Composition for a class of generalized functions in Colombeau's theory

In Colombeau's theory, given an open subset Ω of ℝn, there is a differential algebra G(Ω) of generalized functions which contains in a natural way the space D′(Ω) of distributions as a vector subspace. There is also a simpler version of the algebra G,(Ω). Although this subalgebra does not contain, in canonical way, the space D′(Ω) is enough for most applications. This work is developed in the simplified generalized functions framework. In several applications it is necessary to compute higher intrinsic derivatives of generalized functions, and since these derivatives are multilinear maps, it is necessary to define the space of generalized functions in Banach spaces. In this article we introduce the composite function for a special class of generalized mappings (defined in open subsets of Banach spaces with values in Banach spaces) and we compute the higher intrinsic derivative of this composite function.

On partial derivative-Neumann's problem in generalized functions framework

In this paper, we show that the equation delta u/delta (z) over bar + Gu = f, where the elements involved are in generalized functions context, has a local solution in the generalized functions context.

INFLAMMATORY RESPONSE AND NEUTROPHIL FUNCTIONS IN PLAYERS AFTER A FUTSAL MATCH

de Moura, NR, Cury-Boaventura, MF, Santos, VC, Levada-Pires, AC, Bortolon, JR, Fiamoncini, J, Pithon-Curi, TC, Curi, R, and Hatanaka, E. Inflammatory response and neutrophil functions in players after a futsal match. J Strength Cond Res 26(9): 2507-2514, 2012-Futsal players suffer injuries resulting from muscle fatigue and contact or collision among players. Muscle lesions can be detected by measuring muscle lesion markers such as creatine kinase (CK) and lactate dehydrogenase (LDH) in plasma. After an initial lesion, there is an increase in the plasma levels of C-reactive protein (CRP) and proinflammatory cytokines. These mediators may activate neutrophils and contribute to tissue damage and increase susceptibility to invasive microorganisms. In this study, we investigated the effect of a futsal match on muscle lesion markers, cytokines, and CRP in elite players. The basal and stimulated neutrophil responsiveness after a match was also evaluated based on measurements of neutrophil necrosis, apoptosis, phagocytic capacity, reactive oxygen species (ROS) production, and cytokines (tumor necrosis factor-alpha [TNF-alpha], interleukin [IL]-8, IL-1 beta, IL-10, and IL-1ra) production. Blood samples were taken from 16 players (26.4 +/- 3.2 years, 70.2 +/- 6.9 kg, 59.7 +/- 5.1 ml.kg(-1).min(-1), sports experience of 4.4 +/- 0.9 years) before and immediately after a match. Exercise increased the serum activities of CK (2.5-fold) and LDH (1.3-fold). Playing futsal also increased the serum concentrations of IL-6 (1.6-fold) and CRP (1.6-fold). The TNF-alpha, IL-1 beta, IL-8, IL-1ra, and IL-10 serum levels were not modified in the conditions studied. The futsal match induced neutrophil apoptosis, as indicated by phosphatidylserine externalization (6.0-fold). The exercise induced priming of neutrophils by increasing ROS (1.3-fold), TNF-alpha (5.8-fold), and IL-1 beta (4.8-fold) released in nonstimulated cells. However, in the stimulated condition, the exercise decreased neutrophil function, diminishing the release of ROS by phorbol myristate acetate-stimulated neutrophils (1.5-fold), and the phagocytic capacity (1.6-fold). We concluded that playing futsal induces inflammation, primes and activates neutrophils, and reduces the efficiency of neutrophil phagocytosis immediately after a match.

Continuity of Lyapunov functions and of energy level for generalized gradient semigroup

The global attractor of a gradient-like semigroup has a Morse decomposition. Associated to this Morse decomposition there is a Lyapunov function (differentiable along solutions)-defined on the whole phase space- which proves relevant information on the structure of the attractor. In this paper we prove the continuity of these Lyapunov functions under perturbation. On the other hand, the attractor of a gradient-like semigroup also has an energy level decomposition which is again a Morse decomposition but with a total order between any two components. We claim that, from a dynamical point of view, this is the optimal decomposition of a global attractor; that is, if we start from the finest Morse decomposition, the energy level decomposition is the coarsest Morse decomposition that still produces a Lyapunov function which gives the same information about the structure of the attractor. We also establish sufficient conditions which ensure the stability of this kind of decomposition under perturbation. In particular, if connections between different isolated invariant sets inside the attractor remain under perturbation, we show the continuity of the energy level Morse decomposition. The class of Morse-Smale systems illustrates our results.

