leticia velazquez

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 interpre...

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. susceptible-infected-recovered model | R 0 | reproductive number | bioeconomics T he science and management of infectious disease is entering a new stage. The increasing focus on incentive structures to motivate people to engage in social distancing-reducing in-terpersonal contacts and hence public disease risk (1)-changes what health authorities need from epidemiological models. Social distancing is not new-for centuries humans quarantined infected individuals and shunned the obviously ill, but new approaches are being used to deal with modern social interactions. Scientific development of social distancing public policies requires that epidemiological models explicitly address be-havioral responses to disease risk and other incentives affecting contact behavior. This paper models the role of adaptive behavior in an epidemiological system. Recognizing adaptive behavior means explicitly incorporating behavioral responses to disease risk and other incentives into epidemiological models (2, 3). The workhorse of modern epidemiology, the compartmental epidemiological model (4, 5), does not explicitly include behav-ioral responses to disease risk. The transmission factors in these models combine and confound human behavior and biological processes. We develop a simple compartmental model that explicitly incorporates adaptive behavior and show that this modification alters understanding of standard epidemiological metrics. For example, the basic reproductive number, R 0 , is a function of biological processes and human behavior, but R 0 lacks a behav-ioral interpretation in the existing literature. Biological and be-havioral feedbacks muddle R 0 's biological interpretation and confound its estimation. Prior approaches that incorporate behavior into epidemiological models generally fall into three categories: specification of nonlinear contact rate functions, expanded epidemiological compartments or agent-based models, and epidemiological-economic (epi-economic) models. Classical epidemiological models assume contact rates are constant (frequency dependent) or proportional to density (density dependent), although many extensions exist (6). A common extension is to specify a contact rate that is non-linear in the state variables-generally in the density of infected individuals (e.g., refs. 6-8). Such extensions are a reduced-form approach to modeling behavioral responses to disease risks. This approach is limited in that it does not model the underlying decision process and does not readily help decision makers design incentives for socially desirable behaviors during an epidemic. A second approach is to include behaviorally related compartments in addition to health status compartments. This approach involves developing behavioral rules for types of individuals in different compartments, such as hospitalization and fear compartments (9, 10) or spatial compartments joined as a network (11). Individuals in these compartments experience different disease incidence. Extending this approach, so that all individuals have unique behavioral rules, yields an agent-based model (e.g., ref. 12). This approach often requires the analyst to specify ex ante how changing incentives alters behavior and thus is restricted in its ability to aid in designing social distancing incentives. Epi-economic models merge economics and epidemiology by explicitly analyzing individual behavioral choices in response to disease risk (13-18). People are assumed to make decisions to maximize utility, an index of well-being. People weigh the expected utility associated with decisions that include the possibility of future infection when choosing between behaviors such as vaccination choices (17) or different levels of interpersonal contact (12-15). Disease risks simultaneously affect and are affected by agents' decisions, creating a risk feedback-infection levels drive behaviors and contact rate decisions shape disease spread. The epi-economics literature is largely built on top of classical epidemiology, so that the impact of economic behaviors on epidemiological processes and metrics generally is not explored. In this paper, we explore how economic feedbacks alter the underlying epidemiology and can fundamentally shift interpretation of epidemiological processes and metrics. The approach to modeling behavior has implications for public health policy design. Nonlinear contact rate models and models involving increasing compartmentalization generally focus on estimating the basic reproductive number of the disease,

We implemented a joint inversion least-squares (LSQ) algorithm to characterize 1-D crustal velocity Earth structure using geophysical data sets with two different optimization methods: truncated singular value decomposition (TSVD), and primal-dual interior-point (PDIP). We used receiver function and surface wave dispersion velocity observations, and created a framework to incorporate other data sets. An improvement in the final outcome (model) is expected by providing better physical constraints than using just one single data set. The TSVD and PDIP methods solve a regularized unconstrained and an inherent regularized constrained minimization problems, respectively. Both techniques implement the inclusion of bounds into the layered shear velocities in a different fashion. We conduct a numerical experimentation with synthetic data, and find that the PDID method’s solution was more robust in terms of satisfying geophysical constraints, accuracy, and efficiency than the TSVD approach. Finally, we apply the PDIP method for characterizing material properties of the Rio Grande Rift region using real recorded seismic data with promising numerical results.

Iteratively reweighted least-squares (IRLS) algorithms have been successfully used in compressive sensing to reconstruct sparse signals from incomplete linear measurements taken in nonsparse domains. The underlying optimization problem corresponds to finding the vector that solves the lp minimization while explaining the measurements, and IRLS allows to easily control the used value of p, with effect on the number of required

Iteratively reweighted least-squares (IRLS) algorithms have been successfully used in compressive sensing to reconstruct sparse signals from incomplete linear measurements taken in nonsparse domains. The underlying optimization problem corresponds to finding the vector that solves the lp minimization while explaining the measurements, and IRLS allows to easily control the used value of p, with effect on the number of required

In this paper, we consider approximating global minima of zero or small residual, nonlinear least-squares problems. We propose a selective search approach based on the concept of selective minimization recently introduced in Zhang et al. (Technical Report TR99-12, Rice University, Department of Computational and Applied Mathematics MS-134, Houston, TX 77005, 1999). To test the viability of the proposed approach, we construct a simple implementation using a Levenberg-Marquardt type method combined with a multi-start scheme, and compare it with several existing global optimization techniques. Numerical experiments were performed on zero residual nonlinear least-squares problems chosen from structural biology applications and from the literature. On the problems of significant sizes, the performance of the new approach compared favorably with other tested methods, indicating that the new approach is promising for the intended class of problems.

