B. B. G. K. Y. Hierarchy Methods for Sums of Lyapunov Exponents for Dilute Gases

We consider a general method for computing the sum of positive Lyapunov exponents for moderately dense gases. This method is based upon hierarchy techniques used previously to derive the generalized Boltzmann equation for the time dependent spatial and velocity distribution functions for such systems. We extend the variables in the generalized Boltzmann equation to include a new set of quantities that describe the separation of trajectories in phase space needed for a calculation of the Lyapunov exponents. The method described here is especially suitable for calculating the sum of all of the positive Lyapunov exponents for the system, and may be applied to equilibrium as well as non-equilibrium situations. For low densities we obtain an extended Boltzmann equation, from which, under a simplifying approximation, we recover the sum of positive Lyapunov exponents for hard disk and hard sphere systems, obtained before by a simpler method. In addition we indicate how to improve these results by avoiding the simplifying approximation. The restriction to hard sphere systems in $d$-dimensions is made to keep the somewhat complicated formalism as clear as possible, but the method can be easily generalized to apply to gases of particles that interact with strong short range forces.Comment: submitted to CHAOS, special issue, T. Tel. P. Gaspard, and G. Nicolis, ed

SARS-Coronavirus-2 nucleocapsid protein measured in blood using a Simoa ultra-sensitive immunoassay differentiates COVID-19 infection with high clinical sensitivity. [preprint]

The COVID-19 pandemic continues to have an unprecedented impact on societies and economies worldwide. Despite rapid advances in diagnostic test development and scale-up, there remains an ongoing need for SARS-CoV-2 tests which are highly sensitive, specific, minimally invasive, cost-effective and scalable for broad testing and surveillance. Here we report development of a highly sensitive single molecule array (Simoa) immunoassay on the automated HD-X platform for the detection of SARS-CoV-2 Nucleocapsid protein (N-protein) in venous and capillary blood (fingerstick). In pre-pandemic and clinical sample sets, the assay has 100% specificity and 97.4% sensitivity for serum / plasma samples. The limit of detection (LoD) estimated by titration of inactivated SARS-CoV-2 virus is 0.2 pg/ml, corresponding to 0.05 Median Tissue Culture Infectious Dose (TCID50) per ml, \u3e 2000 times more sensitive than current EUA approved antigen tests. No cross-reactivity to other common respiratory viruses, including hCoV229E, hCoVOC43, hCoVNL63, Influenza A or Influenza B, was observed. We detected elevated N-protein concentrations in symptomatic, asymptomatic, and pre-symptomatic PCR+ individuals using capillary blood from a finger-stick collection device. The Simoa SARS-CoV-2 N-protein assay has the potential to detect COVID-19 infection via antigen in blood with similar or better performance characteristics of molecular tests, while also enabling at home and point of care sample collection

Analysis of stochastic gradient descent in continuous time

Stochastic gradient descent is an optimisation method that combines classical gradient descent with random subsampling within the target functional. In this work, we introduce the stochastic gradient process as a continuous-time representation of stochastic gradient descent. The stochastic gradient process is a dynamical system that is coupled with a continuous-time Markov process living on a finite state space. The dynamical system -- a gradient flow -- represents the gradient descent part, the process on the finite state space represents the random subsampling. Processes of this type are, for instance, used to model clonal populations in fluctuating environments. After introducing it, we study theoretical properties of the stochastic gradient process: We show that it converges weakly to the gradient flow with respect to the full target function, as the learning rate approaches zero. We give conditions under which the stochastic gradient process with constant learning rate is exponentially ergodic in the Wasserstein sense. Then we study the case, where the learning rate goes to zero sufficiently slowly and the single target functions are strongly convex. In this case, the process converges weakly to the point mass concentrated in the global minimum of the full target function; indicating consistency of the method. We conclude after a discussion of discretisation strategies for the stochastic gradient process and numerical experiments

Income-related inequalities in chronic conditions, physical functioning and psychological distress among older people in Australia: cross-sectional findings from the 45 and up study

