Special Frobenius Traces in Galois Representations

This thesis studies Frobenius traces in Galois representations from two different directions. In the first problem we explore how often they vanish in Artin-type representations. We give an upper bound for the density of the set of vanishing Frobenius traces in terms of the multiplicities of the irreducible components of the adjoint representation. Towards that, we construct an infinite family of representations of finite groups with an irreducible adjoint action.

In the second problem we partially extend for Hilbert modular forms a result of Coleman and Edixhoven that the Hecke eigenvalues a_p of classical elliptical modular newforms f of weight 2 are never extremal, i.e., a_p is strictly less than 2[square root]p. The generalization currently applies only to prime ideals p of degree one, though we expect it to hold for p of any odd degree. However, an even degree prime can be extremal for f. We prove our result in each of the following instances: when one can move to a Shimura curve defined by a quaternion algebra, when f is a CM form, when the crystalline Frobenius is semi-simple, and when the strong Tate conjecture holds for a product of two Hilbert modular surfaces (or quaternionic Shimura surfaces) over a finite field.

Programming chemical kinetics: engineering dynamic reaction networks with DNA strand displacement

Over the last century, the silicon revolution has enabled us to build faster, smaller and more sophisticated computers. Today, these computers control phones, cars, satellites, assembly lines, and other electromechanical devices. Just as electrical wiring controls electromechanical devices, living organisms employ "chemical wiring" to make decisions about their environment and control physical processes. Currently, the big difference between these two substrates is that while we have the abstractions, design principles, verification and fabrication techniques in place for programming with silicon, we have no comparable understanding or expertise for programming chemistry.

In this thesis we take a small step towards the goal of learning how to systematically engineer prescribed non-equilibrium dynamical behaviors in chemical systems. We use the formalism of chemical reaction networks (CRNs), combined with mass-action kinetics, as our programming language for specifying dynamical behaviors. Leveraging the tools of nucleic acid nanotechnology (introduced in Chapter 1), we employ synthetic DNA molecules as our molecular architecture and toehold-mediated DNA strand displacement as our reaction primitive.

Abstraction, modular design and systematic fabrication can work only with well-understood and quantitatively characterized tools. Therefore, we embark on a detailed study of the "device physics" of DNA strand displacement (Chapter 2). We present a unified view of strand displacement biophysics and kinetics by studying the process at multiple levels of detail, using an intuitive model of a random walk on a 1-dimensional energy landscape, a secondary structure kinetics model with single base-pair steps, and a coarse-grained molecular model that incorporates three-dimensional geometric and steric effects. Further, we experimentally investigate the thermodynamics of three-way branch migration. Our findings are consistent with previously measured or inferred rates for hybridization, fraying, and branch migration, and provide a biophysical explanation of strand displacement kinetics. Our work paves the way for accurate modeling of strand displacement cascades, which would facilitate the simulation and construction of more complex molecular systems.

In Chapters 3 and 4, we identify and overcome the crucial experimental challenges involved in using our general DNA-based technology for engineering dynamical behaviors in the test tube. In this process, we identify important design rules that inform our choice of molecular motifs and our algorithms for designing and verifying DNA sequences for our molecular implementation. We also develop flexible molecular strategies for "tuning" our reaction rates and stoichiometries in order to compensate for unavoidable non-idealities in the molecular implementation, such as imperfectly synthesized molecules and spurious "leak" pathways that compete with desired pathways.

We successfully implement three distinct autocatalytic reactions, which we then combine into a de novo chemical oscillator. Unlike biological networks, which use sophisticated evolved molecules (like proteins) to realize such behavior, our test tube realization is the first to demonstrate that Watson-Crick base pairing interactions alone suffice for oscillatory dynamics. Since our design pipeline is general and applicable to any CRN, our experimental demonstration of a de novo chemical oscillator could enable the systematic construction of CRNs with other dynamic behaviors.

MODIFIED DIRECT TWOS-COMPLEMENT PARALLEL ARRAY MULTIPLICATION ALGORITHM FOR COMPLEX MATRIX OPERATION

A direct twos-complement parallel array multiplication algorithm is introduced and modified for digital optical numerical computation. The modified version overcomes the problems encountered in the conventional optical twos-complement algorithm. In the array, all the summands are generated in parallel, and the relevant summands having the same weights are added simultaneously without carries, resulting in the product expressed in a mixed twos-complement system. In a two-stage array, complex multiplication is possible with using four real subarrays. Furthermore, with a three-stage array architecture, complex matrix operation is straightforwardly accomplished. In the experiment, parallel two-stage array complex multiplication with liquid-crystal panels is demonstrated.

