Parametrizations of elliptic curves by Shimura curves and by classical modular curves

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SMART, a simple modular architecture research tool: Identification of signaling domains

Accurate multiple alignments of 86 domains that occur in signaling proteins have been constructed and used to provide a Web-based tool (SMART: simple modular architecture research tool) that allows rapid identification and annotation of signaling domain sequences. The majority of signaling proteins are multidomain in character with a considerable variety of domain combinations known. Comparison with established databases showed that 25% of our domain set could not be deduced from SwissProt and 41% could not be annotated by Pfam. SMART is able to determine the modular architectures of single sequences or genomes; application to the entire yeast genome revealed that at least 6.7% of its genes contain one or more signaling domains, approximately 350 greater than previously annotated. The process of constructing SMART predicted (i) novel domain homologues in unexpected locations such as band 4.1-homologous domains in focal adhesion kinases; (ii) previously unknown domain families, including a citron-homology domain; (iii) putative functions of domain families after identification of additional family members, for example, a ubiquitin-binding role for ubiquitin-associated domains (UBA); (iv) cellular roles for proteins, such predicted DEATH domains in netrin receptors further implicating these molecules in axonal guidance; (v) signaling domains in known disease genes such as SPRY domains in both marenostrin/pyrin and Midline 1; (vi) domains in unexpected phylogenetic contexts such as diacylglycerol kinase homologues in yeast and bacteria; and (vii) likely protein misclassifications exemplified by a predicted pleckstrin homology domain in a Candida albicans protein, previously described as an integrin.

Adjoint modular Galois representations and their Selmer groups

In the last 15 years, many class number formulas and main conjectures have been proven. Here, we discuss such formulas on the Selmer groups of the three-dimensional adjoint representation ad(φ) of a two-dimensional modular Galois representation φ. We start with the p-adic Galois representation φ0 of a modular elliptic curve E and present a formula expressing in terms of L(1, ad(φ0)) the intersection number of the elliptic curve E and the complementary abelian variety inside the Jacobian of the modular curve. Then we explain how one can deduce a formula for the order of the Selmer group Sel(ad(φ0)) from the proof of Wiles of the Shimura–Taniyama conjecture. After that, we generalize the formula in an Iwasawa theoretic setting of one and two variables. Here the first variable, T, is the weight variable of the universal p-ordinary Hecke algebra, and the second variable is the cyclotomic variable S. In the one-variable case, we let φ denote the p-ordinary Galois representation with values in GL2(Zp[[T]]) lifting φ0, and the characteristic power series of the Selmer group Sel(ad(φ)) is given by a p-adic L-function interpolating L(1, ad(φk)) for weight k + 2 specialization φk of φ. In the two-variable case, we state a main conjecture on the characteristic power series in Zp[[T, S]] of Sel(ad(φ) ⊗ ν−1), where ν is the universal cyclotomic character with values in Zp[[S]]. Finally, we describe our recent results toward the proof of the conjecture and a possible strategy of proving the main conjecture using p-adic Siegel modular forms.

Congruences between modular forms: Raising the level and dropping Euler factors

We discuss the relationship among certain generalizations of results of Hida, Ribet, and Wiles on congruences between modular forms. Hida’s result accounts for congruences in terms of the value of an L-function, and Ribet’s result is related to the behavior of the period that appears there. Wiles’ theory leads to a class number formula relating the value of the L-function to the size of a Galois cohomology group. The behavior of the period is used to deduce that a formula at “nonminimal level” is obtained from one at “minimal level” by dropping Euler factors from the L-function.

Modular organization of intrinsic connections associated with spectral tuning in cat auditory cortex

Many response properties in primary auditory cortex (AI) are segregated spatially and organized topographically as those in primary visual cortex. Intensive study has not revealed an intrinsic, anatomical organizing principle related to an AI functional topography. We used retrograde anatomic tracing and topographic physiologic mapping of acoustic response properties to reveal long-range (≥1.5 mm) convergent intrinsic horizontal connections between AI subregions with similar bandwidth and characteristic frequency selectivity. This suggests a modular organization for processing spectral bandwidth in AI.

Modular construction for function of a ribonucleoprotein enzyme: the catalytic domain of Bacillus subtilis RNase P complexed with B.subtilis RNase P protein

The bacterial RNase P holoenzyme catalyzes the formation of the mature 5′-end of tRNAs and is composed of an RNA and a protein subunit. Among the two folding domains of the RNase P RNA, the catalytic domain (C-domain) contains the active site of this ribozyme. We investigated specific binding of the Bacillus subtilis C-domain with the B.subtilis RNase P protein and examined the catalytic activity of this C-domain–P protein complex. The C-domain forms a specific complex with the P protein with a binding constant of ∼0.1 µM. The C-domain–P protein complex and the holoenzyme are equally efficient in cleaving single-stranded RNA (∼0.9 min–1 at pH 7.8) and substrates with a hairpin–loop 3′ to the cleavage site (∼40 min–1). The holoenzyme reaction is much more efficient with a pre-tRNA substrate, binding at least 100-fold better and cleaving 10–500 times more efficiently. These results demonstrate that the RNase P holoenzyme is functionally constructed in three parts. The catalytic domain alone contains the active site, but has little specificity and affinity for most substrates. The specificity and affinity for the substrate is generated by either the specificity domain of RNase P RNA binding to a T stem–loop-like hairpin or RNase P protein binding to a single-stranded RNA. This modular construction may be exploited to obtain RNase P-based ribonucleoprotein complexes with altered substrate specificity.

