Large Deviations for Brownian Intersection Measures

We consider $p$ independent Brownian motions in $\R^d$. We assume that $p\geq 2$ and $p(d-2)<d$. Let $\ell_t$ denote the intersection measure of the $p$ paths by time $t$, i.e., the random measure on $\R^d$ that assigns to any measurable set $A\subset \R^d$ the amount of intersection local time of the motions spent in $A$ by time $t$. Earlier results of Chen \cite{Ch09} derived the logarithmic asymptotics of the upper tails of the total mass $\ell_t(\R^d)$ as $t\to\infty$. In this paper, we derive a large-deviation principle for the normalised intersection measure $t^{-p}\ell_t$ on the set of positive measures on some open bounded set $B\subset\R^d$ as $t\to\infty$ before exiting $B$. The rate function is explicit and gives some rigorous meaning, in this asymptotic regime, to the understanding that the intersection measure is the pointwise product of the densities of the normalised occupation times measures of the $p$ motions. Our proof makes the classical Donsker-Varadhan principle for the latter applicable to the intersection measure. A second version of our principle is proved for the motions observed until the individual exit times from $B$, conditional on a large total mass in some compact set $U\subset B$. This extends earlier studies on the intersection measure by K\"onig and M\"orters \cite{KM01,KM05}.Comment: To appear in "Communications on Pure and Applied Mathematics

Metastability of Asymptotically Well-Behaved Potential Games

One of the main criticisms to game theory concerns the assumption of full rationality. Logit dynamics is a decentralized algorithm in which a level of irrationality (a.k.a. "noise") is introduced in players' behavior. In this context, the solution concept of interest becomes the logit equilibrium, as opposed to Nash equilibria. Logit equilibria are distributions over strategy profiles that possess several nice properties, including existence and uniqueness. However, there are games in which their computation may take time exponential in the number of players. We therefore look at an approximate version of logit equilibria, called metastable distributions, introduced by Auletta et al. [SODA 2012]. These are distributions that remain stable (i.e., players do not go too far from it) for a super-polynomial number of steps (rather than forever, as for logit equilibria). The hope is that these distributions exist and can be reached quickly by logit dynamics. We identify a class of potential games, called asymptotically well-behaved, for which the behavior of the logit dynamics is not chaotic as the number of players increases so to guarantee meaningful asymptotic results. We prove that any such game admits distributions which are metastable no matter the level of noise present in the system, and the starting profile of the dynamics. These distributions can be quickly reached if the rationality level is not too big when compared to the inverse of the maximum difference in potential. Our proofs build on results which may be of independent interest, including some spectral characterizations of the transition matrix defined by logit dynamics for generic games and the relationship of several convergence measures for Markov chains

The Wnt5a Receptor, Receptor Tyrosine Kinase-Like Orphan Receptor 2, Is a Predictive Cell Surface Marker of Human Mesenchymal Stem Cells with an Enhanced Capacity for Chondrogenic Differentiation

Multipotent mesenchymal stem cells (MSCs) have enormous potential in tissue engineering and regenerative medicine. However until now their development for clinical use has been severely limited as they are a mixed population of cells with varying capacities for lineage differentiation and tissue formation. Here we identify ROR2 as a cell surface marker expressed by those MSCs with an enhanced capacity for cartilage formation. We generated clonal human MSC populations with varying capacities for chondrogenesis. ROR2 was identified through screening for upregulated genes in the most chondrogenic clones. When isolated from un-cloned populations, ROR2+ve MSCs were significantly more chondrogenic than either ROR2-ve or unfractionated MSCs. In a sheep cartilage-repair model they produced significantly more defect filling with no loss of cartilage quality compared with controls. ROR2+ve MSCs/perivascular cells were present in developing human cartilage, adult bone marrow and adipose tissue. Their frequency in bone marrow was significantly lower in patients with osteoarthritis than in controls. However after isolation of these cells and their initial expansion in vitro, there was greater ROR2 expression in the population derived from osteoarthritis patients compared with controls. Furthermore, osteoarthritis-derived MSCs were better able to form cartilage than MSCs from control patients in a tissue engineering assay. We conclude that MSCs expressing high levels of ROR2 provide a defined population capable of predictably enhanced cartilage production. This article is protected by copyright. All rights reserved

Variational description of Gibbs-non-Gibbs dynamical transitions for the Curie-Weiss model

