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

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

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

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

Evaluating the impact of topological protein features on the negative examples selection

Supervised machine learning methods when applied to the problem of automated protein-function prediction (AFP) require the availability of both positive examples (i.e., proteins which are known to possess a given protein function) and negative examples (corresponding to proteins not associated with that function). Unfortunately, publicly available proteome and genome data sources such as the Gene Ontology rarely store the functions not possessed by a protein. Thus the negative selection, consisting in identifying informative negative examples, is currently a central and challenging problem in AFP. Several heuristics have been proposed through the years to solve this problem; nevertheless, despite their effectiveness, to the best of our knowledge no previous existing work studied which protein features are more relevant to this task, that is, which protein features help more in discriminating reliable and unreliable negatives

Fostering Computational Thinking in Primary School through a LEGO®-based Music Notation

This paper presents a teaching methodology mixing elements from the domains of music and informatics as a key enabling to expose primary school pupils to basic aspects of computational thinking. This methodology is organized in two phases exploiting LEGO\uae bricks respectively as a physical tool and as a metaphor in order to let participants discover a simple notation encoding several basic concepts of the classical musical notation. The related activities, grounded on active learning theory, challenge groups of students to solve musical encoding problems of increasing difficulty

Tight Bounds for SVM Classification Error

We find very tight bounds on the accuracy of a Support Vector Machine classification error within the Algorithmic Inference framework. The framework is specially suitable for this kind of classifier since (i) we know the number of support vectors really employed, as an ancillary output of the learning procedure, and (ii) we can appreciate confidence intervals of misclassifying probability exactly in function of the cardinality of these vectors. As a result we obtain confidence intervals that are up to an order narrower than those supplied in the literature, having a slight different meaning due to the different approach they come from, but the same operational function. We numerically check the covering of these intervals

Coxiella burnetii and Leishmania Mexicana Residing Within Similar Parasitophorous Vacuoles Elicit Disparate Host Responses

Coxiella burnetii is a bacterium that thrives in an acidic parasitophorous vacuole (PV) derived from lysosomes. Leishmania mexicana, a eukaryote, has also independently evolved to live in a morphologically similar PV. As Coxiella and Leishmania are highly divergent organisms that cause different diseases, we reasoned that their respective infections would likely elicit distinct host responses despite producing phenotypically similar parasite-containing vacuoles. The objective of this study was to investigate, at the molecular level, the macrophage response to each pathogen. Infection of THP-1 (human monocyte/macrophage) cells with Coxiella and Leishmania elicited disparate host responses. At 5 days post-infection, when compared to uninfected cells, 1057 genes were differentially expressed (746 genes up-regulated and 311 genes downregulated) in C. burnetii infected cells, whereas 698 genes (534 genes up-regulated and 164 genes down-regulated) were differentially expressed in L. mexicana infected cells. Interestingly, of the 1755 differentially expressed genes identified in this study, only 126 genes (∼7%) are common to both infections. We also discovered that 1090 genes produced mRNA isoforms at significantly different levels under the two infection conditions, suggesting that alternate proteins encoded by the same gene might have important roles in host response to each infection. Additionally, we detected 257 micro RNAs (miRNAs) that were expressed in THP-1 cells, and identified miRNAs that were specifically expressed during Coxiella or Leishmania infections. Collectively, this study identified host mRNAs and miRNAs that were influenced by Coxiella and/or Leishmania infections, and our data indicate that although their PVs are morphologically similar, Coxiella and Leishmania have evolved different strategies that perturb distinct host processes to create and thrive within their respective intracellular niches