Precision and scaling in morphogen gradient read-out

Morphogen gradients infer cell fate as a function of cellular position. Experiments in Drosophila embryos have shown that the Bicoid (Bcd) gradient is precise and exhibits some degree of scaling. We present experimental results on the precision of Bcd target genes for embryos with a single, double or quadruple dose of bicoid demonstrating that precision is highest at mid-embryo and position dependent, rather than gene dependent. This confirms that the major contribution to precision is achieved already at the Bcd gradient formation. Modeling this dynamic process, we investigate precision for inter-embryo fluctuations in different parameters affecting gradient formation. Within our modeling framework, the observed precision can only be achieved by a transient Bcd profile. Studying different extensions of our modeling framework reveals that scaling is generally position dependent and decreases toward the posterior pole. Our measurements confirm this trend, indicating almost perfect scaling except for anterior most expression domains, which overcompensate fluctuations in embryo length

On the criticality of inferred models

Advanced inference techniques allow one to reconstruct the pattern of interaction from high dimensional data sets. We focus here on the statistical properties of inferred models and argue that inference procedures are likely to yield models which are close to a phase transition. On one side, we show that the reparameterization invariant metrics in the space of probability distributions of these models (the Fisher Information) is directly related to the model's susceptibility. As a result, distinguishable models tend to accumulate close to critical points, where the susceptibility diverges in infinite systems. On the other, this region is the one where the estimate of inferred parameters is most stable. In order to illustrate these points, we discuss inference of interacting point processes with application to financial data and show that sensible choices of observation time-scales naturally yield models which are close to criticality.Comment: 6 pages, 2 figures, version to appear in JSTA

Beyond inverse Ising model: structure of the analytical solution for a class of inverse problems

I consider the problem of deriving couplings of a statistical model from measured correlations, a task which generalizes the well-known inverse Ising problem. After reminding that such problem can be mapped on the one of expressing the entropy of a system as a function of its corresponding observables, I show the conditions under which this can be done without resorting to iterative algorithms. I find that inverse problems are local (the inverse Fisher information is sparse) whenever the corresponding models have a factorized form, and the entropy can be split in a sum of small cluster contributions. I illustrate these ideas through two examples (the Ising model on a tree and the one-dimensional periodic chain with arbitrary order interaction) and support the results with numerical simulations. The extension of these methods to more general scenarios is finally discussed.Comment: 15 pages, 6 figure

A simple mean field model for social interactions: dynamics, fluctuations, criticality

We study the dynamics of a spin-flip model with a mean field interaction. The system is non reversible, spacially inhomogeneous, and it is designed to model social interactions. We obtain the limiting behavior of the empirical averages in the limit of infinitely many interacting individuals, and show that phase transition occurs. Then, after having obtained the dynamics of normal fluctuations around this limit, we analize long time fluctuations for critical values of the parameters. We show that random inhomogeneities produce critical fluctuations at a shorter time scale compared to the homogeneous system.Comment: 37 pages, 2 figure

A Semi-Lagrangian scheme for a modified version of the Hughes model for pedestrian flow

In this paper we present a Semi-Lagrangian scheme for a regularized version of the Hughes model for pedestrian flow. Hughes originally proposed a coupled nonlinear PDE system describing the evolution of a large pedestrian group trying to exit a domain as fast as possible. The original model corresponds to a system of a conservation law for the pedestrian density and an Eikonal equation to determine the weighted distance to the exit. We consider this model in presence of small diffusion and discuss the numerical analysis of the proposed Semi-Lagrangian scheme. Furthermore we illustrate the effect of small diffusion on the exit time with various numerical experiments

Universal cures for idiosyncratic illnesses: a genealogy of therapeutic reasoning in the mental health field

Over the past decades, there has been a significant increase in prescriptions of psychotropic drugs for mental disorders. So far, most of the explanations of the phenomenon have focused on the process of medicalization, but little attention has been cast towards physicians' day-to-day clinical reasoning, and the way it affects therapeutic decision-making. This article addresses the complex relationship between aetiology, diagnosis and drug treatment by examining the style of reasoning underlying prescribing practices through an historical lens. A genealogy of contemporary prescribing practices is proposed, that draws significant comparisons between 19th-century medicine and modern psychiatry. Tensions between specific, standardized cures and specific, idiosyncratic patients have been historically at play in clinical reasoning - and still are today. This inquiry into the epistemological foundations of contemporary drug prescription reveals an underlying search for scientific legitimacy

Neighbourhood, Route and Workplace-Related Environmental Characteristics Predict Adults' Mode of Travel to Work

Commuting provides opportunities for regular physical activity which can reduce the risk of chronic disease. Commuters' mode of travel may be shaped by their environment, but understanding of which specific environmental characteristics are most important and might form targets for intervention is limited. This study investigated associations between mode choice and a range of objectively assessed environmental characteristics.Participants in the Commuting and Health in Cambridge study reported where they lived and worked, their usual mode of travel to work and a variety of socio-demographic characteristics. Using geographic information system (GIS) software, 30 exposure variables were produced capturing characteristics of areas around participants' homes and workplaces and their shortest modelled routes to work. Associations between usual mode of travel to work and personal and environmental characteristics were investigated using multinomial logistic regression.Of the 1124 respondents, 50% reported cycling or walking as their usual mode of travel to work. In adjusted analyses, home-work distance was strongly associated with mode choice, particularly for walking. Lower odds of walking or cycling rather than driving were associated with a less frequent bus service (highest versus lowest tertile: walking OR 0.61 [95% CI 0.20–1.85]; cycling OR 0.43 [95% CI 0.23–0.83]), low street connectivity (OR 0.22, [0.07–0.67]; OR 0.48 [0.26–0.90]) and free car parking at work (OR 0.24 [0.10–0.59]; OR 0.55 [0.32–0.95]). Participants were less likely to cycle if they had access to fewer destinations (leisure facilities, shops and schools) close to work (OR 0.36 [0.21–0.62]) and a railway station further from home (OR 0.53 [0.30–0.93]). Covariates strongly predicted travel mode (pseudo r-squared 0.74).Potentially modifiable environmental characteristics, including workplace car parking, street connectivity and access to public transport, are associated with travel mode choice, and could be addressed as part of transport policy and infrastructural interventions to promote active commuting

Analysis of scalar perturbations in cosmological models with a non-local scalar field

We develop the cosmological perturbations formalism in models with a single non-local scalar field originating from the string field theory description of the rolling tachyon dynamics. We construct the equation for the energy density perturbations of the non-local scalar field in the presence of the arbitrary potential and formulate the local system of equations for perturbations in the linearized model when both simple and double roots of the characteristic equation are present. We carry out the general analysis related to the curvature and entropy perturbations and consider the most specific example of perturbations when important quantities in the model become complex.Comment: LaTeX, 25 pages, 1 figure, v2: Subsection 3.2 and Section 5 added, references added, accepted for publication in Class. Quant. Grav. arXiv admin note: text overlap with arXiv:0903.517

Why have asset price properties changed so little in 200 years

We first review empirical evidence that asset prices have had episodes of large fluctuations and been inefficient for at least 200 years. We briefly review recent theoretical results as well as the neurological basis of trend following and finally argue that these asset price properties can be attributed to two fundamental mechanisms that have not changed for many centuries: an innate preference for trend following and the collective tendency to exploit as much as possible detectable price arbitrage, which leads to destabilizing feedback loops.Comment: 16 pages, 4 figure