Variable Smoothing for Weakly Convex Composite Functions.

We study minimization of a structured objective function, being the sum of a smooth function and a composition of a weakly convex function with a linear operator. Applications include image reconstruction problems with regularizers that introduce less bias than the standard convex regularizers. We develop a variable smoothing algorithm, based on the Moreau envelope with a decreasing sequence of smoothing parameters, and prove a complexity of O ( ϵ - 3 ) to achieve an ϵ -approximate solution. This bound interpolates between the O ( ϵ - 2 ) bound for the smooth case and the O ( ϵ - 4 ) bound for the subgradient method. Our complexity bound is in line with other works that deal with structured nonsmoothness of weakly convex functions.

The importance of individual movement and feeding behaviour for long-distance seed dispersal by red deer: a data-driven model.

BACKGROUND: Long-distance seed dispersal (LDD) has strong impacts on the spatiotemporal dynamics of plants. Large animals are important LDD vectors because they regularly transport seeds of many plant species over long distances. While there is now ample evidence that behaviour varies considerably between individual animals, it is not clear to what extent inter-individual variation in behaviour alters seed dispersal by animals. METHODS: We study how inter-individual variation in the movement and feeding behaviour of one of Europe's largest herbivores (the red deer, Cervus elaphus) affects internal seed dispersal (endozoochory) of multiple plant species. We combine movement data of 21 individual deer with measurements of seed loads in the dung of the same individuals and with data on gut passage time. These data serve to parameterize a model of passive dispersal that predicts LDD in three orientations (horizontal as well as upward and downward in elevation).With this model we investigate to what extent per-seed probabilities of LDD and seed load vary between individuals and throughout the vegetation period (May-December). Subsequently, we test whether per-seed LDD probability and seed load are positively (or negatively) correlated so that more mobile animals disperse more (or less) seeds. Finally, we examine whether non-random associations between per-seed LDD probability and seed load affect the LDD of individual plant species. RESULTS: The studied deer dispersed viable seeds of at least 62 plant species. Deer individuals varied significantly in per-seed LDD probability and seed loads. However, more mobile animals did not disperse more or less seeds than less mobile ones. Plant species also did not differ significantly in the relationship between per-seed LDD probability and seed load. Yet plant species differed in how their seed load was distributed across deer individuals and in time, and this caused their LDD potential to differ more than twofold. For several plant species, we detected non-random associations between per-seed LDD probability and seed load that generally increased LDD potential. CONCLUSIONS: Inter-individual variation in movement and feeding behaviour means that certain deer are substantially more effective LDD vectors than others. This inter-individual variation reduces the reliability of LDD and increases the sensitivity of LDD to the decline of deer populations. Variation in the dispersal services of individual animals should thus be taken into account in models in order to improve LDD projections.

Predicting kinase inhibitors using bioactivity matrix derived informer sets.

Prediction of compounds that are active against a desired biological target is a common step in drug discovery efforts. Virtual screening methods seek some active-enriched fraction of a library for experimental testing. Where data are too scarce to train supervised learning models for compound prioritization, initial screening must provide the necessary data. Commonly, such an initial library is selected on the basis of chemical diversity by some pseudo-random process (for example, the first few plates of a larger library) or by selecting an entire smaller library. These approaches may not produce a sufficient number or diversity of actives. An alternative approach is to select an informer set of screening compounds on the basis of chemogenomic information from previous testing of compounds against a large number of targets. We compare different ways of using chemogenomic data to choose a small informer set of compounds based on previously measured bioactivity data. We develop this Informer-Based-Ranking (IBR) approach using the Published Kinase Inhibitor Sets (PKIS) as the chemogenomic data to select the informer sets. We test the informer compounds on a target that is not part of the chemogenomic data, then predict the activity of the remaining compounds based on the experimental informer data and the chemogenomic data. Through new chemical screening experiments, we demonstrate the utility of IBR strategies in a prospective test on three kinase targets not included in the PKIS.

Efficient optimization of natural resonance theory weightings and bond orders by gram-based convex programming.

We describe the formal algorithm and numerical applications of a novel convex quadratic programming (QP) strategy for performing the variational minimization that underlies natural resonance theory (NRT). The QP algorithm vastly improves the numerical efficiency, thoroughness, and accuracy of variational NRT description, which now allows uniform treatment of all reference structures at the high level of detail previously reserved only for leading "reference" structures, with little or no user guidance. We illustrate overall QPNRT search strategy, program I/O, and numerical results for a specific application to adenine, and we summarize more extended results for a data set of 338 species from throughout the organic, bioorganic, and inorganic domain. The improved QP-based implementation of NRT is a principal feature of the newly released NBO 7.0 program version. © 2019 Wiley Periodicals, Inc.

Bioactive Polycyclic Tetramate Macrolactams from Lysobacter enzymogenes and Their Absolute Configurations by Theoretical ECD Calculations.

Two new polycyclic tetramate macrolactams, lysobacteramides A (1) and B (2), together with HSAF (heat-stable antifungal factor, 3), 3-dehydroxy HSAF (4), and alteramide A (5) were isolated from a culture of Lysobacter enzymogenes C3 in nutrient yeast glycerol medium. Their structures were determined by MS and extensive NMR analysis. The absolute configurations of 1-5 were assigned by theoretical calculations of their ECD spectra. Although HSAF and analogues were reported from several microorganisms, their absolute configurations had not been established. The isolation and the absolute configurations of these compounds revealed new insights into the biosynthetic mechanism for formation of the polycycles. Compounds 1-4 exhibited cytotoxic activity against human carcinoma A549, HepG2, and MCF-7 cells with IC50 values ranging from 0.26 to 10.3 µM. Compounds 2 and 3 showed antifungal activity against Fusarium verticillioides with IC50 value of 47.9 and 6.90 µg/mL, respectively.

