On analytic properties of Meixner-Sobolev orthogonal polynomials of higher order difference operators

In this contribution we consider sequences of monic polynomials orthogonal with respect to Sobolev-type inner product $$\left\langle f,g\right\rangle= \langle {\bf u}^{\tt M},fg\rangle+\lambda \mathscr T^j f (\alpha)\mathscr T^{j}g(\alpha),$$ where ${\bf u}^{\tt M}$ is the Meixner linear operator, $\lambda\in\mathbb{R}_{+}$, $j\in\mathbb{N}$, $\alpha \leq 0$, and $\mathscr T$ is the forward difference operator $\Delta$, or the backward difference operator $\nabla$. We derive an explicit representation for these polynomials. The ladder operators associated with these polynomials are obtained, and the linear difference equation of second order is also given. In addition, for these polynomials we derive a $(2j+3)$-term recurrence relation. Finally, we find the Mehler-Heine type formula for the $\alpha\le 0$ case

Estudio de la constante de hiperbolicidad en grafos

Esta tesis se dedica al estudio de los grafos hiperbólicos y está dividida en cuatro capítulos. El primer capítulo es una intoducción a la teoría de grafos y a los espacios hiperbólicos en sentido de Gromov. En los demás capítulos se incluyen los resultados de investigación que hemos conseguido. Aunque se dispone de ejemplos interesantes de espacios hiperbólicos, no existen criterios generales que permitan determinar la hiperbolicidad de un espacio. Por tanto, uno de los problemas más importantes en el estudio de los grafos hiperbólicos es obtener criterios que garanticen si un determinado grafo es hiperbólico o no. Por otra parte, existen numerosos parámetros en teoría de grafos que tienen gran importancia, tales como: el número de vértices, el núumero de aristas, el grado máximo, el grado mínimo, el diámetro, el cuello,... Por tanto, otro problema tan natural como importante es encontrar desigualdades que relacionen alguno de estos parámetros (o varios de ellos simultáneamente) con la constante de hiperbolicidad del grafo, encontrando y clasificando (como es importante en teoría de grafos) aquellos grafos para los que se tenga la igualdad. En esta tesis se demuestra que el estudio de la hiperbolicidad de los grafos se puede reducir al estudio de la hiperbolicidad de grafos más sencillos. En particular, hemos demostrado que el estudio de la hiperbolicidad de un grafo G con lazos y aristas múltiples se puede reducir al estudio de la hiperbolicidad del grafo obtenido al eliminar de G sus lazos y aristas múltiples; también se demuestra que el estudio de la hiperbolicidad de un grafo arbitrario es equivalente al estudio de la hiperbolicidad de un grafo 3-regular obtenido añadiendo algunas aristas y vértices. En resumen, probamos que el estudio de la hiperbolicidad para grafos generales (posiblemente con lazos y aristas múltiples) se reduce al estudio de la hiperbolicidad de grafos cúbicos sin lazos ni aristas múltiples. Adicionalmente, se estudia cómo la constante de hiperbolicidad de un grafo puede cambiar añadiendo o eliminando una cantidad finita o infinita de aristas

On the hyperbolicity constant in graphs

AbstractIf X is a geodesic metric space and x1,x2,x3∈X, a geodesic triangle T={x1,x2,x3} is the union of the three geodesics [x1x2], [x2x3] and [x3x1] in X. The space X is δ-hyperbolic (in the Gromov sense) if, for every geodesic triangle T in X, every side of T is contained in a δ-neighborhood of the union of the other two sides. We denote by δ(X) the sharpest hyperbolicity constant of X, i.e. δ(X)≔inf{δ≥0:X is δ-hyperbolic}. In this paper, we obtain several tight bounds for the hyperbolicity constant of a graph and precise values of this constant for some important families of graphs. In particular, we investigate the relationship between the hyperbolicity constant of a graph and its number of edges, diameter and cycles. As a consequence of our results, we show that if G is any graph with m edges with lengths {lk}k=1m, then δ(G)≤∑k=1mlk/4, and δ(G)=∑k=1mlk/4 if and only if G is isomorphic to Cm. Moreover, we prove the inequality δ(G)≤12diamG for every graph, and we use this inequality in order to compute the precise value δ(G) for some common graphs