A modular misexpression screen in Drosophila detecting tissue-specific phenotypes.

Genetic screens in Drosophila have lead to the discovery of many genes important for patterning and signal transduction in diverse organisms. Traditionally, the phenotypic effects of loss-of-function mutations are analyzed. As an alternative way to link genes and function, I have developed a versatile misexpression screen in Drosophila, the first such screen in higher eukaryotes. The screen identifies genes that, when over- or misexpressed in a pattern of interest, give a specific phenotype or modulate an existing mutant phenotype. It is based on Gal4 transactivation of a mobile enhancer and promoter that "targets" random endogenous genes for expression. The modular design of the screen allows directed expression in any temporal or spatial pattern. When activated in the developing eye, 4% of target inserts gave dominant phenotypes. One insertion was in the gene encoding Ras GTPase-activating protein; its overexpression phenotype was strongly enhanced by a mutation in Ras1. Thus, biologically relevant phenotypes and genetic interactions are identified using this method. The screen is a powerful new tool for developmental genetics; similar approaches can also be developed for other organisms.

Modular cis-regulatory organization of developmentally expressed genes: two genes transcribed territorially in the sea urchin embryo, and additional examples.

The cis-regulatory systems that control developmental expression of two sea urchin genes have been subjected to detailed functional analysis. Both systems are modular in organization: specific, separable fragments of the cis-regulatory DNA each containing multiple transcription factor target sites execute particular regulatory subfunctions when associated with reporter genes and introduced into the embryo. The studies summarized here were carried out on the CyIIIa gene, expressed in the embryonic aboral ectoderm and on the Endo16 gene, expressed in the embryonic vegetal plate, archenteron, and then midgut. The regulatory systems of both genes include modules that control particular aspects of temporal and spatial expression, and in both the territorial boundaries of expression depend on a combination of negative and positive functions. In both genes different regulatory modules control early and late embryonic expression. Modular cis-regulatory organization is widespread in developmentally regulated genes, and we present a tabular summary that includes many examples from mouse and Drosophila. We regard cis-regulatory modules as units of developmental transcription control, and also of evolution, in the assembly of transcription control systems.

Structure-activity relationships derived by machine learning: the use of atoms and their bond connectivities to predict mutagenicity by inductive logic programming.

We present a general approach to forming structure-activity relationships (SARs). This approach is based on representing chemical structure by atoms and their bond connectivities in combination with the inductive logic programming (ILP) algorithm PROGOL. Existing SAR methods describe chemical structure by using attributes which are general properties of an object. It is not possible to map chemical structure directly to attribute-based descriptions, as such descriptions have no internal organization. A more natural and general way to describe chemical structure is to use a relational description, where the internal construction of the description maps that of the object described. Our atom and bond connectivities representation is a relational description. ILP algorithms can form SARs with relational descriptions. We have tested the relational approach by investigating the SARs of 230 aromatic and heteroaromatic nitro compounds. These compounds had been split previously into two subsets, 188 compounds that were amenable to regression and 42 that were not. For the 188 compounds, a SAR was found that was as accurate as the best statistical or neural network-generated SARs. The PROGOL SAR has the advantages that it did not need the use of any indicator variables handcrafted by an expert, and the generated rules were easily comprehensible. For the 42 compounds, PROGOL formed a SAR that was significantly (P < 0.025) more accurate than linear regression, quadratic regression, and back-propagation. This SAR is based on an automatically generated structural alert for mutagenicity.

Broadening the Scope of Ethnic Identity: A Social Sustainability Solution for Pan African Communities through Ethnically Relevant Educational Programming

This conceptual study explores ethnic identity development theory in order to argue that ethnic identity development education is a means of developing broad senses of community in the African Diaspora that expand beyond a tribal, local, familial level. This study suggests that the broadening of community understanding would contribute to establishing social sustainability on regional, national and international levels within the Pan African community. Establishing such social sustainability would have direct effects on the areas of economic and environmental sustainability. One of the goals of this project is to offer suggestions for ethnically relevant education that can develop social sustainability in several places throughout the Diaspora, such as in Nigeria where ethnic conflicts are a contemporary concern.