Visual pattern recognition network: Its training algorithm and its optoelectronic architecture

A visual pattern recognition network and its training algorithm are proposed. The network constructed of a one-layer morphology network and a two-layer modified Hamming net. This visual network can implement invariant pattern recognition with respect to image translation and size projection. After supervised learning takes place, the visual network extracts image features and classifies patterns much the same as living beings do. Moreover we set up its optoelectronic architecture for real-time pattern recognition. (C) 1996 Optical Society of America

Code conversion from signed-digit to complement representation based on look-ahead optical logic operations

We present, for the first time to our knowledge, a generalized lookahead logic algorithm for number conversion from signed-digit to complement representation. By properly encoding the signed-digits, all the operations are performed by binary logic, and unified logical expressions can be obtained for conversion from modified-signed-digit (MSD) to 2's complement, trinary signed-digit (TSD) to 3's complement, and quarternary signed-digit (QSD) to 4's complement. For optical implementation, a parallel logical array module using an electron-trapping device is employed and experimental results are shown. This optical module is suitable for implementing complex logic functions in the form of the sum of the product. The algorithm and architecture are compatible with a general-purpose optoelectronic computing system. (C) 2001 Society of Photo-Optical Instrumentation Engineers.

Caretta caretta (Loggerhead Sea Turtle). Nest Architecture.

Researchers compared nest architecture in loggerhead sea turtles at natural beaches in Florida, USA and Brazil to determine how similarities and differences in female morphology and reproductive output in these two populations are reflected in the structure of the nest.

4th European Conference on Energy Efficiency and Sustainability in Architecture and Planning : Donostia-San Sebastián, 1-3 Julio 2013

XXXII Cursos de Verano de la UPV/EHU

5th European Conference on Energy Efficiency and Sustainability in Architecture and Planning : Donostia-San Sebastián, 7-9 Julio 2014

XXXIII Cursos de Verano de la UPV/EHU

Distributed Optimal Control of Cyber-Physical Systems: Controller Synthesis, Architecture Design and System Identification

The centralized paradigm of a single controller and a single plant upon which modern control theory is built is no longer applicable to modern cyber-physical systems of interest, such as the power-grid, software defined networks or automated highways systems, as these are all large-scale and spatially distributed. Both the scale and the distributed nature of these systems has motivated the decentralization of control schemes into local sub-controllers that measure, exchange and act on locally available subsets of the globally available system information. This decentralization of control logic leads to different decision makers acting on asymmetric information sets, introduces the need for coordination between them, and perhaps not surprisingly makes the resulting optimal control problem much harder to solve. In fact, shortly after such questions were posed, it was realized that seemingly simple decentralized optimal control problems are computationally intractable to solve, with the Wistenhausen counterexample being a famous instance of this phenomenon. Spurred on by this perhaps discouraging result, a concerted 40 year effort to identify tractable classes of distributed optimal control problems culminated in the notion of quadratic invariance, which loosely states that if sub-controllers can exchange information with each other at least as quickly as the effect of their control actions propagates through the plant, then the resulting distributed optimal control problem admits a convex formulation.

The identification of quadratic invariance as an appropriate means of "convexifying" distributed optimal control problems led to a renewed enthusiasm in the controller synthesis community, resulting in a rich set of results over the past decade. The contributions of this thesis can be seen as being a part of this broader family of results, with a particular focus on closing the gap between theory and practice by relaxing or removing assumptions made in the traditional distributed optimal control framework. Our contributions are to the foundational theory of distributed optimal control, and fall under three broad categories, namely controller synthesis, architecture design and system identification.

We begin by providing two novel controller synthesis algorithms. The first is a solution to the distributed H-infinity optimal control problem subject to delay constraints, and provides the only known exact characterization of delay-constrained distributed controllers satisfying an H-infinity norm bound. The second is an explicit dynamic programming solution to a two player LQR state-feedback problem with varying delays. Accommodating varying delays represents an important first step in combining distributed optimal control theory with the area of Networked Control Systems that considers lossy channels in the feedback loop. Our next set of results are concerned with controller architecture design. When designing controllers for large-scale systems, the architectural aspects of the controller such as the placement of actuators, sensors, and the communication links between them can no longer be taken as given -- indeed the task of designing this architecture is now as important as the design of the control laws themselves. To address this task, we formulate the Regularization for Design (RFD) framework, which is a unifying computationally tractable approach, based on the model matching framework and atomic norm regularization, for the simultaneous co-design of a structured optimal controller and the architecture needed to implement it. Our final result is a contribution to distributed system identification. Traditional system identification techniques such as subspace identification are not computationally scalable, and destroy rather than leverage any a priori information about the system's interconnection structure. We argue that in the context of system identification, an essential building block of any scalable algorithm is the ability to estimate local dynamics within a large interconnected system. To that end we propose a promising heuristic for identifying the dynamics of a subsystem that is still connected to a large system. We exploit the fact that the transfer function of the local dynamics is low-order, but full-rank, while the transfer function of the global dynamics is high-order, but low-rank, to formulate this separation task as a nuclear norm minimization problem. Finally, we conclude with a brief discussion of future research directions, with a particular emphasis on how to incorporate the results of this thesis, and those of optimal control theory in general, into a broader theory of dynamics, control and optimization in layered architectures.