We perform a detailed study of Gibbs-non-Gibbs transitions for the Curie-Weiss model subject to independent spin-flip dynamics ("infinite-temperature" dynamics). We show that, in this setup, the program outlined in van Enter, Fern\'andez, den Hollander and Redig can be fully completed, namely that Gibbs-non-Gibbs transitions are equivalent to bifurcations in the set of global minima of the large-deviation rate function for the trajectories of the magnetization conditioned on their endpoint. As a consequence, we show that the time-evolved model is non-Gibbs if and only if this set is not a singleton for some value of the final magnetization. A detailed description of the possible scenarios of bifurcation is given, leading to a full characterization of passages from Gibbs to non-Gibbs -and vice versa- with sharp transition times (under the dynamics Gibbsianness can be lost and can be recovered). Our analysis expands the work of Ermolaev and Kulske who considered zero magnetic field and finite-temperature spin-flip dynamics. We consider both zero and non-zero magnetic field but restricted to infinite-temperature spin-flip dynamics. Our results reveal an interesting dependence on the interaction parameters, including the presence of forbidden regions for the optimal trajectories and the possible occurrence of overshoots and undershoots in the optimal trajectories. The numerical plots provided are obtained with the help of MATHEMATICA.Comment: Key words and phrases: Curie-Weiss model, spin-flip dynamics, Gibbs vs. non-Gibbs, dynamical transition, large deviations, action integral, bifurcation of rate functio

Stem Cells and Cartilage Development: Complexities of a Simple Tissue

Cartilage is considered to be a simple tissue that should be easy to engineer because it is avascular and contains just one cell type, the chondrocyte. Despite this apparent simplicity, regenerating cartilage in a form that can function effectively after implantation in the joint has proven difficult. This may be because we have not fully appreciated the importance of different structural regions of articular cartilage or of understanding the origins of chondrocytes and how this cell population is maintained in the normal tissue. This review considers what is known about different regions of cartilage and the types of stem cells in articulating joints and emphasizes the potential importance of regeneration of the lamina splendens at the joint surface and calcified cartilage at the junction with bone for long-term survival of regenerated tissue in vivo. Stem Cells 2010;28:1992–199

Big issues for small feet : developmental, biomechanical and clinical narratives on children's footwear

The effects of footwear on the development of children's feet has been debated for many years and recent work from the developmental and biomechanical literature has challenged long-held views about footwear and the impact on foot development. This narrative review draws upon existing studies from developmental, biomechanical and clinical literature to explore the effects of footwear on the development of the foot. The emerging findings from this support the need for progress in [children's] footwear science and advance understanding of the interaction between the foot and shoe. Ensuring clear and credible messages inform practice requires a progressive evidence base but this remains big issue in children's footwear research

A detailed clinical and molecular survey of subjects with nonsyndromic USH2A retinopathy reveals an allelic hierarchy of disease-causing variants.

Defects in USH2A cause both isolated retinal disease and Usher syndrome (ie, retinal disease and deafness). To gain insights into isolated/nonsyndromic USH2A retinopathy, we screened USH2A in 186 probands with recessive retinal disease and no hearing complaint in childhood (discovery cohort) and in 84 probands with recessive retinal disease (replication cohort). Detailed phenotyping, including retinal imaging and audiological assessment, was performed in individuals with two likely disease-causing USH2A variants. Further genetic testing, including screening for a deep-intronic disease-causing variant and large deletions/duplications, was performed in those with one likely disease-causing change. Overall, 23 of 186 probands (discovery cohort) were found to harbour two likely disease-causing variants in USH2A. Some of these variants were predominantly associated with nonsyndromic retinal degeneration ('retinal disease-specific'); these included the common c.2276 G>T, p.(Cys759Phe) mutation and five additional variants: c.2802 T>G, p.(Cys934Trp); c.10073 G>A, p.(Cys3358Tyr); c.11156 G>A, p.(Arg3719His); c.12295-3 T>A; and c.12575 G>A, p.(Arg4192His). An allelic hierarchy was observed in the discovery cohort and confirmed in the replication cohort. In nonsyndromic USH2A disease, retinopathy was consistent with retinitis pigmentosa and the audiological phenotype was variable. USH2A retinopathy is a common cause of nonsyndromic recessive retinal degeneration and has a different mutational spectrum to that observed in Usher syndrome. The following model is proposed: the presence of at least one 'retinal disease-specific' USH2A allele in a patient with USH2A-related disease results in the preservation of normal hearing. Careful genotype-phenotype studies such as this will become increasingly important, especially now that high-throughput sequencing is widely used in the clinical setting.European Journal of Human Genetics advance online publication, 4 February 2015; doi:10.1038/ejhg.2014.283

Leser-Trélat syndrome in patients affected by six multiple metachronous primitive cancers

