Twist/Writhe Partitioning in a Coarse-Grained DNA Minicircle Model

Here we present a systematic study of supercoil formation in DNA minicircles under varying linking number by using molecular dynamics simulations of a two-bead coarse-grained model. Our model is designed with the purpose of simulating long chains without sacrificing the characteristic structural properties of the DNA molecule, such as its helicity, backbone directionality and the presence of major and minor grooves. The model parameters are extracted directly from full-atomistic simulations of DNA oligomers via Boltzmann inversion, therefore our results can be interpreted as an extrapolation of those simulations to presently inaccessible chain lengths and simulation times. Using this model, we measure the twist/writhe partitioning in DNA minicircles, in particular its dependence on the chain length and excess linking number. We observe an asymmetric supercoiling transition consistent with experiments. Our results suggest that the fraction of the linking number absorbed as twist and writhe is nontrivially dependent on chain length and excess linking number. Beyond the supercoiling transition, chains of the order of one persistence length carry equal amounts of twist and writhe. For longer chains, an increasing fraction of the linking number is absorbed by the writhe.Comment: 21 pages, 7 figures, 1 tabl

Approximate dynamic programming for anemia management.

The focus of this dissertation work is the formulation and improvement of anemia management process involving trial-and-error. A two-stage method is adopted toward this objective. Given a medical treatment process, a discrete Markov representation is first derived as a formal translation of the treatment process to a control problem under uncertainty. A simulative numerical solution of the control problem is then obtained on-the-fly in the form of a control law maximizing the long-term benefit at each decision stage. Approximate dynamic programming methods are employed in the proposed solution. The motivation underlying this choice is that, in reality, some patient characteristics, which are critical for the sake of treatment, cannot be determined through diagnosis and remain unknown until early stages of treatment, when the patient demonstrates them upon actions by the decision maker. A review of these simulative control tools, which are studied extensively in reinforcement learning theory, is presented. Two approximate dynamic programming tools, namely SARSA and Q -learning, are introduced. Their performance in discovering the optimal individualized drug dosing policy is illustrated on hypothetical patients made up as fuzzy models for simulations. As an addition to these generic reinforcement learning methods, a state abstraction scheme for the considered application domain is also proposed. The control methods of this study, capturing the essentials of a drug delivery problem, constitutes a novel computational framework for model-free medical treatment. Experimental evaluation of the dosing strategies produced by the proposed methods against the standard policy, which is being followed actually by human experts in Kidney Diseases Program, University of Louisville, shows the advantages for use of reinforcement learning in the drug dosing problem in particular and in medical decision making in general

Bayesian estimation of the transmissivity spatial structure from pumping test data

Estimating the statistical parameters (mean, variance, and integral scale) that define the spatial structure of the transmissivity or hydraulic conductivity fields is a fundamental step for the accurate prediction of subsurface flow and contaminant transport. In practice, the determination of the spatial structure is a challenge because of spatial heterogeneity and data scarcity. In this paper, we describe a novel approach that uses time drawdown data from multiple pumping tests to determine the transmissivity statistical spatial structure. The method builds on the pumping test interpretation procedure of Copty et al. (2011) (Continuous Derivation method, CD), which uses the time-drawdown data and its time derivative to estimate apparent transmissivity values as a function of radial distance from the pumping well. A Bayesian approach is then used to infer the statistical parameters of the transmissivity field by combining prior information about the parameters and the likelihood function expressed in terms of radially-dependent apparent transmissivities determined from pumping tests. A major advantage of the proposed Bayesian approach is that the likelihood function is readily determined from randomly generated multiple realizations of the transmissivity field, without the need to solve the groundwater flow equation. Applying the method to synthetically-generated pumping test data, we demonstrate that, through a relatively simple procedure, information on the spatial structure of the transmissivity may be inferred from pumping tests data. It is also shown that the prior parameter distribution has a significant influence on the estimation procedure, given the non-uniqueness of the estimation procedure. Results also indicate that the reliability of the estimated transmissivity statistical parameters increases with the number of available pumping tests.Peer ReviewedPostprint (author's final draft

Suboptimal eye movements for seeing fine details.

Human eyes are never stable, even during attempts of maintaining gaze on a visual target. Considering transient response characteristics of retinal ganglion cells, a certain amount of motion of the eyes is required to efficiently encode information and to prevent neural adaptation. However, excessive motion of the eyes leads to insufficient exposure to the stimuli, which creates blur and reduces visual acuity. Normal miniature eye movements fall in between these extremes, but it is unclear if they are optimally tuned for seeing fine spatial details. We used a state-of-the-art retinal imaging technique with eye tracking to address this question. We sought to determine the optimal gain (stimulus/eye motion ratio) that corresponds to maximum performance in an orientation-discrimination task performed at the fovea. We found that miniature eye movements are tuned but may not be optimal for seeing fine spatial details

A new approach to dynamic finite-size scaling

In this work we have considered the Taylor series expansion of the dynamic scaling relation of the magnetization with respect to small initial magnetization values in order to study the dynamic scaling behaviour of 2- and 3-dimensional Ising models. We have used the literature values of the critical exponents and of the new dynamic exponent $x_0$ to observe the dynamic finite-size scaling behaviour of the time evolution of the magnetization during early stages of the Monte Carlo simulation. For 3-dimensional Ising Model we have also presented that this method opens the possibility of calculating $z$ and $x_0$ separately. Our results show good agreement with the literature values. Measurements done on lattices with different sizes seem to give very good scaling.Comment: Latex file with six figures. Accepted for publication in IJM