates proved feasible, and A. anomala was revealed to be a tractable, 2D-movement study system.

Subdiffusive exciton transport in quantum dot solids.

PubMed

Akselrod, Gleb M; Prins, Ferry; Poulikakos, Lisa V; Lee, Elizabeth M Y; Weidman, Mark C; Mork, A Jolene; Willard, Adam P; Bulović, Vladimir; Tisdale, William A

2014-06-11

Colloidal quantum dots (QDs) are promising materials for use in solar cells, light-emitting diodes, lasers, and photodetectors, but the mechanism and length of exciton transport in QD materials is not well understood. We use time-resolved optical microscopy to spatially visualize exciton transport in CdSe/ZnCdS core/shell QD assemblies. We find that the exciton diffusion length, which exceeds 30 nm in some cases, can be tuned by adjusting the inorganic shell thickness and organic ligand length, offering a powerful strategy for controlling exciton movement. Moreover, we show experimentally and through kinetic Monte Carlo simulations that exciton diffusion in QD solids does not occur by a random-walk process; instead, energetic disorder within the inhomogeneously broadened ensemble causes the exciton diffusivity to decrease over time. These findings reveal new insights into exciton dynamics in disordered systems and demonstrate the flexibility of QD materials for photonic and optoelectronic applications.

Observation of topologically protected bound states in photonic quantum walks.

PubMed

Kitagawa, Takuya; Broome, Matthew A; Fedrizzi, Alessandro; Rudner, Mark S; Berg, Erez; Kassal, Ivan; Aspuru-Guzik, Alán; Demler, Eugene; White, Andrew G

2012-06-06

Topological phases exhibit some of the most striking phenomena in modern physics. Much of the rich behaviour of quantum Hall systems, topological insulators, and topological superconductors can be traced to the existence of robust bound states at interfaces between different topological phases. This robustness has applications in metrology and holds promise for future uses in quantum computing. Engineered quantum systems--notably in photonics, where wavefunctions can be observed directly--provide versatile platforms for creating and probing a variety of topological phases. Here we use photonic quantum walks to observe bound states between systems with different bulk topological properties and demonstrate their robustness to perturbations--a signature of topological protection. Although such bound states are usually discussed for static (time-independent) systems, here we demonstrate their existence in an explicitly time-dependent situation. Moreover, we discover a new phenomenon: a topologically protected pair of bound states unique to periodically driven systems.

A new time domain random walk method for solute transport in 1-D heterogeneous media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Banton, O.; Delay, F.; Porel, G.

A new method to simulate solute transport in 1-D heterogeneous media is presented. This time domain random walk method (TDRW), similar in concept to the classical random walk method, calculates the arrival time of a particle cloud at a given location (directly providing the solute breakthrough curve). The main advantage of the method is that the restrictions on the space increments and the time steps which exist with the finite differences and random walk methods are avoided. In a homogeneous zone, the breakthrough curve (BTC) can be calculated directly at a given distance using a few hundred particles or directlymore » at the boundary of the zone. Comparisons with analytical solutions and with the classical random walk method show the reliability of this method. The velocity and dispersivity calculated from the simulated results agree within two percent with the values used as input in the model. For contrasted heterogeneous media, the random walk can generate high numerical dispersion, while the time domain approach does not.« less

Spectrum of walk matrix for Koch network and its application

NASA Astrophysics Data System (ADS)

Xie, Pinchen; Lin, Yuan; Zhang, Zhongzhi

2015-06-01

Various structural and dynamical properties of a network are encoded in the eigenvalues of walk matrix describing random walks on the network. In this paper, we study the spectra of walk matrix of the Koch network, which displays the prominent scale-free and small-world features. Utilizing the particular architecture of the network, we obtain all the eigenvalues and their corresponding multiplicities. Based on the link between the eigenvalues of walk matrix and random target access time defined as the expected time for a walker going from an arbitrary node to another one selected randomly according to the steady-state distribution, we then derive an explicit solution to the random target access time for random walks on the Koch network. Finally, we corroborate our computation for the eigenvalues by enumerating spanning trees in the Koch network, using the connection governing eigenvalues and spanning trees, where a spanning tree of a network is a subgraph of the network, that is, a tree containing all the nodes.

Random walks exhibiting anomalous diffusion: elephants, urns and the limits of normality

NASA Astrophysics Data System (ADS)

Kearney, Michael J.; Martin, Richard J.

2018-01-01

A random walk model is presented which exhibits a transition from standard to anomalous diffusion as a parameter is varied. The model is a variant on the elephant random walk and differs in respect of the treatment of the initial state, which in the present work consists of a given number N of fixed steps. This also links the elephant random walk to other types of history dependent random walk. As well as being amenable to direct analysis, the model is shown to be asymptotically equivalent to a non-linear urn process. This provides fresh insights into the limiting form of the distribution of the walker’s position at large times. Although the distribution is intrinsically non-Gaussian in the anomalous diffusion regime, it gradually reverts to normal form when N is large under quite general conditions.

The Not-so-Random Drunkard's Walk

ERIC Educational Resources Information Center

Ehrhardt, George

2013-01-01

This dataset contains the results of a quasi-experiment, testing Karl Pearson's "drunkard's walk" analogy for an abstract random walk. Inspired by the alternate hypothesis that drunkards stumble to the side of their dominant hand, it includes data on intoxicated test subjects walking a 10' line. Variables include: the…

Antipersistent dynamics in kinetic models of wealth exchange

NASA Astrophysics Data System (ADS)

Goswami, Sanchari; Chatterjee, Arnab; Sen, Parongama

2011-11-01

We investigate the detailed dynamics of gains and losses made by agents in some kinetic models of wealth exchange. An earlier work suggested that a walk in an abstract gain-loss space can be conceived for the agents. For models in which agents do not save, or save with uniform saving propensity, the walk has diffusive behavior. For the case in which the saving propensity λ is distributed randomly (0≤λ<1), the resultant walk showed a ballistic nature (except at a particular value of λ*≈0.47). Here we consider several other features of the walk with random λ. While some macroscopic properties of this walk are comparable to a biased random walk, at microscopic level, there are gross differences. The difference turns out to be due to an antipersistent tendency toward making a gain (loss) immediately after making a loss (gain). This correlation is in fact present in kinetic models without saving or with uniform saving as well, such that the corresponding walks are not identical to ordinary random walks. In the distributed saving case, antipersistence occurs with a simultaneous overall bias.

Tailoring Quantum Dot Assemblies to Extend Exciton Coherence Times and Improve Exciton Transport

NASA Astrophysics Data System (ADS)

Seward, Kenton; Lin, Zhibin; Lusk, Mark

2012-02-01

The motion of excitons through nanostructured assemblies plays a central role in a wide range of physical phenomena including quantum computing, molecular electronics, photosynthetic processes, excitonic transistors and light emitting diodes. All of these technologies are severely handicapped, though, by quasi-particle lifetimes on the order of a nanosecond. The movement of excitons must therefore be as efficient as possible in order to move excitons meaningful distances. This is problematic for assemblies of small Si quantum dots (QDs), where excitons quickly localize and entangle with dot phonon modes. Ensuing exciton transport is then characterized by a classical random walk reduced to very short distances because of efficient recombination. We use a combination of master equation (Haken-Strobl) formalism and density functional theory to estimate the rate of decoherence in Si QD assemblies and its impact on exciton mobility. Exciton-phonon coupling and Coulomb interactions are calculated as a function of dot size, spacing and termination to minimize the rate of intra-dot phonon entanglement. This extends the time over which more efficient exciton transport, characterized by partial coherence, can be maintained.

A New Method of Random Environmental Walking for Assessing Behavioral Preferences for Different Lighting Applications

PubMed Central

Patching, Geoffrey R.; Rahm, Johan; Jansson, Märit; Johansson, Maria

2017-01-01

Accurate assessment of people’s preferences for different outdoor lighting applications is increasingly considered important in the development of new urban environments. Here a new method of random environmental walking is proposed to complement current methods of assessing urban lighting applications, such as self-report questionnaires. The procedure involves participants repeatedly walking between different lighting applications by random selection of a lighting application and preferred choice or by random selection of a lighting application alone. In this manner, participants are exposed to all lighting applications of interest more than once and participants’ preferences for the different lighting applications are reflected in the number of times they walk to each lighting application. On the basis of an initial simulation study, to explore the feasibility of this approach, a comprehensive field test was undertaken. The field test included random environmental walking and collection of participants’ subjective ratings of perceived pleasantness (PP), perceived quality, perceived strength, and perceived flicker of four lighting applications. The results indicate that random environmental walking can reveal participants’ preferences for different lighting applications that, in the present study, conformed to participants’ ratings of PP and perceived quality of the lighting applications. As a complement to subjectively stated environmental preferences, random environmental walking has the potential to expose behavioral preferences for different lighting applications. PMID:28337163

Adaptive random walks on the class of Web graphs

NASA Astrophysics Data System (ADS)

Tadić, B.

2001-09-01

We study random walk with adaptive move strategies on a class of directed graphs with variable wiring diagram. The graphs are grown from the evolution rules compatible with the dynamics of the world-wide Web [B. Tadić, Physica A 293, 273 (2001)], and are characterized by a pair of power-law distributions of out- and in-degree for each value of the parameter β, which measures the degree of rewiring in the graph. The walker adapts its move strategy according to locally available information both on out-degree of the visited node and in-degree of target node. A standard random walk, on the other hand, uses the out-degree only. We compute the distribution of connected subgraphs visited by an ensemble of walkers, the average access time and survival probability of the walks. We discuss these properties of the walk dynamics relative to the changes in the global graph structure when the control parameter β is varied. For β≥ 3, corresponding to the world-wide Web, the access time of the walk to a given level of hierarchy on the graph is much shorter compared to the standard random walk on the same graph. By reducing the amount of rewiring towards rigidity limit β↦βc≲ 0.1, corresponding to the range of naturally occurring biochemical networks, the survival probability of adaptive and standard random walk become increasingly similar. The adaptive random walk can be used as an efficient message-passing algorithm on this class of graphs for large degree of rewiring.

A scaling law for random walks on networks

PubMed Central

Perkins, Theodore J.; Foxall, Eric; Glass, Leon; Edwards, Roderick

2014-01-01

The dynamics of many natural and artificial systems are well described as random walks on a network: the stochastic behaviour of molecules, traffic patterns on the internet, fluctuations in stock prices and so on. The vast literature on random walks provides many tools for computing properties such as steady-state probabilities or expected hitting times. Previously, however, there has been no general theory describing the distribution of possible paths followed by a random walk. Here, we show that for any random walk on a finite network, there are precisely three mutually exclusive possibilities for the form of the path distribution: finite, stretched exponential and power law. The form of the distribution depends only on the structure of the network, while the stepping probabilities control the parameters of the distribution. We use our theory to explain path distributions in domains such as sports, music, nonlinear dynamics and stochastic chemical kinetics. PMID:25311870

A scaling law for random walks on networks

NASA Astrophysics Data System (ADS)

Perkins, Theodore J.; Foxall, Eric; Glass, Leon; Edwards, Roderick

2014-10-01

The dynamics of many natural and artificial systems are well described as random walks on a network: the stochastic behaviour of molecules, traffic patterns on the internet, fluctuations in stock prices and so on. The vast literature on random walks provides many tools for computing properties such as steady-state probabilities or expected hitting times. Previously, however, there has been no general theory describing the distribution of possible paths followed by a random walk. Here, we show that for any random walk on a finite network, there are precisely three mutually exclusive possibilities for the form of the path distribution: finite, stretched exponential and power law. The form of the distribution depends only on the structure of the network, while the stepping probabilities control the parameters of the distribution. We use our theory to explain path distributions in domains such as sports, music, nonlinear dynamics and stochastic chemical kinetics.

A scaling law for random walks on networks.

PubMed

Perkins, Theodore J; Foxall, Eric; Glass, Leon; Edwards, Roderick

2014-10-14

The dynamics of many natural and artificial systems are well described as random walks on a network: the stochastic behaviour of molecules, traffic patterns on the internet, fluctuations in stock prices and so on. The vast literature on random walks provides many tools for computing properties such as steady-state probabilities or expected hitting times. Previously, however, there has been no general theory describing the distribution of possible paths followed by a random walk. Here, we show that for any random walk on a finite network, there are precisely three mutually exclusive possibilities for the form of the path distribution: finite, stretched exponential and power law. The form of the distribution depends only on the structure of the network, while the stepping probabilities control the parameters of the distribution. We use our theory to explain path distributions in domains such as sports, music, nonlinear dynamics and stochastic chemical kinetics.

A Pearson Random Walk with Steps of Uniform Orientation and Dirichlet Distributed Lengths

NASA Astrophysics Data System (ADS)

Le Caër, Gérard

2010-08-01

A constrained diffusive random walk of n steps in ℝ d and a random flight in ℝ d , which are equivalent, were investigated independently in recent papers (J. Stat. Phys. 127:813, 2007; J. Theor. Probab. 20:769, 2007, and J. Stat. Phys. 131:1039, 2008). The n steps of the walk are independent and identically distributed random vectors of exponential length and uniform orientation. Conditioned on the sum of their lengths being equal to a given value l, closed-form expressions for the distribution of the endpoint of the walk were obtained altogether for any n for d=1,2,4. Uniform distributions of the endpoint inside a ball of radius l were evidenced for a walk of three steps in 2D and of two steps in 4D. The previous walk is generalized by considering step lengths which have independent and identical gamma distributions with a shape parameter q>0. Given the total walk length being equal to 1, the step lengths have a Dirichlet distribution whose parameters are all equal to q. The walk and the flight above correspond to q=1. Simple analytical expressions are obtained for any d≥2 and n≥2 for the endpoint distributions of two families of walks whose q are integers or half-integers which depend solely on d. These endpoint distributions have a simple geometrical interpretation. Expressed for a two-step planar walk whose q=1, it means that the distribution of the endpoint on a disc of radius 1 is identical to the distribution of the projection on the disc of a point M uniformly distributed over the surface of the 3D unit sphere. Five additional walks, with a uniform distribution of the endpoint in the inside of a ball, are found from known finite integrals of products of powers and Bessel functions of the first kind. They include four different walks in ℝ3, two of two steps and two of three steps, and one walk of two steps in ℝ4. Pearson-Liouville random walks, obtained by distributing the total lengths of the previous Pearson-Dirichlet walks according to some specified probability law are finally discussed. Examples of unconstrained random walks, whose step lengths are gamma distributed, are more particularly considered.

The First Order Correction to the Exit Distribution for Some Random Walks

NASA Astrophysics Data System (ADS)

Kennedy, Tom

2016-07-01

We study three different random walk models on several two-dimensional lattices by Monte Carlo simulations. One is the usual nearest neighbor random walk. Another is the nearest neighbor random walk which is not allowed to backtrack. The final model is the smart kinetic walk. For all three of these models the distribution of the point where the walk exits a simply connected domain D in the plane converges weakly to harmonic measure on partial D as the lattice spacing δ → 0. Let ω (0,\\cdot ;D) be harmonic measure for D, and let ω _δ (0,\\cdot ;D) be the discrete harmonic measure for one of the random walk models. Our definition of the random walk models is unusual in that we average over the orientation of the lattice with respect to the domain. We are interested in the limit of (ω _δ (0,\\cdot ;D)- ω (0,\\cdot ;D))/δ . Our Monte Carlo simulations of the three models lead to the conjecture that this limit equals c_{M,L} ρ _D(z) times Lebesgue measure with respect to arc length along the boundary, where the function ρ _D(z) depends on the domain, but not on the model or lattice, and the constant c_{M,L} depends on the model and on the lattice, but not on the domain. So there is a form of universality for this first order correction. We also give an explicit formula for the conjectured density ρ _D.

IS THE SUICIDE RATE A RANDOM WALK?

PubMed

Yang, Bijou; Lester, David; Lyke, Jennifer; Olsen, Robert

2015-06-01

The yearly suicide rates for the period 1933-2010 and the daily suicide numbers for 1990 and 1991 were examined for whether the distribution of difference scores (from year to year and from day to day) fitted a normal distribution, a characteristic of stochastic processes that follow a random walk. If the suicide rate were a random walk, then any disturbance to the suicide rate would have a permanent effect and national suicide prevention efforts would likely fail. The distribution of difference scores from day to day (but not the difference scores from year to year) fitted a normal distribution and, therefore, were consistent with a random walk.

Resonant quantum kicked rotor with two internal levels

NASA Astrophysics Data System (ADS)

Hernández, Guzmán; Romanelli, Alejandro

2013-04-01

We study a system consisting of a quantum kicked rotor with an additional degree of freedom. We show analytically and numerically that this model is characterized by its quantum resonances with ballistic spreading and by the entanglement between the internal and momentum degrees of freedom. We conclude that the model shows certain interesting similarities with the standard quantum walk on the line.

A New Family of Solvable Pearson-Dirichlet Random Walks

NASA Astrophysics Data System (ADS)

Le Caër, Gérard

2011-07-01

An n-step Pearson-Gamma random walk in ℝ d starts at the origin and consists of n independent steps with gamma distributed lengths and uniform orientations. The gamma distribution of each step length has a shape parameter q>0. Constrained random walks of n steps in ℝ d are obtained from the latter walks by imposing that the sum of the step lengths is equal to a fixed value. Simple closed-form expressions were obtained in particular for the distribution of the endpoint of such constrained walks for any d≥ d 0 and any n≥2 when q is either q = d/2 - 1 ( d 0=3) or q= d-1 ( d 0=2) (Le Caër in J. Stat. Phys. 140:728-751, 2010). When the total walk length is chosen, without loss of generality, to be equal to 1, then the constrained step lengths have a Dirichlet distribution whose parameters are all equal to q and the associated walk is thus named a Pearson-Dirichlet random walk. The density of the endpoint position of a n-step planar walk of this type ( n≥2), with q= d=2, was shown recently to be a weighted mixture of 1+ floor( n/2) endpoint densities of planar Pearson-Dirichlet walks with q=1 (Beghin and Orsingher in Stochastics 82:201-229, 2010). The previous result is generalized to any walk space dimension and any number of steps n≥2 when the parameter of the Pearson-Dirichlet random walk is q= d>1. We rely on the connection between an unconstrained random walk and a constrained one, which have both the same n and the same q= d, to obtain a closed-form expression of the endpoint density. The latter is a weighted mixture of 1+ floor( n/2) densities with simple forms, equivalently expressed as a product of a power and a Gauss hypergeometric function. The weights are products of factors which depends both on d and n and Bessel numbers independent of d.

Self-Attractive Random Walks: The Case of Critical Drifts

NASA Astrophysics Data System (ADS)

Ioffe, Dmitry; Velenik, Yvan

2012-07-01

Self-attractive random walks (polymers) undergo a phase transition in terms of the applied drift (force): If the drift is strong enough, then the walk is ballistic, whereas in the case of small drifts self-attraction wins and the walk is sub-ballistic. We show that, in any dimension d ≥ 2, this transition is of first order. In fact, we prove that the walk is already ballistic at critical drifts, and establish the corresponding LLN and CLT.

Parallelizing quantum circuit synthesis

NASA Astrophysics Data System (ADS)

Di Matteo, Olivia; Mosca, Michele

2016-03-01

Quantum circuit synthesis is the process in which an arbitrary unitary operation is decomposed into a sequence of gates from a universal set, typically one which a quantum computer can implement both efficiently and fault-tolerantly. As physical implementations of quantum computers improve, the need is growing for tools that can effectively synthesize components of the circuits and algorithms they will run. Existing algorithms for exact, multi-qubit circuit synthesis scale exponentially in the number of qubits and circuit depth, leaving synthesis intractable for circuits on more than a handful of qubits. Even modest improvements in circuit synthesis procedures may lead to significant advances, pushing forward the boundaries of not only the size of solvable circuit synthesis problems, but also in what can be realized physically as a result of having more efficient circuits. We present a method for quantum circuit synthesis using deterministic walks. Also termed pseudorandom walks, these are walks in which once a starting point is chosen, its path is completely determined. We apply our method to construct a parallel framework for circuit synthesis, and implement one such version performing optimal T-count synthesis over the Clifford+T gate set. We use our software to present examples where parallelization offers a significant speedup on the runtime, as well as directly confirm that the 4-qubit 1-bit full adder has optimal T-count 7 and T-depth 3.

The Dynamical Classification of Centaurs which Evolve into Comets

NASA Astrophysics Data System (ADS)

Wood, Jeremy R.; Horner, Jonathan; Hinse, Tobias; Marsden, Stephen; Swinburne University of Technology

2016-10-01

Centaurs are small Solar system bodies with semi-major axes between Jupiter and Neptune and perihelia beyond Jupiter. Centaurs can be further subclassified into two dynamical categories - random walk and resonance hopping. Random walk Centaurs have mean square semi-major axes (< a2 >) which vary in time according to a generalized diffusion equation where < a2 > ~t2H. H is the Hurst exponent with 0 < H < 1, and t is time. The behavior of < a2 > for resonance hopping Centaurs is not well described by generalized diffusion.The aim of this study is to determine which dynamical type of Centaur is most likely to evolve into each class of comet. 31,722 fictional massless test particles were integrated for 3 Myr in the 6-body problem (Sun, Jovian planets, test particle). Initially each test particle was a member of one of four groups. The semi-major axes of all test particles in a group were clustered within 0.27 au from a first order, interior Mean Motion resonance of Neptune. The resonances were centered at 18.94 au, 22.95 au, 24.82 au and 28.37 au.If the perihelion of a test particle reached < 4 au then the test particle was considered to be a comet and classified as either a random walk or resonance hopping Centaur. The results showed that over 4,000 test particles evolved into comets within 3 Myr. 59% of these test particles were random walk and 41% were resonance hopping. The behavior of the semi-major axis in time was usually well described by generalized diffusion for random walk Centaurs (ravg = 0.98) and poorly described for resonance hopping Centaurs (ravg = 0.52). The average Hurst exponent was 0.48 for random walk Centaurs and 0.20 for resonance hopping Centaurs. Random walk Centaurs were more likely to evolve into short period comets while resonance hopping Centaurs were more likely to evolve into long period comets. For each initial cluster, resonance hopping Centaurs took longer to evolve into comets than random walk Centaurs. Overall the population of random walk Centaurs averaged 143 kyr to evolve into comets, and the population of resonance hopping Centaurs averaged 164 kyr.

Coherent exciton transport in dendrimers and continuous-time quantum walks

NASA Astrophysics Data System (ADS)

Mülken, Oliver; Bierbaum, Veronika; Blumen, Alexander

2006-03-01

We model coherent exciton transport in dendrimers by continuous-time quantum walks. For dendrimers up to the second generation the coherent transport shows perfect recurrences when the initial excitation starts at the central node. For larger dendrimers, the recurrence ceases to be perfect, a fact which resembles results for discrete quantum carpets. Moreover, depending on the initial excitation site, we find that the coherent transport to certain nodes of the dendrimer has a very low probability. When the initial excitation starts from the central node, the problem can be mapped onto a line which simplifies the computational effort. Furthermore, the long time average of the quantum mechanical transition probabilities between pairs of nodes shows characteristic patterns and allows us to classify the nodes into clusters with identical limiting probabilities. For the (space) average of the quantum mechanical probability to be still or to be again at the initial site, we obtain, based on the Cauchy-Schwarz inequality, a simple lower bound which depends only on the eigenvalue spectrum of the Hamiltonian.

Pólya number and first return of bursty random walk: Rigorous solutions

NASA Astrophysics Data System (ADS)

Wan, J.; Xu, X. P.

2012-03-01

The recurrence properties of random walks can be characterized by Pólya number, i.e., the probability that the walker has returned to the origin at least once. In this paper, we investigate Pólya number and first return for bursty random walk on a line, in which the walk has different step size and moving probabilities. Using the concept of the Catalan number, we obtain exact results for first return probability, the average first return time and Pólya number for the first time. We show that Pólya number displays two different functional behavior when the walk deviates from the recurrent point. By utilizing the Lagrange inversion formula, we interpret our findings by transferring Pólya number to the closed-form solutions of an inverse function. We also calculate Pólya number using another approach, which corroborates our results and conclusions. Finally, we consider the recurrence properties and Pólya number of two variations of the bursty random walk model.

Mesoscopic description of random walks on combs

NASA Astrophysics Data System (ADS)

Méndez, Vicenç; Iomin, Alexander; Campos, Daniel; Horsthemke, Werner

2015-12-01

Combs are a simple caricature of various types of natural branched structures, which belong to the category of loopless graphs and consist of a backbone and branches. We study continuous time random walks on combs and present a generic method to obtain their transport properties. The random walk along the branches may be biased, and we account for the effect of the branches by renormalizing the waiting time probability distribution function for the motion along the backbone. We analyze the overall diffusion properties along the backbone and find normal diffusion, anomalous diffusion, and stochastic localization (diffusion failure), respectively, depending on the characteristics of the continuous time random walk along the branches, and compare our analytical results with stochastic simulations.

Home-based walking during pregnancy affects mood and birth outcomes among sedentary women: A randomized controlled trial.

PubMed

Taniguchi, Chie; Sato, Chifumi

2016-10-01

We examined the effects of home-based walking on sedentary Japanese women's pregnancy outcomes and mood. A randomized controlled trial was conducted, involving 118 women aged 22-36 years. Participants were randomly assigned to walking intervention (n = 60) or control (n = 58) groups. The walking group was instructed to walk briskly for 30 min, three times weekly from 30 weeks' gestation until delivery. Both groups counted their daily steps using pedometers. Pregnancy and delivery outcomes were assessed, participants completed the Profile of Mood States, and we used the intention-to-treat principle. Groups showed no differences regarding pregnancy or delivery outcomes. The walking group exhibited decreased scores on the depression-dejection and confusion subscales of the Profile of Mood States. Five of the 54 women in the intervention group who remained in the study (9.2%) completed 100% of the prescribed walking program; 32 (59.3%) women completed 80% or more. Unsupervised walking improves sedentary pregnant women's mood, indicating that regular walking during pregnancy should be promoted in this group. © 2016 John Wiley & Sons Australia, Ltd.

The one-dimensional asymmetric persistent random walk

NASA Astrophysics Data System (ADS)

Rossetto, Vincent

2018-04-01

Persistent random walks are intermediate transport processes between a uniform rectilinear motion and a Brownian motion. They are formed by successive steps of random finite lengths and directions travelled at a fixed speed. The isotropic and symmetric 1D persistent random walk is governed by the telegrapher’s equation, also called the hyperbolic heat conduction equation. These equations have been designed to resolve the paradox of the infinite speed in the heat and diffusion equations. The finiteness of both the speed and the correlation length leads to several classes of random walks: Persistent random walk in one dimension can display anomalies that cannot arise for Brownian motion such as anisotropy and asymmetries. In this work we focus on the case where the mean free path is anisotropic, the only anomaly leading to a physics that is different from the telegrapher’s case. We derive exact expression of its Green’s function, for its scattering statistics and distribution of first-passage time at the origin. The phenomenology of the latter shows a transition for quantities like the escape probability and the residence time.

An invariance property of generalized Pearson random walks in bounded geometries

NASA Astrophysics Data System (ADS)

Mazzolo, Alain

2009-03-01

Invariance properties of random walks in bounded domains are a topic of growing interest since they contribute to improving our understanding of diffusion in confined geometries. Recently, limited to Pearson random walks with exponentially distributed straight paths, it has been shown that under isotropic uniform incidence, the average length of the trajectories through the domain is independent of the random walk characteristic and depends only on the ratio of the volume's domain over its surface. In this paper, thanks to arguments of integral geometry, we generalize this property to any isotropic bounded stochastic process and we give the conditions of its validity for isotropic unbounded stochastic processes. The analytical form for the traveled distance from the boundary to the first scattering event that ensures the validity of the Cauchy formula is also derived. The generalization of the Cauchy formula is an analytical constraint that thus concerns a very wide range of stochastic processes, from the original Pearson random walk to a Rayleigh distribution of the displacements, covering many situations of physical importance.

Human mammary epithelial cells exhibit a bimodal correlated random walk pattern.

PubMed

Potdar, Alka A; Jeon, Junhwan; Weaver, Alissa M; Quaranta, Vito; Cummings, Peter T

2010-03-10

Organisms, at scales ranging from unicellular to mammals, have been known to exhibit foraging behavior described by random walks whose segments confirm to Lévy or exponential distributions. For the first time, we present evidence that single cells (mammary epithelial cells) that exist in multi-cellular organisms (humans) follow a bimodal correlated random walk (BCRW). Cellular tracks of MCF-10A pBabe, neuN and neuT random migration on 2-D plastic substrates, analyzed using bimodal analysis, were found to reveal the BCRW pattern. We find two types of exponentially distributed correlated flights (corresponding to what we refer to as the directional and re-orientation phases) each having its own correlation between move step-lengths within flights. The exponential distribution of flight lengths was confirmed using different analysis methods (logarithmic binning with normalization, survival frequency plots and maximum likelihood estimation). Because of the presence of non-uniform turn angle distribution of move step-lengths within a flight and two different types of flights, we propose that the epithelial random walk is a BCRW comprising of two alternating modes with varying degree of correlations, rather than a simple persistent random walk. A BCRW model rather than a simple persistent random walk correctly matches the super-diffusivity in the cell migration paths as indicated by simulations based on the BCRW model.

Contact Time in Random Walk and Random Waypoint: Dichotomy in Tail Distribution

NASA Astrophysics Data System (ADS)

Zhao, Chen; Sichitiu, Mihail L.

Contact time (or link duration) is a fundamental factor that affects performance in Mobile Ad Hoc Networks. Previous research on theoretical analysis of contact time distribution for random walk models (RW) assume that the contact events can be modeled as either consecutive random walks or direct traversals, which are two extreme cases of random walk, thus with two different conclusions. In this paper we conduct a comprehensive research on this topic in the hope of bridging the gap between the two extremes. The conclusions from the two extreme cases will result in a power-law or exponential tail in the contact time distribution, respectively. However, we show that the actual distribution will vary between the two extremes: a power-law-sub-exponential dichotomy, whose transition point depends on the average flight duration. Through simulation results we show that such conclusion also applies to random waypoint.

Existence of the Harmonic Measure for Random Walks on Graphs and in Random Environments

NASA Astrophysics Data System (ADS)

Boivin, Daniel; Rau, Clément

2013-01-01

We give a sufficient condition for the existence of the harmonic measure from infinity of transient random walks on weighted graphs. In particular, this condition is verified by the random conductance model on ℤ d , d≥3, when the conductances are i.i.d. and the bonds with positive conductance percolate. The harmonic measure from infinity also exists for random walks on supercritical clusters of ℤ2. This is proved using results of Barlow (Ann. Probab. 32:3024-3084, 2004) and Barlow and Hambly (Electron. J. Probab. 14(1):1-27, 2009).

Random walk study of electron motion in helium in crossed electromagnetic fields

NASA Technical Reports Server (NTRS)

Englert, G. W.

1972-01-01

Random walk theory, previously adapted to electron motion in the presence of an electric field, is extended to include a transverse magnetic field. In principle, the random walk approach avoids mathematical complexity and concomitant simplifying assumptions and permits determination of energy distributions and transport coefficients within the accuracy of available collisional cross section data. Application is made to a weakly ionized helium gas. Time of relaxation of electron energy distribution, determined by the random walk, is described by simple expressions based on energy exchange between the electron and an effective electric field. The restrictive effect of the magnetic field on electron motion, which increases the required number of collisions per walk to reach a terminal steady state condition, as well as the effect of the magnetic field on electron transport coefficients and mean energy can be quite adequately described by expressions involving only the Hall parameter.

Noteworthy fractal features and transport properties of Cantor tartans

NASA Astrophysics Data System (ADS)

Balankin, Alexander S.; Golmankhaneh, Alireza K.; Patiño-Ortiz, Julián; Patiño-Ortiz, Miguel

2018-06-01

This Letter is focused on the impact of fractal topology on the transport processes governed by different kinds of random walks on Cantor tartans. We establish that the spectral dimension of the infinitely ramified Cantor tartan ds is equal to its fractal (self-similarity) dimension D. Consequently, the random walk on the Cantor tartan leads to a normal diffusion. On the other hand, the fractal geometry of Cantor tartans allows for a natural definition of power-law distributions of the waiting times and step lengths of random walkers. These distributions are Lévy stable if D > 1.5. Accordingly, we found that the random walk with rests leads to sub-diffusion, whereas the Lévy walk leads to ballistic diffusion. The Lévy walk with rests leads to super-diffusion, if D >√{ 3 }, or sub-diffusion, if 1.5 < D <√{ 3 }.

Self-avoiding walks on scale-free networks

NASA Astrophysics Data System (ADS)

Herrero, Carlos P.

2005-01-01

Several kinds of walks on complex networks are currently used to analyze search and navigation in different systems. Many analytical and computational results are known for random walks on such networks. Self-avoiding walks (SAW’s) are expected to be more suitable than unrestricted random walks to explore various kinds of real-life networks. Here we study long-range properties of random SAW’s on scale-free networks, characterized by a degree distribution P (k) ˜ k-γ . In the limit of large networks (system size N→∞ ), the average number sn of SAW’s starting from a generic site increases as μn , with μ= < k2 > / -1 . For finite N , sn is reduced due to the presence of loops in the network, which causes the emergence of attrition of the paths. For kinetic growth walks, the average maximum length increases as a power of the system size: ˜ Nα , with an exponent α increasing as the parameter γ is raised. We discuss the dependence of α on the minimum allowed degree in the network. A similar power-law dependence is found for the mean self-intersection length of nonreversal random walks. Simulation results support our approximate analytical calculations.

Two-Dimensional Anisotropic Random Walks: Fixed Versus Random Column Configurations for Transport Phenomena

NASA Astrophysics Data System (ADS)

Csáki, Endre; Csörgő, Miklós; Földes, Antónia; Révész, Pál

2018-04-01

We consider random walks on the square lattice of the plane along the lines of Heyde (J Stat Phys 27:721-730, 1982, Stochastic processes, Springer, New York, 1993) and den Hollander (J Stat Phys 75:891-918, 1994), whose studies have in part been inspired by the so-called transport phenomena of statistical physics. Two-dimensional anisotropic random walks with anisotropic density conditions á la Heyde (J Stat Phys 27:721-730, 1982, Stochastic processes, Springer, New York, 1993) yield fixed column configurations and nearest-neighbour random walks in a random environment on the square lattice of the plane as in den Hollander (J Stat Phys 75:891-918, 1994) result in random column configurations. In both cases we conclude simultaneous weak Donsker and strong Strassen type invariance principles in terms of appropriately constructed anisotropic Brownian motions on the plane, with self-contained proofs in both cases. The style of presentation throughout will be that of a semi-expository survey of related results in a historical context.

Random walk of passive tracers among randomly moving obstacles.

PubMed

Gori, Matteo; Donato, Irene; Floriani, Elena; Nardecchia, Ilaria; Pettini, Marco

2016-04-14

This study is mainly motivated by the need of understanding how the diffusion behavior of a biomolecule (or even of a larger object) is affected by other moving macromolecules, organelles, and so on, inside a living cell, whence the possibility of understanding whether or not a randomly walking biomolecule is also subject to a long-range force field driving it to its target. By means of the Continuous Time Random Walk (CTRW) technique the topic of random walk in random environment is here considered in the case of a passively diffusing particle among randomly moving and interacting obstacles. The relevant physical quantity which is worked out is the diffusion coefficient of the passive tracer which is computed as a function of the average inter-obstacles distance. The results reported here suggest that if a biomolecule, let us call it a test molecule, moves towards its target in the presence of other independently interacting molecules, its motion can be considerably slowed down.

Two-Dimensional Anisotropic Random Walks: Fixed Versus Random Column Configurations for Transport Phenomena

NASA Astrophysics Data System (ADS)

Csáki, Endre; Csörgő, Miklós; Földes, Antónia; Révész, Pál

2018-06-01

We consider random walks on the square lattice of the plane along the lines of Heyde (J Stat Phys 27:721-730, 1982, Stochastic processes, Springer, New York, 1993) and den Hollander (J Stat Phys 75:891-918, 1994), whose studies have in part been inspired by the so-called transport phenomena of statistical physics. Two-dimensional anisotropic random walks with anisotropic density conditions á la Heyde (J Stat Phys 27:721-730, 1982, Stochastic processes, Springer, New York, 1993) yield fixed column configurations and nearest-neighbour random walks in a random environment on the square lattice of the plane as in den Hollander (J Stat Phys 75:891-918, 1994) result in random column configurations. In both cases we conclude simultaneous weak Donsker and strong Strassen type invariance principles in terms of appropriately constructed anisotropic Brownian motions on the plane, with self-contained proofs in both cases. The style of presentation throughout will be that of a semi-expository survey of related results in a historical context.

Origins and applications of the Montroll-Weiss continuous time random walk

NASA Astrophysics Data System (ADS)

Shlesinger, Michael F.

2017-05-01

The Continuous Time Random Walk (CTRW) was introduced by Montroll and Weiss in 1965 in a purely mathematical paper. Its antecedents and later applications beginning in 1973 are discussed, especially for the case of fractal time where the mean waiting time between jumps is infinite. Contribution to the Topical Issue: "Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.

Random walks with shape prior for cochlea segmentation in ex vivo μCT.

PubMed

Ruiz Pujadas, Esmeralda; Kjer, Hans Martin; Piella, Gemma; Ceresa, Mario; González Ballester, Miguel Angel

2016-09-01

Cochlear implantation is a safe and effective surgical procedure to restore hearing in deaf patients. However, the level of restoration achieved may vary due to differences in anatomy, implant type and surgical access. In order to reduce the variability of the surgical outcomes, we previously proposed the use of a high-resolution model built from [Formula: see text] images and then adapted to patient-specific clinical CT scans. As the accuracy of the model is dependent on the precision of the original segmentation, it is extremely important to have accurate [Formula: see text] segmentation algorithms. We propose a new framework for cochlea segmentation in ex vivo [Formula: see text] images using random walks where a distance-based shape prior is combined with a region term estimated by a Gaussian mixture model. The prior is also weighted by a confidence map to adjust its influence according to the strength of the image contour. Random walks is performed iteratively, and the prior mask is aligned in every iteration. We tested the proposed approach in ten [Formula: see text] data sets and compared it with other random walks-based segmentation techniques such as guided random walks (Eslami et al. in Med Image Anal 17(2):236-253, 2013) and constrained random walks (Li et al. in Advances in image and video technology. Springer, Berlin, pp 215-226, 2012). Our approach demonstrated higher accuracy results due to the probability density model constituted by the region term and shape prior information weighed by a confidence map. The weighted combination of the distance-based shape prior with a region term into random walks provides accurate segmentations of the cochlea. The experiments suggest that the proposed approach is robust for cochlea segmentation.

A short walk in quantum probability

NASA Astrophysics Data System (ADS)

Hudson, Robin

2018-04-01

This is a personal survey of aspects of quantum probability related to the Heisenberg commutation relation for canonical pairs. Using the failure, in general, of non-negativity of the Wigner distribution for canonical pairs to motivate a more satisfactory quantum notion of joint distribution, we visit a central limit theorem for such pairs and a resulting family of quantum planar Brownian motions which deform the classical planar Brownian motion, together with a corresponding family of quantum stochastic areas. This article is part of the themed issue `Hilbert's sixth problem'.

Random walks with long-range steps generated by functions of Laplacian matrices

NASA Astrophysics Data System (ADS)

Riascos, A. P.; Michelitsch, T. M.; Collet, B. A.; Nowakowski, A. F.; Nicolleau, F. C. G. A.

2018-04-01

In this paper, we explore different Markovian random walk strategies on networks with transition probabilities between nodes defined in terms of functions of the Laplacian matrix. We generalize random walk strategies with local information in the Laplacian matrix, that describes the connections of a network, to a dynamic determined by functions of this matrix. The resulting processes are non-local allowing transitions of the random walker from one node to nodes beyond its nearest neighbors. We find that only two types of Laplacian functions are admissible with distinct behaviors for long-range steps in the infinite network limit: type (i) functions generate Brownian motions, type (ii) functions Lévy flights. For this asymptotic long-range step behavior only the lowest non-vanishing order of the Laplacian function is relevant, namely first order for type (i), and fractional order for type (ii) functions. In the first part, we discuss spectral properties of the Laplacian matrix and a series of relations that are maintained by a particular type of functions that allow to define random walks on any type of undirected connected networks. Once described general properties, we explore characteristics of random walk strategies that emerge from particular cases with functions defined in terms of exponentials, logarithms and powers of the Laplacian as well as relations of these dynamics with non-local strategies like Lévy flights and fractional transport. Finally, we analyze the global capacity of these random walk strategies to explore networks like lattices and trees and different types of random and complex networks.

Estimating rate uncertainty with maximum likelihood: differences between power-law and flicker–random-walk models

USGS Publications Warehouse

Langbein, John O.

2012-01-01

Recent studies have documented that global positioning system (GPS) time series of position estimates have temporal correlations which have been modeled as a combination of power-law and white noise processes. When estimating quantities such as a constant rate from GPS time series data, the estimated uncertainties on these quantities are more realistic when using a noise model that includes temporal correlations than simply assuming temporally uncorrelated noise. However, the choice of the specific representation of correlated noise can affect the estimate of uncertainty. For many GPS time series, the background noise can be represented by either: (1) a sum of flicker and random-walk noise or, (2) as a power-law noise model that represents an average of the flicker and random-walk noise. For instance, if the underlying noise model is a combination of flicker and random-walk noise, then incorrectly choosing the power-law model could underestimate the rate uncertainty by a factor of two. Distinguishing between the two alternate noise models is difficult since the flicker component can dominate the assessment of the noise properties because it is spread over a significant portion of the measurable frequency band. But, although not necessarily detectable, the random-walk component can be a major constituent of the estimated rate uncertainty. None the less, it is possible to determine the upper bound on the random-walk noise.

Sunspot random walk and 22-year variation

USGS Publications Warehouse

Love, Jeffrey J.; Rigler, E. Joshua

2012-01-01

We examine two stochastic models for consistency with observed long-term secular trends in sunspot number and a faint, but semi-persistent, 22-yr signal: (1) a null hypothesis, a simple one-parameter random-walk model of sunspot-number cycle-to-cycle change, and, (2) an alternative hypothesis, a two-parameter random-walk model with an imposed 22-yr alternating amplitude. The observed secular trend in sunspots, seen from solar cycle 5 to 23, would not be an unlikely result of the accumulation of multiple random-walk steps. Statistical tests show that a 22-yr signal can be resolved in historical sunspot data; that is, the probability is low that it would be realized from random data. On the other hand, the 22-yr signal has a small amplitude compared to random variation, and so it has a relatively small effect on sunspot predictions. Many published predictions for cycle 24 sunspots fall within the dispersion of previous cycle-to-cycle sunspot differences. The probability is low that the Sun will, with the accumulation of random steps over the next few cycles, walk down to a Dalton-like minimum. Our models support published interpretations of sunspot secular variation and 22-yr variation resulting from cycle-to-cycle accumulation of dynamo-generated magnetic energy.

Short-term and practice effects of metronome pacing in Parkinson's disease patients with gait freezing while in the 'on' state: randomized single blind evaluation.

PubMed

Cubo, Esther; Leurgans, Sue; Goetz, Christopher G

2004-12-01

In a randomized single blind parallel study, we tested the efficacy of an auditory metronome on walking speed and freezing in Parkinson's disease (PD) patients with freezing gait impairment during their 'on' function. No pharmacological treatment is effective in managing 'on' freezing in PD. Like visual cues that can help overcome freezing, rhythmic auditory pacing may provide cues that help normalize walking pace and overcome freezing. Non-demented PD patients with freezing during their 'on' state walked under two conditions, in randomized order: unassisted walking and walking with the use of an audiocassette with a metronome recording. The walking trials were randomized and gait variables were rated from videotapes by a blinded evaluator. Outcome measures were total walking time (total trial time-total freezing time), which was considered the time over a course of specified length, freezing time, average freeze duration and number of freezes. All outcomes were averaged across trials for each person and then compared across conditions using Signed Rank tests. Twelve non-demented PD patients with a mean age of 65.8 +/- 11.2 years, and mean PD duration of 12.4 +/- 7.3 years were included. The use of the metronome slowed ambulation and increased the total walking time (P < 0.0005) only during the first visit, without affecting any freezing variable. In the nine patients who took the metronome recording home and used it daily for 1 week while walking, freezing remained unimproved. Though advocated in prior publications as a walking aid for PD patients, auditory metronome pacing slows walking and is not a beneficial intervention for freezing during their 'on' periods.

A randomized controlled trial to evaluate the feasibility of the Wii Fit for improving walking in older adults with lower limb amputation.