Varieties generated by modular lattices of width four

A variety (equational class) of lattices is said to be finitely based if there exists a finite set of identities defining the variety. Let M^∞_n denote the lattice variety generated by all modular lattices of width not exceeding n. M^∞₁ and M^∞₂ are both the class of all distributive lattices and consequently finitely based. B. Jónsson has shown that M^∞₃ is also finitely based. On the other hand, K. Baker has shown that M^∞_n is not finitely based for 5 ≤ n ˂ ω. This thesis settles the finite basis problem for M^∞₄. M^∞₄ is shown to be finitely based by proving the stronger result that there exist ten varieties which properly contain M^∞₄ and such that any variety which properly contains M^∞₄ contains one of these ten varieties.

The methods developed also yield a characterization of sub-directly irreducible width four modular lattices. From this characterization further results are derived. It is shown that the free M^∞₄ lattice with n generators is finite. A variety with exactly k covers is exhibited for all k ≥ 15. It is further shown that there are 2^Ӄo sub- varieties of M^∞₄.

6th European Conference on Energy Efficiency and Sustainability in Architecture and Planning

[ES]Esta obra recoge las comunicaciones seleccionadas para el 6º Congreso Europeo sobre Eficiencia Energética y Sostenibilidad en Arquitectura, organizado por el grupo de investigación Calidad de Vida en Arquitectura de la Universidad del País Vasco/Euskal Herriko Unibertsitatea. El congreso, que se celebra en el marco de los XXXIV Cursos de Verano de la UPV/EHU, aborda en esta cuarta edición el tema “Ciudades en riesgo: resiliencia y redundancia”. Alrededor de este tema general se desarrollan cinco ponencias magistrales, a cargo de Margaretha Breil (Centro Euro-Mediterráneo para el Cambio Climático), Cristina Garzillo Leemhuis (ICLEI), Ignasi Fontanals (OptiCits), Juan Carlos Barrios Montenegro (Global Action Plan) y Manuel Valdés López (Ajuntament de Barcelona). Además, 24 comunicaciones seleccionadas por el comité científico presentarán trabajos de investigaciones actuales en las sesiones orales y póster. Es objetivo paralelo del congreso es fortalecer las líneas de investigación en eficiencia energética y sostenibilidad de los grupos de investigación y formación de la UPV/ EHU comprometidos con esta propuesta, con objeto de colaborar en el reforzamiento de la I D i en su ámbito de conocimiento y apoyar la apuesta específica de los Gobiernos Central y Vasco, así como de otras instituciones nacionales e internacionales respecto a las actividades de I D i en las materias relacionadas con el cambio climático, la eficiencia energética y la sostenibilidad ambiental [ENG] This work contains the selected abstracts of the 6th European Conference on Energy Efficiency and Sustainability in Architecture and Planning, organized by the research group Quality of life in Architecture of the University of the Basque Country. The conference is part of the XXXIV Summer Courses of the UPV/EHU and deals, in its fourth edition, with the topic “Cities at risk: resilience and redundancy”. Around this general theme there are five invited speakers: Margaretha Breil (Euro-Mediterranean Centre for Climate Change), Cristina Garzillo Leemhuis (ICLEI), Ignasi Fontanals (OptiCits), Juan Carlos Barrios Montenegro (Global Action Plan) y Manuel Valdés López (Barcelona City Council). 24 abstracts additional have been selected by the scientific committee that offer actual research works in presentations and posters. The purpose of the conferences is to strengthen the investigation lines in energy efficiency and sustainability of the research and education groups of the University of the Basque Country (UPV/EHU) involved, with the purpose of collaborating in the reinforcement of the I D i in its field of knowledge, and support the specific projects of the Central and Basque Governments, as well as other national and international institutions related to the I Di activities in similar fields of climate change, energy efficiency and environmental sustainability.

Generación dinámica de parrillas de productos en Magento en base al análisis de datos de fuentes abiertas

En este Trabajo de Fin de Grado desarrollado en la empresa On4U, se ha implementado un módulo para Magento, cuya función principal es la generación dinámica de parrillas de productos en base al análisis del tiempo meteorológico, teniendo en cuenta la localización del cliente. Además, el módulo guarda automáticamente las compras efectuadas, junto con la información externa, para un posible análisis posterior que relacione los hábitos de compra con el tiempo meteorológico. Aunque se haya centrado en este caso de uso, se ha desarrollado con un enfoque modular, de tal manera que fuese fácil de integrar en el módulo el uso de otra fuente abierta de información. Para poder realizar el proyecto, se ha tenido que profundizar en varios conceptos relacionados con la plataforma de eCommerce Magento, entre ellos, el patrón Modelo-Vista-Controlador y el ciclo de vida de una petición.