Walking Sequence Research Articles

3D Periodic Human Motion Reconstruction from 2D Motion Sequences

We present and evaluate a method of reconstructing three-dimensional (3D) periodic human motion from two-dimensional (2D) motion sequences. Using Fourier decomposition, we construct a compact representation for periodic human motion. A low-dimensional linear motion model is learned from a training set of 3D Fourier representations by means of principal components analysis. Two-dimensional test data are projected onto this model with two approaches: least-square minimization and calculation of a maximum a posteriori probability using the Bayes' rule. We present two different experiments in which both approaches are applied to 2D data obtained from 3D walking sequences projected onto a plane. In the first experiment, we assume the viewpoint is known. In the second experiment, the horizontal viewpoint is unknown and is recovered from the 2D motion data. The results demonstrate that by using the linear model, not only can missing motion data be reconstructed, but unknown view angles for 2D test data can also be retrieved.

The complete mitochondrial genome and phylogenetic analysis of the giant panda ( Ailuropoda melanoleuca)

The complete mitochondrial genome sequence of the giant panda, Ailuropoda melanoleuca, was determined by the long and accurate polymerase chain reaction (LA-PCR) with conserved primers and primer walking sequence methods. The complete mitochondrial DNA is 16,805 nucleotides in length and contains two ribosomal RNA genes, 13 protein-coding genes, 22 transfer RNA genes and one control region. The total length of the 13 protein-coding genes is longer than the American black bear, brown bear and polar bear by 3 amino acids at the end of ND5 gene. The codon usage also followed the typical vertebrate pattern except for an unusual ATT start codon, which initiates the NADH dehydrogenase subunit 5 ( ND5) gene. The molecular phylogenetic analysis was performed on the sequences of 12 concatenated heavy-strand encoded protein-coding genes, and suggested that the giant panda is most closely related to bears.

Lévy flight approximations for scaled transformations of random walks

Complex systems under anomalous diffusive regime can be modelled by approximating sequences of random walks, S n = X 1 + X 2 + ⋯ + X n , where the i.i.d. random variables X j 's have fat-tailed distribution. Such random walks are referred by physicists as Lévy flights or motions and have been used to model financial data. For better adjustment to real-world data several modified Lévy flights have been proposed: truncated, gradually truncated or exponentially damped Lévy flights. On the other hand, scaled transformations of random walks possess a Lévy stable limiting distribution. In this work, under the assumption that the analyzed data belongs to the domain of attraction of a symmetric Lévy stable distribution L α , σ , we present consistent estimates for the stability index α and for the scaling parameter σ . Variations of the model that allow distinct left and right tail behavior will be explored. Illustrations for returns of exchange rates of several countries are also included.

Planning and executing navigation among movable obstacles

This paper explores autonomous locomotion, reaching, grasping and manipulation for the domain of navigation among movable obstacles (NAMO). The robot perceives and constructs a model of an environment filled with various fixed and movable obstacles, and automatically plans a navigation strategy to reach a desired goal location. The planned strategy consists of a sequence of walking and compliant manipulation operations. It is executed by the robot with online feedback. We give an overview of our NAMO system, as well as provide details of the autonomous planning, online grasping and compliant hand positioning during dynamically stable walking. Finally, we present results of a successful implementation running on the humanoid robot HRP-2.

Human body pose detection using Bayesian spatio-temporal templates

We present a template-based approach to detecting human silhouettes in a specific walking pose. Our templates consist of short sequences of 2D silhouettes obtained from motion capture data. This lets us incorporate motion information into them and helps distinguish actual people who move in a predictable way from static objects whose outlines roughly resemble those of humans. Moreover, during the training phase we use statistical learning techniques to estimate and store the relevance of the different silhouette parts to the recognition task. At run-time, we use it to convert Chamfer distance to meaningful probability estimates. The templates can handle six different camera views, excluding the frontal and back view, as well as different scales. We demonstrate the effectiveness of our technique using both indoor and outdoor sequences of people walking in front of cluttered backgrounds and acquired with a moving camera, which makes techniques such as background subtraction impractical.

