Existence of solutions to a higher dimensional mean-field equation on manifolds

For $m\geq 1$ we prove an existence result for the equation $$(-\Delta_g)^m u+\lambda=\lambda\frac{e^{2mu}}{\int_M e^{2mu}d\mu_g}$$ on a closed Riemannian manifold $(M,g)$ of dimension $2m$ for certain values of $\lambda$.Comment: 15 Page

A Codazzi-like equation and the singular set for C1C^{1} smooth surfaces in the Heisenberg group

In this paper, we study the structure of the singular set for a $C^{1}$ smooth surface in the $3$-dimensional Heisenberg group $\boldsymbol{H}_{1}$. We discover a Codazzi-like equation for the $p$-area element along the characteristic curves on the surface. Information obtained from this ordinary differential equation helps us to analyze the local configuration of the singular set and the characteristic curves. In particular, we can estimate the size and obtain the regularity of the singular set. We understand the global structure of the singular set through a Hopf-type index theorem. We also justify that Codazzi-like equation by proving a fundamental theorem for local surfaces in $\boldsymbol{H}_{1}$.Comment: 64 pages, 17 figure

Interjección y extrapredicación

Aquest article versa sobre la interjecció i intenta analitzar el seu comportament de cara a realitzar una aproximació entre aquesta unitat i la extrapredición. Des d’un enfocament essencialment funcional, explora la interjecció així com l’extrapredicació del seu funcionament. Acaba observant que aquesta unitat neurolingüística és eminentment extrapredicativa.Este artículo versa sobre la interjección e intenta analizar su comportamiento con vistas a realizar una aproximación entre esta unidad y la extrapredicación. Desde un enfoque esencialmente funcional, explora la interjección así como la extrapredición de su funcionamiento. Termina observando que esta unidad neurolingüística es eminentemente extrapredicativa.Cet article traite de l’interjection et tente d’analyser son comportement afin de faire une approximation entre cette unité et l’extraprédication. D’une approche essentiellement fonctionnelle, il explore l’interjection ainsi que l’extraprédiction de son fonctionnement. Il conclut en observant que cette unité neurolinguistique est éminemment extra-prédictive.This paper focuses on interjection and aims to explore how it behaves, in order to make an approximation between this linguistic unit and the phenomenon called extrapredication. The perspective used here is essencially functional and, from this theory, the paper analyse the interjection and the extrapredication considering how it operates in the sentence. By the end, the constat is that this neurolinguistic unit is essencially extrapredicative

Time representation in reinforcement learning models of the basal ganglia

Reinforcement learning (RL) models have been influential in understanding many aspects of basal ganglia function, from reward prediction to action selection. Time plays an important role in these models, but there is still no theoretical consensus about what kind of time representation is used by the basal ganglia. We review several theoretical accounts and their supporting evidence. We then discuss the relationship between RL models and the timing mechanisms that have been attributed to the basal ganglia. We hypothesize that a single computational system may underlie both RL and interval timing—the perception of duration in the range of seconds to hours. This hypothesis, which extends earlier models by incorporating a time-sensitive action selection mechanism, may have important implications for understanding disorders like Parkinson's disease in which both decision making and timing are impaired

An improved geometric inequality via vanishing moments, with applications to singular Liouville equations

We consider a class of singular Liouville equations on compact surfaces motivated by the study of Electroweak and Self-Dual Chern-Simons theories, the Gaussian curvature prescription with conical singularities and Onsager's description of turbulence. We analyse the problem of existence variationally, and show how the angular distribution of the conformal volume near the singularities may lead to improvements in the Moser-Trudinger inequality, and in turn to lower bounds on the Euler-Lagrange functional. We then discuss existence and non-existence results.Comment: some references adde

Simultaneous Learning of Fuzzy Sets

We extend a procedure based on support vector clustering and devoted to inferring the membership function of a fuzzy set to the case of a universe of discourse over which several fuzzy sets are defined. The extended approach learns simultaneously these sets without requiring as previous knowledge either their number or labels approximating membership values. This data-driven approach is completed via expert knowledge incorporation in the form of predefined shapes for the membership functions. The procedure is successfully tested on a benchmark

New improved Moser-Trudinger inequalities and singular Liouville equations on compact surfaces

We consider a singular Liouville equation on a compact surface, arising from the study of Chern-Simons vortices in a self dual regime. Using new improved versions of the Moser-Trudinger inequalities (whose main feature is to be scaling invariant) and a variational scheme, we prove new existence results.Comment: to appear in GAF

Inhibition of HIV-1 Replication in Human Monocyte-Derived Macrophages by Parasite Trypanosoma cruzi

and HIV-1 to date.0.01). inhibits HIV-1 replication at several replication stages in macrophages, a major cell target for both pathogens

Sign-changing tower of bubbles for a sinh-Poisson equation with asymmetric exponents

Motivated by the statistical mechanics description of stationary 2D-turbulence, for a sinh-Poisson type equation with asymmetric nonlinearity, we construct a concentrating solution sequence in the form of a tower of singular Liouville bubbles, each of which has a different degeneracy exponent. The asymmetry parameter $\gamma\in(0,1]$ corresponds to the ratio between the intensity of the negatively rotating vortices and the intensity of the positively rotating vortices. Our solutions correspond to a superposition of highly concentrated vortex configurations of alternating orientation; they extend in a nontrivial way some known results for $\gamma=1$. Thus, by analyzing the case $\gamma\neq1$ we emphasize specific properties of the physically relevant parameter $\gamma$ in the vortex concentration phenomena

Mechanisms of oxygenation responses to proning and recruitment in COVID-19 pneumonia

Purpose: This study aimed at investigating the mechanisms underlying the oxygenation response to proning and recruitment maneuvers in coronavirus disease 2019 (COVID-19) pneumonia. Methods: Twenty-five patients with COVID-19 pneumonia, at variable times since admission (from 1 to 3 weeks), underwent computed tomography (CT) lung scans, gas-exchange and lung-mechanics measurement in supine and prone positions at 5 cmH2O and during recruiting maneuver (supine, 35 cmH2O). Within the non-aerated tissue, we differentiated the atelectatic and consolidated tissue (recruitable and non-recruitable at 35 cmH2O of airway pressure). Positive/negative response to proning/recruitment was defined as increase/decrease of PaO2/FiO2. Apparent perfusion ratio was computed as venous admixture/non aerated tissue fraction. Results: The average values of venous admixture and PaO2/FiO2 ratio were similar in supine-5 and prone-5. However, the PaO2/FiO2 changes (increasing in 65% of the patients and decreasing in 35%, from supine to prone) correlated with the balance between resolution of dorsal atelectasis and formation of ventral atelectasis (p = 0.002). Dorsal consolidated tissue determined this balance, being inversely related with dorsal recruitment (p = 0.012). From supine-5 to supine-35, the apparent perfusion ratio increased from 1.38 ± 0.71 to 2.15 ± 1.15 (p = 0.004) while PaO2/FiO2 ratio increased in 52% and decreased in 48% of patients. Non-responders had consolidated tissue fraction of 0.27 ± 0.1 vs. 0.18 ± 0.1 in the responding cohort (p = 0.04). Consolidated tissue, PaCO2 and respiratory system elastance were higher in patients assessed late (all p < 0.05), suggesting, all together, “fibrotic-like” changes of the lung over time. Conclusion: The amount of consolidated tissue was higher in patients assessed during the third week and determined the oxygenation responses following pronation and recruitment maneuvers