DYRK1A and Activity-Dependent Neuroprotective Protein Comparative Diagnosis Interest in Cerebrospinal Fluid and Plasma in the Context of Alzheimer-Related Cognitive Impairment in Down Syndrome Patients

Down syndrome (DS) is a complex genetic condition due to an additional copy of human chromosome 21, which results in the deregulation of many genes. In addition to the intellectual disability associated with DS, adults with DS also have an ultrahigh risk of developing early onset Alzheimer's disease dementia. DYRK1A, a proline-directed serine/threonine kinase, whose gene is located on chromosome 21, has recently emerged as a promising plasma biomarker in patients with sporadic Alzheimer's disease (AD). The protein DYRK1A is truncated in symptomatic AD, the increased truncated form being associated with a decrease in the level of full-length form. Activity-dependent neuroprotective protein (ADNP), a key protein for the brain development, has been demonstrated to be a useful marker for symptomatic AD and disease progression. In this study, we evaluated DYRK1A and ADNP in CSF and plasma of adults with DS and explored the relationship between these proteins. We used mice models to evaluate the effect of DYRK1A overexpression on ADNP levels and then performed a dual-center cross-sectional human study in adults with DS in Barcelona (Spain) and Paris (France). Both cohorts included adults with DS at different stages of the continuum of AD: asymptomatic AD (aDS), prodromal AD (pDS), and AD dementia (dDS). Non-trisomic controls and patients with sporadic AD dementia were included for comparison. Full-form levels of DYRK1A were decreased in plasma and CSF in adults with DS and symptomatic AD (pDS and dDS) compared to aDS, and in patients with sporadic AD compared to controls. On the contrary, the truncated form of DYRK1A was found to increase both in CSF and plasma in adults with DS and symptomatic AD and in patients with sporadic AD with respect to aDS and controls. ADNP levels showed a more complex structure. ADNP levels increased in aDS groups vs. controls, in agreement with the increase in levels found in the brains of mice overexpressing DYRK1A. However, symptomatic individuals had lower levels than aDS individuals. Our results show that the comparison between full-length and truncated-form levels of DYRK1A coupled with ADNP levels could be used in trials targeting pathophysiological mechanisms of dementia in individuals with DS

P A THE RIEMANN BOUNDARY VALUE PROBLEM FOR β-ANALYTIC FUNCTIONS OVER D-SUMMABLE CLOSED CURVES

Abstract: The aim of this paper is to describe solvability conditions of the β-analytic Riemann boundary value problem in a Jordan domain of the complex plane whose boundary is assumed to be a d−summable closed curve

Hyperanalytic Riemann boundary value problem on d-summable closed curves

AbstractWe are interested in finding solvability conditions for the Riemann boundary value problems for hyperanalytic functions in a simply connected bounded open subset of the complex plane whose boundary is merely required to be a d-summable closed curve

Transcriptomic study in women with trisomy 21 identifies a possible role of the GTPases of the immunity-associated proteins (GIMAP) in the protection of breast cancer

Abstract Background: People with trisomy 21 (T21) are predisposed to developing hematological tumors, but have significantly lower-than-expected age-adjusted incidence rates of having a solid tumor. Material and methods: To identify novel genetic factors implicated in the lower breast cancer (BC) frequency observed in women with T21 than in the general population, we compared the transcriptome pattern of women with a homogeneous T21, aged more than 30 years, with or without BC, and tumoral BC tissue of control women with a normal karyotype from the study of Varley et al. (2014). Results: Differential analysis of gene expression between the 15 women in the T21 without BC group and BC patients in the other groups (two women with T21 and fifteen control women, respectively) revealed 154 differentially expressed genes, of which 63 were found to have similar expression profile (up- or downregulated). Of those 63 genes, four were in the same family, namely GIMAP4, GIMAP6, GIMAP7 and GIMAP8, and were strongly upregulated in the T21 without BC group compared to the other groups. A significant decrease in mRNA levels of these genes in BC tissues compared to non-tumor breast tissues was also noted. Conclusion: We found that the expression of some GIMAPs is significantly higher in women with T21 without BC than in patients with sporadic BC. Our findings support the hypothesis that GIMAPs may play a tumor-suppressive role against BC, and open the possibility that they may also have the same role for other solid tumors in T21 patients. The search for new prognostic factors and hopefully new therapeutic or preventive strategies against BC are discussed

