Yannis A. Guzman

New a priori and a posteriori probabilistic bounds for robust counterpart optimization: I. Unknown probability distributions

Abstract Optimization problems often have a subset of parameters whose values are not known exactly or have yet to be realized. Nominal solutions to models under uncertainty can be infeasible or yield overly optimistic objective function values given the actual parameter realizations. Worst-case robust optimization guarantees feasibility but yields overly conservative objective function values. The use of probabilistic guarantees greatly improves the performance of robust counterpart optimization. We present new a priori and a posteriori probabilistic bounds which improve upon existing methods applied to models with uncertain parameters whose possible realizations are bounded and subject to unspecified probability distributions. We also provide new a priori and a posteriori bounds which, for the first time, permit robust counterpart optimization of models with parameters whose means are only known to lie within some range of values. The utility of the bounds is demonstrated through computational case studies involving a mixed-integer linear optimization problem and a linear multiperiod planning problem. These bounds reduce the conservatism, improve the performance, and augment the applicability of robust counterpart optimization.

Discovery of biomarker combinations that predict periodontal health or disease with high accuracy from GCF samples based on high‐throughput proteomic analysis and mixed‐integer linear optimization

AIM To identify optimal combination(s) of proteomic based biomarkers in gingival crevicular fluid (GCF) samples from chronic periodontitis (CP) and periodontally healthy individuals and validate the predictions through known and blind test sets. MATERIALS AND METHODS GCF samples were collected from 96 CP and periodontally healthy subjects and analysed using high-performance liquid chromatography, tandem mass spectrometry and the PILOT_PROTEIN algorithm. A mixed-integer linear optimization (MILP) model was then developed to identify the optimal combination of biomarkers which could clearly distinguish a blind subject sample as healthy or diseased. RESULTS A thorough cross-validation of the MILP model capability was performed on a training set of 55 samples and greater than 99% accuracy was consistently achieved when annotating the testing set samples as healthy or diseased. The model was then trained on all 55 samples and tested on two different blind test sets, and using an optimal combination of 7 human proteins and 3 bacterial proteins, the model was able to correctly predict 40 out of 41 healthy and diseased samples. CONCLUSIONS The proposed large-scale proteomic analysis and MILP model led to the identification of novel combinations of biomarkers for consistent diagnosis of periodontal status with greater than 95% predictive accuracy.

Highly Accurate Structure-Based Prediction of HIV-1 Coreceptor Usage Suggests Intermolecular Interactions Driving Tropism

HIV-1 entry into host cells is mediated by interactions between the V3-loop of viral glycoprotein gp120 and chemokine receptor CCR5 or CXCR4, collectively known as HIV-1 coreceptors. Accurate genotypic prediction of coreceptor usage is of significant clinical interest and determination of the factors driving tropism has been the focus of extensive study. We have developed a method based on nonlinear support vector machines to elucidate the interacting residue pairs driving coreceptor usage and provide highly accurate coreceptor usage predictions. Our models utilize centroid-centroid interaction energies from computationally derived structures of the V3-loop:coreceptor complexes as primary features, while additional features based on established rules regarding V3-loop sequences are also investigated. We tested our method on 2455 V3-loop sequences of various lengths and subtypes, and produce a median area under the receiver operator curve of 0.977 based on 500 runs of 10-fold cross validation. Our study is the first to elucidate a small set of specific interacting residue pairs between the V3-loop and coreceptors capable of predicting coreceptor usage with high accuracy across major HIV-1 subtypes. The developed method has been implemented as a web tool named CRUSH, CoReceptor USage prediction for HIV-1, which is available at http://ares.tamu.edu/CRUSH/.

