Asymptotically Stable Walking of a Five-Link Underactuated 3D Bipedal Robot
Chevallereau, Christine; Shih, Ching-Long; 10.1109/TRO.2008.2010366
2010-01-01
This paper presents three feedback controllers that achieve an asymptotically stable, periodic, and fast walking gait for a 3D (spatial) bipedal robot consisting of a torso, two legs, and passive (unactuated) point feet. The contact between the robot and the walking surface is assumed to inhibit yaw rotation. The studied robot has 8 DOF in the single support phase and 6 actuators. The interest of studying robots with point feet is that the robot's natural dynamics must be explicitly taken into account to achieve balance while walking. We use an extension of the method of virtual constraints and hybrid zero dynamics, in order to simultaneously compute a periodic orbit and an autonomous feedback controller that realizes the orbit. This method allows the computations to be carried out on a 2-DOF subsystem of the 8-DOF robot model. The stability of the walking gait under closed-loop control is evaluated with the linearization of the restricted Poincar\\'e map of the hybrid zero dynamics. Three strategies are explo...
Asymptotic approaches to marginally stable resonators.
Nagel, J; Rogovin, D; Avizonis, P; Butts, R
1979-09-01
We present analytical solutions valid for large Fresnel number of the Fresnel-Kirchhoff integral equation for marginally stable resonators, for the specific case of flat circular mirrors. The asymptotic approaches used for curved mirrors have been extended to the waveguide region given by m diffraction around the mirror edge. PMID:19687883
Tempered stable laws as random walk limits
Chakrabarty, Arijit; Meerschaert, Mark M.
2010-01-01
Stable laws can be tempered by modifying the L\\'evy measure to cool the probability of large jumps. Tempered stable laws retain their signature power law behavior at infinity, and infinite divisibility. This paper develops random walk models that converge to a tempered stable law under a triangular array scheme. Since tempered stable laws and processes are useful in statistical physics, these random walk models can provide a basic physical model for the underlying physical phenomena.
Asymptotic entanglement in the discrete-time quantum walk
Abal, G.; Donangelo, R.; Fort, H.
2007-01-01
The coin-position entanglement generated by the evolution operator of a discrete--time quantum walk converges, in the long time limit, to a well defined value which depends on the initial state. We also discuss the asymptotic bi-partite entanglement generated by several non-separable coin operations for two coherent quantum walkers, for which the entropy of entanglement increases logarithmically.
Stable walking with asymmetric legs
Asymmetric leg function is often an undesired side-effect in artificial legged systems and may reflect functional deficits or variations in the mechanical construction. It can also be found in legged locomotion in humans and animals such as after an accident or in specific gait patterns. So far, it is not clear to what extent differences in the leg function of contralateral limbs can be tolerated during walking or running. Here, we address this issue using a bipedal spring-mass model for simulating walking with compliant legs. With the help of the model, we show that considerable differences between contralateral legs can be tolerated and may even provide advantages to the robustness of the system dynamics. A better understanding of the mechanisms and potential benefits of asymmetric leg operation may help to guide the development of artificial limbs or the design novel therapeutic concepts and rehabilitation strategies.
Stable parabolic Higgs bundles as asymptotically stable decorated swamps
Beck, Nikolai
2016-06-01
Parabolic Higgs bundles can be described in terms of decorated swamps, which we studied in a recent paper. This description induces a notion of stability of parabolic Higgs bundles depending on a parameter, and we construct their moduli space inside the moduli space of decorated swamps. We then introduce asymptotic stability of decorated swamps in order to study the behaviour of the stability condition as one parameter approaches infinity. The main result is the existence of a constant, such that stability with respect to parameters greater than this constant is equivalent to asymptotic stability. This implies boundedness of all decorated swamps which are semistable with respect to some parameter. Finally, we recover the usual stability condition of parabolic Higgs bundles as asymptotic stability.
Stable Parabolic Higgs Bundles as Asymptotically Stable Decorated Swamps
Beck, Nikolai
2014-01-01
Parabolic Higgs bundles can be described in terms of decorated swamps, which we studied in a recent paper. This description induces a notion of stability of parabolic Higgs bundles depending on a parameter, and we construct their moduli space inside the moduli space of decorated swamps. We then introduce asymptotic stability of decorated swamps in order to study the behavior of the stability condition as one parameter approaches infinity. The main result is the existence of a constant, such t...
Percolation induced effects in two-dimensional coined quantum walks: analytic asymptotic solutions
Quantum walks on graphs can model physical processes and serve as efficient tools in quantum information theory. Once we admit random variations in the connectivity of the underlying graph, we arrive at the problem of percolation, where the long-time behaviour appears untreatable with direct numerical methods. We develop novel analytic methods based on the theory of random unitary operations which help us to determine explicitly the asymptotic dynamics of quantum walks on two-dimensional finite integer lattices with percolation. Based on this theory, we find new unexpected features of percolated walks like asymptotic position inhomogeneity or special directional symmetry breaking. (paper)
The turbulent random walk of magnetic field lines plays an important role in the transport of plasmas and energetic particles in a wide variety of astrophysical situations, but most theoretical work has concentrated on determination of the asymptotic field line diffusion coefficient. Here we consider the evolution with distance of the field line random walk using a general ordinary differential equation (ODE), which for most cases of interest in astrophysics describes a transition from free streaming to asymptotic diffusion. By challenging theories of asymptotic diffusion to also describe the evolution, one gains insight on how accurately they describe the random walk process. Previous theoretical work has effectively involved closure of the ODE, often by assuming Corrsin's hypothesis and a Gaussian displacement distribution. Approaches that use quasilinear theory and prescribe the mean squared displacement (Δx 2) according to free streaming (random ballistic decorrelation, RBD) or asymptotic diffusion (diffusive decorrelation, DD) can match computer simulation results, but only over specific parameter ranges, with no obvious 'marker' of the range of validity. Here we make use of a unified description in which the ODE determines (Δx 2) self-consistently, providing a natural transition between the assumptions of RBD and DD. We find that the minimum kurtosis of the displacement distribution provides a good indicator of whether the self-consistent ODE is applicable, i.e., inaccuracy of the self-consistent ODE is associated with non-Gaussian displacement distributions.
Prediction of stable walking for a toy that cannot stand
Coleman, M J; Mombaur, K; Ruina, A; Coleman, Michael J.; Garcia, Mariano; Mombaur, Katja; Ruina, Andy
2001-01-01
Previous experiments [M. J. Coleman and A. Ruina, Phys. Rev. Lett. 80, 3658 (1998)] showed that a gravity-powered toy with no control and which has no statically stable near-standing configurations can walk stably. We show here that a simple rigid-body statically-unstable mathematical model based loosely on the physical toy can predict stable limit-cycle walking motions. These calculations add to the repertoire of rigid-body mechanism behaviors as well as further implicating passive-dynamics as a possible contributor to stability of animal motions.
Chen, Lung-Chi
2010-01-01
We consider random walk and self-avoiding walk whose 1-step distribution is given by D, and oriented percolation whose bond-occupation probability is proportional to D. Suppose that D(x) decays as |x|^{-d-a} with a>0. For random walk in any dimension and for self-avoiding walk and critical/subcritical oriented percolation above the common upper-critical dimension 2min{a,2}, we prove large-t asymptotics of the gyration radius, which is the average end-to-end distance of random walk/self-avoiding walk of length t or the average spatial size of an oriented-percolation cluster at time t. This proves the conjecture for long-range self-avoiding walk by Heydenreich and for long-range oriented percolation in Chen and Sakai (2009).
CHEN Lei; YANG Geng; XU Bi-huan
2011-01-01
Asymptotical stability is an important property of the associative memory neural networks. In this comment, we demonstrate that the asymptotical stability analyses of the MV-ECAM and MV-eBAM in the asynchronous update mode by Wang et al are not rigorous, and then we modify the errors and further prove that the two models are all asymptotically stable in both synchronous and asynchronous update modes.
Asymptotic results for the semi-Markovian random walk with delay
In this study, the semi-Markovian random walk with a discrete interference of chance (X(t) ) is considered and under some weak assumptions the ergodicity of this process is discussed. Characteristic function of the ergodic distribution of X(t) is expressed by means of the probability characteristics of the boundary functionals (N,SN). Some exact formulas for first and second moments of ergodic distribution of the process X(t) are obtained when the random variable ζ1- s, which is describing a discrete interference of chance, has Gamma distribution on the interval [0, ∞) with parameter (α,λ) . Based on these results, the asymptotic expansions with three terms for the first two moments of the ergodic distribution of the process X(t) are obtained, as λ → 0. (author)
Three routes to the exact asymptotics for the one-dimensional quantum walk
We demonstrate an alternative method for calculating the asymptotic behaviour of the discrete one-coin quantum walk on the infinite line, via the Jacobi polynomials that arise in the path-integral representation. We calculate the asymptotics using a method that is significantly easier to use than the Darboux method. It also provides a single integral representation for the wavefunction that works over the full range of positions, n, including throughout the transitional range where the behaviour changes from oscillatory to exponential. Previous analyses of this system have run into difficulties in the transitional range, because the approximations on which they were based break down here. The fact that there are two different kinds of approach to this problem (path integral versus Schroedinger wave mechanics) is ultimately a manifestation of the equivalence between the path-integral formulation of quantum mechanics and the original formulation developed in the 1920s. We also discuss how and why our approach is related to the two methods that have already been used to analyse these systems
Stable Asymptotically Free Extensions (SAFEs) of the Standard Model
Holdom, Bob; Zhang, Chen
2014-01-01
We consider possible extensions of the standard model that are not only completely asymptotically free, but are such that the UV fixed point is completely UV attractive. All couplings flow towards a set of fixed ratios in the UV. Motivated by low scale unification, semi-simple gauge groups with elementary scalars in various representations are explored. The simplest model is a version of the Pati-Salam model. The Higgs boson is truly elementary but dynamical symmetry breaking from strong interactions may be needed at the unification scale. A hierarchy problem, much reduced from grand unified theories, is still in need of a solution.
Rodr, S
1995-01-01
We present a real space renormalization-group map for probabilities of random walks on a hierarchical lattice. From this, we study the asymptotic behavior of the end-to-end distance of a weakly self- avoiding random walk (SARW) that penalizes the (self-)intersection of two random walks in dimension four on the hierarchical lattice.
Asymptotically flat, stable black hole solutions in Einstein-Yang-Mills-Chern-Simons theory.
Brihaye, Yves; Radu, Eugen; Tchrakian, D H
2011-02-18
We construct finite mass, asymptotically flat black hole solutions in d=5 Einstein-Yang-Mills-Chern-Simons theory. Our results indicate the existence of a second order phase transition between Reissner-Nordström solutions and the non-Abelian black holes which generically are thermodynamically preferred. Some of the non-Abelian configurations are also stable under linear, spherically symmetric perturbations. PMID:21405506
An Approach to Stable Walking over Uneven Terrain Using a Reflex-Based Adaptive Gait
Umar Asif
2011-01-01
Full Text Available This paper describes the implementation of an adaptive gait in a six-legged walking robot that is capable of generating reactive stepping actions with the same underlying control methodology as an insect for stable walking over uneven terrains. The proposed method of gait generation uses feedback data from onboard sensors to generate an adaptive gait in order to surmount obstacles, gaps and perform stable walking. The paper addresses its implementation through simulations in a visual dynamic simulation environment. Finally the paper draws conclusions about the significance and performance of the proposed gait in terms of tracking errors while navigating in difficult terrains.
Asymptotic Scaling Behavior of Self-Avoiding Walks on Critical Percolation Clusters
Fricke, Niklas; Janke, Wolfhard
2014-12-01
We study self-avoiding walks on three-dimensional critical percolation clusters using a new exact enumeration method. It overcomes the exponential increase in computation time by exploiting the clusters' fractal nature. We enumerate walks of over 104 steps, far more than has ever been possible. The scaling exponent ν for the end-to-end distance turns out to be smaller than previously thought and appears to be the same on the backbones as on full clusters. We find strong evidence against the widely assumed scaling law for the number of conformations and propose an alternative, which perfectly fits our data.
Random Walks with Bivariate Levy-Stable Jumps in Comparison with Levy Flights
In this paper we compare the Levy flight model on a plane with the random walk resulting from bivariate Levy-stable random jumps with the uniform spectral measure. We show that, in general, both processes exhibit similar properties, i.e. they are characterized by the presence of the jumps with extremely large lengths and uniformly distributed directions (reflecting the same heavy-tail behavior and the spherical symmetry of the jump distributions), connecting characteristic clusters of short steps. The bivariate Levy-stable random walks, belonging to the class of the well investigated stable processes, can enlarge the class of random-walk models for transport phenomena if other than uniform spectral measures are considered. (author)
A botanical compound, Padma 28, increases walking distance in stable intermittent claudication
Drabaek, H; Mehlsen, J; Himmelstrup, H; Winther, K
1993-01-01
and by measurements of the pain-free and the maximal walking distance on a treadmill. The ankle pressure index (ankle systolic pressure/arm systolic pressure) was calculated. The group randomized to active treatment received two tablets bid containing 340 mg of a dried herbal mixture composed.......05) and in the maximal walking distance from 115 m (72-218) to 227 m (73- > 1,000; P <0.05). The patient-group receiving placebo treatments did not show any significant changes in either the painfree or the maximal walking distance. The authors could not demonstrate any significant changes in the ankle...... pressure index either during active or during placebo treatment. In conclusion, this study has shown that treatment with Padma 28 over a period of four months significantly increased the walking distance in patients with stable, intermittent claudication of long duration....
A Fast, Simple, and Stable Chebyshev--Legendre Transform Using an Asymptotic Formula
Hale, Nicholas
2014-02-06
A fast, simple, and numerically stable transform for converting between Legendre and Chebyshev coefficients of a degree N polynomial in O(N(log N)2/ log log N) operations is derived. The fundamental idea of the algorithm is to rewrite a well-known asymptotic formula for Legendre polynomials of large degree as a weighted linear combination of Chebyshev polynomials, which can then be evaluated by using the discrete cosine transform. Numerical results are provided to demonstrate the efficiency and numerical stability. Since the algorithm evaluates a Legendre expansion at an N +1 Chebyshev grid as an intermediate step, it also provides a fast transform between Legendre coefficients and values on a Chebyshev grid. © 2014 Society for Industrial and Applied Mathematics.
To theory of asymptotically stable accelerating Universe in Riemann-Cartan spacetime
Garkun, A.S. [The National Academy of Sciences of Belarus, Nezalezhnosti av. 66, 220072 Minsk (Belarus); Kudin, V.I.; Minkevich, A.V., E-mail: garkun@bsu.by, E-mail: kudzin_w@tut.by, E-mail: minkav@bsu.by [Department of Theoretical Physics and Astrophysics, Belarusian State University, Nezalezhnosti av. 2, 220030 Minsk (Belarus)
2014-12-01
Homogeneous isotropic cosmological models built in the framework of the Poincar'e gauge theory of gravity based on general expression of gravitational Lagrangian with indefinite parameters are analyzed. Special points of cosmological solutions for flat cosmological models at asymptotics and conditions of their stability in dependence of indefinite parameters are found. Procedure of numerical integration of the system of gravitational equations at asymptotics is considered. Numerical solution for accelerating Universe without dark energy is obtained.
Bidikli, Baris; Tatlicioglu, Enver; Zergeroglu, Erkan; Bayrak, Alper
2016-09-01
In this work, we present a novel continuous robust controller for a class of multi-input/multi-output nonlinear systems that contains unstructured uncertainties in their drift vectors and input matrices. The proposed controller compensates uncertainties in the system dynamics and achieves asymptotic tracking while requiring only the knowledge of the sign of the leading principal minors of the input gain matrix. A Lyapunov-based argument backed up with an integral inequality is applied to prove the asymptotic stability of the closed-loop system. Simulation results are presented to illustrate the viability of the proposed method.
A family of asymptotically stable control laws for flexible robots based on a passivity approach
Lanari, Leonardo; Wen, John T.
1991-01-01
A general family of asymptotically stabilizing control laws is introduced for a class of nonlinear Hamiltonian systems. The inherent passivity property of this class of systems and the Passivity Theorem are used to show the closed-loop input/output stability which is then related to the internal state space stability through the stabilizability and detectability condition. Applications of these results include fully actuated robots, flexible joint robots, and robots with link flexibility.
无
2007-01-01
In this article, the dependent steps of a negative drift random walk are modelled as a two-sided linear process Xn =-μ+∞∑j=-∞ψn-jεj, where {ε, εn; -∞＜ n ＜ +∞}is a sequence of independent, identically distributed random variables with zero mean, μ＞0 is a constant and the coefficients {ψi;-∞＜ i ＜∞} satisfy 0 ＜∞∑j=-∞|jψj| ＜∞. Under the conditions that the distribution function of |ε| has dominated variation and ε satisfies certain tail balance conditions, the asymptotic behavior of P{supn≥0(-nμ+∞∑j=-∞εjβnj) ＞ x}is discussed. Then the result is applied to ultimate ruin probability.
Characterizing asymptotically anti-de Sitter black holes with abundant stable gauge field hair
Shepherd, Ben L.; Winstanley, Elizabeth(Consortium for Fundamental Physics, School of Mathematics and Statistics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield, S3 7RH, United Kingdom)
2012-01-01
In the light of the "no-hair" conjecture, we revisit stable black holes in su(N) Einstein-Yang-Mills theory with a negative cosmological constant. These black holes are endowed with copious amounts of gauge field hair, and we address the question of whether these black holes can be uniquely characterized by their mass and a set of global non-Abelian charges defined far from the black hole. For the su(3) case, we present numerical evidence that stable black hole configurations are fixed by the...
Young-Dae Hong
2016-02-01
Full Text Available This paper proposes a method to produce the stable walking of humanoid robots by incorporating the vertical center of mass (COM and foot motions, which are generated by the evolutionary optimized central pattern generator (CPG, into the modifiable walking pattern generator (MWPG. The MWPG extends the conventional 3-D linear inverted pendulum model (3-D LIPM by allowing a zero moment point (ZMP variation. The disturbance caused by the vertical COM motion is compensated in real time by the sensory feedback in the CPG. In this paper, the vertical foot trajectory of the swinging leg, as well as the vertical COM trajectory of the 3-D LIPM, are generated by the CPG for the effective compensation of the disturbance. Consequently, using the proposed method, the humanoid robot is able to walk with a vertical COM and the foot motions generated by the CPG, while modifying its walking patterns by using the MWPG in real time. The CPG with the sensory feedback is optimized to obtain the desired output signals. The optimization of the CPG is formulated as a constrained optimization problem with equality constraints and is solved by two-phase evolutionary programming (TPEP. The validity of the proposed method is verified through walking experiments for the small-sized humanoid robot, HanSaRam-IX (HSR-IX.
Walker, David J; Windisch, Wolfram; Dreher, Michael
2016-08-01
We are grateful to Ulasli and Esquinas for their comments to our paper.. They argued that arterial blood gas analyses were not performed without oxygen prior to the 6-minute walk test with noninvasive ventilation (6MWT-NPPV). This point has already been discussed in our original work by indicating the limitations of our study. The reason for using oxygen prior to exercise testing was to guarantee comparable starting conditions. PMID:27015039
Improving Inverse Dynamics Accuracy in a Planar Walking Model Based on Stable Reference Point
Alaa Abdulrahman; Kamran Iqbal; Gannon White
2014-01-01
Physiologically and biomechanically, the human body represents a complicated system with an abundance of degrees of freedom (DOF). When developing mathematical representations of the body, a researcher has to decide on how many of those DOF to include in the model. Though accuracy can be enhanced at the cost of complexity by including more DOF, their necessity must be rigorously examined. In this study a planar seven-segment human body walking model with single DOF joints was developed. A ref...
