A note on a practical relationship between filter coefficients and scaling and wavelet functions of Discrete Wavelet Transforms

In this paper, the relationship between the filter coefficients and the scaling and wavelet functions of the Discrete Wavelet Transform is presented and exemplified from a practical point-of-view. The explanations complement the wavelet theory, that is well documented in the literature, being important for researchers who work with this tool for time-frequency analysis. (c) 2011 Elsevier Ltd. All rights reserved.

CCP1/Nna1 functions in protein turnover in mouse brain: Implications for cell death in Purkinje cell degeneration mice

Purkinje cell degeneration (pcd) mice have a mutation within the gene encoding cytosolic carboxypeptidase 1 (CCP1/Nna1), which has homology to metallocarboxypeptidases. To assess the function of CCP1/Nna1, quantitative proteomics and peptidomics approaches were used to compare proteins and peptides in mutant and wild-type mice. Hundreds of peptides derived from cytosolic and mitochondrial proteins are greatly elevated in pcd mouse hypothalamus, amygdala, cortex, prefrontal cortex, and striatum. However, the major proteins detected on 2-D gel electrophoresis were present in mutant and wild-type mouse cortex and hypothalamus at comparable levels, and proteasome activity is normal in these brain regions of pcd mice, suggesting that the increase in cellular peptide levels in the pcd mice is due to reduced degradation of the peptides downstream of the proteasome. Both nondegenerating and degenerating regions of pcd mouse brain, but not wild-type mouse brain, show elevated autophagy, which can be triggered by a decrease in amino acid levels. Taken together with previous studies on CCP1/Nna1, these data suggest that CCP1/Nna1 plays a role in protein turnover by cleaving proteasome-generated peptides into amino acids and that decreased peptide turnover in the pcd mice leads to cell death.-Berezniuk, I., Sironi, J., Callaway, M. B., Castro, L. M., Hirata, I. Y., Ferro, E. S., Fricker, L. D. CCP1/Nna1 functions in protein turnover in mouse brain: Implications for cell death in Purkinje cell degeneration mice. FASEB J. 24, 1813-1823 (2010). www.fasebj.org

A novel trypsin Kazal-type inhibitor from Aedes aegypti with thrombin coagulant inhibitory activity

Kazal-type inhibitors play several important roles in invertebrates, such as anticoagulant, vasodilator and antimicrobial activities. Putative Kazal-type inhibitors were described in several insect transcriptomes. In this paper we characterized for the first time a Kazal unique domain trypsin inhibitor from the Aedes aegypti mosquito. Previously, analyses of sialotranscriptome of A. aegypti showed the potential presence of a Kazal-type serine protease inhibitor, in female salivary glands, carcass and also in whole male, which we named AaTI (A. aegypti trypsin inhibitor). AaTI sequence showed amino acid sequence similarity with insect thrombin inhibitors, serine protease inhibitor from Litopenaeus vannamei hemocytes and tryptase inhibitor from leech Hirudo medicinalis (LDTI). In this work we expressed, purified and characterized the recombinant AaTI (rAaTI). Molecular weight of purified rAaTI was 7 kDa rAaTI presented dissociation constant (K(i)) of 0.15 and 3.8 nM toward trypsin and plasmin, respectively, and it weakly inhibited thrombin amidolytic activity. The rAaTI was also able to prolong prothrombin time, activated partial thromboplastin time and thrombin time. AaTI transcription was confirmed in A. aegypti female salivary gland and gut 3 h and 24 h after blood feeding, suggesting that this molecule can act as anticoagulant during the feeding and digestive processes. Its transcription in larvae and pupae suggested that AaTI may also play other functions during the mosquito`s development. (C) 2010 Elsevier Masson SAS. All rights reserved.

C(k)-solvability near the characteristic set for a class of planar complex vector fields of infinite type

This paper deals with semi-global C(k)-solvability of complex vector fields of the form L = partial derivative/partial derivative t + x(r) (a(x) + ib(x))partial derivative/partial derivative x, r >= 1, defined on Omega(epsilon) = (-epsilon, epsilon) x S(1), epsilon > 0, where a and b are C(infinity) real-valued functions in (-epsilon, epsilon). It is shown that the interplay between the order of vanishing of the functions a and b at x = 0 influences the C(k)-solvability at Sigma = {0} x S(1). When r = 1, it is permitted that the functions a and b of L depend on the x and t variables, that is, L = partial derivative/partial derivative t + x(a(x, t) + ib(x, t))partial derivative/partial derivative x, where (x, t) is an element of Omega(epsilon).

