The Probabilistic Representative Values

In this paper we define a new family of solutions for the class of cooperative games with transferable utility, in which the set of players exhibits a structure of a priori unions.This family is deeply connected with the Shapley value for games with transferable utility but, moreover, we assume a solidarity strong connection among all the components of each union.As a consequence of this, they are disposed to delegate one coalition of members of the union to negotiate with the other unions, and, therefore, each union will have a representative coalition.Furthermore, three interesting solutions that belong to this family of values are studied, as well as the non cooperative selection of the best representative coalition for each union.TU-games with unions;Shapley value;representative coalition

The Two-stage Constrained Equal Awards and Losses Rules for Multi-Issue Allocation Situation

This paper considers two-stage solutions for multi-issue allocation situations.Characterisations are provided for the two-stage constrained equal awards and constrained equal losses rules, based on the properties of composition and path independence.multi-issue allocation situations;constrained equal awards;constrained equal losses;two-stage solutions

The Probabilistic Representative Values

In this paper we define a new family of solutions for the class of cooperative games with transferable utility, in which the set of players exhibits a structure of a priori unions.This family is deeply connected with the Shapley value for games with transferable utility but, moreover, we assume a solidarity strong connection among all the components of each union.As a consequence of this, they are disposed to delegate one coalition of members of the union to negotiate with the other unions, and, therefore, each union will have a representative coalition.Furthermore, three interesting solutions that belong to this family of values are studied, as well as the non cooperative selection of the best representative coalition for each union.

The Two-stage Constrained Equal Awards and Losses Rules for Multi-Issue Allocation Situation

This paper considers two-stage solutions for multi-issue allocation situations.Characterisations are provided for the two-stage constrained equal awards and constrained equal losses rules, based on the properties of composition and path independence.

The Constrained Equal Award Rule for Bankruptcy Problems with a Priori Unions

In this paper, we provide four extensions of the constrained equal award rule for bankruptcy situations to the class of bankruptcy situations with a priori unions. We present some characterisations and relations with corresponding games. The four new extensions are illustrated by a specific application.bankruptcy;a priori unions;constrained equal award

The Constrained Equal Award Rule for Bankruptcy Problems with a Priori Unions

In this paper, we provide four extensions of the constrained equal award rule for bankruptcy situations to the class of bankruptcy situations with a priori unions. We present some characterisations and relations with corresponding games. The four new extensions are illustrated by a specific application.

Neurodegeneration of the retina in mouse models of Alzheimer’s disease: what can we learn from the retina?

Alzheimer’s disease (AD) is an age-related progressive neurodegenerative disease commonly found among elderly. In addition to cognitive and behavioral deficits, vision abnormalities are prevalent in AD patients. Recent studies investigating retinal changes in AD double-transgenic mice have shown altered processing of amyloid precursor protein and accumulation of β-amyloid peptides in neurons of retinal ganglion cell layer (RGCL) and inner nuclear layer (INL). Apoptotic cells were also detected in the RGCL. Thus, the pathophysiological changes of retinas in AD patients are possibly resembled by AD transgenic models. The retina is a simple model of the brain in the sense that some pathological changes and therapeutic strategies from the retina may be observed or applicable to the brain. Furthermore, it is also possible to advance our understanding of pathological mechanisms in other retinal degenerative diseases. Therefore, studying AD-related retinal degeneration is a promising way for the investigation on (1) AD pathologies and therapies that would eventually benefit the brain and (2) cellular mechanisms in other retinal degenerations such as glaucoma and age-related macular degeneration. This review will highlight the efforts on retinal degenerative research using AD transgenic mouse models

Diminishing benefits of urban living for children and adolescents’ growth and development