Walking in circles: a modelling approach.
Maus, Horst-Moritz; Seyfarth, Andre
2014-10-01
Blindfolded or disoriented people have the tendency to walk in circles rather than on a straight line even if they wanted to. Here, we use a minimalistic walking model to examine this phenomenon. The bipedal spring-loaded inverted pendulum exhibits asymptotically stable gaits with centre of mass (CoM) dynamics and ground reaction forces similar to human walking in the sagittal plane. We extend this model into three dimensions, and show that stable walking patterns persist if the leg is aligned with respect to the body (here: CoM velocity) instead of a world reference frame. Further, we demonstrate that asymmetric leg configurations, which are common in humans, will typically lead to walking in circles. The diameter of these circles depends strongly on parameter configuration, but is in line with empirical data from human walkers. Simulation results suggest that walking radius and especially direction of rotation are highly dependent on leg configuration and walking velocity, which explains inconsistent veering behaviour in repeated trials in human data. Finally, we discuss the relation between findings in the model and implications for human walking. PMID:25056215
Chen, Xiankun; May, Brian; Di, Yuan Ming; Zhang, Anthony Lin; Lu, Chuanjian; Xue, Charlie Changli; Lin, Lin
2014-01-01
This systematic review evaluated the effects of Chinese herbal medicine (CHM) plus routine pharmacotherapy (RP) on the objective outcome measures BODE index, 6-minute walk test (6MWT), and 6-minute walk distance (6MWD) in individuals with stable chronic obstructive pulmonary disease (COPD). Searches were conducted of six English and Chinese databases (PubMed, EMBASE, CENTRAL, CINAHL, CNKI and CQVIP) from their inceptions until 18th November 2013 for randomized controlled trials involving oral...
CHEN Hong; LIANG Bin-miao; FANG Yong-jiang; XU Zhi-bo; WANG Ke; YI Qun; OU Xue-mei; FENG Yu-lin
2012-01-01
Background The relationship between the 6-minute walk test (6MWT) and pulmonary function test in stable chronic obstructive pulmonary disease (COPD) remains unclear.We evaluate the correlation of 6MWT and spirometric parameters in stable COPD with different severities.6MWT data assessed included three variables:the 6-minute walk distance (6MWD),6-minute walk work (6MWORK),and pulse oxygen desaturation rate (SPO2％).Methods 6MWT and pulmonary function test were assessed for 150 stable COPD patients with different severities.Means and standard deviations were calculated for the variables of interest.Analysis of variance was performed to compare means.Correlation coefficients were calculated for 6MWT data with the spirometric parameters and dyspnea Borg scale.Multiple stepwise regression analysis was used to screen pulmonary function-related predictors of 6MWT data.Results The three variables of 6MWT all varied as the severities of the disease.The 6MWD and 6MWORK both correlated with some spirometric parameters (positive or negative correlation; the absolute value of r ranging from 0.34 to 0.67; P＜0.05) in severe and very severe patients,and the SPO2％ correlated with the dyspnea Borg scale in four severities (r=-0.33,-0.34,-0.39,-0.53 respectively; P ＜0.05).The 6MWD was correlated with the 6MWORK in four severities (r=0.56,0.57,0.72,0.81 respectively,P ＜0.05),and neither of them correlated with the SPO2％.The percent of predicted forced expiratory volume in 1 second (FEV1％ predicted) and residual volume to total lung capacity ratio (RV/TLC) were predictors of the 6MWD,and the maximum voluntary ventilation (MW) was the predictor of the 6MWORK.Conclusions 6MWT correlated with the spirometric parameters in severe and very severe COPD patients.6MWT may be used to monitor changes of pulmonary function in these patients.
Improving Inverse Dynamics Accuracy in a Planar Walking Model Based on Stable Reference Point
Alaa Abdulrahman
2014-01-01
Full Text Available Physiologically and biomechanically, the human body represents a complicated system with an abundance of degrees of freedom (DOF. When developing mathematical representations of the body, a researcher has to decide on how many of those DOF to include in the model. Though accuracy can be enhanced at the cost of complexity by including more DOF, their necessity must be rigorously examined. In this study a planar seven-segment human body walking model with single DOF joints was developed. A reference point was added to the model to track the body’s global position while moving. Due to the kinematic instability of the pelvis, the top of the head was selected as the reference point, which also assimilates the vestibular sensor position. Inverse dynamics methods were used to formulate and solve the equations of motion based on Newton-Euler formulae. The torques and ground reaction forces generated by the planar model during a regular gait cycle were compared with similar results from a more complex three-dimensional OpenSim model with muscles, which resulted in correlation errors in the range of 0.9–0.98. The close comparison between the two torque outputs supports the use of planar models in gait studies.
Platkowski, Tadeusz; Zakrzewski, Jan
2011-11-01
We investigate a population of individuals who play the Rock-Paper-Scissors (RPS) game. The players choose strategies not only by optimizing their payoffs, but also taking into account the popularity of the strategies. For the standard RPS game, we find an asymptotically stable polymorphism with coexistence of all strategies. For the general RPS game we find the limit cycles. Their stability depends exclusively on two model parameters: the sum of the entries of the RPS payoff matrix, and a sensitivity parameter which characterizes the personality of the players. Apart from the supercritical Hopf bifurcation, we found the subcritical bifurcation numerically for some intervals of the parameters of the model.
Barbe, Ph
2011-01-01
Motivated by applications to insurance mathematics, we prove some heavy-traffic limit theorems for process which encompass the fractionally integrated random walk as well as some FARIMA processes, when the innovations are in the domain of attraction of a nonGaussian stable distribution.
Barbe, Ph
2011-01-01
Motivated by applications to insurance mathematics, we prove some heavy-traffic limit theorems for processes which encompass the fractionally differentiated random walk as well as some FARIMA processes, when the innovations are in the domain of attraction of a nonGaussian stable distribution.
Satake M
2015-01-01
Full Text Available Masahiro Satake,1 Takanobu Shioya,1 Sachiko Uemura,1 Hitomi Takahashi,2 Keiyu Sugawara,2 Chikage Kasai,2 Noritaka Kiyokawa,2 Toru Watanabe,2 Sayaka Sato,2 Atsuyoshi Kawagoshi2 1Department of Physical Therapy, Akita University Graduate School of Health Sciences, Akita, Japan; 2Department of Rehabilitation, Akita City Hospital, Akita, Japan Abstract: The purpose of this study was to investigate the relationship between dynamic hyperinflation and dyspnea and to clarify the characteristics of dyspnea during the 6-minute walk test (6MWT in chronic obstructive pulmonary disease patients. Twenty-three subjects with stable moderate chronic obstructive pulmonary disease (age 73.8±5.8 years, all male took part in this study. During the 6MWT, ventilatory and gas exchange parameters were measured using a portable respiratory gas analysis system. Dyspnea and oxygen saturation were recorded at the end of every 2 minute period during the test. There was a significant decrease in inspiratory capacity during the 6MWT. This suggested that dynamic hyperinflation had occurred. Dyspnea showed a significant linear increase, and there was a significant negative correlation with inspiratory capacity. It was suggested that one of the reasons that dyspnea developed during the 6MWT was the dynamic hyperinflation. Even though the tidal volume increased little after 2 minutes, dyspnea increased linearly to the end of the 6MWT. These results suggest that the mechanisms generating dyspnea during the 6MWT were the sense of respiratory effort at an early stage and then the mismatch between central motor command output and respiratory system movement. Keywords: field walking test, chronic respiratory diseases, respiratory gas analysis, inspiratory capacity, IC, inspiratory reserve volume, IRV, Borg CR-10 scale, COPD
Satake, Masahiro; Shioya, Takanobu; Uemura, Sachiko; Takahashi, Hitomi; Sugawara, Keiyu; Kasai, Chikage; Kiyokawa, Noritaka; Watanabe, Toru; Sato, Sayaka; Kawagoshi, Atsuyoshi
2015-01-01
The purpose of this study was to investigate the relationship between dynamic hyperinflation and dyspnea and to clarify the characteristics of dyspnea during the 6-minute walk test (6MWT) in chronic obstructive pulmonary disease patients. Twenty-three subjects with stable moderate chronic obstructive pulmonary disease (age 73.8±5.8 years, all male) took part in this study. During the 6MWT, ventilatory and gas exchange parameters were measured using a portable respiratory gas analysis system. Dyspnea and oxygen saturation were recorded at the end of every 2 minute period during the test. There was a significant decrease in inspiratory capacity during the 6MWT. This suggested that dynamic hyperinflation had occurred. Dyspnea showed a significant linear increase, and there was a significant negative correlation with inspiratory capacity. It was suggested that one of the reasons that dyspnea developed during the 6MWT was the dynamic hyperinflation. Even though the tidal volume increased little after 2 minutes, dyspnea increased linearly to the end of the 6MWT. These results suggest that the mechanisms generating dyspnea during the 6MWT were the sense of respiratory effort at an early stage and then the mismatch between central motor command output and respiratory system movement. PMID:25632228
Randomized random walk on a random walk
This paper discusses generalizations of the model introduced by Kehr and Kunter of the random walk of a particle on a one-dimensional chain which in turn has been constructed by a random walk procedure. The superimposed random walk is randomised in time according to the occurrences of a stochastic point process. The probability of finding the particle in a particular position at a certain instant is obtained explicitly in the transform domain. It is found that the asymptotic behaviour for large time of the mean-square displacement of the particle depends critically on the assumed structure of the basic random walk, giving a diffusion-like term for an asymmetric walk or a square root law if the walk is symmetric. Many results are obtained in closed form for the Poisson process case, and these agree with those given previously by Kehr and Kunter. (author)
Uniform asymptotic estimates of transition probabilities on combs
Bertacchi, Daniela; Zucca, Fabio
2000-01-01
We investigate the asymptotical behaviour of the transition probabilities of the simple random walk on the 2-comb. In particular we obtain space-time uniform asymptotical estimates which show the lack of symmetry of this walk better than local limit estimates. Our results also point out the impossibility of getting Jones-type non-Gaussian estimates.
ATP forms a stable complex with the essential histidine kinase WalK (YycG) domain
The histidine WalK (YycG) plays a crucial role in coordinating murein synthesis with cell division and the crystal structure of its ATP binding domain has been determined. Interestingly the bound ATP was not hydrolyzed during crystallization and remains intact in the crystal lattice. In Bacillus subtilis, the WalRK (YycFG) two-component system coordinates murein synthesis with cell division. It regulates the expression of autolysins that function in cell-wall remodeling and of proteins that modulate autolysin activity. The transcription factor WalR is activated upon phosphorylation by the histidine kinase WalK, a multi-domain homodimer. It autophosphorylates one of its histidine residues by transferring the γ-phosphate from ATP bound to its ATP-binding domain. Here, the high-resolution crystal structure of the ATP-binding domain of WalK in complex with ATP is presented at 1.61 Å resolution. The bound ATP remains intact in the crystal lattice. It appears that the strong binding interactions and the nature of the binding pocket contribute to its stability. The triphosphate moiety of ATP wraps around an Mg2+ ion, providing three O atoms for coordination in a near-ideal octahedral geometry. The ATP molecule also makes strong interactions with the protein. In addition, there is a short contact between the exocyclic O3′ of the sugar ring and O2B of the β-phosphate, implying an internal hydrogen bond. The stability of the WalK–ATP complex in the crystal lattice suggests that such a complex may exist in vivo poised for initiation of signal transmission. This feature may therefore be part of the sensing mechanism by which the WalRK two-component system is so rapidly activated when cells encounter conditions conducive for growth
Chen, Xiankun; May, Brian; Di, Yuan Ming; Zhang, Anthony Lin; Lu, Chuanjian; Xue, Charlie Changli; Lin, Lin
2014-01-01
This systematic review evaluated the effects of Chinese herbal medicine (CHM) plus routine pharmacotherapy (RP) on the objective outcome measures BODE index, 6-minute walk test (6MWT), and 6-minute walk distance (6MWD) in individuals with stable chronic obstructive pulmonary disease (COPD). Searches were conducted of six English and Chinese databases (PubMed, EMBASE, CENTRAL, CINAHL, CNKI and CQVIP) from their inceptions until 18th November 2013 for randomized controlled trials involving oral administration of CHM plus RP compared to the same RP, with BODE Index and/or 6MWT/D as outcomes. Twenty-five studies were identified. BODE Index was used in nine studies and 6MWT/D was used in 22 studies. Methodological quality was assessed using the Cochrane Risk of Bias tool. Weaknesses were identified in most studies. Six studies were judged as 'low' risk of bias for randomisation sequence generation. Twenty-two studies involving 1,834 participants were included in the meta-analyses. The main meta-analysis results showed relative benefits for BODE Index in nine studies (mean difference [MD] -0.71, 95% confidence interval [CI] -0.94, -0.47) and 6MWT/D in 17 studies (MD 54.61 meters, 95%CI 33.30, 75.92) in favour of the CHM plus RP groups. The principal plants used were Astragalus membranaceus, Panax ginseng and Cordyceps sinensis. A. membranaceus was used in combination with other herbs in 18 formulae in 16 studies. Detailed sub-group and sensitivity analyses were conducted. Clinically meaningful benefits for BODE Index and 6MWT were found in multiple studies. These therapeutic effects were promising but need to be interpreted with caution due to variations in the CHMs and RPs used and methodological weakness in the studies. These issues should be addressed in future trials. PMID:24622390
Xiankun Chen
Full Text Available This systematic review evaluated the effects of Chinese herbal medicine (CHM plus routine pharmacotherapy (RP on the objective outcome measures BODE index, 6-minute walk test (6MWT, and 6-minute walk distance (6MWD in individuals with stable chronic obstructive pulmonary disease (COPD. Searches were conducted of six English and Chinese databases (PubMed, EMBASE, CENTRAL, CINAHL, CNKI and CQVIP from their inceptions until 18th November 2013 for randomized controlled trials involving oral administration of CHM plus RP compared to the same RP, with BODE Index and/or 6MWT/D as outcomes. Twenty-five studies were identified. BODE Index was used in nine studies and 6MWT/D was used in 22 studies. Methodological quality was assessed using the Cochrane Risk of Bias tool. Weaknesses were identified in most studies. Six studies were judged as 'low' risk of bias for randomisation sequence generation. Twenty-two studies involving 1,834 participants were included in the meta-analyses. The main meta-analysis results showed relative benefits for BODE Index in nine studies (mean difference [MD] -0.71, 95% confidence interval [CI] -0.94, -0.47 and 6MWT/D in 17 studies (MD 54.61 meters, 95%CI 33.30, 75.92 in favour of the CHM plus RP groups. The principal plants used were Astragalus membranaceus, Panax ginseng and Cordyceps sinensis. A. membranaceus was used in combination with other herbs in 18 formulae in 16 studies. Detailed sub-group and sensitivity analyses were conducted. Clinically meaningful benefits for BODE Index and 6MWT were found in multiple studies. These therapeutic effects were promising but need to be interpreted with caution due to variations in the CHMs and RPs used and methodological weakness in the studies. These issues should be addressed in future trials.
Dettmann, Carl P.
2002-01-01
Recent advances in the periodic orbit theory of stochastically perturbed systems have permitted a calculation of the escape rate of a noisy chaotic map to order 64 in the noise strength. Comparison with the usual asymptotic expansions obtained from integrals and with a previous calculation of the electrostatic potential of exactly selfsimilar fractal charge distributions, suggests a remarkably accurate form for the late terms in the expansion, with parameters determined independently from the...
Banderier, Cyril; Nicodeme, Pierre
2010-01-01
This article tackles the enumeration and asymptotics of directed lattice paths (that are isomorphic to unidimensional paths) of bounded height (walks below one wall, or between two walls, for \\emphany finite set of jumps). Thus, for any lattice paths, we give the generating functions of bridges (``discrete'' Brownian bridges) and reflected bridges (``discrete'' reflected Brownian bridges) of a given height. It is a new success of the ``kernel method'' that the generating functions of such wal...
Maximum occupation time of a transient excited random walk on Z
Rastegar, Reza
2011-01-01
We consider a transient excited random walk on $Z$ and study the asymptotic behavior of the occupation time of a currently most visited site. In particular, our results imply that, in contrast to the random walks in random environment, a transient excited random walk does not spend an asymptotically positive fraction of time at its favorite (most visited up to a date) sites.
Fluctuations of Quantum Random Walks on Circles
Inui, Norio; Konishi, Yoshinao; Konno, Norio; Soshi, Takahiro
2003-01-01
Temporal fluctuations in the Hadamard walk on circles are studied. A temporal standard deviation of probability that a quantum random walker is positive at a given site is introduced to manifest striking differences between quantum and classical random walks. An analytical expression of the temporal standard deviation on a circle with odd sites is shown and its asymptotic behavior is considered for large system size. In contrast with classical random walks, the temporal fluctuation of quantum...
Exponential asymptotic stability for linear volterra equations
John A. D. Appleby
2000-01-01
This note studies the exponential asymptotic stability of the zero solution of the linear Volterra equation x˙ (t) = Ax(t) + t 0 K(t − s)x(s) ds by extending results in the paper of Murakami “Exponential Asymptotic Stability for scalar linear Volterra Equations”, Differential and Integral Equations, 4, 1991. In particular, when K isi ntegrable and has entries which do not change sign, and the equation has a uniformly asymptotically stable solution, exponential asympto...
... safety reasons, especially on uneven ground. See a physical therapist for exercise therapy and walking retraining. For a ... the right position for standing and walking. A physical therapist can supply these and provide exercise therapy, if ...
Hattori, Kumiko; Ogo, Noriaki; Otsuka, Takafumi
2015-01-01
We show that the `erasing-larger-loops-first' (ELLF) method, which was first introduced for erasing loops from the simple random walk on the Sierpinski gasket, does work also for non-Markov random walks, in particular, self-repelling walks to construct a new family of self-avoiding walks on the Sierpinski gasket. The one-parameter family constructed in this method continuously connects the loop-erased random walk and a self-avoiding walk which has the same asymptotic behavior as the `standard...
Asymptotic Behavior for Random Walks in Time-Random Environment on Z1%直线上时间随机环境下随机游动的渐近性质
胡学平; 祝东进
2008-01-01
In this paper,we give a general model of random walks in time-random environment in any countable space.Moreover,when the environment is independently identically distributed,a recurrence-transience criterion and the law of large numbers are derived in the nearest-neighbor case on Z1.At last,under regularity conditions,we prove that the RWIRE {Xn} on Z1 satisfies a central limit theorem,which is similar to the corresponding results in the case of classical random walks.
Asymptotically Safe Dark Matter
Sannino, Francesco; Shoemaker, Ian M.
2015-01-01
We introduce a new paradigm for dark matter (DM) interactions in which the interaction strength is asymptotically safe. In models of this type, the coupling strength is small at low energies but increases at higher energies, and asymptotically approaches a finite constant value. The resulting...... searches are the primary ways to constrain or discover asymptotically safe dark matter....