BACKGROUND: The burden of chronic disease continues to rise as populations age. There is relatively little published on the socioeconomic distribution of this burden in older people. This study quantifies absolute and relative income-related inequalities in prevalence of chronic diseases, severe physical functioning limitation and high psychological distress in mid-age and older people in Australia. METHODS: Cross-sectional study of 208,450 participants in the 45 and Up Study, a population-based cohort of men and women aged 45–106 years from New South Wales, Australia. Chronic conditions included self-reported heart disease, diabetes, Parkinson’s disease, cancer and osteoarthritis; physical functioning limitation (severe/not) was measured using Medical Outcomes Study measures and psychological distress (high/not) using the Kessler Psychological Distress Scale. For each outcome, prevalence was estimated in relation to annual household income (6 categories). Prevalence differences (PDs) and ratios (PRs) were generated, comparing the lowest income category (<$20,000) to the highest (≥$70,000), using Poisson regression with robust standard errors, weighted for age, sex and region of residence. Analyses were stratified by age group (45–64, 65–79 and ≥80 years) and sex and adjusted for age and country of birth. RESULTS: With few exceptions, there were income gradients in the prevalence of chronic conditions among all age-sex groups, with prevalence decreasing with increasing income. Of the chronic diseases, PDs were highest for diabetes (ranging between 5.69% and 10.36% across age-sex groups) and in women, also for osteoarthritis (5.72% to 8.14%); PRs were highest for osteoarthritis in men aged 45–64 years (4.01), otherwise they were highest for diabetes (1.78 to 3.43). Inequalities were very high for both physical functioning limitation and psychological distress, particularly among those aged 45–64 (PDs between 18.67% and 29.23% and PRs between 4.63 and 16.51). Absolute and relative inequalities tended to decrease with age, but remained relatively high for diabetes and physical functioning in the elderly (≥80 years). CONCLUSIONS: Significant inequalities in the prevalence of chronic conditions, physical functioning and psychological distress persist into old age. The additional health burden placed on those who are already disadvantaged is likely to become an increasingly important issue in an ageing population

Aging in a simple glassformer

Using molecular dynamics computer simulations we investigate the out-of-equilibrium dynamics of a Lennard-Jones system after a quench from a high temperature to one below the glass transition temperature. By studying the radial distribution function we give evidence that during the aging the system is very close to the critical surface of mode-coupling theory. Furthermore we show that two-time correlation functions show a strong dependence on the waiting time since the quench and that their shape is very different from the one in equilibrium. By investigating the temperature and time dependence of the frequency distribution of the normal modes we show that the energy of the inherent structures can be used to define an effective (time dependent) temperature of the aging system.Comment: Talk presented at ``Unifying Concepts in Glass Physics'', ICTP, Trieste 15 - 18 September 1999; 12 pages of Late

Inflammasome-induced extracellular vesicles harbour distinct RNA signatures and alter bystander macrophage responses

Infectious organisms and damage of cells can activate inflammasomes, which mediate tissue inflammation and adaptive immunity. These mechanisms evolved to curb the spread of microbes and to induce repair of the damaged tissue. Chronic activation of inflammasomes, however, contributes to non-resolving inflammatory responses that lead to immuno-pathologies. Inflammasome-activated cells undergo an inflammatory cell death associated with the release of potent pro-inflammatory cytokines and poorly characterized extracellular vesicles (EVs). Since inflammasome-induced EVs could signal inflammasome pathway activation in patients with chronic inflammation and modulate bystander cell activation, we performed a systems analysis of the ribonucleic acid (RNA) content and function of two EV classes. We show that EVs released from inflammasome-activated macrophages carry a specific RNA signature and contain interferon beta (IFNbeta). EV-associated IFNbeta induces an interferon signature in bystander cells and results in dampening of NLRP3 inflammasome responses. EVs could, therefore, serve as biomarkers for inflammasome activation and act to prevent systemic hyper-inflammatory states by restricting NLRP3 activation in bystander cells

Chaotic Properties of Dilute Two and Three Dimensional Random Lorentz Gases I: Equilibrium Systems

We compute the Lyapunov spectrum and the Kolmogorov-Sinai entropy for a moving particle placed in a dilute, random array of hard disk or hard sphere scatterers - i.e. the dilute Lorentz gas model. This is carried out in two ways: First we use simple kinetic theory arguments to compute the Lyapunov spectrum for both two and three dimensional systems. In order to provide a method that can easily be generalized to non-uniform systems we then use a method based upon extensions of the Lorentz-Boltzmann (LB) equation to include variables that characterize the chaotic behavior of the system. The extended LB equations depend upon the number of dimensions and on whether one is computing positive or negative Lyapunov exponents. In the latter case the extended LB equation is closely related to an "anti-Lorentz-Boltzmann equation" where the collision operator has the opposite sign from the ordinary LB equation. Finally we compare our results with computer simulations of Dellago and Posch and find very good agreement.Comment: 48 pages, 3 ps fig

Chaotic Properties of Dilute Two and Three Dimensional Random Lorentz Gases II: Open Systems

We calculate the spectrum of Lyapunov exponents for a point particle moving in a random array of fixed hard disk or hard sphere scatterers, i.e. the disordered Lorentz gas, in a generic nonequilibrium situation. In a large system which is finite in at least some directions, and with absorbing boundary conditions, the moving particle escapes the system with probability one. However, there is a set of zero Lebesgue measure of initial phase points for the moving particle, such that escape never occurs. Typically, this set of points forms a fractal repeller, and the Lyapunov spectrum is calculated here for trajectories on this repeller. For this calculation, we need the solution of the recently introduced extended Boltzmann equation for the nonequilibrium distribution of the radius of curvature matrix and the solution of the standard Boltzmann equation. The escape-rate formalism then gives an explicit result for the Kolmogorov Sinai entropy on the repeller.Comment: submitted to Phys Rev