Differentiability of bizonal positive definite kernels on complex spheres

We prove that any continuous function with domain {z ∈ C: |z| ≤ 1} that generates a bizonal positive definite kernel on the unit sphere in 'C POT.Q' , q ⩾ 3, is continuously differentiable in {z ∈ C: |z| < 1} up to order q − 2, with respect to both z and 'Z BARRA'. In particular, the partial derivatives of the function with respect to x = Re z and y = Im z exist and are continuous in {z ∈ C: |z| < 1} up to the same order.

Measurement of flow harmonics with multi-particle cumulants in Pb+Pb collisions at √sNN=2.76 TeV with the ATLAS detector

ATLAS measurements of the azimuthal anisotropy in lead–lead collisions at √sNN = 2.76 TeV are shown using a dataset of approximately 7μb−1 collected at the LHC in 2010. The measurements are performed for charged particles with transversemomenta 0.5 < pT < 20 GeV and in the pseudorapidity range |η| < 2.5. The anisotropy is characterized by the Fourier coefficients, vn, of the charged-particle azimuthal angle distribution for n = 2–4. The Fourier coefficients are evaluated using multi-particle cumulants calculated with the generating function method. Results on the transverse momentum, pseudorapidity and centrality dependence of the vn coefficients are presented. The elliptic flow, v2, is obtained from the two-, four-, six- and eight-particle cumulants while higher-order coefficients, v3 and v4, are determined with two- and four-particle cumulants. Flow harmonics vn measured with four-particle cumulants are significantly reduced compared to the measurement involving two-particle cumulants. A comparison to vn measurements obtained using different analysis methods and previously reported by the LHC experiments is also shown. Results of measurements of flow fluctuations evaluated with multiparticle cumulants are shown as a function of transverse momentum and the collision centrality. Models of the initial spatial geometry and its fluctuations fail to describe the flow fluctuations measurements.

Modeling a health promotion campaign process

In this work we will present a model that describes how the number of healthy and unhealthy subjects that belong to a cohort, changes through time when there are occurrences of health promotion campaigns aiming to change the undesirable behavior. This model also includes immigration and emigration components for each group and a component taking into account when a subject that used to perform a healthy behavior changes to perform the unhealthy behavior. We will express the model in terms of a bivariate probability generating function and in addition we will simulate the model. ^ An illustrative example on how to apply the model to the promotion of condom use among adolescents will be created and we will use it to compare the results obtained from the simulations and the results obtained by the probability generating function. ^

Prospective run theory for multinomial outcomes

The focus of this study was to generalize the theory of runs to multinomial outcomes using the generating function approach. Detailed discussion is provided for determining the probability distributions for all runs of length i in a sequence of n trials for the binomial and trinomial cases. The generalization to multinomial case is also presented. Application to data for patients from a long term disability care facility is presented to illustrate the use of Run Theory in determining the probability of a dominant state of treatment associated with a patient during his/her hospitalization. ^

Characterization of cellular and molecular functions of the p21 -activated kinase, Shk1, in the fission yeast, Schizosaccharomyces pombe

The p21-activated kinase, Shk1, is an essential serine/threonine kinase required for normal cell polarity, proper mating response, and hyperosmotic stress response, in the fission yeast, Schizosaccharomyces pombe. This study has established a novel role for Shk1 as a microtubule regulator in fission yeast and, in addition, characterized a potential biological substrate of Shk1. Cells defective in Shk1 function were found to exhibit malformed interphase and mitotic microtubules, are hypersensitive to the microtubule disrupting drug thiabendazole (TBZ), and are cold sensitive for growth. Microtubule disruption by TBZ results in a significant reduction of Shk1 kinase activity, which is restored after cells are released from the drug, thus providing a correlation between Shk1 kinase activity and active microtubule polymerization. Consistent with a role for Shk1 as a microtubule regulator, GFP-Shk1 fusion proteins localize to interphase microtubules and mitotic microtubule spindles. Furthermore, loss of Tea1, a presumptive microtubule regulator in fission yeast, exacerbates the growth and microtubule defects of cells deficient in Shk1 function, and results in illicit Shk1 localization. Moreover, loss of the Cdc2 inhibitory kinase Wee1, which has been implicated as a mediator of the Shk1 pathway, leads to significant microtubule defects. Intriguingly, Wee1 protein levels are markedly reduced both by partial loss of Shk1 function and by treatment with TBZ. These results suggest that Shk1 is required for proper regulation of microtubule dynamics in fission yeast and may interact with Tea1 and Wee1 in this regulatory process. ^ To further understand Shk1 function in fission yeast, a yeast two-hybrid screen for proteins that interact with the Shk1 catalytic domain was performed. This screen led to the identification of a novel protein, Skb10 (for S&barbelow;hk1 k&barbelow;inase b&barbelow;inding protein 10). Coprecipitation experiments demonstrated that Skb10 associates with Shk1 in S. pombe cells. (Abstract shortened by UMI.) ^