PubMed

Imam, Bita; Miller, William C; Finlayson, Heather; Eng, Janice J; Jarus, Tal

2017-01-01

To assess the feasibility of Wii.n.Walk for improving walking capacity in older adults with lower limb amputation. A parallel, evaluator-blind randomized controlled feasibility trial. Community-living. Individuals who were ⩾50 years old with a unilateral lower limb amputation. Wii.n.Walk consisted of Wii Fit training, 3x/week (40 minute sessions), for 4 weeks. Training started in the clinic in groups of 3 and graduated to unsupervised home training. Control group were trained using cognitive games. Feasibility indicators: trial process (recruitment, retention, participants' perceived benefit from the Wii.n.Walk intervention measured by exit questionnaire), resources (adherence), management (participant processing, blinding), and treatment (adverse event, and Cohen's d effect size and variance). Primary clinical outcome: walking capacity measured using the 2 Minute Walk Test at baseline, end of treatment, and 3-week retention. Of 28 randomized participants, 24 completed the trial (12/arm). Median (range) age was 62.0 (50-78) years. Mean (SD) score for perceived benefit from the Wii.n.Walk intervention was 38.9/45 (6.8). Adherence was 83.4%. The effect sizes for the 2 Minute Walk Test were 0.5 (end of treatment) and 0.6 (3-week retention) based on intention to treat with imputed data; and 0.9 (end of treatment) and 1.2 (3-week retention) based on per protocol analysis. The required sample size for a future larger RCT was deemed to be 72 (36 per arm). The results suggested the feasibility of the Wii.n.Walk with a medium effect size for improving walking capacity. Future larger randomized controlled trials investigating efficacy are warranted.

Some Metric Properties of Planar Gaussian Free Field

NASA Astrophysics Data System (ADS)

Goswami, Subhajit

In this thesis we study the properties of some metrics arising from two-dimensional Gaussian free field (GFF), namely the Liouville first-passage percolation (Liouville FPP), the Liouville graph distance and an effective resistance metric. In Chapter 1, we define these metrics as well as discuss the motivations for studying them. Roughly speaking, Liouville FPP is the shortest path metric in a planar domain D where the length of a path P is given by ∫Pe gammah(z)|dz| where h is the GFF on D and gamma > 0. In Chapter 2, we present an upper bound on the expected Liouville FPP distance between two typical points for small values of gamma (the near-Euclidean regime). A similar upper bound is derived in Chapter 3 for the Liouville graph distance which is, roughly, the minimal number of Euclidean balls with comparable Liouville quantum gravity (LQG) measure whose union contains a continuous path between two endpoints. Our bounds seem to be in disagreement with Watabiki's prediction (1993) on the random metric of Liouville quantum gravity in this regime. The contents of these two chapters are based on a joint work with Jian Ding. In Chapter 4, we derive some asymptotic estimates for effective resistances on a random network which is defined as follows. Given any gamma > 0 and for eta = {etav}v∈Z2 denoting a sample of the two-dimensional discrete Gaussian free field on Z2 pinned at the origin, we equip the edge ( u, v) with conductance egamma(etau + eta v). The metric structure of effective resistance plays a crucial role in our proof of the main result in Chapter 4. The primary motivation behind this metric is to understand the random walk on Z 2 where the edge (u, v) has weight egamma(etau + etav). Using the estimates from Chapter 4 we show in Chapter 5 that for almost every eta, this random walk is recurrent and that, with probability tending to 1 as T → infinity, the return probability at time 2T decays as T-1+o(1). In addition, we prove a version of subdiffusive behavior by showing that the expected exit time from a ball of radius N scales as Npsi(gamma)+o(1) with psi(gamma) > 2 for all gamma > 0. The contents of these chapters are based on a joint work with Marek Biskup and Jian Ding.

Reviews Book: Marie Curie: A Biography Book: Fast Car Physics Book: Beautiful Invisible Equipment: Fun Fly Stick Science Kit Book: Quantum Theory Cannot Hurt You Book: Chaos: The Science of Predictable Random Motion Book: Seven Wonders of the Universe Book: Special Relativity Equipment: LabVIEWTM 2009 Education Edition Places to Visit: Edison and Ford Winter Estates Places to Visit: The Computer History Museum Web Watch

NASA Astrophysics Data System (ADS)

2011-07-01

WE RECOMMEND Fun Fly Stick Science Kit Fun fly stick introduces electrostatics to youngsters Special Relativity Text makes a useful addition to the study of relativity as an undergraduate LabVIEWTM 2009 Education Edition LabVIEW sets industry standard for gathering and analysing data, signal processing, instrumentation design and control, and automation and robotics Edison and Ford Winter Estates Thomas Edison's home is open to the public The Computer History Museum Take a walk through technology history at this computer museum WORTH A LOOK Fast Car Physics Book races through physics Beautiful Invisible The main subject of this book is theoretical physics Quantum Theory Cannot Hurt You A guide to physics on the large and small scale Chaos: The Science of Predictable Random Motion Book explores the mathematics behind chaotic behaviour Seven Wonders of the Universe A textual trip through the wonderful universe HANDLE WITH CARE Marie Curie: A Biography Book fails to capture Curie's science WEB WATCH Web clips to liven up science lessons

In the eye of the beholder: Inhomogeneous distribution of high-resolution shapes within the random-walk ensemble

NASA Astrophysics Data System (ADS)

Müller, Christian L.; Sbalzarini, Ivo F.; van Gunsteren, Wilfred F.; Žagrović, Bojan; Hünenberger, Philippe H.

2009-06-01

The concept of high-resolution shapes (also referred to as folds or states, depending on the context) of a polymer chain plays a central role in polymer science, structural biology, bioinformatics, and biopolymer dynamics. However, although the idea of shape is intuitively very useful, there is no unambiguous mathematical definition for this concept. In the present work, the distributions of high-resolution shapes within the ideal random-walk ensembles with N =3,…,6 beads (or up to N =10 for some properties) are investigated using a systematic (grid-based) approach based on a simple working definition of shapes relying on the root-mean-square atomic positional deviation as a metric (i.e., to define the distance between pairs of structures) and a single cutoff criterion for the shape assignment. Although the random-walk ensemble appears to represent the paramount of homogeneity and randomness, this analysis reveals that the distribution of shapes within this ensemble, i.e., in the total absence of interatomic interactions characteristic of a specific polymer (beyond the generic connectivity constraint), is significantly inhomogeneous. In particular, a specific (densest) shape occurs with a local probability that is 1.28, 1.79, 2.94, and 10.05 times (N =3,…,6) higher than the corresponding average over all possible shapes (these results can tentatively be extrapolated to a factor as large as about 1028 for N =100). The qualitative results of this analysis lead to a few rather counterintuitive suggestions, namely, that, e.g., (i) a fold classification analysis applied to the random-walk ensemble would lead to the identification of random-walk "folds;" (ii) a clustering analysis applied to the random-walk ensemble would also lead to the identification random-walk "states" and associated relative free energies; and (iii) a random-walk ensemble of polymer chains could lead to well-defined diffraction patterns in hypothetical fiber or crystal diffraction experiments. The inhomogeneous nature of the shape probability distribution identified here for random walks may represent a significant underlying baseline effect in the analysis of real polymer chain ensembles (i.e., in the presence of specific interatomic interactions). As a consequence, a part of what is called a polymer shape may actually reside just "in the eye of the beholder" rather than in the nature of the interactions between the constituting atoms, and the corresponding observation-related bias should be taken into account when drawing conclusions from shape analyses as applied to real structural ensembles.

In the eye of the beholder: Inhomogeneous distribution of high-resolution shapes within the random-walk ensemble.

PubMed

Müller, Christian L; Sbalzarini, Ivo F; van Gunsteren, Wilfred F; Zagrović, Bojan; Hünenberger, Philippe H

2009-06-07

The concept of high-resolution shapes (also referred to as folds or states, depending on the context) of a polymer chain plays a central role in polymer science, structural biology, bioinformatics, and biopolymer dynamics. However, although the idea of shape is intuitively very useful, there is no unambiguous mathematical definition for this concept. In the present work, the distributions of high-resolution shapes within the ideal random-walk ensembles with N=3,...,6 beads (or up to N=10 for some properties) are investigated using a systematic (grid-based) approach based on a simple working definition of shapes relying on the root-mean-square atomic positional deviation as a metric (i.e., to define the distance between pairs of structures) and a single cutoff criterion for the shape assignment. Although the random-walk ensemble appears to represent the paramount of homogeneity and randomness, this analysis reveals that the distribution of shapes within this ensemble, i.e., in the total absence of interatomic interactions characteristic of a specific polymer (beyond the generic connectivity constraint), is significantly inhomogeneous. In particular, a specific (densest) shape occurs with a local probability that is 1.28, 1.79, 2.94, and 10.05 times (N=3,...,6) higher than the corresponding average over all possible shapes (these results can tentatively be extrapolated to a factor as large as about 10(28) for N=100). The qualitative results of this analysis lead to a few rather counterintuitive suggestions, namely, that, e.g., (i) a fold classification analysis applied to the random-walk ensemble would lead to the identification of random-walk "folds;" (ii) a clustering analysis applied to the random-walk ensemble would also lead to the identification random-walk "states" and associated relative free energies; and (iii) a random-walk ensemble of polymer chains could lead to well-defined diffraction patterns in hypothetical fiber or crystal diffraction experiments. The inhomogeneous nature of the shape probability distribution identified here for random walks may represent a significant underlying baseline effect in the analysis of real polymer chain ensembles (i.e., in the presence of specific interatomic interactions). As a consequence, a part of what is called a polymer shape may actually reside just "in the eye of the beholder" rather than in the nature of the interactions between the constituting atoms, and the corresponding observation-related bias should be taken into account when drawing conclusions from shape analyses as applied to real structural ensembles.

Superdiffusive Dispersals Impart the Geometry of Underlying Random Walks

NASA Astrophysics Data System (ADS)

Zaburdaev, V.; Fouxon, I.; Denisov, S.; Barkai, E.

2016-12-01

It is recognized now that a variety of real-life phenomena ranging from diffusion of cold atoms to the motion of humans exhibit dispersal faster than normal diffusion. Lévy walks is a model that excelled in describing such superdiffusive behaviors albeit in one dimension. Here we show that, in contrast to standard random walks, the microscopic geometry of planar superdiffusive Lévy walks is imprinted in the asymptotic distribution of the walkers. The geometry of the underlying walk can be inferred from trajectories of the walkers by calculating the analogue of the Pearson coefficient.

What is quantum in quantum randomness?

PubMed

Grangier, P; Auffèves, A

2018-07-13

It is often said that quantum and classical randomness are of different nature, the former being ontological and the latter epistemological. However, so far the question of 'What is quantum in quantum randomness?', i.e. what is the impact of quantization and discreteness on the nature of randomness, remains to be answered. In a first part, we make explicit the differences between quantum and classical randomness within a recently proposed ontology for quantum mechanics based on contextual objectivity. In this view, quantum randomness is the result of contextuality and quantization. We show that this approach strongly impacts the purposes of quantum theory as well as its areas of application. In particular, it challenges current programmes inspired by classical reductionism, aiming at the emergence of the classical world from a large number of quantum systems. In a second part, we analyse quantum physics and thermodynamics as theories of randomness, unveiling their mutual influences. We finally consider new technological applications of quantum randomness that have opened up in the emerging field of quantum thermodynamics.This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'. © 2018 The Author(s).

Sensorimotor-Conceptual Integration in Free Walking Enhances Divergent Thinking for Young and Older Adults

PubMed Central

Kuo, Chun-Yu; Yeh, Yei-Yu

2016-01-01

Prior research has shown that free walking can enhance creative thinking. Nevertheless, it remains unclear whether bidirectional body-mind links are essential for the positive effect of free walking on creative thinking. Moreover, it is unknown whether the positive effect can be generalized to older adults. In Experiment 1, we replicated previous findings with two additional groups of young participants. Participants in the rectangular-walking condition walked along a rectangular path while generating unusual uses for chopsticks. Participants in the free-walking group walked freely as they wished, and participants in the free-generation condition generated unconstrained free paths while the participants in the random-experienced condition walked those paths. Only the free-walking group showed better performance in fluency, flexibility, and originality. In Experiment 2, two groups of older adults were randomly assigned to the free-walking and rectangular-walking conditions. The free-walking group showed better performance than the rectangular-walking group. Moreover, older adults in the free-walking group outperformed young adults in the rectangular-walking group in originality and performed comparably in fluency and flexibility. Bidirectional links between proprioceptive-motor kinematics and metaphorical abstract concepts can enhance divergent thinking for both young and older adults. PMID:27790178

Random Walks in a One-Dimensional Lévy Random Environment

NASA Astrophysics Data System (ADS)

Bianchi, Alessandra; Cristadoro, Giampaolo; Lenci, Marco; Ligabò, Marilena

2016-04-01

We consider a generalization of a one-dimensional stochastic process known in the physical literature as Lévy-Lorentz gas. The process describes the motion of a particle on the real line in the presence of a random array of marked points, whose nearest-neighbor distances are i.i.d. and long-tailed (with finite mean but possibly infinite variance). The motion is a continuous-time, constant-speed interpolation of a symmetric random walk on the marked points. We first study the quenched random walk on the point process, proving the CLT and the convergence of all the accordingly rescaled moments. Then we derive the quenched and annealed CLTs for the continuous-time process.

Universal principles governing multiple random searchers on complex networks: The logarithmic growth pattern and the harmonic law

NASA Astrophysics Data System (ADS)

Weng, Tongfeng; Zhang, Jie; Small, Michael; Harandizadeh, Bahareh; Hui, Pan

2018-03-01

We propose a unified framework to evaluate and quantify the search time of multiple random searchers traversing independently and concurrently on complex networks. We find that the intriguing behaviors of multiple random searchers are governed by two basic principles—the logarithmic growth pattern and the harmonic law. Specifically, the logarithmic growth pattern characterizes how the search time increases with the number of targets, while the harmonic law explores how the search time of multiple random searchers varies relative to that needed by individual searchers. Numerical and theoretical results demonstrate these two universal principles established across a broad range of random search processes, including generic random walks, maximal entropy random walks, intermittent strategies, and persistent random walks. Our results reveal two fundamental principles governing the search time of multiple random searchers, which are expected to facilitate investigation of diverse dynamical processes like synchronization and spreading.

Integrated devices for quantum information and quantum simulation with polarization encoded qubits

NASA Astrophysics Data System (ADS)

Sansoni, Linda; Sciarrino, Fabio; Mataloni, Paolo; Crespi, Andrea; Ramponi, Roberta; Osellame, Roberto

2012-06-01

The ability to manipulate quantum states of light by integrated devices may open new perspectives both for fundamental tests of quantum mechanics and for novel technological applications. The technology for handling polarization-encoded qubits, the most commonly adopted approach, was still missing in quantum optical circuits until the ultrafast laser writing (ULW) technique was adopted for the first time to realize integrated devices able to support and manipulate polarization encoded qubits.1 Thanks to this method, polarization dependent and independent devices can be realized. In particular the maintenance of polarization entanglement was demonstrated in a balanced polarization independent integrated beam splitter1 and an integrated CNOT gate for polarization qubits was realized and carachterized.2 We also exploited integrated optics for quantum simulation tasks: by adopting the ULW technique an integrated quantum walk circuit was realized3 and, for the first time, we investigate how the particle statistics, either bosonic or fermionic, influences a two-particle discrete quantum walk. Such experiment has been realized by adopting two-photon entangled states and an array of integrated symmetric directional couplers. The polarization entanglement was exploited to simulate the bunching-antibunching feature of non interacting bosons and fermions. To this scope a novel three-dimensional geometry for the waveguide circuit is introduced, which allows accurate polarization independent behaviour, maintaining a remarkable control on both phase and balancement of the directional couplers.

Operator Spreading in Random Unitary Circuits

NASA Astrophysics Data System (ADS)

Nahum, Adam; Vijay, Sagar; Haah, Jeongwan

2018-04-01

Random quantum circuits yield minimally structured models for chaotic quantum dynamics, which are able to capture, for example, universal properties of entanglement growth. We provide exact results and coarse-grained models for the spreading of operators by quantum circuits made of Haar-random unitaries. We study both 1 +1 D and higher dimensions and argue that the coarse-grained pictures carry over to operator spreading in generic many-body systems. In 1 +1 D , we demonstrate that the out-of-time-order correlator (OTOC) satisfies a biased diffusion equation, which gives exact results for the spatial profile of the OTOC and determines the butterfly speed vB. We find that in 1 +1 D , the "front" of the OTOC broadens diffusively, with a width scaling in time as t1 /2. We address fluctuations in the OTOC between different realizations of the random circuit, arguing that they are negligible in comparison to the broadening of the front within a realization. Turning to higher dimensions, we show that the averaged OTOC can be understood exactly via a remarkable correspondence with a purely classical droplet growth problem. This implies that the width of the front of the averaged OTOC scales as t1 /3 in 2 +1 D and as t0.240 in 3 +1 D (exponents of the Kardar-Parisi-Zhang universality class). We support our analytic argument with simulations in 2 +1 D . We point out that, in two or higher spatial dimensions, the shape of the spreading operator at late times is affected by underlying lattice symmetries and, in general, is not spherical. However, when full spatial rotational symmetry is present in 2 +1 D , our mapping implies an exact asymptotic form for the OTOC, in terms of the Tracy-Widom distribution. For an alternative perspective on the OTOC in 1 +1 D , we map it to the partition function of an Ising-like statistical mechanics model. As a result of special structure arising from unitarity, this partition function reduces to a random walk calculation which can be performed exactly. We also use this mapping to give exact results for entanglement growth in 1 +1 D circuits.

A Mixed-Methods Randomized Controlled Trial of Financial Incentives and Peer Networks to Promote Walking among Older Adults

ERIC Educational Resources Information Center

Kullgren, Jeffrey T.; Harkins, Kristin A.; Bellamy, Scarlett L.; Gonzales, Amy; Tao, Yuanyuan; Zhu, Jingsan; Volpp, Kevin G.; Asch, David A.; Heisler, Michele; Karlawish, Jason

2014-01-01

Background: Financial incentives and peer networks could be delivered through eHealth technologies to encourage older adults to walk more. Methods: We conducted a 24-week randomized trial in which 92 older adults with a computer and Internet access received a pedometer, daily walking goals, and weekly feedback on goal achievement. Participants…

Random Walks on Cartesian Products of Certain Nonamenable Groups and Integer Lattices

NASA Astrophysics Data System (ADS)

Vishnepolsky, Rachel

A random walk on a discrete group satisfies a local limit theorem with power law exponent \\alpha if the return probabilities follow the asymptotic law. P{ return to starting point after n steps } ˜ Crhonn-alpha.. A group has a universal local limit theorem if all random walks on the group with finitely supported step distributions obey a local limit theorem with the same power law exponent. Given two groups that obey universal local limit theorems, it is not known whether their cartesian product also has a universal local limit theorem. We settle the question affirmatively in one case, by considering a random walk on the cartesian product of a nonamenable group whose Cayley graph is a tree, and the integer lattice. As corollaries, we derive large deviations estimates and a central limit theorem.

A short walk in quantum probability.

PubMed

Hudson, Robin

2018-04-28

This is a personal survey of aspects of quantum probability related to the Heisenberg commutation relation for canonical pairs. Using the failure, in general, of non-negativity of the Wigner distribution for canonical pairs to motivate a more satisfactory quantum notion of joint distribution, we visit a central limit theorem for such pairs and a resulting family of quantum planar Brownian motions which deform the classical planar Brownian motion, together with a corresponding family of quantum stochastic areas.This article is part of the themed issue 'Hilbert's sixth problem'. © 2018 The Author(s).

Atomic clocks and the continuous-time random-walk

NASA Astrophysics Data System (ADS)

Formichella, Valerio; Camparo, James; Tavella, Patrizia

2017-11-01

Atomic clocks play a fundamental role in many fields, most notably they generate Universal Coordinated Time and are at the heart of all global navigation satellite systems. Notwithstanding their excellent timekeeping performance, their output frequency does vary: it can display deterministic frequency drift; diverse continuous noise processes result in nonstationary clock noise (e.g., random-walk frequency noise, modelled as a Wiener process), and the clock frequency may display sudden changes (i.e., "jumps"). Typically, the clock's frequency instability is evaluated by the Allan or Hadamard variances, whose functional forms can identify the different operative noise processes. Here, we show that the Allan and Hadamard variances of a particular continuous-time random-walk, the compound Poisson process, have the same functional form as for a Wiener process with drift. The compound Poisson process, introduced as a model for observed frequency jumps, is an alternative to the Wiener process for modelling random walk frequency noise. This alternate model fits well the behavior of the rubidium clocks flying on GPS Block-IIR satellites. Further, starting from jump statistics, the model can be improved by considering a more general form of continuous-time random-walk, and this could bring new insights into the physics of atomic clocks.

Quenched Large Deviations for Simple Random Walks on Percolation Clusters Including Long-Range Correlations

NASA Astrophysics Data System (ADS)

Berger, Noam; Mukherjee, Chiranjib; Okamura, Kazuki

2018-03-01

We prove a quenched large deviation principle (LDP) for a simple random walk on a supercritical percolation cluster (SRWPC) on {Z^d} ({d ≥ 2}). The models under interest include classical Bernoulli bond and site percolation as well as models that exhibit long range correlations, like the random cluster model, the random interlacement and the vacant set of random interlacements (for {d ≥ 3}) and the level sets of the Gaussian free field ({d≥ 3}). Inspired by the methods developed by Kosygina et al. (Commun Pure Appl Math 59:1489-1521, 2006) for proving quenched LDP for elliptic diffusions with a random drift, and by Yilmaz (Commun Pure Appl Math 62(8):1033-1075, 2009) and Rosenbluth (Quenched large deviations for multidimensional random walks in a random environment: a variational formula. Ph.D. thesis, NYU, arXiv:0804.1444v1) for similar results regarding elliptic random walks in random environment, we take the point of view of the moving particle and prove a large deviation principle for the quenched distribution of the pair empirical measures of the environment Markov chain in the non-elliptic case of SRWPC. Via a contraction principle, this reduces easily to a quenched LDP for the distribution of the mean velocity of the random walk and both rate functions admit explicit variational formulas. The main difficulty in our set up lies in the inherent non-ellipticity as well as the lack of translation-invariance stemming from conditioning on the fact that the origin belongs to the infinite cluster. We develop a unifying approach for proving quenched large deviations for SRWPC based on exploiting coercivity properties of the relative entropies in the context of convex variational analysis, combined with input from ergodic theory and invoking geometric properties of the supercritical percolation cluster.

Quenched Large Deviations for Simple Random Walks on Percolation Clusters Including Long-Range Correlations

NASA Astrophysics Data System (ADS)

Berger, Noam; Mukherjee, Chiranjib; Okamura, Kazuki

2017-12-01

We prove a quenched large deviation principle (LDP) for a simple random walk on a supercritical percolation cluster (SRWPC) on {Z^d} ({d ≥ 2} ). The models under interest include classical Bernoulli bond and site percolation as well as models that exhibit long range correlations, like the random cluster model, the random interlacement and the vacant set of random interlacements (for {d ≥ 3} ) and the level sets of the Gaussian free field ({d≥ 3} ). Inspired by the methods developed by Kosygina et al. (Commun Pure Appl Math 59:1489-1521, 2006) for proving quenched LDP for elliptic diffusions with a random drift, and by Yilmaz (Commun Pure Appl Math 62(8):1033-1075, 2009) and Rosenbluth (Quenched large deviations for multidimensional random walks in a random environment: a variational formula. Ph.D. thesis, NYU, arXiv:0804.1444v1) for similar results regarding elliptic random walks in random environment, we take the point of view of the moving particle and prove a large deviation principle for the quenched distribution of the pair empirical measures of the environment Markov chain in the non-elliptic case of SRWPC. Via a contraction principle, this reduces easily to a quenched LDP for the distribution of the mean velocity of the random walk and both rate functions admit explicit variational formulas. The main difficulty in our set up lies in the inherent non-ellipticity as well as the lack of translation-invariance stemming from conditioning on the fact that the origin belongs to the infinite cluster. We develop a unifying approach for proving quenched large deviations for SRWPC based on exploiting coercivity properties of the relative entropies in the context of convex variational analysis, combined with input from ergodic theory and invoking geometric properties of the supercritical percolation cluster.

A random-walk/giant-loop model for interphase chromosomes.

PubMed Central

Sachs, R K; van den Engh, G; Trask, B; Yokota, H; Hearst, J E

1995-01-01

Fluorescence in situ hybridization data on distances between defined genomic sequences are used to construct a quantitative model for the overall geometric structure of a human chromosome. We suggest that the large-scale geometry during the G0/G1 part of the cell cycle may consist of flexible chromatin loops, averaging approximately 3 million bp, with a random-walk backbone. A fully explicit, three-parametric polymer model of this random-walk/giant-loop structure can account well for the data. More general models consistent with the data are briefly discussed. PMID:7708711

Random Walks on Homeo( S 1)

NASA Astrophysics Data System (ADS)

Malicet, Dominique

2017-12-01

In this paper, we study random walks {g_n=f_{n-1}\\ldots f_0} on the group Homeo ( S 1) of the homeomorphisms of the circle, where the homeomorphisms f k are chosen randomly, independently, with respect to a same probability measure {ν}. We prove that under the only condition that there is no probability measure invariant by {ν}-almost every homeomorphism, the random walk almost surely contracts small intervals. It generalizes what has been known on this subject until now, since various conditions on {ν} were imposed in order to get the phenomenon of contractions. Moreover, we obtain the surprising fact that the rate of contraction is exponential, even in the lack of assumptions of smoothness on the f k 's. We deduce various dynamical consequences on the random walk ( g n ): finiteness of ergodic stationary measures, distribution of the trajectories, asymptotic law of the evaluations, etc. The proof of the main result is based on a modification of the Ávila-Viana's invariance principle, working for continuous cocycles on a space fibred in circles.

The Walking School Bus and children's physical activity: A pilot cluster randomized controlled trial

USDA-ARS?s Scientific Manuscript database

To evaluate the impact of a "walking school bus" program on children's rates of active commuting to school and physical activity. We conducted a pilot cluster randomized controlled trial among 4th-graders from 8 schools in Houston, Texas (N = 149). Random allocation to treatment or control condition...

Branching random walk with step size coming from a power law

NASA Astrophysics Data System (ADS)

Bhattacharya, Ayan; Subhra Hazra, Rajat; Roy, Parthanil

2015-09-01

In their seminal work, Brunet and Derrida made predictions on the random point configurations associated with branching random walks. We shall discuss the limiting behavior of such point configurations when the displacement random variables come from a power law. In particular, we establish that two prediction of remains valid in this setup and investigate various other issues mentioned in their paper.

Spectral stability of unitary network models

NASA Astrophysics Data System (ADS)

Asch, Joachim; Bourget, Olivier; Joye, Alain

2015-08-01

We review various unitary network models used in quantum computing, spectral analysis or condensed matter physics and establish relationships between them. We show that symmetric one-dimensional quantum walks are universal, as are CMV matrices. We prove spectral stability and propagation properties for general asymptotically uniform models by means of unitary Mourre theory.

Hybrid glowworm swarm optimization for task scheduling in the cloud environment

NASA Astrophysics Data System (ADS)

Zhou, Jing; Dong, Shoubin

2018-06-01

In recent years many heuristic algorithms have been proposed to solve task scheduling problems in the cloud environment owing to their optimization capability. This article proposes a hybrid glowworm swarm optimization (HGSO) based on glowworm swarm optimization (GSO), which uses a technique of evolutionary computation, a strategy of quantum behaviour based on the principle of neighbourhood, offspring production and random walk, to achieve more efficient scheduling with reasonable scheduling costs. The proposed HGSO reduces the redundant computation and the dependence on the initialization of GSO, accelerates the convergence and more easily escapes from local optima. The conducted experiments and statistical analysis showed that in most cases the proposed HGSO algorithm outperformed previous heuristic algorithms to deal with independent tasks.

Size dependence of single-photon superradiance of cold and dilute atomic ensembles

NASA Astrophysics Data System (ADS)

Kuraptsev, A. S.; Sokolov, I. M.

2017-11-01

We report a theoretical investigation of angular distribution of a single-photon superradiance from cold and dilute atomic clouds. In the present work we focus our attention on the dependence of superradiance on the size and shape of the cloud. We analyze the dynamics of the afterglow of atomic ensemble excited by pulse radiation. Two theoretical approaches are used. The first is the quantum microscopic approach based on a coupled-dipole model. The second approach is random walk approximation. We show that the results obtained in both approaches coincide with a good accuracy for incoherent fluorescence excited by short resonant pulses. We also show that the superradiance decay rate changes with size differently for radiation emitted into different directions.

Anomalous Diffusion of Single Particles in Cytoplasm

PubMed Central

Regner, Benjamin M.; Vučinić, Dejan; Domnisoru, Cristina; Bartol, Thomas M.; Hetzer, Martin W.; Tartakovsky, Daniel M.; Sejnowski, Terrence J.

2013-01-01

The crowded intracellular environment poses a formidable challenge to experimental and theoretical analyses of intracellular transport mechanisms. Our measurements of single-particle trajectories in cytoplasm and their random-walk interpretations elucidate two of these mechanisms: molecular diffusion in crowded environments and cytoskeletal transport along microtubules. We employed acousto-optic deflector microscopy to map out the three-dimensional trajectories of microspheres migrating in the cytosolic fraction of a cellular extract. Classical Brownian motion (BM), continuous time random walk, and fractional BM were alternatively used to represent these trajectories. The comparison of the experimental and numerical data demonstrates that cytoskeletal transport along microtubules and diffusion in the cytosolic fraction exhibit anomalous (nonFickian) behavior and posses statistically distinct signatures. Among the three random-walk models used, continuous time random walk provides the best representation of diffusion, whereas microtubular transport is accurately modeled with fractional BM. PMID:23601312

Scaling behavior for random walks with memory of the largest distance from the origin

NASA Astrophysics Data System (ADS)

Serva, Maurizio

2013-11-01

We study a one-dimensional random walk with memory. The behavior of the walker is modified with respect to the simple symmetric random walk only when he or she is at the maximum distance ever reached from his or her starting point (home). In this case, having the choice to move farther or to move closer, the walker decides with different probabilities. If the probability of a forward step is higher then the probability of a backward step, the walker is bold, otherwise he or she is timorous. We investigate the asymptotic properties of this bold-timorous random walk, showing that the scaling behavior varies continuously from subdiffusive (timorous) to superdiffusive (bold). The scaling exponents are fully determined with a new mathematical approach based on a decomposition of the dynamics in active journeys (the walker is at the maximum distance) and lazy journeys (the walker is not at the maximum distance).

Simulating Pre-Asymptotic, Non-Fickian Transport Although Doing Simple Random Walks - Supported By Empirical Pore-Scale Velocity Distributions and Memory Effects

NASA Astrophysics Data System (ADS)

Most, S.; Jia, N.; Bijeljic, B.; Nowak, W.

2016-12-01

Pre-asymptotic characteristics are almost ubiquitous when analyzing solute transport processes in porous media. These pre-asymptotic aspects are caused by spatial coherence in the velocity field and by its heterogeneity. For the Lagrangian perspective of particle displacements, the causes of pre-asymptotic, non-Fickian transport are skewed velocity distribution, statistical dependencies between subsequent increments of particle positions (memory) and dependence between the x, y and z-components of particle increments. Valid simulation frameworks should account for these factors. We propose a particle tracking random walk (PTRW) simulation technique that can use empirical pore-space velocity distributions as input, enforces memory between subsequent random walk steps, and considers cross dependence. Thus, it is able to simulate pre-asymptotic non-Fickian transport phenomena. Our PTRW framework contains an advection/dispersion term plus a diffusion term. The advection/dispersion term produces time-series of particle increments from the velocity CDFs. These time series are equipped with memory by enforcing that the CDF values of subsequent velocities change only slightly. The latter is achieved through a random walk on the axis of CDF values between 0 and 1. The virtual diffusion coefficient for that random walk is our only fitting parameter. Cross-dependence can be enforced by constraining the random walk to certain combinations of CDF values between the three velocity components in x, y and z. We will show that this modelling framework is capable of simulating non-Fickian transport by comparison with a pore-scale transport simulation and we analyze the approach to asymptotic behavior.

Virtual reality-based training improves community ambulation in individuals with stroke: a randomized controlled trial.

PubMed

Yang, Yea-Ru; Tsai, Meng-Pin; Chuang, Tien-Yow; Sung, Wen-Hsu; Wang, Ray-Yau

2008-08-01

This is a single blind randomized controlled trial to examine the effect of virtual reality-based training on the community ambulation in individuals with stroke. Twenty subjects with stroke were assigned randomly to either the control group (n=9) or the experimental group (n=11). Subjects in the control group received the treadmill training. Subjects in the experimental group underwent the virtual reality-based treadmill training. Walking speed, community walking time, walking ability questionnaire (WAQ), and activities-specific balance confidence (ABC) scale were evaluated. Subjects in the experimental group improved significantly in walking speed, community walking time, and WAQ score at posttraining and 1-month follow-up periods. Their ABC score also significantly increased at posttraining but did not maintain at follow-up period. Regarding the between-group comparisons, the experimental group improved significantly more than control group in walking speed (P=0.03) and community walking time (P=0.04) at posttraining period and in WAQ score (P=0.03) at follow-up period. Our results support the perceived benefits of gait training programs that incorporate virtual reality to augment the community ambulation of individuals with stroke.

Systematic Dimensionality Reduction for Quantum Walks: Optimal Spatial Search and Transport on Non-Regular Graphs

PubMed Central

Novo, Leonardo; Chakraborty, Shantanav; Mohseni, Masoud; Neven, Hartmut; Omar, Yasser

2015-01-01

Continuous time quantum walks provide an important framework for designing new algorithms and modelling quantum transport and state transfer problems. Often, the graph representing the structure of a problem contains certain symmetries that confine the dynamics to a smaller subspace of the full Hilbert space. In this work, we use invariant subspace methods, that can be computed systematically using the Lanczos algorithm, to obtain the reduced set of states that encompass the dynamics of the problem at hand without the specific knowledge of underlying symmetries. First, we apply this method to obtain new instances of graphs where the spatial quantum search algorithm is optimal: complete graphs with broken links and complete bipartite graphs, in particular, the star graph. These examples show that regularity and high-connectivity are not needed to achieve optimal spatial search. We also show that this method considerably simplifies the calculation of quantum transport efficiencies. Furthermore, we observe improved efficiencies by removing a few links from highly symmetric graphs. Finally, we show that this reduction method also allows us to obtain an upper bound for the fidelity of a single qubit transfer on an XY spin network. PMID:26330082

Emergence of an optimal search strategy from a simple random walk

PubMed Central

Sakiyama, Tomoko; Gunji, Yukio-Pegio

2013-01-01

In reports addressing animal foraging strategies, it has been stated that Lévy-like algorithms represent an optimal search strategy in an unknown environment, because of their super-diffusion properties and power-law-distributed step lengths. Here, starting with a simple random walk algorithm, which offers the agent a randomly determined direction at each time step with a fixed move length, we investigated how flexible exploration is achieved if an agent alters its randomly determined next step forward and the rule that controls its random movement based on its own directional moving experiences. We showed that our algorithm led to an effective food-searching performance compared with a simple random walk algorithm and exhibited super-diffusion properties, despite the uniform step lengths. Moreover, our algorithm exhibited a power-law distribution independent of uniform step lengths. PMID:23804445

Emergence of an optimal search strategy from a simple random walk.

PubMed

Sakiyama, Tomoko; Gunji, Yukio-Pegio

2013-09-06

In reports addressing animal foraging strategies, it has been stated that Lévy-like algorithms represent an optimal search strategy in an unknown environment, because of their super-diffusion properties and power-law-distributed step lengths. Here, starting with a simple random walk algorithm, which offers the agent a randomly determined direction at each time step with a fixed move length, we investigated how flexible exploration is achieved if an agent alters its randomly determined next step forward and the rule that controls its random movement based on its own directional moving experiences. We showed that our algorithm led to an effective food-searching performance compared with a simple random walk algorithm and exhibited super-diffusion properties, despite the uniform step lengths. Moreover, our algorithm exhibited a power-law distribution independent of uniform step lengths.

Anomalous diffusion analysis of the lifting events in the event-chain Monte Carlo for the classical XY models

NASA Astrophysics Data System (ADS)

Kimura, Kenji; Higuchi, Saburo

2017-11-01

We introduce a novel random walk model that emerges in the event-chain Monte Carlo (ECMC) of spin systems. In the ECMC, the lifting variable specifying the spin to be updated changes its value to one of its interacting neighbor spins. This movement can be regarded as a random walk in a random environment with a feedback. We investigate this random walk numerically in the case of the classical XY model in 1, 2, and 3 dimensions to find that it is superdiffusive near the critical point of the underlying spin system. It is suggested that the performance improvement of the ECMC is related to this anomalous behavior.

Faster than classical quantum algorithm for dense formulas of exact satisfiability and occupation problems

NASA Astrophysics Data System (ADS)

Mandrà, Salvatore; Giacomo Guerreschi, Gian; Aspuru-Guzik, Alán

2016-07-01

We present an exact quantum algorithm for solving the Exact Satisfiability problem, which belongs to the important NP-complete complexity class. The algorithm is based on an intuitive approach that can be divided into two parts: the first step consists in the identification and efficient characterization of a restricted subspace that contains all the valid assignments of the Exact Satisfiability; while the second part performs a quantum search in such restricted subspace. The quantum algorithm can be used either to find a valid assignment (or to certify that no solution exists) or to count the total number of valid assignments. The query complexities for the worst-case are respectively bounded by O(\\sqrt{{2}n-{M\\prime }}) and O({2}n-{M\\prime }), where n is the number of variables and {M}\\prime the number of linearly independent clauses. Remarkably, the proposed quantum algorithm results to be faster than any known exact classical algorithm to solve dense formulas of Exact Satisfiability. As a concrete application, we provide the worst-case complexity for the Hamiltonian cycle problem obtained after mapping it to a suitable Occupation problem. Specifically, we show that the time complexity for the proposed quantum algorithm is bounded by O({2}n/4) for 3-regular undirected graphs, where n is the number of nodes. The same worst-case complexity holds for (3,3)-regular bipartite graphs. As a reference, the current best classical algorithm has a (worst-case) running time bounded by O({2}31n/96). Finally, when compared to heuristic techniques for Exact Satisfiability problems, the proposed quantum algorithm is faster than the classical WalkSAT and Adiabatic Quantum Optimization for random instances with a density of constraints close to the satisfiability threshold, the regime in which instances are typically the hardest to solve. The proposed quantum algorithm can be straightforwardly extended to the generalized version of the Exact Satisfiability known as Occupation problem. The general version of the algorithm is presented and analyzed.

Efficient Quantum Pseudorandomness.

PubMed

Brandão, Fernando G S L; Harrow, Aram W; Horodecki, Michał

2016-04-29

Randomness is both a useful way to model natural systems and a useful tool for engineered systems, e.g., in computation, communication, and control. Fully random transformations require exponential time for either classical or quantum systems, but in many cases pseudorandom operations can emulate certain properties of truly random ones. Indeed, in the classical realm there is by now a well-developed theory regarding such pseudorandom operations. However, the construction of such objects turns out to be much harder in the quantum case. Here, we show that random quantum unitary time evolutions ("circuits") are a powerful source of quantum pseudorandomness. This gives for the first time a polynomial-time construction of quantum unitary designs, which can replace fully random operations in most applications, and shows that generic quantum dynamics cannot be distinguished from truly random processes. We discuss applications of our result to quantum information science, cryptography, and understanding the self-equilibration of closed quantum dynamics.

Random-Walk Type Model with Fat Tails for Financial Markets

NASA Astrophysics Data System (ADS)

Matuttis, Hans-Geors

Starting from the random-walk model, practices of financial markets are included into the random-walk so that fat tail distributions like those in the high frequency data of the SP500 index are reproduced, though the individual mechanisms are modeled by normally distributed data. The incorporation of local correlation narrows the distribution for "frequent" events, whereas global correlations due to technical analysis leads to fat tails. Delay of market transactions in the trading process shifts the fat tail probabilities downwards. Such an inclusion of reactions to market fluctuations leads to mini-trends which are distributed with unit variance.

Optoenergy storage and random walks assisted broadband amplification in Er3+-doped (Pb,La)(Zr,Ti)O3 disordered ceramics.

PubMed

Xu, Long; Zhao, Hua; Xu, Caixia; Zhang, Siqi; Zou, Yingyin K; Zhang, Jingwen

2014-02-01

A broadband optical amplification was observed and investigated in Er3+-doped electrostrictive ceramics of lanthanum-modified lead zirconate titanate under a corona atmosphere. The ceramic structure change caused by UV light, electric field, and random walks originated from the diffusive process in intrinsically disordered materials may all contribute to the optical amplification and the associated energy storage. Discussion based on optical energy storage and diffusive equations was given to explain the findings. Those experiments performed made it possible to study random walks and optical amplification in transparent ceramics materials.

A complexity theory model in science education problem solving: random walks for working memory and mental capacity.

PubMed

Stamovlasis, Dimitrios; Tsaparlis, Georgios

2003-07-01

The present study examines the role of limited human channel capacity from a science education perspective. A model of science problem solving has been previously validated by applying concepts and tools of complexity theory (the working memory, random walk method). The method correlated the subjects' rank-order achievement scores in organic-synthesis chemistry problems with the subjects' working memory capacity. In this work, we apply the same nonlinear approach to a different data set, taken from chemical-equilibrium problem solving. In contrast to the organic-synthesis problems, these problems are algorithmic, require numerical calculations, and have a complex logical structure. As a result, these problems cause deviations from the model, and affect the pattern observed with the nonlinear method. In addition to Baddeley's working memory capacity, the Pascual-Leone's mental (M-) capacity is examined by the same random-walk method. As the complexity of the problem increases, the fractal dimension of the working memory random walk demonstrates a sudden drop, while the fractal dimension of the M-capacity random walk decreases in a linear fashion. A review of the basic features of the two capacities and their relation is included. The method and findings have consequences for problem solving not only in chemistry and science education, but also in other disciplines.

Topological bound states of a quantum walk with cold atoms

NASA Astrophysics Data System (ADS)

Mugel, Samuel; Celi, Alessio; Massignan, Pietro; Asbóth, János K.; Lewenstein, Maciej; Lobo, Carlos

2016-08-01

We suggest a method for engineering a quantum walk, with cold atoms as walkers, which presents topologically nontrivial properties. We derive the phase diagram, and show that we are able to produce a boundary between topologically distinct phases using the finite beam width of the applied lasers. A topologically protected bound state can then be observed, which is pinned to the interface and is robust to perturbations. We show that it is possible to identify this bound state by averaging over spin sensitive measures of the atom's position, based on the spin distribution that these states display. Interestingly, there exists a parameter regime in which our system maps on to the Creutz ladder.

Modeling 2D and 3D diffusion.

PubMed

Saxton, Michael J

2007-01-01

Modeling obstructed diffusion is essential to the understanding of diffusion-mediated processes in the crowded cellular environment. Simple Monte Carlo techniques for modeling obstructed random walks are explained and related to Brownian dynamics and more complicated Monte Carlo methods. Random number generation is reviewed in the context of random walk simulations. Programming techniques and event-driven algorithms are discussed as ways to speed simulations.

Walking Aids Moderate Exercise Effects on Gait Speed in People With Dementia: A Randomized Controlled Trial.

PubMed

Toots, Annika; Littbrand, Håkan; Holmberg, Henrik; Nordström, Peter; Lundin-Olsson, Lillemor; Gustafson, Yngve; Rosendahl, Erik

2017-03-01

To investigate the effects of exercise on gait speed, when tested using walking aids and without, and whether effects differed according to amount of support in the test. A cluster-randomized controlled trial. The Umeå Dementia and Exercise (UMDEX) study was set in 16 nursing homes in Umeå, Sweden. One hundred forty-one women and 45 men (mean age 85 years) with dementia, of whom 145 (78%) habitually used walking aids. Participants were randomized to the high-intensity functional exercise program or a seated attention control activity. Blinded assessors measured 4-m usual gait speed with walking aids if any gait speed (GS), and without walking aids and with minimum amount of support, at baseline, 4 months (on intervention completion), and 7 months. Linear mixed models showed no between-group effect in either gait speed test at 4 or 7 months. In interaction analyses exercise effects differed significantly between participants who walked unsupported compared with when walking aids or minimum support was used. Positive between-group exercise effects on gait speed (m/s) were found in subgroups that walked unsupported at 4 and 7 months (GS: 0.07, P = .009 and 0.13, P < .001; and GS test without walking aids: 0.05, P = .011 and 0.07, P = .029, respectively). In people with dementia living in nursing homes exercise had positive effects on gait when tested unsupported compared with when walking aids or minimum support was used. The study suggests that the use of walking aids in gait speed tests may conceal exercise effects. Copyright © 2016 AMDA – The Society for Post-Acute and Long-Term Care Medicine. Published by Elsevier Inc. All rights reserved.

A randomized trial of functional electrical stimulation for walking in incomplete spinal cord injury: Effects on walking competency

PubMed Central

Kapadia, Naaz; Masani, Kei; Catharine Craven, B.; Giangregorio, Lora M.; Hitzig, Sander L.; Richards, Kieva; Popovic, Milos R.

