Robust optimization in countably infinite linear programs

A robust optimization framework for countably infinite linear programs (CILPs) is developed. It is shown that a particular robust counterpart of a nominal CILP can be reformulated as another CILP. A bound on the probability of constraint violation is derived. A convergent algorithm for solving this robust CILP is proposed.     

Adjoint L-Values and Primes of Congruence for Hilbert Modular Forms

Let f be a primitive Hilbert modular cusp form of arbitrary level and parallel weight k, defined over a totally real number field F. We define a finite set of primes that depends on the weight and level of f, the field F, and the torsion in the boundary cohomology groups of the Borel–Serre compactification of the underlying Hilbert-Blumenthal variety. We show that, outside , any prime that divides the algebraic part of the value at s=1 of the adjoint L-function of f is a congruence prime for f. In special cases we identify the boundary primes in terms of expressions of the form , where is a totally positive unit of F.     

Dynamic lot-sizing in sequential online retail auctions

Retailers often conduct non-overlapping sequential online auctions as a revenue generation and inventory clearing tool. We build a stochastic dynamic programming model for the seller’s lot-size decision problem in these auctions. The model incorporates a random number of participating bidders in each auction, allows for any bid distribution, and is not restricted to any specific price-determination mechanism. Using stochastic monotonicity/stochastic concavity and supermodularity arguments, we present a complete structural characterization of optimal lot-sizing policies under a second order condition on the single-auction expected revenue function. We show that a monotone staircase with unit jumps policy is optimal and provide a simple inequality to determine the locations of these staircase jumps. Our analytical examples demonstrate that the second order condition is met in common online auction mechanisms. We also present numerical experiments and sensitivity analyses using real online auction data.     

Spherically symmetric inhomogeneous dust collapse in higher dimensional space-time and cosmic censorship hypothesis

We consider a collapsing spherically symmetric inhomogeneous dust cloud in higher dimensional space-time. We show that the central singularity of collapse can be a strong curvature or a weak curvature naked singularity depending on the initial density distribution.     

Development of docking-based 3D QSAR models for the design of substituted quinoline derivatives as human dihydroorotate dehydrogenase (hDHODH) inhibitors

Abstract

This study has investigated docking-based 3D quantitative structure–activity relationships (QSARs) for a range of quinoline carboxylic acid derivatives by comparative molecular field analysis (CoMFA) and comparative molecular similarity indices analysis (CoMSIA). A docking study has shown that most of the compounds formed H-bonds with Arg136 and Gln47, which have already been shown to be essential for the binding of ligands at the active site of the hydroorotate dehydrogenase adenovirus (hDHODH). Bioactive conformations of all the molecules obtained from the docking study were used for the 3D QSAR study. The best CoMFA and CoMSIA models were obtained for the training set and were found to be statistically significant, with cross-validated coefficients (q² ) of 0.672 and 0.613, r² _cv of 0.635 and 0.598 and coefficients of determination (r² ) of 0.963 and 0.896, respectively. Both models were validated by a test set of 15 compounds, giving satisfactory predicted correlation coefficients (r² _pred) of 0.824 and 0.793 for the CoMFA and CoMSIA models, respectively. From the docking-based 3D QSAR study we designed 34 novel quinoline-based compounds and performed structure-based virtual screening. Finally, in silico pharmacokinetics and toxicities were predicted for 24 of the best docked molecules. The study provides valuable information for the understanding of interactions between hDHODH and the novel compounds.     

A dynamic programming approach to efficient sampling from Boltzmann distributions

Markov chain methods for Boltzmann sampling work in phases with decreasing temperatures. The number of transitions in each phase crucially affects terminal state distribution. We employ dynamic programming to allocate iterations to phases to improve guarantees on sample quality. Numerical experiments on the Ising model are presented.     

Design,synthesis, pharmacological evaluation and in silico ADMET prediction of novel substituted benzimidazole derivatives as angiotensin II–AT1 receptor antagonists based on predictive 3D QSAR models

In this study we designed novel substituted benzimidazole derivatives and predicted their absorption, distribution, metabolism, excretion and toxicity (ADMET) properties, based on a predictive 3D QSAR study on 132 substituted benzimidazoles as AngII–AT₁ receptor antagonists. The two best predicted compounds were synthesized and evaluated for AngII–AT₁ receptor antagonism. Three different alignment tools for comparative molecular field analysis (CoMFA) and comparative molecular similarity indices analysis (CoMSIA) were used. The best 3D QSAR models were obtained using the rigid body (Distill) alignment method. CoMFA and CoMSIA models were found to be statistically significant with leave-one-out correlation coefficients (q²) of 0.630 and 0.623, respectively, cross-validated coefficients (r²_cv) of 0.651 and 0.630, respectively, and conventional coefficients of determination (r²) of 0.848 and 0.843, respectively. 3D QSAR models were validated using a test set of 24 compounds, giving satisfactory predicted results (r²_pred) of 0.727 and 0.689 for the CoMFA and CoMSIA models, respectively. We have identified some key features in substituted benzimidazole derivatives, such as lipophilicity and H-bonding at the 2- and 5-positions of the benzimidazole nucleus, respectively, for AT₁ receptor antagonistic activity. We designed 20 novel substituted benzimidazole derivatives and predicted their activity. In silico ADMET properties were also predicted for these designed molecules. Finally, the compounds with best predicted activity were synthesized and evaluated for in vitro angiotensin II–AT₁ receptor antagonism.     

A stochastic control formalism for dynamic biologically conformal radiation therapy

State-of-the-art methods for optimizing cancer treatment over several weeks of external beam radiotherapy take a static–deterministic view of the treatment planning process, mainly focusing on spatial distribution of dose. Recent progress in quantitative functional imaging as well as mathematical models of tumor response to radiotherapy is increasingly enabling treatment planners to monitor/predict a patient’s biological response over weeks of treatment. In this paper we introduce dynamic biologically conformal radiation therapy (DBCRT), a mathematical framework intended to exploit these emerging technological and biological modeling advances to design patient-specific radiation treatment strategies that dynamically adapt to the spatiotemporal evolution of a patient’s biological response over several treatment sessions in order to achieve the best possible health outcome. More specifically, we propose a discrete-time stochastic control formalism where we use the patient’s biological condition to model the system state and the beam intensities as controls. Three approximate control schemes are then applied and compared for efficiency. Numerical simulations on test cases show that DBCRT results in a 64–98% improvement in treatment efficacy as compared to the more conventional static–deterministic approach.     

Genericity and stability of naked singularities arising in an inhomogeneous dust collapse

In this paper, we consider an inhomogeneous dust collapse, and extend earlier works of Jhingan, Joshi, and Singh to the case where initial density and velocity distributions are finitely differentiable functions of co-moving coordinate r. We study the occurrence of naked singularities under various conditions on the derivatives of initial density and velocity distributions in marginally as well as non-marginally bound case. We then study their stability and genericity with respect to perturbations in the initial data in an appropriate topological sense.