Precise Asymptotics for Lévy Processes
Zhi Shui HU; Chun SU
2007-01-01
Let {X(t), t ≥ 0} be a Lévy process with EX(1)=0 and EX2(1)＜∞. In this paper, we shall give two precise asymptotic theorems for {X(t), t≥0}. By the way, we prove the corresponding conclusions for strictly stable processes and a general precise asymptotic proposition for sums of i.i.d.random variables.
Sharp asymptotic results for simplified mutation-selection algorithms
Bérard, J.; Bienvenüe, A
2003-01-01
We study the asymptotic behavior of a mutation--selection genetic algorithm on the integers with finite population of size $p\\ge 1$. The mutation is defined by the steps of a simple random walk and the fitness function is linear. We prove that the normalized population satisfies an invariance principle, that a large-deviations principle holds and that the relative positions converge in law. After $n$ steps, the population is asymptotically around $\\sqrt{n}$ times the posi...
A random walk with a branching system in random environments
Ying-qiu LI; Xu LI; Quan-sheng LIU
2007-01-01
We consider a branching random walk in random environments, where the particles are reproduced as a branching process with a random environment (in time), and move independently as a random walk on Z with a random environment (in locations). We obtain the asymptotic properties on the position of the rightmost particle at time n, revealing a phase transition phenomenon of the system.
Florescu, Laura; Levine, Lionel; Peres, Yuval
2014-01-01
In a \\emph{rotor walk} the exits from each vertex follow a prescribed periodic sequence. On an infinite Eulerian graph embedded periodically in $\\R^d$, we show that any simple rotor walk, regardless of rotor mechanism or initial rotor configuration, visits at least on the order of $t^{d/(d+1)}$ distinct sites in $t$ steps. We prove a shape theorem for the rotor walk on the comb graph with i.i.d.\\ uniform initial rotors, showing that the range is of order $t^{2/3}$ and the asymptotic shape of ...
Limit theorems for random walks on a strip in subdiffusive regime
Dolgopyat, Dmitry; Goldsheid, Ilya
2012-01-01
We study the asymptotic behaviour of occupation times of a transient random walk in quenched random environment on a strip in a sub-diffusive regime. The asymptotic behaviour of hitting times, which is a more traditional object of study, is the exactly same. As a particular case, we solve a long standing problem of describing the asymptotic behaviour of a random walk with bounded jumps on a one-dimensional lattice
Method of calculating densities for isotropic L\\'evy Walks
Magdziarz, Marcin; Zorawik, Tomasz
2016-01-01
We provide explicit formulas for asymptotic densities of $d$-dimensional isotropic L\\'evy walks, when $d>1$. The densities of multidimensional undershooting and overshooting L\\'evy walks are presented as well. Interestingly, when the number of dimensions is odd the densities of all these L\\'evy walks are given by elementary functions. When $d$ is even, we can express the densities as fractional derivatives of hypergeometric functions, which makes an efficient numerical evaluation possible.
姜山; 程君实; 陈佳品; 包志军; 马培荪
2001-01-01
针对多自由度仿人机器人的运动控制，从神经生理学和机器人学的角度研究了基于中枢模式生成器（CPGs）的仿人运动控制策略．提出了一种将多目标遗传算法应用于(CPGs)参数优化的方法．首先构造用于仿人机器人运动控制的(CPGs)的结构，其参数通过遗传算法按相应的评价函数得到优化．%This paper describes the design of CPGs for stable humanoid bipedal locomotion, using an evolutionary approach. In this research, each joint of the humanoid is driven by a neuron that consists of two coupled neural oscillators. Corresponding joint's neurons are connected by strength weight, to achieve more natural and robust walking pattern, an evolutionary-based multi-objective optimization algorithm is used to solve the weight optimization problem. The fitness functions are formulated based on ZMP and global attitude of the robot. In the algorthms, real value coding and tournament selection are applied, the crossover and mutation operators are chosen as heuristic crossover and boundary mutation respectively. Following evolving, the robot is able to walk in the given environment and a simulation shows the results.
Quantum walk on the line: Entanglement and nonlocal initial conditions
The conditional shift in the evolution operator of a quantum walk generates entanglement between the coin and position degrees of freedom. This entanglement can be quantified by the von Neumman entropy of the reduced density operator (entropy of entanglement). We show analytically that for a Hadamard walk with local initial conditions the asymptotic entanglement is 0.872 for all initial coin states. When nonlocal initial conditions are considered, the asymptotic entanglement varies smoothly between almost complete entanglement and no entanglement (product state). An exact expression for the asymptotic (long-time) entanglement is obtained for initial conditions in the position subspace spanned by [±1>
Renewal theorems for random walks in random scenery
Guillotin-Plantard, Nadine
2011-01-01
Random walks in random scenery are processes defined by $Z_n:=\\sum_{k=1}^n\\xi_{X_1+...+X_k}$, where $(X_k,k\\ge 1)$ and $(\\xi_y,y\\in\\mathbb Z)$ are two independent sequences of i.i.d. random variables. We suppose that the distributions of $X_1$ and $\\xi_0$ belong to the normal domain of attraction of strictly stable distributions with index $\\alpha\\in[1,2]$ and $\\beta\\in(0,2)$ respectively. We are interested in the asymptotic behaviour as $|a|$ goes to infinity of quantities of the form $\\sum_{n\\ge 1}{\\mathbb E}[h(Z_n-a)]$ (when $(Z_n)_n$ is transient) or $\\sum_{n\\ge 1}{\\mathbb E}[h(Z_n)-h(Z_n-a)]$ (when $(Z_n)_n$ is recurrent) where $h$ is some complex-valued function defined on $\\mathbb{R}$ or $\\mathbb{Z}$.
Asymptotics and Borel summability
Costin, Ovidiu
2008-01-01
Incorporating substantial developments from the last thirty years into one resource, Asymptotics and Borel Summability provides a self-contained introduction to asymptotic analysis with special emphasis on topics not covered in traditional asymptotics books. The author explains basic ideas, concepts, and methods of generalized Borel summability, transseries, and exponential asymptotics. He provides complete mathematical rigor while supplementing it with heuristic material and examples, so that some proofs may be omitted by applications-oriented readers.To give a sense of how new methods are us
An asymptotic safety scenario for gauged chiral Higgs-Yukawa models
We investigate chiral Higgs-Yukawa models with a non-abelian gauged left-handed sector reminiscent to a sub-sector of the standard model. We discover a new weak-coupling fixed-point behavior that allows for ultraviolet complete RG trajectories which can be connected with a conventional long-range infrared behavior in the Higgs phase. This non-trivial ultraviolet behavior is characterized by asymptotic freedom in all interaction couplings, but a quasi conformal behavior in all mass-like parameters. The stable microscopic scalar potential asymptotically approaches flatness in the ultraviolet, however, with a non-vanishing minimum increasing inversely proportional to the asymptotically free gauge coupling. This gives rise to non-perturbative - though weak-coupling - threshold effects which induce ultraviolet stability along a line of fixed points. Despite the weak-coupling properties, the system exhibits non-Gaussian features which are distinctly different from its standard perturbative counterpart: e.g., on a branch of the line of fixed points, we find linear instead of quadratically running renormalization constants. Whereas the Fermi constant and the top mass are naturally of the same order of magnitude, our model generically allows for light Higgs boson masses. Realistic mass ratios are related to particular RG trajectories with a ''walking'' mid-momentum regime. (orig.)
Numerical integration of asymptotic solutions of ordinary differential equations
Thurston, Gaylen A.
1989-01-01
Classical asymptotic analysis of ordinary differential equations derives approximate solutions that are numerically stable. However, the analysis also leads to tedious expansions in powers of the relevant parameter for a particular problem. The expansions are replaced with integrals that can be evaluated by numerical integration. The resulting numerical solutions retain the linear independence that is the main advantage of asymptotic solutions. Examples, including the Falkner-Skan equation from laminar boundary layer theory, illustrate the method of asymptotic analysis with numerical integration.
On asymptotic extension dimension
Repovš, Dušan; Zarichnyi, Mykhailo
2011-01-01
The aim of this paper is to introduce an asymptotic counterpart of the extension dimension defined by Dranishnikov. The main result establishes a relation between the asymptotic extensional dimension of a proper metric space and extension dimension of its Higson corona.
Large-time asymptotics of the gyration radius for long-range statistical-mechanical models
Sakai, Akira
2009-01-01
The aim of this short article is to convey the basic idea of the original paper [3], without going into too much detail, about how to derive sharp asymptotics of the gyration radius for random walk, self-avoiding walk and oriented percolation above the model-dependent upper critical dimension.
Kang An
2013-10-01
Full Text Available This paper presents a passive dynamic walking model based on knee-bend behaviour, which is inspired by the way human beings walk. The length and mass parameters of human beings are used in the walking model. The knee-bend mechanism of the stance leg is designed in the phase between knee-strike and heel- strike. q* which is the angular difference of the stance leg between the two events, knee-strike and knee-bend, is adjusted in order to find a stable walking motion. The results show that the stable periodic walking motion on a slope of r <0.4 can be found by adjusting q*. Furthermore, with a particular q* in the range of 0.12walk down more steps before falling down on an arbitrary slope. The walking motion is more stable and adaptable than the conventional walking motion, especially for steep slopes.
ASYMPTOTIC QUANTIZATION OF PROBABILITY DISTRIBUTIONS
Klaus P(o)tzelberger
2003-01-01
We give a brief introduction to results on the asymptotics of quantization errors.The topics discussed include the quantization dimension,asymptotic distributions of sets of prototypes,asymptotically optimal quantizations,approximations and random quantizations.
Asymptotic Resource Usage Bounds
Albert E.; Alonso D.; Arenas P.; Genaim S.; Puebla G.
2009-01-01
When describing the resource usage of a program, it is usual to talk in asymptotic terms, such as the well-known “big O” notation, whereby we focus on the behaviour of the program for large input data and make a rough approximation by considering as equivalent programs whose resource usage grows at the same rate. Motivated by the existence of non-asymptotic resource usage analyzers, in this paper, we develop a novel transformation from a non-asymptotic cost function (which can be produced by ...
Nonstandard asymptotic analysis
Berg, Imme
1987-01-01
This research monograph considers the subject of asymptotics from a nonstandard view point. It is intended both for classical asymptoticists - they will discover a new approach to problems very familiar to them - and for nonstandard analysts but includes topics of general interest, like the remarkable behaviour of Taylor polynomials of elementary functions. Noting that within nonstandard analysis, "small", "large", and "domain of validity of asymptotic behaviour" have a precise meaning, a nonstandard alternative to classical asymptotics is developed. Special emphasis is given to applications in numerical approximation by convergent and divergent expansions: in the latter case a clear asymptotic answer is given to the problem of optimal approximation, which is valid for a large class of functions including many special functions. The author's approach is didactical. The book opens with a large introductory chapter which can be read without much knowledge of nonstandard analysis. Here the main features of the t...
Global asymptotic stability for a class of nonlinear chemical equations
Anderson, David F.
2007-01-01
We consider a class of nonlinear differential equations that arises in the study of chemical reaction systems that are known to be locally asymptotically stable and prove that they are in fact globally asymptotically stable. More specifically, we will consider chemical reaction systems that are weakly reversible, have a deficiency of zero, and are equipped with mass action kinetics. We show that if for each $c \\in \\R_{> 0}^m$ the intersection of the stoichiometric compatibility class $c + S$ ...
Bousso, Raphael
2016-01-01
We show that known entropy bounds constrain the information carried off by radiation to null infinity. We consider distant, planar null hypersurfaces in asymptotically flat spacetime. Their focussing and area loss can be computed perturbatively on a Minkowski background, yielding entropy bounds in terms of the energy flux of the outgoing radiation. In the asymptotic limit, we obtain boundary versions of the Quantum Null Energy Condition, of the Generalized Second Law, and of the Quantum Bousso Bound.
Asymptotically Safe Dark Matter
Sannino, Francesco
2014-01-01
We introduce a new paradigm for dark matter interactions according to which the interaction strength is asymptotically safe. In models of this type, the interaction strength is small at low energies but increases at higher energies towards a finite constant value of the coupling. The net effect is to partially offset direct detection constraints without affecting thermal freeze-out at higher energies. High-energy collider and indirect annihilation searches are the primary ways to constrain or discover asymptotically safe dark matter.
Quasi-extended asymptotic functions
The class F of ''quasi-extended asymptotic functions'' is introduced. It contains all extended asymptotic functions as well as some new asymptotic functions very similar to the Schwartz distributions. On the other hand, every two quasiextended asymptotic functions can be multiplied as opposed to the Schwartz distributions; in particular, the square delta2 of an asymptotic function delta similar to Dirac's delta-function, is constructed as an example
Puschnigg, Michael
1996-01-01
The aim of cyclic cohomology theories is the approximation of K-theory by cohomology theories defined by natural chain complexes. The basic example is the approximation of topological K-theory by de Rham cohomology via the classical Chern character. A cyclic cohomology theory for operator algebras is developed in the book, based on Connes' work on noncommutative geometry. Asymptotic cyclic cohomology faithfully reflects the basic properties and features of operator K-theory. It thus becomes a natural target for a Chern character. The central result of the book is a general Grothendieck-Riemann-Roch theorem in noncommutative geometry with values in asymptotic cyclic homology. Besides this, the book contains numerous examples and calculations of asymptotic cyclic cohomology groups.
Asymptotic stability properties of θ-methods for delay differential equations
无
2001-01-01
Deals with the asymptotic stability properties of θ- methods for the pantograph equation and the linear delay differential-algebraic equation with emphasis on the linear θ- methods with variable stepsize schemes for the pantograph equation, proves that asymptotic stability is obtained if and only if θ ＞ 1/2, and studies further the one-leg θ- method for the linear delay differential-algebraic equation and establishes the sufficient asymptotic-ally differential-algebraic stable condition θ = 1.
A large part of physics consists of learning which asymptotic methods to apply where, yet physicists are not always taught asymptotics in a systematic way. Asymptotology is given using an example from aerodynamics, and a rent Phys. Rev. Letter Comment is used as a case study of one subtle way things can go wrong. It is shown that the application of local analysis leads to erroneous conclusions regarding the existence of a continuous spectrum in a simple test problem, showing that a global analysis must be used. The final section presents results on a more sophisticated example, namely the WKBJ solution of Mathieu equation. 13 refs., 2 figs
Jones, D S
1997-01-01
Many branches of science and engineering involve applications of mathematical analysis. An important part of applied analysis is asymptotic approximation which is, therefore, an active area of research with new methods and publications being found constantly. This book gives an introduction to the subject sufficient for scientists and engineers to grasp the fundamental techniques, both those which have been known for some time and those which have been discovered more recently. The asymptotic approximation of both integrals and differential equations is discussed and the discussion includes hy
Asymptotics for spherical needlets
Baldi, P.; Kerkyacharian, G.; Marinucci, D.; Picard, D.
We investigate invariant random fields on the sphere using a new type of spherical wavelets, called needlets. These are compactly supported in frequency and enjoy excellent localization properties in real space, with quasi-exponentially decaying tails. We show that, for random fields on the sphere, the needlet coefficients are asymptotically uncorrelated for any fixed angular distance. This property is used to derive CLT and functional CLT convergence results for polynomial functionals of the needlet coefficients: here the asymptotic theory is considered in the high-frequency sense. Our proposals emerge from strong empirical motivations, especially in connection with the analysis of cosmological data sets.
One-dimensional quantum walks with one defect
Cantero, M J; Moral, L; Velazquez, L
2010-01-01
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 non negative 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 at the origin.
A new exponent in self-avoiding walks
Existence of a new exponent is reported in the problem of nonintersecting self-avoiding random walks. It is connected with the asymptotic behaviour of the growth of number of such walks of larger and larger length. The value of the exponent is found to be nearly 0.90 for all two-dimensional and nearly 0.96 for all three-dimensional lattices studied here. (author)
Asymptotic freedom, asymptotic flatness and cosmology
Holographic RG flows in some cases are known to be related to cosmological solutions. In this paper another example of such correspondence is provided. Holographic RG flows giving rise to asymptotically-free β-functions have been analyzed in connection with holographic models of QCD. They are shown upon Wick rotation to provide a large class of inflationary models with logarithmically-soft inflaton potentials. The scalar spectral index is universal and depends only on the number of e-foldings. The ratio of tensor to scalar power depends on the single extra real parameter that defines this class of models. The Starobinsky inflationary model as well as the recently proposed models of T-inflation are members of this class. The holographic setup gives a completely new (and contrasting) view to the stability, naturalness and other problems of such inflationary models
Litim, Daniel F.; Sannino, Francesco
2014-01-01
We study the ultraviolet behaviour of four-dimensional quantum field theories involving non-abelian gauge fields, fermions and scalars in the Veneziano limit. In a regime where asymptotic freedom is lost, we explain how the three types of fields cooperate to develop fully interacting ultraviolet ...
Cristallini, Achille
2016-07-01
A new and intriguing machine may be obtained replacing the moving pulley of a gun tackle with a fixed point in the rope. Its most important feature is the asymptotic efficiency. Here we obtain a satisfactory description of this machine by means of vector calculus and elementary trigonometry. The mathematical model has been compared with experimental data and briefly discussed.
Asymptotic Consensus Without Self-Confidence
Nowak, Thomas
2015-01-01
This paper studies asymptotic consensus in systems in which agents do not necessarily have self-confidence, i.e., may disregard their own value during execution of the update rule. We show that the prevalent hypothesis of self-confidence in many convergence results can be replaced by the existence of aperiodic cores. These are stable aperiodic subgraphs, which allow to virtually store information about an agent's value distributedly in the network. Our results are applicable to systems with m...
Complementarity and quantum walks
We show that quantum walks interpolate between a coherent 'wave walk' and a random walk depending on how strongly the walker's coin state is measured; i.e., the quantum walk exhibits the quintessentially quantum property of complementarity, which is manifested as a tradeoff between knowledge of which path the walker takes vs the sharpness of the interference pattern. A physical implementation of a quantum walk (the quantum quincunx) should thus have an identifiable walker and the capacity to demonstrate the interpolation between wave walk and random walk depending on the strength of measurement
Optimistic Agents are Asymptotically Optimal
Sunehag, Peter; Hutter, Marcus
2012-01-01
We use optimism to introduce generic asymptotically optimal reinforcement learning agents. They achieve, with an arbitrary finite or compact class of environments, asymptotically optimal behavior. Furthermore, in the finite deterministic case we provide finite error bounds.
Chiral symmetry breaking in asymptotically free and non-asymptotically free gauge theories
An essential distinction in the realization of the PCAC-dynamics in vector-like asymptotically free and non-asymptotically free (with a non-trival ultraviolet stable fixed point) gauge theories is revealed. For the latter theories an analytical expression for the condensate is obtained in the two-loop approximation and the arguments in support of a soft behaviour at small distances of composite operators are given. The problem of factorizing the low-energy region for the Wess-Zumino-Witten action is discussed
Willey, David
2010-01-01
This article gives a brief history of fire-walking and then deals with the physics behind fire-walking. The author has performed approximately 50 fire-walks, took the data for the world's hottest fire-walk and was, at one time, a world record holder for the longest fire-walk (www.dwilley.com/HDATLTW/Record_Making_Firewalks.html). He currently…
Self-avoiding walks and polygons on quasiperiodic tilings
We enumerate self-avoiding walks and polygons, counted by perimeter, on the quasiperiodic rhombic Penrose and Ammann-Beenker tilings, thereby considerably extending previous results. In contrast to similar problems on regular lattices, these numbers depend on the chosen initial vertex. We compare different ways of counting and demonstrate that suitable averaging improves convergence to the asymptotic regime. This leads to improved estimates for critical points and exponents, which support the conjecture that self-avoiding walks on quasiperiodic tilings belong to the same universality class as self-avoiding walks on the square lattice. For polygons, the obtained enumeration data do not allow us to draw decisive conclusions about the exponent
Asymptotic Flatness in Rainbow Gravity
Hackett, Jonathan
2005-01-01
A construction of conformal infinity in null and spatial directions is constructed for the Rainbow-flat space-time corresponding to doubly special relativity. From this construction a definition of asymptotic DSRness is put forward which is compatible with the correspondence principle of Rainbow gravity. Furthermore a result equating asymptotically flat space-times with asymptotically DSR spacetimes is presented.
