A model of feedback control for the charge-balanced suppression of epileptic seizures

Here we present several refinements to a model of feedback control for the suppression of epileptic seizures. We utilize a stochastic partial differential equation (SPDE) model of the human cortex. First, we verify the strong convergence of numerical solutions to this model, paying special attention to the sharp spatial changes that occur at electrode edges. This allows us to choose appropriate step sizes for our simulations; because the spatial step size must be small relative to the size of an electrode in order to resolve its electrical behavior, we are able to include a more detailed electrode profile in the simulation. Then, based on evidence that the mean soma potential is not the variable most closely related to the measurement of a cortical surface electrode, we develop a new model for this. The model is based on the currents flowing in the cortex and is used for a simulation of feedback control. The simulation utilizes a new control algorithm incorporating the total integral of the applied electrical potential. Not only does this succeed in suppressing the seizure-like oscillations, but it guarantees that the applied signal will be charge-balanced and therefore unlikely to cause cortical damage

The genetic contribution of single male immigrants to small, inbred populations: A laboratory study using drosophila melanogaster

This study examined the genetic contribution of single male immigrants to small, inbred laboratory populations of Drosophila melanogaster. Genetic contribution was assessed by measuring the relative frequency of immigrant marker alleles in the first and second generations after immigration, while controlling for any selection effects at the marker locus, and for the experience of male immigrants. When immigrants were outbred, the mean frequency of the immigrant allele was significantly higher than its initial frequency, in both the first and second generations after immigration. There was no significant change in allele frequency for populations receiving inbred immigrants. The increase in allele frequency for outbred immigrants was attributed to an initial outbred vigour fitness advantage of immigrant males over resident males experiencing inbreeding depression. Hybrid vigour of immigrant progeny and the rare-male effect did not have a statistically significant role in the fitness advantage of the immigrant allele. The results suggest that inbreeding may have a considerable impact on the contribution of immigrants to the genetic diversity of populations

Almost sure stability of the Euler-Maruyama method with random variable stepsize for stochastic differential equations

In this paper, the Euler–Maruyama (EM) method with random variable stepsize is studied to reproduce the almost sure stability of the true solutions of stochastic differential equations. Since the choice of the time step is based on the current state of the solution, the time variable is proved to be a stopping time. Then the semimartingale convergence theory is employed to obtain the almost sure stability of the random variable stepsize EM solution. To our best knowledge, this is the first paper to apply the random variable stepsize (with clear proof of the stopping time) to the analysis of the almost sure stability of the EM method

Construction of a Mean Square Error Adaptive Euler--Maruyama Method with Applications in Multilevel Monte Carlo

A formal mean square error expansion (MSE) is derived for Euler--Maruyama numerical solutions of stochastic differential equations (SDE). The error expansion is used to construct a pathwise a posteriori adaptive time stepping Euler--Maruyama method for numerical solutions of SDE, and the resulting method is incorporated into a multilevel Monte Carlo (MLMC) method for weak approximations of SDE. This gives an efficient MSE adaptive MLMC method for handling a number of low-regularity approximation problems. In low-regularity numerical example problems, the developed adaptive MLMC method is shown to outperform the uniform time stepping MLMC method by orders of magnitude, producing output whose error with high probability is bounded by TOL>0 at the near-optimal MLMC cost rate O(TOL^{-2}log(TOL)^4).Comment: 43 pages, 12 figure

Hepatobiliary and pancreatic imaging in children—techniques and an overview of non-neoplastic disease entities

Imaging plays a major role in the diagnostic work-up of children with hepatobiliary or pancreatic diseases. It consists mainly of US, CT and MRI, with US and MRI being the preferred imaging modalities because of the lack of ionizing radiation. In this review the technique of US, CT and MRI in children will be addressed, followed by a comprehensive overview of the imaging characteristics of several hepatobiliary and pancreatic disease entities most common in the paediatric age group