2014-01-01

Background Multi-channel surface functional electrical stimulation (FES) for walking has been used to improve voluntary walking and balance in individuals with spinal cord injury (SCI). Objective To investigate short- and long-term benefits of 16 weeks of thrice-weekly FES-assisted walking program, while ambulating on a body weight support treadmill and harness system, versus a non-FES exercise program, on improvements in gait and balance in individuals with chronic incomplete traumatic SCI, in a randomized controlled trial design. Methods Individuals with traumatic and chronic (≥18 months) motor incomplete SCI (level C2 to T12, American Spinal Cord Injury Association Impairment Scale C or D) were recruited from an outpatient SCI rehabilitation hospital, and randomized to FES-assisted walking therapy (intervention group) or aerobic and resistance training program (control group). Outcomes were assessed at baseline, and after 4, 6, and 12 months. Gait, balance, spasticity, and functional measures were collected. Results Spinal cord independence measure (SCIM) mobility sub-score improved over time in the intervention group compared with the control group (baseline/12 months: 17.27/21.33 vs. 19.09/17.36, respectively). On all other outcome measures the intervention and control groups had similar improvements. Irrespective of group allocation walking speed, endurance, and balance during ambulation all improved upon completion of therapy, and majority of participants retained these gains at long-term follow-ups. Conclusions Task-oriented training improves walking ability in individuals with incomplete SCI, even in the chronic stage. Further randomized controlled trials, involving a large number of participants are needed, to verify if FES-assisted treadmill training is superior to aerobic and strength training. PMID:25229735

Answer (in part) blowing in the wind. Comment on "Liberating Lévy walk research from the shackles of optimal foraging" by A. Reynolds

NASA Astrophysics Data System (ADS)

Cheng, Ken

2015-09-01

In a perspective in this issue based on thorough review, Andy Reynolds [1] tackles the issue of how the by now ubiquitously found Lévy walks can be generated, by animals, by organisms other than animals, and other forms of life below the level of organisms, such as cells. The answer comes not in a single whole cloth, but rather in a patchwork of generating factors. Lévy-like movements arise in objects blowing in the wind, or from travelers encountering turbulence in the seas or being repelled by boundaries. A variety of desiderata in movements, not related to achieving optimal foraging, may also engender Lévy-like movements. These include avoiding other organisms or not crossing one's traveled path. Adding to that plethora are ways in which variations on the theme of garden-variety random walks can at least approach a Lévy walk, if not capturing the mathematical form perfectly. Such variations include executing random walks on multiple scales, a strategy exhibited by desert ants [2,3], mussels [4], and quite likely extant hunter-gatherer humans as well [5]. It is possible that fossil tracks over 50 million years old also show this strategy, as the curve fitting with multiple random walks, characterized by multiple exponential distributions, is as good or better than curve fits having the power-law distribution characteristic of Lévy walks [6]. Another variation is to have a random walk search whose scale is expanding over time. In great detail and based on extensive literature - the review has over 200 references - a range of other ways in which Lévy-like movements might come about are also discussed.

Asymptotic properties of a bold random walk

NASA Astrophysics Data System (ADS)

Serva, Maurizio

2014-08-01

In a recent paper we proposed a non-Markovian random walk model with memory of the maximum distance ever reached from the starting point (home). The behavior of the walker is different from the simple symmetric random walk only when she is at this maximum distance, where, having the choice to move either farther or closer, she decides with different probabilities. If the probability of a forward step is higher than the probability of a backward step, the walker is bold and her behavior turns out to be superdiffusive; otherwise she is timorous and her behavior turns out to be subdiffusive. The scaling behavior varies continuously from subdiffusive (timorous) to superdiffusive (bold) according to a single parameter γ ∈R. We investigate here the asymptotic properties of the bold case in the nonballistic region γ ∈[0,1/2], a problem which was left partially unsolved previously. The exact results proved in this paper require new probabilistic tools which rely on the construction of appropriate martingales of the random walk and its hitting times.

Random walk to a nonergodic equilibrium concept

NASA Astrophysics Data System (ADS)

Bel, G.; Barkai, E.

2006-01-01

Random walk models, such as the trap model, continuous time random walks, and comb models, exhibit weak ergodicity breaking, when the average waiting time is infinite. The open question is, what statistical mechanical theory replaces the canonical Boltzmann-Gibbs theory for such systems? In this paper a nonergodic equilibrium concept is investigated, for a continuous time random walk model in a potential field. In particular we show that in the nonergodic phase the distribution of the occupation time of the particle in a finite region of space approaches U- or W-shaped distributions related to the arcsine law. We show that when conditions of detailed balance are applied, these distributions depend on the partition function of the problem, thus establishing a relation between the nonergodic dynamics and canonical statistical mechanics. In the ergodic phase the distribution function of the occupation times approaches a δ function centered on the value predicted based on standard Boltzmann-Gibbs statistics. The relation of our work to single-molecule experiments is briefly discussed.

Walking adaptability therapy after stroke: study protocol for a randomized controlled trial.

PubMed

Timmermans, Celine; Roerdink, Melvyn; van Ooijen, Marielle W; Meskers, Carel G; Janssen, Thomas W; Beek, Peter J

2016-08-26

Walking in everyday life requires the ability to adapt walking to the environment. This adaptability is often impaired after stroke, and this might contribute to the increased fall risk after stroke. To improve safe community ambulation, walking adaptability training might be beneficial after stroke. This study is designed to compare the effects of two interventions for improving walking speed and walking adaptability: treadmill-based C-Mill therapy (therapy with augmented reality) and the overground FALLS program (a conventional therapy program). We hypothesize that C-Mill therapy will result in better outcomes than the FALLS program, owing to its expected greater amount of walking practice. This is a single-center parallel group randomized controlled trial with pre-intervention, post-intervention, retention, and follow-up tests. Forty persons after stroke (≥3 months) with deficits in walking or balance will be included. Participants will be randomly allocated to either C-Mill therapy or the overground FALLS program for 5 weeks. Both interventions will incorporate practice of walking adaptability and will be matched in terms of frequency, duration, and therapist attention. Walking speed, as determined by the 10 Meter Walking Test, will be the primary outcome measure. Secondary outcome measures will pertain to walking adaptability (10 Meter Walking Test with context or cognitive dual-task and Interactive Walkway assessments). Furthermore, commonly used clinical measures to determine walking ability (Timed Up-and-Go test), walking independence (Functional Ambulation Category), balance (Berg Balance Scale), and balance confidence (Activities-specific Balance Confidence scale) will be used, as well as a complementary set of walking-related assessments. The amount of walking practice (the number of steps taken per session) will be registered using the treadmill's inbuilt step counter (C-Mill therapy) and video recordings (FALLS program). This process measure will be compared between the two interventions. This study will assess the effects of treadmill-based C-Mill therapy compared with the overground FALLS program and thereby the relative importance of the amount of walking practice as a key aspect of effective intervention programs directed at improving walking speed and walking adaptability after stroke. Netherlands Trial Register NTR4030 . Registered on 11 June 2013, amendment filed on 17 June 2016.

Methods for a Randomized Trial of Weight-Supported Treadmill Training versus Conventional Training for Walking during Inpatient Rehabilitation after Incomplete Traumatic Spinal Cord Injury

PubMed Central

Dobkin, Bruce H.; Apple, David; Barbeau, Hugues; Basso, Michele; Behrman, Andrea; Deforge, Dan; Ditunno, John; Dudley, Gary; Elashoff, Robert; Fugate, Lisa; Harkema, Susan; Saulino, Michael; Scott, Michael

2014-01-01

The authors describe the rationale and methodology for the first prospective, multicenter, randomized clinical trial (RCT) of a task-oriented walking intervention for subjects during early rehabilitation for an acute traumatic spinal cord injury (SCI). The experimental strategy, body weight–supported treadmill training (BWSTT), allows physical therapists to systematically train patients to walk on a treadmill at increasing speeds typical of community ambulation with increasing weight bearing. The therapists provide verbal and tactile cues to facilitate the kinematic, kinetic, and temporal features of walking. Subjects were randomly assigned to a conventional therapy program for mobility versus the same intensity and duration of a combination of BWSTT and over-ground locomotor retraining. Subjects had an incomplete SCI (American Spinal Injury Association grades B, C, and D) from C-4 to T-10 (upper motoneuron group) or from T-11 to L-3 (lower motoneuron group). Within 8 weeks of a SCI, 146 subjects were entered for 12 weeks of intervention. The 2 single-blinded primary outcome measures are the level of independence for ambulation and, for those who are able to walk, the maximal speed for walking 50 feet, tested 6 and 12 months after randomization. The trial’s methodology offers a model for the feasibility of translating neuroscientific experiments into a RCT to develop evidence-based rehabilitation practices. PMID:14503436

Modelling nematode movement using time-fractional dynamics.

PubMed

Hapca, Simona; Crawford, John W; MacMillan, Keith; Wilson, Mike J; Young, Iain M

2007-09-07

We use a correlated random walk model in two dimensions to simulate the movement of the slug parasitic nematode Phasmarhabditis hermaphrodita in homogeneous environments. The model incorporates the observed statistical distributions of turning angle and speed derived from time-lapse studies of individual nematode trails. We identify strong temporal correlations between the turning angles and speed that preclude the case of a simple random walk in which successive steps are independent. These correlated random walks are appropriately modelled using an anomalous diffusion model, more precisely using a fractional sub-diffusion model for which the associated stochastic process is characterised by strong memory effects in the probability density function.

Chemical Distances for Percolation of Planar Gaussian Free Fields and Critical Random Walk Loop Soups

NASA Astrophysics Data System (ADS)

Ding, Jian; Li, Li

2018-05-01

We initiate the study on chemical distances of percolation clusters for level sets of two-dimensional discrete Gaussian free fields as well as loop clusters generated by two-dimensional random walk loop soups. One of our results states that the chemical distance between two macroscopic annuli away from the boundary for the random walk loop soup at the critical intensity is of dimension 1 with positive probability. Our proof method is based on an interesting combination of a theorem of Makarov, isomorphism theory, and an entropic repulsion estimate for Gaussian free fields in the presence of a hard wall.

Chemical Distances for Percolation of Planar Gaussian Free Fields and Critical Random Walk Loop Soups

NASA Astrophysics Data System (ADS)

Ding, Jian; Li, Li

2018-06-01

We initiate the study on chemical distances of percolation clusters for level sets of two-dimensional discrete Gaussian free fields as well as loop clusters generated by two-dimensional random walk loop soups. One of our results states that the chemical distance between two macroscopic annuli away from the boundary for the random walk loop soup at the critical intensity is of dimension 1 with positive probability. Our proof method is based on an interesting combination of a theorem of Makarov, isomorphism theory, and an entropic repulsion estimate for Gaussian free fields in the presence of a hard wall.

Microtubules as mechanical force sensors.

PubMed

Karafyllidis, Ioannis G; Lagoudas, Dimitris C

2007-03-01

Microtubules are polymers of tubulin subunits (dimers) arranged on a hexagonal lattice. Each tubulin dimer comprises two monomers, the alpha-tubulin and beta-tubulin, and can be found in two states. In the first state a mobile negative charge is located into the alpha-tubulin monomer and in the second into the beta-tubulin monomer. Each tubulin dimer is modeled as an electrical dipole coupled to its neighbors by electrostatic forces. The location of the mobile charge in each dimer depends on the location of the charges in the dimer's neighborhood. Mechanical forces that act on the microtubule affect the distances between the dimers and alter the electrostatic potential. Changes in this potential affect the mobile negative charge location in each dimer and the charge distribution in the microtubule. The net effect is that mechanical forces affect the charge distribution in microtubules. We propose to exploit this effect and use microtubules as mechanical force sensors. We model each dimer as a two-state quantum system and, following the quantum computation paradigm, we use discrete quantum random walk on the hexagonal microtubule lattice to determine the charge distribution. Different forces applied on the microtubule are modeled as different coin biases leading to different probability distributions of the quantum walker location, which are directly connected to different charge distributions. Simulation results show that there is a strong indication that microtubules can be used as mechanical force sensors and that they can also detect the force directions and magnitudes.

Treadmill training improves overground walking economy in Parkinson's disease: a randomized, controlled pilot study.

PubMed

Fernández-Del-Olmo, Miguel Angel; Sanchez, Jose Andres; Bello, Olalla; Lopez-Alonso, Virginia; Márquez, Gonzalo; Morenilla, Luis; Castro, Xabier; Giraldez, Manolo; Santos-García, Diego

2014-01-01

Gait disturbances are one of the principal and most incapacitating symptoms of Parkinson's disease (PD). In addition, walking economy is impaired in PD patients and could contribute to excess fatigue in this population. An important number of studies have shown that treadmill training can improve kinematic parameters in PD patients. However, the effects of treadmill and overground walking on the walking economy remain unknown. The goal of this study was to explore the walking economy changes in response to a treadmill and an overground training program, as well as the differences in the walking economy during treadmill and overground walking. Twenty-two mild PD patients were randomly assigned to a treadmill or overground training group. The training program consisted of 5 weeks (3 sessions/week). We evaluated the energy expenditure of overground walking, before and after each of the training programs. The energy expenditure of treadmill walking (before the program) was also evaluated. The treadmill, but not the overground training program, lead to an improvement in the walking economy (the rate of oxygen consumed per distance during overground walking at a preferred speed) in PD patients. In addition, walking on a treadmill required more energy expenditure compared with overground walking at the same speed. This study provides evidence that in mild PD patients, treadmill training is more beneficial compared with that of walking overground, leading to a greater improvement in the walking economy. This finding is of clinical importance for the therapeutic administration of exercise in PD.

Ballistic pulse propagation in quantum wire waveguides: Toward localization and control of electron wave packets in space and time

NASA Astrophysics Data System (ADS)

Hayata, K.; Tsuji, Y.; Koshiba, M.

1992-10-01

A theoretical formulation of electron pulse propagation in quantum wire structures with mesoscopic scale cross sections is presented, assuming quantum ballistic transport of electron wave packets over a certain characteristic length. As typical mesoscopic structures for realizing coherent electron transmission, two traveling-wave configurations are considered: straight quantum wire waveguides and quantum wire bend structures (quantum whispering galleries). To estimate temporal features of the pulse during propagation, the walk off, the dispersion, and the pulse coherence lengths are defined as useful characteristic lengths. Numerical results are shown for ultrashort pulse propagation through rectangular wire waveguides. Effects due to an external electric field are discussed as well.

Convex hulls of random walks in higher dimensions: A large-deviation study

NASA Astrophysics Data System (ADS)

Schawe, Hendrik; Hartmann, Alexander K.; Majumdar, Satya N.

2017-12-01

The distribution of the hypervolume V and surface ∂ V of convex hulls of (multiple) random walks in higher dimensions are determined numerically, especially containing probabilities far smaller than P =10-1000 to estimate large deviation properties. For arbitrary dimensions and large walk lengths T , we suggest a scaling behavior of the distribution with the length of the walk T similar to the two-dimensional case and behavior of the distributions in the tails. We underpin both with numerical data in d =3 and d =4 dimensions. Further, we confirm the analytically known means of those distributions and calculate their variances for large T .

Cardiorespiratory Kinetics Determined by Pseudo-Random Binary Sequences - Comparisons between Walking and Cycling.

PubMed

Koschate, J; Drescher, U; Thieschäfer, L; Heine, O; Baum, K; Hoffmann, U

2016-12-01

This study aims to compare cardiorespiratory kinetics as a response to a standardised work rate protocol with pseudo-random binary sequences between cycling and walking in young healthy subjects. Muscular and pulmonary oxygen uptake (V̇O 2 ) kinetics as well as heart rate kinetics were expected to be similar for walking and cycling. Cardiac data and V̇O 2 of 23 healthy young subjects were measured in response to pseudo-random binary sequences. Kinetics were assessed applying time series analysis. Higher maxima of cross-correlation functions between work rate and the respective parameter indicate faster kinetics responses. Muscular V̇O 2 kinetics were estimated from heart rate and pulmonary V̇O 2 using a circulatory model. Muscular (walking vs. cycling [mean±SD in arbitrary units]: 0.40±0.08 vs. 0.41±0.08) and pulmonary V̇O 2 kinetics (0.35±0.06 vs. 0.35±0.06) were not different, although the time courses of the cross-correlation functions of pulmonary V̇O 2 showed unexpected biphasic responses. Heart rate kinetics (0.50±0.14 vs. 0.40±0.14; P=0.017) was faster for walking. Regarding the biphasic cross-correlation functions of pulmonary V̇O 2 during walking, the assessment of muscular V̇O 2 kinetics via pseudo-random binary sequences requires a circulatory model to account for cardio-dynamic distortions. Faster heart rate kinetics for walking should be considered by comparing results from cycle and treadmill ergometry. © Georg Thieme Verlag KG Stuttgart · New York.

Quantum random number generation

DOE PAGES

Ma, Xiongfeng; Yuan, Xiao; Cao, Zhu; ...

2016-06-28

Quantum physics can be exploited to generate true random numbers, which play important roles in many applications, especially in cryptography. Genuine randomness from the measurement of a quantum system reveals the inherent nature of quantumness -- coherence, an important feature that differentiates quantum mechanics from classical physics. The generation of genuine randomness is generally considered impossible with only classical means. Based on the degree of trustworthiness on devices, quantum random number generators (QRNGs) can be grouped into three categories. The first category, practical QRNG, is built on fully trusted and calibrated devices and typically can generate randomness at a highmore » speed by properly modeling the devices. The second category is self-testing QRNG, where verifiable randomness can be generated without trusting the actual implementation. The third category, semi-self-testing QRNG, is an intermediate category which provides a tradeoff between the trustworthiness on the device and the random number generation speed.« less

Random walks with random velocities.

PubMed

Zaburdaev, Vasily; Schmiedeberg, Michael; Stark, Holger

2008-07-01

We consider a random walk model that takes into account the velocity distribution of random walkers. Random motion with alternating velocities is inherent to various physical and biological systems. Moreover, the velocity distribution is often the first characteristic that is experimentally accessible. Here, we derive transport equations describing the dispersal process in the model and solve them analytically. The asymptotic properties of solutions are presented in the form of a phase diagram that shows all possible scaling regimes, including superdiffusive, ballistic, and superballistic motion. The theoretical results of this work are in excellent agreement with accompanying numerical simulations.

Switching effect of the side chain on quantum walks on triple graphs

NASA Astrophysics Data System (ADS)

Du, Yi-Mu; Lu, Li-Hua; Li, You-Quan

2015-07-01

We consider a continuous-time quantum walk on a triple graph and investigate the influence of the side chain on propagation in the main chain. Calculating the interchange of the probabilities between the two parts of the main chain, we find that a switching effect appears if there is an odd number of points in the side chain when concrete conditions between the length of the main chain and the position of the side chain are satisfied. However, such an effect does not occur if there is an even number of points in the side chain. We also suggest two proposals for experiments to demonstrate this effect, which may be employed to design a new type of switching device.

Continuous-time quantum search on balanced trees

NASA Astrophysics Data System (ADS)

Philipp, Pascal; Tarrataca, Luís; Boettcher, Stefan

2016-03-01

We examine the effect of network heterogeneity on the performance of quantum search algorithms. To this end, we study quantum search on a tree for the oracle Hamiltonian formulation employed by continuous-time quantum walks. We use analytical and numerical arguments to show that the exponent of the asymptotic running time ˜Nβ changes uniformly from β =0.5 to β =1 as the searched-for site is moved from the root of the tree towards the leaves. These results imply that the time complexity of the quantum search algorithm on a balanced tree is closely correlated with certain path-based centrality measures of the searched-for site.

Exploring activity-driven network with biased walks

NASA Astrophysics Data System (ADS)

Wang, Yan; Wu, Ding Juan; Lv, Fang; Su, Meng Long

We investigate the concurrent dynamics of biased random walks and the activity-driven network, where the preferential transition probability is in terms of the edge-weighting parameter. We also obtain the analytical expressions for stationary distribution and the coverage function in directed and undirected networks, all of which depend on the weight parameter. Appropriately adjusting this parameter, more effective search strategy can be obtained when compared with the unbiased random walk, whether in directed or undirected networks. Since network weights play a significant role in the diffusion process.

Financial Data Analysis by means of Coupled Continuous-Time Random Walk in Rachev-Rűschendorf Model

NASA Astrophysics Data System (ADS)

Jurlewicz, A.; Wyłomańska, A.; Żebrowski, P.

2008-09-01

We adapt the continuous-time random walk formalism to describe asset price evolution. We expand the idea proposed by Rachev and Rűschendorf who analyzed the binomial pricing model in the discrete time with randomization of the number of price changes. As a result, in the framework of the proposed model we obtain a mixture of the Gaussian and a generalized arcsine laws as the limiting distribution of log-returns. Moreover, we derive an European-call-option price that is an extension of the Black-Scholes formula. We apply the obtained theoretical results to model actual financial data and try to show that the continuous-time random walk offers alternative tools to deal with several complex issues of financial markets.

An online social network to increase walking in dog owners: a randomized trial.

PubMed

Schneider, Kristin L; Murphy, Deirdra; Ferrara, Cynthia; Oleski, Jessica; Panza, Emily; Savage, Clara; Gada, Kimberly; Bozzella, Brianne; Olendzki, Effie; Kern, Daniel; Lemon, Stephenie C

2015-03-01

Encouraging dog walking may increase physical activity in dog owners. This cluster-randomized controlled trial investigated whether a social networking Web site (Meetup™) could be used to deliver a multicomponent dog walking intervention to increase physical activity. Sedentary dog owners (n = 102) participated. Eight neighborhoods were randomly assigned to the Meetup™ condition (Meetup™) or a condition where participants received monthly e-mails with content from the American Heart Association regarding increasing physical activity. The Meetup™ intervention was delivered over 6 months and consisted of newsletters, dog walks, community events, and an activity monitor. The primary outcome was steps; secondary outcomes included social support for walking, sense of community, perceived dog walking outcomes, barriers to dog walking, and feasibility of the intervention. Mixed-model analyses examined change from baseline to postintervention (6 months) and whether change in outcomes differed by condition. Daily steps increased over time (P = 0.04, d = 0.28), with no differences by condition. The time-condition interaction was significant for the perceived outcomes of dog walking (P = 0.04, d = 0.40), such that the Meetup™ condition reported an increase in the perceived positive outcomes of dog walking, whereas the American Heart Association condition did not. Social support, sense of community, and dog walking barriers did not significantly change. Meetup™ logins averaged 58.38 per week (SD, 11.62). Within 2 months of the intervention ending, organization of the Meetup™ groups transitioned from the study staff to Meetup™ members. Results suggest that a Meetup™ group is feasible for increasing physical activity in dog owners. Further research is needed to understand how to increase participation in the Meetup™ group and facilitate greater connection among dog owners.

Evaluation of the Dogs, Physical Activity, and Walking (Dogs PAW) Intervention: A Randomized Controlled Trial.

PubMed

Richards, Elizabeth A; Ogata, Niwako; Cheng, Ching-Wei

2016-01-01

To facilitate physical activity (PA) adoption and maintenance, promotion of innovative population-level strategies that focus on incorporating moderate-intensity lifestyle PAs are needed. The purpose of this randomized controlled trial was to evaluate the Dogs, Physical Activity, and Walking intervention, a 3-month, social cognitive theory (SCT), e-mail-based PA intervention. In a longitudinal, repeated-measures design, 49 dog owners were randomly assigned to a control (n = 25) or intervention group (n = 24). The intervention group received e-mail messages (twice weekly for 4 weeks and weekly for 8 weeks) designed to influence SCT constructs of self-efficacy, self-regulation, outcome expectations and expectancies, and social support. At baseline and every 3 months through 1 year, participants completed self-reported questionnaires of individual, interpersonal, and PA variables. Linear mixed models were used to assess for significant differences in weekly minutes of dog walking and theoretical constructs between groups (intervention and control) across time. To test self-efficacy as a mediator of social support for dog walking, tests for mediation were conducted using the bootstrapping technique. With the exception of Month 9, participants in the intervention group accumulated significantly more weekly minutes of dog walking than the control group. On average, the intervention group accumulated 58.4 more minutes (SD = 18.1) of weekly dog walking than the control group (p < .05). Self-efficacy partially mediated the effect of social support variables on dog walking. Results indicate that a simple SCT-based e-mail intervention is effective in increasing and maintaining an increase in dog walking among dog owners at 12-month follow-up. In light of these findings, it may be advantageous to design dog walking interventions that focus on increasing self-efficacy for dog walking by fostering social support.

An Online Social Network to Increase Walking in Dog Owners: A Randomized Trial

PubMed Central

Schneider, Kristin L.; Murphy, Deirdra; Ferrara, Cynthia; Oleski, Jessica; Panza, Emily; Savage, Clara; Gada, Kimberly; Bozzella, Brianne; Olendzki, Effie; Kern, Daniel; Lemon, Stephenie C.

2014-01-01

PURPOSE Encouraging dog walking may increase physical activity in dog owners. This cluster randomized controlled trial investigated whether a social networking website (Meetup™) could be used to deliver a multi-component dog walking intervention to increase physical activity. METHODS Sedentary dog owners (n=102) participated. Eight neighborhoods were randomly assigned to the Meetup condition (Meetup) or a condition where participants received monthly emails with content from the American Heart Association on increasing physical activity (AHA). The Meetup intervention was delivered over 6 months and consisted of newsletters, dog walks, community events and an activity monitor. The primary outcome was steps; secondary outcomes included social support for walking, sense of community, perceived dog walking outcomes, barriers to dog walking and feasibility of the intervention. RESULTS Mixed model analyses examined change from baseline to post-intervention (6 months) and whether change in outcomes differed by condition. Daily steps increased over time (p=0.04, d=0.28), with no differences by condition. The time x condition interaction was significant for the perceived outcomes of dog walking (p=0.04, d=0.40), such that the Meetup condition reported an increase in the perceived positive outcomes of dog walking, whereas the AHA condition did not. Social support, sense of community and dog walking barriers did not significantly change. Meetup logins averaged 58.38 per week (SD=11.62). Within two months of the intervention ending, organization of the Meetup groups transitioned from study staff to Meetup members. CONCLUSION Results suggest that a Meetup group is feasible for increasing physical activity in dog owners. Further research is needed to understand how to increase participation in the Meetup group and facilitate greater connection among dog owners. PMID:25003777

Return probabilities and hitting times of random walks on sparse Erdös-Rényi graphs.

PubMed

Martin, O C; Sulc, P

2010-03-01

We consider random walks on random graphs, focusing on return probabilities and hitting times for sparse Erdös-Rényi graphs. Using the tree approach, which is expected to be exact in the large graph limit, we show how to solve for the distribution of these quantities and we find that these distributions exhibit a form of self-similarity.

Stationary Random Metrics on Hierarchical Graphs Via {(min,+)}-type Recursive Distributional Equations

NASA Astrophysics Data System (ADS)

Khristoforov, Mikhail; Kleptsyn, Victor; Triestino, Michele

2016-07-01

This paper is inspired by the problem of understanding in a mathematical sense the Liouville quantum gravity on surfaces. Here we show how to define a stationary random metric on self-similar spaces which are the limit of nice finite graphs: these are the so-called hierarchical graphs. They possess a well-defined level structure and any level is built using a simple recursion. Stopping the construction at any finite level, we have a discrete random metric space when we set the edges to have random length (using a multiplicative cascade with fixed law {m}). We introduce a tool, the cut-off process, by means of which one finds that renormalizing the sequence of metrics by an exponential factor, they converge in law to a non-trivial metric on the limit space. Such limit law is stationary, in the sense that glueing together a certain number of copies of the random limit space, according to the combinatorics of the brick graph, the obtained random metric has the same law when rescaled by a random factor of law {m} . In other words, the stationary random metric is the solution of a distributional equation. When the measure m has continuous positive density on {mathbf{R}+}, the stationary law is unique up to rescaling and any other distribution tends to a rescaled stationary law under the iterations of the hierarchical transformation. We also investigate topological and geometric properties of the random space when m is log-normal, detecting a phase transition influenced by the branching random walk associated to the multiplicative cascade.

A Stochastic Simulation Framework for the Prediction of Strategic Noise Mapping and Occupational Noise Exposure Using the Random Walk Approach

PubMed Central

Haron, Zaiton; Bakar, Suhaimi Abu; Dimon, Mohamad Ngasri

2015-01-01

Strategic noise mapping provides important information for noise impact assessment and noise abatement. However, producing reliable strategic noise mapping in a dynamic, complex working environment is difficult. This study proposes the implementation of the random walk approach as a new stochastic technique to simulate noise mapping and to predict the noise exposure level in a workplace. A stochastic simulation framework and software, namely RW-eNMS, were developed to facilitate the random walk approach in noise mapping prediction. This framework considers the randomness and complexity of machinery operation and noise emission levels. Also, it assesses the impact of noise on the workers and the surrounding environment. For data validation, three case studies were conducted to check the accuracy of the prediction data and to determine the efficiency and effectiveness of this approach. The results showed high accuracy of prediction results together with a majority of absolute differences of less than 2 dBA; also, the predicted noise doses were mostly in the range of measurement. Therefore, the random walk approach was effective in dealing with environmental noises. It could predict strategic noise mapping to facilitate noise monitoring and noise control in the workplaces. PMID:25875019

Correlated random walks induced by dynamical wavefunction collapse

NASA Astrophysics Data System (ADS)

Bedingham, Daniel

2015-03-01

Wavefunction collapse models modify Schrödinger's equation so that it describes the collapse of a superposition of macroscopically distinguishable states as a genuine physical process [PRA 42, 78 (1990)]. This provides a basis for the resolution of the quantum measurement problem. An additional generic consequence of the collapse mechanism is that it causes particles to exhibit a tiny random diffusive motion. Furthermore, the diffusions of two sufficiently nearby particles are positively correlated -- it is more likely that the particles diffuse in the same direction than would happen if they behaved independently [PRA 89, 032713 (2014)]. The use of this effect is proposed as an experimental test of wave function collapse models in which pairs of nanoparticles are simultaneously released from nearby traps and allowed a brief period of free fall. The random displacements of the particles are then measured. The experiment must be carried out at sufficiently low temperature and pressure for the collapse effects to dominate over the ambient environmental noise. It is argued that these constraints can be satisfied by current technologies for a large class of viable wavefunction collapse models. Work supported by the Templeton World Charity Foundation.

Superdiffusion in a non-Markovian random walk model with a Gaussian memory profile

NASA Astrophysics Data System (ADS)

Borges, G. M.; Ferreira, A. S.; da Silva, M. A. A.; Cressoni, J. C.; Viswanathan, G. M.; Mariz, A. M.

2012-09-01

Most superdiffusive Non-Markovian random walk models assume that correlations are maintained at all time scales, e.g., fractional Brownian motion, Lévy walks, the Elephant walk and Alzheimer walk models. In the latter two models the random walker can always "remember" the initial times near t = 0. Assuming jump size distributions with finite variance, the question naturally arises: is superdiffusion possible if the walker is unable to recall the initial times? We give a conclusive answer to this general question, by studying a non-Markovian model in which the walker's memory of the past is weighted by a Gaussian centered at time t/2, at which time the walker had one half the present age, and with a standard deviation σt which grows linearly as the walker ages. For large widths we find that the model behaves similarly to the Elephant model, but for small widths this Gaussian memory profile model behaves like the Alzheimer walk model. We also report that the phenomenon of amnestically induced persistence, known to occur in the Alzheimer walk model, arises in the Gaussian memory profile model. We conclude that memory of the initial times is not a necessary condition for generating (log-periodic) superdiffusion. We show that the phenomenon of amnestically induced persistence extends to the case of a Gaussian memory profile.

A generalized model via random walks for information filtering

NASA Astrophysics Data System (ADS)

Ren, Zhuo-Ming; Kong, Yixiu; Shang, Ming-Sheng; Zhang, Yi-Cheng

2016-08-01

There could exist a simple general mechanism lurking beneath collaborative filtering and interdisciplinary physics approaches which have been successfully applied to online E-commerce platforms. Motivated by this idea, we propose a generalized model employing the dynamics of the random walk in the bipartite networks. Taking into account the degree information, the proposed generalized model could deduce the collaborative filtering, interdisciplinary physics approaches and even the enormous expansion of them. Furthermore, we analyze the generalized model with single and hybrid of degree information on the process of random walk in bipartite networks, and propose a possible strategy by using the hybrid degree information for different popular objects to toward promising precision of the recommendation.

Statistical projection effects in a hydrodynamic pilot-wave system

NASA Astrophysics Data System (ADS)

Sáenz, Pedro J.; Cristea-Platon, Tudor; Bush, John W. M.

2018-03-01

Millimetric liquid droplets can walk across the surface of a vibrating fluid bath, self-propelled through a resonant interaction with their own guiding or `pilot' wave fields. These walking droplets, or `walkers', exhibit several features previously thought to be peculiar to the microscopic, quantum realm. In particular, walkers confined to circular corrals manifest a wave-like statistical behaviour reminiscent of that of electrons in quantum corrals. Here we demonstrate that localized topological inhomogeneities in an elliptical corral may lead to resonant projection effects in the walker's statistics similar to those reported in quantum corrals. Specifically, we show that a submerged circular well may drive the walker to excite specific eigenmodes in the bath that result in drastic changes in the particle's statistical behaviour. The well tends to attract the walker, leading to a local peak in the walker's position histogram. By placing the well at one of the foci, a mode with maxima near the foci is preferentially excited, leading to a projection effect in the walker's position histogram towards the empty focus, an effect strongly reminiscent of the quantum mirage. Finally, we demonstrate that the mean pilot-wave field has the same form as the histogram describing the walker's statistics.

Non-Markovian continuous-time quantum walks on lattices with dynamical noise

NASA Astrophysics Data System (ADS)

Benedetti, Claudia; Buscemi, Fabrizio; Bordone, Paolo; Paris, Matteo G. A.

2016-04-01

We address the dynamics of continuous-time quantum walks on one-dimensional disordered lattices inducing dynamical noise in the system. Noise is described as time-dependent fluctuations of the tunneling amplitudes between adjacent sites, and attention is focused on non-Gaussian telegraph noise, going beyond the usual assumption of fast Gaussian noise. We observe the emergence of two different dynamical behaviors for the walker, corresponding to two opposite noise regimes: slow noise (i.e., strong coupling with the environment) confines the walker into few lattice nodes, while fast noise (weak coupling) induces a transition between quantum and classical diffusion over the lattice. A phase transition between the two dynamical regimes may be observed by tuning the ratio between the autocorrelation time of the noise and the coupling between the walker and the external environment generating the noise. We also address the non-Markovianity of the quantum map by assessing its memory effects, as well as evaluating the information backflow to the system. Our results suggest that the non-Markovian character of the evolution is linked to the dynamical behavior in the slow noise regime, and that fast noise induces a Markovian dynamics for the walker.

Use of Accelerometer-Based Feedback of Walking Activity for Appraising Progress With Walking-Related Goals in Inpatient Stroke Rehabilitation: A Randomized Controlled Trial.

PubMed

Mansfield, Avril; Wong, Jennifer S; Bryce, Jessica; Brunton, Karen; Inness, Elizabeth L; Knorr, Svetlana; Jones, Simon; Taati, Babak; McIlroy, William E

2015-10-01

Regaining independent ambulation is important to those with stroke. Increased walking practice during "down time" in rehabilitation could improve walking function for individuals with stroke. To determine the effect of providing physiotherapists with accelerometer-based feedback on patient activity and walking-related goals during inpatient stroke rehabilitation. Participants with stroke wore accelerometers around both ankles every weekday during inpatient rehabilitation. Participants were randomly assigned to receive daily feedback about walking activity via their physiotherapists (n = 29) or to receive no feedback (n = 28). Changes in measures of daily walking (walking time, number of steps, average cadence, longest bout duration, and number of "long" walking bouts) and changes in gait control and function assessed in-laboratory were compared between groups. There was no significant increase in walking time, number of steps, longest bout duration, or number of long walking bouts for the feedback group compared with the control group (P values > .20). However, individuals who received feedback significantly increased cadence of daily walking more than the control group (P = .013). From the in-laboratory gait assessment, individuals who received feedback had a greater increase in walking speed and decrease in step time variability than the control group (P values < .030). Feedback did not increase the amount of walking completed by individuals with stroke. However, there was a significant increase in cadence, indicating that intensity of daily walking was greater for those who received feedback than the control group. Additionally, more intense daily walking activity appeared to translate to greater improvements in walking speed. © The Author(s) 2015.

Quantum enigma cipher as a generalization of the quantum stream cipher

NASA Astrophysics Data System (ADS)

Kato, Kentaro

2016-09-01

Various types of randomizations for the quantum stream cipher by Y00 protocol have been developed so far. In particular, it must be noted that the analysis of immunity against correlation attacks with a new type of randomization by Hirota and Kurosawa prompted a new look at the quantum stream cipher by Y00 protocol (Quant. Inform. Process. 6(2) 2007). From the preceding study on the quantum stream cipher, we recognized that the quantum stream cipher by Y00 protocol would be able to be generalized to a new type of physical cipher that has potential to exceed the Shannon limit by installing additional randomization mechanisms, in accordance with the law of quantum mechanics. We call this new type of physical random cipher the quantum enigma cipher. In this article, we introduce the recent developments for the quantum stream cipher by Y00 protocol and future plans toward the quantum enigma cipher.

Metastability of Reversible Random Walks in Potential Fields

NASA Astrophysics Data System (ADS)

Landim, C.; Misturini, R.; Tsunoda, K.

2015-09-01

Let be an open and bounded subset of , and let be a twice continuously differentiable function. Denote by the discretization of , , and denote by the continuous-time, nearest-neighbor, random walk on which jumps from to at rate . We examine in this article the metastable behavior of among the wells of the potential F.

Electrical Resistance of the Low Dimensional Critical Branching Random Walk

NASA Astrophysics Data System (ADS)

Járai, Antal A.; Nachmias, Asaf

2014-10-01

We show that the electrical resistance between the origin and generation n of the incipient infinite oriented branching random walk in dimensions d < 6 is O( n 1- α ) for some universal constant α > 0. This answers a question of Barlow et al. (Commun Math Phys 278:385-431, 2008).

Exits in order: How crowding affects particle lifetimes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Penington, Catherine J.; Simpson, Matthew J.; Baker, Ruth E.

2016-06-28

Diffusive processes are often represented using stochastic random walk frameworks. The amount of time taken for an individual in a random walk to intersect with an absorbing boundary is a fundamental property that is often referred to as the particle lifetime, or the first passage time. The mean lifetime of particles in a random walk model of diffusion is related to the amount of time required for the diffusive process to reach a steady state. Mathematical analysis describing the mean lifetime of particles in a standard model of diffusion without crowding is well known. However, the lifetime of agents inmore » a random walk with crowding has received much less attention. Since many applications of diffusion in biology and biophysics include crowding effects, here we study a discrete model of diffusion that incorporates crowding. Using simulations, we show that crowding has a dramatic effect on agent lifetimes, and we derive an approximate expression for the mean agent lifetime that includes crowding effects. Our expression matches simulation results very well, and highlights the importance of crowding effects that are sometimes overlooked.« less

Accumulator and random-walk models of psychophysical discrimination: a counter-evaluation.

PubMed

Vickers, D; Smith, P

1985-01-01

In a recent assessment of models of psychophysical discrimination, Heath criticises the accumulator model for its reliance on computer simulation and qualitative evidence, and contrasts it unfavourably with a modified random-walk model, which yields exact predictions, is susceptible to critical test, and is provided with simple parameter-estimation techniques. A counter-evaluation is presented, in which the approximations employed in the modified random-walk analysis are demonstrated to be seriously inaccurate, the resulting parameter estimates to be artefactually determined, and the proposed test not critical. It is pointed out that Heath's specific application of the model is not legitimate, his data treatment inappropriate, and his hypothesis concerning confidence inconsistent with experimental results. Evidence from adaptive performance changes is presented which shows that the necessary assumptions for quantitative analysis in terms of the modified random-walk model are not satisfied, and that the model can be reconciled with data at the qualitative level only by making it virtually indistinguishable from an accumulator process. A procedure for deriving exact predictions for an accumulator process is outlined.

Saddlepoint approximation to the distribution of the total distance of the continuous time random walk

NASA Astrophysics Data System (ADS)

Gatto, Riccardo

2017-12-01

This article considers the random walk over Rp, with p ≥ 2, where a given particle starts at the origin and moves stepwise with uniformly distributed step directions and step lengths following a common distribution. Step directions and step lengths are independent. The case where the number of steps of the particle is fixed and the more general case where it follows an independent continuous time inhomogeneous counting process are considered. Saddlepoint approximations to the distribution of the distance from the position of the particle to the origin are provided. Despite the p-dimensional nature of the random walk, the computations of the saddlepoint approximations are one-dimensional and thus simple. Explicit formulae are derived with dimension p = 3: for uniformly and exponentially distributed step lengths, for fixed and for Poisson distributed number of steps. In these situations, the high accuracy of the saddlepoint approximations is illustrated by numerical comparisons with Monte Carlo simulation. Contribution to the "Topical Issue: Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.

Varied overground walking training versus body-weight-supported treadmill training in adults within 1 year of stroke: a randomized controlled trial.

PubMed

DePaul, Vincent G; Wishart, Laurie R; Richardson, Julie; Thabane, Lehana; Ma, Jinhui; Lee, Timothy D

2015-05-01

Although task-related walking training has been recommended after stroke, the theoretical basis, content, and impact of interventions vary across the literature. There is a need for a comparison of different approaches to task-related walking training after stroke. To compare the impact of a motor-learning-science-based overground walking training program with body-weight-supported treadmill training (BWSTT) in ambulatory, community-dwelling adults within 1 year of stroke onset. In this rater-blinded, 1:1 parallel, randomized controlled trial, participants were stratified by baseline gait speed. Participants assigned to the Motor Learning Walking Program (MLWP) practiced various overground walking tasks under the supervision of 1 physiotherapist. Cognitive effort was encouraged through random practice and limited provision of feedback and guidance. The BWSTT program emphasized repetition of the normal gait cycle while supported on a treadmill and assisted by 1 to 3 therapy staff. The primary outcome was comfortable gait speed at postintervention assessment (T2). In total, 71 individuals (mean age = 67.3; standard deviation = 11.6 years) with stroke (mean onset = 20.9 [14.1] weeks) were randomized (MLWP, n = 35; BWSTT, n = 36). There was no significant between-group difference in gait speed at T2 (0.002 m/s; 95% confidence interval [CI] = -0.11, 0.12; P > .05). The MLWP group improved by 0.14 m/s (95% CI = 0.09, 0.19), and the BWSTT group improved by 0.14 m/s (95% CI = 0.08, 0.20). In this sample of community-dwelling adults within 1 year of stroke, a 15-session program of varied overground walking-focused training was not superior to a BWSTT program of equal frequency, duration, and in-session step activity. © The Author(s) 2014.

On the genealogy of branching random walks and of directed polymers

NASA Astrophysics Data System (ADS)

Derrida, Bernard; Mottishaw, Peter

2016-08-01

It is well known that the mean-field theory of directed polymers in a random medium exhibits replica symmetry breaking with a distribution of overlaps which consists of two delta functions. Here we show that the leading finite-size correction to this distribution of overlaps has a universal character which can be computed explicitly. Our results can also be interpreted as genealogical properties of branching Brownian motion or of branching random walks.

Nonergodic property of the space-time coupled CTRW: Dependence on the long-tailed property and correlation

NASA Astrophysics Data System (ADS)

Liu, Jian; Li, Baohe; Chen, Xiaosong

2018-02-01

The space-time coupled continuous time random walk model is a stochastic framework of anomalous diffusion with many applications in physics, geology and biology. In this manuscript the time averaged mean squared displacement and nonergodic property of a space-time coupled continuous time random walk model is studied, which is a prototype of the coupled continuous time random walk presented and researched intensively with various methods. The results in the present manuscript show that the time averaged mean squared displacements increase linearly with lag time which means ergodicity breaking occurs, besides, we find that the diffusion coefficient is intrinsically random which shows both aging and enhancement, the analysis indicates that the either aging or enhancement phenomena are determined by the competition between the correlation exponent γ and the waiting time's long-tailed index α.

Aerobic treadmill plus Bobath walking training improves walking in subacute stroke: a randomized controlled trial.

PubMed

Eich, H-J; Mach, H; Werner, C; Hesse, S

2004-09-01

To evaluate the immediate and long-term effects of aerobic treadmill plus Bobath walking training in subacute stroke survivors compared with Bobath walking training alone. Randomized controlled trial. Rehabilitation unit. Fifty patients, first-time supratentorial stroke, stroke interval less than six weeks, Barthel Index (0-100) from 50 to 80, able to walk a minimum distance of 12 m with either intermittent help or stand-by while walking, cardiovascular stable, minimum 50 W in the bicycle ergometry, randomly allocated to two groups, A and B. Group A 30 min of treadmill training, harness secured and minimally supported according to patients' needs, and 30 min of physiotherapy, every workday for six weeks, speed and inclination of the treadmill were adjusted to achieve a heart rate of HR: (Hrmax-HRrest)*0.6+HRrest; in group B 60 min of daily physiotherapy for six weeks. Primary outcome variables were the absolute improvement of walking velocity (m/s) and capacity (m), secondary were gross motor function including walking ability (score out of 13) and walking quality (score out of 41), blindly assessed before and after the intervention, and at follow-up three months later. Patients tolerated the aerobic training well with no side-effects, significantly greater improvement of walking velocity and capacity both at study end (p =0.001 versus p =0.002) and at follow-up (p <0.001 versus p <0.001) in the experimental group. Between weeks 0 and 6, the experimental group improved walking speed and capacity by a mean of.31 m/s and 91 m, the control group by a mean of 0.16 m/s and 56 m. Between weeks 0 and 18, the experimental group improved walking speed and capacity by a mean of 0.36 m/s and 111 m, the control group by a mean of 0.15 m/s and 57 m. Gross motor function and walking quality did not differ at any time. Aerobic treadmill plus Bobath walking training in moderately affected stroke patients was better than Bobath walking training alone with respect to the improvement of walking velocity and capacity. The treatment approach is recommended in patients meeting the inclusion criteria. A multicentre trial should follow to strengthen the evidence.