Over‐expression of Dyrk1A affects bleeding by modulating plasma fibronectin and fibrinogen level in mice

International audienceDown syndrome is the most common chromosomal abnormality in humans. Patients with Down syndrome have hematologic disorders, including mild to moderate thrombocytopenia. In case of Down syndrome, thrombocytopenia is not associated with bleeding, and it remains poorly characterized regarding molecular mechanisms. We investigated the effects of overexpression of Dyrk1A, an important factor contributing to some major Down syndrome phenotypes, on platelet number and bleeding in mice. Mice overexpressing Dyrk1A have a decrease in platelet number by 20%. However, bleeding time was found to be reduced by 50%. The thrombocytopenia and the decreased bleeding time observed were not associated to an abnormal platelet receptors expression, to a defect of platelet activation by ADP, thrombin or convulxin, to the presence of activated platelets in the circulation or to an abnormal half-life of the platelets. To propose molecular mechanisms explaining this discrepancy, we performed a network analysis of Dyrk1A interactome and demonstrated that Dyrk1A, fibronectin and fibrinogen interact indirectly through two distinct clusters of proteins. Moreover, in mice overexpressing Dyrk1A, increased plasma fibronectin and fibrinogen levels were found, linked to an increase of the hepatic fibrinogen production. Our results indicate that overexpression of Dyrk1A in mice induces decreased bleeding consistent with increased plasma fibronectin and fibrinogen levels, revealing a new role of Dyrk1A depending on its indirect interaction with these two proteins

Table_1_DNA methylation profiling in Trisomy 21 females with and without breast cancer.xlsx

BackgroundDown Syndrome (DS) is the most common chromosome anomaly in humans and occurs due to an extra copy of chromosome 21. The malignancy profile in DS is unique, since DS patients have a low risk of developing solid tumors such as breast cancer however they are at higher risk of developing acute myeloid leukemia and acute lymphoblastic leukemia.MethodsIn this study, we investigated DNA methylation signatures and epigenetic aging in DS individuals with and without breast cancer. We analyzed DNA methylation patterns in Trisomy 21 (T21) individuals without breast cancer (T21-BCF) and DS individuals with breast cancer (T21-BC), using the Infinium Methylation EPIC BeadChip array.ResultsOur results revealed several differentially methylated sites and regions in the T21-BC patients that were associated with changes in gene expression. The differentially methylated CpG sites were enriched for processes related to serine-type peptidase activity, epithelial cell development, GTPase activity, bicellular tight junction, Ras protein signal transduction, etc. On the other hand, the epigenetic age acceleration analysis showed no difference between T21-BC and T21-BCF patients.ConclusionsThis is the first study to investigate DNA methylation changes in Down syndrome women with and without breast cancer and it could help shed light on factors that protect against breast cancer in DS.</p

Image_1_DNA methylation profiling in Trisomy 21 females with and without breast cancer.tiff

BackgroundDown Syndrome (DS) is the most common chromosome anomaly in humans and occurs due to an extra copy of chromosome 21. The malignancy profile in DS is unique, since DS patients have a low risk of developing solid tumors such as breast cancer however they are at higher risk of developing acute myeloid leukemia and acute lymphoblastic leukemia.MethodsIn this study, we investigated DNA methylation signatures and epigenetic aging in DS individuals with and without breast cancer. We analyzed DNA methylation patterns in Trisomy 21 (T21) individuals without breast cancer (T21-BCF) and DS individuals with breast cancer (T21-BC), using the Infinium Methylation EPIC BeadChip array.ResultsOur results revealed several differentially methylated sites and regions in the T21-BC patients that were associated with changes in gene expression. The differentially methylated CpG sites were enriched for processes related to serine-type peptidase activity, epithelial cell development, GTPase activity, bicellular tight junction, Ras protein signal transduction, etc. On the other hand, the epigenetic age acceleration analysis showed no difference between T21-BC and T21-BCF patients.ConclusionsThis is the first study to investigate DNA methylation changes in Down syndrome women with and without breast cancer and it could help shed light on factors that protect against breast cancer in DS.</p