We present the numerical performance of orthogonal and biorthogonal wavelet-based parameterization schemes for solving parameter estimation problems for finding a global solution using the Simultaneous Perturbation Stochastic Approximation (SPSA) algorithm. The two schemes are tested on a two-phase flow problem using the Integrated Parallel Accurate Reservoir Simulators (IPARS) simulator in MATLAB. This work is an extension of the research described in (Velazquez et al., 2008) where wavelet parameterization was limited to the orthogonal Haar wavelet. We extend this work by considering the orthogonal Daubechies, Coiflet, and Symlet families of wavelets, and the biorthogonal Spline family of wavelets. In addition to a comparison of the various wavelet families, an analysis of the performance of each at different levels of decomposition will also be discussed.

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.

We implemented a joint inversion least-squares (LSQ) algorithm to characterize 1-D crustal velocity Earth structure using geophysical data sets with two different optimization methods: truncated singular value decomposition (TSVD), and primal-dual interior-point (PDIP). We used receiver function and surface wave dispersion velocity observations, and created a framework to incorporate other data sets. An improvement in the final outcome (model) is expected by providing better physical constraints than using just one single data set. The TSVD and PDIP methods solve a regularized unconstrained and an inherent regularized constrained minimization problems, respectively. Both techniques implement the inclusion of bounds into the layered shear velocities in a different fashion. We conduct a numerical experimentation with synthetic data, and find that the PDID method’s solution was more robust in terms of satisfying geophysical constraints, accuracy, and efficiency than the TSVD approach. Finally, we apply the PDIP method for characterizing material properties of the Rio Grande Rift region using real recorded seismic data with promising numerical results.

In this paper we discuss an efficient methodology for the characterization of Microelectrode Recordings (MER) obtained during deep brain stimulation surgery for Parkinson's 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.

Iteratively reweighted least-squares (IRLS) algorithms have been successfully used in compressive sensing to reconstruct sparse signals from incomplete linear measurements taken in nonsparse domains. The underlying optimization problem corresponds to finding the vector that solves the lp minimization while explaining the measurements, and IRLS allows to easily control the used value of p, with effect on the number of required

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 $ {{\hbox{C}}_\alpha } $ 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.

We present a numerical experimentation of the global optimization algorithm presented by Velazquez et al. (2001) applied to a nonlinear hyperboloid least squares problem. This problem arises when beta sheet residues from an allosteric enzyme are fitted onto a hyperboloid by using Newton type methods. The results show that the algorithm performs well on three test cases. An important side result of this study is that the nonlinear fitting procedure is vastly superior to the linear least squares procedures traditionally used for this type of problems.

Iteratively reweighted least-squares (IRLS) algorithms have been successfully used in compressive sensing to reconstruct sparse signals from incomplete linear measurements taken in nonsparse domains. The underlying optimization problem corresponds to finding the vector that solves the lp minimization while explaining the measurements, and IRLS allows to easily control the used value of p, with effect on the number of required

In this paper, we consider approximating global minima of zero or small residual, nonlinear least-squares problems. We propose a selective search approach based on the concept of selective minimization recently introduced in Zhang et al. (Technical Report TR99-12, Rice University, Department of Computational and Applied Mathematics MS-134, Houston, TX 77005, 1999). To test the viability of the proposed approach, we construct a simple implementation using a Levenberg-Marquardt type method combined with a multi-start scheme, and compare it with several existing global optimization techniques. Numerical experiments were performed on zero residual nonlinear least-squares problems chosen from structural biology applications and from the literature. On the problems of significant sizes, the performance of the new approach compared favorably with other tested methods, indicating that the new approach is promising for the intended class of problems.

We present the numerical performance of orthogonal and biorthogonal wavelet-based parameterization schemes for solving parameter estimation problems for finding a global solution using the Simultaneous Perturbation Stochastic Approximation (SPSA) algorithm. The two schemes are tested on a two-phase flow problem using the Integrated Parallel Accurate Reservoir Simulators (IPARS) simulator in MATLAB. This work is an extension of the research described in (Velazquez et al., 2008) where wavelet parameterization was limited to the orthogonal Haar wavelet. We extend this work by considering the orthogonal Daubechies, Coiflet, and Symlet families of wavelets, and the biorthogonal Spline family of wavelets. In addition to a comparison of the various wavelet families, an analysis of the performance of each at different levels of decomposition will also be discussed.

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.

In this paper we discuss an efficient methodology for the characterization of Microelectrode Recordings (MER) obtained during deep brain stimulation surgery for Parkinson's 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 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 $ {{\hbox{C}}_\alpha } $ 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.

We present a numerical experimentation of the global optimization algorithm presented by Velazquez et al. (2001) applied to a nonlinear hyperboloid least squares problem. This problem arises when beta sheet residues from an allosteric enzyme are fitted onto a hyperboloid by using Newton type methods. The results show that the algorithm performs well on three test cases. An important side result of this study is that the nonlinear fitting procedure is vastly superior to the linear least squares procedures traditionally used for this type of problems.