Set-optimization meets variational inequalities

We study necessary and sufficient conditions to attain solutions of set-optimization problems in therms of variational inequalities of Stampacchia and Minty type. The notion of a solution we deal with has been introduced Heyde and Loehne, for convex set-valued objective functions. To define the set-valued variational inequality, we introduce a set-valued directional derivative and we relate it to the Dini derivatives of a family of linearly scalarized problems. The optimality conditions are given by Stampacchia and Minty type Variational inequalities, defined both by the set valued directional derivative and by the Dini derivatives of the scalarizations. The main results allow to obtain known variational characterizations for vector valued optimization problems

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

Association Testing Of Copy Number Variants in Schizophrenia and Autism Spectrum Disorders

Background: Autism spectrum disorders and schizophrenia have been associated with an overlapping set of copynumber variant loci, but the nature and degree of overlap in copy number variants (deletions compared toduplications) between these two disorders remains unclear.Methods: We systematically evaluated three lines of evidence: (1) the statistical bases for associations of autismspectrum disorders and schizophrenia with a set of the primary CNVs thus far investigated, from previous studies;(2) data from case series studies on the occurrence of these CNVs in autism spectrum disorders, especially amongchildren, and (3) data on the extent to which the CNVs were associated with intellectual disability anddevelopmental, speech, or language delays. We also conducted new analyses of existing data on these CNVs inautism by pooling data from seven case control studies.Results: Four of the CNVs considered, dup 1q21.1, dup 15q11-q13, del 16p11.2, and dup 22q11.21, showed clearstatistical evidence as autism risk factors, whereas eight CNVs, del 1q21.1, del 3q29, del 15q11.2, del 15q13.3, dup16p11.2, dup 16p13.1, del 17p12, and del 22q11.21, were strongly statistically supported as risk factors forschizophrenia. Three of the CNVs, dup 1q21.1, dup 16p11.2, and dup 16p13.1, exhibited statistical support as riskfactors for both autism and schizophrenia, although for each of these CNVs statistical significance was nominal fortests involving one of the two disorders. For the CNVs that were statistically associated with schizophrenia but werenot statistically associated with autism, a notable number of children with the CNVs have been diagnosed withautism or ASD; children with these CNVs also demonstrate a high incidence of intellectual disability anddevelopmental, speech, or language delays.Conclusions: These findings suggest that although CNV loci notably overlap between autism and schizophrenia,the degree of strongly statistically supported overlap in specific CNVs at these loci remains limited. These analysesalso suggest that relatively severe premorbidity to CNV-associated schizophrenia in children may sometimes bediagnosed as autism spectrum disorder

Understanding tumor heterogeneity as functional compartments - superorganisms revisited

Compelling evidence broadens our understanding of tumors as highly heterogeneous populations derived from one common progenitor. In this review we portray various stages of tumorigenesis, tumor progression, self-seeding and metastasis in analogy to the superorganisms of insect societies to exemplify the highly complex architecture of a neoplasm as a system of functional "castes.

Evolution of Mutational Robustness in the Yeast Genome: A Link to Essential Genes and Meiotic Recombination Hotspots

Deleterious mutations inevitably emerge in any evolutionary process and are speculated to decisively influence the structure of the genome. Meiosis, which is thought to play a major role in handling mutations on the population level, recombines chromosomes via non-randomly distributed hot spots for meiotic recombination. In many genomes, various types of genetic elements are distributed in patterns that are currently not well understood. In particular, important (essential) genes are arranged in clusters, which often cannot be explained by a functional relationship of the involved genes. Here we show by computer simulation that essential gene (EG) clustering provides a fitness benefit in handling deleterious mutations in sexual populations with variable levels of inbreeding and outbreeding. We find that recessive lethal mutations enforce a selective pressure towards clustered genome architectures. Our simulations correctly predict (i) the evolution of non-random distributions of meiotic crossovers, (ii) the genome-wide anti-correlation of meiotic crossovers and EG clustering, (iii) the evolution of EG enrichment in pericentromeric regions and (iv) the associated absence of meiotic crossovers (cold centromeres). Our results furthermore predict optimal crossover rates for yeast chromosomes, which match the experimentally determined rates. Using a Saccharomyces cerevisiae conditional mutator strain, we show that haploid lethal phenotypes result predominantly from mutation of single loci and generally do not impair mating, which leads to an accumulation of mutational load following meiosis and mating. We hypothesize that purging of deleterious mutations in essential genes constitutes an important factor driving meiotic crossover. Therefore, the increased robustness of populations to deleterious mutations, which arises from clustered genome architectures, may provide a significant selective force shaping crossover distribution. Our analysis reveals a new aspect of the evolution of genome architectures that complements insights about molecular constraints, such as the interference of pericentromeric crossovers with chromosome segregation

Trasparenza precontrattuale e costo del mutuo

La disciplina comunitaria, recepita nell\u2019ordinamento italiano, prevede alcune informazioni minime che gli istituti eroganti devono fornire ai clienti prima della sottoscrizione di un contratto di mutuo. Partendo dalla lettura dei fogli informativi di un campione di istituti di credito italiano, la nota approfondisce gli effetti sul calcolo del monte interessi di due clausole comuni nei mutui con ammortamento \u201calla francese\u201d: il metodo di calcolo del tasso effettivo con cui determinare l\u2019importo della rata e la scelta di diverse frequenze della rata in costanza del tasso d\u2019interesse applicato. Scopo della nota \ue8 evidenziare come queste scelte possano modificare il monte interessi corrisposto, anche, nel secondo caso, in costanza di TAN e TAEG. Inoltre si osserva che la pratica di indicare il Tasso Annuo Nominale del finanziamento scomposto in un tasso privo di rischio di riferimento normalmente in capitalizzazione composta) e uno spread (che dovrebbe rappresentare il profilo di rischio del debitore) non permettere di cogliere completamente il costo degli interessi in percentuale annua sul capitale erogato

Pointwise and global well-posedness in set optimization: a direct approach

3sinoneThe aim of this paper is to characterize some of the pointwise and global wellposedness notions available in literature for a set optimization problem completely by compactness or upper continuity of an appropriate minimal solution set maps. The characterizations of compactness of set-valued maps, lead directly to many characterizations for well-posedness. Sufficient conditions are also given for global well-posedness.mixedCrespi, GIOVANNI PAOLO; Mansi, Dhingra; Lalitha, C. S.Crespi, Giovanni P.; Dhingra, Mansi; Lalitha, C. S