Abstract.A branch and bound global optimization method, BB, for general continuous optimization problems involving nonconvexities in the objective function and/or constraints is presented. The nonconvexities are categorized as being either of special structure or generic. A convex relaxation of the original nonconvex problem is obtained by (i) replacing all nonconvex terms of special structure (i.e. bilinear, fractional, signomial) with customized tight convex lower bounding functions and (ii) by utilizing the parameter as defined in [17] to underestimate nonconvex terms of generic structure. The proposed branch and bound type algorithm attains finite -convergence to the global minimum through the successive subdivision of the original region and the subsequent solution of a series of nonlinear convex minimization problems. The global optimization method, BB, is implemented in C and tested on a variety of example problems.

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Stem cells that adopt distinct lineages cannot be distinguished based on traditional cell shape. This study reports that higher-order variations in cell shape and cytoskeletal organization that occur within hours of stimulation forecast the lineage commitment fates of human mesenchymal stem cells (hMSCs). The unique approach captures numerous early (24 h), quantitative features of actin fluororeporter shapes, intensities, textures, and spatial distributions (collectively termed morphometric descriptors). The large number of descriptors are reduced into "combinations" through which distinct subpopulations of cells featuring unique combinations are identified. We demonstrate that hMSCs cultured on fibronectin-treated glass substrates under environments permissive to bone lineage induction could be readily discerned within the first 24 h from those cultured in basal-or fat-inductive conditions by such cytoskeletal feature groupings. We extend the utility of this approach to forecast osteogenic stem cell lineage fates across a series of synthetic polymeric materials of diverse physicochemical properties. Within the first 24 h following stem cell seeding, we could successfully "profile" the substrate responsiveness prospectively in terms of the degree of bone versus nonbone predisposition. The morphometric methodology also provided insights into how substrates may modulate the pace of osteogenic lineage specification. Cells on glass substrates deficient in fibronectin showed a similar divergence of lineage fates, but delayed beyond 48 h. In summary, this high-content imaging and single cell modeling approach offers a framework to elucidate and manipulate determinants of stem cell behaviors, as well as to screen stem cell lineage modulating materials and environments.biomaterials | differentiation | imaging and modeling | stem cells | actin organization

Cancer is a devastating disease that takes the lives of hundreds of thousands of people every year. Due to disease heterogeneity, standard treatments, such as chemotherapy or radiation, are effective in only a subset of the patient population. Tumors can have different underlying genetic causes and may express different proteins in one patient versus another. This inherent variability of cancer lends itself to the growing field of precision and personalized medicine (PPM). There are many ongoing efforts to acquire PPM data in order to characterize molecular differences between tumors. Some PPM products are already available to link these differences to an effective drug. It is clear that PPM cancer treatments can result in immense patient benefits, and companies and regulatory agencies have begun to recognize this. However, broader changes to the healthcare and insurance systems must be addressed if PPM is to become part of standard cancer care.

Two no®el deterministic global optimization algorithms for noncon®ex mixed-integer ( ) problems MINLPs are proposed, using the ad®ances of the ␣ BB algorithm for noncon®ex NLPs of Adjiman et al. The special structure mixed-integer ␣ BB algorithm ( ) SMIN-␣ BB addresses problems with noncon®exities in the continuous ®ariables and linear and mixed-bilinear participation of the binary ®ariables. The general structure ( ) mixed-integer ␣ BB algorithm GMIN-␣ BB is applicable to a ®ery general class of problems for which the continuous relaxation is twice continuously differentiable. Both algorithms are de®eloped using the concepts of branch-and-bound, but they differ in their approach to each of the required steps. The SMIN-␣ BB algorithm is based on the con®ex underestimation of the continuous functions, while the GMIN-␣ BB algorithm is centered around the con®ex relaxation of the entire problem. Both algorithms rely on optimization or inter®al-based ®ariable-bound updates to enhance efficiency. A series of medium-size engineering applications demonstrates the performance of the algorithms. Finally, a comparison of the two algorithms on the same problems highlights the ®alue of algorithms that can handle binary or integer ®ariables without reformulation. IntroductionThe decision-making processes that take place during the design of new products or chemical plants can be made more rational and efficient thanks to the use of mathematical models within a global optimization framework. For instance, ap-Ž . proaches based on nonlinear programming NLP , such as Ž . those described in Horst and Tuy 1996 , have been used to determine optimum equipment sizes and operating condi-Ž . tions for a given process Floudas, 1995; Grossmann, 1996 . The economic benefits to be derived from identifying the global solution of the many nonconvex problems that arise in Ž chemical engineering has been amply illustrated Grossmann, . 1996 . The most significant contribution of mathematical approaches, however, comes from their ability to incorporate many alternative structures within a single problem. This is achieved through the introduction of integer variables, which leads to the formulation of a mixed-integer nonlinear prob-Ž .Ž lem MINLP Floudas, 1995;Floudas and Grossmann, 1995; . Grossmann, 1996 . Such an approach has already been used for a wide array of applications, including process synthesis.Correspondence concerning this article should be addressed to C. A. Floudas. Present address of: C. S. Adjiman, Centre for Process Systems Engineering, Imperial College of Science, Technology and Medicine, Prince Consort Road, London SW7 2BY, UK; I. P. Androulakis, Exxon Research and Development, Annandale, NJ.The solution of many MINLPs relevant to chemical engineering is made challenging not only by the presence of integer variables but also by the nonconvexities in the models. As a result, the potential contributions of mixed-integer nonlinear optimization to general design problems have not yet been fully realized. The deterministic ap...

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Systems biology has primarily focused on studying genomics, transcriptomics, and proteomics and their dynamic interactions. These, however, represent only the potential for a biological outcome since the ultimate phenotype at the level of the eventually produced metabolites is not taken into consideration. The emerging field of metabolomics provides complementary guidance toward an integrated approach to this problem: It allows global profiling of the metabolites of a cell, tissue, or host and presents information on the actual end points of a response. A wide range of data collection methods are currently used and allow the extraction of global or tissue-specific metabolic profiles. The great amount and complexity of data that are collected require multivariate analysis techniques, but the increasing amount of work in this field has made easy-to-use analysis programs readily available. Metabolomics has already shown great potential in drug toxicity studies, disease modeling, and diagnostics and may be integrated with genomic and proteomic data in the future to provide in-depth understanding of systems, pathways, and their functionally dynamic interactions. In this review we discuss the current state of the art of metabolomics, its applications, and future potential.

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