Gevrey solvability near the characteristic set for a class of planar complex vector fields of infinite type

We study the Gevrey solvability of a class of complex vector fields, defined on Omega(epsilon) = (-epsilon, epsilon) x S(1), given by L = partial derivative/partial derivative t + (a(x) + ib(x))partial derivative/partial derivative x, b not equivalent to 0, near the characteristic set Sigma = {0} x S(1). We show that the interplay between the order of vanishing of the functions a and b at x = 0 plays a role in the Gevrey solvability. (C) 2008 Elsevier Inc. All rights reserved.

UNIFORM DISSIPATIVENESS, ROBUST SYNCHRONIZATION AND LOCATION OF THE ATTRACTOR OF PARAMETRIZED NONAUTONOMOUS DISCRETE SYSTEMS

In this series of papers, we study issues related to the synchronization of two coupled chaotic discrete systems arising from secured communication. The first part deals with uniform dissipativeness with respect to parameter variation via the Liapunov direct method. We obtain uniform estimates of the global attractor for a general discrete nonautonomous system, that yields a uniform invariance principle in the autonomous case. The Liapunov function is allowed to have positive derivative along solutions of the system inside a bounded set, and this reduces substantially the difficulty of constructing a Liapunov function for a given system. In particular, we develop an approach that incorporates the classical Lagrange multiplier into the Liapunov function method to naturally extend those Liapunov functions from continuous dynamical system to their discretizations, so that the corresponding uniform dispativeness results are valid when the step size of the discretization is small. Applications to the discretized Lorenz system and the discretization of a time-periodic chaotic system are given to illustrate the general results. We also show how to obtain uniform estimation of attractors for parametrized linear stable systems with nonlinear perturbation.

Exact vortex solutions in a CP(N) Skyrme-Faddeev type model

We consider a four dimensional field theory with target space being CP(N) which constitutes a generalization of the usual Skyrme-Faddeev model defined on CP(1). We show that it possesses an integrable sector presenting an infinite number of local conservation laws, which are associated to the hidden symmetries of the zero curvature representation of the theory in loop space. We construct an infinite class of exact solutions for that integrable submodel where the fields are meromorphic functions of the combinations (x(1) + i x(2)) and (x(3) + x(0)) of the Cartesian coordinates of four dimensional Minkowski space-time. Among those solutions we have static vortices and also vortices with waves traveling along them with the speed of light. The energy per unity of length of the vortices show an interesting and intricate interaction among the vortices and waves.

On E-functions of semisimple Lie groups

We develop and describe continuous and discrete transforms of class functions on a compact semisimple, but not simple, Lie group G as their expansions into series of special functions that are invariant under the action of the even subgroup of the Weyl group of G. We distinguish two cases of even Weyl groups-one is the direct product of even Weyl groups of simple components of G and the second is the full even Weyl group of G. The problem is rather simple in two dimensions. It is much richer in dimensions greater than two-we describe in detail E-transforms of semisimple Lie groups of rank 3.

The iron stimulon of Xylella fastidiosa includes genes for type IV pilus and colicin V-like bacteriocins

Xylella fastidiosa is the etiologic agent of a wide range of plant diseases, including citrus variegated chlorosis (CVC), a major threat to citrus industry. The genomes of several strains of this phytopathogen were completely sequenced, enabling large-scale functional studies. DNA microarrays representing 2,608 (91.6%) coding sequences (CDS) of X. fastidiosa CVC strain 9a5c were used to investigate transcript levels during growth with different iron availabilities. When treated with the iron chelator 2,2`-dipyridyl, 193 CDS were considered up-regulated and 216 were considered down-regulated. Upon incubation with 100 mu M ferric pyrophosphate, 218 and 256 CDS were considered up- and down-regulated, respectively. Differential expression for a subset of 44 CDS was further evaluated by reverse transcription-quantitative PCR. Several CDS involved with regulatory functions, pathogenicity, and cell structure were modulated under both conditions assayed, suggesting that major changes in cell architecture and metabolism occur when X. fastidiosa cells are exposed to extreme variations in iron concentration. Interestingly, the modulated CDS include those related to colicin V-like bacteriocin synthesis and secretion and to functions of pili/fimbriae. We also investigated the contribution of the ferric uptake regulator Fur to the iron stimulon of X. fastidiosa. The promoter regions of the strain 9a5c genome were screened for putative Fur boxes, and candidates were analyzed by electrophoretic mobility shift assays. Taken together, our data support the hypothesis that Fur is not solely responsible for the modulation of the iron stimulon of X fastidiosa, and they present novel evidence for iron regulation of pathogenicity determinants.