Propagation of chaos for rank-based interacting diffusions and long time behaviour of a scalar quasilinear parabolic equation

We study a quasilinear parabolic Cauchy problem with a cumulative distribution function on the real line as an initial condition. We call 'probabilistic solution' a weak solution which remains a cumulative distribution function at all times. We prove the uniqueness of such a solution and we deduce the existence from a propagation of chaos result on a system of scalar diffusion processes, the interactions of which only depend on their ranking. We then investigate the long time behaviour of the solution. Using a probabilistic argument and under weak assumptions, we show that the flow of the Wasserstein distance between two solutions is contractive. Under more stringent conditions ensuring the regularity of the probabilistic solutions, we finally derive an explicit formula for the time derivative of the flow and we deduce the convergence of solutions to equilibrium.Comment: Stochastic partial differential equations: analysis and computations (2013) http://dx.doi.org/10.1007/s40072-013-0014-

Timescales of Massive Human Entrainment

The past two decades have seen an upsurge of interest in the collective behaviors of complex systems composed of many agents entrained to each other and to external events. In this paper, we extend concepts of entrainment to the dynamics of human collective attention. We conducted a detailed investigation of the unfolding of human entrainment - as expressed by the content and patterns of hundreds of thousands of messages on Twitter - during the 2012 US presidential debates. By time locking these data sources, we quantify the impact of the unfolding debate on human attention. We show that collective social behavior covaries second-by-second to the interactional dynamics of the debates: A candidate speaking induces rapid increases in mentions of his name on social media and decreases in mentions of the other candidate. Moreover, interruptions by an interlocutor increase the attention received. We also highlight a distinct time scale for the impact of salient moments in the debate: Mentions in social media start within 5-10 seconds after the moment; peak at approximately one minute; and slowly decay in a consistent fashion across well-known events during the debates. Finally, we show that public attention after an initial burst slowly decays through the course of the debates. Thus we demonstrate that large-scale human entrainment may hold across a number of distinct scales, in an exquisitely time-locked fashion. The methods and results pave the way for careful study of the dynamics and mechanisms of large-scale human entrainment.Comment: 20 pages, 7 figures, 6 tables, 4 supplementary figures. 2nd version revised according to peer reviewers' comments: more detailed explanation of the methods, and grounding of the hypothese

Overfeeding, Autonomic Regulation and Metabolic Consequences

The autonomic nervous system plays an important role in the regulation of body processes in health and disease. Overfeeding and obesity (a disproportional increase of the fat mass of the body) are often accompanied by alterations in both sympathetic and parasympathetic autonomic functions. The overfeeding-induced changes in autonomic outflow occur with typical symptoms such as adiposity and hyperinsulinemia. There might be a causal relationship between autonomic disturbances and the consequences of overfeeding and obesity. Therefore studies were designed to investigate autonomic functioning in experimentally and genetically hyperphagic rats. Special emphasis was given to the processes that are involved in the regulation of peripheral energy substrate homeostasis. The data revealed that overfeeding is accompanied by increased parasympathetic outflow. Typical indices of vagal activity (such as the cephalic insulin release during food ingestion) were increased in all our rat models for hyperphagia. Overfeeding was also accompanied by increased sympathetic tone, reflected by enhanced baseline plasma norepinephrine (NE) levels in both VMH-lesioned animals and rats rendered obese by hyperalimentation. Plasma levels of NE during exercise were, however, reduced in these two groups of animals. This diminished increase in the exercise-induced NE outflow could be normalized by prior food deprivation. It was concluded from these experiments that overfeeding is associated with increased parasympathetic and sympathetic tone. In models for hyperphagia that display a continuously elevated nutrient intake such as the VMH-lesioned and the overfed rat, this increased sympathetic tone was accompanied by a diminished NE response to exercise. This attenuated outflow of NE was directly related to the size of the fat reserves, indicating that the feedback mechanism from the periphery to the central nervous system is altered in the overfed state.

