Connecting N-representability to Weyl's problem: The one particle density matrix for N = 3 and R = 6

An analytic proof is given of the necessity of the Borland-Dennis conditions for 3-representability of a one particle density matrix with rank 6. This may shed some light on Klyachko's recent use of Schubert calculus to find general conditions for N-representability

Promoting fairness in Sheffield

In the light of growing inequalities, several urban areas in the UK established Fairness Commissions between 2010 and 2013. In one of these areas, Sheffield, there was an attempt to do something different and innovative. Sheffield on average was, and remains one of the least deprived major cities in England, but also one of the most unequal. Following the publication of the Commission’s report which included an analysis of evidence and 90 recommendations, Sheffield responded by pursuing a number of city-wide initiatives involving different stakeholders. These included monitoring progress towards a fairer city, action on the living wage, a city-wide campaign to promote Sheffield as the fairest city, and ‘Sheffield Money’ to provide support for those households facing financial exclusion. The continuation of austerity measures still creates severe challenges to the ambitions and work of the Sheffield Fairness Commission, but experiences have shown how leadership through example and the co-production of an active campaign can give articulation to a shared desire to address injustices in the city

Volatility Effects on the Escape Time in Financial Market Models

We shortly review the statistical properties of the escape times, or hitting times, for stock price returns by using different models which describe the stock market evolution. We compare the probability function (PF) of these escape times with that obtained from real market data. Afterwards we analyze in detail the effect both of noise and different initial conditions on the escape time in a market model with stochastic volatility and a cubic nonlinearity. For this model we compare the PF of the stock price returns, the PF of the volatility and the return correlation with the same statistical characteristics obtained from real market data.Comment: 12 pages, 9 figures, to appear in Int. J. of Bifurcation and Chaos, 200

Consequences of the H-Theorem from Nonlinear Fokker-Planck Equations

A general type of nonlinear Fokker-Planck equation is derived directly from a master equation, by introducing generalized transition rates. The H-theorem is demonstrated for systems that follow those classes of nonlinear Fokker-Planck equations, in the presence of an external potential. For that, a relation involving terms of Fokker-Planck equations and general entropic forms is proposed. It is shown that, at equilibrium, this relation is equivalent to the maximum-entropy principle. Families of Fokker-Planck equations may be related to a single type of entropy, and so, the correspondence between well-known entropic forms and their associated Fokker-Planck equations is explored. It is shown that the Boltzmann-Gibbs entropy, apart from its connection with the standard -- linear Fokker-Planck equation -- may be also related to a family of nonlinear Fokker-Planck equations.Comment: 19 pages, no figure

Nonlinear equation for anomalous diffusion: unified power-law and stretched exponential exact solution

The nonlinear diffusion equation $\frac{\partial \rho}{\partial t}=D \tilde{\Delta} \rho^\nu$ is analyzed here, where $\tilde{\Delta}\equiv \frac{1}{r^{d-1}}\frac{\partial}{\partial r} r^{d-1-\theta} \frac{\partial}{\partial r}$, and $d$, $\theta$ and $\nu$ are real parameters. This equation unifies the anomalous diffusion equation on fractals ($\nu =1$) and the spherical anomalous diffusion for porous media ($\theta=0$). Exact point-source solution is obtained, enabling us to describe a large class of subdiffusion ($\theta > (1-\nu)d$), normal diffusion ($\theta= (1-\nu)d$) and superdiffusion ($\theta < (1-\nu)d$). Furthermore, a thermostatistical basis for this solution is given from the maximum entropic principle applied to the Tsallis entropy.Comment: 3 pages, 2 eps figure

Reduced axonal transport in Parkinson's disease cybrid neurites is restored by light therapy