Translation initiation factor eIF4G mediates in vitro poly(A) tail-dependent translation

The yeast translation factor eIF4G associates with both the cap-binding protein eIF4E and the poly(A)-binding protein Pab1p. Here we report that the two yeast eIF4G homologs, Tif4631p and Tif4632p, share a conserved Pab1p-binding site. This site is required for Pab1p and poly(A) tails to stimulate the in vitro translation of uncapped polyadenylylated mRNA, and the region encompassing it is required for the cap and the poly(A) tail to synergistically stimulate translation. This region on Tif4631p becomes essential for cell growth when the eIF4E binding site on Tif4631p is mutated. Pab1p mutations also show synthetic lethal interactions with eIF4E mutations. These data suggest that eIF4G mediates poly(A) tail stimulated translation in vitro, and that Pab1p and the domain encompassing the Pab1p-binding site on eIF4G can compensate for partial loss of eIF4E function in vivo.

Global GacA-steered control of cyanide and exoprotease production in Pseudomonas fluorescens involves specific ribosome binding sites

The conserved two-component regulatory system GacS/GacA determines the expression of extracellular products and virulence factors in a variety of Gram-negative bacteria. In the biocontrol strain CHA0 of Pseudomonas fluorescens, the response regulator GacA is essential for the synthesis of extracellular protease (AprA) and secondary metabolites including hydrogen cyanide. GacA was found to exert its control on the hydrogen cyanide biosynthetic genes (hcnABC) and on the aprA gene indirectly via a posttranscriptional mechanism. Expression of a translational hcnA′-′lacZ fusion was GacA-dependent whereas a transcriptional hcnA-lacZ fusion was not. A distinct recognition site overlapping with the ribosome binding site appears to be primordial for GacA-steered regulation. GacA-dependence could be conferred to the Escherichia coli lacZ mRNA by a 3-bp substitution in the ribosome binding site. The gene coding for the global translational repressor RsmA of P. fluorescens was cloned. RsmA overexpression mimicked partial loss of GacA function and involved the same recognition site, suggesting that RsmA is a downstream regulatory element of the GacA control cascade. Mutational inactivation of the chromosomal rsmA gene partially suppressed a gacS defect. Thus, a central, GacA-dependent switch from primary to secondary metabolism may operate at the level of translation.

Advances in random matrix theory, zeta functions, and sphere packing

Over four hundred years ago, Sir Walter Raleigh asked his mathematical assistant to find formulas for the number of cannonballs in regularly stacked piles. These investigations aroused the curiosity of the astronomer Johannes Kepler and led to a problem that has gone centuries without a solution: why is the familiar cannonball stack the most efficient arrangement possible? Here we discuss the solution that Hales found in 1998. Almost every part of the 282-page proof relies on long computer verifications. Random matrix theory was developed by physicists to describe the spectra of complex nuclei. In particular, the statistical fluctuations of the eigenvalues (“the energy levels”) follow certain universal laws based on symmetry types. We describe these and then discuss the remarkable appearance of these laws for zeros of the Riemann zeta function (which is the generating function for prime numbers and is the last special function from the last century that is not understood today.) Explaining this phenomenon is a central problem. These topics are distinct, so we present them separately with their own introductory remarks.

Formal group laws and hypergraph colorings

Thesis (Ph.D.)--University of Washington, 2016-06

Diplacanthid acanthodians from the Aztec Siltstone (late Middle Devonian) of southern Victoria Land, Antartica

