The Bonenblust-Hille inequality for homogeneous polynomials is hypercontractive

The Bohnenblust-Hille inequality says that the $\ell^{\frac{2m}{m+1}}$ -norm of the coefficients of an $m$-homogeneous polynomial $P$ on $\Bbb{C}^n$ is bounded by $\| P \|_\infty$ times a constant independent of $n$, where $\|\cdot \|_\infty$ denotes the supremum norm on the polydisc $\mathbb{D}^n$. The main result of this paper is that this inequality is hypercontractive, i.e., the constant can be taken to be $C^m$ for some $C>1$. Combining this improved version of the Bohnenblust-Hille inequality with other results, we obtain the following: The Bohr radius for the polydisc $\mathbb{D}^n$ behaves asymptotically as $\sqrt{(\log n)/n}$ modulo a factor bounded away from 0 and infinity, and the Sidon constant for the set of frequencies $\bigl\{ \log n: n \text{a positive integer} \le N\bigr\}$ is $\sqrt{N}\exp\{(-1/\sqrt{2}+o(1))\sqrt{\log N\log\log N}\}$.

Numerical quadrature over a rectangular domain in two or more dimensions /

"This work was supported in part by the Office of Naval Research under Contract Nonr-1834(27)."

Elementar entwickelte Theorie und Praxis der Functionen einer complexen Variabelen in organischer Verbindung mit der Geometrie.

Mode of access: Internet.

Elemente der Theorie der Funktionen einer complexen veränderlichen Grösse, mit besonderer Berücksichtigung der Schöpfungen Riemann's.

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Leçons sur les séries de polynomes à une variable complexe;

Available on demand as hard copy or computer file from Cornell University Library.

Abriss einer theorie der algebraischen funktionen einer veränderlichen in neuer fassung ...

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Elemente der Theorie der Funktionen einer komplexen veränderlichen grösse.

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Elementare theorie der analytischen functionen einer complexen veränderlichen.

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Leçons sur les fonctions monogènes uniformes d'une variable complexe;

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Reducing the number of membership functions in linguistic variables

Dissertation presented at Universidade Nova de Lisboa, Faculdade de Ciências e Tecnologia in fulfilment of the requirements for the Masters degree in Mathematics and Applications, specialization in Actuarial Sciences, Statistics and Operations Research

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.

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.

Nonlinear indicial response of complex nonstationary oscillations as pulmonary hypertension responding to step hypoxia

This paper is devoted to the quantization of the degree of nonlinearity of the relationship between two biological variables when one of the variables is a complex nonstationary oscillatory signal. An example of the situation is the indicial responses of pulmonary blood pressure (P) to step changes of oxygen tension (ΔpO2) in the breathing gas. For a step change of ΔpO2 beginning at time t1, the pulmonary blood pressure is a nonlinear function of time and ΔpO2, which can be written as P(t-t1 | ΔpO2). An effective method does not exist to examine the nonlinear function P(t-t1 | ΔpO2). A systematic approach is proposed here. The definitions of mean trends and oscillations about the means are the keys. With these keys a practical method of calculation is devised. We fit the mean trends of blood pressure with analytic functions of time, whose nonlinearity with respect to the oxygen level is clarified here. The associated oscillations about the mean can be transformed into Hilbert spectrum. An integration of the square of the Hilbert spectrum over frequency yields a measure of oscillatory energy, which is also a function of time, whose mean trends can be expressed by analytic functions. The degree of nonlinearity of the oscillatory energy with respect to the oxygen level also is clarified here. Theoretical extension of the experimental nonlinear indicial functions to arbitrary history of hypoxia is proposed. Application of the results to tissue remodeling and tissue engineering of blood vessels is discussed.