The Master Equation for Large Population Equilibriums

We use a simple N-player stochastic game with idiosyncratic and common noises to introduce the concept of Master Equation originally proposed by Lions in his lectures at the Coll\`ege de France. Controlling the limit N tends to the infinity of the explicit solution of the N-player game, we highlight the stochastic nature of the limit distributions of the states of the players due to the fact that the random environment does not average out in the limit, and we recast the Mean Field Game (MFG) paradigm in a set of coupled Stochastic Partial Differential Equations (SPDEs). The first one is a forward stochastic Kolmogorov equation giving the evolution of the conditional distributions of the states of the players given the common noise. The second is a form of stochastic Hamilton Jacobi Bellman (HJB) equation providing the solution of the optimization problem when the flow of conditional distributions is given. Being highly coupled, the system reads as an infinite dimensional Forward Backward Stochastic Differential Equation (FBSDE). Uniqueness of a solution and its Markov property lead to the representation of the solution of the backward equation (i.e. the value function of the stochastic HJB equation) as a deterministic function of the solution of the forward Kolmogorov equation, function which is usually called the decoupling field of the FBSDE. The (infinite dimensional) PDE satisfied by this decoupling field is identified with the \textit{master equation}. We also show that this equation can be derived for other large populations equilibriums like those given by the optimal control of McKean-Vlasov stochastic differential equations. The paper is written more in the style of a review than a technical paper, and we spend more time and energy motivating and explaining the probabilistic interpretation of the Master Equation, than identifying the most general set of assumptions under which our claims are true

Economic analysis of royalactin production under uncertainty: Evaluating the effect of parameter optimization.

Royalactin is a protein with several different potential uses in humans. Research, in insects and in mammalian cells, has shown that it can accelerate cell division and prevent apoptosis. The method of action is through the use of the epidermal growth factor receptor, which is present in humans. Potential use in humans could be to lower cholesterolemic levels in blood, and to elicit similar effects to those seen in bees, e.g., increased lifespan. Mass production of Royalactin has not been accomplished, though a recent article presented a Pichia pastoris fermentation and recovery by aqueous two-phase systems at laboratory scale as a possible basis for production. Economic modelling is a useful tool with which compare possible outcomes for the production of such a molecule and in particular, to locate areas where additional research is needed and optimization may be required. This study uses the BioSolve software to perform an economic analysis on the scale-up of the putative process for Royalactin. The key parameters affecting the cost of production were located via a sensitivity analysis and then evaluated by Monte Carlo analysis. Results show that if titer is not optimized the strategy to maintain a low cost of goods is process oriented. After optimization of this parameter the strategy changes to a product-oriented and the target output becomes the critical parameter determining the cost of goods. This study serves to provide a framework for the evaluation of strategies for future production of Royalactin, by analyzing the factors that influence its cost of manufacture. © 2015 The Authors Biotechnology Progress published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers Biotechnol. Prog., 2015

Correlation of oral health home-care practices, snacking habits and dental caries experience among HIV-positive children in Nairobi, Kenya

Objective: To determine the correlation of oral health home-care practices, snacking habits and dental caries experience among 3-15 year-old- HIV-positive children attending out-patient clinic at the Kenyatta National Hospital, Kenya.Design: Cross-sectional descriptive study.Setting: Kenyatta National Hospital comprehensive care centre out-patient clinic.Subjects:Two hundred and twenty participants were selected by consecutive sampling. The children’s socio-demographic characteristics and oral health home-care practices were obtained from parent or guardian interviews. Oral examination of the children was carried out to determine the presence of dental caries.Results: Of the 220 children in the study, 126 (57.3%) brushed their teeth at least once a day. Forty one (18.6%) children regularly consumed sweetened snacks daily. Almost all children (75.5%) were taking medication in the form of tablets and capsules. One hundred and seventy nine (81.4%) children had never had a dental visit. The prevalence of dental caries was 65% while the mean dmft and DMFT scores were 1.75 and 1.08 respectively. Caries experience was significantly higher for those children who frequently consumed sweetened snacks and those who took their medication in the form of sweetened syrups while it was lowest in those who brushed their teeth at least twice a day.Conclusion: Dental caries experience was significantly higher among HIV-infected children who had increased frequency of consumption of sweetened snacks and those who used syrupy medication. There was poor attendance for dental treatment among the children

Relative proximity of chromosome territories influences chromosome exchange partners in radiation-induced chromosome rearrangements in primary human bronchial epithelial cells