Integration by Parts Formulae for Wiener Measures on a Path Space between two Curves

This paper is concerned with the integration by parts formulae for the pinned or the standard Wiener measures restricted on a space of paths staying between two curves. The boundary measures, concentrated on the set of paths touching one of the curves once, are specified. Our approach is based on the polygonal approximations. In particular, to establish the convergence of boundary terms, a uniform estimate is derived by means of comparison argument for a sequence of random walks conditioned to stay between two polygons. Applying the Brascamp–Lieb inequality, the stochastic integrals of Wiener type are constructed relative to the three-dimensional Bessel bridge or the Brownian meander.

Adaptations in the Walking Pattern of Spinal Cord Injured Rats

Walking ability is a measure of recovery used in many studies that test experimental strategies to treat injuries or diseases of the central nervous system (CNS) in animal models. A common measure in the rat animal model of thoracic spinal cord injury (SCI) is visual inspection and scoring of hind limb activity, which allows the documentation of movements associated with the recovery of locomotor function. In this study, we expand on previously documented visible changes in the locomotor pattern following SCI. The spontaneous recovery of locomotion in rats with thoracic SCIs of variable extent was evaluated using electromyographic (EMG) and kinematic analysis while rats walked on an elevated runway. Comparisons with pre-lesion walking sequences revealed changes in the kinematics and in the muscle activation pattern of various muscles, including enhanced fore limb extensor activity, possibly reflecting an increased contribution to propulsion, altered recruitment of back muscles inserting into the hip (possibly to support stepping movements), and elevated posture during stance, which may compensate for deficits in weight support. These changes were noted in spinal cord injured rats with varying degrees of impairment, including animals with no visually detectable deficit in open-field walking. In summary, the presented results demonstrate that spinal cord injured rats develop alternative locomotor patterns following SCI that cannot be discriminated by the use of qualitative visually based analysis, thus urging the use of quantitative outcome measures in assessing motor function after SCI.

Coordination of fore and hind leg stepping in cats on a transversely-split treadmill

To gain insight into the mechanism of coordination of stepping in the fore and hind legs of quadrupeds, we examined the kinematics of leg movements and the motor patterns in fore and hind leg flexor muscles in decerebrate walking cats when the two pairs of legs stepped on separate treadmills running at different speeds. When the front treadmill was slowed progressively from 0.6 to 0.3 m/s with the rear treadmill running at 0.6 m/s, the rate of stepping in both the fore and hind legs decreased and a 1:1 stepping ratio was maintained. The decrease in the rate of stepping in the hind legs was due primarily to an increase in the duration of the swing phase. Slowing the speed of the rear treadmill while keeping the front treadmill speed at 0.6 m/s decreased the rate of stepping of the hind legs, but had relatively little influence on the average rate of stepping in the forelegs. In this situation stepping in the fore and hind legs was uncoupled and the time of stepping in one hind leg relative to the ipsilateral foreleg progressively shifted during a walking sequence. Analysis of the timing of electromyographic (EMG) recordings from flexor muscles of the hip and elbow joints yielded insight into the neuronal mechanisms underlying the asymmetry in slowing either the front or rear treadmill. We propose that ipsilateral pattern generating networks are asymmetrically coupled via descending inhibitory pathways and an ascending excitatory pathway. We discuss how the characteristics of these linkages are functionally appropriate for establishing the normal timing of stepping in the hind and forelegs during slow walking.

Anomalous Diffusion Index for Lévy Motions

In modelling complex systems as real diffusion processes it is common to analyse its diffusive regime through the study of approximating sequences of random walks. For the partial sums \(S_n=\xi_1 + \xi_2 + \ldots + \xi_n\) one considers the approximating sequence of processes \(X^{(n)}(t)= a_n (S_{[k_nt]}-b_n)\). Then, under sufficient smoothness requirements we have the convergence to the desired diffusion, \(X^{(n)}(t) \to X(t)\). A key assumption usually presumed is the finiteness of the second moment, and, hence the validity of the Central Limit Theorem. Under anomalous diffusive regime the asymptotic behavior of S n may well be non-Gaussian and \(n^{-1}E(S^2_n) \to\infty\). Such random walks have been referred by physicists as Levy motions or Levy flights. In this work, we introduce an alternative notion to classify these regimes, the diffusion index \(\gamma_X\). For some \(\gamma^0_X\) properly chosen let \(\gamma_X=\inf \{ \gamma:0 < \gamma\leq\gamma^0_X,\limsup_{t\to \infty}t^{-1}E|X(t)|^{1/\gamma} < \infty \}\). Relationship between \(\gamma_X\), the infinitesimal diffusion coefficients and the diffusion constant will be explored. Illustrative examples as well as estimates, based on extreme order statistics, for \(\gamma_X\) will also be presented.

