Complex variable positive definite functions

In this paper we develop an appropriate theory of positive definite functions on the complex plane from first principles and show some consequences of positive definiteness for meromorphic functions.

Mitotic functions for SNAP45, a subunit of the small nuclear RNA-activating protein complex SNAPc.

The small nuclear RNA-activating protein complex SNAP(c) is required for transcription of small nuclear RNA genes and binds to a proximal sequence element in their promoters. SNAP(c) contains five types of subunits stably associated with each other. Here we show that one of these polypeptides, SNAP45, also known as PTF delta, localizes to centrosomes during parts of mitosis, as well as to the spindle midzone during anaphase and the mid-body during telophase. Consistent with localization to these mitotic structures, both down- and up-regulation of SNAP45 lead to a G(2)/M arrest with cells displaying abnormal mitotic structures. In contrast, down-regulation of SNAP190, another SNAP(c) subunit, leads to an accumulation of cells with a G(0)/G(1) DNA content. These results are consistent with the proposal that SNAP45 plays two roles in the cell, one as a subunit of the transcription factor SNAP(c) and another as a factor required for proper mitotic progression.

Using spatially distributed parameters and multi-response objective functions to solve parameterization of complex applications of semi-distributed hydrological models

Application of semi-distributed hydrological models to large, heterogeneous watersheds deals with several problems. On one hand, the spatial and temporal variability in catchment features should be adequately represented in the model parameterization, while maintaining the model complexity in an acceptable level to take advantage of state-of-the-art calibration techniques. On the other hand, model complexity enhances uncertainty in adjusted model parameter values, therefore increasing uncertainty in the water routing across the watershed. This is critical for water quality applications, where not only streamflow, but also a reliable estimation of the surface versus subsurface contributions to the runoff is needed. In this study, we show how a regularized inversion procedure combined with a multiobjective function calibration strategy successfully solves the parameterization of a complex application of a water quality-oriented hydrological model. The final value of several optimized parameters showed significant and consistentdifferences across geological and landscape features. Although the number of optimized parameters was significantly increased by the spatial and temporal discretization of adjustable parameters, the uncertainty in water routing results remained at reasonable values. In addition, a stepwise numerical analysis showed that the effects on calibration performance due to inclusion of different data types in the objective function could be inextricably linked. Thus caution should be taken when adding or removing data from an aggregated objective function.

A novel trinuclear nickel(II) complex of an unsymmetrical tetradentate ligand involving bridging oxime and acetylacetone functions

A novel trinuclear nickel(II) complex, [Ni-3(L)(2)(H2O)(2)](ClO4)(2), where L is a bridging unsymmetrical tetradentate ligand, involving o-phenylenediamine, diacetyl monoxime and acetylacetone (H2L = 4-[2-(3-hydroxy-1-methyl-but-2-enylideneamino)-phenylimino]-pentan-2- one oxime) has been synthesized and characterized structurally. In the complex, an octahedral Ni( II) centre is held in the middle by two square planar units with the aid of oxime and ketonic bridges. (c) 2007 Elsevier B. V. All rights reserved.

Intelligence functions disorders in patients with complex partial epilepsy

Objective: To compare the performance of patients with complex partial epilepsy with the normal controls in the subtests of an instrument used to assess intelligence function. Method: Fifty epileptic patients, whose ages ranged from 19 to 49 years and 20 normal controls without any neuropsychiatric disorders. The Wechsler-Bellevue adult intelligence test was applied in groups, epileptic patients and control subjects. This test is composed of several subtests that assess specific cognitive functions. A statistical analysis was performed using non-parametric tests. Results: All the Wechsler-Bellevue subtests revealed that the intelligence functions of the patients were significantly inferior to that of the controls (p<0.05). This performance was supported by the patient's complaints in relation to their cognitive performance. Conclusion: Patients with complex partial epilepsy presented poorer results in the intelligence test when compared with individuals without neuropsychiatric disorders.

