Solving ill-posed bilevel programs

This paper deals with ill-posed bilevel programs, i.e., problems admitting multiple lower-level solutions for some upper-level parameters. Many publications have been devoted to the standard optimistic case of this problem, where the difficulty is essentially moved from the objective function to the feasible set. This new problem is simpler but there is no guaranty to obtain local optimal solutions for the original optimistic problem by this process. Considering the intrinsic non-convexity of bilevel programs, computing local optimal solutions is the best one can hope to get in most cases. To achieve this goal, we start by establishing an equivalence between the original optimistic problem an a certain set-valued optimization problem. Next, we develop optimality conditions for the latter problem and show that they generalize all the results currently known in the literature on optimistic bilevel optimization. Our approach is then extended to multiobjective bilevel optimization, and completely new results are derived for problems with vector-valued upper- and lower-level objective functions. Numerical implementations of the results of this paper are provided on some examples, in order to demonstrate how the original optimistic problem can be solved in practice, by means of a special set-valued optimization problem

A comparison of flexural strengths of polymer (SBR and PVA) modified, roller compacted concrete

This brief article aims to reveal the flexural performance, including the equivalent flexural strength of PVA (Polyvinyl Alcohol) modified concrete by comparing it primarily with that of SBR (Styrene Butadiene Rubber) concrete. This data article is directly related to Karadelis and Lin [6]

A new method to assess spatial variations of outdoor thermal comfort: Onsite monitoring results and implications for precinct planning

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Input-to-state stability of infinite-dimensional control systems

We develop tools for investigation of input-to-state stability (ISS) of infinite-dimensional control systems. We show that for certain classes of admissible inputs the existence of an ISS-Lyapunov function implies the input-to-state stability of a system. Then for the case of systems described by abstract equations in Banach spaces we develop two methods of construction of local and global ISS-Lyapunov functions. We prove a linearization principle that allows a construction of a local ISS-Lyapunov function for a system which linear approximation is ISS. In order to study interconnections of nonlinear infinite-dimensional systems, we generalize the small-gain theorem to the case of infinite-dimensional systems and provide a way to construct an ISS-Lyapunov function for an entire interconnection, if ISS-Lyapunov functions for subsystems are known and the small-gain condition is satisfied. We illustrate the theory on examples of linear and semilinear reaction-diffusion equations.Comment: 33 page

Identification and validation of oncologic miRNA biomarkers for Luminal A-like breast cancer

Introduction: Breast cancer is a common disease with distinct tumor subtypes phenotypically characterized by ER and HER2/neu receptor status. MiRNAs play regulatory roles in tumor initiation and progression, and altered miRNA expression has been demonstrated in a variety of cancer states presenting the potential for exploitation as cancer biomarkers. Blood provides an excellent medium for biomarker discovery. This study investigated systemic miRNAs differentially expressed in Luminal A-like (ER+PR+HER2/neu-) breast cancer and their effectiveness as oncologic biomarkers in the clinical setting. Methods: Blood samples were prospectively collected from patients with Luminal A-like breast cancer (n=54) and controls (n=56). RNA was extracted, reverse transcribed and subjected to microarray analysis (n=10 Luminal A-like; n=10 Control). Differentially expressed miRNAs were identified by artificial neural network (ANN) data-mining algorithms. Expression of specific miRNAs was validated by RQ-PCR (n=44 Luminal A; n=46 Control) and potential relationships between circulating miRNA levels and clinicopathological features of breast cancer were investigated. Results: Microarray analysis identified 76 differentially expressed miRNAs. ANN revealed 10 miRNAs for further analysis ( miR-19b, miR-29a, miR-93, miR-181a, miR-182, miR-223, miR-301a, miR-423-5p, miR-486-5 and miR-652 ). The biomarker potential of 4 miRNAs ( miR-29a, miR-181a , miR-223 and miR-652 ) was confirmed by RQ-PCR, with significantly reduced expression in blood of women with Luminal A-like breast tumors compared to healthy controls (p=0.001, 0.004, 0.009 and 0.004 respectively). Binary logistic regression confirmed that combination of 3 of these miRNAs ( miR-29a, miR-181a and miR-652 ) could reliably differentiate between cancers and controls with an AUC of 0.80. Conclusion: This study provides insight into the underlying molecular portrait of Luminal A-like breast cancer subtype. From an initial 76 miRNAs, 4 were validated with altered expression in the blood of women with Luminal A-like breast cancer. The expression profiles of these 3 miRNAs, in combination with mammography, has potential to facilitate accurate subtype- specific breast tumor detection