Body weight-supported treadmill training vs. overground walking training for persons with chronic stroke: a pilot randomized controlled trial.

PubMed

Combs-Miller, Stephanie A; Kalpathi Parameswaran, Anu; Colburn, Dawn; Ertel, Tara; Harmeyer, Amanda; Tucker, Lindsay; Schmid, Arlene A

2014-09-01

To compare the effects of body weight-supported treadmill training and overground walking training when matched for task and dose (duration/frequency/intensity) on improving walking function, activity, and participation after stroke. Single-blind, pilot randomized controlled trial with three-month follow-up. University and community settings. A convenience sample of participants (N = 20) at least six months post-stroke and able to walk independently were recruited. Thirty-minute walking interventions (body weight-supported treadmill training or overground walking training) were administered five times a week for two weeks. Intensity was monitored with the Borg Rating of Perceived Exertion Scale at five-minute increments to maintain a moderate training intensity. Walking speed (comfortable/fast 10-meter walk), walking endurance (6-minute walk), spatiotemporal symmetry, and the ICF Measure of Participation and ACTivity were assessed before, immediately after, and three months following the intervention. The overground walking training group demonstrated significantly greater improvements in comfortable walking speed compared with the body weight-supported treadmill training group immediately (change of 0.11 m/s vs. 0.06 m/s, respectively; p = 0.047) and three months (change of 0.14 m/s vs. 0.08 m/s, respectively; p = 0.029) after training. Only the overground walking training group significantly improved comfortable walking speed (p = 0.001), aspects of gait symmetry (p = 0.032), and activity (p = 0.003) immediately after training. Gains were maintained at the three-month follow-up (p < 0.05) for all measures except activity. Improvements in participation were not demonstrated. Overgound walking training was more beneficial than body weight-supported treadmill training at improving self-selected walking speed for the participants in this study. © The Author(s) 2014.

Double-slit experiment with single wave-driven particles and its relation to quantum mechanics.

PubMed

Andersen, Anders; Madsen, Jacob; Reichelt, Christian; Rosenlund Ahl, Sonja; Lautrup, Benny; Ellegaard, Clive; Levinsen, Mogens T; Bohr, Tomas

2015-07-01

In a thought-provoking paper, Couder and Fort [Phys. Rev. Lett. 97, 154101 (2006)] describe a version of the famous double-slit experiment performed with droplets bouncing on a vertically vibrated fluid surface. In the experiment, an interference pattern in the single-particle statistics is found even though it is possible to determine unambiguously which slit the walking droplet passes. Here we argue, however, that the single-particle statistics in such an experiment will be fundamentally different from the single-particle statistics of quantum mechanics. Quantum mechanical interference takes place between different classical paths with precise amplitude and phase relations. In the double-slit experiment with walking droplets, these relations are lost since one of the paths is singled out by the droplet. To support our conclusions, we have carried out our own double-slit experiment, and our results, in particular the long and variable slit passage times of the droplets, cast strong doubt on the feasibility of the interference claimed by Couder and Fort. To understand theoretically the limitations of wave-driven particle systems as analogs to quantum mechanics, we introduce a Schrödinger equation with a source term originating from a localized particle that generates a wave while being simultaneously guided by it. We show that the ensuing particle-wave dynamics can capture some characteristics of quantum mechanics such as orbital quantization. However, the particle-wave dynamics can not reproduce quantum mechanics in general, and we show that the single-particle statistics for our model in a double-slit experiment with an additional splitter plate differs qualitatively from that of quantum mechanics.

The immediate and long-term effects of a walking-skill program compared to usual physiotherapy care in patients who have undergone total knee arthroplasty (TKA): a randomized controlled trial.

PubMed

Bruun-Olsen, Vigdis; Heiberg, Kristi Elisabeth; Wahl, Astrid Klopstad; Mengshoel, Anne Marit

2013-01-01

To examine the immediate and long-term effects of a walking-skill program compared with usual physiotherapy on physical function, pain and perceived self-efficacy in patients after total knee arthroplasty (TKA). A single blind randomized controlled trial design was applied. Fifty-seven patients with primary TKA, mean age of 69 years (SD ± 9), were randomly assigned to a walking-skill program emphasizing weight-bearing exercises or usual physiotherapy. Outcomes were assessed before the interventions started at 6 weeks postoperatively (T1), directly after the interventions at 12-14 weeks (T2) and 9 months after the interventions (T3). Walking was the primary outcome, assessed by the 6 min walk test (6MWT). The secondary outcomes were timed stair climbing, timed stands, Figure-of-eight test, Index of muscle function, active knee range of motion, Knee Injury and Osteoarthritis Outcome Score and self-efficacy score. From T1 to T2, a better 6MWT score was found in favor of the walking-skill program of 39 m (2-76), p = 0.04. The difference between the groups in 6MWT persisted at T3, 44 m (8-80), p = 0.02. No differences in other outcome measures were found. The walking-skill program had better effect on walking than usual physiotherapy. Weight bearing was tolerated. Implications for Rehabilitation Weight-bearing exercises are tolerated by the patients in the early stage after TKA. Physiotherapy that focuses on learning different ways of walking through practice may be a plausible way to train patients after TKA.

Exploration properties of biased evanescent random walkers on a one-dimensional lattice

NASA Astrophysics Data System (ADS)

Esguerra, Jose Perico; Reyes, Jelian

2017-08-01

We investigate the combined effects of bias and evanescence on the characteristics of random walks on a one-dimensional lattice. We calculate the time-dependent return probability, eventual return probability, conditional mean return time, and the time-dependent mean number of visited sites of biased immortal and evanescent discrete-time random walkers on a one-dimensional lattice. We then extend the calculations to the case of a continuous-time step-coupled biased evanescent random walk on a one-dimensional lattice with an exponential waiting time distribution.

Early application of tail nerve electrical stimulation-induced walking training promotes locomotor recovery in rats with spinal cord injury.

PubMed

Zhang, S-X; Huang, F; Gates, M; Shen, X; Holmberg, E G

2016-11-01

This is a randomized controlled prospective trial with two parallel groups. The objective of this study was to determine whether early application of tail nerve electrical stimulation (TANES)-induced walking training can improve the locomotor function. This study was conducted in SCS Research Center in Colorado, USA. A contusion injury to spinal cord T10 was produced using the New York University impactor device with a 25 -mm height setting in female, adult Long-Evans rats. Injured rats were randomly divided into two groups (n=12 per group). One group was subjected to TANES-induced walking training 2 weeks post injury, and the other group, as control, received no TANES-induced walking training. Restorations of behavior and conduction were assessed using the Basso, Beattie and Bresnahan open-field rating scale, horizontal ladder rung walking test and electrophysiological test (Hoffmann reflex). Early application of TANES-induced walking training significantly improved the recovery of locomotor function and benefited the restoration of Hoffmann reflex. TANES-induced walking training is a useful method to promote locomotor recovery in rats with spinal cord injury.

Nordic walking versus walking without poles for rehabilitation with cardiovascular disease: Randomized controlled trial.

PubMed

Girold, Sébastien; Rousseau, Jérome; Le Gal, Magalie; Coudeyre, Emmanuel; Le Henaff, Jacqueline

2017-07-01

With Nordic walking, or walking with poles, one can travel a greater distance and at a higher rate than with walking without poles, but whether the activity is beneficial for patients with cardiovascular disease is unknown. This randomized controlled trial was undertaken to determine whether Nordic walking was more effective than walking without poles on walk distance to support rehabilitation training for patients with acute coronary syndrome (ACS) and peripheral arterial occlusive disease (PAOD). Patients were recruited in a private specialized rehabilitation centre for cardiovascular diseases. The entire protocol, including patient recruitment, took place over 2 months, from September to October 2013. We divided patients into 2 groups: Nordic Walking Group (NWG, n=21) and Walking Group without poles (WG, n=21). All patients followed the same program over 4 weeks, except for the walk performed with or without poles. The main outcome was walk distance on the 6-min walk test. Secondary outcomes were maximum heart rate during exercise and walk distance and power output on a treadmill stress test. We included 42 patients (35 men; mean age 57.2±11 years and BMI 26.5±4.5kg/m 2 ). At the end of the training period, both groups showed improved walk distance on the 6-min walk test and treatment stress test as well as power on the treadmill stress test (P<0.05). The NWG showed significantly greater walk distance than the WG (P<0.05). Both ACS and PAOD groups showed improvement, but improvement was significant for only PAOD patients. After a 4-week training period, Nordic walking training appeared more efficient than training without poles for increasing walk distance on the 6-min walk test for patients with ACS and PAOD. Copyright © 2017. Published by Elsevier Masson SAS.

Generating and using truly random quantum states in Mathematica

NASA Astrophysics Data System (ADS)

Miszczak, Jarosław Adam

2012-01-01

The problem of generating random quantum states is of a great interest from the quantum information theory point of view. In this paper we present a package for Mathematica computing system harnessing a specific piece of hardware, namely Quantis quantum random number generator (QRNG), for investigating statistical properties of quantum states. The described package implements a number of functions for generating random states, which use Quantis QRNG as a source of randomness. It also provides procedures which can be used in simulations not related directly to quantum information processing. Program summaryProgram title: TRQS Catalogue identifier: AEKA_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEKA_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 7924 No. of bytes in distributed program, including test data, etc.: 88 651 Distribution format: tar.gz Programming language: Mathematica, C Computer: Requires a Quantis quantum random number generator (QRNG, http://www.idquantique.com/true-random-number-generator/products-overview.html) and supporting a recent version of Mathematica Operating system: Any platform supporting Mathematica; tested with GNU/Linux (32 and 64 bit) RAM: Case dependent Classification: 4.15 Nature of problem: Generation of random density matrices. Solution method: Use of a physical quantum random number generator. Running time: Generating 100 random numbers takes about 1 second, generating 1000 random density matrices takes more than a minute.

Logical-Rule Models of Classification Response Times: A Synthesis of Mental-Architecture, Random-Walk, and Decision-Bound Approaches

ERIC Educational Resources Information Center

Fific, Mario; Little, Daniel R.; Nosofsky, Robert M.

2010-01-01

We formalize and provide tests of a set of logical-rule models for predicting perceptual classification response times (RTs) and choice probabilities. The models are developed by synthesizing mental-architecture, random-walk, and decision-bound approaches. According to the models, people make independent decisions about the locations of stimuli…

Random Walk Method for Potential Problems

NASA Technical Reports Server (NTRS)

Krishnamurthy, T.; Raju, I. S.

2002-01-01

A local Random Walk Method (RWM) for potential problems governed by Lapalace's and Paragon's equations is developed for two- and three-dimensional problems. The RWM is implemented and demonstrated in a multiprocessor parallel environment on a Beowulf cluster of computers. A speed gain of 16 is achieved as the number of processors is increased from 1 to 23.

Effects of Practice on Task Architecture: Combined Evidence from Interference Experiments and Random-Walk Models of Decision Making

ERIC Educational Resources Information Center

Kamienkowski, Juan E.; Pashler, Harold; Dehaene, Stanislas; Sigman, Mariano

2011-01-01

Does extensive practice reduce or eliminate central interference in dual-task processing? We explored the reorganization of task architecture with practice by combining interference analysis (delays in dual-task experiment) and random-walk models of decision making (measuring the decision and non-decision contributions to RT). The main delay…

Reheating-volume measure for random-walk inflation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Winitzki, Sergei; Yukawa Institute of Theoretical Physics, Kyoto University, Kyoto

2008-09-15

The recently proposed 'reheating-volume' (RV) measure promises to solve the long-standing problem of extracting probabilistic predictions from cosmological multiverse scenarios involving eternal inflation. I give a detailed description of the new measure and its applications to generic models of eternal inflation of random-walk type. For those models I derive a general formula for RV-regulated probability distributions that is suitable for numerical computations. I show that the results of the RV cutoff in random-walk type models are always gauge invariant and independent of the initial conditions at the beginning of inflation. In a toy model where equal-time cutoffs lead to themore » 'youngness paradox', the RV cutoff yields unbiased results that are distinct from previously proposed measures.« less

Exercise training for intermittent claudication.

PubMed

McDermott, Mary M

2017-11-01

The objective of this study was to provide an overview of evidence regarding exercise therapies for patients with lower extremity peripheral artery disease (PAD). This manuscript summarizes the content of a lecture delivered as part of the 2016 Crawford Critical Issues Symposium. Multiple randomized clinical trials demonstrate that supervised treadmill exercise significantly improves treadmill walking performance in people with PAD and intermittent claudication symptoms. A meta-analysis of 25 randomized trials demonstrated a 180-meter increase in treadmill walking distance in response to supervised exercise interventions compared with a nonexercising control group. Supervised treadmill exercise has been inaccessible to many patients with PAD because of lack of medical insurance coverage. However, in 2017, the Centers for Medicare and Medicaid Services issued a decision memorandum to support health insurance coverage of 12 weeks of supervised treadmill exercise for patients with walking impairment due to PAD. Recent evidence also supports home-based walking exercise to improve walking performance in people with PAD. Effective home-exercise programs incorporate behavioral change interventions such as a remote coach, goal setting, and self-monitoring. Supervised treadmill exercise programs preferentially improve treadmill walking performance, whereas home-based walking exercise programs preferentially improve corridor walking, such as the 6-minute walk test. Clinical trial evidence also supports arm or leg ergometry exercise to improve walking endurance in people with PAD. Treadmill walking exercise appears superior to resistance training alone for improving walking endurance. Supervised treadmill exercise significantly improves treadmill walking performance in people with PAD by approximately 180 meters compared with no exercise. Recent evidence suggests that home-based exercise is also effective and preferentially improves over-ground walking performance, such as the 6-minute walk test. Copyright © 2017 Society for Vascular Surgery. Published by Elsevier Inc. All rights reserved.

Using wireless technology in clinical practice: does feedback of daily walking activity improve walking outcomes of individuals receiving rehabilitation post-stroke? Study protocol for a randomized controlled trial

PubMed Central

2013-01-01

Background Regaining independent ambulation is the top priority for individuals recovering from stroke. Thus, physical rehabilitation post-stroke should focus on improving walking function and endurance. However, the amount of walking completed by individuals with stroke attending rehabilitation is far below that required for independent community ambulation. There has been increased interest in accelerometer-based monitoring of walking post-stroke. Walking monitoring could be integrated within the goal-setting process for those with ambulation goals in rehabilitation. The feedback from these devices can be downloaded to a computer to produce reports. The purpose of this study is to determine the effect of accelerometer-based feedback of daily walking activity during rehabilitation on the frequency and duration of walking post-stroke. Methods Participants will be randomly assigned to one of two groups: feedback or no feedback. Participants will wear accelerometers daily during in- and out-patient rehabilitation and, for participants in the feedback group, the participants’ treating physiotherapist will receive regular reports of walking activity. The primary outcome measures are the amount of daily walking completed, as measured using the accelerometers, and spatio-temporal characteristics of walking (e.g. walking speed). We will also examine goal attainment, satisfaction with progress towards goals, stroke self-efficacy, and community-integration. Discussion Increased walking activity during rehabilitation is expected to improve walking function and community re-integration following discharge. In addition, a focus on altering walking behaviour within the rehabilitation setting may lead to altered behaviour and increased activity patterns after discharge. Trial registration ClinicalTrials.gov NCT01521234 PMID:23865593

Quantum random oracle model for quantum digital signature

NASA Astrophysics Data System (ADS)

Shang, Tao; Lei, Qi; Liu, Jianwei

2016-10-01

The goal of this work is to provide a general security analysis tool, namely, the quantum random oracle (QRO), for facilitating the security analysis of quantum cryptographic protocols, especially protocols based on quantum one-way function. QRO is used to model quantum one-way function and different queries to QRO are used to model quantum attacks. A typical application of quantum one-way function is the quantum digital signature, whose progress has been hampered by the slow pace of the experimental realization. Alternatively, we use the QRO model to analyze the provable security of a quantum digital signature scheme and elaborate the analysis procedure. The QRO model differs from the prior quantum-accessible random oracle in that it can output quantum states as public keys and give responses to different queries. This tool can be a test bed for the cryptanalysis of more quantum cryptographic protocols based on the quantum one-way function.

New Quantum Key Distribution Scheme Based on Random Hybrid Quantum Channel with EPR Pairs and GHZ States

NASA Astrophysics Data System (ADS)

Yan, Xing-Yu; Gong, Li-Hua; Chen, Hua-Ying; Zhou, Nan-Run

2018-05-01

A theoretical quantum key distribution scheme based on random hybrid quantum channel with EPR pairs and GHZ states is devised. In this scheme, EPR pairs and tripartite GHZ states are exploited to set up random hybrid quantum channel. Only one photon in each entangled state is necessary to run forth and back in the channel. The security of the quantum key distribution scheme is guaranteed by more than one round of eavesdropping check procedures. It is of high capacity since one particle could carry more than two bits of information via quantum dense coding.

Analysis of Individual Social-ecological Mediators and Moderators and Their Ability to Explain Effect of a Randomized Neighborhood Walking Intervention.

PubMed

Michael, Yvonne L; Carlson, Nichole E

2009-07-30

Using data from the SHAPE trial, a randomized 6-month neighborhood-based intervention designed to increase walking activity among older adults, this study identified and analyzed social-ecological factors mediating and moderating changes in walking activity. Three potential mediators (social cohesion, walking efficacy, and perception of neighborhood problems) and minutes of brisk walking were assessed at baseline, 3-months, and 6-months. One moderator, neighborhood walkability, was assessed using an administrative GIS database. The mediating effect of change in process variables on change in brisk walking was tested using a product-of-coefficients test, and we evaluated the moderating effect of neighborhood walkability on change in brisk walking by testing the significance of the interaction between walkability and intervention status. Only one of the hypothesized mediators, walking efficacy, explained the intervention effect (product of the coefficients (95% CI) = 8.72 (2.53, 15.56). Contrary to hypotheses, perceived neighborhood problems appeared to suppress the intervention effects (product of the coefficients (95% CI = -2.48, -5.6, -0.22). Neighborhood walkability did not moderate the intervention effect. Walking efficacy may be an important mediator of lay-lead walking interventions for sedentary older adults. Social-ecologic theory-based analyses can support clinical interventions to elucidate the mediators and moderators responsible for producing intervention effects.

Random walk with memory enhancement and decay

NASA Astrophysics Data System (ADS)

Tan, Zhi-Jie; Zou, Xian-Wu; Huang, Sheng-You; Zhang, Wei; Jin, Zhun-Zhi

2002-04-01

A model of random walk with memory enhancement and decay was presented on the basis of the characteristics of the biological intelligent walks. In this model, the movement of the walker is determined by the difference between the remaining information at the jumping-out site and jumping-in site. The amount of the memory information si(t) at a site i is enhanced with the increment of visiting times to that site, and decays with time t by the rate e-βt, where β is the memory decay exponent. When β=0, there exists a transition from Brownian motion (BM) to the compact growth of walking trajectory with the density of information energy u increasing. But for β>0, this transition does not appear and the walk with memory enhancement and decay can be considered as the BM of the mass center of the cluster composed of remembered sites in the late stage.

Continuous-Time Random Walk with multi-step memory: an application to market dynamics

NASA Astrophysics Data System (ADS)

Gubiec, Tomasz; Kutner, Ryszard

2017-11-01

An extended version of the Continuous-Time Random Walk (CTRW) model with memory is herein developed. This memory involves the dependence between arbitrary number of successive jumps of the process while waiting times between jumps are considered as i.i.d. random variables. This dependence was established analyzing empirical histograms for the stochastic process of a single share price on a market within the high frequency time scale. Then, it was justified theoretically by considering bid-ask bounce mechanism containing some delay characteristic for any double-auction market. Our model appeared exactly analytically solvable. Therefore, it enables a direct comparison of its predictions with their empirical counterparts, for instance, with empirical velocity autocorrelation function. Thus, the present research significantly extends capabilities of the CTRW formalism. Contribution to the Topical Issue "Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.

Global mean first-passage times of random walks on complex networks.

PubMed

Tejedor, V; Bénichou, O; Voituriez, R

2009-12-01

We present a general framework, applicable to a broad class of random walks on complex networks, which provides a rigorous lower bound for the mean first-passage time of a random walker to a target site averaged over its starting position, the so-called global mean first-passage time (GMFPT). This bound is simply expressed in terms of the equilibrium distribution at the target and implies a minimal scaling of the GMFPT with the network size. We show that this minimal scaling, which can be arbitrarily slow, is realized under the simple condition that the random walk is transient at the target site and independently of the small-world, scale-free, or fractal properties of the network. Last, we put forward that the GMFPT to a specific target is not a representative property of the network since the target averaged GMFPT satisfies much more restrictive bounds.

Emergence of Lévy Walks from Second-Order Stochastic Optimization

NASA Astrophysics Data System (ADS)

Kuśmierz, Łukasz; Toyoizumi, Taro

2017-12-01

In natural foraging, many organisms seem to perform two different types of motile search: directed search (taxis) and random search. The former is observed when the environment provides cues to guide motion towards a target. The latter involves no apparent memory or information processing and can be mathematically modeled by random walks. We show that both types of search can be generated by a common mechanism in which Lévy flights or Lévy walks emerge from a second-order gradient-based search with noisy observations. No explicit switching mechanism is required—instead, continuous transitions between the directed and random motions emerge depending on the Hessian matrix of the cost function. For a wide range of scenarios, the Lévy tail index is α =1 , consistent with previous observations in foraging organisms. These results suggest that adopting a second-order optimization method can be a useful strategy to combine efficient features of directed and random search.

Quantum random access memory.

PubMed

Giovannetti, Vittorio; Lloyd, Seth; Maccone, Lorenzo

2008-04-25

A random access memory (RAM) uses n bits to randomly address N=2(n) distinct memory cells. A quantum random access memory (QRAM) uses n qubits to address any quantum superposition of N memory cells. We present an architecture that exponentially reduces the requirements for a memory call: O(logN) switches need be thrown instead of the N used in conventional (classical or quantum) RAM designs. This yields a more robust QRAM algorithm, as it in general requires entanglement among exponentially less gates, and leads to an exponential decrease in the power needed for addressing. A quantum optical implementation is presented.

Rotational diffusion of a molecular cat

NASA Astrophysics Data System (ADS)

Katz-Saporta, Ori; Efrati, Efi

We show that a simple isolated system can perform rotational random walk on account of internal excitations alone. We consider the classical dynamics of a ''molecular cat'': a triatomic molecule connected by three harmonic springs with non-zero rest lengths, suspended in free space. In this system, much like for falling cats, the angular momentum constraint is non-holonomic allowing for rotations with zero overall angular momentum. The geometric nonlinearities arising from the non-zero rest lengths of the springs suffice to break integrability and lead to chaotic dynamics. The coupling of the non-integrability of the system and its non-holonomic nature results in an angular random walk of the molecule. We study the properties and dynamics of this angular motion analytically and numerically. For low energy excitations the system displays normal-mode-like motion, while for high enough excitation energy we observe regular random-walk. In between, at intermediate energies we observe an angular Lévy-walk type motion associated with a fractional diffusion coefficient interpolating between the two regimes.

Potentials of Mean Force With Ab Initio Mixed Hamiltonian Models of Solvation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dupuis, Michel; Schenter, Gregory K.; Garrett, Bruce C.

2003-08-01

We give an account of a computationally tractable and efficient procedure for the calculation of potentials of mean force using mixed Hamiltonian models of electronic structure where quantum subsystems are described with computationally intensive ab initio wavefunctions. The mixed Hamiltonian is mapped into an all-classical Hamiltonian that is amenable to a thermodynamic perturbation treatment for the calculation of free energies. A small number of statistically uncorrelated (solute-solvent) configurations are selected from the Monte Carlo random walk generated with the all-classical Hamiltonian approximation. Those are used in the averaging of the free energy using the mixed quantum/classical Hamiltonian. The methodology ismore » illustrated for the micro-solvated SN2 substitution reaction of methyl chloride by hydroxide. We also compare the potential of mean force calculated with the above protocol with an approximate formalism, one in which the potential of mean force calculated with the all-classical Hamiltonian is simply added to the energy of the isolated (non-solvated) solute along the reaction path. Interestingly the latter approach is found to be in semi-quantitative agreement with the full mixed Hamiltonian approximation.« less

Action observation training of community ambulation for improving walking ability of patients with post-stroke hemiparesis: a randomized controlled pilot trial.

PubMed

Park, Hyun-Ju; Oh, Duck-Won; Choi, Jong-Duk; Kim, Jong-Man; Kim, Suhn-Yeop; Cha, Yong-Jun; Jeon, Su-Jin

2017-08-01

To investigate the effects of action observation training involving community-based ambulation for improving walking ability after stroke. Randomized, controlled pilot study. Inpatient rehabilitation hospital. A total of 25 inpatients with post-stroke hemiparesis were randomly assigned to either the experimental group ( n = 12) or control group ( n = 13). Subjects of the experimental group watched video clips demonstrating four-staged ambulation training with a more complex environment factor for 30 minutes, three times a week for four weeks. Meanwhile, subjects of the control group watched video clips, which showed different landscape pictures. Walking function was evaluated before and after the four-week intervention using a 10-m walk test, community walk test, activities-specific balance confidence scale, and spatiotemporal gait measures. Changes in the values for the 10-m walk test (0.17 ±0.19 m/s vs. 0.05 ±0.08 m/s), community walk test (-151.42 ±123.82 seconds vs. 67.08 ±176.77 seconds), and activities-specific balance confidence (6.25 ±5.61 scores vs. 0.72 ±2.24 scores) and the spatiotemporal parameters (i.e. stride length (19.00 ±11.34 cm vs. 3.16 ±11.20 cm), single support (5.87 ±5.13% vs. 0.25 ±5.95%), and velocity (15.66 ±12.34 cm/s vs. 2.96 ±10.54 cm/s)) indicated a significant improvement in the experimental group compared with the control group. In the experimental group, walking function and ambulation confidence was significantly different between the pre- and post-intervention, whereas the control group showed a significant difference only in the 10-m walk test. Action observation training of community ambulation may be favorably used for improving walking function of patients with post-stroke hemiparesis.

SIRRACT: An international randomized clinical trial of activity feedback during inpatient stroke rehabilitation enabled by wireless sensing

PubMed Central

Dorsch, Andrew K.; Thomas, Seth; Xu, Xiaoyu; Kaiser, William; Dobkin, Bruce H.

2014-01-01

Background Walking-related disability is the most frequent reason for inpatient stroke rehabilitation. Task-related practice is a critical component for improving patient outcomes. Objective To test the feasibility of providing quantitative feedback about daily walking performance and motivating greater skills practice via remote sensing. Methods In this phase III randomized, single blind clinical trial, patients participated in conventional therapies while wearing wireless sensors (tri-axial accelerometers) at both ankles. Activity-recognition algorithms calculated the speed, distance, and duration of walking bouts. Three times a week, therapists provided either feedback about performance on a 10-meter walk (speed-only) or walking speed feedback plus a review of walking activity recorded by the sensors (augmented). Primary outcomes at discharge included total daily walking time, derived from the sensors, and a timed 15-meter walk. Results Sixteen rehabilitation centers in 11 countries enrolled 135 participants over 15 months. Sensors recorded more than 1800 days of therapy, 37,000 individual walking bouts, and 2.5 million steps. No significant differences were found between the two feedback groups in daily walking time (15.1±13.1min vs. 16.6±14.3min, p=0.54) or 15-meter walking speed (0.93±0.47m/s vs. 0.91±0.53m/s, p=0.96). Remarkably, 30% of participants decreased their total daily walking time over their rehabilitation stay. Conclusions In this first trial of remote monitoring of inpatient stroke rehabilitation, augmented feedback beyond speed alone did not increase the time spent practicing or improve walking outcomes. Remarkably modest time was spent walking. Wireless sensing, however, allowed clinicians to audit skills practice and provided ground truth regarding changes in clinically important, mobility-related activities. PMID:25261154

The Effect of Disorder on the Free-Energy for the Random Walk Pinning Model: Smoothing of the Phase Transition and Low Temperature Asymptotics

NASA Astrophysics Data System (ADS)

Berger, Quentin; Lacoin, Hubert

2011-01-01

We consider the continuous time version of the Random Walk Pinning Model (RWPM), studied in (Berger and Toninelli (Electron. J. Probab., to appear) and Birkner and Sun (Ann. Inst. Henri Poincaré Probab. Stat. 46:414-441, 2010; arXiv:0912.1663). Given a fixed realization of a random walk Y on ℤ d with jump rate ρ (that plays the role of the random medium), we modify the law of a random walk X on ℤ d with jump rate 1 by reweighting the paths, giving an energy reward proportional to the intersection time Lt(X,Y)=int0t {1}_{Xs=Ys} {d}s: the weight of the path under the new measure is exp ( βL t ( X, Y)), β∈ℝ. As β increases, the system exhibits a delocalization/localization transition: there is a critical value β c , such that if β> β c the two walks stick together for almost-all Y realizations. A natural question is that of disorder relevance, that is whether the quenched and annealed systems have the same behavior. In this paper we investigate how the disorder modifies the shape of the free energy curve: (1) We prove that, in dimension d≥3, the presence of disorder makes the phase transition at least of second order. This, in dimension d≥4, contrasts with the fact that the phase transition of the annealed system is of first order. (2) In any dimension, we prove that disorder modifies the low temperature asymptotic of the free energy.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ma, Xiongfeng; Yuan, Xiao; Cao, Zhu

Quantum physics can be exploited to generate true random numbers, which play important roles in many applications, especially in cryptography. Genuine randomness from the measurement of a quantum system reveals the inherent nature of quantumness -- coherence, an important feature that differentiates quantum mechanics from classical physics. The generation of genuine randomness is generally considered impossible with only classical means. Based on the degree of trustworthiness on devices, quantum random number generators (QRNGs) can be grouped into three categories. The first category, practical QRNG, is built on fully trusted and calibrated devices and typically can generate randomness at a highmore » speed by properly modeling the devices. The second category is self-testing QRNG, where verifiable randomness can be generated without trusting the actual implementation. The third category, semi-self-testing QRNG, is an intermediate category which provides a tradeoff between the trustworthiness on the device and the random number generation speed.« less

One Model Fits All: Explaining Many Aspects of Number Comparison within a Single Coherent Model-A Random Walk Account

ERIC Educational Resources Information Center

Reike, Dennis; Schwarz, Wolf

2016-01-01

The time required to determine the larger of 2 digits decreases with their numerical distance, and, for a given distance, increases with their magnitude (Moyer & Landauer, 1967). One detailed quantitative framework to account for these effects is provided by random walk models. These chronometric models describe how number-related noisy…

Random-walk diffusion and drying of porous materials

NASA Astrophysics Data System (ADS)

Mehrafarin, M.; Faghihi, M.

2001-12-01

Based on random-walk diffusion, a microscopic model for drying is proposed to explain the characteristic features of the drying-rate curve of porous materials. The constant drying-rate period is considered as a normal diffusion process. The transition to the falling-rate regime is attributed to the fractal nature of porous materials which results in crossover to anomalous diffusion.

A random walk rule for phase I clinical trials.

PubMed

Durham, S D; Flournoy, N; Rosenberger, W F

1997-06-01

We describe a family of random walk rules for the sequential allocation of dose levels to patients in a dose-response study, or phase I clinical trial. Patients are sequentially assigned the next higher, same, or next lower dose level according to some probability distribution, which may be determined by ethical considerations as well as the patient's response. It is shown that one can choose these probabilities in order to center dose level assignments unimodally around any target quantile of interest. Estimation of the quantile is discussed; the maximum likelihood estimator and its variance are derived under a two-parameter logistic distribution, and the maximum likelihood estimator is compared with other nonparametric estimators. Random walk rules have clear advantages: they are simple to implement, and finite and asymptotic distribution theory is completely worked out. For a specific random walk rule, we compute finite and asymptotic properties and give examples of its use in planning studies. Having the finite distribution theory available and tractable obviates the need for elaborate simulation studies to analyze the properties of the design. The small sample properties of our rule, as determined by exact theory, compare favorably to those of the continual reassessment method, determined by simulation.

Essential energy space random walk via energy space metadynamics method to accelerate molecular dynamics simulations

NASA Astrophysics Data System (ADS)

Li, Hongzhi; Min, Donghong; Liu, Yusong; Yang, Wei

2007-09-01

To overcome the possible pseudoergodicity problem, molecular dynamic simulation can be accelerated via the realization of an energy space random walk. To achieve this, a biased free energy function (BFEF) needs to be priori obtained. Although the quality of BFEF is essential for sampling efficiency, its generation is usually tedious and nontrivial. In this work, we present an energy space metadynamics algorithm to efficiently and robustly obtain BFEFs. Moreover, in order to deal with the associated diffusion sampling problem caused by the random walk in the total energy space, the idea in the original umbrella sampling method is generalized to be the random walk in the essential energy space, which only includes the energy terms determining the conformation of a region of interest. This essential energy space generalization allows the realization of efficient localized enhanced sampling and also offers the possibility of further sampling efficiency improvement when high frequency energy terms irrelevant to the target events are free of activation. The energy space metadynamics method and its generalization in the essential energy space for the molecular dynamics acceleration are demonstrated in the simulation of a pentanelike system, the blocked alanine dipeptide model, and the leucine model.

Do low step count goals inhibit walking behavior: a randomized controlled study.

PubMed

Anson, Denis; Madras, Diane

2016-07-01

Confirmation and quantification of observed differences in goal-directed walking behavior. Single-blind, split-half randomized trial. Small rural university, Pennsylvania, United States. A total of 94 able-bodied subjects (self-selected volunteer students, faculty and staff of a small university) were randomly assigned walking goals, and 53 completed the study. Incentivized pedometer-monitored program requiring recording the step-count for 56-days into a custom-made website providing daily feedback. Steps logged per day. During the first half of the study, the 5000 and 10,000 step group logged significantly different steps 7500 and 9000, respectively (P > 0.05). During the second half of the study, the 5000 and 10,000 step groups logged 7000 and 8600 steps, respectively (significance P > 0.05). The group switched from 5000 to →10,000 steps logged, 7900 steps for the first half and 9500 steps for the second half (significance P > 0.05). The group switched from 10,000 to 5000 steps logged 9700 steps for the first half and 9000 steps for the second half, which was significant (p > 0.05). Levels of walking behavior are influenced by the goals assigned. Subjects with high goals walk more than those with low goals, even if they do not meet the assigned goal. Reducing goals from a high to low level can reduce walking behavior. © The Author(s) 2015.

A fast random walk algorithm for computing the pulsed-gradient spin-echo signal in multiscale porous media.

PubMed

Grebenkov, Denis S

2011-02-01

A new method for computing the signal attenuation due to restricted diffusion in a linear magnetic field gradient is proposed. A fast random walk (FRW) algorithm for simulating random trajectories of diffusing spin-bearing particles is combined with gradient encoding. As random moves of a FRW are continuously adapted to local geometrical length scales, the method is efficient for simulating pulsed-gradient spin-echo experiments in hierarchical or multiscale porous media such as concrete, sandstones, sedimentary rocks and, potentially, brain or lungs. Copyright © 2010 Elsevier Inc. All rights reserved.

Treadmill Training or Progressive Strength Training to Improve Walking in People with Multiple Sclerosis? A Randomized Parallel Group Trial.

PubMed

Braendvik, Siri Merete; Koret, Teija; Helbostad, Jorunn L; Lorås, Håvard; Bråthen, Geir; Hovdal, Harald Olav; Aamot, Inger Lise

2016-12-01

The most effective treatment approach to improve walking in people with multiple sclerosis (MS) is not known. The aim of this trial was to assess the efficacy of treadmill training and progressive strength training on walking in people with MS. A single blinded randomized parallel group trial was carried out. Eligible participants were adults with MS with Expanded Disability Status Scale score ≤6. A total of 29 participants were randomized and 28 received the allocated exercise intervention, treadmill (n = 13) or strength training (n = 15). Both groups exercised 30 minutes, three times a week for 8 weeks. Primary outcome was The Functional Ambulation Profile evaluated by the GAITRite walkway. Secondary outcomes were walking work economy and balance control during walking, measured by a small lightweight accelerometer connected to the lower back. Testing was performed at baseline and the subsequent week after completion of training. Two participants were lost to follow-up, and 11 (treadmill) and 15 (strength training) were left for analysis. The treadmill group increased their Functional Ambulation Profile score significantly compared with the strength training group (p = .037). A significant improvement in walking work economy (p = .024) and a reduction of root mean square of vertical acceleration (p = .047) also favoured the treadmill group. The results indicate that task-specific training by treadmill walking is a favourable approach compared with strength training to improve walking in persons with mild and moderate MS. Implications for Physiotherapy practice, this study adds knowledge for the decision of optimal treatment approaches in people with MS. Copyright © 2015 John Wiley & Sons, Ltd. Copyright © 2015 John Wiley & Sons, Ltd.

Exponential gain of randomness certified by quantum contextuality

NASA Astrophysics Data System (ADS)

Um, Mark; Zhang, Junhua; Wang, Ye; Wang, Pengfei; Kim, Kihwan

2017-04-01

We demonstrate the protocol of exponential gain of randomness certified by quantum contextuality in a trapped ion system. The genuine randomness can be produced by quantum principle and certified by quantum inequalities. Recently, randomness expansion protocols based on inequality of Bell-text and Kochen-Specker (KS) theorem, have been demonstrated. These schemes have been theoretically innovated to exponentially expand the randomness and amplify the randomness from weak initial random seed. Here, we report the experimental evidence of such exponential expansion of randomness. In the experiment, we use three states of a 138Ba + ion between a ground state and two quadrupole states. In the 138Ba + ion system, we do not have detection loophole and we apply a methods to rule out certain hidden variable models that obey a kind of extended noncontextuality.

Quantum random number generation for loophole-free Bell tests

NASA Astrophysics Data System (ADS)

Mitchell, Morgan; Abellan, Carlos; Amaya, Waldimar

2015-05-01

We describe the generation of quantum random numbers at multi-Gbps rates, combined with real-time randomness extraction, to give very high purity random numbers based on quantum events at most tens of ns in the past. The system satisfies the stringent requirements of quantum non-locality tests that aim to close the timing loophole. We describe the generation mechanism using spontaneous-emission-driven phase diffusion in a semiconductor laser, digitization, and extraction by parity calculation using multi-GHz logic chips. We pay special attention to experimental proof of the quality of the random numbers and analysis of the randomness extraction. In contrast to widely-used models of randomness generators in the computer science literature, we argue that randomness generation by spontaneous emission can be extracted from a single source.

The energy cost of quantum information losses

NASA Astrophysics Data System (ADS)

Romanelli, Alejandro; de Lima Marquezino, Franklin; Portugal, Renato; Donangelo, Raul

2018-05-01

We explore the energy cost of the information loss resulting from the passage of an initial density operator to a reduced one. We use the concept of entanglement temperature in order to obtain a lower bound for the energy change associated with this operation. We determine the minimal energy required for the case of the information losses associated with the trace over the space coordinates of a two-dimensional quantum walk.

Quantum random number generator based on quantum nature of vacuum fluctuations

NASA Astrophysics Data System (ADS)

Ivanova, A. E.; Chivilikhin, S. A.; Gleim, A. V.

2017-11-01

Quantum random number generator (QRNG) allows obtaining true random bit sequences. In QRNG based on quantum nature of vacuum, optical beam splitter with two inputs and two outputs is normally used. We compare mathematical descriptions of spatial beam splitter and fiber Y-splitter in the quantum model for QRNG, based on homodyne detection. These descriptions were identical, that allows to use fiber Y-splitters in practical QRNG schemes, simplifying the setup. Also we receive relations between the input radiation and the resulting differential current in homodyne detector. We experimentally demonstrate possibility of true random bits generation by using QRNG based on homodyne detection with Y-splitter.

Body weight supported treadmill training versus traditional training in patients dependent on walking assistance after stroke: a randomized controlled trial.

PubMed

Høyer, Ellen; Jahnsen, Reidun; Stanghelle, Johan Kvalvik; Strand, Liv Inger

2012-01-01

Treadmill training with body weight support (TTBWS) for relearning walking ability after brain damage is an approach under current investigation. Efficiency of this method beyond traditional training is lacking evidence, especially in patients needing walking assistance after stroke. The objective of this study was to investigate change in walking and transfer abilities, comparing TTBWS with traditional walking training. A single-blinded, randomized controlled trial was conducted. Sixty patients referred for multi-disciplinary primary rehabilitation were assigned into one of two intervention groups, one received 30 sessions of TTBWS plus traditional training, the other traditional training alone. Daily training was 1 hr. Outcome measures were Functional Ambulation Categories (FAC), Walking, Functional Independence Measure (FIM); shorter transfer and stairs, 10 m and 6-min walk tests. Substantial improvements in walking and transfer were shown within both groups after 5 and 11 weeks of intervention. Overall no statistical significant differences were found between the groups, but 12 of 17 physical measures tended to show improvements in favour of the treadmill approach. Both training strategies provided significant improvements in the tested activities, suggesting that similar outcomes can be obtained in the two modalities by systematic, intensive and goal directed training.

Dual-Task Does Not Increase Slip and Fall Risk in Healthy Young and Older Adults during Walking

PubMed Central

Soangra, Rahul

2017-01-01

Dual-task tests can identify gait characteristics peculiar to fallers and nonfallers. Understanding the relationship between gait performance and dual-task related cognitive-motor interference is important for fall prevention. Dual-task adapted changes in gait instability/variability can adversely affect fall risks. Although implicated, it is unclear if healthy participants' fall risks are modified by dual-task walking conditions. Seven healthy young and seven healthy older adults were randomly assigned to normal walking and dual-task walking sessions with a slip perturbation. In the dual-task session, the participants walked and simultaneously counted backwards from a randomly provided number. The results indicate that the gait changes in dual-task walking have no destabilizing effect on gait and slip responses in healthy individuals. We also found that, during dual-tasking, healthy individuals adopted cautious gait mode (CGM) strategy that is characterized by reduced walking speed, shorter step length, increased step width, and reduced heel contact velocity and is likely to be an adaptation to minimize attentional demand and decrease slip and fall risk during limited available attentional resources. Exploring interactions between gait variability and cognitive functions while walking may lead to designing appropriate fall interventions among healthy and patient population with fall risk. PMID:28255224

Neighborhood walkability, fear and risk of falling and response to walking promotion: The Easy Steps to Health 12-month randomized controlled trial.

PubMed

Merom, D; Gebel, K; Fahey, P; Astell-Burt, T; Voukelatos, A; Rissel, C; Sherrington, C

2015-01-01

In older adults the relationships between health, fall-related risk factors, perceived neighborhood walkability, walking behavior and intervention impacts are poorly understood. To determine whether: i) health and fall-related risk factors were associated with perceptions of neighborhood walkability; ii) perceived environmental attributes, and fall-related risk factors predicted change in walking behavior at 12 months; and iii) perceived environmental attributes and fall-related risk factors moderated the effect of a self-paced walking program on walking behavior. Randomized trial on walking and falls conducted between 2009 and 2012 involving 315 community-dwelling inactive adults ≥ 65 years living in Sydney, Australia. Measures were: mobility status, fall history, injurious fall and fear of falling (i.e., fall-related risk factors), health status, walking self-efficacy and 11 items from the neighborhood walkability scale and planned walking ≥ 150 min/week at 12 months. Participants with poorer mobility, fear of falling, and poor health perceived their surroundings as less walkable. Walking at 12 months was significantly greater in "less greenery" (AOR = 3.3, 95% CI: 1.11-9.98) and "high traffic" (AOR = 1.98, 95% CI: 1.00-3.91) neighborhoods. The intervention had greater effects in neighborhoods perceived to have poorer pedestrian infrastructure (p for interaction = 0.036). Low perceived walkability was shaped by health status and did not appear to be a barrier to walking behavior. There appears to be a greater impact of, and thus, need for, interventions to encourage walking in environments perceived not to have supportive walking infrastructure. Future studies on built environments and walking should gather information on fall-related risk factors to better understand how these characteristics interact.

Biased and greedy random walks on two-dimensional lattices with quenched randomness: The greedy ant within a disordered environment

NASA Astrophysics Data System (ADS)

Mitran, T. L.; Melchert, O.; Hartmann, A. K.