CELLULAR AND DEVELOPMENTAL FUNCTIONS OF THE XENOPUS ARVCF-CATENIN:KAZRIN COMPLEX

Xenopus ARVCF (xARVCF), a member of p120-catenin subfamily, binds cadherin cytoplasmic domains to enhance cadherin metabolic stability, or when dissociated, modulates Rho-family GTPases. We previously found that xARVCF binds directly to Xenopus KazrinA (xKazrinA), a widely expressed, conserved protein that bears little homology to established protein families. xKazrinA is also known to influence keratinocyte proliferation-differentiation and cytoskeletal activity. In my study, I first evaluated the expression pattern of endogenous Kazrin RNA and protein in Xenopus embryogenesis as well as in adult tissues. We then collaboratively predicted the helical structure of Kazrin’s coiled-coil domain, and I obtained evidence of Kazrin’s dimerization/oligomerization. In considering the intracellular localization of the xARVCF-catenin:xKazrin complex, I did not resolve xKazrinA in a larger ternary complex with cadherin, nor did I detect its co-precipitation with core desmosomal components. Instead, screening revealed that xKazrinA binds spectrin. This suggested a potential means by which xKazrinA localizes to cell-cell junctions, and indeed, biochemical assays confirmed a ternary xARVCF:xKazrinA:xβ2-spectrin complex. Functionally, I demonstrated that xKazrin stabilizes cadherins by negatively modulating the RhoA small-GTPase. I further revealed that xKazrinA binds to p190B RhoGAP (an inhibitor of RhoA), and enhances p190B’s association with xARVCF. Supporting their functional interaction in vivo, Xenopus embryos depleted of xKazrin exhibited ectodermal shedding, a phenotype that could be rescued with exogenous xARVCF. Cell shedding appeared to be caused by RhoA activation, which consequently altered actin organization and cadherin function. Indeed, I was capable of rescuing Kazrin depletion with ectopic expression of p190B RhoGAP. In addition, I obtained evidence that xARVCF and xKazrin participate in craniofacial development, with effects observed upon the neural crest. Finally, I found that xKazrinA associates further with delta-catenin and p0071-catenin, but not with p120-catenin, suggesting that Kazrin interacts selectively with additional members of the p120-catenin sub-family. Taken together, my study supports Kazrin’s essential role in development, and reveals KazrinA’s biochemical and functional association with ARVCF-catenin, spectrin and p190B RhoGAP.

A Genetic Analysis of Interactions with Spc110p Reveals Distinct Functions of Spc97p and Spc98p, Components of the Yeast γ-Tubulin Complex

The spindle pole body (SPB) in Saccharomyces cerevisiae functions as the microtubule-organizing center. Spc110p is an essential structural component of the SPB and spans between the central and inner plaques of this multilamellar organelle. The amino terminus of Spc110p faces the inner plaque, the substructure from which spindle microtubules radiate. We have undertaken a synthetic lethal screen to identify mutations that enhance the phenotype of the temperature-sensitive spc110–221 allele, which encodes mutations in the amino terminus. The screen identified mutations in SPC97 and SPC98, two genes encoding components of the Tub4p complex in yeast. The spc98–63 allele is synthetic lethal only with spc110 alleles that encode mutations in the N terminus of Spc110p. In contrast, the spc97 alleles are synthetic lethal with spc110 alleles that encode mutations in either the N terminus or the C terminus. Using the two-hybrid assay, we show that the interactions of Spc110p with Spc97p and Spc98p are not equivalent. The N terminus of Spc110p displays a robust interaction with Spc98p in two different two-hybrid assays, while the interaction between Spc97p and Spc110p is not detectable in one strain and gives a weak signal in the other. Extra copies of SPC98 enhance the interaction between Spc97p and Spc110p, while extra copies of SPC97 interfere with the interaction between Spc98p and Spc110p. By testing the interactions between mutant proteins, we show that the lethal phenotype in spc98–63 spc110–221 cells is caused by the failure of Spc98–63p to interact with Spc110–221p. In contrast, the lethal phenotype in spc97–62 spc110–221 cells can be attributed to a decreased interaction between Spc97–62p and Spc98p. Together, these studies provide evidence that Spc110p directly links the Tub4p complex to the SPB. Moreover, an interaction between Spc98p and the amino-terminal region of Spc110p is a critical component of the linkage, whereas the interaction between Spc97p and Spc110p is dependent on Spc98p.