COMPENDIUM: una herramienta de generación de resúmenes modular

En este artículo presentamos COMPENDIUM, una herramienta de generación de resúmenes de textos modular. Esta herramienta se compone de un módulo central con cinco etapas bien diferenciadas: i) análisis lingüístico; ii) detección de redundancia; iii) identificación del tópico; iv) detección de relevancia; y v) generación del resumen, y una serie de módulos adicionales que permiten incrementar las funcionalidades de la herramienta permitiendo la generación de distintos tipos de resúmenes, como por ejemplo orientados a un tema concreto. Realizamos una evaluación exhaustiva en dos dominios distintos (noticias de prensa y documentos sobre lugares turísticos) y analizamos diferentes tipos de resúmenes generados con COMPENDIUM (mono-documento, multi-documento, genéricos y orientados a un tema). Además, comparamos nuestro sistema con otros sistemas de generación de resúmenes actuales. Los resultados que se obtienen demuestran que la herramienta COMPENDIUM es capaz de generar resúmenes competitivos para los distintos tipos de resúmenes propuestos.

Robust linear semi-infinite programming duality under uncertainty

In this paper, we propose a duality theory for semi-infinite linear programming problems under uncertainty in the constraint functions, the objective function, or both, within the framework of robust optimization. We present robust duality by establishing strong duality between the robust counterpart of an uncertain semi-infinite linear program and the optimistic counterpart of its uncertain Lagrangian dual. We show that robust duality holds whenever a robust moment cone is closed and convex. We then establish that the closed-convex robust moment cone condition in the case of constraint-wise uncertainty is in fact necessary and sufficient for robust duality. In other words, the robust moment cone is closed and convex if and only if robust duality holds for every linear objective function of the program. In the case of uncertain problems with affinely parameterized data uncertainty, we establish that robust duality is easily satisfied under a Slater type constraint qualification. Consequently, we derive robust forms of the Farkas lemma for systems of uncertain semi-infinite linear inequalities.

Integration of different models in the design of chemical processes: Application to the design of a power plant

With advances in the synthesis and design of chemical processes there is an increasing need for more complex mathematical models with which to screen the alternatives that constitute accurate and reliable process models. Despite the wide availability of sophisticated tools for simulation, optimization and synthesis of chemical processes, the user is frequently interested in using the ‘best available model’. However, in practice, these models are usually little more than a black box with a rigid input–output structure. In this paper we propose to tackle all these models using generalized disjunctive programming to capture the numerical characteristics of each model (in equation form, modular, noisy, etc.) and to deal with each of them according to their individual characteristics. The result is a hybrid modular–equation based approach that allows synthesizing complex processes using different models in a robust and reliable way. The capabilities of the proposed approach are discussed with a case study: the design of a utility system power plant that has been decomposed into its constitutive elements, each treated differently numerically. And finally, numerical results and conclusions are presented.

Mathematical programming model for heat exchanger design through optimization of partial objectives

Mathematical programming can be used for the optimal design of shell-and-tube heat exchangers (STHEs). This paper proposes a mixed integer non-linear programming (MINLP) model for the design of STHEs, following rigorously the standards of the Tubular Exchanger Manufacturers Association (TEMA). Bell–Delaware Method is used for the shell-side calculations. This approach produces a large and non-convex model that cannot be solved to global optimality with the current state of the art solvers. Notwithstanding, it is proposed to perform a sequential optimization approach of partial objective targets through the division of the problem into sets of related equations that are easier to solve. For each one of these problems a heuristic objective function is selected based on the physical behavior of the problem. The global optimal solution of the original problem cannot be ensured even in the case in which each of the sub-problems is solved to global optimality, but at least a very good solution is always guaranteed. Three cases extracted from the literature were studied. The results showed that in all cases the values obtained using the proposed MINLP model containing multiple objective functions improved the values presented in the literature.

La enseñanza de robótica en el Máster en Automática y Robótica mediante un robot modular

Este trabajo muestra cómo se realiza la enseñanza de robótica mediante un robot modular y los resultados educativos obtenidos en el Máster Universitario en Automática y Robótica de la Escuela Politécnica Superior de la Universidad de Alicante. En el artículo se describen los resultados obtenidos con el uso de este robot modular tanto en competencias genéricas como específicas, en las enseñanzas de electrónica, control y programación del Máster. En este artículo se exponen los objetivos de aprendizaje para cada uno de ellos, su aplicación a la enseñanza y los resultados educativos obtenidos. En los resultados del estudio, cabe destacar que el alumno ha mostrado mayor interés y ha fomentado su aprendizaje autónomo. Para ello, el robot modular se construyó con herramientas para fomentar este tipo de enseñanza y aprendizaje, tales como comunicaciones interactivas para monitorizar, cambiar y adaptar diversos parámetros de control y potencia del robot.