Involvement of microbial mats in early fossilization by decay delay and formation of impressions and replicas of vertebrates and invertebrates

Microbial mats have been hypothesized to improve the persistence and the preservation of organic remains during fossilization processes. We test this hypothesis with long-term experiments (up to 5.5 years) using invertebrate and vertebrate corpses.Once placed on mats,the microbial community coats the corpses and forms a three-dimensional sarcophagus composed of microbial cells and exopolymeric substances (EPS). This coverage provides a template for i) moulding superficial features, resulting in negative impressions, and ii) generating replicas.The impressions of fly setulae, fish scales and frog skin verrucae are shaped mainly by small cells in an EPS matrix. Microbes also replicate delicate structures such as the three successive layers that compose a fish eye.The sarcophagus protects the body integrity, allowing the persistence of inner organs such as the ovaries and digestive apparatus in flies,the swim bladder and muscles in fish, and the bone marrow in frog legs.This study brings strong experimental evidence to the idea that mats favour metazoan fossilization by moulding, replicating and delaying decay. Rapid burial has classically been invoked as a mechanism to explain exceptional preservation. However, mats may play a similar role during early fossilization as they can preserve complex features for a long timeThis work, which is part of the research projects CGL2013-42643P and the research grant supporting M. Iniesto were funded by the Spanish Ministry of Economy and Competitiveness. The SEM facility at IMPMC was supported by Region Ile de France grant SESAME 2006 I-07-593/R, INSU-CNRS, INP-CNRS, and University Pierre et Marie Curie, Paris. SEM analyses performed for this study were supported by a grant from the Foundation Simone et Cino Del Duca (PI: K. Benzerara). Some SEM observations were also conducted at SIdI UAM (Madrid). Environmental SEM observations were performed at the MNCN (Madrid

Exceptionally Preserved Jellyfishes from the Middle Cambrian

Cnidarians represent an early diverging animal group and thus insight into their origin and diversification is key to understanding metazoan evolution. Further, cnidarian jellyfish comprise an important component of modern marine planktonic ecosystems. Here we report on exceptionally preserved cnidarian jellyfish fossils from the Middle Cambrian (∼505 million years old) Marjum Formation of Utah. These are the first described Cambrian jellyfish fossils to display exquisite preservation of soft part anatomy including detailed features of structures interpreted as trailing tentacles and subumbrellar and exumbrellar surfaces. If the interpretation of these preserved characters is correct, their presence is diagnostic of modern jellyfish taxa. These new discoveries may provide insight into the scope of cnidarian diversity shortly after the Cambrian radiation, and would reinforce the notion that important taxonomic components of the modern planktonic realm were in place by the Cambrian period

Optimal siting, sizing, and enforcement of marine protected areas

The design of protected areas, whether marine or terrestrial, rarely considers how people respond to the imposition of no-take sites with complete or incomplete enforcement. Consequently, these protected areas may fail to achieve their intended goal. We present and solve a spatial bio-economic model in which a manager chooses the optimal location, size, and enforcement level of a marine protected area (MPA). This manager acts as a Stackelberg leader, and her choices consider villagers’ best response to the MPA in a spatial Nash equilibrium of fishing site and effort decisions. Relevant to lower income country settings but general to other settings, we incorporate limited enforcement budgets, distance costs of traveling to fishing sites, and labor allocation to onshore wage opportunities. The optimal MPA varies markedly across alternative manager goals and budget sizes, but always induce changes in villagers’ decisions as a function of distance, dispersal, and wage. We consider MPA managers with ecological conservation goals and with economic goals, and identify the shortcomings of several common manager decision rules, including those focused on: (1) fishery outcomes rather than broader economic goals, (2) fish stocks at MPA sites rather than across the full marinescape, (3) absolute levels rather than additional values, and (4) costless enforcement. Our results demonstrate that such naïve or overly narrow decision rules can lead to inefficient MPA designs that miss economic and conservation opportunities