Drosophila Heterochromatin Protein 1 (HP1)/Origin Recognition Complex (ORC) Protein Is Associated with HP1 and ORC and Functions in Heterochromatin-induced Silencing

Heterochromatin protein 1 (HP1) is a conserved component of the highly compact chromatin of higher eukaryotic centromeres and telomeres. Cytogenetic experiments in Drosophila have shown that HP1 localization into this chromatin is perturbed in mutants for the origin recognition complex (ORC) 2 subunit. ORC has a multisubunit DNA-binding activity that binds origins of DNA replication where it is required for origin firing. The DNA-binding activity of ORC is also used in the recruitment of the Sir1 protein to silence nucleation sites flanking silent copies of the mating-type genes in Saccharomyces cerevisiae. A fraction of HP1 in the maternally loaded cytoplasm of the early Drosophila embryo is associated with a multiprotein complex containing Drosophila melanogaster ORC subunits. This complex appears to be poised to function in heterochromatin assembly later in embryonic development. Here we report the identification of a novel component of this complex, the HP1/ORC-associated protein. This protein contains similarity to DNA sequence-specific HMG proteins and is shown to bind specific satellite sequences and the telomere-associated sequence in vitro. The protein is shown to have heterochromatic localization in both diploid interphase and mitotic chromosomes and polytene chromosomes. Moreover, the gene encoding HP1/ORC-associated protein was found to display reciprocal dose-dependent variegation modifier phenotypes, similar to those for mutants in HP1 and the ORC 2 subunit.

Generation of representation models for complex systems using Lagrangian functions

In this article, a new methodology is presented to obtain representation models for a priori relation z = u(x1, x2, . . . ,xn) (1), with a known an experimental dataset zi; x1i ; x2i ; x3i ; . . . ; xni i=1;2;...;p· In this methodology, a potential energy is initially defined over each possible model for the relationship (1), what allows the application of the Lagrangian mechanics to the derived system. The solution of the Euler–Lagrange in this system allows obtaining the optimal solution according to the minimal action principle. The defined Lagrangian, corresponds to a continuous medium, where a n-dimensional finite elements model has been applied, so it is possible to get a solution for the problem solving a compatible and determined linear symmetric equation system. The computational implementation of the methodology has resulted in an improvement in the process of get representation models obtained and published previously by the authors.

Disipation Functions of Flow Equations in Models of Complex Systems

In an open system, each disequilibrium causes a force. Each force causes a flow process, these being represented by a flow variable formally written as an equation called flow equation, and if each flow tends to equilibrate the system, these equations mathematically represent the tendency to that equilibrium. In this paper, the authors, based on the concepts of forces and conjugated fluxes and dissipation function developed by Onsager and Prigogine, they expose the following hypothesis: Is replaced in Prigogine’s Theorem the flow by its equation or by a flow orbital considering conjugate force as a gradient. This allows to obtain a dissipation function for each flow equation and a function of orbital dissipation.

The theory of functions of a complex variable. [Lectures] New York University, Institute for Mathematics and Mechanics.

"First edition 1948. Second printing 1952."

Functions of real variables. Functions of a complex variable.

Mode of access: Internet.

Tables of complex hyperbolic and circular functions,

Bibliography: p. 209-212.

Elements of the theory of functions of a complex variable with especial reference to the methods of Riemann,

Translation of Elemente der Theorie der Funktionen einer complexen veränderlichen Grösse.