Copyright © 2013 The Authors. This article is made available through the Brunel Open Access Publishing Fund. This is an open access article distributed under the terms of the Creative Commons Attribution-NonCommercial-No Derivative Works License, which permits non-commercial use, distribution, and reproduction in any medium, provided the original author and source are credited.Copyright © 2013 The Authors. It is well established that chromosomes exist in discrete territories (CTs) in interphase and are positioned in a cell-type specific probabilistic manner. The relative localisation of individual CTs within cell nuclei remains poorly understood, yet many cancers are associated with specific chromosome rearrangements and there is good evidence that relative territorial position influences their frequency of exchange. To examine this further, we characterised the complexity of radiation-induced chromosome exchanges in normal human bronchial epithelial (NHBE) cells by M-FISH analysis of PCC spreads and correlated the exchanges induced with their preferred interphase position, as determined by 1/2-colour 2D-FISH analysis, at the time of irradiation. We found that the frequency and complexity of aberrations induced were reduced in ellipsoid NHBE cells in comparison to previous observations in spherical cells, consistent with aberration complexity being dependent upon the number and proximity of damaged CTs, i.e. lesion proximity. To ask if particular chromosome neighbourhoods could be identified we analysed all radiation-induced pair-wise exchanges using SCHIP (statistics for chromosome interphase positioning) and found that exchanges between chromosomes (1;13), (9;17), (9;18), (12;18) and (16;21) all occurred more often than expected assuming randomness. All of these pairs were also found to be either sharing similar preferred positions in interphase and/or sharing neighbouring territory boundaries. We also analysed a human small cell lung cancer cell line, DMS53, by M-FISH observing the genome to be highly rearranged, yet possessing rearrangements also involving chromosomes (1;13) and (9;17). Our findings show evidence for the occurrence of non-random exchanges that may reflect the territorial organisation of chromosomes in interphase at time of damage and highlight the importance of cellular geometry for the induction of aberrations of varying complexity after exposure to both low and high-LET radiation.Department of Healt

Muscle Fatigue Analysis Using OpenSim

In this research, attempts are made to conduct concrete muscle fatigue analysis of arbitrary motions on OpenSim, a digital human modeling platform. A plug-in is written on the base of a muscle fatigue model, which makes it possible to calculate the decline of force-output capability of each muscle along time. The plug-in is tested on a three-dimensional, 29 degree-of-freedom human model. Motion data is obtained by motion capturing during an arbitrary running at a speed of 3.96 m/s. Ten muscles are selected for concrete analysis. As a result, the force-output capability of these muscles reduced to 60%-70% after 10 minutes' running, on a general basis. Erector spinae, which loses 39.2% of its maximal capability, is found to be more fatigue-exposed than the others. The influence of subject attributes (fatigability) is evaluated and discussed

Flow pattern in inner cores of double emulsion droplets

This paper was presented at the 4th Micro and Nano Flows Conference (MNF2014), which was held at University College, London, UK. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute, ASME Press, LCN London Centre for Nanotechnology, UCL University College London, UCL Engineering, the International NanoScience Community, www.nanopaprika.eu.The efficacy of applications of water-in-oil-in-water (w/o/w) double emulsions moving in microchannels is significantly impacted by the flow conditions in the inner aqueous cores. For example in the case of shear sensitive cells transported in the cores, high shear conditions may be deleterious. This study reports on the flow topology inside w/o/w cores determined by means of micro-particle image velocimetry (μPIV) and compares it to the flow in single water-in-oil (w/o) microdroplets with equal sizes moving in a rectangular microchannel. The multiphase flow system employed in the study had a viscosity ratio, λ, between oil and aqueous phase of the order of unity (λ = 0.8) and both single and compound droplets filled the channels. This configuration resulted in a weak recirculating flow inside the w/o single droplet: the measured flow field exhibited a uniform low velocity flow field in the central region surrounded by small regions of reversed flow near the channel walls. This flow topology was maintained in the inner cores of w/o/w double emulsions for intermediate capillary numbers (Ca) ranging from 10-3 to 10-2, and core morphologies varying from large plug to pancake cores. The core morphology affected the magnitude and distribution of the velocity in the droplets. The similarity in the flow pattern results from the fact that inner cores were located at the back of the outer droplet in such a way that inner and outer interfaces were in contact for half of core surface area and separated by a thin lubricating film

A catalog of Kazarian galaxies

The entire Kazarian galaxies (KG) catalog is presented which combines extensive new measurements of their optical parameters with a literature and database search. The measurements were made using images extracted from the STScI Digitized Sky Survey (DSS) of Jpg(blue), Fpg(red) and Ipg(NIR) band photographic sky survey plates obtained by the Palomar and UK Schmidt telescopes. We provide accurate coordinates, morphological type, spectral and activity classes, blue apparent diameters, axial ratios, position angles, red, blue and NIR apparent magnitudes, as well as counts of neighboring objects in a circle of radius 50 kpc from centers of KG. Special attention was paid to the individual descriptions of the galaxies in the original Kazarian lists, which clarified many cases of misidentifications of the objects, particularly among interacting systems. The total number of individual Kazarian objects in the database is now 706. We also include the redshifts which are now available for 404 galaxies and the 2MASS infrared magnitudes for 598 KG. The database also includes extensive notes, which summarize information about the membership of KG in different systems of galaxies, and about revised activity classes and redshifts. An atlas of several interesting subclasses of KG is also presented.Comment: 15 pages, 5 figures, 1 table, Accepted in Astrophysics, Vol. 53, No. 1, 2010 (English translation of Astrofizika

Spread of Infectious Diseases with a Latent Period

Infectious diseases spread through human networks. Susceptible-Infected-Removed (SIR) model is one of the epidemic models to describe infection dynamics on a complex network connecting individuals. In the metapopulation SIR model, each node represents a population (group) which has many individuals. In this paper, we propose a modified metapopulation SIR model in which a latent period is taken into account. We call it SIIR model. We divide the infection period into two stages: an infected stage, which is the same as the previous model, and a seriously ill stage, in which individuals are infected and cannot move to the other populations. The two infectious stages in our modified metapopulation SIR model produce a discontinuous final size distribution. Individuals in the infected stage spread the disease like individuals in the seriously ill stage and never recover directly, which makes an effective recovery rate smaller than the given recovery rate.Comment: 6 pages, 3 figure