Power series representing Posets

Consider the category of finite posets with a unique maximum and a unique minimum. We prove that two geometrically inspired operations on this category are transported to labeling series. Consequently, we prove new identities of binomial coeficients. We provide an algorithm to determine if a power series is associated to a certain family of posets. We compute the number of labeling functions for a family of posets.Comment: 39 pages. We added an application to Probability. Grammar errors correcte

Polychrony as Chinampas

We study the flow of signals through paths with the following condition: a node emits a signal if two incoming signals from other nodes arrive coincidentally or if it receives an external stimuli. We apply our study to count and describe families of polychrony groups on a line, and we introduce triangular sequences.Comment: 32 pages. We refocus our study on nonlinear signal-flow graphs. We add possible generalizations of our wor

A poset version of Ramanujan results on Eulerian numbers

We explain how several results of Ramanujan follow from the formalism of order series. Consider the operad generated by a binary associative and commutative operation and a binary associative operation, order series are one of the algebras over this operad. In our interpretation, Ramanujan worked with series inheriting the structure of the disjoint union of posets. We then provide new conceptual proofs of a couple of results by Ramanujan and describe a version of his results that depends on a choice of a series parallel poset.Comment: 12 page

Sobre los Análogos Hiperholomorfos de las Series de Potencias en Análisis Cuaterniónico.

Se introduce la noción de Convergencia Fina que permite demostrar un Teorema de Cauchy-Hadamard más general que el conocido para el caso cuaterni ónico y generalizar dos teoremas de Abel sobre la convergencia de Series cuaterniónicas. Es un hecho conocido la validez del Teorema de Cauchy- Hadamard, sin embargo no se sabía nada con respecto a los Teoremas de Abel. Estos resultados, y el enfoque usado, son debidos al autor de la tesis

Polychrony as Chinampas

In this paper, we study the flow of signals through linear paths with the nonlinear condition that a node emits a signal when it receives external stimuli or when two incoming signals from other nodes arrive coincidentally with a combined amplitude above a fixed threshold. Sets of such nodes form a polychrony group and can sometimes lead to cascades. In the context of this work, cascades are polychrony groups in which the number of nodes activated as a consequence of other nodes is greater than the number of externally activated nodes. The difference between these two numbers is the so-called profit. Given the initial conditions, we predict the conditions for a vertex to activate at a prescribed time and provide an algorithm to efficiently reconstruct a cascade. We develop a dictionary between polychrony groups and graph theory. We call the graph corresponding to a cascade a chinampa. This link leads to a topological classification of chinampas. We enumerate the chinampas of profits zero and one and the description of a family of chinampas isomorphic to a family of partially ordered sets, which implies that the enumeration problem of this family is equivalent to computing the Stanley-order polynomials of those partially ordered sets

Dilated cardiomyopathy due to BLC2-associated athanogene 3 (BAG3) mutations

Background The BAG3 (BLC2-associated athanogene 3) gene codes for an antiapoptotic protein located on the sarcomere Z-disc. Mutations in BAG3 are associated with dilated cardiomyopathy (DCM), but only a small number of cases have been reported to date, and the natural history of BAG3 cardiomyopathy is poorly understood. Objectives This study sought to describe the phenotype and prognosis of BAG3 mutations in a large multicenter DCM cohort. Methods The study cohort comprised 129 individuals with a BAG3 mutation (62% males, 35.1 ± 15.0 years of age) followed at 18 European centers. Localization of BAG3 in cardiac tissue was analyzed in patients with truncating BAG3 mutations using immunohistochemistry. Results At first evaluation, 57.4% of patients had DCM. After a median follow-up of 38 months (interquartile range: 7 to 95 months), 68.4% of patients had DCM and 26.1% who were initially phenotype-negative developed DCM. Disease penetrance in individuals >40 years of age was 80% at last evaluation, and there was a trend towards an earlier onset of DCM in men (age 34.6 ± 13.2 years vs. 40.7 ± 12.2 years; p = 0.053). The incidence of adverse cardiac events (death, left ventricular assist device, heart transplantation, and sustained ventricular arrhythmia) was 5.1% per year among individuals with DCM. Male sex, decreased left ventricular ejection fraction. and increased left ventricular end-diastolic diameter were associated with adverse cardiac events. Myocardial tissue from patients with a BAG3 mutation showed myofibril disarray and a relocation of BAG3 protein in the sarcomeric Z-disc. Conclusions DCM caused by mutations in BAG3 is characterized by high penetrance in carriers >40 years of age and a high risk of progressive heart failure. Male sex, decreased left ventricular ejection fraction, and enlarged left ventricular end-diastolic diameter are associated with adverse outcomes in patients with BAG3 mutations

