Approximation Methods for Singular Diffusions Arising in Genetics

Stochastic models in population genetics leading to diffusion equations are considered. When the drift and the square of the diffusion coefficients are polynomials, an infinite system of ordinary differential equations for the moments of the diffusion process can be derived using the Martingale property. An example is provided to show how the classical Fokker-Planck Equation approach may not be appropriate for this derivation. A Gauss-Galerkin method for approximating the laws of the diffusion, originally proposed by Dawson (1980), is examined. In the few special cases for which exact solutions are known, comparison shows that the method is accurate and the new algorithm is efficient. Numerical results relating to population genetics models are presented and discussed. An example where the Gauss-Galerkin method fails is provided

Population Genetics: Estimation of Distributions through Systems of Non-Linear Differential Equations

In stochastic population genetics, the fundamental quantity used for describing the genetic composition of a Mendelian population is the gene frequency. The process of change in the gene frequency is generally modeled as a stochastic process satisfying a stochastic differential equation. The drift and diffusion coefficients in this equation reflect such mechanisms as mutation, selection, and migration that affect the population. Except in very simple cases, it is difficult to determine the probability law of the stochastic process of change in gene frequency. We present a method for obtaining approximations of this process, enabling us to study models more realistic than those treated previously, called the Gauss Galerkin method

Parabolic Deployable Antenna

A deployable antenna is described. The antenna comprises a mesh attached to foldable ribs, a hub and a sub-reflector. The antenna can be stowed in a tight space for launching in space, and later deployed by extending out of its container. The antenna is designed to work in the Ka band or other bands and can increase data rates and function as a radio antenna

Tracking Plasma Lactate Concentration in Vivo with a Catheter-Tip L-Lactate Sensor

To circumvent the problems of repeated blood sampling for in vitro analysis, a catheter-tip L-lactate sensor has been developed. The sensor was tested in anesthetized pigs (n=6). The sensor in vivo tracked the lactate concentration non-linearly, seeming to obey Michaelis-Menten kinetics. Calibration time was short, typically 1.5 min per lactate standard. Furthermore, time drift was small, typically -1.3% to -3.3% per hour of in vivo use

TheCoin: Privacy and security considerations within blockchain transactions

TheChain is a solution to many problems such as monopoly, heavy state transition, and security vulnerabilities. TheChain solves these problems by introducing the intersection of regions as an incentive before allowing validators to nest a client directory. Intersecting their operating territories forces them to keep a watch over each other. The definition of privacy can take many forms, starting from the right to be forgotten beside being away from public attention. Although the pseudonymity of the user within the network can enhance the user's privacy, several pieces of research have studied the techniques to take advantage of the network structure to identify the users of pseudonyms. Moreover, two models have been used to record the updated exchange of values within the blockchain system, which are the unspent transaction output (UTXO) and the balance model. The UTXO suffers from duplication of information and the balance model suffers from having a single point of entry. This paper introduces TheCoin model that defines the protocol of the exchange of valuable datum within TheChain system. The solution has introduced a novel approach of initiating the transaction from the receiver side by taking advantage of mobile agents empowering a topology hiding to the network. Billing within the platform has been introduced to allow advanced contractual logic to be adopted into the system on the information level. Moreover, traceable fuzziness has been used to eliminate duplication. The paper presents an evaluation of the TheCoin model in terms of system security, block size, and search performance

A Partial Response to Reintroduced Chemotherapy in a Resistant Small Cell Lung Cancer Patient after Priming with RRx-001

As an exceedingly recalcitrant and highly aggressive tumor type without Food and Drug Administration-approved treatment or a known cure, the prognosis of recurrent extensive stage platinum-resistant/refractory small cell lung cancer (SCLC) is worse than other types of lung cancer, and many other tumor types, given a response rate of less than 10% and an overall survival of less than six months. It was broadly classified into three groups based on the initial response to cisplatin/etoposide therapy, platinum-refractory, platinum-resistant, and platinum-sensitive, extensive stage SCLC inevitably relapses, at which point the only standard options are to rechallenge with the first-line chemotherapeutic regimen in the case of sensitive disease or to start the topoisomerase I inhibitor, topotecan. Sensitive disease is defined by a response to the first-line therapy and a treatment-free interval of at least 90 days, while the definitions of refractory and resistant disease, respectively, are nonresponse to the first-line treatment or relapse within 90 days. As an important predictor of response to the second-line treatment, the clinical cutoff of three months (or two months in some cases) for resistant and sensitive disease, which along with performance status prognostically separates patients into high- and low-risk categories, dictates subsequent management. This case report presents a resistant SCLC patient enrolled on a Phase II clinical trial called QUADRUPLE THREAT (formerly TRIPLE THREAT, NCT02489903) who responded to reintroduced platinum doublets after sequential priming with the resistance-reversing epi-immunotherapeutic agent, RRx-001. In the QUADRUPLE THREAT clinical trial, both during priming with RRx-001 and during sequential treatment with platinum doublets, the patient maintained a good quality of life and performance status.Peer reviewe

Finite volume simulation of 2-D steady square lid driven cavity flow at high reynolds numbers

In this work, computer simulation results of steady incompressible flow in a 2-D square lid-driven cavity up to Reynolds number (Re) 65000 are presented and compared with those of earlier studies. The governing flow equations are solved by using the finite volume approach. Quadratic upstream interpolation for convective kinematics (QUICK) is used for the approximation of the convective terms in the flow equations. In the implementation of QUICK, the deferred correction technique is adopted. A non-uniform staggered grid arrangement of 768x768 is employed to discretize the flow geometry. Algebraic forms of the coupled flow equations are then solved through the iterative SIMPLE (Semi-Implicit Method for Pressure-Linked Equation) algorithm. The outlined computational methodology allows one to meet the main objective of this work, which is to address the computational convergence and wiggled flow problems encountered at high Reynolds and Peclet (Pe) numbers. Furthermore, after Re > 25000 additional vortexes appear at the bottom left and right corners that have not been observed in earlier studies