2013-12-01

The main characteristics of biased greedy random walks (BGRWs) on two-dimensional lattices with real-valued quenched disorder on the lattice edges are studied. Here the disorder allows for negative edge weights. In previous studies, considering the negative-weight percolation (NWP) problem, this was shown to change the universality class of the existing, static percolation transition. In the presented study, four different types of BGRWs and an algorithm based on the ant colony optimization heuristic were considered. Regarding the BGRWs, the precise configurations of the lattice walks constructed during the numerical simulations were influenced by two parameters: a disorder parameter ρ that controls the amount of negative edge weights on the lattice and a bias strength B that governs the drift of the walkers along a certain lattice direction. The random walks are “greedy” in the sense that the local optimal choice of the walker is to preferentially traverse edges with a negative weight (associated with a net gain of “energy” for the walker). Here, the pivotal observable is the probability that, after termination, a lattice walk exhibits a total negative weight, which is here considered as percolating. The behavior of this observable as function of ρ for different bias strengths B is put under scrutiny. Upon tuning ρ, the probability to find such a feasible lattice walk increases from zero to 1. This is the key feature of the percolation transition in the NWP model. Here, we address the question how well the transition point ρc, resulting from numerically exact and “static” simulations in terms of the NWP model, can be resolved using simple dynamic algorithms that have only local information available, one of the basic questions in the physics of glassy systems.

Interrelations between random walks on diagrams (graphs) with and without cycles.

PubMed

Hill, T L

1988-05-01

Three topics are discussed. A discrete-state, continuous-time random walk with one or more absorption states can be studied by a presumably new method: some mean properties, including the mean time to absorption, can be found from a modified diagram (graph) in which each absorption state is replaced by a one-way cycle back to the starting state. The second problem is a random walk on a diagram (graph) with cycles. The walk terminates on completion of the first cycle. This walk can be replaced by an equivalent walk on a modified diagram with absorption. This absorption diagram can in turn be replaced by another modified diagram with one-way cycles back to the starting state, just as in the first problem. The third problem, important in biophysics, relates to a long-time continuous walk on a diagram with cycles. This diagram can be transformed (in two steps) to a modified, more-detailed, diagram with one-way cycles only. Thus, the one-way cycle fluxes of the original diagram can be found from the state probabilities of the modified diagram. These probabilities can themselves be obtained by simple matrix inversion (the probabilities are determined by linear algebraic steady-state equations). Thus, a simple method is now available to find one-way cycle fluxes exactly (previously Monte Carlo simulation was required to find these fluxes, with attendant fluctuations, for diagrams of any complexity). An incidental benefit of the above procedure is that it provides a simple proof of the one-way cycle flux relation Jn +/- = IIn +/- sigma n/sigma, where n is any cycle of the original diagram.

Effect of Body Weight-supported Walking on Exercise Capacity and Walking Speed in Patients with Knee Osteoarthritis: A Randomized Controlled Trial

PubMed Central

Someya, Fujiko

2013-01-01

Abstract Objective: To compare the effect of body-weight-supported treadmill training (BWSTT) and full-body-weight treadmill training (FBWTT) on patients with knee osteoarthritis (OA). Methods: Design was Randomized controlled trial. Patients with knee osteoarthritis (n = 30; mean age, 76.0±7.5 y) were randomly assigned to BWSTT or FBWTT group. All patients performed 20 min walking exercise twice a week for 6 weeks under the supervision of the therapist. Main measures were 10-meter walking test (10MWT), functional reach test (FRT), timed get up and go test (TUG), one-leg standing test, 6-minute walking test (6MWT), the parameters set on the treadmill, MOS Short-Form 36-Item Health Survey (SF36), Japanese Knee Osteoarthritis Measure (JKOM). Results: Twenty-five patients (10 men, 15 women; mean age, 76.5 ± 8.0 y) completed the experiment. Exercise capacity, indicated by the heart rate, was similar in both groups. After 3 weeks of BWSTT, the patients performed significantly better in the 10-m and 6-min walking tests. This was not the case with FBWTT even after 6 weeks training. Pain levels assessed were significantly improved after 3 weeks of BWSTT and 6 weeks of FBWTT. There were no significant improvements in either group assessed by the FRT, one-leg standing time test, TUG, or SF -36 questionnaire. Conclusions: BWSTT enhanced exercise capacity in terms of walking speed and pain reduction after 3 weeks; however, there was no significant improvement in patients' functional abilities or quality of life. PMID:25792901

Hydrotherapy vs. conventional land-based exercise for improving walking and balance after stroke: a randomized controlled trial.

PubMed

Zhu, Zhizhong; Cui, Liling; Yin, Miaomiao; Yu, Yang; Zhou, Xiaona; Wang, Hongtu; Yan, Hua

2016-06-01

To investigate the effects of hydrotherapy on walking ability and balance in patients with chronic stroke. Single-blind, randomized controlled pilot trial. Outpatient rehabilitation clinic at a tertiary neurological hospital in China. A total of 28 participants with impairments in walking and controlling balance more than six months post-stroke. After baseline evaluations, participants were randomly assigned to a land-based therapy (control group, n = 14) or hydrotherapy (study group, n = 14). Participants underwent individual sessions for four weeks, five days a week, for 45 minutes per session. After four weeks of rehabilitation, all participants were evaluated by a blinded assessor. Functional assessments included the Functional Reach Test, Berg Balance Scale, 2-minute walk test, and Timed Up and Go Test. After four weeks of treatment, the Berg Balance Scale, functional reach test, 2-minute walk test, and the Timed Up and Go Test scores had improved significantly in each group (P < 0.05). The mean improvement of the functional reach test and 2-minute walk test were significantly higher in the aquatic group than in the control group (P < 0.01). The differences in the mean values of the improvements in the Berg Balance Scale and the Timed Up and Go Test were not statistically significant. The results of this study suggest that a relatively short programme (four weeks) of hydrotherapy exercise resulted in a large improvement in a small group (n = 14) of individuals with relatively high balance and walking function following a stroke. © The Author(s) 2015.

Beyond Moore's law: towards competitive quantum devices

NASA Astrophysics Data System (ADS)

Troyer, Matthias

2015-05-01

A century after the invention of quantum theory and fifty years after Bell's inequality we see the first quantum devices emerge as products that aim to be competitive with the best classical computing devices. While a universal quantum computer of non-trivial size is still out of reach there exist a number commercial and experimental devices: quantum random number generators, quantum simulators and quantum annealers. In this colloquium I will present some of these devices and validation tests we performed on them. Quantum random number generators use the inherent randomness in quantum measurements to produce true random numbers, unlike classical pseudorandom number generators which are inherently deterministic. Optical lattice emulators use ultracold atomic gases in optical lattices to mimic typical models of condensed matter physics. In my talk I will focus especially on the devices built by Canadian company D-Wave systems, which are special purpose quantum simulators for solving hard classical optimization problems. I will review the controversy around the quantum nature of these devices and will compare them to state of the art classical algorithms. I will end with an outlook towards universal quantum computing and end with the question: which important problems that are intractable even for post-exa-scale classical computers could we expect to solve once we have a universal quantum computer?

An overview of the "Positive Action for Today's Health" (PATH) trial for increasing walking in low income, ethnic minority communities.

PubMed

Wilson, Dawn K; Trumpeter, Nevelyn N; St George, Sara M; Coulon, Sandra M; Griffin, Sarah; Lee Van Horn, M; Lawman, Hannah G; Wandersman, Abe; Egan, Brent; Forthofer, Melinda; Goodlett, Benjamin D; Kitzman-Ulrich, Heather; Gadson, Barney

2010-11-01

Ethnic minorities and lower-income adults have among the highest rates of obesity and lowest levels of regular physical activity (PA). The Positive Action for Today's Health (PATH) trial compares three communities that are randomly assigned to different levels of an environmental intervention to improve safety and access for walking in low income communities. Three communities matched on census tract information (crime, PA, ethnic minorities, and income) were randomized to receive either: an intervention that combines a police-patrolled-walking program with social marketing strategies to promote PA, a police-patrolled-walking only intervention, or no-walking intervention (general health education only). Measures include PA (7-day accelerometer estimates), body composition, blood pressure, psychosocial measures, and perceptions of safety and access for PA at baseline, 6, 12, 18, and 24 months. The police-patrolled walking plus social marketing intervention targets increasing safety (training community leaders as walking captains, hiring off-duty police officers to patrol the walking trail, and containing stray dogs), increasing access for PA (marking a walking route), and utilizes a social marketing campaign that targets psychosocial and environmental mediators for increasing PA. MAIN HYPOTHESES/OUTCOMES: It is hypothesized that the police-patrolled walking plus social marketing intervention will result in greater increases in moderate-to-vigorous PA as compared to the police-patrolled-walking only or the general health intervention after 12 months and that this effect will be maintained at 18 and 24 months. Implications of this community-based trial are discussed. Copyright © 2010. Published by Elsevier Inc.

An overview of the “Positive Action for Today's Health” (PATH) trial for increasing walking in low income, ethnic minority communities

PubMed Central

Wilson, Dawn K.; Trumpeter, Nevelyn N.; St. George, Sara M.; Coulon, Sandra M.; Griffin, Sarah; Van Horn, M. Lee; Lawman, Hannah G.; Wandersman, Abe; Egan, Brent; Forthofer, Melinda; Goodlett, Benjamin D.; Kitzman-Ulrich, Heather; Gadson, Barney

2012-01-01

Background Ethnic minorities and lower-income adults have among the highest rates of obesity and lowest levels of regular physical activity (PA). The Positive Action for Today's Health (PATH) trial compares three communities that are randomly assigned to different levels of an environmental intervention to improve safety and access for walking in low income communities. Design and setting Three communities matched on census tract information (crime, PA, ethnic minorities, and income) were randomized to receive either: an intervention that combines a police-patrolled-walking program with social marketing strategies to promote PA, a police-patrolled-walking only intervention, or no-walking intervention (general health education only). Measures include PA (7-day accelerometer estimates), body composition, blood pressure, psychosocial measures, and perceptions of safety and access for PA at baseline, 6, 12, 18, and 24 months. Intervention The police-patrolled walking plus social marketing intervention targets increasing safety (training community leaders as walking captains, hiring off-duty police officers to patrol the walking trail, and containing stray dogs), increasing access for PA (marking a walking route), and utilizes a social marketing campaign that targets psychosocial and environmental mediators for increasing PA. Main hypotheses/outcomes It is hypothesized that the police-patrolled walking plus social marketing intervention will result in greater increases in moderate-to-vigorous PA as compared to the police-patrolled-walking only or the general health intervention after 12 months and that this effect will be maintained at 18 and 24 months. Conclusions Implications of this community-based trial are discussed. PMID:20801233

Extreme events and event size fluctuations in biased random walks on networks.

PubMed

Kishore, Vimal; Santhanam, M S; Amritkar, R E

2012-05-01

Random walk on discrete lattice models is important to understand various types of transport processes. The extreme events, defined as exceedences of the flux of walkers above a prescribed threshold, have been studied recently in the context of complex networks. This was motivated by the occurrence of rare events such as traffic jams, floods, and power blackouts which take place on networks. In this work, we study extreme events in a generalized random walk model in which the walk is preferentially biased by the network topology. The walkers preferentially choose to hop toward the hubs or small degree nodes. In this setting, we show that extremely large fluctuations in event sizes are possible on small degree nodes when the walkers are biased toward the hubs. In particular, we obtain the distribution of event sizes on the network. Further, the probability for the occurrence of extreme events on any node in the network depends on its "generalized strength," a measure of the ability of a node to attract walkers. The generalized strength is a function of the degree of the node and that of its nearest neighbors. We obtain analytical and simulation results for the probability of occurrence of extreme events on the nodes of a network using a generalized random walk model. The result reveals that the nodes with a larger value of generalized strength, on average, display lower probability for the occurrence of extreme events compared to the nodes with lower values of generalized strength.

Source-Independent Quantum Random Number Generation

NASA Astrophysics Data System (ADS)

Cao, Zhu; Zhou, Hongyi; Yuan, Xiao; Ma, Xiongfeng

2016-01-01

Quantum random number generators can provide genuine randomness by appealing to the fundamental principles of quantum mechanics. In general, a physical generator contains two parts—a randomness source and its readout. The source is essential to the quality of the resulting random numbers; hence, it needs to be carefully calibrated and modeled to achieve information-theoretical provable randomness. However, in practice, the source is a complicated physical system, such as a light source or an atomic ensemble, and any deviations in the real-life implementation from the theoretical model may affect the randomness of the output. To close this gap, we propose a source-independent scheme for quantum random number generation in which output randomness can be certified, even when the source is uncharacterized and untrusted. In our randomness analysis, we make no assumptions about the dimension of the source. For instance, multiphoton emissions are allowed in optical implementations. Our analysis takes into account the finite-key effect with the composable security definition. In the limit of large data size, the length of the input random seed is exponentially small compared to that of the output random bit. In addition, by modifying a quantum key distribution system, we experimentally demonstrate our scheme and achieve a randomness generation rate of over 5 ×103 bit /s .

A generator for unique quantum random numbers based on vacuum states

NASA Astrophysics Data System (ADS)

Gabriel, Christian; Wittmann, Christoffer; Sych, Denis; Dong, Ruifang; Mauerer, Wolfgang; Andersen, Ulrik L.; Marquardt, Christoph; Leuchs, Gerd

2010-10-01

Random numbers are a valuable component in diverse applications that range from simulations over gambling to cryptography. The quest for true randomness in these applications has engendered a large variety of different proposals for producing random numbers based on the foundational unpredictability of quantum mechanics. However, most approaches do not consider that a potential adversary could have knowledge about the generated numbers, so the numbers are not verifiably random and unique. Here we present a simple experimental setup based on homodyne measurements that uses the purity of a continuous-variable quantum vacuum state to generate unique random numbers. We use the intrinsic randomness in measuring the quadratures of a mode in the lowest energy vacuum state, which cannot be correlated to any other state. The simplicity of our source, combined with its verifiably unique randomness, are important attributes for achieving high-reliability, high-speed and low-cost quantum random number generators.

Bath-induced correlations in an infinite-dimensional Hilbert space

NASA Astrophysics Data System (ADS)

Nizama, Marco; Cáceres, Manuel O.

2017-09-01

Quantum correlations between two free spinless dissipative distinguishable particles (interacting with a thermal bath) are studied analytically using the quantum master equation and tools of quantum information. Bath-induced coherence and correlations in an infinite-dimensional Hilbert space are shown. We show that for temperature T> 0 the time-evolution of the reduced density matrix cannot be written as the direct product of two independent particles. We have found a time-scale that characterizes the time when the bath-induced coherence is maximum before being wiped out by dissipation (purity, relative entropy, spatial dispersion, and mirror correlations are studied). The Wigner function associated to the Wannier lattice (where the dissipative quantum walks move) is studied as an indirect measure of the induced correlations among particles. We have supported the quantum character of the correlations by analyzing the geometric quantum discord.

Record statistics for biased random walks, with an application to financial data

NASA Astrophysics Data System (ADS)

Wergen, Gregor; Bogner, Miro; Krug, Joachim

2011-05-01

We consider the occurrence of record-breaking events in random walks with asymmetric jump distributions. The statistics of records in symmetric random walks was previously analyzed by Majumdar and Ziff [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.101.050601 101, 050601 (2008)] and is well understood. Unlike the case of symmetric jump distributions, in the asymmetric case the statistics of records depends on the choice of the jump distribution. We compute the record rate Pn(c), defined as the probability for the nth value to be larger than all previous values, for a Gaussian jump distribution with standard deviation σ that is shifted by a constant drift c. For small drift, in the sense of c/σ≪n-1/2, the correction to Pn(c) grows proportional to arctan(n) and saturates at the value (c)/(2σ). For large n the record rate approaches a constant, which is approximately given by 1-(σ/2πc)exp(-c2/2σ2) for c/σ≫1. These asymptotic results carry over to other continuous jump distributions with finite variance. As an application, we compare our analytical results to the record statistics of 366 daily stock prices from the Standard & Poor's 500 index. The biased random walk accounts quantitatively for the increase in the number of upper records due to the overall trend in the stock prices, and after detrending the number of upper records is in good agreement with the symmetric random walk. However the number of lower records in the detrended data is significantly reduced by a mechanism that remains to be identified.

Experimental study of a quantum random-number generator based on two independent lasers

NASA Astrophysics Data System (ADS)

Sun, Shi-Hai; Xu, Feihu

2017-12-01

A quantum random-number generator (QRNG) can produce true randomness by utilizing the inherent probabilistic nature of quantum mechanics. Recently, the spontaneous-emission quantum phase noise of the laser has been widely deployed for quantum random-number generation, due to its high rate, its low cost, and the feasibility of chip-scale integration. Here, we perform a comprehensive experimental study of a phase-noise-based QRNG with two independent lasers, each of which operates in either continuous-wave (CW) or pulsed mode. We implement the QRNG by operating the two lasers in three configurations, namely, CW + CW, CW + pulsed, and pulsed + pulsed, and demonstrate their trade-offs, strengths, and weaknesses.

GPU-accelerated algorithms for many-particle continuous-time quantum walks

NASA Astrophysics Data System (ADS)

Piccinini, Enrico; Benedetti, Claudia; Siloi, Ilaria; Paris, Matteo G. A.; Bordone, Paolo

2017-06-01

Many-particle continuous-time quantum walks (CTQWs) represent a resource for several tasks in quantum technology, including quantum search algorithms and universal quantum computation. In order to design and implement CTQWs in a realistic scenario, one needs effective simulation tools for Hamiltonians that take into account static noise and fluctuations in the lattice, i.e. Hamiltonians containing stochastic terms. To this aim, we suggest a parallel algorithm based on the Taylor series expansion of the evolution operator, and compare its performances with those of algorithms based on the exact diagonalization of the Hamiltonian or a 4th order Runge-Kutta integration. We prove that both Taylor-series expansion and Runge-Kutta algorithms are reliable and have a low computational cost, the Taylor-series expansion showing the additional advantage of a memory allocation not depending on the precision of calculation. Both algorithms are also highly parallelizable within the SIMT paradigm, and are thus suitable for GPGPU computing. In turn, we have benchmarked 4 NVIDIA GPUs and 3 quad-core Intel CPUs for a 2-particle system over lattices of increasing dimension, showing that the speedup provided by GPU computing, with respect to the OPENMP parallelization, lies in the range between 8x and (more than) 20x, depending on the frequency of post-processing. GPU-accelerated codes thus allow one to overcome concerns about the execution time, and make it possible simulations with many interacting particles on large lattices, with the only limit of the memory available on the device.

Bridging the gulf between correlated random walks and Lévy walks: autocorrelation as a source of Lévy walk movement patterns.

PubMed

Reynolds, Andy M

2010-12-06

For many years, the dominant conceptual framework for describing non-oriented animal movement patterns has been the correlated random walk (CRW) model in which an individual's trajectory through space is represented by a sequence of distinct, independent randomly oriented 'moves'. It has long been recognized that the transformation of an animal's continuous movement path into a broken line is necessarily arbitrary and that probability distributions of move lengths and turning angles are model artefacts. Continuous-time analogues of CRWs that overcome this inherent shortcoming have appeared in the literature and are gaining prominence. In these models, velocities evolve as a Markovian process and have exponential autocorrelation. Integration of the velocity process gives the position process. Here, through a simple scaling argument and through an exact analytical analysis, it is shown that autocorrelation inevitably leads to Lévy walk (LW) movement patterns on timescales less than the autocorrelation timescale. This is significant because over recent years there has been an accumulation of evidence from a variety of experimental and theoretical studies that many organisms have movement patterns that can be approximated by LWs, and there is now intense debate about the relative merits of CRWs and LWs as representations of non-orientated animal movement patterns.

Random and Directed Walk-Based Top-k Queries in Wireless Sensor Networks

PubMed Central

Fu, Jun-Song; Liu, Yun

2015-01-01

In wireless sensor networks, filter-based top-k query approaches are the state-of-the-art solutions and have been extensively researched in the literature, however, they are very sensitive to the network parameters, including the size of the network, dynamics of the sensors’ readings and declines in the overall range of all the readings. In this work, a random walk-based top-k query approach called RWTQ and a directed walk-based top-k query approach called DWTQ are proposed. At the beginning of a top-k query, one or several tokens are sent to the specific node(s) in the network by the base station. Then, each token walks in the network independently to record and process the readings in a random or directed way. A strategy of choosing the “right” way in DWTQ is carefully designed for the token(s) to arrive at the high-value regions as soon as possible. When designing the walking strategy for DWTQ, the spatial correlations of the readings are also considered. Theoretical analysis and simulation results indicate that RWTQ and DWTQ both are very robust against these parameters discussed previously. In addition, DWTQ outperforms TAG, FILA and EXTOK in transmission cost, energy consumption and network lifetime. PMID:26016914

Random walk, diffusion and mixing in simulations of scalar transport in fluid flows

NASA Astrophysics Data System (ADS)

Klimenko, A. Y.

2008-12-01

Physical similarity and mathematical equivalence of continuous diffusion and particle random walk form one of the cornerstones of modern physics and the theory of stochastic processes. In many applied models used in simulation of turbulent transport and turbulent combustion, mixing between particles is used to reflect the influence of the continuous diffusion terms in the transport equations. We show that the continuous scalar transport and diffusion can be accurately specified by means of mixing between randomly walking Lagrangian particles with scalar properties and assess errors associated with this scheme. This gives an alternative formulation for the stochastic process which is selected to represent the continuous diffusion. This paper focuses on statistical errors and deals with relatively simple cases, where one-particle distributions are sufficient for a complete description of the problem.

Spatial versus sequential correlations for random access coding

NASA Astrophysics Data System (ADS)

Tavakoli, Armin; Marques, Breno; Pawłowski, Marcin; Bourennane, Mohamed

2016-03-01

Random access codes are important for a wide range of applications in quantum information. However, their implementation with quantum theory can be made in two very different ways: (i) by distributing data with strong spatial correlations violating a Bell inequality or (ii) using quantum communication channels to create stronger-than-classical sequential correlations between state preparation and measurement outcome. Here we study this duality of the quantum realization. We present a family of Bell inequalities tailored to the task at hand and study their quantum violations. Remarkably, we show that the use of spatial and sequential quantum correlations imposes different limitations on the performance of quantum random access codes: Sequential correlations can outperform spatial correlations. We discuss the physics behind the observed discrepancy between spatial and sequential quantum correlations.

A randomized controlled trial of movement strategies compared with exercise for people with Parkinson's disease.

PubMed

Morris, Meg E; Iansek, Robert; Kirkwood, Beth

2009-01-15

This randomized controlled clinical trial was conducted to compare the effects of movement rehabilitation strategies and exercise therapy in hospitalized patients with idiopathic Parkinson's disease. Participants were randomly assigned to a group that received movement strategy training or musculoskeletal exercises during 2 consecutive weeks of hospitalization. The primary outcome was disability as measured by the Unified Parkinson's Disease Rating Scale, UPDRS (motor and ADL components). Secondary outcomes were balance, walking speed, endurance, and quality of life. Assessments were carried out by blinded testers at baseline, after the 2 weeks of treatment and 3 months after discharge. The movement strategy group showed improvements on several outcome measures from admission to discharge, including the UPDRS, 10 m walk, 2 minute walk, balance, and PDQ39. However, from discharge to follow up there was significant regression in performance on the 2 minute walk and PDQ39. For the exercise group, quality of life improved significantly during inpatient hospitalization and this was retained at follow-up. Inpatient rehabilitation produces short term reductions in disability and improvements in quality of life in people with Parkinson's disease.

Stochastic resetting in backtrack recovery by RNA polymerases

NASA Astrophysics Data System (ADS)

Roldán, Édgar; Lisica, Ana; Sánchez-Taltavull, Daniel; Grill, Stephan W.

2016-06-01

Transcription is a key process in gene expression, in which RNA polymerases produce a complementary RNA copy from a DNA template. RNA polymerization is frequently interrupted by backtracking, a process in which polymerases perform a random walk along the DNA template. Recovery of polymerases from the transcriptionally inactive backtracked state is determined by a kinetic competition between one-dimensional diffusion and RNA cleavage. Here we describe backtrack recovery as a continuous-time random walk, where the time for a polymerase to recover from a backtrack of a given depth is described as a first-passage time of a random walker to reach an absorbing state. We represent RNA cleavage as a stochastic resetting process and derive exact expressions for the recovery time distributions and mean recovery times from a given initial backtrack depth for both continuous and discrete-lattice descriptions of the random walk. We show that recovery time statistics do not depend on the discreteness of the DNA lattice when the rate of one-dimensional diffusion is large compared to the rate of cleavage.

Patterns of particle distribution in multiparticle systems by random walks with memory enhancement and decay

NASA Astrophysics Data System (ADS)

Tan, Zhi-Jie; Zou, Xian-Wu; Huang, Sheng-You; Zhang, Wei; Jin, Zhun-Zhi

2002-07-01

We investigate the pattern of particle distribution and its evolution with time in multiparticle systems using the model of random walks with memory enhancement and decay. This model describes some biological intelligent walks. With decrease in the memory decay exponent α, the distribution of particles changes from a random dispersive pattern to a locally dense one, and then returns to the random one. Correspondingly, the fractal dimension Df,p characterizing the distribution of particle positions increases from a low value to a maximum and then decreases to the low one again. This is determined by the degree of overlap of regions consisting of sites with remanent information. The second moment of the density ρ(2) was introduced to investigate the inhomogeneity of the particle distribution. The dependence of ρ(2) on α is similar to that of Df,p on α. ρ(2) increases with time as a power law in the process of adjusting the particle distribution, and then ρ(2) tends to a stable equilibrium value.

The Locomotion of Mouse Fibroblasts in Tissue Culture

PubMed Central

Gail, Mitchell H.; Boone, Charles W.

1970-01-01

Time-lapse cinematography was used to investigate the motion of mouse fibroblasts in tissue culture. Observations over successive short time intervals revealed a tendency for the cells to persist in their direction of motion from one 2.5 hr time interval to the next. Over 5.0-hr time intervals, however, the direction of motion appeared random. This fact suggested that D, the diffusion constant of a random walk model, might serve to characterize cellular motility if suitably long observation times were used. We therefore investigated the effect of “persistence” on the pure random walk model, and we found theoretically and confirmed experimentally that the motility of a persisting cell could indeed be characterized by an augmented diffusion constant, D*. A method for determining confidence limits on D* was also developed. Thus a random walk model, modified to comprehend the persistence effect, was found to describe the motion of fibroblasts in tissue culture and to provide a numerical measure of cellular motility. PMID:5531614

Life Outside the Golden Window: Statistical Angles on the Signal-to-Noise Problem

NASA Astrophysics Data System (ADS)

Wagman, Michael

2018-03-01

Lattice QCD simulations of multi-baryon correlation functions can predict the structure and reactions of nuclei without encountering the baryon chemical potential sign problem. However, they suffer from a signal-to-noise problem where Monte Carlo estimates of observables have quantum fluctuations that are exponentially larger than their average values. Recent lattice QCD results demonstrate that the complex phase of baryon correlations functions relates the baryon signal-to-noise problem to a sign problem and exhibits unexpected statistical behavior resembling a heavy-tailed random walk on the unit circle. Estimators based on differences of correlation function phases evaluated at different Euclidean times are discussed that avoid the usual signal-to-noise problem, instead facing a signal-to-noise problem as the time interval associated with the phase difference is increased, and allow hadronic observables to be determined from arbitrarily large-time correlation functions.

Effectiveness of Functional Progressive Resistance Exercise Training on Walking Ability in Children with Cerebral Palsy: A Randomized Controlled Trial

ERIC Educational Resources Information Center

Scholtes, Vanessa A.; Becher, Jules G.; Janssen-Potten, Yvonne J.; Dekkers, Hurnet; Smallenbroek, Linda; Dallmeijer, Annet J.

2012-01-01

The objective of the study was to evaluate the effectiveness of functional progressive resistance exercise (PRE) training on walking ability in children with cerebral palsy (CP). Fifty-one ambulant children with spastic CP (mean age 10 years 5 months, 29 boys) were randomized to an intervention (n=26) or control group (n=25, receiving usual care).…

Some functional limit theorems for compound Cox processes

NASA Astrophysics Data System (ADS)

Korolev, Victor Yu.; Chertok, A. V.; Korchagin, A. Yu.; Kossova, E. V.; Zeifman, Alexander I.

2016-06-01

An improved version of the functional limit theorem is proved establishing weak convergence of random walks generated by compound doubly stochastic Poisson processes (compound Cox processes) to Lévy processes in the Skorokhod space under more realistic moment conditions. As corollaries, theorems are proved on convergence of random walks with jumps having finite variances to Lévy processes with variance-mean mixed normal distributions, in particular, to stable Lévy processes.

Continuous Time Random Walks with memory and financial distributions

NASA Astrophysics Data System (ADS)

Montero, Miquel; Masoliver, Jaume

2017-11-01

We study financial distributions from the perspective of Continuous Time Random Walks with memory. We review some of our previous developments and apply them to financial problems. We also present some new models with memory that can be useful in characterizing tendency effects which are inherent in most markets. We also briefly study the effect on return distributions of fractional behaviors in the distribution of pausing times between successive transactions.

Ages of Records in Random Walks

NASA Astrophysics Data System (ADS)

Szabó, Réka; Vető, Bálint

2016-12-01

We consider random walks with continuous and symmetric step distributions. We prove universal asymptotics for the average proportion of the age of the kth longest lasting record for k=1,2,ldots and for the probability that the record of the kth longest age is broken at step n. Due to the relation to the Chinese restaurant process, the ranked sequence of proportions of ages converges to the Poisson-Dirichlet distribution.

Some functional limit theorems for compound Cox processes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Korolev, Victor Yu.; Institute of Informatics Problems FRC CSC RAS; Chertok, A. V.

2016-06-08

An improved version of the functional limit theorem is proved establishing weak convergence of random walks generated by compound doubly stochastic Poisson processes (compound Cox processes) to Lévy processes in the Skorokhod space under more realistic moment conditions. As corollaries, theorems are proved on convergence of random walks with jumps having finite variances to Lévy processes with variance-mean mixed normal distributions, in particular, to stable Lévy processes.

Propagation in Striated Media

DTIC Science & Technology

1976-05-01

random walk photon scattering, geometric optics refraction at a thin phase screen, plane wave scattering from a thin screen in the Fraunhofer limit and...significant cases. In the geometric optics regime the distribution of density of allowable multipath rays is gsslanly distributed and the power...3.1 Random Walk Approach to Scattering 10 3.2 Phase Screen Approximation to Strong Scattering 13 3.3 Ray Optics and Stationary Phase Analysis 21 3,3,1

Empirical scaling of the length of the longest increasing subsequences of random walks

NASA Astrophysics Data System (ADS)

Mendonça, J. Ricardo G.

2017-02-01

We provide Monte Carlo estimates of the scaling of the length L n of the longest increasing subsequences of n-step random walks for several different distributions of step lengths, short and heavy-tailed. Our simulations indicate that, barring possible logarithmic corrections, {{L}n}∼ {{n}θ} with the leading scaling exponent 0.60≲ θ ≲ 0.69 for the heavy-tailed distributions of step lengths examined, with values increasing as the distribution becomes more heavy-tailed, and θ ≃ 0.57 for distributions of finite variance, irrespective of the particular distribution. The results are consistent with existing rigorous bounds for θ, although in a somewhat surprising manner. For random walks with step lengths of finite variance, we conjecture that the correct asymptotic behavior of L n is given by \\sqrt{n}\\ln n , and also propose the form for the subleading asymptotics. The distribution of L n was found to follow a simple scaling form with scaling functions that vary with θ. Accordingly, when the step lengths are of finite variance they seem to be universal. The nature of this scaling remains unclear, since we lack a working model, microscopic or hydrodynamic, for the behavior of the length of the longest increasing subsequences of random walks.

Ant-inspired density estimation via random walks.

PubMed

Musco, Cameron; Su, Hsin-Hao; Lynch, Nancy A

2017-10-03

Many ant species use distributed population density estimation in applications ranging from quorum sensing, to task allocation, to appraisal of enemy colony strength. It has been shown that ants estimate local population density by tracking encounter rates: The higher the density, the more often the ants bump into each other. We study distributed density estimation from a theoretical perspective. We prove that a group of anonymous agents randomly walking on a grid are able to estimate their density within a small multiplicative error in few steps by measuring their rates of encounter with other agents. Despite dependencies inherent in the fact that nearby agents may collide repeatedly (and, worse, cannot recognize when this happens), our bound nearly matches what would be required to estimate density by independently sampling grid locations. From a biological perspective, our work helps shed light on how ants and other social insects can obtain relatively accurate density estimates via encounter rates. From a technical perspective, our analysis provides tools for understanding complex dependencies in the collision probabilities of multiple random walks. We bound the strength of these dependencies using local mixing properties of the underlying graph. Our results extend beyond the grid to more general graphs, and we discuss applications to size estimation for social networks, density estimation for robot swarms, and random walk-based sampling for sensor networks.

Detection of Zak phases and topological invariants in a chiral quantum walk of twisted photons.

PubMed

Cardano, Filippo; D'Errico, Alessio; Dauphin, Alexandre; Maffei, Maria; Piccirillo, Bruno; de Lisio, Corrado; De Filippis, Giulio; Cataudella, Vittorio; Santamato, Enrico; Marrucci, Lorenzo; Lewenstein, Maciej; Massignan, Pietro

2017-06-01

Topological insulators are fascinating states of matter exhibiting protected edge states and robust quantized features in their bulk. Here we propose and validate experimentally a method to detect topological properties in the bulk of one-dimensional chiral systems. We first introduce the mean chiral displacement, an observable that rapidly approaches a value proportional to the Zak phase during the free evolution of the system. Then we measure the Zak phase in a photonic quantum walk of twisted photons, by observing the mean chiral displacement in its bulk. Next, we measure the Zak phase in an alternative, inequivalent timeframe and combine the two windings to characterize the full phase diagram of this Floquet system. Finally, we prove the robustness of the measure by introducing dynamical disorder in the system. This detection method is extremely general and readily applicable to all present one-dimensional platforms simulating static or Floquet chiral systems.

Detection of Zak phases and topological invariants in a chiral quantum walk of twisted photons

PubMed Central

Cardano, Filippo; D’Errico, Alessio; Dauphin, Alexandre; Maffei, Maria; Piccirillo, Bruno; de Lisio, Corrado; De Filippis, Giulio; Cataudella, Vittorio; Santamato, Enrico; Marrucci, Lorenzo; Lewenstein, Maciej; Massignan, Pietro

2017-01-01

Topological insulators are fascinating states of matter exhibiting protected edge states and robust quantized features in their bulk. Here we propose and validate experimentally a method to detect topological properties in the bulk of one-dimensional chiral systems. We first introduce the mean chiral displacement, an observable that rapidly approaches a value proportional to the Zak phase during the free evolution of the system. Then we measure the Zak phase in a photonic quantum walk of twisted photons, by observing the mean chiral displacement in its bulk. Next, we measure the Zak phase in an alternative, inequivalent timeframe and combine the two windings to characterize the full phase diagram of this Floquet system. Finally, we prove the robustness of the measure by introducing dynamical disorder in the system. This detection method is extremely general and readily applicable to all present one-dimensional platforms simulating static or Floquet chiral systems. PMID:28569741

An aerobic walking programme versus muscle strengthening programme for chronic low back pain: a randomized controlled trial.

PubMed

Shnayderman, Ilana; Katz-Leurer, Michal

2013-03-01

To assess the effect of aerobic walking training as compared to active training, which includes muscle strengthening, on functional abilities among patients with chronic low back pain. Randomized controlled clinical trial with blind assessors. Outpatient clinic. Fifty-two sedentary patients, aged 18-65 years with chronic low back pain. Patients who were post surgery, post trauma, with cardiovascular problems, and with oncological disease were excluded. Experimental 'walking' group: moderate intense treadmill walking; control 'exercise' group: specific low back exercise; both, twice a week for six weeks. Six-minute walking test, Fear-Avoidance Belief Questionnaire, back and abdomen muscle endurance tests, Oswestry Disability Questionnaire, Low Back Pain Functional Scale (LBPFS). Significant improvements were noted in all outcome measures in both groups with non-significant difference between groups. The mean distance in metres covered during 6 minutes increased by 70.7 (95% confidence interval (CI) 12.3-127.7) in the 'walking' group and by 43.8 (95% CI 19.6-68.0) in the 'exercise' group. The trunk flexor endurance test showed significant improvement in both groups, increasing by 0.6 (95% CI 0.0-1.1) in the 'walking' group and by 1.1 (95% CI 0.3-1.8) in the 'exercise' group. A six-week walk training programme was as effective as six weeks of specific strengthening exercises programme for the low back.

The implementation of a community-based aerobic walking program for mild to moderate knee osteoarthritis: A knowledge translation randomized controlled trial: Part II: Clinical outcomes

PubMed Central

2012-01-01

Background Osteoarthritis (OA) is the most common joint disorder in the world, as it is appears to be prevalent among 80% of individuals over the age of 75. Although physical activities such as walking have been scientifically proven to improve physical function and arthritic symptoms, individuals with OA tend to adopt a sedentary lifestyle. There is therefore a need to improve knowledge translation in order to influence individuals to adopt effective self-management interventions, such as an adapted walking program. Methods A single-blind, randomized control trial was conducted. Subjects (n = 222) were randomized to one of three knowledge translation groups: 1) Walking and Behavioural intervention (WB) (18 males, 57 females) which included the supervised community-based aerobic walking program combined with a behavioural intervention and an educational pamphlet on the benefits of walking; 2) Walking intervention (W) (24 males, 57 females) wherein participants only received the supervised community-based aerobic walking program intervention and the educational pamphlet; 3) Self-directed control (C) (32 males, 52 females) wherein participants only received the educational pamphlet. One-way analyses of variance were used to test for differences in quality of life, adherence, confidence, and clinical outcomes among the study groups at each 3 month assessment during the 12-month intervention period and 6-month follow-up period. Results The clinical and quality of life outcomes improved among participants in each of the three comparative groups. However, there were few statistically significant differences observed for quality of life and clinical outcomes at long-term measurements at 12-months end of intervention and at 6- months post intervention (18-month follow-up). Outcome results varied among the three groups. Conclusion The three groups were equivalent when determining the effectiveness of knowledge uptake and improvements in quality of life and other clinical outcomes. OA can be managed through the implementation of a proven effective walking program in existing community-based walking clubs. Trial registration Current Controlled Trials IRSCTNO9193542 PMID:23234575

The effects of free-living interval-walking training on glycemic control, body composition, and physical fitness in type 2 diabetic patients: a randomized, controlled trial.

PubMed

Karstoft, Kristian; Winding, Kamilla; Knudsen, Sine H; Nielsen, Jens S; Thomsen, Carsten; Pedersen, Bente K; Solomon, Thomas P J

2013-02-01

To evaluate the feasibility of free-living walking training in type 2 diabetic patients and to investigate the effects of interval-walking training versus continuous-walking training upon physical fitness, body composition, and glycemic control. Subjects with type 2 diabetes were randomized to a control (n = 8), continuous-walking (n = 12), or interval-walking group (n = 12). Training groups were prescribed five sessions per week (60 min/session) and were controlled with an accelerometer and a heart-rate monitor. Continuous walkers performed all training at moderate intensity, whereas interval walkers alternated 3-min repetitions at low and high intensity. Before and after the 4-month intervention, the following variables were measured: VO(2)max, body composition, and glycemic control (fasting glucose, HbA(1c), oral glucose tolerance test, and continuous glucose monitoring [CGM]). Training adherence was high (89 ± 4%), and training energy expenditure and mean intensity were comparable. VO(2)max increased 16.1 ± 3.7% in the interval-walking group (P < 0.05), whereas no changes were observed in the continuous-walking or control group. Body mass and adiposity (fat mass and visceral fat) decreased in the interval-walking group only (P < 0.05). Glycemic control (elevated mean CGM glucose levels and increased fasting insulin) worsened in the control group (P < 0.05), whereas mean (P = 0.05) and maximum (P < 0.05) CGM glucose levels decreased in the interval-walking group. The continuous walkers showed no changes in glycemic control. Free-living walking training is feasible in type 2 diabetic patients. Continuous walking offsets the deterioration in glycemia seen in the control group, and interval walking is superior to energy expenditure-matched continuous walking for improving physical fitness, body composition, and glycemic control.

The effectiveness of body weight-supported gait training and floor walking in patients with chronic stroke.

PubMed

Peurala, Sinikka H; Tarkka, Ina M; Pitkänen, Kauko; Sivenius, Juhani

2005-08-01

To compare body weight-supported exercise on a gait trainer with walking exercise overground. Randomized controlled trial. Rehabilitation hospital. Forty-five ambulatory patients with chronic stroke. Patients were randomized to 3 groups: (1) gait trainer exercise with functional electric stimulation (GTstim), (2) gait trainer exercise without stimulation (GT), and (3) walking overground (WALK). All patients practiced gait for 15 sessions during 3 weeks (each session, 20 min), and they received additional physiotherapy 55 minutes daily. Ten-meter walk test (10MWT), six-minute walk test (6MWT), lower-limb spasticity and muscle force, postural sway tests, Modified Motor Assessment Scale (MMAS), and FIM instrument scores were recorded before, during, and after the rehabilitation and at 6 months follow-up. The mean walking distance using the gait trainer was 6900+/-1200 m in the GTstim group and 6500+/-1700 m in GT group. In the WALK group, the distance was 4800+/-2800 m, which was less than the walking distance obtained in the GTstim group (P=.027). The body-weight support was individually reduced from 30% to 9% of the body weight over the course of the program. In the pooled 45 patients, the 10MWT (P<.001), 6MWT (P<.001), MMAS (P<.001), dynamic balance test time (P<.001), and test trip (P=.005) scores improved; however, no differences were found between the groups. Both the body weight-supported training and walking exercise training programs resulted in faster gait after the intensive rehabilitation program. Patients' motor performance remained improved at the follow-up.

Effectiveness of Long and Short Bout Walking on Increasing Physical Activity in Women

PubMed Central

Serwe, Katrina M.; Swartz, Ann M.; Hart, Teresa L.; Strath, Scott J.

2011-01-01

Abstract Background The accumulation of physical activity (PA) throughout the day has been suggested as a means to increase PA behavior. It is not known, however, if accumulated PA results in equivalent increases in PA behavior compared with one continuous session. The purpose of this investigation was to compare changes in PA between participants assigned to walk daily in accumulated shorter bouts vs. one continuous session. Methods In this 8-week randomized controlled trial, 60 inactive women were randomly assigned to one of the following: (1) control group, (2) 30 minutes a day of walking 5 days a week in one continuous long bout (LB), or (3) three short 10-minute bouts (SB) of walking a day, all at a prescribed heart rate intensity. Walking was assessed by pedometer and self-reported walking log. Before and after measures were taken of average steps/day, resting systolic and diastolic blood pressure (SBP, DBP), resting heart rate (RHR), six-minute walk test (6MWT) distance, height, weight, body mass index (BMI), and hip and waist circumference. Results Both walking groups significantly increased PA measured as steps/day compared to controls (p < 0.001), and no significant differences were found between LB and SB groups. The LB group demonstrated significant decreases in hip circumference and significant increases in 6MWT distance compared to the control group. Conclusions Both walking groups significantly increased PA participation. LB group participants completed more walking at a higher intensity than the SB and control groups, which resulted in significant increases in health benefits. PMID:21314449

Randomness determines practical security of BB84 quantum key distribution.

PubMed

Li, Hong-Wei; Yin, Zhen-Qiang; Wang, Shuang; Qian, Yong-Jun; Chen, Wei; Guo, Guang-Can; Han, Zheng-Fu

2015-11-10

Unconditional security of the BB84 quantum key distribution protocol has been proved by exploiting the fundamental laws of quantum mechanics, but the practical quantum key distribution system maybe hacked by considering the imperfect state preparation and measurement respectively. Until now, different attacking schemes have been proposed by utilizing imperfect devices, but the general security analysis model against all of the practical attacking schemes has not been proposed. Here, we demonstrate that the general practical attacking schemes can be divided into the Trojan horse attack, strong randomness attack and weak randomness attack respectively. We prove security of BB84 protocol under randomness attacking models, and these results can be applied to guarantee the security of the practical quantum key distribution system.

Randomness determines practical security of BB84 quantum key distribution

PubMed Central

Li, Hong-Wei; Yin, Zhen-Qiang; Wang, Shuang; Qian, Yong-Jun; Chen, Wei; Guo, Guang-Can; Han, Zheng-Fu

2015-01-01

Unconditional security of the BB84 quantum key distribution protocol has been proved by exploiting the fundamental laws of quantum mechanics, but the practical quantum key distribution system maybe hacked by considering the imperfect state preparation and measurement respectively. Until now, different attacking schemes have been proposed by utilizing imperfect devices, but the general security analysis model against all of the practical attacking schemes has not been proposed. Here, we demonstrate that the general practical attacking schemes can be divided into the Trojan horse attack, strong randomness attack and weak randomness attack respectively. We prove security of BB84 protocol under randomness attacking models, and these results can be applied to guarantee the security of the practical quantum key distribution system. PMID:26552359

Randomness determines practical security of BB84 quantum key distribution

NASA Astrophysics Data System (ADS)

Li, Hong-Wei; Yin, Zhen-Qiang; Wang, Shuang; Qian, Yong-Jun; Chen, Wei; Guo, Guang-Can; Han, Zheng-Fu

2015-11-01

Unconditional security of the BB84 quantum key distribution protocol has been proved by exploiting the fundamental laws of quantum mechanics, but the practical quantum key distribution system maybe hacked by considering the imperfect state preparation and measurement respectively. Until now, different attacking schemes have been proposed by utilizing imperfect devices, but the general security analysis model against all of the practical attacking schemes has not been proposed. Here, we demonstrate that the general practical attacking schemes can be divided into the Trojan horse attack, strong randomness attack and weak randomness attack respectively. We prove security of BB84 protocol under randomness attacking models, and these results can be applied to guarantee the security of the practical quantum key distribution system.