One articulated and several partial, semi-articulated specimens of acanthodians were collected in 1970 from the freshwater deposits of the Aztec Siltstone (Middle Devonian; Givetian), Portal Mountain, southern Victoria Land, Antarctica, during a Victoria University of Wellington Antarctic Expedition. The Portal Mountain fish fauna, preserved in a finely laminated, non-calcareous siltstone, includes acanthodians, palaeoniscoids, and bothriolepid placoderms. The articulated acanthodian specimens are the most complete fossil fish remains documented so far from the Aztec assemblage, which is the most diverse fossil vertebrate fauna known from Antarctica. They are described as a new taxon, Milesacanthus antarctica gen. et sp. nov., which is assigned to the family Diplacanthidae. Its fin spines show some similarities to spine fragments named Byssacanthoides debenhami from glacial moraine at Granite Harbour, Antarctica, and much larger spines named Antarctonchus glacialis from outcrops of the Aztec Siltstone in the Boomerang Range, southern Victoria Land. Both of these are reviewed, and retained as form taxa for isolated spines. Various isolated remains of fin spines and scales are described from Portal Mountain and Mount Crean (Lashly Range), and referred to Milesacanthus antarctica gen. et sp. nov. The histology of spines and scales is documented for the first time, and compared with acanthodian material from the Devonian of Australia and Europe. Distinctive fin spines from Mount Crean are provisionally assigned to Culmacanthus antarctica Young, 1989b. Several features on the most complete of the new fish specimens - in particular, the apparent lack of an enlarged cheek plate - suggest a revision of the diagnosis for the Diplacanthidae.

CDMA multiuser detection, neural networks, and statistical mechanics

A novel approach, based on statistical mechanics, to analyze typical performance of optimum code-division multiple-access (CDMA) multiuser detectors is reviewed. A `black-box' view ot the basic CDMA channel is introduced, based on which the CDMA multiuser detection problem is regarded as a `learning-from-examples' problem of the `binary linear perceptron' in the neural network literature. Adopting Bayes framework, analysis of the performance of the optimum CDMA multiuser detectors is reduced to evaluation of the average of the cumulant generating function of a relevant posterior distribution. The evaluation of the average cumulant generating function is done, based on formal analogy with a similar calculation appearing in the spin glass theory in statistical mechanics, by making use of the replica method, a method developed in the spin glass theory.

Inhomogeneous Fractional Diffusion Equations

2000 Mathematics Subject Classification: Primary 26A33; Secondary 35S10, 86A05

Research on reliability evaluation of reconfigurable manufacturing system

It is a crucial task to evaluate the reliability of manufacturing process in product development process. Process reliability is a measurement of production ability of reconfigurable manufacturing system (RMS), which serves as an integrated performance indicator of the production process under specified technical constraints, including time, cost and quality. An integration framework of manufacturing process reliability evaluation is presented together with product development process. A mathematical model and algorithm based on universal generating function (UGF) is developed for calculating the reliability of manufacturing process with respect to task intensity and process capacity, which are both independent random variables. The rework strategies of RMS are analyzed under different task intensity based on process reliability is presented, and the optimization of rework strategies based on process reliability is discussed afterwards.

Randomized Push-Out Mechanisms in Priority Queuing and their Probability Characteristics

2002 Mathematics Subject Classification: 60K25.

Algebraic theory of minimal nondeterministic finite automata with applications

Since the 1950s, the theory of deterministic and nondeterministic finite automata (DFAs and NFAs, respectively) has been a cornerstone of theoretical computer science. In this dissertation, our main object of study is minimal NFAs. In contrast with minimal DFAs, minimal NFAs are computationally challenging: first, there can be more than one minimal NFA recognizing a given language; second, the problem of converting an NFA to a minimal equivalent NFA is NP-hard, even for NFAs over a unary alphabet. Our study is based on the development of two main theories, inductive bases and partials, which in combination form the foundation for an incremental algorithm, ibas, to find minimal NFAs. An inductive basis is a collection of languages with the property that it can generate (through union) each of the left quotients of its elements. We prove a fundamental characterization theorem which says that a language can be recognized by an n-state NFA if and only if it can be generated by an n-element inductive basis. A partial is an incompletely-specified language. We say that an NFA recognizes a partial if its language extends the partial, meaning that the NFA’s behavior is unconstrained on unspecified strings; it follows that a minimal NFA for a partial is also minimal for its language. We therefore direct our attention to minimal NFAs recognizing a given partial. Combining inductive bases and partials, we generalize our characterization theorem, showing that a partial can be recognized by an n-state NFA if and only if it can be generated by an n-element partial inductive basis. We apply our theory to develop and implement ibas, an incremental algorithm that finds minimal partial inductive bases generating a given partial. In the case of unary languages, ibas can often find minimal NFAs of up to 10 states in about an hour of computing time; with brute-force search this would require many trillions of years.