The non-linear Dirichlet problem in Hadamard manifolds

We prove existence theorems for the Dirichlet problem for hypersurfaces of constant special Lagrangian curvature in Hadamard manifolds. The first results are obtained using the continuity method and approximation and then refined using two iterations of the Perron method. The a-priori estimates used in the continuity method are valid in any ambient manifold.

Influence of short time exposure to an insect growth regulator, hexaflumuron, on mortality and adult emergence of vector mosquitoes

Hexaflumuron, an insect growth regulator (IGR), was found to greatly affect the development of immatures and emergence of adults of three species of vector mosquitoes, Culex quinquefasciatus, Aedes aegypti and Anopheles stephensi, when larvae were subjected to short time exposure of < or = 1h. This IGR could completely prevent adult emergence even at a minimum exposure time of 10 min at 0.001, 0.01 and 0.1 mg/l. On treatment, larval and pupal mortality as well as varying degrees of morphogenetic abnormalities were induced in immatures and adults of the three species. Four weeks of control achieved in a slow moving sullage canal breeding Culex quinquefasciatus indicates that this IGR can be of use in such breeding habitats.

Homotopy Batalin-Vilkovisky algebras

This paper provides an explicit cofibrant resolution of the operad encoding Batalin-Vilkovisky algebras. Thus it defines the notion of homotopy Batalin-Vilkovisky algebras with the required homotopy properties. To define this resolution we extend the theory of Koszul duality to operads and properads that are defined by quadratic and linear relations. The operad encoding Batalin-Vilkovisky algebras is shown to be Koszul in this sense. This allows us to prove a Poincaré-Birkhoff-Witt Theorem for such an operad and to give an explicit small quasi-free resolution for it. This particular resolution enables us to describe the deformation theory and homotopy theory of BV-algebras and of homotopy BV-algebras. We show that any topological conformal field theory carries a homotopy BV-algebra structure which lifts the BV-algebra structure on homology. The same result is proved for the singular chain complex of the double loop space of a topological space endowed with an action of the circle. We also prove the cyclic Deligne conjecture with this cofibrant resolution of the operad BV. We develop the general obstruction theory for algebras over the Koszul resolution of a properad and apply it to extend a conjecture of Lian-Zuckerman, showing that certain vertex algebras have an explicit homotopy BV-algebra structure.

Mini-review: Specificity and expression of CIITA, the master regulator of MHC class II genes.

The class II transactivator (CIITA) has been referred to as the "master control factor" for the expression of MHC class II (MHCII) genes. As our knowledge on the specificity and function of CIITA grows, it is becoming increasingly evident that this sobriquet is entirely justified. First, despite extensive investigations, the major target genes of CIITA remain those implicated in the presentation of antigenic peptides by MHCII molecules. Although other putative target genes have been reported, the contribution of CIITA to their expression remains indirect, controversial or comparatively minor relative to its decisive role as a regulator of MHCII and related genes. Second, the most important parameter dictating MHCII expression is by far the expression pattern of the gene encoding CIITA (MHC2TA). The vast majority of signals that activate or repress MHCII expression under physiological and pathological situations converge on one or more of the three alternative promoters that drive transcription of the MHC2TA gene. In short, with respect to its specificity and its exquisitely controlled pattern of expression, CIITA is by a long stretch the single most important transcription factor for the regulation of genes required for MHCII-restricted antigen-presentation.

A functional equation related to the product in a quadratic number field

"Vegeu el resum a l'inici del document del fitxer adjunt."

Gaussian estimates for the density of the non-linear stochastic heat equation in any space dimension

In this paper, we establish lower and upper Gaussian bounds for the probability density of the mild solution to the stochastic heat equation with multiplicative noise and in any space dimension. The driving perturbation is a Gaussian noise which is white in time with some spatially homogeneous covariance. These estimates are obtained using tools of the Malliavin calculus. The most challenging part is the lower bound, which is obtained by adapting a general method developed by Kohatsu-Higa to the underlying spatially homogeneous Gaussian setting. Both lower and upper estimates have the same form: a Gaussian density with a variance which is equal to that of the mild solution of the corresponding linear equation with additive noise.

Linear Aggregation In The Social Accounting Matrix Framework

In economic literature, information deficiencies and computational complexities have traditionally been solved through the aggregation of agents and institutions. In inputoutput modelling, researchers have been interested in the aggregation problem since the beginning of 1950s. Extending the conventional input-output aggregation approach to the social accounting matrix (SAM) models may help to identify the effects caused by the information problems and data deficiencies that usually appear in the SAM framework. This paper develops the theory of aggregation and applies it to the social accounting matrix model of multipliers. First, we define the concept of linear aggregation in a SAM database context. Second, we define the aggregated partitioned matrices of multipliers which are characteristic of the SAM approach. Third, we extend the analysis to other related concepts, such as aggregation bias and consistency in aggregation. Finally, we provide an illustrative example that shows the effects of aggregating a social accounting matrix model.