Optimizing financial effects of HIE: a multi-party linear programming approach.

OBJECTIVE: To describe an analytical framework for quantifying the societal savings and financial consequences of a health information exchange (HIE), and to demonstrate its use in designing pricing policies for sustainable HIEs. MATERIALS AND METHODS: We developed a linear programming model to (1) quantify the financial worth of HIE information to each of its participating institutions and (2) evaluate three HIE pricing policies: fixed-rate annual, charge per visit, and charge per look-up. We considered three desired outcomes of HIE-related emergency care (modeled as parameters): preventing unrequired hospitalizations, reducing duplicate tests, and avoiding emergency department (ED) visits. We applied this framework to 4639 ED encounters over a 12-month period in three large EDs in Milwaukee, Wisconsin, using Medicare/Medicaid claims data, public reports of hospital admissions, published payer mix data, and use data from a not-for-profit regional HIE. RESULTS: For this HIE, data accesses produced net financial gains for all providers and payers. Gains, due to HIE, were more significant for providers with more health maintenance organizations patients. Reducing unrequired hospitalizations and avoiding repeat ED visits were responsible for more than 70% of the savings. The results showed that fixed annual subscriptions can sustain this HIE, while ensuring financial gains to all participants. Sensitivity analysis revealed that the results were robust to uncertainties in modeling parameters. DISCUSSION: Our specific HIE pricing recommendations depend on the unique characteristics of this study population. However, our main contribution is the modeling approach, which is broadly applicable to other populations.

The partitioned LASSO-patternsearch algorithm with application to gene expression data.

BACKGROUND: In systems biology, the task of reverse engineering gene pathways from data has been limited not just by the curse of dimensionality (the interaction space is huge) but also by systematic error in the data. The gene expression barcode reduces spurious association driven by batch effects and probe effects. The binary nature of the resulting expression calls lends itself perfectly to modern regularization approaches that thrive in high-dimensional settings. RESULTS: The Partitioned LASSO-Patternsearch algorithm is proposed to identify patterns of multiple dichotomous risk factors for outcomes of interest in genomic studies. A partitioning scheme is used to identify promising patterns by solving many LASSO-Patternsearch subproblems in parallel. All variables that survive this stage proceed to an aggregation stage where the most significant patterns are identified by solving a reduced LASSO-Patternsearch problem in just these variables. This approach was applied to genetic data sets with expression levels dichotomized by gene expression bar code. Most of the genes and second-order interactions thus selected and are known to be related to the outcomes. CONCLUSIONS: We demonstrate with simulations and data analyses that the proposed method not only selects variables and patterns more accurately, but also provides smaller models with better prediction accuracy, in comparison to several alternative methodologies.

Optimization methods for selecting founder individuals for captive breeding or reintroduction of endangered species.

Methods from genetics and genomics can be employed to help save endangered species. One potential use is to provide a rational strategy for selecting a population of founders for a captive breeding program. The hope is to capture most of the available genetic diversity that remains in the wild population, to provide a safe haven where representatives of the species can be bred, and eventually to release the progeny back into the wild. However, the founders are often selected based on a random-sampling strategy whose validity is based on unrealistic assumptions. Here we outline an approach that starts by using cutting-edge genome sequencing and genotyping technologies to objectively assess the available genetic diversity. We show how combinatorial optimization methods can be applied to these data to guide the selection of the founder population. In particular, we develop a mixed-integer linear programming technique that identifies a set of animals whose genetic profile is as close as possible to specified abundances of alleles (i.e., genetic variants), subject to constraints on the number of founders and their genders and ages.

Optimal design of thermally stable proteins.

MOTIVATION: For many biotechnological purposes, it is desirable to redesign proteins to be more structurally and functionally stable at higher temperatures. For example, chemical reactions are intrinsically faster at higher temperatures, so using enzymes that are stable at higher temperatures would lead to more efficient industrial processes. We describe an innovative and computationally efficient method called Improved Configurational Entropy (ICE), which can be used to redesign a protein to be more thermally stable (i.e. stable at high temperatures). This can be accomplished by systematically modifying the amino acid sequence via local structural entropy (LSE) minimization. The minimization problem is modeled as a shortest path problem in an acyclic graph with nonnegative weights and is solved efficiently using Dijkstra's method.

Efficient schemes for robust IMRT treatment planning.

We use robust optimization techniques to formulate an IMRT treatment planning problem in which the dose matrices are uncertain, due to both dose calculation errors and interfraction positional uncertainty of tumour and organs. When the uncertainty is taken into account, the original linear programming formulation becomes a second-order cone program. We describe a novel and efficient approach for solving this problem, and present results to compare the performance of our scheme with more conventional formulations that assume perfect knowledge of the dose matrix.

Framework for kernel regularization with application to protein clustering.

We develop and apply a previously undescribed framework that is designed to extract information in the form of a positive definite kernel matrix from possibly crude, noisy, incomplete, inconsistent dissimilarity information between pairs of objects, obtainable in a variety of contexts. Any positive definite kernel defines a consistent set of distances, and the fitted kernel provides a set of coordinates in Euclidean space that attempts to respect the information available while controlling for complexity of the kernel. The resulting set of coordinates is highly appropriate for visualization and as input to classification and clustering algorithms. The framework is formulated in terms of a class of optimization problems that can be solved efficiently by using modern convex cone programming software. The power of the method is illustrated in the context of protein clustering based on primary sequence data. An application to the globin family of proteins resulted in a readily visualizable 3D sequence space of globins, where several subfamilies and subgroupings consistent with the literature were easily identifiable.