The Organization and Role During Locomotion of the Proximal Musculature of the Cricket Foreleg. II. Electromyographic Activity During Stepping Patterns

A description is made of the patterns of electrical activity in the proximal muscles of the cricket foreleg during restrained locomotion and seeking movements, while the animal is held by the mesonotum, allowing the legs complete freedom of movement. 1. The initiation of the swing phase corresponds to the onset of the abductor muscle activity (Fig. 1). Its duration is matched by that of abduction-promotion and does not depend on the step frequency. Leg position is more variable at the end of the stance than at the end of the swing. 2. The promotor and abductor muscle activities are linked (Fig. 2). At least three units can be distinguished in each and the duration of their bursts is independent of the period (Fig. 3). 3. In the double depressors of the trochanter, muscles 77-lb,c (Fig. 4), one unit per muscle was identified, bursting during the swing phase. The duration of the burst is independent of the period. Some isolated potentials occasionally occur during the stance phase. 4. The overall activity in the lateral and medial remotors is coupled to the period; three main patterns can be described, depending upon the muscle bundle and the velocity of movement (Fig. 5). 5. In the coxal depressors two patterns of activity are described which depend on velocity of stepping (Fig. 6): (i) during regular and fast stepping (at frequencies greater than 2–5 Hz), the activity is coupled to that of the double depressors; (ii) during slow or irregular stepping, the activity is biphasic: an initial burst is followed after a latency correlated to the period by a second one in the second half of the stance phase. Conversely, the latency between the end of the second burst and the onset of the following abductor burst does not depend on the period. In most cases, a fast neurone (large amplitude, short phasic activation) is recruited when a slow one reaches high rates of discharge

Designing optimal- and fast-on-average pattern matching algorithms

Given a pattern $w$ and a text $t$, the speed of a pattern matching algorithm over $t$ with regard to $w$, is the ratio of the length of $t$ to the number of text accesses performed to search $w$ into $t$. We first propose a general method for computing the limit of the expected speed of pattern matching algorithms, with regard to $w$, over iid texts. Next, we show how to determine the greatest speed which can be achieved among a large class of algorithms, altogether with an algorithm running this speed. Since the complexity of this determination make it impossible to deal with patterns of length greater than 4, we propose a polynomial heuristic. Finally, our approaches are compared with 9 pre-existing pattern matching algorithms from both a theoretical and a practical point of view, i.e. both in terms of limit expected speed on iid texts, and in terms of observed average speed on real data. In all cases, the pre-existing algorithms are outperformed

The Organization and Role During Locomotion of the Proximal Musculature of the Cricket Foreleg : I. Anatomy and Innervation

The structure of the proximal segments of the cricket (Gryllus bimaculatus) foreleg, together with the associated musculature and its innervation are described. The morphology of 50 motor neurones involved in the control of this musculature has been revealed using backfilling techniques with cobalt, horseradish peroxidase and Lucifer Yellow. The ‘ball and socket’ pleurocoxal joint is moved by three sets of anatomical antagonists (promotor-remotor, abductor-adductor, anterior-posterior rotator muscles) inserted on each side of the three axes of rotation. The axial coxotrochanteral joint is moved by the intrinsic levator and the depressor muscles; these depressors are composed of an intrinsic (coxotrochanteral) and a ‘double’ (pleurotrochanteral) subgroup. The double depressors, and all the muscles inserting on the trochantin (promotors) or the anterior coxal rim (adductor, abductors, anterior rotators) are supplied by at least eighteen neurones, whose axons run in nerve 3. The muscles that insert on the posterior coxal rim (remotors, posterior rotators) are innervated by at least twelve similar neurones whose axons run in nerve 4. The intrinsic coxal muscles are supplied by branches of nerve 5 (ten motor neurones to the levators, two to the depressors). Three presumably common inhibitors, and one Dorsal Unpaired Median (DUM) neurone have also been found