EGFR signalling as a negative regulator of Notch1 gene transcription and function in proliferating keratinocytes and cancer.

The Notch1 gene has an important role in mammalian cell-fate decision and tumorigenesis. Upstream control mechanisms for transcription of this gene are still poorly understood. In a chemical genetics screen for small molecule activators of Notch signalling, we identified epidermal growth factor receptor (EGFR) as a key negative regulator of Notch1 gene expression in primary human keratinocytes, intact epidermis and skin squamous cell carcinomas (SCCs). The underlying mechanism for negative control of the Notch1 gene in human cells, as well as in a mouse model of EGFR-dependent skin carcinogenesis, involves transcriptional suppression of p53 by the EGFR effector c-Jun. Suppression of Notch signalling in cancer cells counteracts the differentiation-inducing effects of EGFR inhibitors while, at the same time, synergizing with these compounds in induction of apoptosis. Thus, our data reveal a key role of EGFR signalling in the negative regulation of Notch1 gene transcription, of potential relevance for combinatory approaches for cancer therapy.

A linear optimization technique for graph pebbling

Graph pebbling is a network model for studying whether or not a given supply of discrete pebbles can satisfy a given demand via pebbling moves. A pebbling move across an edge of a graph takes two pebbles from one endpoint and places one pebble at the other endpoint; the other pebble is lost in transit as a toll. It has been shown that deciding whether a supply can meet a demand on a graph is NP-complete. The pebbling number of a graph is the smallest t such that every supply of t pebbles can satisfy every demand of one pebble. Deciding if the pebbling number is at most k is NP 2 -complete. In this paper we develop a tool, called theWeight Function Lemma, for computing upper bounds and sometimes exact values for pebbling numbers with the assistance of linear optimization. With this tool we are able to calculate the pebbling numbers of much larger graphs than in previous algorithms, and much more quickly as well. We also obtain results for many families of graphs, in many cases by hand, with much simpler and remarkably shorter proofs than given in previously existing arguments (certificates typically of size at most the number of vertices times the maximum degree), especially for highly symmetric graphs. Here we apply theWeight Function Lemma to several specific graphs, including the Petersen, Lemke, 4th weak Bruhat, Lemke squared, and two random graphs, as well as to a number of infinite families of graphs, such as trees, cycles, graph powers of cycles, cubes, and some generalized Petersen and Coxeter graphs. This partly answers a question of Pachter, et al., by computing the pebbling exponent of cycles to within an asymptotically small range. It is conceivable that this method yields an approximation algorithm for graph pebbling.

Relaxation methods for solving linear inequality systems: Converging results

The problem of finding a feasible solution to a linear inequality system arises in numerous contexts. In [12] an algorithm, called extended relaxation method, that solves the feasibility problem, has been proposed by the authors. Convergence of the algorithm has been proven. In this paper, we onsider a class of extended relaxation methods depending on a parameter and prove their convergence. Numerical experiments have been provided, as well.

Glut9 is a major regulator of urate homeostasis and its genetic inactivation induces hyperuricosuria and urate nephropathy.

Elevated plasma urate levels are associated with metabolic, cardiovascular, and renal diseases. Urate may also form crystals, which can be deposited in joints causing gout and in kidney tubules inducing nephrolithiasis. In mice, plasma urate levels are controlled by hepatic breakdown, as well as, by incompletely understood renal processes of reabsorption and secretion. Here, we investigated the role of the recently identified urate transporter, Glut9, in the physiological control of urate homeostasis using mice with systemic or liver-specific inactivation of the Glut9 gene. We show that Glut9 is expressed in the basolateral membrane of hepatocytes and in both apical and basolateral membranes of the distal nephron. Mice with systemic knockout of Glut9 display moderate hyperuricemia, massive hyperuricosuria, and an early-onset nephropathy, characterized by obstructive lithiasis, tubulointerstitial inflammation, and progressive inflammatory fibrosis of the cortex, as well as, mild renal insufficiency. In contrast, liver-specific inactivation of the Glut9 gene in adult mice leads to severe hyperuricemia and hyperuricosuria, in the absence of urate nephropathy or any structural abnormality of the kidney. Together, our data show that Glut9 plays a major role in urate homeostasis by its dual role in urate handling in the kidney and uptake in the liver.