New a priori and a posteriori probabilistic bounds for robust counterpart optimization: II. A priori bounds for known symmetric and asymmetric probability distributions

Abstract When optimization problems contain uncertain parameters, their nominal solutions may prove to be overly optimistic or even rendered infeasible given the actual parameter realizations. The application of probabilistic bounds in constructing the robust counterpart formulation of a model under uncertainty can greatly reduce the conservatism of traditional worst-case robust optimization. In Part I, we derived new a priori and a posteriori bounds on the probability of constraint violation for constraints with uncertain parameters whose distributions were unknown. Here, we first present new a priori bounds applicable to uncertain constraints with linearly participating uncertain parameters whose distributions are known or conservatively approximated. We then extend the robust counterpart optimization methodology by allowing attributed known distributions to be symmetric or asymmetric. The new methods greatly reduce the conservatism and significantly augment the performance and applicability of robust counterpart optimization. A mixed-integer linear optimization example and a multiperiod planning problem demonstrate the improvements of the new a priori bounds relative to existing bounds.

Proteomics for the discovery of biomarkers and diagnosis of periodontitis: a critical review

Periodontitis is a common chronic and destructive disease whose pathogenetic mechanisms remain unclear. Due to their sensitivity and global scale, proteomics studies offer the opportunity to uncover critical host and pathogen activity indicators and can elucidate clinically applicable biomarkers for improved diagnosis and treatment of the disease. This review summarizes the literature of proteomics studies on periodontitis and comprehensively discusses commonly found candidate biomarkers. Key considerations in the design of an experimental proteomics platform are also outlined. The applicability of protein biomarkers across the progression of periodontitis and unexplored areas of research are highlighted.

Princeton_TIGRESS 2.0: High refinement consistency and net gains through support vector machines and molecular dynamics in double-blind predictions during the CASP11 experiment: Enhanced Protein Structure Refinement

Protein structure refinement is the challenging problem of operating on any protein structure prediction to improve its accuracy with respect to the native structure in a blind fashion. Although many approaches have been developed and tested during the last four CASP experiments, a majority of the methods continue to degrade models rather than improve them. Princeton_TIGRESS (Khoury et al., Proteins 2014;82:794–814) was developed previously and utilizes separate sampling and selection stages involving Monte Carlo and molecular dynamics simulations and classification using an SVM predictor. The initial implementation was shown to consistently refine protein structures 76% of the time in our own internal benchmarking on CASP 7‐10 targets. In this work, we improved the sampling and selection stages and tested the method in blind predictions during CASP11. We added a decomposition of physics‐based and hybrid energy functions, as well as a coordinate‐free representation of the protein structure through distance‐binning Cα−Cα distances to capture fine‐grained movements. We performed parameter estimation to optimize the adjustable SVM parameters to maximize precision while balancing sensitivity and specificity across all cross‐validated data sets, finding enrichment in our ability to select models from the populations of similar decoys generated for targets in CASPs 7‐10. The MD stage was enhanced such that larger structures could be further refined. Among refinement methods that are currently implemented as web‐servers, Princeton_TIGRESS 2.0 demonstrated the most consistent and most substantial net refinement in blind predictions during CASP11. The enhanced refinement protocol Princeton_TIGRESS 2.0 is freely available as a web server at http://atlas.engr.tamu.edu/refinement/. Proteins 2017; 85:1078–1098.

New a priori and a posteriori probabilistic bounds for robust counterpart optimization: III. Exact and near-exact a posteriori expressions for known probability distributions

The performance of robust optimization is closely connected with probabilistic bounds that determine the probability of constraint violation due to uncertain parameter realizations. In Part I of this work, new a priori and a posteriori probabilistic bounds were developed for cases when robust optimization is applied to uncertain optimization problems with parameters whose probability distributions were unknown. In Part II, the focus shifted to known probability distributions and a priori bounds. In this paper, new, tight a posteriori expressions are developed for constraints containing parameters with specific known distributions, that is, those attributed normal, uniform, discrete, gamma, chi-squared, Erlang, or exponential distributions. The nature of some of the expressions requires efficient implementations, and new algorithmic methods are discussed which greatly improve applicability. These new expressions are much tighter than existing bounds and greatly reduce the conservatism of robust solutions. The theoretical and algorithmic results of Parts I, II, and III allow for wider usage of robust optimization in process synthesis and operations research applications.

Performance of convex underestimators in a branch-and-bound framework

The efficient determination of tight lower bounds in a branch-and-bound algorithm is crucial for the global optimization of models spanning numerous applications and fields. The global optimization method

Computational Comparison of Convex Underestimators for Use in a Branch-and-Bound Global Optimization Framework

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