Fluctuation-Dissipation relations in Driven Granular Gases

We study the dynamics of a 2d driven inelastic gas, by means of Direct Simulation Monte Carlo (DSMC) techniques, i.e. under the assumption of Molecular Chaos. Under the effect of a uniform stochastic driving in the form of a white noise plus a friction term, the gas is kept in a non-equilibrium Steady State characterized by fractal density correlations and non-Gaussian distributions of velocities; the mean squared velocity, that is the so-called {\em granular temperature}, is lower than the bath temperature. We observe that a modified form of the Kubo relation, which relates the autocorrelation and the linear response for the dynamics of a system {\em at equilibrium}, still holds for the off-equilibrium, though stationary, dynamics of the systems under investigation. Interestingly, the only needed modification to the equilibrium Kubo relation is the replacement of the equilibrium temperature with an effective temperature, which results equal to the global granular temperature. We present two independent numerical experiment, i.e. two different observables are studied: (a) the staggered density current, whose response to an impulsive shear is proportional to its autocorrelation in the unperturbed system and (b) the response of a tracer to a small constant force, switched on at time $t_w$, which is proportional to the mean-square displacement in the unperturbed system. Both measures confirm the validity of Kubo's formula, provided that the granular temperature is used as the proportionality factor between response and autocorrelation, at least for not too large inelasticities.Comment: 11 pages, 7 figures, submitted for publicatio

PAC1 receptor-mediated clearance of tau in postsynaptic compartments attenuates tau pathology in mouse brain

Accumulation of pathological tau in synapses has been identified as an early event in Alzheimer's disease (AD) and correlates with cognitive decline in patients with AD. Tau is a cytosolic axonal protein, but under disease conditions, tau accumulates in postsynaptic compartments and presynaptic terminals, due to missorting within neurons, transsynaptic transfer between neurons, or a failure of clearance pathways. Using subcellular fractionation of brain tissue from rTg4510 tau transgenic mice with tauopathy and human postmortem brain tissue from patients with AD, we found accumulation of seed-competent tau predominantly in postsynaptic compartments. Tau-mediated toxicity in postsynaptic compartments was exacerbated by impaired proteasome activity detected by measuring lysine-48 polyubiquitination of proteins targeted for proteasomal degradation. To combat the accumulation of tau and proteasome impairment in the postsynaptic compartments of rTg4510 mouse brain, we stimulated the pituitary adenylate cyclase-activating polypeptide (PACAP) type 1 receptor (PAC1R) with its ligand PACAP administered intracerebroventricularly to rTg4510 mice. We observed enhanced synaptic proteasome activity and reduced total tau in postsynaptic compartments in mouse brain after PACAP treatment. The clearance of tau from postsynaptic compartments correlated with attenuated tauopathy and improved cognitive performance of rTg4510 transgenic mice on two behavioral tests. These results suggest that activating PAC1R could prevent accumulation of aggregate-prone tau and indicate a potential therapeutic approach for AD and other tauopathies

Meat eating and nutritional quality of lambs sired by high and low muscle density rams

Intramuscular fat (IMF) content affects eating and nutritional quality of lamb meat. Muscle density measured by computer tomography is an in vivo proxy measure of IMF content that affects eating and nutritional quality of lamb meat. Lambs sired by high muscle density (HMD) or low muscle density (LMD) rams, selected for slaughter on commercial criteria were measured for meat quality and nutritional traits. A restricted maximum likelihood model was used to compare lamb traits. Additionally, regression analysis of sire estimated breeding value (EBV) for muscle density was performed for each meat quality trait. Muscle density EBV had a negative regression with IMF content (P < 0.001). For each unit increase in muscle density EBV, there was a significant decrease in loin (− 1.69 mg/100 g fresh weight) and topside IMF (− 0.03 mg/100 g fresh weight). Muscle density EBV had a negative regression with grouped saturated and monounsaturated fatty acids concentration (and monounsaturated proportion P < 0.001). Muscle density EBV had a negative regression with loin sensory traits tenderness, juiciness and overall liking and many novel tenderness sensory traits measured (P < 0.05). Selecting for LMD EBV increased IMF content and favourable meat eating quality traits. In contrast, sire muscle density EBV had a positive regression with loin polyunsaturated:saturated fat ratio and grouped polyunsaturated proportion traits (including total polyunsaturated proportion, total omega-6 (n-6) and total omega-3 (n-3) fatty acids (P < 0.001). This is explained by the fact that as sire muscle density EBV increases, polyunsaturated fatty acid proportion increases and the proportion of saturated and monounsaturated fatty acid content decreases. Muscle density EBV had a positive regression with shear force and the novel toughness sensory traits (P < 0.05). Selection for HMD EBV's increased shear force and toughness traits, which is unfavourable for the consumer. Low muscle density sired meat had higher meat colour traits chroma/saturation (+ 0.64, SD 2.30, P = 0.012), redness (+ 0.52, SD 1.91, P = 0.012) and yellowness (+ 0.31, SD 1.49, P = 0.08) compared to HMD sired meat. Selection for LMD could be used within a breeding programme to increase IMF content and enhance both meat colour and improve eating quality parameters

Molecular dynamics simulations of vibrated granular gases

We present molecular dynamics simulations of mono- or bidisperse inelastic granular gases driven by vibrating walls, in two dimensions (without gravity). Because of the energy injection at the boundaries, a situation often met experimentally, density and temperature fields display heterogeneous profiles in the direction perpendicular to the walls. A general equation of state for an arbitrary mixture of fluidized inelastic hard spheres is derived and successfully tested against numerical data. Single-particle velocity distribution functions with non-Gaussian features are also obtained, and the influence of various parameters (inelasticity coefficients, density...) analyzed. The validity of a recently proposed Random Restitution Coefficient model is assessed through the study of projected collisions onto the direction perpendicular to that of energy injection. For the binary mixture, the non-equipartition of translational kinetic energy is studied and compared both to experimental data and to the case of homogeneous energy injection (``stochastic thermostat''). The rescaled velocity distribution functions are found to be very similar for both species