Effective computational methods for hybrid stochastic gene networks

At the scale of the individual cell, protein production is a stochastic process with multiple time scales, combining quick and slow random steps with discontinuous and smooth variation. Hybrid stochastic processes, in particular piecewise-deterministic Markov processes (PDMP), are well adapted for describing such situations. PDMPs approximate the jump Markov processes traditionally used as models for stochastic chemical reaction networks. Although hybrid modelling is now well established in biology, these models remain computationally challenging. We propose several improved methods for computing time dependent multivariate probability distributions (MPD) of PDMP models of gene networks. In these models, the promoter dynamics is described by a finite state, continuous time Markov process, whereas the mRNA and protein levels follow ordinary differential equations (ODEs). The Monte-Carlo method combines direct simulation of the PDMP with analytic solutions of the ODEs. The push-forward method numerically computes the probability measure advected by the deterministic ODE flow, through the use of analytic expressions of the corresponding semigroup. Compared to earlier versions of this method, the probability of the promoter states sequence is computed beyond the naive mean field theory and adapted for non-linear regulation functions

Can disordered mobile phone use be considered a behavioral addiction? An update on current evidence and a comprehensive model for future research

Despite the many positive outcomes, excessive mobile phone use is now often associated with potentially harmful and/or disturbing behaviors (e.g., symptoms of deregulated use, negative impact on various aspects of daily life such as relationship problems, and work intrusion). Problematic mobile phone use (PMPU) has generally been considered as a behavioral addiction that shares many features with more established drug addictions. In light of the most recent data, the current paper reviews the validity of the behavioral addiction model when applied to PMPU. On the whole, it is argued that the evidence supporting PMPU as an addictive behavior is scarce. In particular, it lacks studies that definitively show behavioral and neurobiological similarities between mobile phone addiction and other types of legitimate addictive behaviors. Given this context, an integrative pathway model is proposed that aims to provide a theoretical framework to guide future research in the field of PMPU. This model highlights that PMPU is a heterogeneous and multi-faceted condition

Set optimization - a rather short introduction

Recent developments in set optimization are surveyed and extended including various set relations as well as fundamental constructions of a convex analysis for set- and vector-valued functions, and duality for set optimization problems. Extensive sections with bibliographical comments summarize the state of the art. Applications to vector optimization and financial risk measures are discussed along with algorithmic approaches to set optimization problems

Analysis of symmetries in models of multi-strain infections

In mathematical studies of the dynamics of multi-strain diseases caused by antigenically diverse pathogens, there is a substantial interest in analytical insights. Using the example of a generic model of multi-strain diseases with cross-immunity between strains, we show that a significant understanding of the stability of steady states and possible dynamical behaviours can be achieved when the symmetry of interactions between strains is taken into account. Techniques of equivariant bifurcation theory allow one to identify the type of possible symmetry-breaking Hopf bifurcation, as well as to classify different periodic solutions in terms of their spatial and temporal symmetries. The approach is also illustrated on other models of multi-strain diseases, where the same methodology provides a systematic understanding of bifurcation scenarios and periodic behaviours. The results of the analysis are quite generic, and have wider implications for understanding the dynamics of a large class of models of multi-strain diseases

Hot Jupiters from Secular Planet--Planet Interactions

About 25 per cent of `hot Jupiters' (extrasolar Jovian-mass planets with close-in orbits) are actually orbiting counter to the spin direction of the star. Perturbations from a distant binary star companion can produce high inclinations, but cannot explain orbits that are retrograde with respect to the total angular momentum of the system. Such orbits in a stellar context can be produced through secular (that is, long term) perturbations in hierarchical triple-star systems. Here we report a similar analysis of planetary bodies, including both octupole-order effects and tidal friction, and find that we can produce hot Jupiters in orbits that are retrograde with respect to the total angular momentum. With distant stellar mass perturbers, such an outcome is not possible. With planetary perturbers, the inner orbit's angular momentum component parallel to the total angular momentum need not be constant. In fact, as we show here, it can even change sign, leading to a retrograde orbit. A brief excursion to very high eccentricity during the chaotic evolution of the inner orbit allows planet-star tidal interactions to rapidly circularize that orbit, decoupling the planets and forming a retrograde hot Jupiter.Comment: accepted for publication by Nature, 3 figures (version after proof - some typos corrected