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

Interlobular and intralobular mammary stroma: Genotype may not reflect phenotype

<p>Abstract</p> <p>Background</p> <p>The normal growth and function of mammary epithelial cells depend on interactions with the supportive stroma. Alterations in this communication can lead to the progression or expansion of malignant growth. The human mammary gland contains two distinctive types of fibroblasts within the stroma. The epithelial cells are surrounded by loosely connected intralobular fibroblasts, which are subsequently surrounded by the more compacted interlobular fibroblasts. The different proximity of these fibroblasts to the epithelial cells suggests distinctive functions for these two subtypes. In this report, we compared the gene expression profiles between the two stromal subtypes.</p> <p>Methods</p> <p>Fresh normal breast tissue was collected from reduction mammoplasty patients and immediately placed into embedding medium and frozen on dry ice. Tissue sections were subjected to laser capture microscopy to isolate the interlobular from the intralobular fibroblasts. RNA was prepared and subjected to microarray analysis using the Affymetrix Human Genome U133 GeneChip^®. Data was analyzed using the Affy and Limma packages available from Bioconductor. Findings from the microarray analysis were validated by RT-PCR and immunohistochemistry.</p> <p>Results</p> <p>No statistically significant difference was detected between the gene expression profiles of the interlobular and intralobular fibroblasts by microarray analysis and RT-PCR. However, for some of the genes tested, the protein expression patterns between the two subtypes of fibroblasts were significantly different.</p> <p>Conclusion</p> <p>This study is the first to report the gene expression profiles of the two distinct fibroblast populations within the human mammary gland. While there was no significant difference in the gene expression profiles between the groups, there was an obvious difference in the expression pattern of several proteins tested. This report also highlights the importance of studying gene regulation at both the transcriptional and post-translational level.</p

Synchrotron validation of inline coherent imaging for tracking laser keyhole depth

In situ monitoring is critical to the increasing adoption of laser powder bed fusion (LPBF) and laser welding by industry for manufacture of complex metallic components. Optical coherence tomography (OCT), an interferometric imaging technique adapted from medical applications, is now widely used for operando monitoring of morphology during high-power laser material processing. However, even in stable processing regimes, some OCT depth measurements from the keyhole (vapor cavity formed at laser beam spot) appear too shallow or too deep when compared to ex situ measurements of weld depth. It has remained unclear whether these outliers are due to imaging artifacts, multiple scattering of the imaging beam within the keyhole, or real changes in keyhole depth, making it difficult to accurately extract weld depth and determine error bounds. To provide a definitive explanation, we combine inline coherent imaging (ICI), a type of OCT, with synchrotron X-ray imaging for simultaneous, operando monitoring of the full 2-dimensional keyhole profile at high-speed (280 kHz and 140 kHz, respectively). Even in a highly turbulent pore-generation mode, the depth measured with ICI closely follows the keyhole depth extracted from radiography (>80% within ± 14 µm). Ray-tracing simulations are used to confirm that the outliers in ICI depth measurements (that significantly disagree with radiography) primarily result from multiple reflections of the imaging light (57%). Synchrotron X-ray imaging also enables tracking of bubble and pore formation events. Pores are generated during laser welding when the sidewalls of the keyhole rapidly (>10 m/s) collapse inwards, pinching off a bubble from the keyhole root and resulting in a rapid decrease in keyhole depth. Evidence of bubble formation can be found in ICI depth profiles alone, as rapid depth changes exhibit moderate correlation with bubble formation events (0.26). This work moves closer to accurate, localized defect detection during laser welding and LPBF using ICI

Inferring subjective states through the observation of actions

Estimating another person's subjective confidence is crucial for social interaction, but how this inference is achieved is unknown. Previous research has demonstrated that the speed at which people make decisions is correlated with their confidence in their decision. Here, we show that (i) subjects are able to infer the subjective confidence of another person simply through the observation of their actions and (ii) this inference is dependent upon the performance of each subject when executing the action. Crucially, the latter result supports a model in which motor simulation of an observed action mediates the successful understanding of other minds. We conclude that kinematic understanding allows access to the higher-order cognitive processes of others, and that this access plays a central role in social interactions

Novel Characteristics of Valveless Pumping

This study investigates the occurrence of valveless pumping in a fluidfilled system consisting of two open tanks connected by an elastic tube. We show that directional flow can be achieved by introducing a periodic pinching applied at an asymmetrical location along the tube, and that the flow direction depends on the pumping frequency. We propose a relation between wave propagation velocity, tube length, and resonance frequencies associated with shifts in the pumping direction using numerical simulations. The eigenfrequencies of the system are estimated from the linearized system, and we show that these eigenfrequencies constitute the resonance frequencies and the horizontal slope frequencies of the system; 'horizontal slope frequency' being a new concept. A simple model is suggested, explaining the effect of the gravity driven part of the oscillation observed in response to the tank and tube diameter changes. Results are partly compared with experimental findings.Art. no. 22450

The male handicap: male-biased mortality explains skewed sex ratios in brown trout embryos