Leser-Trélat syndrome is characterized by the eruptive appearance of multiple seborrheic keratoses in association with underlying malignant disease. Usually, the sign of Leser-Trélat is associated with adenocarcinoma, most frequently of the colon, breast, or stomach, but also of the lung, kidney, liver, and pancreas. Herein, we present a case that we believe is the first report of the sign of Leser-Trélat in association with occult gastric adenocarcinoma and the anamnestic oncologic history of five other multiple primitive cancers. Epidermal growth factor receptor (EGFR) immunohistochemical expression analysis of multiple seborrheic keratoses revealed an intense membranous staining in the basal keratinocytes and in all the upper epidermal layers. Patients with the sign of Leser-Trélat should undergo a diagnostic screening programme for malignant disease along with patients with known Leser-Trélat syndrome who present with a recent acute and florid eruption of their seborrheic keratoses. We propose the importance of combining the molecular features of multiple seborrheic keratoses with EGFR immunohistochemistry analyses to determine the likelihood of Leser-Trélat syndrome and the consequent high risk of underlying multiple visceral malignancies

Heart rate variability and target organ damage in hypertensive patients

Background: We evaluated the association between linear standard Heart Rate Variability (HRV) measures and vascular, renal and cardiac target organ damage (TOD). Methods: A retrospective analysis was performed including 200 patients registered in the Regione Campania network (aged 62.4 ± 12, male 64%). HRV analysis was performed by 24-h holter ECG. Renal damage was assessed by estimated glomerular filtration rate (eGFR), vascular damage by carotid intima-media thickness (IMT), and cardiac damage by left ventricular mass index. Results: Significantly lower values of the ratio of low to high frequency power (LF/HF) were found in the patients with moderate or severe eGFR (p-value < 0.001). Similarly, depressed values of indexes of the overall autonomic modulation on heart were found in patients with plaque compared to those with a normal IMT (p-value <0.05). These associations remained significant after adjustment for other factors known to contribute to the development of target organ damage, such as age. Moreover, depressed LF/HF was found also in patients with left ventricular hypertrophy but this association was not significant after adjustment for other factors. Conclusions: Depressed HRV appeared to be associated with vascular and renal TOD, suggesting the involvement of autonomic imbalance in the TOD. However, as the mechanisms by which abnormal autonomic balance may lead to TOD, and, particularly, to renal organ damage are not clearly known, further prospective studies with longitudinal design are needed to determine the association between HRV and the development of TOD

Phylogenetic relationships of cone snails endemic to Cabo Verde based on mitochondrial genomes

Background: Due to their great species and ecological diversity as well as their capacity to produce hundreds of different toxins, cone snails are of interest to evolutionary biologists, pharmacologists and amateur naturalists alike. Taxonomic identification of cone snails still relies mostly on the shape, color, and banding patterns of the shell. However, these phenotypic traits are prone to homoplasy. Therefore, the consistent use of genetic data for species delimitation and phylogenetic inference in this apparently hyperdiverse group is largely wanting. Here, we reconstruct the phylogeny of the cones endemic to Cabo Verde archipelago, a well-known radiation of the group, using mitochondrial (mt) genomes. Results: The reconstructed phylogeny grouped the analyzed species into two main clades, one including Kalloconus from West Africa sister to Trovaoconus from Cabo Verde and the other with a paraphyletic Lautoconus due to the sister group relationship of Africonus from Cabo Verde and Lautoconus ventricosus from Mediterranean Sea and neighboring Atlantic Ocean to the exclusion of Lautoconus endemic to Senegal (plus Lautoconus guanche from Mauritania, Morocco, and Canary Islands). Within Trovaoconus, up to three main lineages could be distinguished. The clade of Africonus included four main lineages (named I to IV), each further subdivided into two monophyletic groups. The reconstructed phylogeny allowed inferring the evolution of the radula in the studied lineages as well as biogeographic patterns. The number of cone species endemic to Cabo Verde was revised under the light of sequence divergence data and the inferred phylogenetic relationships. Conclusions: The sequence divergence between continental members of the genus Kalloconus and island endemics ascribed to the genus Trovaoconus is low, prompting for synonymization of the latter. The genus Lautoconus is paraphyletic. Lautoconus ventricosus is the closest living sister group of genus Africonus. Diversification of Africonus was in allopatry due to the direct development nature of their larvae and mainly triggered by eustatic sea level changes during the Miocene-Pliocene. Our study confirms the diversity of cone endemic to Cabo Verde but significantly reduces the number of valid species. Applying a sequence divergence threshold, the number of valid species within the sampled Africonus is reduced to half.Spanish Ministry of Science and Innovation [CGL2013-45211-C2-2-P, CGL2016-75255-C2-1-P, BES-2011-051469, BES-2014-069575, Doctorado Nacional-567]info:eu-repo/semantics/publishedVersio