Coarse geometry and asymptotic dimension
Grave, Bernd
2006-01-01
We consider asymptotic dimension of coarse spaces. We analyse coarse structures induced by metrisable compactifications. We calculate asymptotic dimension of coarse cell complexes. We calculate the asymptotic dimension of certain negatively curved spaces, e.g. for complete, simply connected manifolds with bounded, strictly negative sectional curvature.
Currow David C; Everett Bronwyn; Salamonson Yenna; Denniss Robert; Zecchin Robert; Newton Phillip J; Du Hui Y; Macdonald Peter S; Davidson Patricia M
2011-01-01
Abstract Background Chronic heart failure (CHF) is a chronic debilitating condition with economic consequences, mostly because of frequent hospitalisations. Physical activity and adequate self-management capacity are important risk reduction strategies in the management of CHF. The Home-Heart-Walk is a self-monitoring intervention. This model of intervention has adapted the 6-minute walk test as a home-based activity that is self-administered and can be used for monitoring physical functional...
Du, Hui Y; Newton, Phillip J.; Zecchin, Robert; Denniss, Robert; Salamonson, Yenna; Everett, Bronwyn; Currow, David C; Macdonald, Peter S; Davidson, Patricia M
2011-01-01
Background Chronic heart failure (CHF) is a chronic debilitating condition with economic consequences, mostly because of frequent hospitalisations. Physical activity and adequate self-management capacity are important risk reduction strategies in the management of CHF. The Home-Heart-Walk is a self-monitoring intervention. This model of intervention has adapted the 6-minute walk test as a home-based activity that is self-administered and can be used for monitoring physical functional capacity...
Asymptotically hyperbolic connections
Fine, Joel; Krasnov, Kirill; Scarinci, Carlos
2015-01-01
General Relativity in 4 dimensions can be equivalently described as a dynamical theory of SO(3)-connections rather than metrics. We introduce the notion of asymptotically hyperbolic connections, and work out an analog of the Fefferman-Graham expansion in the language of connections. As in the metric setup, one can solve the arising "evolution" equations order by order in the expansion in powers of the radial coordinate. The solution in the connection setting is arguably simpler, and very straightforward algebraic manipulations allow one to see how the obstruction appears at third order in the expansion. Another interesting feature of the connection formulation is that the "counter terms" required in the computation of the renormalised volume all combine into the Chern-Simons functional of the restriction of the connection to the boundary. As the Chern-Simons invariant is only defined modulo large gauge transformations, the requirement that the path integral over asymptotically hyperbolic connections is well-d...
Persistence of unvisited sites in quantum walks on a line
Štefaňák, M.; Jex, I.
2016-03-01
We analyze the asymptotic scaling of persistence of unvisited sites for quantum walks on a line. In contrast to the classical random walk, there is no connection between the behavior of persistence and the scaling of variance. In particular, we find that for a two-state quantum walk persistence follows an inverse power law where the exponent is determined solely by the coin parameter. Moreover, for a one-parameter family of three-state quantum walks containing the Grover walk, the scaling of persistence is given by two contributions. The first is the inverse power law. The second contribution to the asymptotic behavior of persistence is an exponential decay coming from the trapping nature of the studied family of quantum walks. In contrast to the two-state walks, both the exponent of the inverse power-law and the decay constant of the exponential decay depend also on the initial coin state and its coherence. Hence, one can achieve various regimes of persistence by altering the initial condition, ranging from purely exponential decay to purely inverse power-law behavior.
Another Asymptotic Notation : "Almost"
Mondal, Nabarun; Ghosh, Partha P.
2013-01-01
Asymptotic notations are heavily used while analysing runtimes of algorithms. Present paper argues that some of these usages are non trivial, therefore incurring errors in communication of ideas. After careful reconsidera- tion of the various existing notations a new notation is proposed. This notation has similarities with the other heavily used notations like Big-Oh, Big Theta, while being more accurate when describing the order relationship. It has been argued that this notation is more su...
Forces and pressures in adsorbing partially directed walks
Janse van Rensburg, E. J.; Prellberg, T.
2016-05-01
Polymers in confined spaces lose conformational entropy. This induces a net repulsive entropic force on the walls of the confining space. A model for this phenomenon is a lattice walk between confining walls, and in this paper a model of an adsorbing partially directed walk is used. The walk is placed in a half square lattice {{{L}}}+2 with boundary \\partial {{{L}}}+2, and confined between two vertical parallel walls, which are vertical lines in the lattice, a distance w apart. The free energy of the walk is determined, as a function of w, for walks with endpoints in the confining walls and adsorbing in \\partial {{{L}}}+2. This gives the entropic force on the confining walls as a function of w. It is shown that there are zero force points in this model and the locations of these points are determined, in some cases exactly, and in other cases asymptotically.
Self Avoiding Walks in Four Dimensions: Logarithmic Corrections
Grassberger, Peter; Hegger, Rainer; Schaefer, Lothar
1994-01-01
We present simulation results for long ($N\\leq 4000$) self-avoiding walks in four dimensions. We find definite indications of logarithmic corrections, but the data are poorly described by the asymptotically leading terms. Detailed comparisons are presented with renormalization group flow equations derived in direct renormalization and with results of a field theoretic calculation.
Duality and asymptotic geometries
Boonstra, H J; Skenderis, K
1997-01-01
We consider a series of duality transformations that leads to a constant shift in the harmonic functions appearing in the description of a configuration of branes. This way, for several intersections of branes, we can relate the original brane configuration which is asymptotically flat to a geometry of the type $adS_k \\xx E^l \\xx S^m$. The implications of our results for supersymmetry enhancement, M(atrix) theory at finite N, and for supergravity theories in diverse dimensions are discussed.
Asymptotically anti-de Sitter Proca Stars
Duarte, Miguel
2016-01-01
We show that complex, massive spin-1 fields minimally coupled to Einstein's gravity with a negative cosmological constant, admit asymptotically anti-de Sitter self-gravitating solutions. Focusing on 4-dimensional spacetimes, we start by obtaining analytical solutions in the test-field limit, where the Proca field equations can be solved in a fixed anti-de Sitter background, and then find fully non-linear solutions numerically. These solutions are a natural extension of the recently found asymptotically flat Proca stars and share similar properties with scalar boson stars. In particular, we show that they are stable against spherically symmetric linear perturbations for a range of fundamental frequencies limited by their point of maximum mass. We finish with an overview of the behavior of Proca stars in $5$ dimensions.
Kendon, Viv
2011-01-01
Quantum versions of random walks have diverse applications that are motivating experimental implementations as well as theoretical studies. However, the main impetus behind this interest is their use in quantum algorithms, which have always employed the quantum walk in the form of a program running on a quantum computer. Recent results showing that quantum walks are "universal for quantum computation" relate entirely to algorithms, and do not imply that a physical quantum walk could provide a...
Mason, Nick
2007-01-01
A generation ago, it was part of growing up for all kids when they biked or walked to school. But in the last 30 years, heavier traffic, wider roads and more dangerous intersections have made it riskier for students walking or pedaling. Today, fewer than 15 percent of kids bike or walk to school compared with more than 50 percent in 1969. In the…
Kendon, Viv [School of Physics and Astronomy, University of Leeds, LS2 9JT (United Kingdom)
2014-12-04
Quantum versions of random walks have diverse applications that are motivating experimental implementations as well as theoretical studies. Recent results showing quantum walks are “universal for quantum computation” relate to algorithms, to be run on quantum computers. We consider whether an experimental implementation of a quantum walk could provide useful computation before we have a universal quantum computer.
Direction-Dependent Control of Balance During Walking and Standing
O'Connor, Shawn M.; Kuo, Arthur D.
2009-01-01
Human walking has previously been described as “controlled falling.” Some computational models, however, suggest that gait may also have self-stabilizing aspects requiring little CNS control. The fore–aft component of walking may even be passively stable from step to step, whereas lateral motion may be unstable and require motor control for balance, as through active foot placement. If this is the case, walking humans might rely less on integrative sensory feedback, such as vision, for antero...
Asymptotic Symmetries from finite boxes
Andrade, Tomas
2015-01-01
It is natural to regulate an infinite-sized system by imposing a boundary condition at finite distance, placing the system in a "box." This breaks symmetries, though the breaking is small when the box is large. One should thus be able to obtain the asymptotic symmetries of the infinite system by studying regulated systems. We provide concrete examples in the context of Einstein-Hilbert gravity (with negative or zero cosmological constant) by showing in 4 or more dimensions how the Anti-de Sitter and Poincar\\'e asymptotic symmetries can be extracted from gravity in a spherical box with Dirichlet boundary conditions. In 2+1 dimensions we obtain the full double-Virasoro algebra of asymptotic symmetries for AdS$_3$ and, correspondingly, the full Bondi-Metzner-Sachs (BMS) algebra for asymptotically flat space. In higher dimensions, a related approach may continue to be useful for constructing a good asymptotically flat phase space with BMS asymptotic symmetries.
Asymptotic symmetries from finite boxes
Andrade, Tomás; Marolf, Donald
2016-01-01
It is natural to regulate an infinite-sized system by imposing a boundary condition at finite distance, placing the system in a 'box.' This breaks symmetries, though the breaking is small when the box is large. One should thus be able to obtain the asymptotic symmetries of the infinite system by studying regulated systems. We provide concrete examples in the context of Einstein-Hilbert gravity (with negative or zero cosmological constant) by showing in 4 or more dimensions how the anti-de Sitter and Poincaré asymptotic symmetries can be extracted from gravity in a spherical box with Dirichlet boundary conditions. In 2 + 1 dimensions we obtain the full double-Virasoro algebra of asymptotic symmetries for AdS3 and, correspondingly, the full Bondi-Metzner-Sachs (BMS) algebra for asymptotically flat space. In higher dimensions, a related approach may continue to be useful for constructing a good asymptotically flat phase space with BMS asymptotic symmetries.
Regular Variation and Smile Asymptotics
Benaim, Shalom; Friz, Peter
2006-01-01
We consider risk-neutral returns and show how their tail asymptotics translate directly to asymptotics of the implied volatility smile, thereby sharpening Roger Lee's celebrated moment formula. The theory of regular variation provides the ideal mathematical framework to formulate and prove such results. The practical value of our formulae comes from the vast literature on tail asymptotics and our conditions are often seen to be true by simple inspection of known results.
Extended asymptotic functions - some examples
Several examples of extended asymptotic functions are exposed. These examples will illustrate the notions introduced in another paper but at the same time they have a significance as realizations of some Schwartz disctibutions: delta(x), H(x), P(1/xsup(n)), etc. The important thing is that the asymptotic functions of these examples (which, on their part, are realizations of the above-mentioned distributions) can be multiplied in the class of the asymptotic functions as opposed to the theory of Schwartz distributions. Some properties of the set of all extended asymptotic functions are considered which are essential for the next step of this approach
Asymptotic Efficiency in OLEDS
Nelson, Mitchell C
2015-01-01
Asymptotic efficiency (high output without droop) was recently reported for OLEDS in which a thin emitter layer is located at the anti-node in a resonant microcavity. Here we extend our theoretical analysis to treat multi-mode devices with isotropic emitter orientation. We recover our efficiency equations for the limiting cases with an isotropic emitter layer located at the anti-node where output is linear in current, and for an isotropic emitter located at the node where output can exhibit second order losses with an overall efficiency coefficient that depends on loss terms in competition with a cavity factor. Additional scenarios are described where output is driven by spontaneous emission, or mixed spontaneous and stimulated emission, with stimulated emission present in a loss mode, potentially resulting in cavity driven droop or output clamping, and where the emitter layer is a host-guest system.
Shirai, Tomoyuki
2003-01-01
For a certain class of reversible random walks possibly with drift on an abelian covering graph of a finite graph, using the technique of twisted transition operator, we obtain the asymptotic behavior of the $n$-step transition probability $p_n(x,y)$ as $n \\to \\infty$ and give an expression of the constant which appears in the asymptotics.
LI Hong; L(U) Shu; ZHONG Shou-ming
2005-01-01
The global uniform asymptotic stability of competitive neural networks with different time scales and delay is investigated. By the method of variation of parameters and the method of inequality analysis, the condition for global uniformly asymptotically stable are given. A strict Lyapunov function for the flow of a competitive neural system with different time scales and delay is presented. Based on the function, the global uniform asymptotic stability of the equilibrium point can be proved.
On asymptotics for difference equations
Rafei, M.
2012-01-01
In this thesis a class of nonlinear oscillator equations is studied. Asymptotic approximations of first integrals for nonlinear difference equations are constructed by using the recently developed perturbation method based on invariance vectors. The asymptotic approximations of the solutions of the
Random Walks on Stochastic Temporal Networks
Hoffmann, Till; Lambiotte, Renaud
2013-01-01
In the study of dynamical processes on networks, there has been intense focus on network structure -- i.e., the arrangement of edges and their associated weights -- but the effects of the temporal patterns of edges remains poorly understood. In this chapter, we develop a mathematical framework for random walks on temporal networks using an approach that provides a compromise between abstract but unrealistic models and data-driven but non-mathematical approaches. To do this, we introduce a stochastic model for temporal networks in which we summarize the temporal and structural organization of a system using a matrix of waiting-time distributions. We show that random walks on stochastic temporal networks can be described exactly by an integro-differential master equation and derive an analytical expression for its asymptotic steady state. We also discuss how our work might be useful to help build centrality measures for temporal networks.
Environment-dependent continuous time random walk
Lin Fang; Bao Jing-Dong
2011-01-01
A generalized continuous time random walk model which is dependent on environmental damping is proposed in which the two key parameters of the usual random walk theory:the jumping distance and the waiting time, are replaced by two new ones:the pulse velocity and the flight time. The anomalous diffusion of a free particle which is characterized by the asymptotical mean square displacement ～tα is realized numerically and analysed theoretically, where the value of the power index a is in a region of 0<α<2. Particularly, the damping leads to a sub-diffusion when the impact velocities are drawn from a Gaussian density function and the super-diffusive effect is related to statistical extremes, which are called rare-though-dominant events.
Asymptotic Phase for Stochastic Oscillators
Thomas, Peter J.; Lindner, Benjamin
2014-12-01
Oscillations and noise are ubiquitous in physical and biological systems. When oscillations arise from a deterministic limit cycle, entrainment and synchronization may be analyzed in terms of the asymptotic phase function. In the presence of noise, the asymptotic phase is no longer well defined. We introduce a new definition of asymptotic phase in terms of the slowest decaying modes of the Kolmogorov backward operator. Our stochastic asymptotic phase is well defined for noisy oscillators, even when the oscillations are noise dependent. It reduces to the classical asymptotic phase in the limit of vanishing noise. The phase can be obtained either by solving an eigenvalue problem, or by empirical observation of an oscillating density's approach to its steady state.
Small-Space Controllability of a Walking Humanoid Robot
Dalibard, Sébastien; El Khoury, Antonio; Lamiraux, Florent; Taïx, Michel; Laumond, Jean-Paul
2011-01-01
This paper presents a two-stage motion planner for walking humanoid robots. A first draft path is computed using random motion planning techniques that ensure collision avoidance. In a second step, the draft path is approximated by a whole-body dynamically stable walk trajectory. The contributions of this work are: (i) a formal guarantee, based on small-space controllability criteria, that the first draft path can be approximated by a collision-free dynamically stable trajectory; (ii) an algo...
Chover-Type Laws of the Iterated Logarithm for Continuous Time Random Walks
Kyo-Shin Hwang; Wensheng Wang
2012-01-01
A continuous time random walk is a random walk subordinated to a renewal process used in physics to model anomalous diffusion. In this paper, we establish Chover-type laws of the iterated logarithm for continuous time random walks with jumps and waiting times in the domains of attraction of stable laws.
Currow David C
2011-03-01
Full Text Available Abstract Background Chronic heart failure (CHF is a chronic debilitating condition with economic consequences, mostly because of frequent hospitalisations. Physical activity and adequate self-management capacity are important risk reduction strategies in the management of CHF. The Home-Heart-Walk is a self-monitoring intervention. This model of intervention has adapted the 6-minute walk test as a home-based activity that is self-administered and can be used for monitoring physical functional capacity in people with CHF. The aim of the Home-Heart-Walk program is to promote adherence to physical activity recommendations and improving self-management in people with CHF. Methods/Design A randomised controlled trial is being conducted in English speaking people with CHF in four hospitals in Sydney, Australia. Individuals diagnosed with CHF, in New York Heart Association Functional Class II or III, with a previous admission to hospital for CHF are eligible to participate. Based on a previous CHF study and a loss to follow-up of 10%, 166 participants are required to be able to detect a 12-point difference in the study primary endpoint (SF-36 physical function domain. All enrolled participant receive an information session with a cardiovascular nurse. This information session covers key self-management components of CHF: daily weight; diet (salt reduction; medication adherence; and physical activity. Participants are randomised to either intervention or control group through the study randomisation centre after baseline questionnaires and assessment are completed. For people in the intervention group, the research nurse also explains the weekly Home-Heart-Walk protocol. All participants receive monthly phone calls from a research coordinator for six months, and outcome measures are conducted at one, three and six months. The primary outcome of the trial is the physical functioning domain of quality of life, measured by the physical functioning subscale
WU An-Cai; XU Xin-Jian; WU Zhi-Xi; WANG Ying-Hai
2007-01-01
We investigate the dynamics of random walks on weighted networks. Assuming that the edge weight and the node strength are used as local information by a random walker. Two kinds of walks, weight-dependent walk and strength-dependent walk, are studied. Exact expressions for stationary distribution and average return time are derived and confirmed by computer simulations. The distribution of average return time and the mean-square that a weight-dependent walker can arrive at a new territory more easily than a strength-dependent one.
Subexponential loss rate asymptotics for Lévy processes
Andersen, Lars Nørvang
We consider a Lévy process reflected in barriers at 0 and K > 0. The loss rate is the mean time spent at the upper barrier K at time 1 when the process is started in stationarity, and is a natural continuous-time analogue of the stationary expected loss rate for a reflected random walk. We derive...... asymptotics for the loss rate when K tends to infinity, when the mean of the Lévy process is negative and the positive jumps are subexponential. In the course of this derivation, we achieve a formula, which is a generalization of the celebrated Pollaczeck-Khinchine formula....
Subexponential loss rate asymptotics for Lévy processes
Andersen, Lars Nørvang
2011-01-01
We consider a Lévy process reflected in barriers at 0 and K > 0. The loss rate is the mean of the local time at K at time 1 when the process is started in stationarity, and is a natural continuous-time analogue of the stationary expected loss rate for a reflected random walk. We derive asymptotics...... for the loss rate when K tends to infinity, when the mean of the Lévy process is negative and the positive jumps are subexponential. In the course of this derivation, we achieve a formula, which is a generalization of the celebrated Pollaczeck-Khinchine formula....