Simultaneous pose recovery and camera registration from multiple views of a walking person

We present an algorithm to estimate the body pose of a walking person given synchronized video input from multiple uncalibrated cameras. We construct an appearance model of human walking motion by generating examples from the space of body poses and camera locations, and clustering them using expectation–maximization. Given a segmented input video sequence, we find the closest matching appearance cluster for each silhouette and use the sequence of matched clusters to extrapolate the position of the camera with respect to the person's direction of motion. For each frame, the matching cluster also provides an estimate of the walking phase. We combine these estimates from all views and find the most likely sequence of walking poses using a cyclical, feed-forward hidden Markov model. Our algorithm requires no manual initialization and no prior knowledge about the locations of the cameras.

Improved Lower Bounds for the Critical Probability of Oriented Bond Percolation in Two Dimensions

We present a coupled decreasing sequence of random walks on Z that dominate the edge process of oriented bond percolation in two dimensions. Using the concept of random walk in a strip, we describe an algorithm that generates an increasing sequence of lower bounds that converges to the critical probability of oriented percolation pc. From the 7th term on, these lower bounds improve upon 0.6298, the best rigorous lower bound at present, establishing 0.63328 as a rigorous lower bound for pc. Finally, a Monte Carlo simulation technique is presented; the use thereof establishes 0.64450 as a non-rigorous five-digit-precision (lower) estimate for pc.

Solving, Estimating and Selecting Nonlinear Dynamic Economic Models without the Curse of Dimensionality

A welfare analysis of policies for risk averse preferences is handicapped within linear or linearized models and their certainty equivalence property. I calculate the optimal policy in a nonlinear stochastic dynamic general equilibrium model. Then I estimate the posterior density of structural parameters and the marginal likelihood within a nonlinear state space model. The computational challenges are considerable and I concentrate on the numerics and statistics for a simple model of dynamic consumption and labor choice. It is estimated on simulated data in order to test the routines with known true parameters. The code is written for a general model class. The policy function is approximated by Smolyak Chebyshev polynomials and the rational expectation integral by Smolyak Gaussian quadrature. The Smolyak operator is used to extend univariate approximation and integration operators to many dimensions. It is also called boolean method, hyperbolic cross points, discrete or sparse grids, fully symmetrical integration rules or complete polynomials. It reduces the curse of dimensionality from exponential to polynomial growth. The likelihood integrals are evaluated by a Gaussian quadrature and Gaussian quadrature particle filter. The bootstrap or sequential importance resampling particle filter, based on a Monte Carlo integration, is used as an accuracy benchmark. The posterior is estimated by the Gaussian filter and a Metropolis-Hastings algorithm. I propose a genetic extension of the standard Metropolis-Hastings algorithm by parallel random walk sequences. The candidate parameter vectors are constructed by innovation from the parallel sequences in addition to the usual random walk shocks. This improves the robustness of start values and the global maximization properties. Moreover it simplifies a cluster implementation and the random walk variances decision is reduced to only two parameters so that almost no trial sequences are needed. Finally the marginal likelihood is calculated as a criterion for nonnested and quasi-true models in order to select between the nonlinear estimates and a first order perturbation solution combined with the Kalman filter.

Non-extensive random walks

Stochastic variables whose addition leads to q-Gaussian distributions G q ( x ) ∝ [ 1 + ( q - 1 ) β x 2 ] + 1 / ( 1 - q ) (with β > 0 , 1 ⩽ q < 3 and where [ f ( x ) ] + = max { f ( x ) , 0 } ) as limit law for a large number of terms are investigated. Random walk sequences related to this problem possess a simple additive–multiplicative structure commonly found in several contexts, thus justifying the ubiquity of those distributions. A characterization of the statistical properties of the random walk step lengths is performed. Moreover, a connection with non-linear stochastic processes is exhibited. q-Gaussian distributions have special relevance within the framework of non-extensive statistical mechanics, a generalization of the standard Boltzmann–Gibbs formalism, introduced by Tsallis over one decade ago. Therefore, the present findings may give insights on the domain of applicability of such generalization.