Generalized correlation functions for conductance fluctuations and the mesoscopic spin Hall effect

We study the spin Hall conductance fluctuations in ballistic mesoscopic systems. We obtain universal expressions for the spin and charge current fluctuations, cast in terms of current-current autocorrelation functions. We show that the latter are conveniently parametrized as deformed Lorentzian shape lines, functions of an external applied magnetic field and the Fermi energy. We find that the charge current fluctuations show quite unique statistical features at the symplectic-unitary crossover regime. Our findings are based on an evaluation of the generalized transmission coefficients correlation functions within the stub model and are amenable to experimental test. DOI: 10.1103/PhysRevB.86.235112

Differential calculus and integration of generalized functions over membranes

In this paper we continue the development of the differential calculus started in Aragona et al. (Monatsh. Math. 144: 13-29, 2005). Guided by the so-called sharp topology and the interpretation of Colombeau generalized functions as point functions on generalized point sets, we introduce the notion of membranes and extend the definition of integrals, given in Aragona et al. (Monatsh. Math. 144: 13-29, 2005), to integrals defined on membranes. We use this to prove a generalized version of the Cauchy formula and to obtain the Goursat Theorem for generalized holomorphic functions. A number of results from classical differential and integral calculus, like the inverse and implicit function theorems and Green's theorem, are transferred to the generalized setting. Further, we indicate that solution formulas for transport and wave equations with generalized initial data can be obtained as well.

On the Hilbert transform in the framework of generalized functions

In this paper, a definition of the Hilbert transform operating on Colombeau's temperated generalized functions is given. Similar results to some theorems that hold in the classical theory, or in certain subspaces of Schwartz distributions, have been obtained in this framework.

A generalized finite element method with global-local enrichment functions for confined plasticity problems

The main feature of partition of unity methods such as the generalized or extended finite element method is their ability of utilizing a priori knowledge about the solution of a problem in the form of enrichment functions. However, analytical derivation of enrichment functions with good approximation properties is mostly limited to two-dimensional linear problems. This paper presents a procedure to numerically generate proper enrichment functions for three-dimensional problems with confined plasticity where plastic evolution is gradual. This procedure involves the solution of boundary value problems around local regions exhibiting nonlinear behavior and the enrichment of the global solution space with the local solutions through the partition of unity method framework. This approach can produce accurate nonlinear solutions with a reduced computational cost compared to standard finite element methods since computationally intensive nonlinear iterations can be performed on coarse global meshes after the creation of enrichment functions properly describing localized nonlinear behavior. Several three-dimensional nonlinear problems based on the rate-independent J (2) plasticity theory with isotropic hardening are solved using the proposed procedure to demonstrate its robustness, accuracy and computational efficiency.

Thyroid disruption in zebrafish (Danio rerio) larvae: Different molecular response patterns lead to impaired eye development and visual functions

The vertebrate thyroid system is important for multiple developmental processes, including eye development. Thus, its environmentally induced disruption may impact important fitness-related parameters like visual capacities and behaviour. The present study investigated the relation between molecular effects of thyroid disruption and morphological and physiological changes of eye development in zebrafish (Danio rerio). Two test compounds representing different molecular modes of thyroid disruption were used: propylthiouracil (PTU), which is an enzyme-inhibitor of thyroid hormone synthesis, and tetrabromobisphenol A (TBBPA), which interacts with the thyroid hormone receptors. Both chemicals significantly altered transcript levels of thyroid system-related genes (TRα, TRβ, TPO, TSH, DIO1, DIO2 and DIO3) in a compound-specific way. Despite these different molecular response patterns, both treatments resulted in similar pathological alterations of the eyes such as reduced size, RPE cell diameter and pigmentation, which were concentration-dependent. The morphological changes translated into impaired visual performance of the larvae: the optokinetic response was significantly and concentration-dependently decreased in both treatments, together with a significant increase of light preference of PTU-treated larvae. In addition, swimming activity was impacted. This study provides first evidence that different modes of molecular action of the thyroid disruptors can be associated with uniform apical responses. Furthermore, this study is the first to show that pathological eye development, as it can be induced by exposure to thyroid disruptors, indeed translates into impaired visual capacities of zebrafish early life stages.