The pharmacokinetics of the interstitial space in humans

BACKGROUND: The pharmacokinetics of extracellular solutes is determined by the blood-tissue exchange kinetics and the volume of distribution in the interstitial space in the different organs. This information can be used to develop a general physiologically based pharmacokinetic (PBPK) model applicable to most extracellular solutes. METHODS: The human pharmacokinetic literature was surveyed to tabulate the steady state and equilibrium volume of distribution of the solutes mannitol, EDTA, morphine-6-glucuronide, morphine-3-glucuronide, inulin and β-lactam antibiotics with a range of protein binding (amoxicillin, piperacillin, cefatrizine, ceforanide, flucloxacillin, dicloxacillin). A PBPK data set was developed for extracellular solutes based on the literature for interstitial organ volumes. The program PKQuest was used to generate the PBPK model predictions. The pharmacokinetics of the protein (albumin) bound β-lactam antibiotics were characterized by two parameters: 1) the free fraction of the solute in plasma; 2) the interstitial albumin concentration. A new approach to estimating the capillary permeability is described, based on the pharmacokinetics of the highly protein bound antibiotics. RESULTS: About 42% of the total body water is extracellular. There is a large variation in the organ distribution of this water – varying from about 13% of total tissue water for skeletal muscle, up to 70% for skin and connective tissue. The weakly bound antibiotics have flow limited capillary-tissue exchange kinetics. The highly protein bound antibiotics have a significant capillary permeability limitation. The experimental pharmacokinetics of the 11 solutes is well described using the new PBPK data set and PKQuest. CONCLUSIONS: Only one adjustable parameter (systemic clearance) is required to completely characterize the PBPK for these extracellular solutes. Knowledge of just this systemic clearance allows one to predict the complete time course of the absolute drug concentrations in the major organs. PKQuest is freely available

A mixed methods study to evaluate the feasibility of using the Adolescent Diabetes Needs Assessment Tool App in paediatric diabetes care in preparation for a longitudinal cohort study

An evaluation study was carried out to determine the feasibility of integrating the Adolescent Diabetes Needs Assessment Tool (ADNAT) App into UK paediatric diabetes care, to ascertain best practice standards and to determine methodological recommendations for a future cohort study. Methods A non-randomised, cohort, mixed methods study design was used to ensure equality of access to ADNAT for all participants at three sites in the North West of England. Following UK Medical Research Council guidance, the RE-AIM (reach, effectiveness (potential and perceived), adoption, implementation, maintenance) framework was used to guide study objectives and feasibility outcomes. Patients who completed ADNAT (completers) were compared with those who failed to complete (non-completers). Patients’ glycaemic control (HbA1c) was accessed from their clinical data at baseline and at 6 months, alongside their ADNAT scores which were correlated with changes in HbA1c levels. The diabetes teams (respondents) completed a web-based survey and attended focus group interviews. Results Eighty-nine patients were recruited. Withdrawal rates were low at 4.5% (n = 4). Forty-four patients (49.4%) completed ADNAT, leaving 45 (50.6%) non-completers. There were large baseline differences in HbA1c and variable rates of change at 6 months. After adjusting for baseline HbA1C and site in an analysis of covariance, completers had a lower post-ADNAT mean HbA1C level than non-completers at 6 months (-5.42 mmol/mol, 95% CI −11.48, 0.64). Patients’ glycaemic control (HbA1c) at 6 months correlated reasonably well with their ADNAT scores (Spearman’s rho = 0.46). Survey and focus group data showed that ADNAT was judged to be an effective clinical tool by the diabetes teams. Value to patients was perceived by the teams to be linked to parental support, age and previous diabetes education. The combined data triangulated. It served to capture different dimensions which were used to define changes to achieve practice standards and methodological recommendations. Conclusions The combined data showed that ADNAT has the potential to be a clinically viable tool. It has demonstrated the need for a randomised design that is tailored for a ‘hard to reach’ adolescent population. A cluster randomised controlled trial that involves sequential but random rollout of ADNAT over multiple time periods may be the most appropriate and is currently being considered for the larger study

