Volume of the quantum mechanical state space

The volume of the quantum mechanical state space over $n$-dimensional real, complex and quaternionic Hilbert-spaces with respect to the canonical Euclidean measure is computed, and explicit formulas are presented for the expected value of the determinant in the general setting too. The case when the state space is endowed with a monotone metric or a pull-back metric is considered too, we give formulas to compute the volume of the state space with respect to the given Riemannian metric. We present the volume of the space of qubits with respect to various monotone metrics. It turns out that the volume of the space of qubits can be infinite too. We characterize those monotone metrics which generates infinite volume.Comment: 17 page

Applications of the gamma/hadron discriminator LCmLCm to realistic air shower array experiments

In this article, it is shown that the $C_k$ and $LCm$ variables, recently introduced as an effective way to discriminate gamma and proton-induced showers in large wide-field gamma-ray observatories, can be generalised to be used in arrays of different detectors and variable fill factors. In particular, the $C_k$ profile discrimination capabilities are evaluated for scintillator and water Cherenkov detector arrays

Metric adjusted skew information: Convexity and restricted forms of superadditivity

We give a truly elementary proof of the convexity of metric adjusted skew information following an idea of Effros. We extend earlier results of weak forms of superadditivity to general metric adjusted skew informations. Recently, Luo and Zhang introduced the notion of semi-quantum states on a bipartite system and proved superadditivity of the Wigner-Yanase-Dyson skew informations for such states. We extend this result to general metric adjusted skew informations. We finally show that a recently introduced extension to parameter values $1<p\le 2$ of the WYD-information is a special case of (unbounded) metric adjusted skew information.Comment: An error in the literature is pointed ou

Nonparametric Information Geometry

The differential-geometric structure of the set of positive densities on a given measure space has raised the interest of many mathematicians after the discovery by C.R. Rao of the geometric meaning of the Fisher information. Most of the research is focused on parametric statistical models. In series of papers by author and coworkers a particular version of the nonparametric case has been discussed. It consists of a minimalistic structure modeled according the theory of exponential families: given a reference density other densities are represented by the centered log likelihood which is an element of an Orlicz space. This mappings give a system of charts of a Banach manifold. It has been observed that, while the construction is natural, the practical applicability is limited by the technical difficulty to deal with such a class of Banach spaces. It has been suggested recently to replace the exponential function with other functions with similar behavior but polynomial growth at infinity in order to obtain more tractable Banach spaces, e.g. Hilbert spaces. We give first a review of our theory with special emphasis on the specific issues of the infinite dimensional setting. In a second part we discuss two specific topics, differential equations and the metric connection. The position of this line of research with respect to other approaches is briefly discussed.Comment: Submitted for publication in the Proceedings od GSI2013 Aug 28-30 2013 Pari

A Class of Non-Parametric Statistical Manifolds modelled on Sobolev Space

We construct a family of non-parametric (infinite-dimensional) manifolds of finite measures on Rd. The manifolds are modelled on a variety of weighted Sobolev spaces, including Hilbert-Sobolev spaces and mixed-norm spaces. Each supports the Fisher-Rao metric as a weak Riemannian metric. Densities are expressed in terms of a deformed exponential function having linear growth. Unusually for the Sobolev context, and as a consequence of its linear growth, this "lifts" to a nonlinear superposition (Nemytskii) operator that acts continuously on a particular class of mixed-norm model spaces, and on the fixed norm space W²'¹ i.e. it maps each of these spaces continuously into itself. It also maps continuously between other fixed-norm spaces with a loss of Lebesgue exponent that increases with the number of derivatives. Some of the results make essential use of a log-Sobolev embedding theorem. Each manifold contains a smoothly embedded submanifold of probability measures. Applications to the stochastic partial differential equations of nonlinear filtering (and hence to the Fokker-Planck equation) are outlined

Pattern recognition receptors as potential therapeutic targets in inflammatory rheumatic disease

The pattern recognition receptors of the innate immune system are part of the first line of defence against pathogens. However, they also have the ability to respond to danger signals that are frequently elevated during tissue damage and at sites of inflammation. Inadvertent activation of pattern recognition receptors has been proposed to contribute to the pathogenesis of many conditions including inflammatory rheumatic diseases. Prolonged inflammation most often results in pain and damage to tissues. In particular, the Toll-like receptors and nucleotide-binding oligomerisation domain-like receptors that form inflammasomes have been postulated as key contributors to the inflammation observed in rheumatoid arthritis, osteoarthritis, gout and systemic lupus erythematosus. As such, there is increasing interest in targeting these receptors for therapeutic treatment in the clinic. Here the role of pattern recognition receptors in the pathogenesis of these diseases is discussed, with an update on the development of interventions to modulate the activity of these potential therapeutic targets

Carnivore Translocations and Conservation: Insights from Population Models and Field Data for Fishers (Martes pennanti)

Translocations are frequently used to restore extirpated carnivore populations. Understanding the factors that influence translocation success is important because carnivore translocations can be time consuming, expensive, and controversial. Using population viability software, we modeled reintroductions of the fisher, a candidate for endangered or threatened status in the Pacific states of the US. Our model predicts that the most important factor influencing successful re-establishment of a fisher population is the number of adult females reintroduced (provided some males are also released). Data from 38 translocations of fishers in North America, including 30 reintroductions, 5 augmentations and 3 introductions, show that the number of females released was, indeed, a good predictor of success but that the number of males released, geographic region and proximity of the source population to the release site were also important predictors. The contradiction between model and data regarding males may relate to the assumption in the model that all males are equally good breeders. We hypothesize that many males may need to be released to insure a sufficient number of good breeders are included, probably large males. Seventy-seven percent of reintroductions with known outcomes (success or failure) succeeded; all 5 augmentations succeeded; but none of the 3 introductions succeeded. Reintroductions were instrumental in reestablishing fisher populations within their historical range and expanding the range from its most-contracted state (43% of the historical range) to its current state (68% of the historical range). To increase the likelihood of translocation success, we recommend that managers: 1) release as many fishers as possible, 2) release more females than males (55–60% females) when possible, 3) release as many adults as possible, especially large males, 4) release fishers from a nearby source population, 5) conduct a formal feasibility assessment, and 6) develop a comprehensive implementation plan that includes an active monitoring program