A human Cds1-related kinase that functions downstream of ATM protein in the cellular response to DNA damage

Checkpoints maintain the order and fidelity of the eukaryotic cell cycle, and defects in checkpoints contribute to genetic instability and cancer. Much of our current understanding of checkpoints comes from genetic studies conducted in yeast. In the fission yeast Schizosaccharomyces pombe (Sp), SpRad3 is an essential component of both the DNA damage and DNA replication checkpoints. The SpChk1 and SpCds1 protein kinases function downstream of SpRad3. SpChk1 is an effector of the DNA damage checkpoint and, in the absence of SpCds1, serves an essential function in the DNA replication checkpoint. SpCds1 functions in the DNA replication checkpoint and in the S phase DNA damage checkpoint. Human homologs of both SpRad3 and SpChk1 but not SpCds1 have been identified. Here we report the identification of a human cDNA encoding a protein (designated HuCds1) that shares sequence, structural, and functional similarity to SpCds1. HuCds1 was modified by phosphorylation and activated in response to ionizing radiation. It was also modified in response to hydroxyurea treatment. Functional ATM protein was required for HuCds1 modification after ionizing radiation but not after hydroxyurea treatment. Like its fission yeast counterpart, human Cds1 phosphorylated Cdc25C to promote the binding of 14-3-3 proteins. These findings suggest that the checkpoint function of HuCds1 is conserved in yeast and mammals.

LXRα functions as a cAMP-responsive transcriptional regulator of gene expression

LXRα is a member of a nuclear receptor superfamily that regulates transcription. LXRα forms a heterodimer with RXRα, another member of this family, to regulate the expression of cholesterol 7α-hydroxylase by means of binding to the DR4-type cis-element. Here, we describe a function for LXRα as a cAMP-responsive regulator of renin and c-myc gene transcriptions by the interaction with a specific cis-acting DNA element, CNRE (an overlapping cAMP response element and a negative response element). Our previous studies showed that renin gene expression is regulated by cAMP, at least partly, through the CNRE sequence in its 5′-flanking region. This sequence is also found in c-myc and several other genes. Based on our cloning results using the yeast one-hybrid system, we discovered that the mouse homologue of human LXRα binds to the CNRE and demonstrated that it binds as a monomer. To define the function of LXRα on gene expression, we transfected the renin-producing renal As4.1 cells with LXRα expression plasmid. Overexpression of LXRα in As4.1 cells confers cAMP inducibility to reporter constructs containing the renin CNRE. After stable transfection of LXRα, As4.1 cells show a cAMP-inducible up-regulation of renin mRNA expression. In parallel experiments, we demonstrated that LXRα can also bind to the homologous CNRE in the c-myc promoter. cAMP promotes transcription through c-myc/CNRE:LXRα interaction in LXRα transiently transfected cells and increases c-myc mRNA expression in stably transfected cells. Identification of LXRα as a cAMP-responsive nuclear modulator of renin and c-myc expression not only has cardiovascular significance but may have generalized implication in the regulation of gene transcription.

Functions of the DNA damage response pathway target Ho endonuclease of yeast for degradation via the ubiquitin-26S proteasome system

Ho endonuclease of Saccharomyces cerevisiae is a homing endonuclease that makes a site-specific double-strand break in the MAT gene in late G1. Here we show that Ho is rapidly degraded via the ubiquitin-26S proteasome system through two ubiquitin-conjugating enzymes UBC2Rad6 and UBC3Cdc34. UBC2Rad6 is complexed with the ring finger DNA-binding protein Rad18, and we find that Ho is stabilized in rad18 mutants. We show that the Ho degradation pathway involving UBC3Cdc34 goes through the Skp1/Cdc53/F-box (SCF) ubiquitin ligase complex and identify a F-box protein, Yml088w, that is required for Ho degradation. Components of a defined pathway of the DNA damage response, MEC1, RAD9, and CHK1, are also necessary for Ho degradation, whereas functions of the RAD24 epistasis group and the downstream effector RAD53 have no role in degradation of Ho. Our results indicate a link between the endonuclease function of Ho and its destruction.

Response of Catch-Per-Unit-Effort to Spatial and Environmental Factors: an Exploratory Data Analysis Using Generalized Additive Models

Understanding spatial distributions and how environmental conditions influence catch-per-unit-effort (CPUE) is important for increased fishing efficiency and sustainable fisheries management. This study investigated the relationship between CPUE, spatial factors, temperature, and depth using generalized additive models. Combinations of factors, and not one single factor, were frequently included in the best model. Parameters which best described CPUE varied by geographic region. The amount of variance, or deviance, explained by the best models ranged from a low of 29% (halibut, Charlotte region) to a high of 94% (sablefish, Charlotte region). Depth, latitude, and longitude influenced most species in several regions. On the broad geographic scale, depth was associated with CPUE for every species, except dogfish. Latitude and longitude influenced most species, except halibut (Areas 4 A/D), sablefish, and cod. Temperature was important for describing distributions of halibut in Alaska, arrowtooth flounder in British Columbia, dogfish, Alaska skate, and Aleutian skate. The species-habitat relationships revealed in this study can be used to create improved fishing and management strategies.