Necessary and sufficient condition on global optimality without convexity and second order differentiability

The main goal of this paper is to give a necessary and sufficient condition of global optimality for unconstrained optimization problems, when the objective function is not necessarily convex. We use Gâteaux differentiability of the objective function and its bidual (the latter is known from convex analysis)

Robust physiological mappings: from non-invasive to invasive

The goal of this paper is to highlight the challenges on the three methods of data analysis, namely: robust, component, and dynamical analysis with respect to the epilepsey. A forward and inverse mapping model for the human brain is presented. Research directions for obtaining robust inverse mapping, and conducting dynamical analysis of the epileptic brain are discussed.Проаналізовано проблеми, пов’язані з трьома методами аналізу даних щодо епілепсії головного мозку: робастним, покомпонентним і динамічним. Запропоновано пряму і обернену моделі відображення головного мозку. Також обговорюються напрями досліджень для отримання робастних обернених відображень і проведення динамічного аналізу епілептичного мозк

Chromatin accessibility reveals insights into androgen receptor activation and transcriptional specificity

BACKGROUND: Epigenetic mechanisms such as chromatin accessibility impact transcription factor binding to DNA and transcriptional specificity. The androgen receptor (AR), a master regulator of the male phenotype and prostate cancer pathogenesis, acts primarily through ligand-activated transcription of target genes. Although several determinants of AR transcriptional specificity have been elucidated, our understanding of the interplay between chromatin accessibility and AR function remains incomplete. RESULTS: We used deep sequencing to assess chromatin structure via DNase I hypersensitivity and mRNA abundance, and paired these datasets with three independent AR ChIP-seq datasets. Our analysis revealed qualitative and quantitative differences in chromatin accessibility that corresponded to both AR binding and an enrichment of motifs for potential collaborating factors, one of which was identified as SP1. These quantitative differences were significantly associated with AR-regulated mRNA transcription across the genome. Base-pair resolution of the DNase I cleavage profile revealed three distinct footprinting patterns associated with the AR-DNA interaction, suggesting multiple modes of AR interaction with the genome. CONCLUSIONS: In contrast with other DNA-binding factors, AR binding to the genome does not only target regions that are accessible to DNase I cleavage prior to hormone induction. AR binding is invariably associated with an increase in chromatin accessibility and, consequently, changes in gene expression. Furthermore, we present the first in vivo evidence that a significant fraction of AR binds only to half of the full AR DNA motif. These findings indicate a dynamic quantitative relationship between chromatin structure and AR-DNA binding that impacts AR transcriptional specificity

Regularity of a kind of marginal functions in Hilbert spaces

We study well-posedness of some mathematical programming problem depending on a parameter that generalizes in a certain sense the metric projection onto a closed nonconvex set. We are interested in regularity of the set of minimizers as well as of the value function, which can be seen, on one hand, as the viscosity solution to a Hamilton-Jacobi equation, while, on the other, as the minimal time in some related optimal time control problem. The regularity includes both the Fréchet differentiability of the value function and the Hölder continuity of its (Fréchet) gradient

A MODEST review

We present an account of the state of the art in the fields explored by the research community invested in 'Modeling and Observing DEnse STellar systems'. For this purpose, we take as a basis the activities of the MODEST-17 conference, which was held at Charles University, Prague, in September 2017. Reviewed topics include recent advances in fundamental stellar dynamics, numerical methods for the solution of the gravitational N-body problem, formation and evolution of young and old star clusters and galactic nuclei, their elusive stellar populations, planetary systems, and exotic compact objects, with timely attention to black holes of different classes of mass and their role as sources of gravitational waves. Such a breadth of topics reflects the growing role played by collisional stellar dynamics in numerous areas of modern astrophysics. Indeed, in the next decade, many revolutionary instruments will enable the derivation of positions and velocities of individual stars in the Milky Way and its satellites and will detect signals from a range of astrophysical sources in different portions of the electromagnetic and gravitational spectrum, with an unprecedented sensitivity. On the one hand, this wealth of data will allow us to address a number of long-standing open questions in star cluster studies; on the other hand, many unexpected properties of these systems will come to light, stimulating further progress of our understanding of their formation and evolution.Comment: 42 pages; accepted for publication in 'Computational Astrophysics and Cosmology'. We are much grateful to the organisers of the MODEST-17 conference (Charles University, Prague, September 2017). We acknowledge the input provided by all MODEST-17 participants, and, more generally, by the members of the MODEST communit

Event Horizon Telescope observations of the jet launching and collimation in Centaurus A

InstrumentationLarge scale structure and cosmolog

Optimization techniques for data representions with biomedical applications.

Handbook of Optimization in Medicine is devoted to examining the dramatic increase in the application of effective optimization techniques to the delivery of health care. The articles, written by experts from the areas of optimization (operations research), computer science, and medicine, focus on models and algorithms that have led to more efficient and sophisticated treatments of patients