Optimal growth and development in childhood and adolescence is crucial for lifelong health and well-being1–6. Here we used data from 2,325 population-based studies, with measurements of height and weight from 71 million participants, to report the height and body-mass index (BMI) of children and adolescents aged 5–19 years on the basis of rural and urban place of residence in 200 countries and territories from 1990 to 2020. In 1990, children and adolescents residing in cities were taller than their rural counterparts in all but a few high-income countries. By 2020, the urban height advantage became smaller in most countries, and in many high-income western countries it reversed into a small urban-based disadvantage. The exception was for boys in most countries in sub-Saharan Africa and in some countries in Oceania, south Asia and the region of central Asia, Middle East and north Africa. In these countries, successive cohorts of boys from rural places either did not gain height or possibly became shorter, and hence fell further behind their urban peers. The difference between the age-standardized mean BMI of children in urban and rural areas was <1.1 kg m–2 in the vast majority of countries. Within this small range, BMI increased slightly more in cities than in rural areas, except in south Asia, sub-Saharan Africa and some countries in central and eastern Europe. Our results show that in much of the world, the growth and developmental advantages of living in cities have diminished in the twenty-first century, whereas in much of sub-Saharan Africa they have amplified

Identification of genetic variants associated with Huntington's disease progression: a genome-wide association study

Background Huntington's disease is caused by a CAG repeat expansion in the huntingtin gene, HTT. Age at onset has been used as a quantitative phenotype in genetic analysis looking for Huntington's disease modifiers, but is hard to define and not always available. Therefore, we aimed to generate a novel measure of disease progression and to identify genetic markers associated with this progression measure. Methods We generated a progression score on the basis of principal component analysis of prospectively acquired longitudinal changes in motor, cognitive, and imaging measures in the 218 indivduals in the TRACK-HD cohort of Huntington's disease gene mutation carriers (data collected 2008–11). We generated a parallel progression score using data from 1773 previously genotyped participants from the European Huntington's Disease Network REGISTRY study of Huntington's disease mutation carriers (data collected 2003–13). We did a genome-wide association analyses in terms of progression for 216 TRACK-HD participants and 1773 REGISTRY participants, then a meta-analysis of these results was undertaken. Findings Longitudinal motor, cognitive, and imaging scores were correlated with each other in TRACK-HD participants, justifying use of a single, cross-domain measure of disease progression in both studies. The TRACK-HD and REGISTRY progression measures were correlated with each other (r=0·674), and with age at onset (TRACK-HD, r=0·315; REGISTRY, r=0·234). The meta-analysis of progression in TRACK-HD and REGISTRY gave a genome-wide significant signal (p=1·12 × 10−10) on chromosome 5 spanning three genes: MSH3, DHFR, and MTRNR2L2. The genes in this locus were associated with progression in TRACK-HD (MSH3 p=2·94 × 10−8 DHFR p=8·37 × 10−7 MTRNR2L2 p=2·15 × 10−9) and to a lesser extent in REGISTRY (MSH3 p=9·36 × 10−4 DHFR p=8·45 × 10−4 MTRNR2L2 p=1·20 × 10−3). The lead single nucleotide polymorphism (SNP) in TRACK-HD (rs557874766) was genome-wide significant in the meta-analysis (p=1·58 × 10−8), and encodes an aminoacid change (Pro67Ala) in MSH3. In TRACK-HD, each copy of the minor allele at this SNP was associated with a 0·4 units per year (95% CI 0·16–0·66) reduction in the rate of change of the Unified Huntington's Disease Rating Scale (UHDRS) Total Motor Score, and a reduction of 0·12 units per year (95% CI 0·06–0·18) in the rate of change of UHDRS Total Functional Capacity score. These associations remained significant after adjusting for age of onset. Interpretation The multidomain progression measure in TRACK-HD was associated with a functional variant that was genome-wide significant in our meta-analysis. The association in only 216 participants implies that the progression measure is a sensitive reflection of disease burden, that the effect size at this locus is large, or both. Knockout of Msh3 reduces somatic expansion in Huntington's disease mouse models, suggesting this mechanism as an area for future therapeutic investigation