Improving Motor Control in Walking: A Randomized Clinical Trial in Older Adults with Subclinical Walking Difficulty

PubMed Central

Brach, Jennifer S.; Lowry, Kristin; Perera, Subashan; Hornyak, Victoria; Wert, David; Studenski, Stephanie A.; VanSwearingen, Jessie M.

2016-01-01

Objective The objective was to test the proposed mechanism of action of a task-specific motor learning intervention by examining its effect on measures of the motor control of gait. Design Single blinded randomized clinical trial. Setting University research laboratory. Participants Forty older adults 65 years of age and older, with gait speed >1.0 m/s and impaired motor skill (Figure of 8 walk time > 8 secs). Interventions The two interventions included a task-oriented motor learning and a standard exercise program. Both interventions lasted 12 weeks, with twice weekly one hour physical therapist supervised sessions. Main Outcome Measures Two measure of the motor control of gait, gait variability and smoothness of walking, were assessed pre and post intervention by assessors masked to treatment arm. Results Of 40 randomized subjects; 38 completed the trial (mean age 77.1±6.0 years). Motor control group improved more than standard group in double support time variability (0.13 vs. 0.05 m/s; adjusted difference, AD=0.006, p=0.03). Smoothness of walking in the anterior/posterior direction improved more in motor control than standard for all conditions (usual: AD=0.53, p=0.05; narrow: AD=0.56, p=0.01; dual task: AD=0.57, p=0.04). Conclusions Among older adults with subclinical walking difficulty, there is initial evidence that task-oriented motor learning exercise results in gains in the motor control of walking, while standard exercise does not. Task-oriented motor learning exercise is a promising intervention for improving timing and coordination deficits related to mobility difficulties in older adults, and needs to be evaluated in a definitive larger trial. PMID:25448244

Comparison of the Effect of Lateral and Backward Walking Training on Walking Function in Patients with Poststroke Hemiplegia: A Pilot Randomized Controlled Trial.

PubMed

Kim, Chang-Yong; Lee, Jung-Sun; Kim, Hyeong-Dong

2017-02-01

The purposes of the present study were to compare the effects of backward and lateral walking training and to identify whether additional backward or lateral walking training would be more effective in increasing the walking function of poststroke patients. Fifty-one subjects with hemiplegic stroke were randomly allocated to 3 groups, each containing 17 subjects: the control group, the backward walking training group, and the lateral walking training group. The walking abilities of each group were assessed using a 10-m walk test and the GAITRite system for spatiotemporal gait. The results show that there were significantly greater posttest increases in gait velocity (F = -12.09, P = 0.02) and stride length (F = -11.50, P = 0.02), decreases in the values of the 10-m walk test (F = -7.10, P = 0.03) (P < 0.05) and double-limb support period (F = 40.15, P = 0.000), and improvements in gait asymmetry (F = 13.88, P = 0.002) (P < 0.01) in subjects in the lateral walking training group compared with those in the other 2 groups. These findings demonstrate that asymmetric gait patterns in poststroke patients could be improved by receiving additional lateral walking training therapy rather than backward walking training. Complete the self-assessment activity and evaluation online at http://www.physiatry.org/JournalCME CME OBJECTIVES: Upon completion of this article, the reader should be able to: (1) understand the potential benefits of backward walking (BW) and lateral walking (LW) training on improving muscle strength and gait; (2) appreciate the potential value of backward and lateral walking gait training in the treatment of hemiplegic stroke patients; and (3) appropriately incorporate backward and lateral walking gait training into the treatment plan of hemiplegic stroke patients. Advanced ACCREDITATION: The Association of Academic Physiatrists is accredited by the Accreditation Council for Continuing Medical Education to provide continuing medical education for physicians.The Association of Academic Physiatrists designates this activity for a maximum of 1.5 AMA PRA Category 1 Credit(s)™. Physicians should only claim credit commensurate with the extent of their participation in the activity.

Intermediate quantum maps for quantum computation

NASA Astrophysics Data System (ADS)

Giraud, O.; Georgeot, B.

2005-10-01

We study quantum maps displaying spectral statistics intermediate between Poisson and Wigner-Dyson. It is shown that they can be simulated on a quantum computer with a small number of gates, and efficiently yield information about fidelity decay or spectral statistics. We study their matrix elements and entanglement production and show that they converge with time to distributions which differ from random matrix predictions. A randomized version of these maps can be implemented even more economically and yields pseudorandom operators with original properties, enabling, for example, one to produce fractal random vectors. These algorithms are within reach of present-day quantum computers.

Diffraction and interference of walking drops

NASA Astrophysics Data System (ADS)

Pucci, Giuseppe; Harris, Daniel M.; Bush, John W. M.

2016-11-01

A decade ago, Yves Couder and Emmanuel Fort discovered a wave-particle association on the macroscopic scale: a drop can bounce indefinitely on a vibrating bath of the same liquid and can be piloted by the waves that it generates. These walking droplets have been shown to exhibit several quantum-like features, including single-particle diffraction and interference. Recently, the original diffraction and interference experiments of Couder and Fort have been revisited and contested. We have revisited this system using an improved experimental set-up, and observed a strong dependence of the behavior on system parameters, including drop size and vibrational forcing. In both the single- and the double-slit geometries, the diffraction pattern is dominated by the interaction of the walking droplet with a planar boundary. Critically, in the double-slit geometry, the walking droplet is influenced by both slits by virtue of its spatially extended wave field. NSF support via CMMI-1333242.

Quantum transport in the FMO photosynthetic light-harvesting complex.

PubMed

Karafyllidis, Ioannis G

2017-06-01

The very high light-harvesting efficiency of natural photosynthetic systems in conjunction with recent experiments, which showed quantum-coherent energy transfer in photosynthetic complexes, raised questions regarding the presence of non-trivial quantum effects in photosynthesis. Grover quantum search, quantum walks, and entanglement have been investigated as possible effects that lead to this efficiency. Here we explain the near-unit photosynthetic efficiency without invoking non-trivial quantum effects. Instead, we use non-equilibrium Green's functions, a mesoscopic method used to study transport in nano-conductors to compute the transmission function of the Fenna-Matthews-Olson (FMO) complex using an experimentally derived exciton Hamiltonian. The chlorosome antenna and the reaction center play the role of input and output contacts, connected to the FMO complex. We show that there are two channels for which the transmission is almost unity. Our analysis also revealed a dephasing-driven regulation mechanism that maintains the efficiency in the presence of varying dephasing potentials.

Non-classical photon correlation in a two-dimensional photonic lattice.

PubMed

Gao, Jun; Qiao, Lu-Feng; Lin, Xiao-Feng; Jiao, Zhi-Qiang; Feng, Zhen; Zhou, Zheng; Gao, Zhen-Wei; Xu, Xiao-Yun; Chen, Yuan; Tang, Hao; Jin, Xian-Min

2016-06-13

Quantum interference and quantum correlation, as two main features of quantum optics, play an essential role in quantum information applications, such as multi-particle quantum walk and boson sampling. While many experimental demonstrations have been done in one-dimensional waveguide arrays, it remains unexplored in higher dimensions due to tight requirement of manipulating and detecting photons in large-scale. Here, we experimentally observe non-classical correlation of two identical photons in a fully coupled two-dimensional structure, i.e. photonic lattice manufactured by three-dimensional femtosecond laser writing. Photon interference consists of 36 Hong-Ou-Mandel interference and 9 bunching. The overlap between measured and simulated distribution is up to 0.890 ± 0.001. Clear photon correlation is observed in the two-dimensional photonic lattice. Combining with controllably engineered disorder, our results open new perspectives towards large-scale implementation of quantum simulation on integrated photonic chips.

Megahertz-Rate Semi-Device-Independent Quantum Random Number Generators Based on Unambiguous State Discrimination

NASA Astrophysics Data System (ADS)

Brask, Jonatan Bohr; Martin, Anthony; Esposito, William; Houlmann, Raphael; Bowles, Joseph; Zbinden, Hugo; Brunner, Nicolas

2017-05-01

An approach to quantum random number generation based on unambiguous quantum state discrimination is developed. We consider a prepare-and-measure protocol, where two nonorthogonal quantum states can be prepared, and a measurement device aims at unambiguously discriminating between them. Because the states are nonorthogonal, this necessarily leads to a minimal rate of inconclusive events whose occurrence must be genuinely random and which provide the randomness source that we exploit. Our protocol is semi-device-independent in the sense that the output entropy can be lower bounded based on experimental data and a few general assumptions about the setup alone. It is also practically relevant, which we demonstrate by realizing a simple optical implementation, achieving rates of 16.5 Mbits /s . Combining ease of implementation, a high rate, and a real-time entropy estimation, our protocol represents a promising approach intermediate between fully device-independent protocols and commercial quantum random number generators.

The Effect of a Home-Based Walking Intervention on Quality of Life Body Composition and Estrogen Metabolism in Postmenopausal Breast Cancer Survivors

DTIC Science & Technology

2003-09-01

the effect of a 12-week home-based walking intervention on quality of life , body composition, and estrogen metabolism in survivors of breast cancer...randomized to the walking intervention will report higher levels of quality of life , experience less weight gain, and have more favorable estrogen

The Effect of a Home-Based Walking Intervention on Quality of Life, Body Composition, and Estrogen Metabolism in Postmenopausal Breast Cancer Survivors

DTIC Science & Technology

2004-09-01

the effect of a 12-week home-based walking intervention on quality of life , body composition, and estrogen metabolism in survivors of breast cancer...randomized to the walking intervention will report higher levels of quality of life , experience less weight gain, and have more favorable estrogen

Testing self-regulation interventions to increase walking using factorial randomized N-of-1 trials.

PubMed

Sniehotta, Falko F; Presseau, Justin; Hobbs, Nicola; Araújo-Soares, Vera

2012-11-01

To investigate the suitability of N-of-1 randomized controlled trials (RCTs) as a means of testing the effectiveness of behavior change techniques based on self-regulation theory (goal setting and self-monitoring) for promoting walking in healthy adult volunteers. A series of N-of-1 RCTs in 10 normal and overweight adults ages 19-67 (M = 36.9 years). We randomly allocated 60 days within each individual to text message-prompted daily goal-setting and/or self-monitoring interventions in accordance with a 2 (step-count goal prompt vs. alternative goal prompt) × 2 (self-monitoring: open vs. blinded Omron-HJ-113-E pedometer) factorial design. Aggregated data were analyzed using random intercept multilevel models. Single cases were analyzed individually. The primary outcome was daily pedometer step counts over 60 days. Single-case analyses showed that 4 participants significantly increased walking: 2 on self-monitoring days and 2 on goal-setting days, compared with control days. Six participants did not benefit from the interventions. In aggregated analyses, mean step counts were higher on goal-setting days (8,499.9 vs. 7,956.3) and on self-monitoring days (8,630.3 vs. 7,825.9). Multilevel analyses showed a significant effect of the self-monitoring condition (p = .01), the goal-setting condition approached significance (p = .08), and there was a small linear increase in walking over time (p = .03). N-of-1 randomized trials are a suitable means to test behavioral interventions in individual participants.

Random walk on p-adics and hierarchical systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lukierska-Walasek, K.; Topolski, K.; Institute of Mathematics, Wroclaw University, pl. Grunwaldzki 2/4, 50-384 Wroclaw

2006-02-01

We show that p-adic analysis provides a quite natural basis for the description of relaxation in hierarchical systems. For our purposes, we specify the Markov stochastic process considered by Albeverio and Karwowski. As a result we have obtained a random walk on the p-adic integer numbers, which provides the generalization of Cayley tree proposed by Ogielski and Stein. The temperature-dependent power-law decay and the Kohlrausch law are derived.

Expert Assessment of Stigmergy: A Report for the Department of National Defence

DTIC Science & Technology

2005-10-01

pheromone table may be reduced by implementing a clustering scheme. Termite can take advantage of the wireless broadcast medium, since it is possible for...comparing it with any other routing scheme. The Termite scheme [RW] differs from the source routing [ITT] by applying pheromone trails or random walks...rather than uniform or probabilistic ones. Random walk ants differ from uniform ants since they follow pheromone trails, if any. Termite [RW] also

Autocatalytic polymerization generates persistent random walk of crawling cells.

PubMed

Sambeth, R; Baumgaertner, A

2001-05-28

The autocatalytic polymerization kinetics of the cytoskeletal actin network provides the basic mechanism for a persistent random walk of a crawling cell. It is shown that network remodeling by branching processes near the cell membrane is essential for the bimodal spatial stability of the network which induces a spontaneous breaking of isotropic cell motion. Details of the phenomena are analyzed using a simple polymerization model studied by analytical and simulation methods.

A Random Walk Picture of Basketball

NASA Astrophysics Data System (ADS)

Gabel, Alan; Redner, Sidney

2012-02-01

We analyze NBA basketball play-by-play data and found that scoring is well described by a weakly-biased, anti-persistent, continuous-time random walk. The time between successive scoring events follows an exponential distribution, with little memory between events. We account for a wide variety of statistical properties of scoring, such as the distribution of the score difference between opponents and the fraction of game time that one team is in the lead.

Approximate scaling properties of RNA free energy landscapes

NASA Technical Reports Server (NTRS)

Baskaran, S.; Stadler, P. F.; Schuster, P.

1996-01-01

RNA free energy landscapes are analysed by means of "time-series" that are obtained from random walks restricted to excursion sets. The power spectra, the scaling of the jump size distribution, and the scaling of the curve length measured with different yard stick lengths are used to describe the structure of these "time series". Although they are stationary by construction, we find that their local behavior is consistent with both AR(1) and self-affine processes. Random walks confined to excursion sets (i.e., with the restriction that the fitness value exceeds a certain threshold at each step) exhibit essentially the same statistics as free random walks. We find that an AR(1) time series is in general approximately self-affine on timescales up to approximately the correlation length. We present an empirical relation between the correlation parameter rho of the AR(1) model and the exponents characterizing self-affinity.

Narrow log-periodic modulations in non-Markovian random walks

NASA Astrophysics Data System (ADS)

Diniz, R. M. B.; Cressoni, J. C.; da Silva, M. A. A.; Mariz, A. M.; de Araújo, J. M.

2017-12-01

What are the necessary ingredients for log-periodicity to appear in the dynamics of a random walk model? Can they be subtle enough to be overlooked? Previous studies suggest that long-range damaged memory and negative feedback together are necessary conditions for the emergence of log-periodic oscillations. The role of negative feedback would then be crucial, forcing the system to change direction. In this paper we show that small-amplitude log-periodic oscillations can emerge when the system is driven by positive feedback. Due to their very small amplitude, these oscillations can easily be mistaken for numerical finite-size effects. The models we use consist of discrete-time random walks with strong memory correlations where the decision process is taken from memory profiles based either on a binomial distribution or on a delta distribution. Anomalous superdiffusive behavior and log-periodic modulations are shown to arise in the large time limit for convenient choices of the models parameters.

Elephant random walks and their connection to Pólya-type urns

NASA Astrophysics Data System (ADS)

Baur, Erich; Bertoin, Jean

2016-11-01

In this paper, we explain the connection between the elephant random walk (ERW) and an urn model à la Pólya and derive functional limit theorems for the former. The ERW model was introduced in [Phys. Rev. E 70, 045101 (2004), 10.1103/PhysRevE.70.045101] to study memory effects in a highly non-Markovian setting. More specifically, the ERW is a one-dimensional discrete-time random walk with a complete memory of its past. The influence of the memory is measured in terms of a memory parameter p between zero and one. In the past years, a considerable effort has been undertaken to understand the large-scale behavior of the ERW, depending on the choice of p . Here, we use known results on urns to explicitly solve the ERW in all memory regimes. The method works as well for ERWs in higher dimensions and is widely applicable to related models.

Observing random walks of atoms in buffer gas through resonant light absorption

NASA Astrophysics Data System (ADS)

Aoki, Kenichiro; Mitsui, Takahisa

2016-07-01

Using resonant light absorption, random-walk motions of rubidium atoms in nitrogen buffer gas are observed directly. The transmitted light intensity through atomic vapor is measured, and its spectrum is obtained, down to orders of magnitude below the shot-noise level to detect fluctuations caused by atomic motions. To understand the measured spectra, the spectrum for atoms performing random walks in a Gaussian light beam is computed, and its analytical form is obtained. The spectrum has 1 /f2 (f is frequency) behavior at higher frequencies, crossing over to a different, but well-defined, behavior at lower frequencies. The properties of this theoretical spectrum agree excellently with the measured spectrum. This understanding also enables us to obtain the diffusion constant, the photon cross section of atoms in buffer gas, and the atomic number density from a single spectral measurement. We further discuss other possible applications of our experimental method and analysis.

A partially reflecting random walk on spheres algorithm for electrical impedance tomography

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maire, Sylvain, E-mail: maire@univ-tln.fr; Simon, Martin, E-mail: simon@math.uni-mainz.de

2015-12-15

In this work, we develop a probabilistic estimator for the voltage-to-current map arising in electrical impedance tomography. This novel so-called partially reflecting random walk on spheres estimator enables Monte Carlo methods to compute the voltage-to-current map in an embarrassingly parallel manner, which is an important issue with regard to the corresponding inverse problem. Our method uses the well-known random walk on spheres algorithm inside subdomains where the diffusion coefficient is constant and employs replacement techniques motivated by finite difference discretization to deal with both mixed boundary conditions and interface transmission conditions. We analyze the global bias and the variance ofmore » the new estimator both theoretically and experimentally. Subsequently, the variance of the new estimator is considerably reduced via a novel control variate conditional sampling technique which yields a highly efficient hybrid forward solver coupling probabilistic and deterministic algorithms.« less

Network Dynamics of Innovation Processes.

PubMed

Iacopini, Iacopo; Milojević, Staša; Latora, Vito

2018-01-26

We introduce a model for the emergence of innovations, in which cognitive processes are described as random walks on the network of links among ideas or concepts, and an innovation corresponds to the first visit of a node. The transition matrix of the random walk depends on the network weights, while in turn the weight of an edge is reinforced by the passage of a walker. The presence of the network naturally accounts for the mechanism of the "adjacent possible," and the model reproduces both the rate at which novelties emerge and the correlations among them observed empirically. We show this by using synthetic networks and by studying real data sets on the growth of knowledge in different scientific disciplines. Edge-reinforced random walks on complex topologies offer a new modeling framework for the dynamics of correlated novelties and are another example of coevolution of processes and networks.

Statistical Modeling of Robotic Random Walks on Different Terrain

NASA Astrophysics Data System (ADS)

Naylor, Austin; Kinnaman, Laura

Issues of public safety, especially with crowd dynamics and pedestrian movement, have been modeled by physicists using methods from statistical mechanics over the last few years. Complex decision making of humans moving on different terrains can be modeled using random walks (RW) and correlated random walks (CRW). The effect of different terrains, such as a constant increasing slope, on RW and CRW was explored. LEGO robots were programmed to make RW and CRW with uniform step sizes. Level ground tests demonstrated that the robots had the expected step size distribution and correlation angles (for CRW). The mean square displacement was calculated for each RW and CRW on different terrains and matched expected trends. The step size distribution was determined to change based on the terrain; theoretical predictions for the step size distribution were made for various simple terrains. It's Dr. Laura Kinnaman, not sure where to put the Prefix.

Network Dynamics of Innovation Processes

NASA Astrophysics Data System (ADS)

Iacopini, Iacopo; Milojević, Staša; Latora, Vito

2018-01-01

We introduce a model for the emergence of innovations, in which cognitive processes are described as random walks on the network of links among ideas or concepts, and an innovation corresponds to the first visit of a node. The transition matrix of the random walk depends on the network weights, while in turn the weight of an edge is reinforced by the passage of a walker. The presence of the network naturally accounts for the mechanism of the "adjacent possible," and the model reproduces both the rate at which novelties emerge and the correlations among them observed empirically. We show this by using synthetic networks and by studying real data sets on the growth of knowledge in different scientific disciplines. Edge-reinforced random walks on complex topologies offer a new modeling framework for the dynamics of correlated novelties and are another example of coevolution of processes and networks.

Effective degrees of freedom of a random walk on a fractal

NASA Astrophysics Data System (ADS)

Balankin, Alexander S.

2015-12-01

We argue that a non-Markovian random walk on a fractal can be treated as a Markovian process in a fractional dimensional space with a suitable metric. This allows us to define the fractional dimensional space allied to the fractal as the ν -dimensional space Fν equipped with the metric induced by the fractal topology. The relation between the number of effective spatial degrees of freedom of walkers on the fractal (ν ) and fractal dimensionalities is deduced. The intrinsic time of random walk in Fν is inferred. The Laplacian operator in Fν is constructed. This allows us to map physical problems on fractals into the corresponding problems in Fν. In this way, essential features of physics on fractals are revealed. Particularly, subdiffusion on path-connected fractals is elucidated. The Coulomb potential of a point charge on a fractal embedded in the Euclidean space is derived. Intriguing attributes of some types of fractals are highlighted.

The implementation of a community-based aerobic walking program for mild to moderate knee osteoarthritis (OA): a knowledge translation (KT) randomized controlled trial (RCT): Part I: The Uptake of the Ottawa Panel clinical practice guidelines (CPGs)

PubMed Central

2012-01-01

Background The implementation of evidence based clinical practice guidelines on self-management interventions to patients with chronic diseases is a complex process. A multifaceted strategy may offer an effective knowledge translation (KT) intervention to promote knowledge uptake and improve adherence in an effective walking program based on the Ottawa Panel Evidence Based Clinical Practice Guidelines among individuals with moderate osteoarthritis (OA). Methods A single-blind, randomized control trial was conducted. Patients with mild to moderate (OA) of the knee (n=222) were randomized to one of three KT groups: 1) Walking and Behavioural intervention (WB) (18 males, 57 females) which included the supervised community-based aerobic walking program combined with a behavioural intervention and an educational pamphlet on the benefits of walking for OA; 2) Walking intervention (W) (24 males, 57 females) wherein participants only received the supervised community-based aerobic walking program intervention and the educational pamphlet; 3) Self-directed control (C) (32 males, 52 females) wherein participants only received the educational pamphlet. One-way analyses of variance were used to test for differences in quality of life, adherence, confidence, and clinical outcomes among the study groups at each 3 month assessment during the 12-month intervention period and 6-month follow-up period. Results Short-term program adherence was greater in WB compared to C (p<0.012) after 3 months. No statistical significance (p> 0.05) was observed for long-term adherence (6 to 12 months), and total adherence between the three groups. The three knowledge translation strategies demonstrated equivalent long-term results for the implementation of a walking program for older individuals with moderate OA. Lower dropout rates as well as higher retention rates were observed for WB at 12 and 18 months. Conclusion The additional knowledge translation behavioural component facilitated the implementation of clinical practice guidelines on walking over a short-term period. More studies are needed to improve the long-term walking adherence or longer guidelines uptake on walking among participants with OA. Particular attention should be taken into account related to patient’s characteristic and preference. OA can be managed through the implementation of a walking program based on clinical practice guidelines in existing community-based walking clubs as well as at home with the minimal support of an exercise therapist or a trained volunteer. Trial Registration Current Controlled Trials IRSCTNO9193542 PMID:23061875

Free-Space Quantum Communication with a Portable Quantum Memory

NASA Astrophysics Data System (ADS)

Namazi, Mehdi; Vallone, Giuseppe; Jordaan, Bertus; Goham, Connor; Shahrokhshahi, Reihaneh; Villoresi, Paolo; Figueroa, Eden

2017-12-01

The realization of an elementary quantum network that is intrinsically secure and operates over long distances requires the interconnection of several quantum modules performing different tasks. In this work, we report the realization of a communication network functioning in a quantum regime, consisting of four different quantum modules: (i) a random polarization qubit generator, (ii) a free-space quantum-communication channel, (iii) an ultralow-noise portable quantum memory, and (iv) a qubit decoder, in a functional elementary quantum network possessing all capabilities needed for quantum-information distribution protocols. We create weak coherent pulses at the single-photon level encoding polarization states |H ⟩ , |V ⟩, |D ⟩, and |A ⟩ in a randomized sequence. The random qubits are sent over a free-space link and coupled into a dual-rail room-temperature quantum memory and after storage and retrieval are analyzed in a four-detector polarization analysis akin to the requirements of the BB84 protocol. We also show ultralow noise and fully portable operation, paving the way towards memory-assisted all-environment free-space quantum cryptographic networks.

Implementation of a quantum random number generator based on the optimal clustering of photocounts

NASA Astrophysics Data System (ADS)

Balygin, K. A.; Zaitsev, V. I.; Klimov, A. N.; Kulik, S. P.; Molotkov, S. N.

2017-10-01

To implement quantum random number generators, it is fundamentally important to have a mathematically provable and experimentally testable process of measurements of a system from which an initial random sequence is generated. This makes sure that randomness indeed has a quantum nature. A quantum random number generator has been implemented with the use of the detection of quasi-single-photon radiation by a silicon photomultiplier (SiPM) matrix, which makes it possible to reliably reach the Poisson statistics of photocounts. The choice and use of the optimal clustering of photocounts for the initial sequence of photodetection events and a method of extraction of a random sequence of 0's and 1's, which is polynomial in the length of the sequence, have made it possible to reach a yield rate of 64 Mbit/s of the output certainly random sequence.

When human walking becomes random walking: fractal analysis and modeling of gait rhythm fluctuations

NASA Astrophysics Data System (ADS)

Hausdorff, Jeffrey M.; Ashkenazy, Yosef; Peng, Chang-K.; Ivanov, Plamen Ch.; Stanley, H. Eugene; Goldberger, Ary L.

2001-12-01

We present a random walk, fractal analysis of the stride-to-stride fluctuations in the human gait rhythm. The gait of healthy young adults is scale-free with long-range correlations extending over hundreds of strides. This fractal scaling changes characteristically with maturation in children and older adults and becomes almost completely uncorrelated with certain neurologic diseases. Stochastic modeling of the gait rhythm dynamics, based on transitions between different “neural centers”, reproduces distinctive statistical properties of the gait pattern. By tuning one model parameter, the hopping (transition) range, the model can describe alterations in gait dynamics from childhood to adulthood - including a decrease in the correlation and volatility exponents with maturation.

Systematic dimensionality reduction for continuous-time quantum walks of interacting fermions

NASA Astrophysics Data System (ADS)

Izaac, J. A.; Wang, J. B.

2017-09-01

To extend the continuous-time quantum walk (CTQW) to simulate P distinguishable particles on a graph G composed of N vertices, the Hamiltonian of the system is expanded to act on an NP-dimensional Hilbert space, in effect, simulating the multiparticle CTQW on graph G via a single-particle CTQW propagating on the Cartesian graph product G□P. The properties of the Cartesian graph product have been well studied, and classical simulation of multiparticle CTQWs are common in the literature. However, the above approach is generally applied as is when simulating indistinguishable particles, with the particle statistics then applied to the propagated NP state vector to determine walker probabilities. We address the following question: How can we modify the underlying graph structure G□P in order to simulate multiple interacting fermionic CTQWs with a reduction in the size of the state space? In this paper, we present an algorithm for systematically removing "redundant" and forbidden quantum states from consideration, which provides a significant reduction in the effective dimension of the Hilbert space of the fermionic CTQW. As a result, as the number of interacting fermions in the system increases, the classical computational resources required no longer increases exponentially for fixed N .

Preparing and probing many-body correlated systems in a Quantum Gas Microscope by engineering arbitrary landscape potentials

NASA Astrophysics Data System (ADS)

Rispoli, Matthew; Lukin, Alexander; Ma, Ruichao; Preiss, Philipp; Tai, M. Eric; Islam, Rajibul; Greiner, Markus

2015-05-01

Ultracold atoms in optical lattices provide a versatile tool box for observing the emergence of strongly correlated physics in quantum systems. Dynamic control of optical potentials on the single-site level allows us to prepare and probe many-body quantum states through local Hamiltonian engineering. We achieve these high precision levels of optical control through spatial light modulation with a DMD (digital micro-mirror device). This allows for both arbitrary beam shaping and aberration compensation in our imaging system to produce high fidelity optical potentials. We use these techniques to control state initialization, Hamiltonian dynamics, and measurement in experiments investigating low-dimensional many-body physics - from one-dimensional correlated quantum walks to characterizing entanglement.

Random-walk approach to the d -dimensional disordered Lorentz gas

NASA Astrophysics Data System (ADS)

Adib, Artur B.

2008-02-01

A correlated random walk approach to diffusion is applied to the disordered nonoverlapping Lorentz gas. By invoking the Lu-Torquato theory for chord-length distributions in random media [J. Chem. Phys. 98, 6472 (1993)], an analytic expression for the diffusion constant in arbitrary number of dimensions d is obtained. The result corresponds to an Enskog-like correction to the Boltzmann prediction, being exact in the dilute limit, and better or nearly exact in comparison to renormalized kinetic theory predictions for all allowed densities in d=2,3 . Extensive numerical simulations were also performed to elucidate the role of the approximations involved.

High-Speed Device-Independent Quantum Random Number Generation without a Detection Loophole

NASA Astrophysics Data System (ADS)

Liu, Yang; Yuan, Xiao; Li, Ming-Han; Zhang, Weijun; Zhao, Qi; Zhong, Jiaqiang; Cao, Yuan; Li, Yu-Huai; Chen, Luo-Kan; Li, Hao; Peng, Tianyi; Chen, Yu-Ao; Peng, Cheng-Zhi; Shi, Sheng-Cai; Wang, Zhen; You, Lixing; Ma, Xiongfeng; Fan, Jingyun; Zhang, Qiang; Pan, Jian-Wei

2018-01-01

Quantum mechanics provides the means of generating genuine randomness that is impossible with deterministic classical processes. Remarkably, the unpredictability of randomness can be certified in a manner that is independent of implementation devices. Here, we present an experimental study of device-independent quantum random number generation based on a detection-loophole-free Bell test with entangled photons. In the randomness analysis, without the independent identical distribution assumption, we consider the worst case scenario that the adversary launches the most powerful attacks against the quantum adversary. After considering statistical fluctuations and applying an 80 Gb ×45.6 Mb Toeplitz matrix hashing, we achieve a final random bit rate of 114 bits /s , with a failure probability less than 10-5. This marks a critical step towards realistic applications in cryptography and fundamental physics tests.

Scanning method as an unbiased simulation technique and its application to the study of self-attracting random walks

NASA Astrophysics Data System (ADS)

Meirovitch, Hagai

1985-12-01

The scanning method proposed by us [J. Phys. A 15, L735 (1982); Macromolecules 18, 563 (1985)] for simulation of polymer chains is further developed and applied, for the first time, to a model with finite interactions. In addition to ``importance sampling,'' we remove the bias introduced by the scanning method with a procedure suggested recently by Schmidt [Phys. Rev. Lett. 51, 2175 (1983)]; this procedure has the advantage of enabling one to estimate the statistical error. We find these two procedures to be equally efficient. The model studied is an N-step random walk on a lattice, in which a random walk i has a statistical weight &, where p<1 is an attractive energy parameter and Mi is the number of distinct sites visited by walk i. This model, which corresponds to a model of random walks moving in a medium with randomly distributed static traps, has been solved analytically for N-->∞ for any dimension d by Donsker and Varadhan (DV) and by others. and lnφ, where φ is the survival probability in the trapping problem, diverge like Nα with α=d/(d+2). Most numerical studies, however, have failed to reach the DV regime in which d/(d+2) becomes a good approximation for α. On the other hand, our results for α (obtained for N<=150) are close to the DV values for p<=0.7 and p<=0.6 for d=2 and 3, respectively. This suggests that the scanning method is more efficient than both the commonly used direct Monte Carlo technique, and the Rosenbluth and Rosenbluth method [J. Chem. Phys. 23, 356 (1954)]. Our results support the conclusion of Havlin et al. [Phys. Rev. Lett. 53, 407 (1984)] that the DV regime exists already for φ<=10-13 for both d=2 and 3. We also find that at the percolation threshold pc the exponents for the end-to-end distance are small, but larger than zero, and that the probability of a walk returning to the origin behaves approximately as N-1/3 for both d=2 and 3.

Musical motor feedback (MMF) in walking hemiparetic stroke patients: randomized trials of gait improvement.

PubMed

Schauer, Michael; Mauritz, Karl-Heinz

2003-11-01

To demonstrate the effect of rhythmical auditory stimulation in a musical context for gait therapy in hemiparetic stroke patients, when the stimulation is played back measure by measure initiated by the patient's heel-strikes (musical motor feedback). Does this type of musical feedback improve walking more than a less specific gait therapy? The randomized controlled trial considered 23 registered stroke patients. Two groups were created by randomization: the control group received 15 sessions of conventional gait therapy and the test group received 15 therapy sessions with musical motor feedback. Inpatient rehabilitation hospital. Median post-stroke interval was 44 days and the patients were able to walk without technical aids with a speed of approximately 0.71 m/s. Gait velocity, step duration, gait symmetry, stride length and foot rollover path length (heel-on-toe-off distance). The test group showed more mean improvement than the control group: stride length increased by 18% versus 0%, symmetry deviation decreased by 58% versus 20%, walking speed increased by 27% versus 4% and rollover path length increased by 28% versus 11%. Musical motor feedback improves the stroke patient's walk in selected parameters more than conventional gait therapy. A fixed memory in the patient's mind about the song and its timing may stimulate the improvement of gait even without the presence of an external pacemaker.

Conflicting results of robot-assisted versus usual gait training during postacute rehabilitation of stroke patients: a randomized clinical trial

PubMed Central

Taveggia, Giovanni; Borboni, Alberto; Mulé, Chiara; Negrini, Stefano

2016-01-01

Robot gait training has the potential to increase the effectiveness of walking therapy. Clinical outcomes after robotic training are often not superior to conventional therapy. We evaluated the effectiveness of a robot training compared with a usual gait training physiotherapy during a standardized rehabilitation protocol in inpatient participants with poststroke hemiparesis. This was a randomized double-blind clinical trial in a postacute physical and rehabilitation medicine hospital. Twenty-eight patients, 39.3% women (72±6 years), with hemiparesis (<6 months after stroke) receiving a conventional treatment according to the Bobath approach were assigned randomly to an experimental or a control intervention of robot gait training to improve walking (five sessions a week for 5 weeks). Outcome measures included the 6-min walk test, the 10 m walk test, Functional Independence Measure, SF-36 physical functioning and the Tinetti scale. Outcomes were collected at baseline, immediately following the intervention period and 3 months following the end of the intervention. The experimental group showed a significant increase in functional independence and gait speed (10 m walk test) at the end of the treatment and follow-up, higher than the minimal detectable change. The control group showed a significant increase in the gait endurance (6-min walk test) at the follow-up, higher than the minimal detectable change. Both treatments were effective in the improvement of gait performances, although the statistical analysis of functional independence showed a significant improvement in the experimental group, indicating possible advantages during generic activities of daily living compared with overground treatment. PMID:26512928

Effects of mirror therapy combined with neuromuscular electrical stimulation on motor recovery of lower limbs and walking ability of patients with stroke: a randomized controlled study.

PubMed

Xu, Qun; Guo, Feng; Salem, Hassan M Abo; Chen, Hong; Huang, Xiaolin

2017-12-01

To investigate the effectiveness of mirror therapy combined with neuromuscular electrical stimulation in promoting motor recovery of the lower limbs and walking ability in patients suffering from foot drop after stroke. Randomized controlled study. Inpatient rehabilitation center of a teaching hospital. Sixty-nine patients with foot drop. Patients were randomly divided into three groups: control, mirror therapy, and mirror therapy + neuromuscular electrical stimulation. All groups received interventions for 0.5 hours/day and five days/week for four weeks. 10-Meter walk test, Brunnstrom stage of motor recovery of the lower limbs, Modified Ashworth Scale score of plantar flexor spasticity, and passive ankle joint dorsiflexion range of motion were assessed before and after the four-week period. After four weeks of intervention, Brunnstrom stage ( P = 0.04), 10-meter walk test ( P < 0.05), and passive range of motion ( P < 0.05) showed obvious improvements between patients in the mirror therapy and control groups. Patients in the mirror therapy + neuromuscular electrical stimulation group showed better results than those in the mirror therapy group in the 10-meter walk test ( P < 0.05). There was no significant difference in spasticity between patients in the two intervention groups. However, compared with patients in the control group, patients in the mirror therapy + neuromuscular electrical stimulation group showed a significant decrease in spasticity ( P < 0.001). Therapy combining mirror therapy and neuromuscular electrical stimulation may help improve walking ability and reduce spasticity in stroke patients with foot drop.

Employing online quantum random number generators for generating truly random quantum states in Mathematica

NASA Astrophysics Data System (ADS)

Miszczak, Jarosław Adam

2013-01-01

The presented package for the Mathematica computing system allows the harnessing of quantum random number generators (QRNG) for investigating the statistical properties of quantum states. The described package implements a number of functions for generating random states. The new version of the package adds the ability to use the on-line quantum random number generator service and implements new functions for retrieving lists of random numbers. Thanks to the introduced improvements, the new version provides faster access to high-quality sources of random numbers and can be used in simulations requiring large amount of random data. New version program summaryProgram title: TRQS Catalogue identifier: AEKA_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEKA_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 18 134 No. of bytes in distributed program, including test data, etc.: 2 520 49 Distribution format: tar.gz Programming language: Mathematica, C. Computer: Any supporting Mathematica in version 7 or higher. Operating system: Any platform supporting Mathematica; tested with GNU/Linux (32 and 64 bit). RAM: Case-dependent Supplementary material: Fig. 1 mentioned below can be downloaded. Classification: 4.15. External routines: Quantis software library (http://www.idquantique.com/support/quantis-trng.html) Catalogue identifier of previous version: AEKA_v1_0 Journal reference of previous version: Comput. Phys. Comm. 183(2012)118 Does the new version supersede the previous version?: Yes Nature of problem: Generation of random density matrices and utilization of high-quality random numbers for the purpose of computer simulation. Solution method: Use of a physical quantum random number generator and an on-line service providing access to the source of true random numbers generated by quantum real number generator. Reasons for new version: Added support for the high-speed on-line quantum random number generator and improved methods for retrieving lists of random numbers. Summary of revisions: The presented version provides two signicant improvements. The first one is the ability to use the on-line Quantum Random Number Generation service developed by PicoQuant GmbH and the Nano-Optics groups at the Department of Physics of Humboldt University. The on-line service supported in the version 2.0 of the TRQS package provides faster access to true randomness sources constructed using the laws of quantum physics. The service is freely available at https://qrng.physik.hu-berlin.de/. The use of this service allows using the presented package with the need of a physical quantum random number generator. The second improvement introduced in this version is the ability to retrieve arrays of random data directly for the used source. This increases the speed of the random number generation, especially in the case of an on-line service, where it reduces the time necessary to establish the connection. Thanks to the speed improvement of the presented version, the package can now be used in simulations requiring larger amounts of random data. Moreover, the functions for generating random numbers provided by the current version of the package more closely follow the pattern of functions for generating pseudo- random numbers provided in Mathematica. Additional comments: Speed comparison: The implementation of the support for the QRNG on-line service provides a noticeable improvement in the speed of random number generation. For the samples of real numbers of size 101; 102,…,107 the times required to generate these samples using Quantis USB device and QRNG service are compared in Fig. 1. The presented results show that the use of the on-line service provides faster access to random numbers. One should note, however, that the speed gain can increase or decrease depending on the connection speed between the computer and the server providing random numbers. Running time: Depends on the used source of randomness and the amount of random data used in the experiment. References: [1] M. Wahl, M. Leifgen, M. Berlin, T. Röhlicke, H.-J. Rahn, O. Benson., An ultrafast quantum random number generator with provably bounded output bias based on photon arrival time measurements, Applied Physics Letters, Vol. 098, 171105 (2011). http://dx.doi.org/10.1063/1.3578456.

A random walk model for evaluating clinical trials involving serial observations.

PubMed

Hopper, J L; Young, G P

1988-05-01

For clinical trials where the variable of interest is ordered and categorical (for example, disease severity, symptom scale), and where measurements are taken at intervals, it might be possible to achieve a greater discrimination between the efficacy of treatments by modelling each patient's progress as a stochastic process. The random walk is a simple, easily interpreted model that can be fitted by maximum likelihood using a maximization routine with inference based on standard likelihood theory. In general the model can allow for randomly censored data, incorporates measured prognostic factors, and inference is conditional on the (possibly non-random) allocation of patients. Tests of fit and of model assumptions are proposed, and application to two therapeutic trials of gastroenterological disorders are presented. The model gave measures of the rate of, and variability in, improvement for patients under different treatments. A small simulation study suggested that the model is more powerful than considering the difference between initial and final scores, even when applied to data generated by a mechanism other than the random walk model assumed in the analysis. It thus provides a useful additional statistical method for evaluating clinical trials.

Varied overground walking-task practice versus body-weight-supported treadmill training in ambulatory adults within one year of stroke: a randomized controlled trial protocol.

PubMed

DePaul, Vincent G; Wishart, Laurie R; Richardson, Julie; Lee, Timothy D; Thabane, Lehana

2011-10-21

Although task-oriented training has been shown to improve walking outcomes after stroke, it is not yet clear whether one task-oriented approach is superior to another. The purpose of this study is to compare the effectiveness of the Motor Learning Walking Program (MLWP), a varied overground walking task program consistent with key motor learning principles, to body-weight-supported treadmill training (BWSTT) in community-dwelling, ambulatory, adults within 1 year of stroke. A parallel, randomized controlled trial with stratification by baseline gait speed will be conducted. Allocation will be controlled by a central randomization service and participants will be allocated to the two active intervention groups (1:1) using a permuted block randomization process. Seventy participants will be assigned to one of two 15-session training programs. In MLWP, one physiotherapist will supervise practice of various overground walking tasks. Instructions, feedback, and guidance will be provided in a manner that facilitates self-evaluation and problem solving. In BWSTT, training will emphasize repetition of the normal gait cycle while supported over a treadmill, assisted by up to three physiotherapists. Outcomes will be assessed by a blinded assessor at baseline, post-intervention and at 2-month follow-up. The primary outcome will be post-intervention comfortable gait speed. Secondary outcomes include fast gait speed, walking endurance, balance self-efficacy, participation in community mobility, health-related quality of life, and goal attainment. Groups will be compared using analysis of covariance with baseline gait speed strata as the single covariate. Intention-to-treat analysis will be used. In order to direct clinicians, patients, and other health decision-makers, there is a need for a head-to-head comparison of different approaches to active, task-related walking training after stroke. We hypothesize that outcomes will be optimized through the application of a task-related training program that is consistent with key motor learning principles related to practice, guidance and feedback. ClinicalTrials.gov # NCT00561405.

Varied overground walking-task practice versus body-weight-supported treadmill training in ambulatory adults within one year of stroke: a randomized controlled trial protocol

PubMed Central

2011-01-01

Background Although task-oriented training has been shown to improve walking outcomes after stroke, it is not yet clear whether one task-oriented approach is superior to another. The purpose of this study is to compare the effectiveness of the Motor Learning Walking Program (MLWP), a varied overground walking task program consistent with key motor learning principles, to body-weight-supported treadmill training (BWSTT) in community-dwelling, ambulatory, adults within 1 year of stroke. Methods/Design A parallel, randomized controlled trial with stratification by baseline gait speed will be conducted. Allocation will be controlled by a central randomization service and participants will be allocated to the two active intervention groups (1:1) using a permuted block randomization process. Seventy participants will be assigned to one of two 15-session training programs. In MLWP, one physiotherapist will supervise practice of various overground walking tasks. Instructions, feedback, and guidance will be provided in a manner that facilitates self-evaluation and problem solving. In BWSTT, training will emphasize repetition of the normal gait cycle while supported over a treadmill, assisted by up to three physiotherapists. Outcomes will be assessed by a blinded assessor at baseline, post-intervention and at 2-month follow-up. The primary outcome will be post-intervention comfortable gait speed. Secondary outcomes include fast gait speed, walking endurance, balance self-efficacy, participation in community mobility, health-related quality of life, and goal attainment. Groups will be compared using analysis of covariance with baseline gait speed strata as the single covariate. Intention-to-treat analysis will be used. Discussion In order to direct clinicians, patients, and other health decision-makers, there is a need for a head-to-head comparison of different approaches to active, task-related walking training after stroke. We hypothesize that outcomes will be optimized through the application of a task-related training program that is consistent with key motor learning principles related to practice, guidance and feedback. Trial Registration ClinicalTrials.gov # NCT00561405 PMID:22018267

The "Interval Walking in Colorectal Cancer" (I-WALK-CRC) study: Design, methods and recruitment results of a randomized controlled feasibility trial.