Context-dependent changes in strength and efficacy of leg coordination mechanisms

Appropriate coordination of stepping in adjacent legs is crucial for stable walking. Several leg coordination rules have been derived from behavioural experiments on walking insects, some of which also apply to arthropods with more than six legs and to four-legged walking vertebrates. Three of these rules affect the timing of stance-swing transition [rules 1 to 3 (sensu Cruse)]. They can give rise to normal leg coordination and adaptive responses to disturbances, as shown by kinematic simulations and dynamic hardware tests. In spite of their importance to the study of animal walking, the coupling strength associated with these rules has never been measured experimentally. Generally coupling strength of the underlying mechanisms has been considered constant rather than context-dependent. The present study analyses stepping patterns of the stick insect Carausius morosus during straight and curve walking sequences. To infer strength and efficacy of coupling between pairs of sender and receiver legs, the likelihood of the receiver leg being in swing is determined, given a certain delay relative to the time of a swing-stance (or stance-swing) transition in the sender leg. This is compared to a corresponding measure for independent, hence uncoupled, step sequences. The difference is defined as coupling strength. The ratio of coupling strength and its theoretical maximum is defined as efficacy. Irrespective of the coordination rule, coupling strength between ipsilateral leg pairs is at least twice that of contralateral leg pairs, being strongest between ipsilateral hind and middle legs and weakest between contralateral middle legs. Efficacy is highest for inhibitory rule 1, reaching 84-95% for ipsilateral and 29-65% for contralateral leg pairs. Efficacy of excitatory rules 2 and 3 ranges between 35-56% for ipsilateral and 8-21% for contralateral leg pairs. The behavioural transition from straight to curve walking is associated with context-dependent changes in coupling strength, increasing in both outer leg pairs and decreasing between inner hind and middle leg. Thus, the coordination rules that are thought to underlie many adaptive properties of the walking system, themselves adapt in a context-dependent manner.

A new electrode configuration for recording electromyographic activity in behaving mice

With the increasing use of normal and genetically modified mice in the field of motor physiology, there is a need for a simple and reliable technique for recording electromyographic (EMG) activity in behaving mice. Here, we describe a new method for the fabrication and implantation of fine EMG recording electrodes into multiple muscles of adult mice. This method minimizes surgical damage to the muscles and the connecting leads have only a modest influence on leg movements when electrodes are implanted into distal muscles. We demonstrate that excellent EMG recordings can be obtained during walking, swimming and scratching for the vastus lateralis, tibialis anterior and gastrocnemius muscles in normal adult mice. EMG recordings were also made in a mutant EphA4 mouse to demonstrate the utility of the method for examining motor patterns in genetically modified animals. We also developed a method for constructing highly reflective markers that could be viewed over a range of orientations to measure the kinematics of legs movements during stepping. A commercial motion analysis system was used to track six markers during walking and to synchronize video and EMG data during walking sequences.

Isolation of Nicotiana plumbaginifolia cDNAs encoding isoforms of serine acetyltransferase and O-acetylserine (thiol) lyase in a yeast two-hybrid system with Escherichia coli cysE and cysK genes as baits.

We applied the yeast two-hybrid system for screening of a cDNA library of Nicotiana plumbaginifolia for clones encoding plant proteins interacting with two proteins of Escherichia coli: serine acetyltransferase (SAT, the product of cysE gene) and O-acetylserine (thiol)lyase A, also termed cysteine synthase (OASTL-A, the product of cysK gene). Two plant cDNA clones were identified when using the cysE gene as a bait. These clones encode a probable cytosolic isoform of OASTL and an organellar isoform of SAT, respectively, as indicated by evolutionary trees. The second clone, encoding SAT, was identified independently also as a "prey" when using cysK as a bait. Our results reveal the possibility of applying the two-hybrid system for cloning of plant cDNAs encoding enzymes of the cysteine synthase complex in the two-hybrid system. Additionally, using genome walking sequences located upstream of the sat1 cDNA were identified. Subsequently, in silico analyses were performed aiming towards identification of the potential signal peptide and possible location of the deduced mature protein encoded by sat1.

Isolation of Nicotiana plumbaginifolia cDNAs encoding isoforms of serine acetyltransferase and O-acetylserine (thiol) lyase in a yeast two-hybrid system with Escherichia coli cysE and cysK genes as baits.