Asymptotic behavior of two-terminal series-parallel networks
Golinelli, O.
1997-01-01
This paper discusses the enumeration of two-terminal series-parallel networks, i.e. the number of electrical networks built with n identical elements connected in series or parallel with two-terminal nodes. They frequently occur in applied probability theory as a model for real networks. The number of networks grows asymptotically like R^n/n^alpha, as for some models of statistical physics like self-avoiding walks, lattice animals, meanders, etc. By using a exact recurrence relation, the entr...
Elastohydrodynamic lubrication for line and point contacts asymptotic and numerical approaches
Kudish, Ilya I
2013-01-01
Elastohydrodynamic Lubrication for Line and Point Contacts: Asymptotic and Numerical Approaches describes a coherent asymptotic approach to the analysis of lubrication problems for heavily loaded line and point contacts. This approach leads to unified asymptotic equations for line and point contacts as well as stable numerical algorithms for the solution of these elastohydrodynamic lubrication (EHL) problems. A Unique Approach to Analyzing Lubrication Problems for Heavily Loaded Line and Point Contacts The book presents a robust combination of asymptotic and numerical techniques to solve EHL p
Asymptotic structure of isolated systems
The main methods to formulate asymptotic flatness conditions are introduced and motivation and basic ideas are emphasized. Any asymptotic flatness condition proposed up to now describes space-times which behave somehow like Minkowski space, and a very explicit exposition of the structure at infinity of Minkowski space is given. This structure is used to describe the asymptotic behaviour of fields on Minkowski space in a frame-dependent way. The definition of null infinity for curved space-time according to Penrose is given and attempts to define spacelike infinity are outlined. The conformal bundle approach to the formulation of asymptotic behaviour is described and its relation to null and spacelike infinity is given, as far as known. (Auth.)
Asymptotic algebra of quantum electrodynamics
Herdegen, Andrzej
2004-01-01
The Staruszkiewicz quantum model of the long-range structure in electrodynamics is reviewed in the form of a Weyl algebra. This is followed by a personal view on the asymptotic structure of quantum electrodynamics.
2012-07-31
This podcast is based on the August 2012 CDC Vital Signs report. While more adults are walking, only half get the recommended amount of physical activity. Listen to learn how communities, employers, and individuals may help increase walking. Created: 7/31/2012 by Centers for Disease Control and Prevention (CDC). Date Released: 8/7/2012.
Dertien, Edwin
2006-01-01
This paper describes the design and construction of Dribbel, a passivity-based walking robot. Dribbel has been designed and built at the Control Engineering group of the University of Twente. This paper focuses on the practical side: the design approach, construction, electronics, and software design. After a short introduction of dynamic walking, the design process, starting with simulation, is discussed.
Exponential asymptotics and gravity waves
Chapman, S. J.; Vanden-Broeck, J.
2006-01-01
The problem of irrotational inviscid incompressible free-surface flow is examined in the limit of small Froude number. Since this is a singular perturbation, singularities in the flow field (or its analytic continuation) such as stagnation points, or corners in submerged objects or on rough beds, lead to a divergent asymptotic expansion, with associated Stokes lines. Recent techniques in exponential asymptotics are employed to observe the switching on of exponentially small gravity waves acro...
Asymptotic behavior of atomic momentals
Thakkar, Ajit J.
1987-05-01
Knowledge of the large and small momentum transfer behavior of the electron momentum distribution is an important ingredient in the analysis of experimental isotropic Compton profiles. This behavior ultimately rests upon the asymptotic behavior of atomic momentals (momentum space orbitals). The small momentum Maclaurin expansion and the large momentum asymptotic expansion of atomic momentals with arbitrary angular momentum quantum number are derived in this paper. Their implications for momentum densities and Compton profiles are derived and discussed.
Camilleri, Elizabeth; Rohde, Peter P.; Twamley, Jason
2014-01-01
Quantum walks exhibit many unique characteristics compared to classical random walks. In the classical setting, self-avoiding random walks have been studied as a variation on the usual classical random walk. Classical self-avoiding random walks have found numerous applications, most notably in the modeling of protein folding. We consider the analogous problem in the quantum setting. We complement a quantum walk with a memory register that records where the walker has previously resided. The w...
Kokshenev, V B
2004-01-01
The problem of biped locomotion at steady speeds is discussed through the Lagrangian formulation developed for velocity-dependent, body driving forces. Human walking on a level surface is analyzed in terms of the data on the resultant ground-reaction force and the external work. It is shown that the trajectory of the human center of mass is due to a superposition of its rectilinear motion with a given speed V and a backward rotation along a shortened hypocycloid. A stiff-to-compliant crossover between walking gaits is established at mid speeds, which separate slow walking from fast walking, limited by V_{\\max}=3.4 m/s. Key words: locomotion, bipedalism, human, biomechanics, walking.
Cavagna, G. A.; Willems, P. A.; Heglund, N. C.
1998-06-01
Sometime in the near future humans may walk in the reduced gravity of Mars. Gravity plays an essential role in walking. On Earth, the body uses gravity to `fall forwards' at each step and then the forward speed is used to restore the initial height in a pendulum-like mechanism. When gravity is reduced, as on the Moon or Mars, the mechanism of walking must change. Here we investigate the mechanics of walking on Mars onboard an aircraft undergoing gravity-reducing flight profiles. The optimal walking speed on Mars will be 3.4 km h-1 (down from 5.5 km h-1 on Earth) and the work done per unit distance to move the centre of mass will be half that on Earth.
Conformal Phase Diagram of Complete Asymptotically Free Theories
Pica, Claudio; Sannino, Francesco
2016-01-01
We investigate the ultraviolet and infrared fixed point structure of gauge-Yukawa theories featuring a single gauge coupling, Yukawa coupling and scalar self coupling. Our investigations are performed using the two loop gauge beta function, one loop Yukawa beta function and one loop scalar beta function. We provide the general conditions that the beta function coefficients must abide for the theory to be completely asymptotically free while simultaneously possessing an infrared stable fixed point. We also uncover special trajectories in coupling space along which some couplings are both asymptotically safe and infrared conformal.
Quantum walks on simplicial complexes
Matsue, Kaname; Ogurisu, Osamu; Segawa, Etsuo
2016-05-01
We construct a new type of quantum walks on simplicial complexes as a natural extension of the well-known Szegedy walk on graphs. One can numerically observe that our proposing quantum walks possess linear spreading and localization as in the case of the Grover walk on lattices. Moreover, our numerical simulation suggests that localization of our quantum walks reflects not only topological but also geometric structures. On the other hand, our proposing quantum walk contains an intrinsic problem concerning exhibition of non-trivial behavior, which is not seen in typical quantum walks such as Grover walks on graphs.
Biomechanical analysis of rollator walking
Alkjaer, T; Larsen, Peter K; Pedersen, Gitte;
2006-01-01
The rollator is a very popular walking aid. However, knowledge about how a rollator affects the walking patterns is limited. Thus, the purpose of the study was to investigate the biomechanical effects of walking with and without a rollator on the walking pattern in healthy subjects.......The rollator is a very popular walking aid. However, knowledge about how a rollator affects the walking patterns is limited. Thus, the purpose of the study was to investigate the biomechanical effects of walking with and without a rollator on the walking pattern in healthy subjects....
Feng, Yuanhua; Yu, Keming
2006-01-01
A new multivariate random walk model with slowly changing parameters is introduced and investigated in detail. Nonparametric estimation of local covariance matrix is proposed. The asymptotic distributions, including asymptotic biases, variances and covariances of the proposed estimators are obtained. The properties of the estimated value of a weighted sum of individual nonparametric estimators are also studied in detail. The integrated effect of the estimation errors from the estimation for t...
Properties of Open Quantum Walks on $\\mathbb{Z}$
Sinayskiy, I.; Petruccione, F.
2014-01-01
A connection between the asymptotic behavior of the open quantum walk and the spectrum of a generalized quantum coins is studied. For the case of simultaneously diagonalizable transition operators an exact expression for probability distribution of the position of the walker for arbitrary number of steps is found. For a large number of steps the probability distribution consist of maximally two "soliton"-like solution and a certain number of Gaussian distributions. The number of different con...
Self-avoiding walks and polygons on quasiperiodic tilings
Rogers, A. N.; Richard, C.; Guttmann, A. J.
2003-01-01
We enumerate self-avoiding walks and polygons, counted by perimeter, on the quasiperiodic rhombic Penrose and Ammann-Beenker tilings, thereby considerably extending previous results. In contrast to similar problems on regular lattices, these numbers depend on the chosen start vertex. We compare different ways of counting and demonstrate that suitable averaging improves converge to the asymptotic regime. This leads to improved estimates for critical points and exponents, which support the conj...
Continuous-time random walk theory of superslow diffusion
Denisov, S. I.; Kantz, H.
2010-01-01
Superslow diffusion, i.e., the long-time diffusion of particles whose mean-square displacement (variance) grows slower than any power of time, is studied in the framework of the decoupled continuous-time random walk model. We show that this behavior of the variance occurs when the complementary cumulative distribution function of waiting times is asymptotically described by a slowly varying function. In this case, we derive a general representation of the laws of superslow diffusion for both ...
Global asymptotic stability for Hopfield-type neural networks with diffusion effects
YAN Xiang-ping; LI Wan-tong
2007-01-01
The existence, uniqueness and global asymptotic stability for the equilibrium of Hopfield-type neural networks with diffusion effects are studied. When the activation functions are monotonously nondecreasing, differentiable, and the interconnected matrix is related to the Lyapunov diagonal stable matrix, the sufficient conditions guaranteeing the existence of the equilibrium of the system are obtained by applying the topological degree theory. By means of constructing the suitable average Lyapunov functions, the global asymptotic stability of the equilibrium of the system is also investigated. It is shown that the equilibrium (if it exists) is globally asymptotically stable and this implies that the equilibrium of the system is unique.
Humanoid robot Lola: design and walking control.
Buschmann, Thomas; Lohmeier, Sebastian; Ulbrich, Heinz
2009-01-01
In this paper we present the humanoid robot LOLA, its mechatronic hardware design, simulation and real-time walking control. The goal of the LOLA-project is to build a machine capable of stable, autonomous, fast and human-like walking. LOLA is characterized by a redundant kinematic configuration with 7-DoF legs, an extremely lightweight design, joint actuators with brushless motors and an electronics architecture using decentralized joint control. Special emphasis was put on an improved mass distribution of the legs to achieve good dynamic performance. Trajectory generation and control aim at faster, more flexible and robust walking. Center of mass trajectories are calculated in real-time from footstep locations using quadratic programming and spline collocation methods. Stabilizing control uses hybrid position/force control in task space with an inner joint position control loop. Inertial stabilization is achieved by modifying the contact force trajectories. PMID:19665558
Durhuus, B; Wheater, J; Durhuus, Bergfinnur; Jonsson, Thordur; Wheater, John
2006-01-01
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.
Quantum graph walks I: mapping to quantum walks
Higuchi, Yusuke; Konno, Norio; Sato, Iwao; Segawa, Etsuo
2012-01-01
We clarify that coined quantum walk is determined by only the choice of local quantum coins. To do so, we characterize coined quantum walks on graph by disjoint Euler circles with respect to symmetric arcs. In this paper, we introduce a new class of coined quantum walk by a special choice of quantum coins determined by corresponding quantum graph, called quantum graph walk. We show that a stationary state of quantum graph walk describes the eigenfunction of the quantum graph.
Baez, J C; Egan, G F; Baez, John C.; Egan, Greg
2002-01-01
The Riemannian 10j symbols are spin networks that assign an amplitude to each 4-simplex in the Barrett-Crane model of Riemannian quantum gravity. This amplitude is a function of the areas of the 10 faces of the 4-simplex, and Barrett and Williams have shown that one contribution to its asymptotics comes from the Regge action for all non-degenerate 4-simplices with the specified face areas. However, we show numerically that the dominant contribution comes from degenerate 4-simplices. As a consequence, one can compute the asymptotics of the Riemannian 10j symbols by evaluating a `degenerate spin network', where the rotation group SO(4) is replaced by the Euclidean group of isometries of R^3. We conjecture formulas for the asymptotics of a large class of Riemannian and Lorentzian spin networks, including the Lorentzian 10j symbols, in terms of these degenerate spin networks.
Asymptotics for restricted integer compositions
Malandro, Martin E
2011-01-01
We study the compositions of an integer n where the part sizes of the compositions are restricted to lie in a finite set. We obtain asymptotic formulas for the number of such compositions, the total and average number of parts among all such compositions, and the total and average number of times a particular part size appears among all such compositions. Several of our asymptotics have the additional property that their absolute errors---not just their percentage errors---go to 0 as n goes to infinity. Along the way we also obtain recurrences and generating functions for calculating several of these quantities. Our asymptotic formulas come from the meromorphic analysis of our generating functions. Our results also apply to questions about certain kinds of tilings and rhythm patterns.
Asymptotic analysis and boundary layers
Cousteix, Jean
2007-01-01
This book presents a new method of asymptotic analysis of boundary-layer problems, the Successive Complementary Expansion Method (SCEM). The first part is devoted to a general comprehensive presentation of the tools of asymptotic analysis. It gives the keys to understand a boundary-layer problem and explains the methods to construct an approximation. The second part is devoted to SCEM and its applications in fluid mechanics, including external and internal flows. The advantages of SCEM are discussed in comparison with the standard Method of Matched Asymptotic Expansions. In particular, for the first time, the theory of Interactive Boundary Layer is fully justified. With its chapter summaries, detailed derivations of results, discussed examples and fully worked out problems and solutions, the book is self-contained. It is written on a mathematical level accessible to graduate and post-graduate students of engineering and physics with a good knowledge in fluid mechanics. Researchers and practitioners will estee...
Spiral structures in the rotor-router walk
Papoyan, Vl V.; Poghosyan, V. S.; Priezzhev, V. B.
2016-04-01
We study the rotor-router walk on the infinite square lattice with the outgoing edges at each lattice site ordered clockwise. In the previous paper (Papoyan et al 2015 J. Phys. A: Math. Theor. 48 285203), we considered the loops created by rotors and labeled the sites where the loops become closed. The sequence of labels in the rotor-router walk was conjectured to form a spiral structure asymptotically obeying an Archimedean property. In the present paper, we select a subset of labels called ‘nodes’ and consider the spirals formed by them. The new spirals are directly related to tree-like structures, which represent the evolution of the cluster of vertices visited by the walk. We show that the average number of visits to the origin by the moment t\\gg 1 is =4 +O(1) where is the average number of spiral rotations.
Single integrodifferential wave equation for a Lévy walk
Fedotov, Sergei
2016-02-01
We derive the single integrodifferential wave equation for the probability density function of the position of a classical one-dimensional Lévy walk with continuous sample paths. This equation involves a classical wave operator together with memory integrals describing the spatiotemporal coupling of the Lévy walk. It is valid at all times, not only in the long time limit, and it does not involve any large-scale approximations. It generalizes the well-known telegraph or Cattaneo equation for the persistent random walk with the exponential switching time distribution. Several non-Markovian cases are considered when the particle's velocity alternates at the gamma and power-law distributed random times. In the strong anomalous case we obtain the asymptotic solution to the integrodifferential wave equation. We implement the nonlinear reaction term of Kolmogorov-Petrovsky-Piskounov type into our equation and develop the theory of wave propagation in reaction-transport systems involving Lévy diffusion.
Usherwood, James Richard
2005-01-01
Bipedal walking following inverted pendulum mechanics is constrained by two requirements: sufficient kinetic energy for the vault over midstance and sufficient gravity to provide the centripetal acceleration required for the arc of the body about the stance foot. While the acceleration condition identifies a maximum walking speed at a Froude number of 1, empirical observation indicates favoured walk–run transition speeds at a Froude number around 0.5 for birds, humans and humans under manipul...
The Enumeration of Prudent Polygons by Area and its Unusual Asymptotics
Beaton, Nicholas R; Guttmann, Anthony J
2010-01-01
Prudent walks are special self-avoiding walks that never take a step towards an already occupied site, and \\emph{$k$-sided prudent walks} (with $k=1,2,3,4$) are, in essence, only allowed to grow along $k$ directions. Prudent polygons are prudent walks that return to a point adjacent to their starting point. Prudent walks and polygons have been previously enumerated by length and perimeter (Bousquet-M\\'elou, Schwerdtfeger; 2010). We consider the enumeration of \\emph{prudent polygons} by \\emph{area}. For the 3-sided variety, we find that the generating function is expressed in terms of a $q$-hypergeometric function, with an accumulation of poles towards the dominant singularity. This expression reveals an unusual asymptotic structure of the number of polygons of area $n$, where the critical exponent is the transcendental number $\\log_23$ and and the amplitude involves tiny oscillations. Based on numerical data, we also expect similar phenomena to occur for 4-sided polygons. The asymptotic methodology involves a...
Asymptotic risks of Viterbi segmentation
Kuljus, Kristi
2010-01-01
We consider the maximum likelihood (Viterbi) alignment of a hidden Markov model (HMM). In an HMM, the underlying Markov chain is usually hidden and the Viterbi alignment is often used as the estimate of it. This approach will be referred to as the Viterbi segmentation. The goodness of the Viterbi segmentation can be measured by several risks. In this paper, we prove the existence of asymptotic risks. Being independent of data, the asymptotic risks can be considered as the characteristics of the model that illustrate the long-run behavior of the Viterbi segmentation.
ASYMPTOTIC METHODS OF STATISTICAL CONTROL
Orlov A. I.
2014-10-01
Full Text Available Statistical control is a sampling control based on the probability theory and mathematical statistics. The article presents the development of the methods of statistical control in our country. It discussed the basics of the theory of statistical control – the plans of statistical control and their operational characteristics, the risks of the supplier and the consumer, the acceptance level of defectiveness and the rejection level of defectiveness. We have obtained the asymptotic method of synthesis of control plans based on the limit average output level of defectiveness. We have also developed the asymptotic theory of single sampling plans and formulated some unsolved mathematical problems of the theory of statistical control
Asymptotic perturbation theory of waves
Ostrovsky, Lev
2014-01-01
This book is an introduction to the perturbation theory for linear and nonlinear waves in dispersive and dissipative media. The main focus is on the direct asymptotic method which is based on the asymptotic expansion of the solution in series of one or more small parameters and demanding finiteness of the perturbations; this results in slow variation of the main-order solution. The method, which does not depend on integrability of basic equations, is applied to quasi-harmonic and non-harmonic periodic waves, as well as to localized waves such as solitons, kinks, and autowaves. The basic theor
Asymptotic freedom for nonrelativistic confinement
Some aspects of asymptotic freedom are discussed in the context of a simple two-particle nonrelativistic confining potential model. In this model, asymptotic freedom follows from the similarity of the free-particle and bound state radial wave functions at small distances and for the same angular momentum and the same large energy. This similarity, which can be understood using simple quantum mechanical arguments, can be used to show that the exact response function approaches that obtained when final state interactions are ignored. A method of calculating corrections to this limit is given, and explicit examples are given for the case of a harmonic oscillator
Comment on Asymptotically Safe Inflation
Tye, S -H Henry
2010-01-01
We comment on Weinberg's interesting analysis of asymptotically safe inflation (arXiv:0911.3165). We find that even if the gravity theory exhibits an ultraviolet fixed point, the energy scale during inflation is way too low to drive the theory close to the fixed point value. We choose the specific renormalization groupflow away from the fixed point towards the infrared region that reproduces the Newton's constant and today's cosmological constant. We follow this RG flow path to scales below the Planck scale to study the stability of the inflationary scenario. Again, we find that some fine tuning is necessary to get enough efolds of infflation in the asymptotically safe inflationary scenario.