PubMed

Banck-Petersen, Anna; Olsen, Cecilie K; Djurhuus, Sissal S; Herrstedt, Anita; Thorsen-Streit, Sarah; Ried-Larsen, Mathias; Østerlind, Kell; Osterkamp, Jens; Krarup, Peter-Martin; Vistisen, Kirsten; Mosgaard, Camilla S; Pedersen, Bente K; Højman, Pernille; Christensen, Jesper F

2018-03-01

Low physical activity level is associated with poor prognosis in patients with colorectal cancer (CRC). To increase physical activity, technology-based platforms are emerging and provide intriguing opportunities to prescribe and monitor active lifestyle interventions. The "Interval Walking in Colorectal Cancer"(I-WALK-CRC) study explores the feasibility and efficacy a home-based interval-walking intervention delivered by a smart-phone application in order to improve cardio-metabolic health profile among CRC survivors. The aim of the present report is to describe the design, methods and recruitment results of the I-WALK-CRC study.Methods/Results: The I-WALK-CRC study is a randomized controlled trial designed to evaluate the feasibility and efficacy of a home-based interval walking intervention compared to a waiting-list control group for physiological and patient-reported outcomes. Patients who had completed surgery for local stage disease and patients who had completed surgery and any adjuvant chemotherapy for locally advanced stage disease were eligible for inclusion. Between October 1st , 2015, and February 1st , 2017, 136 inquiries were recorded; 83 patients were eligible for enrollment, and 42 patients accepted participation. Age and employment status were associated with participation, as participants were significantly younger (60.5 vs 70.8 years, P < 0.001) and more likely to be working (OR 5.04; 95%CI 1.96-12.98, P < 0.001) than non-participants. In the present study, recruitment of CRC survivors was feasible but we aim to better the recruitment rate in future studies. Further, the study clearly favored younger participants. The I-WALK-CRC study will provide important information regarding feasibility and efficacy of a home-based walking exercise program in CRC survivors.

Randomized Controlled Trial of a Home-Based Action Observation Intervention to Improve Walking in Parkinson Disease.

PubMed

Jaywant, Abhishek; Ellis, Terry D; Roy, Serge; Lin, Cheng-Chieh; Neargarder, Sandy; Cronin-Golomb, Alice

2016-05-01

To examine the feasibility and efficacy of a home-based gait observation intervention for improving walking in Parkinson disease (PD). Participants were randomly assigned to an intervention or control condition. A baseline walking assessment, a training period at home, and a posttraining assessment were conducted. The laboratory and participants' home and community environments. Nondemented individuals with PD (N=23) experiencing walking difficulty. In the gait observation (intervention) condition, participants viewed videos of healthy and parkinsonian gait. In the landscape observation (control) condition, participants viewed videos of moving water. These tasks were completed daily for 8 days. Spatiotemporal walking variables were assessed using accelerometers in the laboratory (baseline and posttraining assessments) and continuously at home during the training period. Variables included daily activity, walking speed, stride length, stride frequency, leg swing time, and gait asymmetry. Questionnaires including the 39-item Parkinson Disease Questionnaire (PDQ-39) were administered to determine self-reported change in walking, as well as feasibility. At posttraining assessment, only the gait observation group reported significantly improved mobility (PDQ-39). No improvements were seen in accelerometer-derived walking data. Participants found the at-home training tasks and accelerometer feasible to use. Participants found procedures feasible and reported improved mobility, suggesting that observational training holds promise in the rehabilitation of walking in PD. Observational training alone, however, may not be sufficient to enhance walking in PD. A more challenging and adaptive task, and the use of explicit perceptual learning and practice of actions, may be required to effect change. Copyright © 2016 American Congress of Rehabilitation Medicine. Published by Elsevier Inc. All rights reserved.

Nordic Walking as an Exercise Intervention to Reduce Pain in Women With Aromatase Inhibitor-Associated Arthralgia: A Feasibility Study.

PubMed

Fields, Jo; Richardson, Alison; Hopkinson, Jane; Fenlon, Deborah

2016-10-01

Women taking aromatase inhibitors as treatment for breast cancer commonly experience joint pain and stiffness (aromatase inhibitor-associated arthralgia [AIAA]), which can cause problems with adherence. There is evidence that exercise might be helpful, and Nordic walking could reduce joint pain compared to normal walking. To determine the feasibility of a trial of Nordic walking as an exercise intervention for women with AIAA. A feasibility study was carried out in a sample of women with AIAA using a randomized control design. Women were randomized to exercise (six-week supervised group Nordic walking training once per week with an increasing independent element, followed by six weeks 4 × 30 minutes/week independent Nordic walking); or enhanced usual care. Data were collected on recruitment, retention, exercise adherence, safety, and acceptability. The Brief Pain Inventory, GP Physical Activity Questionnaire, and biopsychosocial measures were completed at baseline, six and 12 weeks. Forty of 159 eligible women were recruited and attrition was 10%. There was no increased lymphedema and no long-term or serious injury. Adherence was >90% for weekly supervised group Nordic walking, and during independent Nordic walking, >80% women managed one to two Nordic walking sessions per week. From baseline to study end point, overall activity levels increased and pain reduced in both the intervention and control groups. Our findings indicate that women with AIAA are prepared to take up Nordic walking, complete a six-week supervised course and maintain increased activity levels over a 12-week period with no adverse effects. Copyright © 2016 American Academy of Hospice and Palliative Medicine. Published by Elsevier Inc. All rights reserved.

Effects of curved-walking training on curved-walking performance and freezing of gait in individuals with Parkinson's disease: A randomized controlled trial.

PubMed

Cheng, Fang-Yu; Yang, Yea-Ru; Wu, Yih-Ru; Cheng, Shih-Jung; Wang, Ray-Yau

2017-10-01

The purpose of this study was to investigate the effects of curved-walking training (CWT) on curved-walking performance and freezing of gait (FOG) in people with Parkinson's disease (PD). Twenty-four PD subjects were recruited and randomly assigned to the CWT group or control exercise (CE) group and received 12 sessions of either CWT with a turning-based treadmill or general exercise training for 30 min followed by 10 min of over-ground walking in each session for 4-6 weeks. The primary outcomes included curved-walking performance and FOG. All measurements were assessed at baseline, after training, and at 1-month follow-up. Our results showed significant improvements in curved-walking performance (speed, p = 0.007; cadence, p = 0.003; step length, p < 0.001) and FOG, measured by a FOG questionnaire (p = 0.004). The secondary outcomes including straight-walking performance (speed, cadence and step length, p < 0.001), timed up and go test (p = 0.014), functional gait assessment (p < 0.001), Unified Parkinson's disease Rating Scale III (p = 0.001), and quality of life (p < 0.001) were also improved in the experimental group. We further noted that the improvements were maintained for at least one month after training (p < 0.05). A 12-session CWT program can improve curved-walking ability, FOG, and other measures of functional walking performance in individuals with PD. Most of the improvements were sustained for at least one month after training. Copyright © 2017 Elsevier Ltd. All rights reserved.

Distribution of velocities and acceleration for a particle in Brownian correlated disorder: Inertial case

NASA Astrophysics Data System (ADS)

Le Doussal, Pierre; Petković, Aleksandra; Wiese, Kay Jörg

2012-06-01

We study the motion of an elastic object driven in a disordered environment in presence of both dissipation and inertia. We consider random forces with the statistics of random walks and reduce the problem to a single degree of freedom. It is the extension of the mean-field Alessandro-Beatrice- Bertotti-Montorsi (ABBM) model in presence of an inertial mass m. While the ABBM model can be solved exactly, its extension to inertia exhibits complicated history dependence due to oscillations and backward motion. The characteristic scales for avalanche motion are studied from numerics and qualitative arguments. To make analytical progress, we consider two variants which coincide with the original model whenever the particle moves only forward. Using a combination of analytical and numerical methods together with simulations, we characterize the distributions of instantaneous acceleration and velocity, and compare them in these three models. We show that for large driving velocity, all three models share the same large-deviation function for positive velocities, which is obtained analytically for small and large m, as well as for m=6/25. The effect of small additional thermal and quantum fluctuations can be treated within an approximate method.

Continuous Positive Airway Pressure During Exercise Improves Walking Time in Patients Undergoing Inpatient Cardiac Rehabilitation After Coronary Artery Bypass Graft Surgery: A RANDOMIZED CONTROLLED TRIAL.

PubMed

Pantoni, Camila Bianca Falasco; Di Thommazo-Luporini, Luciana; Mendes, Renata Gonçalves; Caruso, Flávia Cristina Rossi; Mezzalira, Daniel; Arena, Ross; Amaral-Neto, Othon; Catai, Aparecida Maria; Borghi-Silva, Audrey

2016-01-01

Continuous positive airway pressure (CPAP) has been used as an effective support to decrease the negative pulmonary effects of coronary artery bypass graft (CABG) surgery. However, it is unknown whether CPAP can positively influence patients undergoing CABG during exercise. This study evaluated the effectiveness of CPAP on the first day of ambulation after CABG in patients undergoing inpatient cardiac rehabilitation (CR). Fifty-four patients after CABG surgery were randomly assigned to receive either inpatient CR and CPAP (CPG) or standard CR without CPAP (CG). Cardiac rehabilitation included walking and CPAP pressures were set between 10 to 12 cmH2O. Participants were assessed on the first day of walking at rest and during walking. Outcome measures included breathing pattern variables, exercise time in seconds (ETs), dyspnea/leg effort ratings, and peripheral oxygen saturation (SpO2). Twenty-seven patients (13 CPG vs 14 CG) completed the study. Compared with walking without noninvasive ventilation assistance, CPAP increased ETs by 43.4 seconds (P = .040) during walking, promoted better thoracoabdominal coordination, increased ventilation during walking by 12.5 L/min (P = .001), increased SpO2 values at the end of walking by 2.6% (P = .016), and reduced dyspnea ratings by 1 point (P = .008). Continuous positive airway pressure can positively influence exercise tolerance, ventilatory function, and breathing pattern in response to a single bout of exercise after CABG.

Adults' Daily Walking for Travel and Leisure: Interaction Between Attitude Toward Walking and the Neighborhood Environment.

PubMed

Yang, Yong; Diez-Roux, Ana V

2017-09-01

Studies on how the interaction of psychological and environmental characteristics influences walking are limited, and the results are inconsistent. Our aim is to examine how the attitude toward walking and neighborhood environments interacts to influence walking. Cross-sectional phone and mail survey. Participants randomly sampled from 6 study sites including Los Angeles, Chicago, Baltimore, Minneapolis, Manhattan, and Bronx Counties in New York City, and Forsyth and Davidson Counties in North Carolina. The final sample consisted of 2621 persons from 2011 to 2012. Total minutes of walking for travel or leisure, attitude toward walking, and perceptions of the neighborhood environments were self-reported. Street Smart (SS) Walk Score (a measure of walkability derived from a variety of geographic data) was obtained for each residential location. Linear regression models adjusting for age, gender, race/ethnicity, education, and income. Attitude toward walking was positively associated with walking for both purposes. Walking for travel was significantly associated with SS Walk Score, whereas walking for leisure was not. The SS Walk Score and selected perceived environment characteristics were associated with walking in people with a very positive attitude toward walking but were not associated with walking in people with a less positive attitude. Attitudes toward walking and neighborhood environments interact to affect walking behavior.

Multicomponent physical exercise with simultaneous cognitive training to enhance dual-task walking of older adults: a secondary analysis of a 6-month randomized controlled trial with 1-year follow-up.

PubMed

Eggenberger, Patrick; Theill, Nathan; Holenstein, Stefan; Schumacher, Vera; de Bruin, Eling D

2015-01-01

About one-third of people older than 65 years fall at least once a year. Physical exercise has been previously demonstrated to improve gait, enhance physical fitness, and prevent falls. Nonetheless, the addition of cognitive training components may potentially increase these effects, since cognitive impairment is related to gait irregularities and fall risk. We hypothesized that simultaneous cognitive-physical training would lead to greater improvements in dual-task (DT) gait compared to exclusive physical training. Elderly persons older than 70 years and without cognitive impairment were randomly assigned to the following groups: 1) virtual reality video game dancing (DANCE), 2) treadmill walking with simultaneous verbal memory training (MEMORY), or 3) treadmill walking (PHYS). Each program was complemented with strength and balance exercises. Two 1-hour training sessions per week over 6 months were applied. Gait variables, functional fitness (Short Physical Performance Battery, 6-minute walk), and fall frequencies were assessed at baseline, after 3 months and 6 months, and at 1-year follow-up. Multiple regression analyses with planned comparisons were carried out. Eighty-nine participants were randomized to three groups initially; 71 completed the training and 47 were available at 1-year follow-up. DANCE/MEMORY showed a significant advantage compared to PHYS in DT costs of step time variability at fast walking (P=0.044). Training-specific gait adaptations were found on comparing DANCE and MEMORY: DANCE reduced step time at fast walking (P=0.007) and MEMORY reduced gait variability in DT and DT costs at preferred walking speed (both trend P=0.062). Global linear time effects showed improved gait (P<0.05), functional fitness (P<0.05), and reduced fall frequency (-77%, P<0.001). Only single-task fast walking, gait variability at preferred walking speed, and Short Physical Performance Battery were reduced at follow-up (all P<0.05 or trend). Long-term multicomponent cognitive-physical and exclusive physical training programs demonstrated similar potential to counteract age-related decline in physical functioning.

Multicomponent physical exercise with simultaneous cognitive training to enhance dual-task walking of older adults: a secondary analysis of a 6-month randomized controlled trial with 1-year follow-up

PubMed Central

Eggenberger, Patrick; Theill, Nathan; Holenstein, Stefan; Schumacher, Vera; de Bruin, Eling D

2015-01-01

Background About one-third of people older than 65 years fall at least once a year. Physical exercise has been previously demonstrated to improve gait, enhance physical fitness, and prevent falls. Nonetheless, the addition of cognitive training components may potentially increase these effects, since cognitive impairment is related to gait irregularities and fall risk. We hypothesized that simultaneous cognitive–physical training would lead to greater improvements in dual-task (DT) gait compared to exclusive physical training. Methods Elderly persons older than 70 years and without cognitive impairment were randomly assigned to the following groups: 1) virtual reality video game dancing (DANCE), 2) treadmill walking with simultaneous verbal memory training (MEMORY), or 3) treadmill walking (PHYS). Each program was complemented with strength and balance exercises. Two 1-hour training sessions per week over 6 months were applied. Gait variables, functional fitness (Short Physical Performance Battery, 6-minute walk), and fall frequencies were assessed at baseline, after 3 months and 6 months, and at 1-year follow-up. Multiple regression analyses with planned comparisons were carried out. Results Eighty-nine participants were randomized to three groups initially; 71 completed the training and 47 were available at 1-year follow-up. DANCE/MEMORY showed a significant advantage compared to PHYS in DT costs of step time variability at fast walking (P=0.044). Training-specific gait adaptations were found on comparing DANCE and MEMORY: DANCE reduced step time at fast walking (P=0.007) and MEMORY reduced gait variability in DT and DT costs at preferred walking speed (both trend P=0.062). Global linear time effects showed improved gait (P<0.05), functional fitness (P<0.05), and reduced fall frequency (−77%, P<0.001). Only single-task fast walking, gait variability at preferred walking speed, and Short Physical Performance Battery were reduced at follow-up (all P<0.05 or trend). Conclusion Long-term multicomponent cognitive–physical and exclusive physical training programs demonstrated similar potential to counteract age-related decline in physical functioning. PMID:26604719

Continuous-time random walks with reset events. Historical background and new perspectives

NASA Astrophysics Data System (ADS)

Montero, Miquel; Masó-Puigdellosas, Axel; Villarroel, Javier

2017-09-01

In this paper, we consider a stochastic process that may experience random reset events which relocate the system to its starting position. We focus our attention on a one-dimensional, monotonic continuous-time random walk with a constant drift: the process moves in a fixed direction between the reset events, either by the effect of the random jumps, or by the action of a deterministic bias. However, the orientation of its motion is randomly determined after each restart. As a result of these alternating dynamics, interesting properties do emerge. General formulas for the propagator as well as for two extreme statistics, the survival probability and the mean first-passage time, are also derived. The rigor of these analytical results is verified by numerical estimations, for particular but illuminating examples.

Continuous-time random-walk model for financial distributions

NASA Astrophysics Data System (ADS)

Masoliver, Jaume; Montero, Miquel; Weiss, George H.

2003-02-01

We apply the formalism of the continuous-time random walk to the study of financial data. The entire distribution of prices can be obtained once two auxiliary densities are known. These are the probability densities for the pausing time between successive jumps and the corresponding probability density for the magnitude of a jump. We have applied the formalism to data on the U.S. dollar deutsche mark future exchange, finding good agreement between theory and the observed data.

Superimposed Code Theorectic Analysis of DNA Codes and DNA Computing

DTIC Science & Technology

2010-03-01

because only certain collections (partitioned by font type) of sequences are allowed to be in each position (e.g., Arial = position 0, Comic ...rigidity of short oligos and the shape of the polar charge. Oligo movement was modeled by a Brownian motion 3 dimensional random walk. The one...temperature, kB is Boltz he viscosity of the medium. The random walk motion is modeled by assuming the oligo is on a three dimensional lattice and may

Physical interrelation between Fokker-Planck and random walk models with application to Coulomb interactions.

NASA Technical Reports Server (NTRS)

Englert, G. W.

1971-01-01

A model of the random walk is formulated to allow a simple computing procedure to replace the difficult problem of solution of the Fokker-Planck equation. The step sizes and probabilities of taking steps in the various directions are expressed in terms of Fokker-Planck coefficients. Application is made to many particle systems with Coulomb interactions. The relaxation of a highly peaked velocity distribution of particles to equilibrium conditions is illustrated.

Ant-inspired density estimation via random walks

PubMed Central

Musco, Cameron; Su, Hsin-Hao

2017-01-01

Many ant species use distributed population density estimation in applications ranging from quorum sensing, to task allocation, to appraisal of enemy colony strength. It has been shown that ants estimate local population density by tracking encounter rates: The higher the density, the more often the ants bump into each other. We study distributed density estimation from a theoretical perspective. We prove that a group of anonymous agents randomly walking on a grid are able to estimate their density within a small multiplicative error in few steps by measuring their rates of encounter with other agents. Despite dependencies inherent in the fact that nearby agents may collide repeatedly (and, worse, cannot recognize when this happens), our bound nearly matches what would be required to estimate density by independently sampling grid locations. From a biological perspective, our work helps shed light on how ants and other social insects can obtain relatively accurate density estimates via encounter rates. From a technical perspective, our analysis provides tools for understanding complex dependencies in the collision probabilities of multiple random walks. We bound the strength of these dependencies using local mixing properties of the underlying graph. Our results extend beyond the grid to more general graphs, and we discuss applications to size estimation for social networks, density estimation for robot swarms, and random walk-based sampling for sensor networks. PMID:28928146

Noise in two-color electronic distance meter measurements revisited

USGS Publications Warehouse

Langbein, J.

2004-01-01

Frequent, high-precision geodetic data have temporally correlated errors. Temporal correlations directly affect both the estimate of rate and its standard error; the rate of deformation is a key product from geodetic measurements made in tectonically active areas. Various models of temporally correlated errors are developed and these provide relations between the power spectral density and the data covariance matrix. These relations are applied to two-color electronic distance meter (EDM) measurements made frequently in California over the past 15-20 years. Previous analysis indicated that these data have significant random walk error. Analysis using the noise models developed here indicates that the random walk model is valid for about 30% of the data. A second 30% of the data can be better modeled with power law noise with a spectral index between 1 and 2, while another 30% of the data can be modeled with a combination of band-pass-filtered plus random walk noise. The remaining 10% of the data can be best modeled as a combination of band-pass-filtered plus power law noise. This band-pass-filtered noise is a product of an annual cycle that leaks into adjacent frequency bands. For time spans of more than 1 year these more complex noise models indicate that the precision in rate estimates is better than that inferred by just the simpler, random walk model of noise.

Central limit theorem for recurrent random walks on a strip with bounded potential

NASA Astrophysics Data System (ADS)

Dolgopyat, D.; Goldsheid, I.

2018-07-01

We prove that the recurrent random walk (RW) in random environment (RE) on a strip in bounded potential satisfies the central limit theorem (CLT). The key ingredients of the proof are the analysis of the invariant measure equation and construction of a linearly growing martingale for walks in bounded potential. Our main result implies a complete classification of recurrent i.i.d. RWRE on the strip. Namely the walk either exhibits the Sinai behaviour in the sense that converges, as , to a (random) limit (the Sinai law) or, it satisfies the CLT. Another application of our main result is the CLT for the quasiperiodic environments with Diophantine frequencies in the recurrent case. We complement this result by proving that in the transient case the CLT holds for all uniquely ergodic environments. We also investigate the algebraic structure of the environments satisfying the CLT. In particular, we show that there exists a collection of proper algebraic subvarieties in the space of transition probabilities, such that: • If RE is stationary and ergodic and the transition probabilities are con-centrated on one of subvarieties from our collection then the CLT holds. • If the environment is i.i.d then the above condition is also necessary forthe CLT. All these results are valid for one-dimensional RWRE with bounded jumps as a particular case of the strip model.

Distributed clone detection in static wireless sensor networks: random walk with network division.

PubMed

Khan, Wazir Zada; Aalsalem, Mohammed Y; Saad, N M

2015-01-01

Wireless Sensor Networks (WSNs) are vulnerable to clone attacks or node replication attacks as they are deployed in hostile and unattended environments where they are deprived of physical protection, lacking physical tamper-resistance of sensor nodes. As a result, an adversary can easily capture and compromise sensor nodes and after replicating them, he inserts arbitrary number of clones/replicas into the network. If these clones are not efficiently detected, an adversary can be further capable to mount a wide variety of internal attacks which can emasculate the various protocols and sensor applications. Several solutions have been proposed in the literature to address the crucial problem of clone detection, which are not satisfactory as they suffer from some serious drawbacks. In this paper we propose a novel distributed solution called Random Walk with Network Division (RWND) for the detection of node replication attack in static WSNs which is based on claimer-reporter-witness framework and combines a simple random walk with network division. RWND detects clone(s) by following a claimer-reporter-witness framework and a random walk is employed within each area for the selection of witness nodes. Splitting the network into levels and areas makes clone detection more efficient and the high security of witness nodes is ensured with moderate communication and memory overheads. Our simulation results show that RWND outperforms the existing witness node based strategies with moderate communication and memory overheads.

Is walking a random walk? Evidence for long-range correlations in stride interval of human gait

NASA Technical Reports Server (NTRS)

Hausdorff, Jeffrey M.; Peng, C.-K.; Ladin, Zvi; Wei, Jeanne Y.; Goldberger, Ary L.

1995-01-01

Complex fluctuation of unknown origin appear in the normal gait pattern. These fluctuations might be described as being (1) uncorrelated white noise, (2) short-range correlations, or (3) long-range correlations with power-law scaling. To test these possibilities, the stride interval of 10 healthy young men was measured as they walked for 9 min at their usual rate. From these time series we calculated scaling indexes by using a modified random walk analysis and power spectral analysis. Both indexes indicated the presence of long-range self-similar correlations extending over hundreds of steps; the stride interval at any time depended on the stride interval at remote previous times, and this dependence decayed in a scale-free (fractallike) power-law fashion. These scaling indexes were significantly different from those obtained after random shuffling of the original time series, indicating the importance of the sequential ordering of the stride interval. We demonstrate that conventional models of gait generation fail to reproduce the observed scaling behavior and introduce a new type of central pattern generator model that sucessfully accounts for the experimentally observed long-range correlations.

Changes in work affect in response to lunchtime walking in previously physically inactive employees: A randomized trial.

PubMed

Thøgersen-Ntoumani, C; Loughren, E A; Kinnafick, F-E; Taylor, I M; Duda, J L; Fox, K R

2015-12-01

Physical activity may regulate affective experiences at work, but controlled studies are needed and there has been a reliance on retrospective accounts of experience. The purpose of the present study was to examine the effect of lunchtime walks on momentary work affect at the individual and group levels. Physically inactive employees (N = 56; M age = 47.68; 92.86% female) from a large university in the UK were randomized to immediate treatment or delayed treatment (DT). The DT participants completed both a control and intervention period. During the intervention period, participants partook in three weekly 30-min lunchtime group-led walks for 10 weeks. They completed twice daily affective reports at work (morning and afternoon) using mobile phones on two randomly chosen days per week. Multilevel modeling was used to analyze the data. Lunchtime walks improved enthusiasm, relaxation, and nervousness at work, although the pattern of results differed depending on whether between-group or within-person analyses were conducted. The intervention was effective in changing some affective states and may have broader implications for public health and workplace performance. © 2015 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.

Realization of a Quantum Random Generator Certified with the Kochen-Specker Theorem

NASA Astrophysics Data System (ADS)

Kulikov, Anatoly; Jerger, Markus; Potočnik, Anton; Wallraff, Andreas; Fedorov, Arkady

2017-12-01

Random numbers are required for a variety of applications from secure communications to Monte Carlo simulation. Yet randomness is an asymptotic property, and no output string generated by a physical device can be strictly proven to be random. We report an experimental realization of a quantum random number generator (QRNG) with randomness certified by quantum contextuality and the Kochen-Specker theorem. The certification is not performed in a device-independent way but through a rigorous theoretical proof of each outcome being value indefinite even in the presence of experimental imperfections. The analysis of the generated data confirms the incomputable nature of our QRNG.

Realization of a Quantum Random Generator Certified with the Kochen-Specker Theorem.

PubMed

Kulikov, Anatoly; Jerger, Markus; Potočnik, Anton; Wallraff, Andreas; Fedorov, Arkady

2017-12-15

Random numbers are required for a variety of applications from secure communications to Monte Carlo simulation. Yet randomness is an asymptotic property, and no output string generated by a physical device can be strictly proven to be random. We report an experimental realization of a quantum random number generator (QRNG) with randomness certified by quantum contextuality and the Kochen-Specker theorem. The certification is not performed in a device-independent way but through a rigorous theoretical proof of each outcome being value indefinite even in the presence of experimental imperfections. The analysis of the generated data confirms the incomputable nature of our QRNG.

Non-linear continuous time random walk models★

NASA Astrophysics Data System (ADS)

Stage, Helena; Fedotov, Sergei

2017-11-01

A standard assumption of continuous time random walk (CTRW) processes is that there are no interactions between the random walkers, such that we obtain the celebrated linear fractional equation either for the probability density function of the walker at a certain position and time, or the mean number of walkers. The question arises how one can extend this equation to the non-linear case, where the random walkers interact. The aim of this work is to take into account this interaction under a mean-field approximation where the statistical properties of the random walker depend on the mean number of walkers. The implementation of these non-linear effects within the CTRW integral equations or fractional equations poses difficulties, leading to the alternative methodology we present in this work. We are concerned with non-linear effects which may either inhibit anomalous effects or induce them where they otherwise would not arise. Inhibition of these effects corresponds to a decrease in the waiting times of the random walkers, be this due to overcrowding, competition between walkers or an inherent carrying capacity of the system. Conversely, induced anomalous effects present longer waiting times and are consistent with symbiotic, collaborative or social walkers, or indirect pinpointing of favourable regions by their attractiveness. Contribution to the Topical Issue "Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.

Factors Influencing the Efficacy of Aerobic Exercise for Improving Fitness and Walking Capacity After Stroke: A Meta-Analysis With Meta-Regression.

PubMed

Boyne, Pierce; Welge, Jeffrey; Kissela, Brett; Dunning, Kari

2017-03-01

To assess the influence of dosing parameters and patient characteristics on the efficacy of aerobic exercise (AEX) poststroke. A systematic review was conducted using PubMed, MEDLINE, Cumulative Index of Nursing and Allied Health Literature, Physiotherapy Evidence Database, and Academic Search Complete. Studies were selected that compared an AEX group with a nonaerobic control group among ambulatory persons with stroke. Extracted outcome data included peak oxygen consumption (V˙o 2 peak) during exercise testing, walking speed, and walking endurance (6-min walk test). Independent variables of interest were AEX mode (seated or walking), AEX intensity (moderate or vigorous), AEX volume (total hours), stroke chronicity, and baseline outcome scores. Significant between-study heterogeneity was confirmed for all outcomes. Pooled AEX effect size estimates (AEX group change minus control group change) from random effects models were V˙o 2 peak, 2.2mL⋅kg -1 ⋅min -1 (95% confidence interval [CI], 1.3-3.1mL⋅kg -1 ⋅min -1 ); walking speed, .06m/s (95% CI, .01-.11m/s); and 6-minute walk test distance, 29m (95% CI, 15-42m). In meta-regression, larger V˙o 2 peak effect sizes were significantly associated with higher AEX intensity and higher baseline V˙o 2 peak. Larger effect sizes for walking speed and the 6-minute walk test were significantly associated with a walking AEX mode. In contrast, seated AEX did not have a significant effect on walking outcomes. AEX significantly improves aerobic capacity poststroke, but may need to be task specific to affect walking speed and endurance. Higher AEX intensity is associated with better outcomes. Future randomized studies are needed to confirm these results. Copyright © 2016 American Congress of Rehabilitation Medicine. Published by Elsevier Inc. All rights reserved.

Inferring Lévy walks from curved trajectories: A rescaling method

NASA Astrophysics Data System (ADS)

Tromer, R. M.; Barbosa, M. B.; Bartumeus, F.; Catalan, J.; da Luz, M. G. E.; Raposo, E. P.; Viswanathan, G. M.

2015-08-01

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).

Pilot study of a dog walking randomized intervention: effects of a focus on canine exercise.

PubMed

Rhodes, Ryan E; Murray, Holly; Temple, Viviene A; Tuokko, Holly; Higgins, Joan Wharf

2012-05-01

The promotion of dog walking among owners who do not walk their dogs regularly may be a viable physical activity intervention aperture, yet research is very limited and no intervention studies have employed control groups. Therefore, the purpose of this pilot study was to examine the viability of dog walking for physical activity intervention using messages targeting canine exercise. Inactive dog owners (n=58) were randomized to either a standard control condition or the intervention (persuasive material about canine health from walking and a calendar to mark walks) after completing a baseline questionnaire package and wearing a pedometer for one week. Participants (standard condition n=28; intervention condition n=30) completed the six and 12 week follow-up questionnaire packages. Intention to treat analyses showed that both groups increased physical activity significantly across the 12 weeks (η(2)=0.09 to 0.21). The intervention group resulted in significantly higher step-counts compared to the control group (Δ 1823 steps) and showed significantly higher trajectories from baseline to 12 weeks in the self-reported physical activity measures (η(2)=0.11 to 0.27). The results are promising for the viability of increasing dog walking as a means for physical activity promotion and suggest that theoretical fidelity targeting canine exercise may be a helpful approach. Copyright © 2012 Elsevier Inc. All rights reserved.

Quantifying the dose-response of walking in reducing coronary heart disease risk: meta-analysis.

PubMed

Zheng, Henry; Orsini, Nicola; Amin, Janaki; Wolk, Alicja; Nguyen, Van Thi Thuy; Ehrlich, Fred

2009-01-01

The evidence for the efficacy of walking in reducing the risk of and preventing coronary heart disease (CHD) is not completely understood. This meta-analysis aimed to quantify the dose-response relationship between walking and CHD risk reduction for both men and women in the general population. Studies on walking and CHD primary prevention between 1954 and 2007 were identified through Medline, SportDiscus and the Cochrane Database of Systematic Reviews. Random-effect meta-regression models were used to pool the relative risks from individual studies. A total of 11 prospective cohort studies and one randomized control trial study met the inclusion criteria, with 295,177 participants free of CHD at baseline and 7,094 cases at follow-up. The meta-analysis indicated that an increment of approximately 30 min of normal walking a day for 5 days a week was associated with 19% CHD risk reduction (95% CI = 14-23%; P-heterogeneity = 0.56; I (2) = 0%). We found no evidence of heterogeneity between subgroups of studies defined by gender (P = 0.67); age of the study population (P = 0.52); or follow-up duration (P = 0.77). The meta-analysis showed that the risk for developing CHD decreases as walking dose increases. Walking should be prescribed as an evidence-based effective exercise modality for CHD prevention in the general population.

A wave-mechanical model of incoherent quasielastic scattering in complex systems.

PubMed

Frauenfelder, Hans; Fenimore, Paul W; Young, Robert D

2014-09-02

Quasielastic incoherent neutron scattering (QENS) is an important tool for the exploration of the dynamics of complex systems such as biomolecules, liquids, and glasses. The dynamics is reflected in the energy spectra of the scattered neutrons. Conventionally these spectra are decomposed into a narrow elastic line and a broad quasielastic band. The band is interpreted as being caused by Doppler broadening due to spatial motion of the target molecules. We propose a quantum-mechanical model in which there is no separate elastic line. The quasielastic band is composed of sharp lines with twice the natural line width, shifted from the center by a random walk of the protein in the free-energy landscape of the target molecule. The walk is driven by vibrations and by external fluctuations. We first explore the model with the Mössbauer effect. In the subsequent application to QENS we treat the incoming neutron as a de Broglie wave packet. While the wave packet passes the protons in the protein and the hydration shell it exchanges energy with the protein during the passage time of about 100 ns. The energy exchange broadens the ensemble spectrum. Because the exchange involves the free-energy landscape of the protein, the QENS not only provides insight into the protein dynamics, but it may also illuminate the free-energy landscape of the protein-solvent system.

Efficient quantum pseudorandomness with simple graph states

NASA Astrophysics Data System (ADS)

Mezher, Rawad; Ghalbouni, Joe; Dgheim, Joseph; Markham, Damian

2018-02-01

Measurement based (MB) quantum computation allows for universal quantum computing by measuring individual qubits prepared in entangled multipartite states, known as graph states. Unless corrected for, the randomness of the measurements leads to the generation of ensembles of random unitaries, where each random unitary is identified with a string of possible measurement results. We show that repeating an MB scheme an efficient number of times, on a simple graph state, with measurements at fixed angles and no feedforward corrections, produces a random unitary ensemble that is an ɛ -approximate t design on n qubits. Unlike previous constructions, the graph is regular and is also a universal resource for measurement based quantum computing, closely related to the brickwork state.

High-Speed Device-Independent Quantum Random Number Generation without a Detection Loophole.

PubMed

Liu, Yang; Yuan, Xiao; Li, Ming-Han; Zhang, Weijun; Zhao, Qi; Zhong, Jiaqiang; Cao, Yuan; Li, Yu-Huai; Chen, Luo-Kan; Li, Hao; Peng, Tianyi; Chen, Yu-Ao; Peng, Cheng-Zhi; Shi, Sheng-Cai; Wang, Zhen; You, Lixing; Ma, Xiongfeng; Fan, Jingyun; Zhang, Qiang; Pan, Jian-Wei

2018-01-05

Quantum mechanics provides the means of generating genuine randomness that is impossible with deterministic classical processes. Remarkably, the unpredictability of randomness can be certified in a manner that is independent of implementation devices. Here, we present an experimental study of device-independent quantum random number generation based on a detection-loophole-free Bell test with entangled photons. In the randomness analysis, without the independent identical distribution assumption, we consider the worst case scenario that the adversary launches the most powerful attacks against the quantum adversary. After considering statistical fluctuations and applying an 80  Gb×45.6  Mb Toeplitz matrix hashing, we achieve a final random bit rate of 114  bits/s, with a failure probability less than 10^{-5}. This marks a critical step towards realistic applications in cryptography and fundamental physics tests.

Effect of multilayer high-compression bandaging on ankle range of motion and oxygen cost of walking

PubMed Central

Roaldsen, K S; Elfving, B; Stanghelle, J K; Mattsson, E

2012-01-01

Objective To evaluate the effects of multilayer high-compression bandaging on ankle range of motion, oxygen consumption and subjective walking ability in healthy subjects. Method A volunteer sample of 22 healthy subjects (10 women and 12 men; aged 67 [63–83] years) were studied. The intervention included treadmill-walking at self-selected speed with and without multilayer high-compression bandaging (Proforeº), randomly selected. The primary outcome variables were ankle range of motion, oxygen consumption and subjective walking ability. Results Total ankle range of motion decreased 4% with compression. No change in oxygen cost of walking was observed. Less than half the subjects reported that walking-shoe comfort or walking distance was negatively affected. Conclusion Ankle range of motion decreased with compression but could probably be counteracted with a regular exercise programme. There were no indications that walking with compression was more exhausting than walking without. Appropriate walking shoes could seem important to secure gait efficiency when using compression garments. PMID:21810941

Effects of a Flexibility and Relaxation Programme, Walking, and Nordic Walking on Parkinson's Disease

PubMed Central

Reuter, I.; Mehnert, S.; Leone, P.; Kaps, M.; Oechsner, M.; Engelhardt, M.

2011-01-01

Symptoms of Parkinson's disease (PD) progress despite optimized medical treatment. The present study investigated the effects of a flexibility and relaxation programme, walking, and Nordic walking (NW) on walking speed, stride length, stride length variability, Parkinson-specific disability (UPDRS), and health-related quality of life (PDQ 39). 90 PD patients were randomly allocated to the 3 treatment groups. Patients participated in a 6-month study with 3 exercise sessions per week, each lasting 70 min. Assessment after completion of the training showed that pain was reduced in all groups, and balance and health-related quality of life were improved. Furthermore, walking, and Nordic walking improved stride length, gait variability, maximal walking speed, exercise capacity at submaximal level, and PD disease-specific disability on the UPDRS in addition. Nordic walking was superior to the flexibility and relaxation programme and walking in improving postural stability, stride length, gait pattern and gait variability. No significant injuries occurred during the training. All patients of the Nordic walking group continued Nordic walking after completing the study. PMID:21603199

Social aggregation in pea aphids: experiment and random walk modeling.

PubMed

Nilsen, Christa; Paige, John; Warner, Olivia; Mayhew, Benjamin; Sutley, Ryan; Lam, Matthew; Bernoff, Andrew J; Topaz, Chad M

2013-01-01

From bird flocks to fish schools and ungulate herds to insect swarms, social biological aggregations are found across the natural world. An ongoing challenge in the mathematical modeling of aggregations is to strengthen the connection between models and biological data by quantifying the rules that individuals follow. We model aggregation of the pea aphid, Acyrthosiphon pisum. Specifically, we conduct experiments to track the motion of aphids walking in a featureless circular arena in order to deduce individual-level rules. We observe that each aphid transitions stochastically between a moving and a stationary state. Moving aphids follow a correlated random walk. The probabilities of motion state transitions, as well as the random walk parameters, depend strongly on distance to an aphid's nearest neighbor. For large nearest neighbor distances, when an aphid is essentially isolated, its motion is ballistic with aphids moving faster, turning less, and being less likely to stop. In contrast, for short nearest neighbor distances, aphids move more slowly, turn more, and are more likely to become stationary; this behavior constitutes an aggregation mechanism. From the experimental data, we estimate the state transition probabilities and correlated random walk parameters as a function of nearest neighbor distance. With the individual-level model established, we assess whether it reproduces the macroscopic patterns of movement at the group level. To do so, we consider three distributions, namely distance to nearest neighbor, angle to nearest neighbor, and percentage of population moving at any given time. For each of these three distributions, we compare our experimental data to the output of numerical simulations of our nearest neighbor model, and of a control model in which aphids do not interact socially. Our stochastic, social nearest neighbor model reproduces salient features of the experimental data that are not captured by the control.

SU-D-201-06: Random Walk Algorithm Seed Localization Parameters in Lung Positron Emission Tomography (PET) Images

DOE Office of Scientific and Technical Information (OSTI.GOV)

Soufi, M; Asl, A Kamali; Geramifar, P

2015-06-15

Purpose: The objective of this study was to find the best seed localization parameters in random walk algorithm application to lung tumor delineation in Positron Emission Tomography (PET) images. Methods: PET images suffer from statistical noise and therefore tumor delineation in these images is a challenging task. Random walk algorithm, a graph based image segmentation technique, has reliable image noise robustness. Also its fast computation and fast editing characteristics make it powerful for clinical purposes. We implemented the random walk algorithm using MATLAB codes. The validation and verification of the algorithm have been done by 4D-NCAT phantom with spherical lungmore » lesions in different diameters from 20 to 90 mm (with incremental steps of 10 mm) and different tumor to background ratios of 4:1 and 8:1. STIR (Software for Tomographic Image Reconstruction) has been applied to reconstruct the phantom PET images with different pixel sizes of 2×2×2 and 4×4×4 mm{sup 3}. For seed localization, we selected pixels with different maximum Standardized Uptake Value (SUVmax) percentages, at least (70%, 80%, 90% and 100%) SUVmax for foreground seeds and up to (20% to 55%, 5% increment) SUVmax for background seeds. Also, for investigation of algorithm performance on clinical data, 19 patients with lung tumor were studied. The resulted contours from algorithm have been compared with nuclear medicine expert manual contouring as ground truth. Results: Phantom and clinical lesion segmentation have shown that the best segmentation results obtained by selecting the pixels with at least 70% SUVmax as foreground seeds and pixels up to 30% SUVmax as background seeds respectively. The mean Dice Similarity Coefficient of 94% ± 5% (83% ± 6%) and mean Hausdorff Distance of 1 (2) pixels have been obtained for phantom (clinical) study. Conclusion: The accurate results of random walk algorithm in PET image segmentation assure its application for radiation treatment planning and diagnosis.« less

Nonlocal operators, parabolic-type equations, and ultrametric random walks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chacón-Cortes, L. F., E-mail: fchaconc@math.cinvestav.edu.mx; Zúñiga-Galindo, W. A., E-mail: wazuniga@math.cinvestav.edu.mx

2013-11-15

In this article, we introduce a new type of nonlocal operators and study the Cauchy problem for certain parabolic-type pseudodifferential equations naturally associated to these operators. Some of these equations are the p-adic master equations of certain models of complex systems introduced by Avetisov, V. A. and Bikulov, A. Kh., “On the ultrametricity of the fluctuation dynamicmobility of protein molecules,” Proc. Steklov Inst. Math. 265(1), 75–81 (2009) [Tr. Mat. Inst. Steklova 265, 82–89 (2009) (Izbrannye Voprosy Matematicheskoy Fiziki i p-adicheskogo Analiza) (in Russian)]; Avetisov, V. A., Bikulov, A. Kh., and Zubarev, A. P., “First passage time distribution and the numbermore » of returns for ultrametric random walks,” J. Phys. A 42(8), 085003 (2009); Avetisov, V. A., Bikulov, A. Kh., and Osipov, V. A., “p-adic models of ultrametric diffusion in the conformational dynamics of macromolecules,” Proc. Steklov Inst. Math. 245(2), 48–57 (2004) [Tr. Mat. Inst. Steklova 245, 55–64 (2004) (Izbrannye Voprosy Matematicheskoy Fiziki i p-adicheskogo Analiza) (in Russian)]; Avetisov, V. A., Bikulov, A. Kh., and Osipov, V. A., “p-adic description of characteristic relaxation in complex systems,” J. Phys. A 36(15), 4239–4246 (2003); Avetisov, V. A., Bikulov, A. H., Kozyrev, S. V., and Osipov, V. A., “p-adic models of ultrametric diffusion constrained by hierarchical energy landscapes,” J. Phys. A 35(2), 177–189 (2002); Avetisov, V. A., Bikulov, A. Kh., and Kozyrev, S. V., “Description of logarithmic relaxation by a model of a hierarchical random walk,” Dokl. Akad. Nauk 368(2), 164–167 (1999) (in Russian). The fundamental solutions of these parabolic-type equations are transition functions of random walks on the n-dimensional vector space over the field of p-adic numbers. We study some properties of these random walks, including the first passage time.« less

Simulating intrafraction prostate motion with a random walk model.

PubMed

Pommer, Tobias; Oh, Jung Hun; Munck Af Rosenschöld, Per; Deasy, Joseph O

2017-01-01

Prostate motion during radiation therapy (ie, intrafraction motion) can cause unwanted loss of radiation dose to the prostate and increased dose to the surrounding organs at risk. A compact but general statistical description of this motion could be useful for simulation of radiation therapy delivery or margin calculations. We investigated whether prostate motion could be modeled with a random walk model. Prostate motion recorded during 548 radiation therapy fractions in 17 patients was analyzed and used for input in a random walk prostate motion model. The recorded motion was categorized on the basis of whether any transient excursions (ie, rapid prostate motion in the anterior and superior direction followed by a return) occurred in the trace and transient motion. This was separately modeled as a large step in the anterior/superior direction followed by a returning large step. Random walk simulations were conducted with and without added artificial transient motion using either motion data from all observed traces or only traces without transient excursions as model input, respectively. A general estimate of motion was derived with reasonable agreement between simulated and observed traces, especially during the first 5 minutes of the excursion-free simulations. Simulated and observed diffusion coefficients agreed within 0.03, 0.2 and 0.3 mm 2 /min in the left/right, superior/inferior, and anterior/posterior directions, respectively. A rapid increase in variance at the start of observed traces was difficult to reproduce and seemed to represent the patient's need to adjust before treatment. This could be estimated somewhat using artificial transient motion. Random walk modeling is feasible and recreated the characteristics of the observed prostate motion. Introducing artificial transient motion did not improve the overall agreement, although the first 30 seconds of the traces were better reproduced. The model provides a simple estimate of prostate motion during delivery of radiation therapy.

The effects of a walking/talking program on communication, ambulation, and functional status in residents with Alzheimer disease.