Prosthetic Valve Candida spp. Endocarditis: New Insights Into Long-term Prognosis—The ESCAPE Study

International audienceBackground: Prosthetic valve endocarditis caused by Candida spp. (PVE-C) is rare and devastating, with international guidelines based on expert recommendations supporting the combination of surgery and subsequent azole treatment.Methods: We retrospectively analyzed PVE-C cases collected in Spain and France between 2001 and 2015, with a focus on management and outcome.Results: Forty-six cases were followed up for a median of 9 months. Twenty-two patients (48%) had a history of endocarditis, 30 cases (65%) were nosocomial or healthcare related, and 9 (20%) patients were intravenous drug users. "Induction" therapy consisted mainly of liposomal amphotericin B (L-amB)-based (n = 21) or echinocandin-based therapy (n = 13). Overall, 19 patients (41%) were operated on. Patients <66 years old and without cardiac failure were more likely to undergo cardiac surgery (adjusted odds ratios [aORs], 6.80 [95% confidence interval [CI], 1.59-29.13] and 10.92 [1.15-104.06], respectively). Surgery was not associated with better survival rates at 6 months. Patients who received L-amB alone had a better 6-month survival rate than those who received an echinocandin alone (aOR, 13.52; 95% CI, 1.03-838.10). "Maintenance" fluconazole therapy, prescribed in 21 patients for a median duration of 13 months (range, 2-84 months), led to minor adverse effects.Conclusion: L-amB induction treatment improves survival in patients with PVE-C. Medical treatment followed by long-term maintenance fluconazole may be the best treatment option for frail patients

Management of coronary disease in patients with advanced kidney disease

BACKGROUND Clinical trials that have assessed the effect of revascularization in patients with stable coronary disease have routinely excluded those with advanced chronic kidney disease. METHODS We randomly assigned 777 patients with advanced kidney disease and moderate or severe ischemia on stress testing to be treated with an initial invasive strategy consisting of coronary angiography and revascularization (if appropriate) added to medical therapy or an initial conservative strategy consisting of medical therapy alone and angiography reserved for those in whom medical therapy had failed. The primary outcome was a composite of death or nonfatal myocardial infarction. A key secondary outcome was a composite of death, nonfatal myocardial infarction, or hospitalization for unstable angina, heart failure, or resuscitated cardiac arrest. RESULTS At a median follow-up of 2.2 years, a primary outcome event had occurred in 123 patients in the invasive-strategy group and in 129 patients in the conservative-strategy group (estimated 3-year event rate, 36.4% vs. 36.7%; adjusted hazard ratio, 1.01; 95% confidence interval [CI], 0.79 to 1.29; P=0.95). Results for the key secondary outcome were similar (38.5% vs. 39.7%; hazard ratio, 1.01; 95% CI, 0.79 to 1.29). The invasive strategy was associated with a higher incidence of stroke than the conservative strategy (hazard ratio, 3.76; 95% CI, 1.52 to 9.32; P=0.004) and with a higher incidence of death or initiation of dialysis (hazard ratio, 1.48; 95% CI, 1.04 to 2.11; P=0.03). CONCLUSIONS Among patients with stable coronary disease, advanced chronic kidney disease, and moderate or severe ischemia, we did not find evidence that an initial invasive strategy, as compared with an initial conservative strategy, reduced the risk of death or nonfatal myocardial infarction