Asymptotically free SU(5) models
The behaviour of Yukawa and Higgs effective charges of the minimal SU(5) unification model is investigated. The model includes ν=3 (or more, up to ν=7) generations of quarks and leptons and, in addition, the 24-plet of heavy fermions. A number of solutions of the renorm-group equations are found, which reproduce the known data about quarks and leptons and, due to a special choice of the coupling constants at the unification point are asymptotically free in all charges. The requirement of the asymptotical freedom leads to some restrictions on the masses of particles and on their mixing angles
Probability of walking in children with cerebral palsy in Europe
Beckung, E.; Hagberg, G.; Uldall, P.;
2008-01-01
OBJECTIVES: The purpose of this work was to describe walking ability in children with cerebral palsy from the Surveillance of Cerebral Palsy in Europe common database through 21 years and to examine the association between walking ability and predicting factors. PATIENTS AND METHODS: Anonymous data...... on 10042 children with cerebral palsy born between 1976 and 1996 were gathered from 14 European centers; 9012 patients were eligible for the analyses. RESULTS: Unaided walking as the primary way of walking at 5 years of age was reported for 54%, walking with assistive devices was reported for 16......: The collaboration Surveillance of Cerebral Palsy in Europe provides a powerful means of monitoring trends in cerebral palsy and its functional consequences. The proportion of nonwalking in children with cerebral palsy seems to be rather stable over years and across centers despite the changes that...
Chiral fermions in asymptotically safe quantum gravity
Meibohm, J.; Pawlowski, J. M.
2016-05-01
We study the consistency of dynamical fermionic matter with the asymptotic safety scenario of quantum gravity using the functional renormalisation group. Since this scenario suggests strongly coupled quantum gravity in the UV, one expects gravity-induced fermion self-interactions at energies of the Planck scale. These could lead to chiral symmetry breaking at very high energies and thus to large fermion masses in the IR. The present analysis which is based on the previous works (Christiansen et al., Phys Rev D 92:121501, 2015; Meibohm et al., Phys Rev D 93:084035, 2016), concludes that gravity-induced chiral symmetry breaking at the Planck scale is avoided for a general class of NJL-type models. We find strong evidence that this feature is independent of the number of fermion fields. This finding suggests that the phase diagram for these models is topologically stable under the influence of gravitational interactions.
The broken supersymmetry phase of a self-avoiding random walk
We consider a weakly self-avoiding random walk on a hierarchical lattice in d = 4 dimensions. We show that for choices of the killing rate a less than the critical value ac the dominant walks fill space, which corresponds to a spontaneously broken supersymmetry phase. We identify the asymptotic density to which walks fill space, ρ(a), to be a supersymmetric order parameter for this transition. We prove that ρ(a) ∼ (ac - a) (-log(ac -a))1/2 as a → ac, which is mean-field behavior with logarithmic corrections, as expected for a system in its upper critical dimension. (orig.)
Asymptotics of weighted random sums
Corcuera, José Manuel; Nualart, David; Podolskij, Mark
2014-01-01
In this paper we study the asymptotic behaviour of weighted random sums when the sum process converges stably in law to a Brownian motion and the weight process has continuous trajectories, more regular than that of a Brownian motion. We show that these sums converge in law to the integral of the...
Ruin problems and tail asymptotics
Rønn-Nielsen, Anders
The thesis Ruin Problems and Tail Asymptotics provides results on ruin problems for several classes of Markov processes. For a class of diffusion processes with jumps an explicit expression for the joint Laplace transform of the first passage time and the corresponding undershoot is derived. An...
Asymptotic expansions of Jacobi functions
The author presents an asymptotic expansion of the Jacobi polynomials which is based on the fact, that these polynomials are special hypergeometric functions. He uses an integral representation of these functions and expands the integrand in a power series. He derives explicit error bounds on this expansion. (HSI)
Thermodynamics of asymptotically safe theories
Rischke, Dirk H.; Sannino, Francesco
2015-01-01
We investigate the thermodynamic properties of a novel class of gauge-Yukawa theories that have recently been shown to be completely asymptotically safe, because their short-distance behaviour is determined by the presence of an interacting fixed point. Not only do all the coupling constants freeze...
Unitary equivalence of quantum walks
Highlights: • We have found unitary equivalent classes in coined quantum walks. • A single parameter family of coin operators is sufficient to realize all simple one-dimensional quantum walks. • Electric quantum walks are unitarily equivalent to time dependent quantum walks. - Abstract: A simple coined quantum walk in one dimension can be characterized by a SU(2) operator with three parameters which represents the coin toss. However, different such coin toss operators lead to equivalent dynamics of the quantum walker. In this manuscript we present the unitary equivalence classes of quantum walks and show that all the nonequivalent quantum walks can be distinguished by a single parameter. Moreover, we argue that the electric quantum walks are equivalent to quantum walks with time dependent coin toss operator
Borel type bounds for the self-avoiding walk connective constant
Graham, B T
2009-01-01
Let $\\mu$ be the self-avoiding walk connective constant on $\\ZZ^d$. We show that the asymptotic expansion for $\\beta_c=1/\\mu$ in powers of $1/(2d)$ satisfies Borel type bounds. This supports the conjecture that the expansion is Borel summable.
Borel-type bounds for the self-avoiding walk connective constant
Let μ be the self-avoiding walk connective constant on Zd. We show that the asymptotic expansion for βc = 1/μ in powers of 1/(2d) satisfies Borel-type bounds. This supports the conjecture that the expansion is Borel summable.
On Asymptotically Efficient Estimation in Semiparametric Models
Schick, Anton
1986-01-01
A general method for the construction of asymptotically efficient estimates in semiparametric models is presented. It improves and modifies Bickel's (1982) construction of adaptive estimates and obtains asymptotically efficient estimates under conditions weaker than those in Bickel.
On transfinite extension of asymptotic dimension
Radul, Taras
2006-01-01
We prove that a transfinite extension of asymptotic dimension asind is trivial. We introduce a transfinite extension of asymptotic dimension asdim and give an example of metric proper space which has transfinite infinite dimension.
Biomechanical conditions of walking
Fan, Y F; Luo, L P; Li, Z Y; Han, S Y; Lv, C S; Zhang, B
2015-01-01
The development of rehabilitation training program for lower limb injury does not usually include gait pattern design. This paper introduced a gait pattern design by using equations (conditions of walking). Following the requirements of reducing force to the injured side to avoid further injury, we developed a lower limb gait pattern to shorten the stride length so as to reduce walking speed, to delay the stance phase of the uninjured side and to reduce step length of the uninjured side. This gait pattern was then verified by the practice of a rehabilitation training of an Achilles tendon rupture patient, whose two-year rehabilitation training (with 24 tests) has proven that this pattern worked as intended. This indicates that rehabilitation training program for lower limb injury can rest on biomechanical conditions of walking based on experimental evidence.
Vestergaard, Maria Quvang Harck; Olesen, Mette; Helmer, Pernille Falborg
2014-01-01
’ of mobility (Jensen 2013:111) such as the urban environment, and the infrastructures. Walking has indeed also a ‘software dimension’ as an embodied performance that trigger the human senses (Jensen 2013) and which is closely related to the habitus and identity of the individual (Halprin 1963). The...... individual perception of ‘walkability’ is based upon a subjective judgement of different physical factors, such as sidewalk width, traffic volumes and building height (Ewing and Handy 2009:67). And iIn order to understand the act of walking it is therefore necessary to create a vocabulary to understand how...... and why the individuals evaluate, interpret and act (Bourdieu 1984), and how this affects their choice to walk. Therefore it could be questioned if whether an assessment of the physical environment is sufficient to identify all the factors that influence the individual perception of ‘walkability’, or...
Quantum walk on the line: entanglement and non-local initial conditions
Abal, G; Donangelo, R; Romanelli, A
2005-01-01
The conditional shift in the evolution operator of a quantum walk generates entanglement between the coin and position degrees of freedom. This entanglement can be quantified by the von Neumman entropy of the reduced density operator (entropy of entanglement). We show analytically that for a Hadamard walk with local initial conditions the asymptotic entanglement is 0.872, as was recently noted in [1]. When non-local initial conditions are considered, the asymptotic value of entanglement varies smoothly between allmost complete entanglement and a minimum of 0.661. An exact expression for the asymptotic (long-time) entanglement is obtained for initial conditions in the position subspace spanned by |+1> and |-1>.
Asymptotic functions and multiplication of distributions
Considered is a new type of generalized asymptotic functions, which are not functionals on some space of test functions as the Schwartz distributions. The definition of the generalized asymptotic functions is given. It is pointed out that in future the particular asymptotic functions will be used for solving some topics of quantum mechanics and quantum theory
Asymptotic structure of isolated systems
I discuss the general ideas underlying the subject of ''asymptotics'' in general relativity and describe the current status of the concepts resulting from these ideas. My main concern will be the problem of consistency. By this I mean the question as to whether the geometric assumptions inherent in these concepts are compatible with the dynamics of the theory, as determined by Einstein's equations. This rather strong bias forces me to leave untouched several issues related to asymptotics, discussed in the recent literature, some of which are perhaps thought equally, or more important, by other workers in the field. In addition I shall, for coherence of presentation, mainly consider Einstein's equations in vacuo. When attention is confined to small neighbourhoods of null and spacelike infinity, this restriction is not important, but is surely relevant for more global issues. (author)
Asymptotic safety goes on shell
It is well known in quantum field theory that the off-shell effective action depends on the gauge choice and field parametrization used in calculating it. Nevertheless, the typical scheme in which the scenario of asymptotically safe gravity is investigated is an off-shell version of the functional renormalization group equation. Working with the Einstein-Hilbert truncation as a test bed, we develop a new scheme for the analysis of asymptotically safe gravity in which the on-shell part of the effective action is singled out and we show that the beta function for the essential coupling has no explicit gauge dependence. In order to reach our goal, we introduce several technical novelties, including a different decomposition of the metric fluctuations, a new implementation of the ghost sector and a new cut-off scheme. We find a nontrivial fixed point, with a value of the cosmological constant that is independent of the gauge-fixing parameters. (paper)
Asymptotic safety goes on shell
Benedetti, Dario
2012-01-01
It is well known in quantum field theory that the off-shell effective action depends on the gauge choice and field parametrization used in calculating it. Nevertheless, the typical scheme in which the scenario of asymptotically safe gravity is investigated is an off-shell version of the functional renormalization group equation. Working with the Einstein-Hilbert truncation as a test bed, we develop a new scheme for the analysis of asymptotically safe gravity in which the on-shell part of the effective action is singled out and we show that the beta function for the essential coupling has no explicit gauge dependence. In order to reach our goal, we introduce several technical novelties, including a different decomposition of the metric fluctuations, a new implementation of the ghost sector and a new cut-off scheme. We find a nontrivial fixed point, with a value of the cosmological constant that is independent of the gauge-fixing parameters.
Asymptotic analysis of Hoppe trees
Leckey, Kevin
2012-01-01
We introduce and analyze a random tree model associated to Hoppe's urn. The tree is built successively by adding nodes to the existing tree when starting with the single root node. In each step a node is added to the tree as a child of an existing node where these parent nodes are chosen randomly with probabilities proportional to their weights. The root node has weight $\\vartheta>0$, a given fixed parameter, all other nodes have weight 1. This resembles the stochastic dynamic of Hoppe's urn. For $\\vartheta=1$ the resulting tree is the well-studied random recursive tree. We analyze the height, internal path length and number of leaves of the Hoppe tree with $n$ nodes as well as the depth of the last inserted node asymptotically as $n\\to \\infty$. Mainly expectations, variances and asymptotic distributions of these parameters are derived.
Asymptotic Excisions of Metric Spaces and Ideals of Asymptotic Coarse Roe Algebras
LI Jin-xiu; WANG Qin
2006-01-01
We introduce in this note the notions of asymptotic excision of proper metric spaces and asymptotic equivalence relation for subspaces of metric spaces, which are relevant in characterizing spatial ideals of the asymptotic coarse Roe algebras. We show that the lattice of the asymptotic equivalence classes of the subspaces of a proper metric space is isomorphic to the lattice of the spatial ideals of the asymptotic Roe algebra. For asymptotic excisions of the metric space, we also establish a Mayer-Vietoris sequence in K-theory of the asymptotic coarse Roe algebras.
Exponential asymptotics and capillary waves
Chapman, S. J.; Vanden-Broeck, J.
2002-01-01
Recently developed techniques in exponential asymptotics beyond all orders are employed on the problem of potential flows with a free surface and small surface tension, in the absence of gravity. Exponentially small capillary waves are found to be generated on the free surface where the equipotentials from singularities in the flow (for example, stagnation points and corners) meet it. The amplitude of these waves is determined, and the implications are considered for many quite general flows....
Asymptotic safety: A simple example
We use the Gross-Neveu model in 2f expansion where the model is known to be renormalizable to all orders. In this limit, the fixed-point action as well as all universal critical exponents can be computed analytically. As asymptotic safety has become an important scenario for quantizing gravity, our description of a well-understood model is meant to provide for an easily accessible and controllable example of modern nonperturbative quantum field theory.
Slow walking model for children with multiple disabilities via an application of humanoid robot
Wang, ZeFeng; Peyrodie, Laurent; Cao, Hua; Agnani, Olivier; Watelain, Eric; Wang, HaoPing
2016-02-01
Walk training research with children having multiple disabilities is presented. Orthosis aid in walking for children with multiple disabilities such as Cerebral Palsy continues to be a clinical and technological challenge. In order to reduce pain and improve treatment strategies, an intermediate structure - humanoid robot NAO - is proposed as an assay platform to study walking training models, to be transferred to future special exoskeletons for children. A suitable and stable walking model is proposed for walk training. It would be simulated and tested on NAO. This comparative study of zero moment point (ZMP) supports polygons and energy consumption validates the model as more stable than the conventional NAO. Accordingly direction variation of the center of mass and the slopes of linear regression knee/ankle angles, the Slow Walk model faithfully emulates the gait pattern of children.
Clisby, Nathan
2013-01-01
We introduce a self-avoiding walk model for which end-effects are completely eliminated. We enumerate the number of these walks for various lattices in dimensions two and three, and use these enumerations to study the properties of this model. We find that endless self-avoiding walks have the same connective constant as self-avoiding walks, and the same Flory exponent $\
Walking and Sensing Mobile Lives
Bødker, Mads; Meinhardt, Nina Dam
In this position paper, we discuss how mindful walking with people allow us to explore sensory aspects of mobile lives that are typically absent from research. We present an app that aids researchers collect impressions from a walk.......In this position paper, we discuss how mindful walking with people allow us to explore sensory aspects of mobile lives that are typically absent from research. We present an app that aids researchers collect impressions from a walk....
Walking - Sensing - Participation
Bødker, Mads; Meinhardt, Nina Dam; Browning, David
Building on ethnographic research and social theory in the field of ‘mobilities’, this workshop paper suggests that field work based on simply walking with people entails a form of embodied participation that informs technological interventions by creating a space within which to address a wider...
Rasmussen, Mattias Borg
2014-01-01
Steep slopes, white peaks and deep valleys make up the Andes. As phenomenologists of landscape have told us, different people have different landscapes. By moving across the terrain, walking along, we might get a sense of how this has been carved out by the movement of wind and water, tectonics...
Bødker, Mads; Browning, David; Meinhardt, Nina Dam
We suggest that ‘walking’ in ethnographic work sensitizes researchers to a particular means of making sense of place. Following a brief conceptual exposition, we present our research tool iMaCam) that supports capturing and representing activities such as walking....
Frandsen, Mads Toudal
2007-01-01
I report on our construction and analysis of the effective low energy Lagrangian for the Minimal Walking Technicolor (MWT) model. The parameters of the effective Lagrangian are constrained by imposing modified Weinberg sum rules and by imposing a value for the S parameter estimated from the...
Asymptotic algebra for charged particles and radiation
A C*-algebra of asymptotic fields which properly describes the infrared structure in quantum electrodynamics is proposed. The algebra is generated by the null asymptotic of electromagnetic field and the time asymptotic of charged matter fields which incorporate the corresponding Coulomb fields. As a consequence Gauss' law is satisfied in the algebraic setting. Within this algebra the observables can be identified by the principle of gauge invariance. A class of representations of the asymptotic algebra is constructed which resembles the Kulish-Faddeev treatment of electrically charged asymptotic fields. (orig.)
Cooper, Colin; Frieze, Alan
The aim of this article is to discuss some of the notions and applications of random walks on finite graphs, especially as they apply to random graphs. In this section we give some basic definitions, in Section 2 we review applications of random walks in computer science, and in Section 3 we focus on walks in random graphs.
Anthony J. Guttmann
2008-09-01
Full Text Available We have produced extended series for prudent self-avoiding walks on the square lattice. These are subsets of self-avoiding walks. We conjecture the exact growth constant and critical exponent for the walks, and show that the (anisotropic generating function is almost certainly not differentiably-finite.
Guttmann, Anthony J.; Dethridge, John C.
2008-01-01
We have produced extended series for prudent self-avoiding walks on the square lattice. These are subsets of self-avoiding walks. We conjecture the exact growth constant and critical exponent for the walks, and show that the (anisotropic) generating function is almost certainly not differentiably-finite.
Models of Walking Technicolor on the Lattice
Sinclair, D K
2014-01-01
We study QCD with 2 colour-sextet quarks as a walking-Technicolor candidate. As such it provides a description of the Higgs sector of the standard model, in which the Higgs field is replaced by the Goldstone `pions' of this QCD-like theory, and the Higgs itself is the $\\sigma$. Such a theory will need to be extended if it is to also give masses to the quarks and leptons. What we are attempting to determine is whether it is indeed QCD-like and hence walking, or if it has an infrared fixed point making it a conformal field theory. We do this by simulating its lattice version at finite temperature and observing the running of the bare (lattice) coupling at the chiral transition, as the lattice spacing is varied, and comparing this running with that predicted by 2-loop perturbation theory. Our results on lattices with temporal extents ($N_t$) up to 12 indicate that the coupling runs, but not as fast as asymptotic freedom predicts. We discuss our program for studying the zero-temperature phenomenology of this theo...
Scaling of Hamiltonian walks on fractal lattices.
Elezović-Hadzić, Suncica; Marcetić, Dusanka; Maletić, Slobodan
2007-07-01
We investigate asymptotical behavior of numbers of long Hamiltonian walks (HWs), i.e., self-avoiding random walks that visit every site of a lattice, on various fractal lattices. By applying an exact recursive technique we obtain scaling forms for open HWs on three-simplex lattice, Sierpinski gasket, and their generalizations: Given-Mandelbrot (GM), modified Sierpinski gasket (MSG), and n -simplex fractal families. For GM, MSG and n -simplex lattices with odd values of n , the number of open HWs Z(N), for the lattice with N>1 sites, varies as omega(N)}N(gamma). We explicitly calculate the exponent gamma for several members of GM and MSG families, as well as for n-simplices with n=3, 5, and 7. For n-simplex fractals with even n we find different scaling form: Z(N) approximately omega(N)mu(N1/d(f), where d(f) is the fractal dimension of the lattice, which also differs from the formula expected for homogeneous lattices. We discuss possible implications of our results on studies of real compact polymers. PMID:17677410
Walking Algorithm of Humanoid Robot on Uneven Terrain with Terrain Estimation
Jiang Yi; Qiuguo Zhu; Rong Xiong; Jun Wu
2016-01-01
Humanoid robots are expected to achieve stable walking on uneven terrains. In this paper, a control algorithm for humanoid robots walking on previously unknown terrains with terrain estimation is proposed, which requires only minimum modification to the original walking gait. The swing foot trajectory is redesigned to ensure that the foot lands at the desired horizontal positions under various terrain height. A compliant terrain adaptation method is applied to the landing foot to achieve a fi...