Symptoms associated with victimization in patients with schizophrenia and related disorders

Background: Patients with psychoses have an increased risk of becoming victims of violence. Previous studies have suggested that higher symptom levels are associated with a raised risk of becoming a victim of physical violence. There has been, however, no evidence on the type of symptoms that are linked with an increased risk of recent victimization. Methods: Data was taken from two studies on involuntarily admitted patients, one national study in England and an international one in six other European countries. In the week following admission, trained interviewers asked patients whether they had been victims of physical violence in the year prior to admission, and assessed symptoms on the Brief Psychiatric Rating Scale (BPRS). Only patients with a diagnosis of schizophrenia or related disorders (ICD-10 F20–29) were included in the analysis which was conducted separately for the two samples. Symptom levels assessed on the BPRS subscales were tested as predictors of victimization. Univariable and multivariable logistic regression models were fitted to estimate adjusted odds ratios. Results: Data from 383 patients in the English sample and 543 patients in the European sample was analysed. Rates of victimization were 37.8% and 28.0% respectively. In multivariable models, the BPRS manic subscale was significantly associated with victimization in both samples. Conclusions: Higher levels of manic symptoms indicate a raised risk of being a victim of violence in involuntary patients with schizophrenia and related disorders. This might be explained by higher activity levels, impaired judgement or poorer self-control in patients with manic symptoms. Such symptoms should be specifically considered in risk assessments

Diffusion of impurities in a granular gas

Diffusion of impurities in a granular gas undergoing homogeneous cooling state is studied. The results are obtained by solving the Boltzmann--Lorentz equation by means of the Chapman--Enskog method. In the first order in the density gradient of impurities, the diffusion coefficient $D$ is determined as the solution of a linear integral equation which is approximately solved by making an expansion in Sonine polynomials. In this paper, we evaluate $D$ up to the second order in the Sonine expansion and get explicit expressions for $D$ in terms of the restitution coefficients for the impurity--gas and gas--gas collisions as well as the ratios of mass and particle sizes. To check the reliability of the Sonine polynomial solution, analytical results are compared with those obtained from numerical solutions of the Boltzmann equation by means of the direct simulation Monte Carlo (DSMC) method. In the simulations, the diffusion coefficient is measured via the mean square displacement of impurities. The comparison between theory and simulation shows in general an excellent agreement, except for the cases in which the gas particles are much heavier and/or much larger than impurities. In theses cases, the second Sonine approximation to $D$ improves significantly the qualitative predictions made from the first Sonine approximation. A discussion on the convergence of the Sonine polynomial expansion is also carried out.Comment: 9 figures. to appear in Phys. Rev.

Jacobi-Lie systems: Fundamentals and low-dimensional classification

A Lie system is a system of differential equations describing the integral curves of a $t$-dependent vector field taking values in a finite-dimensional real Lie algebra of vector fields, a Vessiot-Guldberg Lie algebra. We define and analyze Lie systems possessing a Vessiot-Guldberg Lie algebra of Hamiltonian vector fields relative to a Jacobi manifold, the hereafter called Jacobi-Lie systems. We classify Jacobi-Lie systems on $\mathbb{R}$ and $\mathbb{R}^2$. Our results shall be illustrated through examples of physical and mathematical interest.Comment: 15 pages. Examples, references and comments added. Based on the contribution presented at "The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications", July 07-11, 2014, Madrid, Spain. To appear in the Proceedings of the 10th AIMS Conferenc

The gene structure and expression of human ABHD1: overlapping polyadenylation signal sequence with Sec12

BACKGROUND: Overlapping sense/antisense genes orientated in a tail-to-tail manner, often involving only the 3'UTRs, form the majority of gene pairs in mammalian genomes and can lead to the formation of double-stranded RNA that triggers the destruction of homologous mRNAs. Overlapping polyadenylation signal sequences have not been described previously. RESULTS: An instance of gene overlap has been found involving a shared single functional polyadenylation site. The genes involved are the human alpha/beta hydrolase domain containing gene 1 (ABHD1) and Sec12 genes. The nine exon human ABHD1 gene is located on chromosome 2p23.3 and encodes a 405-residue protein containing a catalytic triad analogous to that present in serine proteases. The Sec12 protein promotes efficient guanine nucleotide exchange on the Sar1 GTPase in the ER. Their sequences overlap for 42 bp in the 3'UTR in an antisense manner. Analysis by 3' RACE identified a single functional polyadenylation site, ATTAAA, within the 3'UTR of ABHD1 and a single polyadenylation signal, AATAAA, within the 3'UTR of Sec12. These polyadenylation signals overlap, sharing three bp. They are also conserved in mouse and rat. ABHD1 was expressed in all tissues and cells examined, but levels of ABHD1 varied greatly, being high in skeletal muscle and testis and low in spleen and fibroblasts. CONCLUSIONS: Mammalian ABHD1 and Sec12 genes contain a conserved 42 bp overlap in their 3'UTR, and share a conserved TTTATTAAA/TTTAATAAA sequence that serves as a polyadenylation signal for both genes. No inverse correlation between the respective levels of ABHD1 and Sec12 RNA was found to indicate that any RNA interference occurred