We applied the yeast two-hybrid system for screening of a cDNA library of Nicotiana plumbaginifolia for clones encoding plant proteins interacting with two proteins of Escherichia coli: serine acetyltransferase (SAT, the product of cysE gene) and O-acetylserine (thiol)lyase A, also termed cysteine synthase (OASTL-A, the product of cysK gene). Two plant cDNA clones were identified when using the cysE gene as a bait. These clones encode a probable cytosolic isoform of OASTL and an organellar isoform of SAT, respectively, as indicated by evolutionary trees. The second clone, encoding SAT, was identified independently also as a "prey" when using cysK as a bait. Our results reveal the possibility of applying the two-hybrid system for cloning of plant cDNAs encoding enzymes of the cysteine synthase complex in the two-hybrid system. Additionally, using genome walking sequences located upstream of the sat1 cDNA were identified. Subsequently, in silico analyses were performed aiming towards identification of the potential signal peptide and possible location of the deduced mature protein encoded by sat1.

A computational method to detect epistatic effects contributing to a quantitative trait

We develop a new computational method to detect epistatic effects that contribute to a complex quantitative trait. Rather than looking for epistatic effects that show statistical significance when considered in isolation, we search for a close approximation to the quantitative trait by a sum of epistatic effects. Our search algorithm consists of a sequence of random walks around the space of sums of epistatic effects. An important feature of our approach is that there is learning between random walks, i.e. the control mechanism that chooses steps in our random walks adapts to the experiences of earlier random walks. We test the effectiveness of our algorithms by applying them to synthetic datasets where the phenotype is a sum of epistatic effects plus normally distributed noise. Our test statistic is the rate of success that our methods achieve in identifying the underlying epistatic effects. We report on the effectiveness of our methods as we vary parameters that are intrinsic to the computation (length of random walks and degree of learning) as well as parameters that are extrinsic to the computation (number of markers, number of individuals, noise level, architecture of the epistatic effects).

A posture optimization algorithm for model-based motion capture of movement sequences

We have developed and evaluated a new optical motion capture approach that is suitable for a wide range of studies in neuroethology and motor control. Based on the stochastic search algorithm of Simulated Annealing (SA), it utilizes a kinematic body model that includes joint angle constraints to reconstruct posture from an arbitrary number of views. Rather than tracking marker trajectories in time, the algorithm minimizes an error function that compares predicted model projections to the recorded views. Thus, each video-frame is analyzed independently from other frames, enabling the system to recover from incorrectly analyzed postures. The system works with standard computer and video equipment. Its accuracy is evaluated using videos of animated locust leg movements, recorded by two orthogonal views. The resulting joint angle RMS errors range between 0.7° and 4.9°, limited by the pixel resolution of the digital video. 3D-movement reconstruction is possible even from a single view. In a real experimental application, stick insect walking sequences are analyzed with leg joint angle deviations between 0.5° and 3.0°. This robust and accurate performance is reached in spite of marker fusions and occlusions, simply by exploiting the natural contraints imposed by a kinematic chain and a known experimental setup.

Increased amplification proximal to the MLL gene in acute myeloid leukemia

Amplification of the chromosomal region 11q23 encompassing the MLL gene has been observed in patients with acute myeloid leukemia (AML). Patients with this abnormality often have a poor response to chemotherapy and short survival. We have studied the regions flanking the MLL gene using 8 bacterial artificial chromosome (BAC) probes and dual color fluorescence in situ hybridization (FISH) analysis. Two contigs of BAC probes flanking the MLL gene, were constructed by standard primer walking and BAC end sequencing. For comparison, metaphase chromosome preparations were also hybridized with a commercial MLL specific probe. Metaphase chromosomes were prepared from the bone marrow sample of an 80-year old female patient with AML-M1 and the cytogenetic aberration der(11)hsr(11) (q23). FISH analysis on metaphase chromosomes showed amplification on the homogeneously staining region (hsr) and marker chromosomes for both the MLL gene and the BAC probes. Using dual color FISH, probes proximal to MLL showed greater amplification than those distal to MLL, as represented by additional red signals on both metaphase and interphase chromosomes. Ratios of the copy numbers of the BAC probes relative to the chromosome 11 centromere copy number confirmed a higher copy number for probes proximal to MLL. These results suggest that other gene(s) proximal to MLL could be the target gene(s) of amplification in this case and not the MLL gene as previously assumed.