PubMed

Cott, Cheryl A; Dawson, Pamela; Sidani, Souraya; Wells, Donna

2002-01-01

The purpose of this study was to investigate the effects of a walking/talking program on residents' communication, ambulation, and level of function when there were two residents to one care provider (2:1). A randomized control trial design was used. Subjects were residents with Alzheimer disease in three geriatric long-term care facilities in Metropolitan Toronto. Residents who met the inclusion criteria were randomly assigned to one of three groups: walk-and-talk group (30 min, 5 times per week for 16 weeks, walking/talking in pairs), talk-only group (30 min, 5 times per week for 16 weeks, talk only in pairs), or no intervention. The outcome measures were the Functional Assessment of Communication Skills for Adults, the 2-min walk test, and London Psychogeriatric Rating Scale. Residents who received the walk-and-talk intervention did not demonstrate statistically significant differences in the outcome variables measured posttest when compared with residents who received the talk-only intervention or no intervention, even after controlling for individual differences. Variability in the outcomes measured posttest is explained by differences in the residents' level of cognitive impairment before the study rather than by study group membership. These findings are contradictory to those of previous studies.

Effects of Buddhism walking meditation on depression, functional fitness, and endothelium-dependent vasodilation in depressed elderly.

PubMed

Prakhinkit, Susaree; Suppapitiporn, Siriluck; Tanaka, Hirofumi; Suksom, Daroonwan

2014-05-01

The objectives of this study were to determine the effects of the novel Buddhism-based walking meditation (BWM) and the traditional walking exercise (TWE) on depression, functional fitness, and vascular reactivity. This was a randomized exercise intervention study. The study was conducted in a university hospital setting. Forty-five elderly participants aged 60-90 years with mild-to-moderate depressive symptoms were randomly allocated to the sedentary control, TWE, and BWM groups. The BWM program was based on aerobic walking exercise incorporating the Buddhist meditations performed 3 times/week for 12 weeks. Depression score, functional fitness, and endothelium-dependent vasodilation as measured by the flow-mediated dilation (FMD) were the outcome measures used. Muscle strength, flexibility, agility, dynamic balance, and cardiorespiratory endurance increased in both exercise groups (p<0.05). Depression score decreased (p<0.05) only in the BWM group. FMD improved (p<0.05) in both exercise groups. Significant reduction in plasma cholesterol, triglyceride, high-density lipoprotein cholesterol, and C-reactive protein were found in both exercise groups, whereas low-density lipoprotein cholesterol, cortisol, and interleukin-6 concentrations decreased only in the BWM group. Buddhist walking meditation was effective in reducing depression, improving functional fitness and vascular reactivity, and appears to confer greater overall improvements than the traditional walking program.

The time-fractional radiative transport equation—Continuous-time random walk, diffusion approximation, and Legendre-polynomial expansion

NASA Astrophysics Data System (ADS)

Machida, Manabu

2017-01-01

We consider the radiative transport equation in which the time derivative is replaced by the Caputo derivative. Such fractional-order derivatives are related to anomalous transport and anomalous diffusion. In this paper we describe how the time-fractional radiative transport equation is obtained from continuous-time random walk and see how the equation is related to the time-fractional diffusion equation in the asymptotic limit. Then we solve the equation with Legendre-polynomial expansion.

Superimposed Code Theoretic Analysis of Deoxyribonucleic Acid (DNA) Codes and DNA Computing

DTIC Science & Technology

2010-01-01

partitioned by font type) of sequences are allowed to be in each position (e.g., Arial = position 0, Comic = position 1, etc. ) and within each collection...movement was modeled by a Brownian motion 3 dimensional random walk. The one dimensional diffusion coefficient D for the ellipsoid shape with 3...temperature, kB is Boltzmann’s constant, and η is the viscosity of the medium. The random walk motion is modeled by assuming the oligo is on a three

First passage time: Connecting random walks to functional responses in heterogeneous environments (Invited)

NASA Astrophysics Data System (ADS)

Lewis, M. A.; McKenzie, H.; Merrill, E.

2010-12-01

In this talk I will outline first passage time analysis for animals undertaking complex movement patterns, and will demonstrate how first passage time can be used to derive functional responses in predator prey systems. The result is a new approach to understanding type III functional responses based on a random walk model. I will extend the analysis to heterogeneous environments to assess the effects of linear features on functional responses in wolves and elk using GPS tracking data.

Coordinated Search for a Random Walk Target Motion

NASA Astrophysics Data System (ADS)

El-Hadidy, Mohamed Abd Allah; Abou-Gabal, Hamdy M.

This paper presents the cooperation between two searchers at the origin to find a Random Walk moving target on the real line. No information is not available about the target’s position all the time. Rather than finding the conditions that make the expected value of the first meeting time between one of the searchers and the target is finite, we show the existence of the optimal search strategy which minimizes this first meeting time. The effectiveness of this model is illustrated using a numerical example.

The Effect of a Home-Based Walking Intervention on Quality of Life, Body Composition, and Estrogen Metabolism in Postmenopausal Breast Cancer Survivors

DTIC Science & Technology

2006-09-01

Effect sizes are also shown for each randomization group (i.e., effect size from pretest to posttest ) and for the comparison of the two randomization...questions were answered. This study was designed to be a pilot study to quantify effect sizes of the effect of walking on quality of life...physical activity, body composition, and depending on inclusion criteria, estrogen metabolism. Second, this study was designed to assess the degree to

Evaluating the Bias of Alternative Cost Progress Models: Tests Using Aerospace Industry Acquisition Programs

DTIC Science & Technology

1992-12-01

suspect :mat, -n2 extent predict:.on cas jas ccsiziveiv crrei:=e amonc e v:arious models, :he fandom *.;aik, learn ha r ur e, i;<ea- variable and Bemis...Functions, Production Rate Adjustment Model, Learning Curve Model. Random Walk Model. Bemis Model. Evaluating Model Bias, Cost Prediction Bias. Cost...of four cost progress models--a random walk model, the tradiuonai learning curve model, a production rate model Ifixed-variable model). and a model

On Connected Diagrams and Cumulants of Erdős-Rényi Matrix Models

NASA Astrophysics Data System (ADS)

Khorunzhiy, O.

2008-08-01

Regarding the adjacency matrices of n-vertex graphs and related graph Laplacian we introduce two families of discrete matrix models constructed both with the help of the Erdős-Rényi ensemble of random graphs. Corresponding matrix sums represent the characteristic functions of the average number of walks and closed walks over the random graph. These sums can be considered as discrete analogues of the matrix integrals of random matrix theory. We study the diagram structure of the cumulant expansions of logarithms of these matrix sums and analyze the limiting expressions as n → ∞ in the cases of constant and vanishing edge probabilities.

Programmable quantum random number generator without postprocessing.

PubMed

Nguyen, Lac; Rehain, Patrick; Sua, Yong Meng; Huang, Yu-Ping

2018-02-15

We demonstrate a viable source of unbiased quantum random numbers whose statistical properties can be arbitrarily programmed without the need for any postprocessing such as randomness distillation or distribution transformation. It is based on measuring the arrival time of single photons in shaped temporal modes that are tailored with an electro-optical modulator. We show that quantum random numbers can be created directly in customized probability distributions and pass all randomness tests of the NIST and Dieharder test suites without any randomness extraction. The min-entropies of such generated random numbers are measured close to the theoretical limits, indicating their near-ideal statistics and ultrahigh purity. Easy to implement and arbitrarily programmable, this technique can find versatile uses in a multitude of data analysis areas.

Random numbers certified by Bell's theorem.

PubMed

Pironio, S; Acín, A; Massar, S; de la Giroday, A Boyer; Matsukevich, D N; Maunz, P; Olmschenk, S; Hayes, D; Luo, L; Manning, T A; Monroe, C

2010-04-15

Randomness is a fundamental feature of nature and a valuable resource for applications ranging from cryptography and gambling to numerical simulation of physical and biological systems. Random numbers, however, are difficult to characterize mathematically, and their generation must rely on an unpredictable physical process. Inaccuracies in the theoretical modelling of such processes or failures of the devices, possibly due to adversarial attacks, limit the reliability of random number generators in ways that are difficult to control and detect. Here, inspired by earlier work on non-locality-based and device-independent quantum information processing, we show that the non-local correlations of entangled quantum particles can be used to certify the presence of genuine randomness. It is thereby possible to design a cryptographically secure random number generator that does not require any assumption about the internal working of the device. Such a strong form of randomness generation is impossible classically and possible in quantum systems only if certified by a Bell inequality violation. We carry out a proof-of-concept demonstration of this proposal in a system of two entangled atoms separated by approximately one metre. The observed Bell inequality violation, featuring near perfect detection efficiency, guarantees that 42 new random numbers are generated with 99 per cent confidence. Our results lay the groundwork for future device-independent quantum information experiments and for addressing fundamental issues raised by the intrinsic randomness of quantum theory.

Quantum games on evolving random networks

NASA Astrophysics Data System (ADS)

Pawela, Łukasz

2016-09-01

We study the advantages of quantum strategies in evolutionary social dilemmas on evolving random networks. We focus our study on the two-player games: prisoner's dilemma, snowdrift and stag-hunt games. The obtained result show the benefits of quantum strategies for the prisoner's dilemma game. For the other two games, we obtain regions of parameters where the quantum strategies dominate, as well as regions where the classical strategies coexist.

Effect of a Home-Based Exercise Intervention of Wearable Technology and Telephone Coaching on Walking Performance in Peripheral Artery Disease: The HONOR Randomized Clinical Trial.

PubMed

McDermott, Mary M; Spring, Bonnie; Berger, Jeffrey S; Treat-Jacobson, Diane; Conte, Michael S; Creager, Mark A; Criqui, Michael H; Ferrucci, Luigi; Gornik, Heather L; Guralnik, Jack M; Hahn, Elizabeth A; Henke, Peter; Kibbe, Melina R; Kohlman-Trighoff, Debra; Li, Lingyu; Lloyd-Jones, Donald; McCarthy, Walter; Polonsky, Tamar S; Skelly, Christopher; Tian, Lu; Zhao, Lihui; Zhang, Dongxue; Rejeski, W Jack

2018-04-24

Clinical practice guidelines support home-based exercise for patients with peripheral artery disease (PAD), but no randomized trials have tested whether an exercise intervention without periodic medical center visits improves walking performance. To determine whether a home-based exercise intervention consisting of a wearable activity monitor and telephone coaching improves walking ability over 9 months in patients with PAD. Randomized clinical trial conducted at 3 US medical centers. Patients with PAD were randomized between June 18, 2015, and April 4, 2017, to home-based exercise vs usual care for 9 months. Final follow-up was on December 5, 2017. The exercise intervention group (n = 99) received 4 weekly medical center visits during the first month followed by 8 months of a wearable activity monitor and telephone coaching. The usual care group (n = 101) received no onsite sessions, active exercise, or coaching intervention. The primary outcome was change in 6-minute walk distance at 9-month follow-up (minimal clinically important difference [MCID], 20 m). Secondary outcomes included 9-month change in subcomponents of the Walking Impairment Questionnaire (WIQ) (0-100 score; 100, best), SF-36 physical functioning score, Patient-Reported Outcomes Measurement Information System (PROMIS) mobility questionnaire (higher = better; MCID, 2 points), PROMIS satisfaction with social roles questionnaire, PROMIS pain interference questionnaire (lower = better; MCID range, 3.5-4.5 points), and objectively measured physical activity. Among 200 randomized participants (mean [SD] age, 70.2 [10.4] years; 105 [52.5%] women), 182 (91%) completed 9-month follow-up. The mean change from baseline to 9-month follow-up in the 6-minute walk distance was 5.5 m in the intervention group vs 14.4 m in the usual care group (difference, -8.9 m; 95% CI, -26.0 to 8.2 m; P = .31). The exercise intervention worsened the PROMIS pain interference score, mean change from baseline to 9 months was 0.7 in the intervention group vs -2.8 in the usual care group (difference, 3.5; 95% CI, 1.3 to 5.8; P = .002). There were no significant between-group differences in the WIQ score, the SF-36 physical functioning score, or the PROMIS mobility or satisfaction with social roles scores. Among patients with PAD, a home-based exercise intervention consisting of a wearable activity monitor and telephone coaching, compared with usual care, did not improve walking performance at 9-month follow-up. These results do not support home-based exercise interventions of wearable devices and telephone counseling without periodic onsite visits to improve walking performance in patients with PAD. clinicaltrials.gov Identifier: NCT02462824.

Probability Distributions for Random Quantum Operations

NASA Astrophysics Data System (ADS)

Schultz, Kevin

Motivated by uncertainty quantification and inference of quantum information systems, in this work we draw connections between the notions of random quantum states and operations in quantum information with probability distributions commonly encountered in the field of orientation statistics. This approach identifies natural sample spaces and probability distributions upon these spaces that can be used in the analysis, simulation, and inference of quantum information systems. The theory of exponential families on Stiefel manifolds provides the appropriate generalization to the classical case. Furthermore, this viewpoint motivates a number of additional questions into the convex geometry of quantum operations relative to both the differential geometry of Stiefel manifolds as well as the information geometry of exponential families defined upon them. In particular, we draw on results from convex geometry to characterize which quantum operations can be represented as the average of a random quantum operation. This project was supported by the Intelligence Advanced Research Projects Activity via Department of Interior National Business Center Contract Number 2012-12050800010.

Potential Engineering of Fermi-Hubbard Systems using a Quantum Gas Microscope

NASA Astrophysics Data System (ADS)

Ji, Geoffrey; Mazurenko, Anton; Chiu, Christie; Parsons, Maxwell; Kanász-Nagy, Márton; Schmidt, Richard; Grusdt, Fabian; Demler, Eugene; Greif, Daniel; Greiner, Markus

2017-04-01

Arbitrary control of optical potentials has emerged as an important tool in manipulating ultracold atomic systems, especially when combined with the single-site addressing afforded by quantum gas microscopy. Already, experiments have used digital micromirror devices (DMDs) to initialize and control ultracold atomic systems in the context of studying quantum walks, quantum thermalization, and many-body localization. Here, we report on progress in using a DMD located in the image plane of a quantum gas microscope to explore static and dynamic properties of a 2D Fermi-Hubbard system. By projecting a large, ring-shaped anti-confining potential, we demonstrate entropy redistribution and controlled doping of the system. Moreover, we use the DMD to prepare localized holes, which upon release interact with and disrupt the surrounding spin environment. These techniques pave the way for controlled investigations of dynamics in the low-temperature phases of the Hubbard model.

Analog model for quantum gravity effects: phonons in random fluids.

PubMed

Krein, G; Menezes, G; Svaiter, N F

2010-09-24

We describe an analog model for quantum gravity effects in condensed matter physics. The situation discussed is that of phonons propagating in a fluid with a random velocity wave equation. We consider that there are random fluctuations in the reciprocal of the bulk modulus of the system and study free phonons in the presence of Gaussian colored noise with zero mean. We show that, in this model, after performing the random averages over the noise function a free conventional scalar quantum field theory describing free phonons becomes a self-interacting model.

Extracting random numbers from quantum tunnelling through a single diode.

PubMed

Bernardo-Gavito, Ramón; Bagci, Ibrahim Ethem; Roberts, Jonathan; Sexton, James; Astbury, Benjamin; Shokeir, Hamzah; McGrath, Thomas; Noori, Yasir J; Woodhead, Christopher S; Missous, Mohamed; Roedig, Utz; Young, Robert J

2017-12-19

Random number generation is crucial in many aspects of everyday life, as online security and privacy depend ultimately on the quality of random numbers. Many current implementations are based on pseudo-random number generators, but information security requires true random numbers for sensitive applications like key generation in banking, defence or even social media. True random number generators are systems whose outputs cannot be determined, even if their internal structure and response history are known. Sources of quantum noise are thus ideal for this application due to their intrinsic uncertainty. In this work, we propose using resonant tunnelling diodes as practical true random number generators based on a quantum mechanical effect. The output of the proposed devices can be directly used as a random stream of bits or can be further distilled using randomness extraction algorithms, depending on the application.

3D exemplar-based random walks for tooth segmentation from cone-beam computed tomography images

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pei, Yuru, E-mail: peiyuru@cis.pku.edu.cn; Ai, Xin

Purpose: Tooth segmentation is an essential step in acquiring patient-specific dental geometries from cone-beam computed tomography (CBCT) images. Tooth segmentation from CBCT images is still a challenging task considering the comparatively low image quality caused by the limited radiation dose, as well as structural ambiguities from intercuspation and nearby alveolar bones. The goal of this paper is to present and discuss the latest accomplishments in semisupervised tooth segmentation with adaptive 3D shape constraints. Methods: The authors propose a 3D exemplar-based random walk method of tooth segmentation from CBCT images. The proposed method integrates semisupervised label propagation and regularization by 3Dmore » exemplar registration. To begin with, the pure random walk method is to get an initial segmentation of the teeth, which tends to be erroneous because of the structural ambiguity of CBCT images. And then, as an iterative refinement, the authors conduct a regularization by using 3D exemplar registration, as well as label propagation by random walks with soft constraints, to improve the tooth segmentation. In the first stage of the iteration, 3D exemplars with well-defined topologies are adapted to fit the tooth contours, which are obtained from the random walks based segmentation. The soft constraints on voxel labeling are defined by shape-based foreground dentine probability acquired by the exemplar registration, as well as the appearance-based probability from a support vector machine (SVM) classifier. In the second stage, the labels of the volume-of-interest (VOI) are updated by the random walks with soft constraints. The two stages are optimized iteratively. Instead of the one-shot label propagation in the VOI, an iterative refinement process can achieve a reliable tooth segmentation by virtue of exemplar-based random walks with adaptive soft constraints. Results: The proposed method was applied for tooth segmentation of twenty clinically captured CBCT images. Three metrics, including the Dice similarity coefficient (DSC), the Jaccard similarity coefficient (JSC), and the mean surface deviation (MSD), were used to quantitatively analyze the segmentation of anterior teeth including incisors and canines, premolars, and molars. The segmentation of the anterior teeth achieved a DSC up to 98%, a JSC of 97%, and an MSD of 0.11 mm compared with manual segmentation. For the premolars, the average values of DSC, JSC, and MSD were 98%, 96%, and 0.12 mm, respectively. The proposed method yielded a DSC of 95%, a JSC of 89%, and an MSD of 0.26 mm for molars. Aside from the interactive definition of label priors by the user, automatic tooth segmentation can be achieved in an average of 1.18 min. Conclusions: The proposed technique enables an efficient and reliable tooth segmentation from CBCT images. This study makes it clinically practical to segment teeth from CBCT images, thus facilitating pre- and interoperative uses of dental morphologies in maxillofacial and orthodontic treatments.« less

3D exemplar-based random walks for tooth segmentation from cone-beam computed tomography images.

PubMed

Pei, Yuru; Ai, Xingsheng; Zha, Hongbin; Xu, Tianmin; Ma, Gengyu

2016-09-01

Tooth segmentation is an essential step in acquiring patient-specific dental geometries from cone-beam computed tomography (CBCT) images. Tooth segmentation from CBCT images is still a challenging task considering the comparatively low image quality caused by the limited radiation dose, as well as structural ambiguities from intercuspation and nearby alveolar bones. The goal of this paper is to present and discuss the latest accomplishments in semisupervised tooth segmentation with adaptive 3D shape constraints. The authors propose a 3D exemplar-based random walk method of tooth segmentation from CBCT images. The proposed method integrates semisupervised label propagation and regularization by 3D exemplar registration. To begin with, the pure random walk method is to get an initial segmentation of the teeth, which tends to be erroneous because of the structural ambiguity of CBCT images. And then, as an iterative refinement, the authors conduct a regularization by using 3D exemplar registration, as well as label propagation by random walks with soft constraints, to improve the tooth segmentation. In the first stage of the iteration, 3D exemplars with well-defined topologies are adapted to fit the tooth contours, which are obtained from the random walks based segmentation. The soft constraints on voxel labeling are defined by shape-based foreground dentine probability acquired by the exemplar registration, as well as the appearance-based probability from a support vector machine (SVM) classifier. In the second stage, the labels of the volume-of-interest (VOI) are updated by the random walks with soft constraints. The two stages are optimized iteratively. Instead of the one-shot label propagation in the VOI, an iterative refinement process can achieve a reliable tooth segmentation by virtue of exemplar-based random walks with adaptive soft constraints. The proposed method was applied for tooth segmentation of twenty clinically captured CBCT images. Three metrics, including the Dice similarity coefficient (DSC), the Jaccard similarity coefficient (JSC), and the mean surface deviation (MSD), were used to quantitatively analyze the segmentation of anterior teeth including incisors and canines, premolars, and molars. The segmentation of the anterior teeth achieved a DSC up to 98%, a JSC of 97%, and an MSD of 0.11 mm compared with manual segmentation. For the premolars, the average values of DSC, JSC, and MSD were 98%, 96%, and 0.12 mm, respectively. The proposed method yielded a DSC of 95%, a JSC of 89%, and an MSD of 0.26 mm for molars. Aside from the interactive definition of label priors by the user, automatic tooth segmentation can be achieved in an average of 1.18 min. The proposed technique enables an efficient and reliable tooth segmentation from CBCT images. This study makes it clinically practical to segment teeth from CBCT images, thus facilitating pre- and interoperative uses of dental morphologies in maxillofacial and orthodontic treatments.

Robotic Resistance Treadmill Training Improves Locomotor Function in Children With Cerebral Palsy: A Randomized Controlled Pilot Study.

PubMed

Wu, Ming; Kim, Janis; Gaebler-Spira, Deborah J; Schmit, Brian D; Arora, Pooja

2017-11-01

To determine whether applying controlled resistance forces to the legs during the swing phase of gait may improve the efficacy of treadmill training as compared with applying controlled assistance forces in children with cerebral palsy (CP). Randomized controlled study. Research unit of a rehabilitation hospital. Children with spastic CP (N=23; mean age, 10.6y; range, 6-14y; Gross Motor Function Classification System levels, I-IV). Participants were randomly assigned to receive controlled assistance (n=11) or resistance (n=12) loads applied to the legs at the ankle. Participants underwent robotic treadmill training 3 times a week for 6 weeks (18 sessions). A controlled swing assistance/resistance load was applied to both legs starting from the toe-off to mid-swing phase of gait during training. Outcome measures consisted of overground walking speed, 6-minute walk distance, and Gross Motor Function Measure scores and were assessed pre and post 6 weeks of training and 8 weeks after the end of training. After 6 weeks of treadmill training in participants from the resistance training group, fast walking speed and 6-minute walk distance significantly improved (18% and 30% increases, respectively), and 6-minute walk distance was still significantly greater than that at baseline (35% increase) 8 weeks after the end of training. In contrast, overground gait speed and 6-minute walk distance had no significant changes after robotic assistance training. The results of the present study indicated that robotic resistance treadmill training is more effective than assistance training in improving locomotor function in children with CP. Copyright © 2017 American Congress of Rehabilitation Medicine. Published by Elsevier Inc. All rights reserved.

The effect of walking and vitamin B supplementation on quality of life in community-dwelling adults with mild cognitive impairment: a randomized, controlled trial

PubMed Central

van Uffelen, Jannique G. Z.; Hopman-Rock, Marijke; van Mechelen, Willem

2007-01-01

Objectives To examine the effect of walking and vitamin B supplementation on quality-of-life (QoL) in community-dwelling adults with mild cognitive impairment. Methods One year, double-blind, placebo-controlled trial. Participants were randomized to: (1) twice-weekly, group-based, moderate-intensity walking program (n = 77) or a light-intensity placebo activity program (n = 75); and (2) daily vitamin B pills containing 5 mg folic acid, 0.4 mg B12, 50 mg B6 (n = 78) or placebo pills (n = 74). QoL was measured at baseline, after six and 12 months using the population-specific Dementia Quality-of-Life (D-QoL) to assess overall QoL and the generic Short-Form 12 mental and physical component scales (SF12-MCS and SF12-PCS) to assess health-related QoL. Results Baseline levels of QoL were relatively high. Modified intention-to-treat analyses revealed no positive main intervention effect of walking or vitamin supplementation. In both men and women, ratings of D-QoL-belonging and D-QoL-positive affect subscales improved with 0.003 (P = 0.04) and 0.002 points (P = 0.06) with each percent increase in attendance to the walking program. Only in men, SF12-MCS increased with 0.03 points with each percent increase in attendance (P = 0.08). Conclusion Several small but significant improvements in QoL were observed with increasing attendance to the walking program. No effect of vitamin B supplementation was observed. Trial Registration International Standard Randomized Controlled Trial Number Register, 19227688, http://www.controlled-trials.com/isrctn/. PMID:17616840

Unexpected perturbations training improves balance control and voluntary stepping times in older adults - a double blind randomized control trial.

PubMed

Kurz, Ilan; Gimmon, Yoav; Shapiro, Amir; Debi, Ronen; Snir, Yoram; Melzer, Itshak

2016-03-04

Falls are common among elderly, most of them occur while slipping or tripping during walking. We aimed to explore whether a training program that incorporates unexpected loss of balance during walking able to improve risk factors for falls. In a double-blind randomized controlled trial 53 community dwelling older adults (age 80.1±5.6 years), were recruited and randomly allocated to an intervention group (n = 27) or a control group (n = 26). The intervention group received 24 training sessions over 3 months that included unexpected perturbation of balance exercises during treadmill walking. The control group performed treadmill walking with no perturbations. The primary outcome measures were the voluntary step execution times, traditional postural sway parameters and Stabilogram-Diffusion Analysis. The secondary outcome measures were the fall efficacy Scale (FES), self-reported late life function (LLFDI), and Performance-Oriented Mobility Assessment (POMA). Compared to control, participation in intervention program that includes unexpected loss of balance during walking led to faster Voluntary Step Execution Times under single (p = 0.002; effect size [ES] =0.75) and dual task (p = 0.003; [ES] = 0.89) conditions; intervention group subjects showed improvement in Short-term Effective diffusion coefficients in the mediolateral direction of the Stabilogram-Diffusion Analysis under eyes closed conditions (p = 0.012, [ES] = 0.92). Compared to control there were no significant changes in FES, LLFDI, and POMA. An intervention program that includes unexpected loss of balance during walking can improve voluntary stepping times and balance control, both previously reported as risk factors for falls. This however, did not transferred to a change self-reported function and FES. ClinicalTrials.gov NCT01439451 .

Reducing The Cost of Transport and Increasing Walking Distance After Stroke: A Randomized Controlled Trial on Fast Locomotor Training Combined With Functional Electrical Stimulation

PubMed Central

Awad, Louis N.; Reisman, Darcy S.; Pohlig, Ryan T.; Binder-Macleod, Stuart A.

2015-01-01

Background Neurorehabilitation efforts have been limited in their ability to restore walking function after stroke. Recent work has demonstrated proof-of-concept for a Functional Electrical Stimulation (FES)-based combination therapy designed to improve poststroke walking by targeting deficits in paretic propulsion. Objectives To determine the effects on the energy cost of walking (EC) and long-distance walking ability of locomotor training that combines fast walking with FES to the paretic ankle musculature (FastFES). Methods Fifty participants >6 months poststroke were randomized to 12 weeks of gait training at self-selected speeds (SS), fast speeds (Fast), or FastFES. Participants’ 6-Minute Walk Test (6MWT) distance and EC at comfortable (EC-CWS) and fast (EC-Fast) walking speeds were measured pretraining, posttraining, and at a 3-month follow-up. A reduction in EC-CWS, independent of changes in speed, was the primary outcome. Also evaluated were group differences in the number of 6MWT responders and moderation by baseline speed. Results When compared with SS and Fast, FastFES produced larger reductions in EC (p’s ≤0.03). FastFES produced reductions of 24% and 19% in EC-CWS and EC-Fast (p’s <0.001), whereas neither Fast nor SS influenced EC. Between-group 6MWT differences were not observed; however, 73% of FastFES and 68% of Fast participants were responders, in contrast to 35% of SS participants. Conclusions Combining fast locomotor training with FES is an effective approach to reducing the high EC of persons poststroke. Surprisingly, differences in 6MWT gains were not observed between groups. Closer inspection of the 6MWT and EC relationship and elucidation of how reduced EC may influence walking-related disability is warranted. PMID:26621366

Pilates exercise training vs. physical therapy for improving walking and balance in people with multiple sclerosis: a randomized controlled trial.

PubMed

Kalron, Alon; Rosenblum, Uri; Frid, Lior; Achiron, Anat

2017-03-01

Evaluate the effects of a Pilates exercise programme on walking and balance in people with multiple sclerosis and compare this exercise approach to conventional physical therapy sessions. Randomized controlled trial. Multiple Sclerosis Center, Sheba Medical Center, Tel-Hashomer, Israel. Forty-five people with multiple sclerosis, 29 females, mean age (SD) was 43.2 (11.6) years; mean Expanded Disability Status Scale (S.D) was 4.3 (1.3). Participants received 12 weekly training sessions of either Pilates ( n=22) or standardized physical therapy ( n=23) in an outpatient basis. Spatio-temporal parameters of walking and posturography parameters during static stance. Functional tests included the Time Up and Go Test, 2 and 6-minute walk test, Functional Reach Test, Berg Balance Scale and the Four Square Step Test. In addition, the following self-report forms included the Multiple Sclerosis Walking Scale and Modified Fatigue Impact Scale. At the termination, both groups had significantly increased their walking speed ( P=0.021) and mean step length ( P=0.023). According to the 2-minute and 6-minute walking tests, both groups at the end of the intervention program had increased their walking speed. Mean (SD) increase in the Pilates and physical therapy groups were 39.1 (78.3) and 25.3 (67.2) meters, respectively. There was no effect of group X time in all instrumented and clinical balance and gait measures. Pilates is a possible treatment option for people with multiple sclerosis in order to improve their walking and balance capabilities. However, this approach does not have any significant advantage over standardized physical therapy.

Effect of pretesting on intentions and behaviour: a pedometer and walking intervention.

PubMed

Spence, John C; Burgess, Jenny; Rodgers, Wendy; Murray, Terra

2009-09-01

This study addressed the influence of pedometers and a pretest on walking intentions and behaviour. Using a Solomon four-group design, 63 female university students were randomly assigned to one of four conditions: pedometer and pretest (n = 16), pedometer and no pretest (n = 16), no pedometer and pretest (n = 15), no pedometer and no pretest (n = 16). The pretest conditions included questions on walking, intentions to walk 12,500 steps per day, and self-efficacy for walking 12,500 steps per day. In the pedometer conditions a Yamax Digi-Walker SW-650 pedometer was worn for one week. All participants completed posttest questions. While significant pretest x pedometer interactions would have indicated the presence of pretest sensitisation, no such interactions were observed for either intention or self-reported walking. Wearing pedometers reduced intentions for future walking and coping self-efficacy. However, after controlling for pretest self-reported walking, pedometer use resulted in more self-reported walking. We conclude that wearing a pedometer increased self-reported walking behaviour but that a pretest did not differentially influence walking intentions, behaviour, or self-efficacy.

Comparative Effectiveness of Two Walking Interventions on Participation, Step Counts, and Health.

PubMed

Smith-McLallen, Aaron; Heller, Debbie; Vernisi, Kristin; Gulick, Diana; Cruz, Samantha; Snyder, Richard L

2017-03-01

To (1) compare the effects of two worksite-based walking interventions on employee participation rates; (2) compare average daily step counts between conditions, and; (3) examine the effects of increases in average daily step counts on biometric and psychologic outcomes. We conducted a cluster-randomized trial in which six employer groups were randomly selected and randomly assigned to condition. Four manufacturing worksites and two office-based worksite served as the setting. A total of 474 employees from six employer groups were included. A standard walking program was compared to an enhanced program that included incentives, feedback, competitive challenges, and monthly wellness workshops. Walking was measured by self-reported daily step counts. Survey measures and biometric screenings were administered at baseline and 3, 6, and 9 months after baseline. Analysis used linear mixed models with repeated measures. During 9 months, participants in the enhanced condition averaged 726 more steps per day compared with those in the standard condition (p < .001). A 1000-step increase in average daily steps was associated with significant weight loss for both men (-3.8 lbs.) and women (-2.1 lbs.), and reductions in body mass index (-0.41 men, -0.31 women). Higher step counts were also associated with improvements in mood, having more energy, and higher ratings of overall health. An enhanced walking program significantly increases participation rates and daily step counts, which were associated with weight loss and reductions in body mass index.

Efficacy of gait trainer as an adjunct to traditional physical therapy on walking performance in hemiparetic cerebral palsied children: a randomized controlled trial.

PubMed

Gharib, Nevein Mm; El-Maksoud, Gehan M Abd; Rezk-Allah, Soheir S

2011-10-01

To assess the effects of additional gait trainer assisted walking exercises on walking performance in children with hemiparetic cerebral palsy. A randomized controlled study. Paediatric physical therapy outpatient clinic. Thirty spastic hemiparetic cerebral palsied children of both sexes (10-13 years - 19 girls and 11 boys). Children were randomly assigned into two equal groups; experimental and control groups. Participants in both groups received a traditional physical therapy exercise programme. Those in the experimental group received additional gait trainer based walking exercises which aimed to improve walking performance. Treatment was provided three times per week for three successive months. Children received baseline and post-treatment assessments using Biodex Gait Trainer 2 assessment device to evaluate gait parameters including: average step length, walking speed, time on each foot (% of gait cycle) and ambulation index. Children in the experimental group showed a significant improvement as compared with those in the control group. The ambulation index was 75.53±7.36 (11.93 ± 2.89 change score) for the experimental group and 66.06 ± 5.48 (2.13 ± 4.43 change score) for the control group (t = 3.99 and P = 0.0001). Time of support for the affected side was 42.4 ± 3.37 (7 ± 2.20 change score) for the experimental group and 38.06 ± 4.63 (3.33 ± 6.25 change score) for the control group (t = 2.92 and P = 0.007). Also, there was a significant improvement in step length and walking speed in both groups. Gait trainer combined with traditional physiotherapy increase the chance of improving gait performance in children with spastic hemiparetic cerebral palsy.

Longitudinal Relationship Among Physical Fitness, Walking-Related Physical Activity, and Fatigue in Children With Cerebral Palsy.

PubMed

Balemans, Astrid C J; van Wely, Leontien; Becher, Jules G; Dallmeijer, Annet J

2015-07-01

A vicious circle of decreased physical fitness, early fatigue, and low physical activity levels (PAL) is thought to affect children with cerebral palsy (CP). However, the relationship of changes in physical fitness to changes in PAL and fatigue is unclear. The objective of this study was to investigate the associations among changes in physical fitness, walking-related PAL, and fatigue in children with CP. This study was a secondary analysis of a randomized controlled trial with measurements at baseline, 6 months (after the intervention period), and 12 months. Twenty-four children with bilateral spastic CP and 22 with unilateral spastic CP, aged 7 to 13 years, all walking, participated in this study. Physical fitness was measured by aerobic capacity, anaerobic threshold, anaerobic capacity, and isometric and functional muscle strength. Walking-related PAL was measured using an ankle-worn activity monitor for 1 week. Fatigue was determined with the Pediatric Quality of Life (PedsQL) Multidimensional Fatigue Scale. Longitudinal associations were analyzed by random coefficient regression analysis. In children with bilateral CP, all fitness parameters showed a positive, significant association with walking-related PAL, whereas no associations between physical fitness and walking-related PAL were seen in children with unilateral CP. No clinically relevant association between physical fitness and fatigue was found. Although random coefficient regression analysis can be used to investigate longitudinal associations between parameters, a causal relationship cannot be determined. The actual direction of the association between physical fitness and walking-related PAL, therefore, remains inconclusive. Children with bilateral spastic CP might benefit from improved physical fitness to increase their PAL or vice versa, although this is not the case in children with unilateral CP. There appears to be no relationship between physical fitness and self-reported fatigue in children with CP. Interventions aimed at improving PAL may be differently targeted in children with either bilateral or unilateral CP. © 2015 American Physical Therapy Association.

A Telehealth Intervention Using Nintendo Wii Fit Balance Boards and iPads to Improve Walking in Older Adults With Lower Limb Amputation (Wii.n.Walk): Study Protocol for a Randomized Controlled Trial.

PubMed

Imam, Bita; Miller, William C; Finlayson, Heather C; Eng, Janice J; Payne, Michael Wc; Jarus, Tal; Goldsmith, Charles H; Mitchell, Ian M

2014-12-22

The number of older adults living with lower limb amputation (LLA) who require rehabilitation for improving their walking capacity and mobility is growing. Existing rehabilitation practices frequently fail to meet this demand. Nintendo Wii Fit may be a valuable tool to enable rehabilitation interventions. Based on pilot studies, we have developed "Wii.n.Walk", an in-home telehealth Wii Fit intervention targeted to improve walking capacity in older adults with LLA. The objective of this study is to determine whether the Wii.n.Walk intervention enhances walking capacity compared to an attention control group. This project is a multi-site (Vancouver BC, London ON), parallel, evaluator-blind randomized controlled trial. Participants include community-dwelling older adults over the age of 50 years with unilateral transtibial or transfemoral amputation. Participants will be stratified by site and block randomized in triplets to either the Wii.n.Walk intervention or an attention control group employing the Wii Big Brain cognitive software. This trial will include both supervised and unsupervised phases. During the supervised phase, both groups will receive 40-minute sessions of supervised group training three times per week for a duration of 4 weeks. Participants will complete the first week of the intervention in groups of three at their local rehabilitation center with a trainer. The remaining 3 weeks will take place at participants' homes using remote supervision by the trainer using Apple iPad technology. At the end of 4 weeks, the supervised period will end and the unsupervised period will begin. Participants will retain the Wii console and be encouraged to continue using the program for an additional 4 weeks' duration. The primary outcome measure will be the "Two-Minute Walk Test" to measure walking capacity. Outcome measures will be evaluated for all participants at baseline, after the end of both the supervised and unsupervised phases, and after 1-year follow up. Study staff have been hired and trained at both sites and recruitment is currently underway. No participants have been enrolled yet. Wii.n.Walk is a promising in-home telehealth intervention that may have useful applications for older adults with LLA who are discharged from rehabilitation or live in remote areas having limited or no access to existing rehabilitation programs. Clinicaltrial.gov NCT01942798; http://clinicaltrials.gov/ct2/show/NCT01942798 (Archived by WebCite at http://www.webcitation.org/6V0w8baKP).

Robot-assisted gait training in multiple sclerosis: a pilot randomized trial.

PubMed

Beer, S; Aschbacher, B; Manoglou, D; Gamper, E; Kool, J; Kesselring, J

2008-03-01

To evaluate feasibility and perform an explanatory analysis of the efficacy of robot-assisted gait training (RAGT) in MS patients with severe walking disabilities (Expanded Disability Status Scale [EDSS] 6.0-7.5) in a pilot trial. Prospective, randomized, controlled clinical trial comparing RAGT with conventional walking training (CWT) in a group of stable MS patients (n = 35) during an inpatient rehabilitation stay, 15 sessions over three weeks. All patients participated additionally in a multimodal rehabilitation program. The primary outcome measure was walking velocity and secondary measures were 6-min-walking distance, stride length and knee-extensor strength. All tests were performed by an external blinded assessor at baseline after three weeks and at follow-up after six months. Additionally, Extended Barthel Index (EBI) at entry and discharge was assessed (not blinded), and acceptance/convenience of RAGT rated by patients (Visual Analogue Scale [VAS]) was recorded. Nineteen patients were randomly allocated to RAGT and 16 patients to CWT. Groups were comparable at baseline. There were 5 drop-outs (2 related directly to treatment) in the RAGT group and 1 in the CWT group, leaving 14 RAGT patients and 15 CWT patients for final analysis. Acceptance and convenience of RAGT as rated by patients were high. Effect sizes were moderate to large, although not significant, for walking velocity (0.700, 95% CI -0.089 to 1.489), walking distance (0.401, 95% CI - 0.370 to 1.172) and knee-extensor strength (right: 1.105, 95% CI 0.278 to 1.932, left 0.650, 95% CI -0.135 to 1.436) favouring RAGT. Prepost within-group analysis revealed an increase of walking velocity, walking distance and knee-extensor strength in the RAGT group, whereas in CWT group only walking velocity was improved. In both groups outcome values returned to baseline at follow-up after six months (n = 23). Robot-assisted gait training is feasible and may be an effective therapeutic option in MS patients with severe walking disabilities. Effect size calculation and prepost analysis suggest a higher benefit on walking velocity and knee-extensor strength by RAGT compared to CWT. Due to several limitations, however, our results should be regarded as preliminary. Post hoc power calculation showed that two groups of 106 patients are needed to demonstrate a significant moderate effect size of 0.4 after three weeks of RAGT. Thus, further studies with a larger number of patients are needed to investigate the impact of this new treatment option in MS patients.

Feasibility and Preliminary Efficacy of Visual Cue Training to Improve Adaptability of Walking after Stroke: Multi-Centre, Single-Blind Randomised Control Pilot Trial.

PubMed

Hollands, Kristen L; Pelton, Trudy A; Wimperis, Andrew; Whitham, Diane; Tan, Wei; Jowett, Sue; Sackley, Catherine M; Wing, Alan M; Tyson, Sarah F; Mathias, Jonathan; Hensman, Marianne; van Vliet, Paulette M

2015-01-01

Given the importance of vision in the control of walking and evidence indicating varied practice of walking improves mobility outcomes, this study sought to examine the feasibility and preliminary efficacy of varied walking practice in response to visual cues, for the rehabilitation of walking following stroke. This 3 arm parallel, multi-centre, assessor blind, randomised control trial was conducted within outpatient neurorehabilitation services. Community dwelling stroke survivors with walking speed <0.8m/s, lower limb paresis and no severe visual impairments. Over-ground visual cue training (O-VCT), Treadmill based visual cue training (T-VCT), and Usual care (UC) delivered by physiotherapists twice weekly for 8 weeks. Participants were randomised using computer generated random permutated balanced blocks of randomly varying size. Recruitment, retention, adherence, adverse events and mobility and balance were measured before randomisation, post-intervention and at four weeks follow-up. Fifty-six participants participated (18 T-VCT, 19 O-VCT, 19 UC). Thirty-four completed treatment and follow-up assessments. Of the participants that completed, adherence was good with 16 treatments provided over (median of) 8.4, 7.5 and 9 weeks for T-VCT, O-VCT and UC respectively. No adverse events were reported. Post-treatment improvements in walking speed, symmetry, balance and functional mobility were seen in all treatment arms. Outpatient based treadmill and over-ground walking adaptability practice using visual cues are feasible and may improve mobility and balance. Future studies should continue a carefully phased approach using identified methods to improve retention. Clinicaltrials.gov NCT01600391.

A Random Walk Approach to Query Informative Constraints for Clustering.

PubMed

Abin, Ahmad Ali

2017-08-09

This paper presents a random walk approach to the problem of querying informative constraints for clustering. The proposed method is based on the properties of the commute time, that is the expected time taken for a random walk to travel between two nodes and return, on the adjacency graph of data. Commute time has the nice property of that, the more short paths connect two given nodes in a graph, the more similar those nodes are. Since computing the commute time takes the Laplacian eigenspectrum into account, we use this property in a recursive fashion to query informative constraints for clustering. At each recursion, the proposed method constructs the adjacency graph of data and utilizes the spectral properties of the commute time matrix to bipartition the adjacency graph. Thereafter, the proposed method benefits from the commute times distance on graph to query informative constraints between partitions. This process iterates for each partition until the stop condition becomes true. Experiments on real-world data show the efficiency of the proposed method for constraints selection.

Mean first passage time for random walk on dual structure of dendrimer

NASA Astrophysics Data System (ADS)

Li, Ling; Guan, Jihong; Zhou, Shuigeng

2014-12-01

The random walk approach has recently been widely employed to study the relations between the underlying structure and dynamic of complex systems. The mean first-passage time (MFPT) for random walks is a key index to evaluate the transport efficiency in a given system. In this paper we study analytically the MFPT in a dual structure of dendrimer network, Husimi cactus, which has different application background and different structure (contains loops) from dendrimer. By making use of the iterative construction, we explicitly determine both the partial mean first-passage time (PMFT, the average of MFPTs to a given target) and the global mean first-passage time (GMFT, the average of MFPTs over all couples of nodes) on Husimi cactus. The obtained closed-form results show that PMFPT and EMFPT follow different scaling with the network order, suggesting that the target location has essential influence on the transport efficiency. Finally, the impact that loop structure could bring is analyzed and discussed.

[Plaque segmentation of intracoronary optical coherence tomography images based on K-means and improved random walk algorithm].

PubMed

Wang, Guanglei; Wang, Pengyu; Han, Yechen; Liu, Xiuling; Li, Yan; Lu, Qian

2017-06-01

In recent years, optical coherence tomography (OCT) has developed into a popular coronary imaging technology at home and abroad. The segmentation of plaque regions in coronary OCT images has great significance for vulnerable plaque recognition and research. In this paper, a new algorithm based on K -means clustering and improved random walk is proposed and Semi-automated segmentation of calcified plaque, fibrotic plaque and lipid pool was achieved. And the weight function of random walk is improved. The distance between the edges of pixels in the image and the seed points is added to the definition of the weight function. It increases the weak edge weights and prevent over-segmentation. Based on the above methods, the OCT images of 9 coronary atherosclerotic patients were selected for plaque segmentation. By contrasting the doctor's manual segmentation results with this method, it was proved that this method had good robustness and accuracy. It is hoped that this method can be helpful for the clinical diagnosis of coronary heart disease.