Leticia Velázquez

Adaptive human behavior in epidemiological models

The science and management of infectious disease are entering a new stage. Increasingly public policy to manage epidemics focuses on motivating people, through social distancing policies, to alter their behavior to reduce contacts and reduce public disease risk. Person-to-person contacts drive human disease dynamics. People value such contacts and are willing to accept some disease risk to gain contact-related benefits. The cost–benefit trade-offs that shape contact behavior, and hence the course of epidemics, are often only implicitly incorporated in epidemiological models. This approach creates difficulty in parsing out the effects of adaptive behavior. We use an epidemiological–economic model of disease dynamics to explicitly model the trade-offs that drive person-to-person contact decisions. Results indicate that including adaptive human behavior significantly changes the predicted course of epidemics and that this inclusion has implications for parameter estimation and interpretation and for the development of social distancing policies. Acknowledging adaptive behavior requires a shift in thinking about epidemiological processes and parameters.

Numerical comparisons of path-following strategies for a primal-dual interior-point method for nonlinear programming

An important research activity in primal-dual interior-point methods for general nonlinear programming is to determine effective path-following strategies and their implementations. The objective of this work is to present numerical comparisons of several path-following strategies for the local interior-point Newton method given by El-Bakry, Tapia, Tsuchiya, and Zhang. We conduct numerical experimentation of nine strategies using two central regions, three notions of proximity measures, and three merit functions to obtain an optimal solution. Six of these strategies are implemented for the first time. The numerical results show that the best path-following strategy is that given by Argáez and Tapia.

Characterization of subcortical structures during deep brain stimulation utilizing support vector machines

In this paper we discuss an efficient methodology for the characterization of Microelectrode Recordings (MER) obtained during deep brain stimulation surgery for Parkinsons disease using Support Vector Machines and present the results of a preliminary study. The methodology is based in two algorithms: (1) an algorithm extracts multiple computational features from the microelectrode neurophysiology, and (2) integrates them in the support vector machines algorithm for classification. It has been applied to the problem of the recognition of subcortical structures: thalamus nucleus, zona incerta, subthalamic nucleus and substantia nigra. The SVM (support vector machines) algorithm performed quite well achieving 99.4% correct classification. In conclusion, the use of a computer-based system, like the one described in this paper, is intended to avoid human subjectivity in the localization of the subcortical structures and mainly the subthalamic nucleus (STN) for neurostimulation.

A note on the use of optimal control on a discrete time model of influenza dynamics

A discrete time Susceptible - Asymptomatic - Infectious - Treated - Recovered (SAITR) model is introduced in the context of influenza transmission. We evaluate the potential effect of control measures such as social distancing and antiviral treatment on the dynamics of a single outbreak. Optimal control theory is applied to identify the best way of reducing morbidity and mortality at a minimal cost. The problem is solved by using a discrete version of Pontryagins maximum principle. Numerical results show that dual strategies have stronger impact in the reduction of the final epidemic size.

On convergence of minimization methods: attraction, repulsion, and selection

In this paper, we revisit the convergence properties of the iterationprocess xk+1=xk−α(xk)B(xk)−1∇f(xk)for minimizing a function f(x). After reviewing some classic results andintroducing the notion of strong attraction, we give necessary andsufficient conditions for a stationary point of f(x) to be a point of strongattraction for the iteration process. Not only this result gives a newalgorithmic interpretation to the classic Ostrowski theorem, but alsoprovides insight into the interesting phenomenon called selectiveminimization. We present also illustrative numerical examples for nonlinearleast squares problems.

Allosteric transition and binding of small molecule effectors causes curvature change in central β-sheets of selected enzymes.

A quantitative description of allosteric transition remains a significant science challenge. Many allosteric enzymes contain a central β-sheet in their catalytic domain. When an allosteric protein undergoes the transition between T (tense) and R (relaxed) allosteric states, this central β-sheet undergoes a conformational change. A traditional method of measuring this change, the root mean square deviation (RMSD), appears to be inadequate to describe such changes in meaningful quantitative manner. We designed a novel quantitative method to demonstrate this conformational transition by measuring the change in curvature of the central β-sheet when enzymes transition between allosteric states. The curvature was established by calculating the semiaxes of a 3-D hyperboloid fitted by least squares to the

Data mining in the process of localization and classification of subcorticals structures

{{\hbox{C}}_\alpha }

A new infeasible interior-point algorithm for linear programming

atomic positions of the β-sheet. The two enzymes selected for this study, fructose 1,6-bisphosphatase (FBPase) from pig kidney and aspartate carbamoyltransferase (ATCase) from E. coli, showed while transitioning between the allosteric states (T ⇔ R) a notable change in β-sheet curvature (∼5%) that results in a large lateral shift at the sheet’s edge, which is necessary to convey the signal. The results suggest that the β-sheet participates in storing elastic energy associated with the transition. Establishing a tentative link between the energetics of the β-sheet in different allosteric states provides a more objective basis for the naming convention of allosteric states (tense or relaxed), and provides insight into the hysteretic nature of the transition. The approach presented here allows for a better understanding of the internal dynamics of allosteric enzymes by defining the domains that directly participate in the transition.