The role of the pion cloud in the interpretation of the valence light-cone wavefunction of the nucleon

The pion cloud renormalises the light-cone wavefunction of the nucleon which is measured in hard, exclusive photon-nucleon reactions. We discuss the leading twist contributions to high-energy exclusive reactions taking into account both the pion cloud and perturbative QCD physics. The nucleon's electromagnetic form-factor at high $Q^2$ is proportional to the bare nucleon probability $Z$ and the cross-sections for hard (real at large angle or deeply virtual) Compton scattering are proportional to $Z^2$. Our present knowledge of the pion-nucleon system is consistent with $Z = 0.7 \pm 0.2$. If we apply just perturbative QCD to extract a light-cone wavefunction directly from these hard exclusive cross-sections, then the light-cone wavefunction that we extract measures the three valence quarks partially screened by the pion cloud of the nucleon. We discuss how this pion cloud renormalisation effect might be understood at the quark level in terms of the (in-)stability of the perturbative Dirac vacuum in low energy QCD.Comment: Expanded Discussion of Phenomenology and Spin Physic

Retinoid-Binding Proteins: Similar Protein Architectures Bind Similar Ligands via Completely Different Ways

Background: Retinoids are a class of compounds that are chemically related to vitamin A, which is an essential nutrient that plays a key role in vision, cell growth and differentiation. In vivo, retinoids must bind with specific proteins to perform their necessary functions. Plasma retinol-binding protein (RBP) and epididymal retinoic acid binding protein (ERABP) carry retinoids in bodily fluids, while cellular retinol-binding proteins (CRBPs) and cellular retinoic acid-binding proteins (CRABPs) carry retinoids within cells. Interestingly, although all of these transport proteins possess similar structures, the modes of binding for the different retinoid ligands with their carrier proteins are different. Methodology/Principal Findings: In this work, we analyzed the various retinoid transport mechanisms using structure and sequence comparisons, binding site analyses and molecular dynamics simulations. Our results show that in the same family of proteins and subcellular location, the orientation of a retinoid molecule within a binding protein is same, whereas when different families of proteins are considered, the orientation of the bound retinoid is completely different. In addition, none of the amino acid residues involved in ligand binding is conserved between the transport proteins. However, for each specific binding protein, the amino acids involved in the ligand binding are conserved. The results of this study allow us to propose a possible transport model for retinoids. Conclusions/Significance: Our results reveal the differences in the binding modes between the different retinoid-bindin

Transhiatal vs extended transthoracic resection in oesophageal carcinoma: patients' utilities and treatment preferences

To assess patients' utilities for health state outcomes after transhiatal or transthoracic oesophagectomy for oesophageal cancer and to investigate the patients' treatment preferences for either procedure. The study group consisted of 48 patients who had undergone either transhiatal or transthoracic oesophagectomy. In an interview they were presented with eight possible health states following oesophagectomy. Visual Analogue Scale and standard gamble techniques were used to measure utilities. Treatment preference for either transhiatal or transthoracic oesophagectomy was assessed. Highest scores were found for the patients' own current health state (Visual Analogue Scale: 0.77; standard gamble: 0.97). Lowest scores were elicited for the health state ‘irresectable tumour’ (Visual Analogue Scale: 0.13; standard gamble: 0.34). The Visual Analogue Scale method produced lower estimates (P<0.001) than the standard gamble method for all health states. Most patient characteristics and clinical factors did not correlate with the utilities. Ninety-five per cent of patients who underwent a transthoracic procedure and 52% of patients who underwent a transhiatal resection would prefer the transthoracic treatment. No significant associations between any patient characteristics or clinical characteristics and treatment preference were found. Utilities after transhiatal or transthoracic oesophagectomy were robust because they generally did not vary by patient or clinical characteristics. Overall, most patients preferred the transthoracic procedure