[Walking abnormalities in children].
Segawa, Masaya
2010-11-01
Walking is a spontaneous movement termed locomotion that is promoted by activation of antigravity muscles by serotonergic (5HT) neurons. Development of antigravity activity follows 3 developmental epochs of the sleep-wake (S-W) cycle and is modulated by particular 5HT neurons in each epoch. Activation of antigravity activities occurs in the first epoch (around the age of 3 to 4 months) as restriction of atonia in rapid eye movement (REM) stage and development of circadian S-W cycle. These activities strengthen in the second epoch, with modulation of day-time sleep and induction of crawling around the age of 8 months and induction of walking by 1 year. Around the age of 1 year 6 months, absence of guarded walking and interlimb cordination is observed along with modulation of day-time sleep to once in the afternoon. Bipedal walking in upright position occurs in the third epoch, with development of a biphasic S-W cycle by the age of 4-5 years. Patients with infantile autism (IA), Rett syndrome (RTT), or Tourette syndrome (TS) show failure in the development of the first, second, or third epoch, respectively. Patients with IA fail to develop interlimb coordination; those with RTT, crawling and walking; and those with TS, walking in upright posture. Basic pathophysiology underlying these condition is failure in restricting atonia in REM stage; this induces dysfunction of the pedunculopontine nucleus and consequently dys- or hypofunction of the dopamine (DA) neurons. DA hypofunction in the developing brain, associated with compensatory upward regulation of the DA receptors causes psychobehavioral disorders in infancy (IA), failure in synaptogenesis in the frontal cortex and functional development of the motor and associate cortexes in late infancy through the basal ganglia (RTT), and failure in functional development of the prefrontal cortex through the basal ganglia (TS). Further, locomotion failure in early childhood causes failure in development of functional
Fractional random walk lattice dynamics
Michelitsch, Thomas; Riascos, Alejandro Perez; Nowakowski, Andrzeij; Nicolleau, Franck
2016-01-01
We analyze time-discrete and continuous `fractional' random walks on undirected regular networks with special focus on cubic periodic lattices in $n=1,2,3,..$ dimensions.The fractional random walk dynamics is governed by a master equation involving {\\it fractional powers of Laplacian matrices $L^{\\frac{\\alpha}{2}}$}where $\\alpha=2$ recovers the normal walk.First we demonstrate thatthe interval $0\\textless{}\\alpha\\leq 2$ is admissible for the fractional random walk. We derive analytical expressions for fractional transition matrix and closely related the average return probabilities. We further obtain thefundamental matrix $Z^{(\\alpha)}$, and the mean relaxation time (Kemeny constant) for the fractional random walk.The representation for the fundamental matrix $Z^{(\\alpha)}$ relates fractional random walks with normal random walks.We show that the fractional transition matrix elements exihibit for large cubic $n$-dimensional lattices a power law decay of an $n$-dimensional infinite spaceRiesz fractional deriva...
Asymptotic black hole quasinormal frequencies
Motl, Lubos; Neitzke, Andrew
2003-01-01
We give a new derivation of the quasinormal frequencies of Schwarzschild black holes in d greater than or equal to 4 and Reissner-Nordstrom black holes in d = 4, in the limit of infinite damping. For Schwarzschild in d greater than or equal to 4 we find that the asymptotic real part is THawkinglog(3) for scalar perturbations and for some gravitational perturbations; this confirms a result previously obtained by other means in the case d = 4. For Reissner-Nordstrom in d = 4 w...
Asymptotics of robust utility maximization
Knispel, Thomas
2012-01-01
For a stochastic factor model we maximize the long-term growth rate of robust expected power utility with parameter $\\lambda\\in(0,1)$. Using duality methods the problem is reformulated as an infinite time horizon, risk-sensitive control problem. Our results characterize the optimal growth rate, an optimal long-term trading strategy and an asymptotic worst-case model in terms of an ergodic Bellman equation. With these results we propose a duality approach to a "robust large deviations" criterion for optimal long-term investment.
Asymptotics for Associated Random Variables
Oliveira, Paulo Eduardo
2012-01-01
The book concerns the notion of association in probability and statistics. Association and some other positive dependence notions were introduced in 1966 and 1967 but received little attention from the probabilistic and statistics community. The interest in these dependence notions increased in the last 15 to 20 years, and many asymptotic results were proved and improved. Despite this increased interest, characterizations and results remained essentially scattered in the literature published in different journals. The goal of this book is to bring together the bulk of these results, presenting
Böttcher, S
1997-01-01
Aging refers to the property of two-time correlation functions to decay very slowly on (at least) two time scales. This phenomenon has gained recent attention due to experimental observations of the history dependent relaxation behavior in amorphous materials (``Glasses'') which pose a challenge to theorist. Aging signals the breaking of time-translational invariance and the violation of the fluctuation dissipation theorem during the relaxation process. But while the origin of aging in disordered media is profound, and the discussion is clad in the language of a well-developed theory, systems as simple as a random walk near a wall can exhibit aging. Such a simple walk serves well to illustrate the phenomenon and some of the physics behind it.
Fujie, Futaba
2014-01-01
Covering Walks in Graphs is aimed at researchers and graduate students in the graph theory community and provides a comprehensive treatment on measures of two well studied graphical properties, namely Hamiltonicity and traversability in graphs. This text looks into the famous Kӧnigsberg Bridge Problem, the Chinese Postman Problem, the Icosian Game and the Traveling Salesman Problem as well as well-known mathematicians who were involved in these problems. The concepts of different spanning walks with examples and present classical results on Hamiltonian numbers and upper Hamiltonian numbers of graphs are described; in some cases, the authors provide proofs of these results to illustrate the beauty and complexity of this area of research. Two new concepts of traceable numbers of graphs and traceable numbers of vertices of a graph which were inspired by and closely related to Hamiltonian numbers are introduced. Results are illustrated on these two concepts and the relationship between traceable concepts and...
Fitness Club
2015-01-01
Four classes of one hour each are held on Tuesdays. RDV barracks parking at Entrance A, 10 minutes before class time. Spring Course 2015: 05.05/12.05/19.05/26.05 Prices 40 CHF per session + 10 CHF club membership 5 CHF/hour pole rental Check out our schedule and enroll at: https://espace.cern.ch/club-fitness/Lists/Nordic%20Walking/NewForm.aspx? Hope to see you among us! fitness.club@cern.ch
Sugar, Thomas G.; Hollander, Kevin W.; Hitt, Joseph K.
2011-04-01
Developing bionic ankles poses great challenges due to the large moment, power, and energy that are required at the ankle. Researchers have added springs in series with a motor to reduce the peak power and energy requirements of a robotic ankle. We developed a "robotic tendon" that reduces the peak power by altering the required motor speed. By changing the required speed, the spring acts as a "load variable transmission." If a simple motor/gearbox solution is used, one walking step would require 38.8J and a peak motor power of 257 W. Using an optimized robotic tendon, the energy required is 21.2 J and the peak motor power is reduced to 96.6 W. We show that adding a passive spring in parallel with the robotic tendon reduces peak loads but the power and energy increase. Adding a passive spring in series with the robotic tendon reduces the energy requirements. We have built a prosthetic ankle SPARKy, Spring Ankle with Regenerative Kinetics, that allows a user to walk forwards, backwards, ascend and descend stairs, walk up and down slopes as well as jog.
Asymptotic black hole quasinormal frequencies
Motl, L; Motl, Lubos; Neitzke, Andrew
2003-01-01
We give a simple derivation of the quasinormal frequencies of Schwarzschild black holes in d>=4 and non-extremal Reissner-Nordstrom black holes in d=4, in the limit of infinite damping. For Schwarzschild in d=4 the asymptotic real part of the frequency is (T_Hawking)log(1+2cos(pi.j)), where j is the spin of the perturbation; this confirms a result previously obtained by other means. For Schwarzschild in d>4 we find that the asymptotic real part is (T_Hawking)log(3) for scalar perturbations. For non-extremal Reissner-Nordstrom in d=4 we find a specific but generally aperiodic behavior for the quasinormal frequencies, both for scalar perturbations and for axial electromagnetic-gravitational perturbations; there is nevertheless a hint that the value (T_Hawking)log(2) may be special in this case. The formulae are obtained by studying the monodromy of the perturbation analytically continued to the complex plane.
Asymptotically Free Gauge Theories. I
Wilczek, Frank; Gross, David J.
1973-07-01
Asymptotically free gauge theories of the strong interactions are constructed and analyzed. The reasons for doing this are recounted, including a review of renormalization group techniques and their application to scaling phenomena. The renormalization group equations are derived for Yang-Mills theories. The parameters that enter into the equations are calculated to lowest order and it is shown that these theories are asymptotically free. More specifically the effective coupling constant, which determines the ultraviolet behavior of the theory, vanishes for large space-like momenta. Fermions are incorporated and the construction of realistic models is discussed. We propose that the strong interactions be mediated by a "color" gauge group which commutes with SU(3)xSU(3). The problem of symmetry breaking is discussed. It appears likely that this would have a dynamical origin. It is suggested that the gauge symmetry might not be broken, and that the severe infrared singularities prevent the occurrence of non-color singlet physical states. The deep inelastic structure functions, as well as the electron position total annihilation cross section are analyzed. Scaling obtains up to calculable logarithmic corrections, and the naive lightcone or parton model results follow. The problems of incorporating scalar mesons and breaking the symmetry by the Higgs mechanism are explained in detail.
The maximum drag reduction asymptote
Choueiri, George H.; Hof, Bjorn
2015-11-01
Addition of long chain polymers is one of the most efficient ways to reduce the drag of turbulent flows. Already very low concentration of polymers can lead to a substantial drag and upon further increase of the concentration the drag reduces until it reaches an empirically found limit, the so called maximum drag reduction (MDR) asymptote, which is independent of the type of polymer used. We here carry out a detailed experimental study of the approach to this asymptote for pipe flow. Particular attention is paid to the recently observed state of elasto-inertial turbulence (EIT) which has been reported to occur in polymer solutions at sufficiently high shear. Our results show that upon the approach to MDR Newtonian turbulence becomes marginalized (hibernation) and eventually completely disappears and is replaced by EIT. In particular, spectra of high Reynolds number MDR flows are compared to flows at high shear rates in small diameter tubes where EIT is found at Re Marie Curie Actions) of the European Union's Seventh Framework Programme (FP7/2007-2013) under REA grant agreement n° [291734].
Asymptotic safety goes on shell
Benedetti, Dario
2011-01-01
It is well known in quantum field theory that the off-shell effective action depends on the gauge choice and field parametrization used in calculating it. Nevertheless, the typical scheme in which the scenario of asymptotically safe gravity is investigated is an off-shell version of the functional renormalization group equation. Working with the Einstein-Hilbert truncation as a test bed, we develop a new scheme for the analysis of asymptotically safe gravity in which the on-shell part of the effective action is singled out and we show that the beta function for the essential coupling has no explicit gauge-dependence. In order to reach our goal, we introduce several technical novelties, including a different decomposition of the metric fluctuations, a new implementation of the ghost sector, and a new cut-off scheme. We find a non-trivial fixed point, with a value of the cosmological constant which is independent of the gauge-fixing parameters.
Linearly Bounded Liars, Adaptive Covering Codes, and Deterministic Random Walks
Cooper, Joshua N
2009-01-01
We analyze a deterministic form of the random walk on the integer line called the {\\em liar machine}, similar to the rotor-router model, finding asymptotically tight pointwise and interval discrepancy bounds versus random walk. This provides an improvement in the best-known winning strategies in the binary symmetric pathological liar game with a linear fraction of responses allowed to be lies. Equivalently, this proves the existence of adaptive binary block covering codes with block length $n$, covering radius $\\leq fn$ for $f\\in(0,1/2)$, and cardinality $O(\\sqrt{\\log \\log n}/(1-2f))$ times the sphere bound $2^n/\\binom{n}{\\leq \\lfloor fn\\rfloor}$.
Free Dirac evolution as a quantum random walk
Bracken, A J; Smyrnakis, I
2006-01-01
Any positive-energy state of a free Dirac particle that is initially highly-localized, evolves in time by spreading at speeds close to the speed of light. This general phenomenon is explained by the fact that the Dirac evolution can be approximated arbitrarily closely by a quantum random walk, where the roles of coin and walker systems are naturally attributed to the spin and position degrees of freedom of the particle. Initially entangled and spatially localized spin-position states evolve with asymptotic two-horned distributions of the position probability, familiar from earlier studies of quantum walks. For the Dirac particle, the two horns travel apart at close to the speed of light.
An essential distinction in the relaization of the PCAC dynamics in asymptotically free and non-asymptotically free (with a non-trivial ultraviolet-stable fixed point) gauge theories is revealed. For the latter theories an analytical expressions for the condensate is obtained in the two-loop approximation and arguments of support of a soft behaviour at small distances of composite operators are given. The problem of factorizing the low-energy region for the Wess-Zumino-Witten action is discussed. Besides, the mass relations for pseudoscalar mesons in arbitrary Θ-sector are obtained in the first order in fermion bare masses and the impossibility for spontaneous P and CP-symmetries breaking in vector-like gauge theories at Θ=0 is shown
Counting self-avoiding walks on free products of graphs
Gilch, Lorenz A.; Müller, Sebastian
2015-01-01
The connective constant $\\mu(G)$ of a graph $G$ is the asymptotic growth rate of the number $\\sigma_{n}$ of self-avoiding walks of length $n$ in $G$ from a given vertex. We prove a formula for the connective constant for free products of quasi-transitive graphs and show that $\\sigma_{n}\\sim A_{G} \\mu(G)^{n}$ for some constant $A_{G}$ that depends on $G$. In the case of finite products $\\mu(G)$ can be calculated explicitly and is shown to be an algebraic number.
Fractional telegrapher's equation from fractional persistent random walks
Masoliver, Jaume
2016-05-01
We generalize the telegrapher's equation to allow for anomalous transport. We derive the space-time fractional telegrapher's equation using the formalism of the persistent random walk in continuous time. We also obtain the characteristic function of the space-time fractional process and study some particular cases and asymptotic approximations. Similarly to the ordinary telegrapher's equation, the time-fractional equation also presents distinct behaviors for different time scales. Specifically, transitions between different subdiffusive regimes or from superdiffusion to subdiffusion are shown by the fractional equation as time progresses.
Asymptotic conservation laws in field theory
Anderson, Ian M.; Torre, Charles G.
1996-01-01
A new, general, field theoretic approach to the derivation of asymptotic conservation laws is presented. In this approach asymptotic conservation laws are constructed directly from the field equations according to a universal prescription which does not rely upon the existence of Noether identities or any Lagrangian or Hamiltonian formalisms. The resulting general expressions of the conservation laws enjoy important invariance properties and synthesize all known asymptotic conservation...
Asymptotically Plane Wave Spacetimes and their Actions
Witt, Julian Le; Ross, Simon F.
2008-01-01
We propose a definition of asymptotically plane wave spacetimes in vacuum gravity in terms of the asymptotic falloff of the metric, and discuss the relation to previously constructed exact solutions. We construct a well-behaved action principle for such spacetimes, using the formalism developed by Mann and Marolf. We show that this action is finite on-shell and that the variational principle is well-defined for solutions of vacuum gravity satisfying our asymptotically plane wave falloff condi...
Asymptotics of near unit roots (in Russian)
Stanislav Anatolyev; Nikolay Gospodinov
2012-01-01
Sometimes the conventional asymptotic theory yields that the limiting distribution changes discontinuously, or that the asymptotic distribution does not approximate accurately the actual finite-sample distribution. In such situations one finds useful an asymptotic tool of drifting parameterizations where certain parameters are allowed to depend explicitly on the sample size. It proves useful, among other things, for impulse response analysis and forecasting of strongly dependent processes at ...
Asymptotic independence and a network traffic model
Maulik, Krishanu; Resnick, Sidney; Rootzén, Holger
2002-01-01
The usual concept of asymptotic independence, as discussed in the context of extreme value theory, requires the distribution of the coordinatewise sample maxima under suitable centering and scaling to converge to a product measure. However, this definition is too broad to conclude anything interesting about the tail behavior of the product of two random variables that are asymptotically independent. Here we introduce a new concept of asymptotic independence which allows u...
Asymptotic safety of gravity-matter systems
Meibohm, J.; Pawlowski, J. M.; Reichert, M.
2016-04-01
We study the ultraviolet stability of gravity-matter systems for general numbers of minimally coupled scalars and fermions. This is done within the functional renormalization group setup put forward in [N. Christiansen, B. Knorr, J. Meibohm, J. M. Pawlowski, and M. Reichert, Phys. Rev. D 92, 121501 (2015).] for pure gravity. It includes full dynamical propagators and a genuine dynamical Newton's coupling, which is extracted from the graviton three-point function. We find ultraviolet stability of general gravity-fermion systems. Gravity-scalar systems are also found to be ultraviolet stable within validity bounds for the chosen generic class of regulators, based on the size of the anomalous dimension. Remarkably, the ultraviolet fixed points for the dynamical couplings are found to be significantly different from those of their associated background counterparts, once matter fields are included. In summary, the asymptotic safety scenario does not put constraints on the matter content of the theory within the validity bounds for the chosen generic class of regulators.
Supersymmetric asymptotic safety is not guaranteed
Intriligator, Kenneth; Sannino, Francesco
It was recently shown that certain perturbatively accessible, non-supersymmetric gauge-Yukawa theories have UV asymptotic safety, without asymptotic freedom: the UV theory is an interacting RG fixed point, and the IR theory is free. We here investigate the possibility of asymptotic safety in...... supersymmetric theories, and use unitarity bounds, and the a-theorem, to rule it out in broad classes of theories. The arguments apply without assuming perturbation theory. Therefore, the UV completion of a non-asymptotically free susy theory must have additional, non-obvious degrees of freedom, such as those of...
Why are tensor field theories asymptotically free?
Rivasseau, Vincent
2015-01-01
In this pedagogic letter we explain the combinatorics underlying the generic asymptotic freedom of tensor field theories. We focus on simple combinatorial models with a $1/p^2$ propagator and quartic interactions and on the comparison between the intermediate field representations of the vector, matrix and tensor cases. The transition from asymptotic freedom (tensor case) to asymptotic safety (matrix case) is related to the crossing symmetry of the matrix vertex whereas in the vector case, the lack of asymptotic freedom ("Landau ghost"), as in the ordinary scalar case, is simply due to the absence of any wave function renormalization at one loop.
Numerical Asymptotic Solutions Of Differential Equations
Thurston, Gaylen A.
1992-01-01
Numerical algorithms derived and compared with classical analytical methods. In method, expansions replaced with integrals evaluated numerically. Resulting numerical solutions retain linear independence, main advantage of asymptotic solutions.
