Autocorrelation function for human gait analysis

The paper presents applying of the autocorrelation function to human gait analysis. The series of angle signals at the hip, knee and ankle joints of patients with different pathological states were analyzed. The signals were processed by means of the autocorrelation function. This approach allowed to apply the simple mathematical function for analytic description of curves. By using curve fitting, parameters of 5th order polynomial function were evaluated. Mean values and standard deviation of six parameters were observed in relation to human gait pathology. The results indicate new possibilities for applying the method to diagnose human gait using the autocorrelation functio

Audits as Signals

A broad array of law enforcement strategies, from income tax to bank regulation, involve self-reporting by regulated agents and auditing of some fraction of the reports by the regulating bureau. Standard models of self-reporting strategies assume that although bureaus only have estimates of the of an agent’s type, agents know the ability of bureaus to detect their misreports. We relax this assumption, and posit that agents only have an estimate of the auditing capabilities of bureaus. Enriching the model to allow two-sided private information changes the behavior of bureaus. A bureau that is weak at auditing, may wish to mimic a bureau that is strong. Strong bureaus may be able to signal their capabilities, but at a cost. We explore the pooling, separating, and semi-separating equilibria that result, and the policy implications. Important possible outcomes are that a cap on penalties increases compliance, audit hit rates are not informative of the quality of bureau behavior, and by mimicking strong bureaus even weak bureaus can induce compliance

Tight Bell inequalities with no quantum violation from qubit unextendible product bases

We investigate the relation between unextendible product bases (UPB) and Bell inequalities found recently in [R. Augusiak et al., Phys. Rev. Lett. 107, 070401 (2011)]. We first review the procedure introduced there that associates to any set of mutually orthogonal product vectors in a many-qubit Hilbert space a Bell inequality. We then show that if a set of mutually orthogonal product vectors can be completed to a full basis, then the associated Bell inequality is trivial, in the sense of not being violated by any nonsignalling correlations. This implies that the relevant Bell inequalities that arise from the construction all come from UPBs, which adds additional weight to the significance of UPBs for Bell inequalities. Then, we provide new examples of tight Bell inequalities with no quantum violation constructed from UPBs in this way. Finally, it is proven that the Bell inequalities with no quantum violation introduced recently in [M. Almeida et al., Phys. Rev. Lett. 104, 230404 (2010)] are tight for any odd number of parties.Comment: 14 pages, 1 figure, some minor improvement

Symplectic geometry of entanglement

We present a description of entanglement in composite quantum systems in terms of symplectic geometry. We provide a symplectic characterization of sets of equally entangled states as orbits of group actions in the space of states. In particular, using Kostant-Sternberg theorem, we show that separable states form a unique Kaehler orbit, whereas orbits of entanglement states are characterized by different degrees of degeneracy of the canonical symplectic form on the complex projective space. The degree of degeneracy may be thus used as a new geometric measure of entanglement and we show how to calculate it for various multiparticle systems providing also simple criteria of separability. The presented method is general and can be applied also under different additional symmetry conditions stemming, eg. from the indistinguishability of particles.Comment: LaTex, 31 pages, typos correcte

The effect of tillage management and its interaction with site conditions and plant functional traits on plant species establishment during meadow restoration

The restoration of grasslands is a key management practice that supports biodiversity across Europe. On species poor grasslands and ex-arable fields, the establishment of plant species is often limited by the availability of habitat niches, in particular space to germinate. We investigated the impacts of full inversion tillage and its interaction with site conditions and functional traits on the abundance of 51 plant species sown into a 2 ha ex-arable site in Poland. Soils of the donor site were characterized by high levels of heterogeneity in terms of water content and plant availability of N, P and K. One year after sowing the cover of species typical of semi-natural grasslands was significantly higher on the tilled plots than on the non-tilled plots. However, in the case of widespread generalist species the tillage of soil resulted in no significant effect on their establishing percentage cover. The establishment of plants on the tilled area was more successful where soils were relatively rich in mineral N. It was also more successful for species with low Ellenberg’s N values. Species indicative of moist soil established poorly where the soil was tilled. This study has clear implications for the applied restoration of grasslands, demonstrating a vital role of soil tillage to promote the establishment of species typical of semi-natural grasslands. This is particularly important where seed mixtures may contain both desirable and undesirable competitive species that would disproportionately benefit from the absence of tillage management

Digging into the extremes: a useful approach for the analysis of rare variants with continuous traits?

The common disease/rare variant hypothesis predicts that rare variants with large effects will have a strong impact on corresponding phenotypes. Therefore it is assumed that rare functional variants are enriched in the extremes of the phenotype distribution. In this analysis of the Genetic Analysis Workshop 17 data set, my aim is to detect genes with rare variants that are associated with quantitative traits using two general approaches: analyzing the association with the complete distribution of values by means of linear regression and using statistical tests based on the tails of the distribution (bottom 10% of values versus top 10%). Three methods are used for this extreme phenotype approach: Fisher’s exact test, weighted-sum method, and beta method. Rare variants were collapsed on the gene level. Linear regression including all values provided the highest power to detect rare variants. Of the three methods used in the extreme phenotype approach, the beta method performed best. Furthermore, the sample size was enriched in this approach by adding additional samples with extreme phenotype values. Doubling the sample size using this approach, which corresponds to only 40% of sample size of the original continuous trait, yielded a comparable or even higher power than linear regression. If samples are selected primarily for sequencing, enriching the analysis by gathering a greater proportion of individuals with extreme values in the phenotype of interest rather than in the general population leads to a higher power to detect rare variants compared to analyzing a population-based sample with equivalent sample size