<p>Abstract</p> <p>Background</p> <p>It has been hypothesized that reduced axonal transport contributes to the degeneration of neuronal processes in Parkinson's disease (PD). Mitochondria supply the adenosine triphosphate (ATP) needed to support axonal transport and contribute to many other cellular functions essential for the survival of neuronal cells. Furthermore, mitochondria in PD tissues are metabolically and functionally compromised. To address this hypothesis, we measured the velocity of mitochondrial movement in human transmitochondrial cybrid "cytoplasmic hybrid" neuronal cells bearing mitochondrial DNA from patients with sporadic PD and disease-free age-matched volunteer controls (CNT). The absorption of low level, near-infrared laser light by components of the mitochondrial electron transport chain (mtETC) enhances mitochondrial metabolism, stimulates oxidative phosphorylation and improves redox capacity. PD and CNT cybrid neuronal cells were exposed to near-infrared laser light to determine if the velocity of mitochondrial movement can be restored by low level light therapy (LLLT). Axonal transport of labeled mitochondria was documented by time lapse microscopy in dopaminergic PD and CNT cybrid neuronal cells before and after illumination with an 810 nm diode laser (50 mW/cm²) for 40 seconds. Oxygen utilization and assembly of mtETC complexes were also determined.</p> <p>Results</p> <p>The velocity of mitochondrial movement in PD cybrid neuronal cells (0.175 +/- 0.005 SEM) was significantly reduced (p < 0.02) compared to mitochondrial movement in disease free CNT cybrid neuronal cells (0.232 +/- 0.017 SEM). For two hours after LLLT, the average velocity of mitochondrial movement in PD cybrid neurites was significantly (p < 0.003) increased (to 0.224 +/- 0.02 SEM) and restored to levels comparable to CNT. Mitochondrial movement in CNT cybrid neurites was unaltered by LLLT (0.232 +/- 0.017 SEM). Assembly of complexes in the mtETC was reduced and oxygen utilization was altered in PD cybrid neuronal cells. PD cybrid neuronal cell lines with the most dysfunctional mtETC assembly and oxygen utilization profiles were least responsive to LLLT.</p> <p>Conclusion</p> <p>The results from this study support our proposal that axonal transport is reduced in sporadic PD and that a single, brief treatment with near-infrared light can restore axonal transport to control levels. These results are the first demonstration that LLLT can increase axonal transport in model human dopaminergic neuronal cells and they suggest that LLLT could be developed as a novel treatment to improve neuronal function in patients with PD.</p

Electronic structure of intentionally disordered AlAs/GaAs superlattices

We use realistic pseudopotentials and a plane-wave basis to study the electronic structure of non-periodic, three-dimensional, 2000-atom (AlAs)_n/(GaAs)_m (001) superlattices, where the individual layer thicknesses n,m = {1,2,3} are randomly selected. We find that while the band gap of the equivalent (n = m = 2) ordered superlattice is indirect, random fluctuations in layer thicknesses lead to a direct gap in the planar Brillouin zone, strong wavefunction localization along the growth direction, short radiative lifetimes, and a significant band-gap reduction, in agreement with experiments on such intentionally grown disordered superlattices.Comment: 10 pages, REVTeX and EPSF macros, 4 figures in postscript. e-mail to [email protected]

Information Theory based on Non-additive Information Content

We generalize the Shannon's information theory in a nonadditive way by focusing on the source coding theorem. The nonadditive information content we adopted is consistent with the concept of the form invariance structure of the nonextensive entropy. Some general properties of the nonadditive information entropy are studied, in addition, the relation between the nonadditivity $q$ and the codeword length is pointed out.Comment: 9 pages, no figures, RevTex, accepted for publication in Phys. Rev. E(an error in proof of theorem 1 was corrected, typos corrected

A CAM- and starch-deficient mutant of the facultative CAM species Mesembryanthemum crystallinum reconciles sink demands by repartitioning carbon during acclimation to salinity

In the halophytic species Mesembryanthemum crystallinum, the induction of crassulacean acid metabolism (CAM) by salinity requires a substantial investment of resources in storage carbohydrates to provide substrate for nocturnal CO2 uptake. Acclimation to salinity also requires the synthesis and accumulation of cyclitols as compatible solutes, maintenance of root respiration, and nitrate assimilation. This study assessed the hierarchy and coordination of sinks for carbohydrate in leaves and roots during acclimation to salinity in M. crystallinum. By comparing wild type and a CAM-/starch-deficient mutant of this species, it was sought to determine if other metabolic sinks could compensate for a curtailment in CAM and enable acclimation to salinity. Under salinity, CAM deficiency reduced 24 h photosynthetic carbon gain by >50%. Cyclitols were accumulated to comparable levels in leaves and roots of both the wild type and mutant, but represented only 5% of 24 h carbon balance. Dark respiration of leaves and roots was a stronger sink for carbohydrate in the mutant compared with the wild type and implied higher maintenance costs for the metabolic processes underpinning acclimation to salinity when CAM was curtailed. CAM required the nocturnal mobilization of >70% of primary carbohydrate in the wild type and >85% of carbohydrate in the mutant. The substantial allocation of carbohydrate to CAM limited the export of sugars to roots, and the root:shoot ratio declined under salinity. The data suggest a key role for the vacuole in regulating the supply and demand for carbohydrate over the day/night cycle in the starch-/CAM-deficient mutant