Nerz, Christopher
2016-01-01
In 1996, Huisen-Yau proved that every three-dimensional, asymptotically Schwarzschilden manifold with positive mass is uniquely foliated by stable spheres of constant mean curvature and they defined the center of mass using this CMC-foliation. Rigger and Neves-Tian showed in 2004 and 2009/10 analogous existence and uniqueness theorems for three-dimensional, asymptotically Anti-de Sitter and asymptotically hyperbolic manifolds with positive mass aspect function, respectively. Last year, Cederbaum-Cortier-Sakovich proved that the CMC-foliation characterizes the center of mass in the hyperbolic setting, too. In this article, the existence and the uniqueness of the CMC-foliation are further generalized to the wider class of asymptotically hyperbolic manifolds which do not necessarily have a well-defined mass aspect function, but only a timelike mass vector. Furthermore, we prove that the CMC-foliation also characterizes the center of mass in this more general setting.
Hante, Falk; Tucsnak, Marius
2011-01-01
We study the asymptotic stability of a dissipative evolution in a Hilbert space subject to intermittent damping. We observe that, even if the intermittence satisfies a persistent excitation condition, if the Hilbert space is infinite-dimensional then the system needs not being asymptotically stable (not even in the weak sense). Exponential stability is recovered under a generalized observability inequality, allowing for time-domains that are not intervals. Weak asymptotic stability is obtained under a similarly generalized unique continuation principle. Finally, strong asymptotic stability is proved for intermittences that do not necessarily satisfy some persistent excitation condition, evaluating their total contribution to the decay of the trajectories of the damped system. Our results are discussed using the example of the wave equation, Schr\\"odinger's equation and, for strong stability, also the special case of finite-dimensional systems.
Ke Yang; XuYang Wang; Tong Ge; Chao Wu
2014-01-01
It will still in lack of a simulation platform used to learn the walking of underwater quadruped walking robot. In order to alleviate this shortage, a simulation platform for the underwater quadruped walking robot based on Kane dynamic model and CPG-based controller is constructed. The Kane dynamic model of the underwater quadruped walking robot is processed with a commercial package MotionGenesis Kane 5�3. The forces between the feet and ground are represented as a spring and damper. The relation between coefficients of spring and damper and stability of underwater quadruped walking robot in the stationary state is studied. The CPG-based controller consisted of Central Pattern Generator ( CPG) and PD controller is presented, which can be used to control walking of the underwater quadruped walking robot. The relation between CPG parameters and walking speed of underwater quadruped walking robot is investigated. The relation between coefficients of spring and damper and walking speed of underwater quadruped walking robot is studied. The results show that the simulation platform can imitate the stable walking of the underwater quadruped walking robot.
Yee, H. C.; Sweby, P. K.
1995-01-01
The global asymptotic nonlinear behavior of 1 1 explicit and implicit time discretizations for four 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODES) is analyzed. The objectives are to gain a basic understanding of the difference in the dynamics of numerics between the scalars and systems of nonlinear autonomous ODEs and to set a baseline global asymptotic solution behavior of these schemes for practical computations in computational fluid dynamics. We show how 'numerical' basins of attraction can complement the bifurcation diagrams in gaining more detailed global asymptotic behavior of time discretizations for nonlinear differential equations (DEs). We show how in the presence of spurious asymptotes the basins of the true stable steady states can be segmented by the basins of the spurious stable and unstable asymptotes. One major consequence of this phenomenon which is not commonly known is that this spurious behavior can result in a dramatic distortion and, in most cases, a dramatic shrinkage and segmentation of the basin of attraction of the true solution for finite time steps. Such distortion, shrinkage and segmentation of the numerical basins of attraction will occur regardless of the stability of the spurious asymptotes, and will occur for unconditionally stable implicit linear multistep methods. In other words, for the same (common) steady-state solution the associated basin of attraction of the DE might be very different from the discretized counterparts and the numerical basin of attraction can be very different from numerical method to numerical method. The results can be used as an explanation for possible causes of error, and slow convergence and nonconvergence of steady-state numerical solutions when using the time-dependent approach for nonlinear hyperbolic or parabolic PDES.
Thermodynamics of asymptotically safe theories
Rischke, Dirk H
2015-01-01
We investigate the thermodynamic properties of a novel class of gauge-Yukawa theories that have recently been shown to be completely asymptotically safe, because their short-distance behaviour is determined by the presence of an interacting fixed point. Not only do all the coupling constants freeze at a constant and calculable value in the ultraviolet, their values can even be made arbitrarily small for an appropriate choice of the ratio $N_c/N_f$ of fermion colours and flavours in the Veneziano limit. Thus, a perturbative treatment can be justified. We compute the pressure, entropy density, and thermal degrees of freedom of these theories to next-to-next-to-leading order in the coupling constants.
Extendable self-avoiding walks
Grimmett, Geoffrey R.; Holroyd, Alexander E; Peres, Yuval
2013-01-01
The connective constant mu of a graph is the exponential growth rate of the number of n-step self-avoiding walks starting at a given vertex. A self-avoiding walk is said to be forward (respectively, backward) extendable if it may be extended forwards (respectively, backwards) to a singly infinite self-avoiding walk. It is called doubly extendable if it may be extended in both directions simultaneously to a doubly infinite self-avoiding walk. We prove that the connective constants for forward,...
Physical implementation of quantum walks
Manouchehri, Kia
2013-01-01
Given the extensive application of random walks in virtually every science related discipline, we may be at the threshold of yet another problem solving paradigm with the advent of quantum walks. Over the past decade, quantum walks have been explored for their non-intuitive dynamics, which may hold the key to radically new quantum algorithms. This growing interest has been paralleled by a flurry of research into how one can implement quantum walks in laboratories. This book presents numerous proposals as well as actual experiments for such a physical realization, underpinned by a wide range of
Persistence of random walk records
We study records generated by Brownian particles in one dimension. Specifically, we investigate an ordinary random walk and define the record as the maximal position of the walk. We compare the record of an individual random walk with the mean record, obtained as an average over infinitely many realizations. We term the walk ‘superior’ if the record is always above average, and conversely, the walk is said to be ‘inferior’ if the record is always below average. We find that the fraction of superior walks, S, decays algebraically with time, S ∼ t−β, in the limit t → ∞, and that the persistence exponent is nontrivial, β = 0.382 258…. The fraction of inferior walks, I, also decays as a power law, I ∼ t−α, but the persistence exponent is smaller, α = 0.241 608…. Both exponents are roots of transcendental equations involving the parabolic cylinder function. To obtain these theoretical results, we analyze the joint density of superior walks with a given record and position, while for inferior walks it suffices to study the density as a function of position. (paper)
Walking. Sensing. Participation
Bødker, Mads
2014-01-01
This paper uses three meditations to contemplate walking, sensing and participation as three ways with which we can extend the notion of ‘experiential computing’ proposed by Yoo (2010). By using the form of meditations, loosely associated concepts that are part introspective and part ‘causative’, i...... intended to also inform the design of technologies for the future. By emphasizing the senses and the body and their importance to an extended notion of sensory apprenticeship (Pink, 2009), the paper suggests alternative routes to knowing and representation in IS related fieldwork....
Lawler, Gregory F.; Ferreras, José A. Trujillo
2004-01-01
The Brownian loop soup introduced in Lawler and Werner (2004) is a Poissonian realization from a sigma-finite measure on unrooted loops. This measure satisfies both conformal invariance and a restriction property. In this paper, we define a random walk loop soup and show that it converges to the Brownian loop soup. In fact, we give a strong approximation result making use of the strong approximation result of Koml\\'os, Major, and Tusn\\'ady. To make the paper self-contained, we include a proof...
Romanelli, Alejandro
2011-01-01
A thermodynamic theory is developed to describe the behavior of the entanglement between the coin and position degrees of freedom of the quantum walk on the line. This theory shows that, in spite of the unitary evolution, a steady state is established after a Markovian transient stage. This study suggests that if a quantum dynamics is developed in a composite Hilbert space (i.e. the tensor product of several sub-spaces) then the behavior of an operator that only belongs to one of the sub-spaces may camouflage the unitary character of the global evolution.
Woof, M.
2002-09-01
The article reports on the activity in the dragline sector which has been greater in the past 18 months than in previous years. One notable event is the recent order by BNI Coal in the USA of a large walking dragline, the Marion 8200 model from Bucyrus, for removal of overburden at the Center Mine in North Dakota. The Marison draglines have an oval rigid structure which provides an effective load and boom support. The article reports uses of other Bucyrus draglines in Canada and Australia. 2 figs.
Number variance for hierarchical random walks and related fluctuations
Bojdecki, Tomasz; Talarczyk, Anna
2010-01-01
We study an infinite system of independent symmetric random walks on a hierarchical group, in particular, the c-random walks. Such walks are used, e.g., in population genetics. The number variance problem consists in investigating if the variance of the number of "particles" N_n(L) lying in the ball of radius L at a given time n remains bounded, or even better, converges to a finite limit, as $L\\to \\infty$. We give a necessary and sufficient condition and discuss its relationship to transience/recurrence property of the walk. Next we consider normalized fluctuations of N_n(L) around the mean as $n\\to \\infty$ and L is increased in an appropriate way. We prove convergence of finite dimensional distributions to a Gaussian process whose properties are discussed. As the c-random walks mimic symmetric stable processes on R, we compare our results to those obtained by Hambly and Jones (2007,2009), where the number variance problem for an infinite system of symmetric stable processes on R was studied. Since the hiera...
The Fixed Irreducible Bridge Ensemble for Self-Avoiding Walks
Gilbert, Michael James
2015-04-01
We define a new ensemble for self-avoiding walks in the upper half-plane, the fixed irredicible bridge ensemble, by considering self-avoiding walks in the upper half-plane up to their -th bridge height, , and scaling the walk by to obtain a curve in the unit strip, and then taking . We then conjecture a relationship between this ensemble to in the unit strip from 0 to a fixed point along the upper boundary of the strip, integrated over the conjectured exit density of self-avoiding walk spanning a strip in the scaling limit. We conjecture that there exists a positive constant such that converges in distribution to that of a stable random variable as . Then the conjectured relationship between the fixed irreducible bridge scaling limit and can be described as follows: If one takes a SAW considered up to and scales by and then weights the walk by to an appropriate power, then in the limit , one should obtain a curve from the scaling limit of the self-avoiding walk spanning the unit strip. In addition to a heuristic derivation, we provide numerical evidence to support the conjecture and give estimates for the boundary scaling exponent.
Antigraviting Bubbles with the Non-Minkowskian Asymptotics
Barnaveli, A T
1996-01-01
The conventional approach describes the spherical domain walls by the same state equation as the flat ones. In such case they also must be gravitationally repulsive, what is seemingly in contradiction with Birkhoff's theorem. However this theorem is not valid for the solutions which do not display Minkowski geometry in the infinity. In this paper the solution of Einstein equations describing the stable gravitationally repulsive spherical domain wall is considered within the thin-wall formalism for the case of the non-Minkowskian asymptotics.
Asymptotic spectral theory for nonlinear time series
Shao, Xiaofeng; Wu, Wei Biao
2007-01-01
We consider asymptotic problems in spectral analysis of stationary causal processes. Limiting distributions of periodograms and smoothed periodogram spectral density estimates are obtained and applications to the spectral domain bootstrap are given. Instead of the commonly used strong mixing conditions, in our asymptotic spectral theory we impose conditions only involving (conditional) moments, which are easily verifiable for a variety of nonlinear time series.
Asymptotically flat and regular Cauchy data
Dain, S
2002-01-01
I describe the construction of a large class of asymptotically flat initial data with non-vanishing mass and angular momentum for which the metric and the extrinsic curvature have asymptotic expansions at space-like infinity in terms of powers of a radial coordinate. I emphasize the motivations and the main ideas behind the proofs.
8. Asymptotically Flat and Regular Cauchy Data
Dain, Sergio
I describe the construction of a large class of asymptotically flat initial data with non-vanishing mass and angular momentum for which the metric and the extrinsic curvature have asymptotic expansions at space-like infinity in terms of powers of a radial coordinate. I emphasize the motivations and the main ideas behind the proofs.
Asymptotics of implied volatility far from maturity
Michael R., Tehranchi
2009-01-01
This note explores the behaviour of the implied volatility of a European call option far from maturity. Asymptotic formulae are derived with precise control over the error terms. The connection between the asymptotic implied volatility and the cumulant generating function of the logarithm of the underlying stock price is discussed in detail and illustrated by examples.
Stability Analysis of Quadruped-imitating Walking Robot Based on Inverted Pendulum Model
Yongming Wang,
2016-01-01
Full Text Available A new kind of quadruped-imitating walking robot is designed, which is composed of a body bracket, leg brackets and walking legs. The walking leg of the robot is comprised of a first swiveling arm, a second swiveling arm and two striding leg rods. Each rod of the walking leg is connected by a rotary joint, and is directly controlled by the steering gear. The walking motion is realized by two striding leg rods alternately contacting the ground. Three assumptions are put forward according to the kinematic characteristics of the quadruped-imitating walking robot, and then the centroid equation of the robot is established. On this basis, this paper simplifies the striding process of the quadruped-imitating walking robot into an inverted pendulum model with a constant fulcrum and variable pendulum length. According to the inverted pendulum model, the stability of the robot is not only related to its centroid position, but also related to its centroid velocity. Takes two typical movement cases for example, such as walking on flat ground and climbing the vertical obstacle, the centroid position, velocity curves of the inverted pendulum model are obtained by MATLAB simulations. The results show that the quadruped-imitating walking robot is stable when walking on flat ground. In the process of climbing the vertical obstacle, the robot also can maintain certain stability through real-time control adjusted by the steering gears.
Universal asymptotic umbrella for hydraulic fracture modeling
Linkov, Aleksandr M
2014-01-01
The paper presents universal asymptotic solution needed for efficient modeling of hydraulic fractures. We show that when neglecting the lag, there is universal asymptotic equation for the near-front opening. It appears that apart from the mechanical properties of fluid and rock, the asymptotic opening depends merely on the local speed of fracture propagation. This implies that, on one hand, the global problem is ill-posed, when trying to solve it as a boundary value problem under a fixed position of the front. On the other hand, when properly used, the universal asymptotics drastically facilitates solving hydraulic fracture problems (both analytically and numerically). We derive simple universal asymptotics and comment on their employment for efficient numerical simulation of hydraulic fractures, in particular, by well-established Level Set and Fast Marching Methods.
Penrose type inequalities for asymptotically hyperbolic graphs
Dahl, Mattias; Sakovich, Anna
2013-01-01
In this paper we study asymptotically hyperbolic manifolds given as graphs of asymptotically constant functions over hyperbolic space $\\bH^n$. The graphs are considered as subsets of $\\bH^{n+1}$ and carry the induced metric. For such manifolds the scalar curvature appears in the divergence of a 1-form involving the integrand for the asymptotically hyperbolic mass. Integrating this divergence we estimate the mass by an integral over an inner boundary. In case the inner boundary satisfies a convexity condition this can in turn be estimated in terms of the area of the inner boundary. The resulting estimates are similar to the conjectured Penrose inequality for asymptotically hyperbolic manifolds. The work presented here is inspired by Lam's article concerning the asymptotically Euclidean case.
Luo, Tao
1997-01-01
This paper concerns the large time behavior toward planar rarefaction waves of solutions for the relaxation approximation of conservation laws in several dimensions. It is shown that a planar rarefaction wave is nonlinear stable in the sense that it is an asymptotic attractor for the relaxation approximation of conservation laws.
ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR A CLASS OF DELAY DIFFERENCE EQUATION
ZhuHuiyan; HuangLihong
2005-01-01
We propose a class of delay difference equation with piecewise constant nonlinearity. Such a delay difference equation can be regarded as the discrete analog of a differential equation. The convergence of solutions and the existence of asymptotically stable periodic solutions are investigated for such a class of difference equation.
Clisby, Nathan
2013-06-01
We introduce a self-avoiding walk model for which end-effects are completely eliminated. We enumerate the number of these walks for various lattices in dimensions two and three, and use these enumerations to study the properties of this model. We find that endless self-avoiding walks have the same connective constant as self-avoiding walks, and the same Flory exponent ν. However, there is no power law correction to the exponential number growth for this new model, i.e. the critical exponent γ = 1 exactly in any dimension. In addition, the number growth has no analytic corrections to scaling, and we have convincing numerical evidence to support the conjecture that the amplitude for the number growth is a universal quantity. The technique by which end-effects are eliminated may be generalized to other models of polymers such as interacting self-avoiding walks.
We introduce a self-avoiding walk model for which end-effects are completely eliminated. We enumerate the number of these walks for various lattices in dimensions two and three, and use these enumerations to study the properties of this model. We find that endless self-avoiding walks have the same connective constant as self-avoiding walks, and the same Flory exponent ν. However, there is no power law correction to the exponential number growth for this new model, i.e. the critical exponent γ = 1 exactly in any dimension. In addition, the number growth has no analytic corrections to scaling, and we have convincing numerical evidence to support the conjecture that the amplitude for the number growth is a universal quantity. The technique by which end-effects are eliminated may be generalized to other models of polymers such as interacting self-avoiding walks. (paper)
Quantum walks and search algorithms
Portugal, Renato
2013-01-01
This book addresses an interesting area of quantum computation called quantum walks, which play an important role in building quantum algorithms, in particular search algorithms. Quantum walks are the quantum analogue of classical random walks. It is known that quantum computers have great power for searching unsorted databases. This power extends to many kinds of searches, particularly to the problem of finding a specific location in a spatial layout, which can be modeled by a graph. The goal is to find a specific node knowing that the particle uses the edges to jump from one node to the next. This book is self-contained with main topics that include: Grover's algorithm, describing its geometrical interpretation and evolution by means of the spectral decomposition of the evolution operater Analytical solutions of quantum walks on important graphs like line, cycles, two-dimensional lattices, and hypercubes using Fourier transforms Quantum walks on generic graphs, describing methods to calculate the limiting d...
ASYMPTOTIC BEHAVIOR OF MULTISTEP RUNGE-KUTTA METHODS FOR SYSTEMS OF DELAY DIFFERENTIAL EQUATIONS
张诚坚; 廖晓昕
2001-01-01
This paper deals with the asymptotic behavior of multistep Runge-Kutta methods for systems of delay differential equations (DDEs). With the help of K.J.in't Hout's analytic technique for the numerical stability of onestep Runge-Kutta methods, we obtain that a multistep Runge-Kutta method for DDEs is stable iff the corresponding methods for ODEs is A-stable under suitable interpolation conditions.
Critical Two-Point Function of the 4-Dimensional Weakly Self-Avoiding Walk
Bauerschmidt, Roland; Brydges, David C.; Slade, Gordon
2015-08-01
We prove decay of the critical two-point function for the continuous-time weakly self-avoiding walk on , in the upper critical dimension d = 4. This is a statement that the critical exponent exists and is equal to zero. Results of this nature have been proved previously for dimensions using the lace expansion, but the lace expansion does not apply when d = 4. The proof is based on a rigorous renormalisation group analysis of an exact representation of the continuous-time weakly self-avoiding walk as a supersymmetric field theory. Much of the analysis applies more widely and has been carried out in a previous paper, where an asymptotic formula for the susceptibility is obtained. Here, we show how observables can be incorporated into the analysis to obtain a pointwise asymptotic formula for the critical two-point function. This involves perturbative calculations similar to those familiar in the physics literature, but with error terms controlled rigorously.