The need for muscle co-contraction prior to a landing

In landings from a flight phase the mass centre of an athlete experiences rapid decelerations. This study investigated the extent to which co-contraction is beneficial or necessary in drop landings, using both experimental data and computer simulations. High speed video and force recordings were made of an elite martial artist performing drop landings onto a force plate from heights of 1.2 m, 1.5 m and 1.8 m. Matching simulations of these landings were produced using a planar 8-segment torque-driven subject-specific computer simulation model. It was found that there was substantial co-activation of joint flexor and extensor torques at touchdown in all three landings. Optimisations were carried out to determine whether landings could be effected without any co-contraction at touchdown. The model was not capable of landing from higher than 1.05 m with no initial flexor or extensor activations. Due to the force-velocity properties of muscle, co-contraction with net zero joint torque at touchdown leads to increased extensor torque and decreased flexor torque as joint flexion velocity increases. The same considerations apply in any activity where rapid changes in net joint torque are required, as for example in jumps from a running approach

Noncolliding Squared Bessel Processes

We consider a particle system of the squared Bessel processes with index $\nu > -1$ conditioned never to collide with each other, in which if $-1 < \nu < 0$ the origin is assumed to be reflecting. When the number of particles is finite, we prove for any fixed initial configuration that this noncolliding diffusion process is determinantal in the sense that any multitime correlation function is given by a determinant with a continuous kernel called the correlation kernel. When the number of particles is infinite, we give sufficient conditions for initial configurations so that the system is well defined. There the process with an infinite number of particles is determinantal and the correlation kernel is expressed using an entire function represented by the Weierstrass canonical product, whose zeros on the positive part of the real axis are given by the particle-positions in the initial configuration. From the class of infinite-particle initial configurations satisfying our conditions, we report one example in detail, which is a fixed configuration such that every point of the square of positive zero of the Bessel function $J_{\nu}$ is occupied by one particle. The process starting from this initial configuration shows a relaxation phenomenon converging to the stationary process, which is determinantal with the extended Bessel kernel, in the long-term limit.Comment: v3: LaTeX2e, 26 pages, no figure, corrections made for publication in J. Stat. Phy

Asymptotics for products of characteristic polynomials in classical β\beta-Ensembles

We study the local properties of eigenvalues for the Hermite (Gaussian), Laguerre (Chiral) and Jacobi $\beta$-ensembles of $N\times N$ random matrices. More specifically, we calculate scaling limits of the expectation value of products of characteristic polynomials as $N\to\infty$. In the bulk of the spectrum of each $\beta$-ensemble, the same scaling limit is found to be $e^{p_{1}}{}_1F_{1}$ whose exact expansion in terms of Jack polynomials is well known. The scaling limit at the soft edge of the spectrum for the Hermite and Laguerre $\beta$-ensembles is shown to be a multivariate Airy function, which is defined as a generalized Kontsevich integral. As corollaries, when $\beta$ is even, scaling limits of the $k$-point correlation functions for the three ensembles are obtained. The asymptotics of the multivariate Airy function for large and small arguments is also given. All the asymptotic results rely on a generalization of Watson's lemma and the steepest descent method for integrals of Selberg type.Comment: [v3] 35 pages; this is a revised and enlarged version of the article with new references, simplified demonstations, and improved presentation. To be published in Constructive Approximation 37 (2013

Integrable structure of Ginibre's ensemble of real random matrices and a Pfaffian integration theorem

In the recent publication [E. Kanzieper and G. Akemann, Phys. Rev. Lett. 95, 230201 (2005)], an exact solution was reported for the probability p_{n,k} to find exactly k real eigenvalues in the spectrum of an nxn real asymmetric matrix drawn at random from Ginibre's Orthogonal Ensemble (GinOE). In the present paper, we offer a detailed derivation of the above result by concentrating on the proof of the Pfaffian integration theorem, the key ingredient of our analysis of the statistics of real eigenvalues in the GinOE. We also initiate a study of the correlations of complex eigenvalues and derive a formula for the joint probability density function of all complex eigenvalues of a GinOE matrix restricted to have exactly k real eigenvalues. In the particular case of k=0, all correlation functions of complex eigenvalues are determined

Logarithmic and complex constant term identities

In recent work on the representation theory of vertex algebras related to the Virasoro minimal models M(2,p), Adamovic and Milas discovered logarithmic analogues of (special cases of) the famous Dyson and Morris constant term identities. In this paper we show how the identities of Adamovic and Milas arise naturally by differentiating as-yet-conjectural complex analogues of the constant term identities of Dyson and Morris. We also discuss the existence of complex and logarithmic constant term identities for arbitrary root systems, and in particular prove complex and logarithmic constant term identities for the root system G_2.Comment: 26 page

Crayfish in lakes and streams: individual and population responses to predation, productivity and substratum availability

1. In a correlative study, we investigated the relative importance of fish predation, refuge availability and resource supply in determining the abundance and size distributions of the introduced and omnivorous signal crayfish (Pacifastacus leniusculus) in lakes and streams. Moreover, the biomass and food selection of predatory fish was estimated in each habitat type and stable isotopes of carbon and nitrogen were measured in perch (Perca fluviatilis), the dominant predator in the lakes, and in its potential food sources (crayfish, juvenile roach and isopods). 2. In lakes, crayfish were the most frequent prey in large perch (46%), followed by other macroinvertebrates (26%, including the isopod Asellus aquaticus) and small fish (25%). Crayfish and fish dominated the gut contents of large perch with respect to biomass. Nitrogen signatures showed that perch were one trophic level above crayfish (approx. 3.4 parts per thousand) and a two-source mixing model using nitrogen isotope values indicated that crayfish (81%) contributed significantly more to perch isotope values than did juvenile roach (19%). A positive correlation was found between the abundance of crayfish and the biomass of large perch. Crayfish abundance in lakes was also positively correlated with the proportion of cobbles in the littoral zone. Lake productivity (chlorophyll a) was positively correlated with crayfish size, but not with crayfish abundance. 3. In streams, brown trout (Salmo trutta) were the most abundant predatory fish. Gut contents of large trout in a forested stream showed that terrestrial insects were the most frequently found prey (60%), followed by small crayfish (27%) and isopods (27%). In contrast to lakes, the relative abundance of crayfish was negatively correlated with the total biomass of predatory fish and with total biomass of trout. However, abundance of crayfish at sites with a low biomass of predatory fish varied considerably and was related to substratum grain size, with fewer crayfish being caught when the substratum was sandy or dominated by large boulders. The mean size of crayfish was greater at stream sites with a high standing stock of periphyton, but neither predator biomass nor substratum grain size was correlated with crayfish size. 4. Our results suggest that bottom-up processes influence crayfish size in lakes and streams independent of predator biomass and substratum availability. However, bottom-up processes do not influence crayfish abundance. Instead, substratum availability (lakes) and interactions between predation and substratum grain size (streams) need to be considered in order to predict crayfish abundance