Juvenile sex ratios are often assumed to be equal for many species with genetic sex determination, but this has rarely been tested in fish embryos due to their small size and absence of sex-specific markers. We artificially crossed three populations of brown trout and used a recently developed genetic marker for sexing the offspring of both pure and hybrid crosses. Sex ratios (SR = proportion of males) varied widely one month after hatching ranging from 0.15 to 0.90 (mean = 0.39 ± 0.03). Families with high survival tended to produce balanced or male-biased sex ratios, but SR was significantly female-biased when survival was low, suggesting that males sustain higher mortality during development. No difference in SR was found between pure and hybrid families, but the existence of sire × dam interactions suggests that genetic incompatibility may play a role in determining sex ratios. Our findings have implications for animal breeding and conservation because skewed sex ratios will tend to reduce effective population size and bias selection estimates

Jet Shapes and Jet Algorithms in SCET

Jet shapes are weighted sums over the four-momenta of the constituents of a jet and reveal details of its internal structure, potentially allowing discrimination of its partonic origin. In this work we make predictions for quark and gluon jet shape distributions in N-jet final states in e+e- collisions, defined with a cone or recombination algorithm, where we measure some jet shape observable on a subset of these jets. Using the framework of Soft-Collinear Effective Theory, we prove a factorization theorem for jet shape distributions and demonstrate the consistent renormalization-group running of the functions in the factorization theorem for any number of measured and unmeasured jets, any number of quark and gluon jets, and any angular size R of the jets, as long as R is much smaller than the angular separation between jets. We calculate the jet and soft functions for angularity jet shapes \tau_a to one-loop order (O(alpha_s)) and resum a subset of the large logarithms of \tau_a needed for next-to-leading logarithmic (NLL) accuracy for both cone and kT-type jets. We compare our predictions for the resummed \tau_a distribution of a quark or a gluon jet produced in a 3-jet final state in e+e- annihilation to the output of a Monte Carlo event generator and find that the dependence on a and R is very similar.Comment: 62 pages plus 21 pages of Appendices, 13 figures, uses JHEP3.cls. v2: corrections to finite parts of NLO jet functions, minor changes to plots, clarified discussion of power corrections. v3: Journal version. Introductory sections significantly reorganized for clarity, classification of logarithmic accuracy clarified, results for non-Mercedes-Benz configurations adde

Historical changes in the phenology of British Odonata are related to climate

Responses of biota to climate change take a number of forms including distributional shifts, behavioural changes and life history changes. This study examined an extensive set of biological records to investigate changes in the timing of life history transitions (specifically emergence) in British Odonata between 1960 and 2004. The results show that there has been a significant, consistent advance in phenology in the taxon as a whole over the period of warming that is mediated by life history traits. British odonates significantly advanced the leading edge (first quartile date) of the flight period by a mean of 1.51 ±0.060 (SEM, n=17) days per decade or 3.08±1.16 (SEM, n=17) days per degree rise in temperature when phylogeny is controlled for. This study represents the first review of changes in odonate phenology in relation to climate change. The results suggest that the damped temperature oscillations experienced by aquatic organisms compared with terrestrial organisms are sufficient to evoke phenological responses similar to those of purely terrestrial taxa

Optimal use of reminders: Metacognition, effort, and cognitive offloading

Individuals frequently choose between accomplishing goals using unaided cognitive abilities or offloading cognitive demands onto external tools and resources. For example, in order to remember an upcoming appointment one might rely on unaided memory or create a reminder by setting a smartphone alert. Setting a reminder incurs both a cost (the time/effort to set it up) and a benefit (increased likelihood of remembering). Here we investigate whether individuals weigh such costs/benefits optimally or show systematic biases. In 3 experiments, participants performed a memory task where they could choose between (a) earning a maximum reward for each remembered item, using unaided memory; or (b) earning a lesser amount per item, using external reminders to increase the number remembered. Participants were significantly biased toward using external reminders, even when they had a financial incentive to choose optimally. Individual differences in this bias were stable over time, and predicted by participants' erroneous metacognitive underconfidence in their memory abilities. Bias was eliminated, however, when participants received metacognitive advice about which strategy was likely to maximize performance. Furthermore, we found that metacognitive interventions (manipulation of feedback valence and practice-trial difficulty) yielded shifts in participants' reminder bias that were mediated by shifts in confidence. However, the bias could not be fully attributed to metacognitive error. We conclude that individuals have stable biases toward using external versus internal cognitive resources, which result at least in part from inaccurate metacognitive evaluations. Finding interventions to mitigate these biases can improve individuals' adaptive use of cognitive tools

Factorization and resummation of s-channel single top quark production

In this paper we study the factorization and resummation of s-channel single top quark production in the Standard Model at both the Tevatron and the LHC. We show that the production cross section in the threshold limit can be factorized into a convolution of hard function, soft function and jet function via soft-collinear-effective-theory (SCET), and resummation can be performed using renormalization group equation in the momentum space resummation formalism. We find that in general, the resummation effects enhance the Next-to-Leading-Order (NLO) cross sections by about $3$ at both the Tevatron and the LHC, and significantly reduce the factorization scale dependence of the total cross section at the Tevatron, while at the LHC we find that the factorization scale dependence has not been improved, compared with the NLO results.Comment: 29 pages, 7 figures; version published in JHE