Semi-classical analysis of a random walk on a manifold

We prove a sharp rate of convergence to stationarity for a natural random walk on a compact Riemannian manifold $(M,g)$. The proof includes a detailed study of the spectral theory of the associated operator.Comment: Published in at http://dx.doi.org/10.1214/09-AOP483 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Low-complexity computation of plate eigenmodes with Vekua approximations and the Method of Particular Solutions

This paper extends the Method of Particular Solutions (MPS) to the computation of eigenfrequencies and eigenmodes of plates. Specific approximation schemes are developed, with plane waves (MPS-PW) or Fourier-Bessel functions (MPS-FB). This framework also requires a suitable formulation of the boundary conditions. Numerical tests, on two plates with various boundary conditions, demonstrate that the proposed approach provides competitive results with standard numerical schemes such as the Finite Element Method, at reduced complexity, and with large flexibility in the implementation choices

Exotic aromatic B-series for the study of long time integrators for a class of ergodic SDEs

We introduce a new algebraic framework based on a modification (called exotic) of aromatic Butcher-series for the systematic study of the accuracy of numerical integrators for the invariant measure of a class of ergodic stochastic differential equations (SDEs) with additive noise. The proposed analysis covers Runge-Kutta type schemes including the cases of partitioned methods and postprocessed methods. We also show that the introduced exotic aromatic B-series satisfy an isometric equivariance property.Comment: 33 page

Density fluctuation correlations in free turbulent binary mixing

This paper is devoted to the analysis of the turbulent mass flux and, more generally, of the density fluctuation correlation (d.f.c.) effects in variable-density fluid motion. The situation is restricted to the free turbulent binary mixing of an inhomogeneous round jet discharging into a quiescent atmosphere. Based on conventional (Reynolds) averaging, a ternary regrouping of the correlations occurring in the statistical averaging of the open equations is first introduced. Then an exact algebraic relationship between the d.f.c. terms and the second-order moments is demonstrated. Some consequences of this result on the global behaviour of variable-density jets are analytically discussed. The effects of the d.f.c. terms are shown to give a qualitative explanation of the influence of the ratio of the densities of the inlet jet and ambient fluid on the centerline decay rates of mean velocity and mass fraction, the entrainment rate and the restructuring of the jet. Finally, the sensitivity of second-order modelling to the d.f.c. terms is illustrated and it is suggested that such terms should be considered as independent variables in the closing procedure

A Model-based transformation process to validate and implement high-integrity systems

Despite numerous advances, building High-Integrity Embedded systems remains a complex task. They come with strong requirements to ensure safety, schedulability or security properties; one needs to combine multiple analysis to validate each of them. Model-Based Engineering is an accepted solution to address such complexity: analytical models are derived from an abstraction of the system to be built. Yet, ensuring that all abstractions are semantically consistent, remains an issue, e.g. when performing model checking for assessing safety, and then for schedulability using timed automata, and then when generating code. Complexity stems from the high-level view of the model compared to the low-level mechanisms used. In this paper, we present our approach based on AADL and its behavioral annex to refine iteratively an architecture description. Both application and runtime components are transformed into basic AADL constructs which have a strict counterpart in classical programming languages or patterns for verification. We detail the benefits of this process to enhance analysis and code generation. This work has been integrated to the AADL-tool support OSATE2

Blind calibration for compressed sensing by convex optimization

We consider the problem of calibrating a compressed sensing measurement system under the assumption that the decalibration consists in unknown gains on each measure. We focus on {\em blind} calibration, using measures performed on a few unknown (but sparse) signals. A naive formulation of this blind calibration problem, using $\ell_{1}$ minimization, is reminiscent of blind source separation and dictionary learning, which are known to be highly non-convex and riddled with local minima. In the considered context, we show that in fact this formulation can be exactly expressed as a convex optimization problem, and can be solved using off-the-shelf algorithms. Numerical simulations demonstrate the effectiveness of the approach even for highly uncalibrated measures, when a sufficient number of (unknown, but sparse) calibrating signals is provided. We observe that the success/failure of the approach seems to obey sharp phase transitions