On the Lyapunov transformation for stable matrices

The matrices studied here are positive stable (or briefly stable). These are matrices, real or complex, whose eigenvalues have positive real parts. A theorem of Lyapunov states that A is stable if and only if there exists H ˃ 0 such that AH + HA* = I. Let A be a stable matrix. Three aspects of the Lyapunov transformation L_A :H → AH + HA* are discussed.

1. Let C₁ (A) = {AH + HA* :H ≥ 0} and C₂ (A) = {H: AH+HA* ≥ 0}. The problems of determining the cones C₁(A) and C₂(A) are still unsolved. Using solvability theory for linear equations over cones it is proved that C₁(A) is the polar of C₂(A*), and it is also shown that C₁ (A) = C₁(A^-1). The inertia assumed by matrices in C₁(A) is characterized.

2. The index of dissipation of A was defined to be the maximum number of equal eigenvalues of H, where H runs through all matrices in the interior of C₂(A). Upper and lower bounds, as well as some properties of this index, are given.

3. We consider the minimal eigenvalue of the Lyapunov transform AH+HA*, where H varies over the set of all positive semi-definite matrices whose largest eigenvalue is less than or equal to one. Denote it by ψ(A). It is proved that if A is Hermitian and has eigenvalues μ₁ ≥ μ₂…≥ μ_n ˃ 0, then ψ(A) = -(μ₁-μ_n)²/(4(μ₁ + μ_n)). The value of ψ(A) is also determined in case A is a normal, stable matrix. Then ψ(A) can be expressed in terms of at most three of the eigenvalues of A. If A is an arbitrary stable matrix, then upper and lower bounds for ψ(A) are obtained.

Efficiency, energy and stoichiometry in pelagic food webs; reciprocal roles of food quality and food quantity

In most lakes, zooplankton production is constrained by food quantity, but frequently high C:P poses an additional constraint on zooplankton production by reducing the carbon transfer efficiency from phytoplankton to zooplankton. This review addresses how the flux of matter and energy in pelagic food webs is regulated by food quantity in terms of C and its stoichiometric quality in terms of C:P. Increased levels of light, CO2 and phosphorus could each increase seston mass and, hence, food quantity for zooplankton, but while light and CO2 each cause increased C:P (i.e. reduced food quality for herbivores), increased P may increase seston mass and its stoichiometric quality by reducing C:P. Development of food quality and food quantity in response to C- or P-enrichments will differ between 'batch-type' lakes (dominated by one major, seasonal input of water and nutrients) and 'continuous-culture' types of lakes with a more steady flow-rate of water and nutrients. The reciprocal role of food quantity and stoichiometric quality will depend strongly on facilitation via grazing and recycling by the grazers, and this effect will be most important in systems with low renewal rates. At high food abundance but low quality, there will be a 'quality starvation' in zooplankton. From a management point of view, stoichiometric theory offers a general tool-kit for understanding the integrated role of C and P in food webs and how food quantity and stoichiometric quality (i.e. C:P) regulate energy flow and trophic efficiency from base to top in food webs.From a management point of view, stoichiometric theory offers a general tool-kit for understanding the integrated role of C and P in food webs and how food quantity and stoichiometric quality (i.e. C:P) regulate energy flow and trophic efficiency from base to top in food webs.

Geometrical-transformation approach to optical two-dimensional beam shaping: comment

I show that the research reported by Arieli et al. [Appl. Opt. 86, 9129 (1997)] has two serious mistakes: One is that an important factor is lost in the formula used in that study to determine the x-direction coordinate transformation; the other is the conclusion that the geometrical-transformation approach given by Arieli et al. can provide a smooth phase distribution. A potential research direction for obtaining a smooth phase distribution for a generic two-dimensional beam-shaping problem is stated. (C) 1998 Optical Society of America.

Design of a highly stable, high-conversion-efficiency pumping source for optical parametric amplifier by extending efficient crystal length

The objective of this study is to improve the stability of pumping source of optical parametric amplifier. Analysis by simulation leads to the conclusion that the stability of the second harmonic can be improved by using properly the intensity of fundamental light and corresponding length of the crystal. By the method of the noncollinear two-pass second harmonic or the tandem second harmonic, the efficient crystal length is extended to a proper value, and the stability of the second harmonic output has been improved two times more than that for the fundamental light, and the conversion-efficiency is about 70% in experiment. When the variation of the fundamental light is about 10%, the variation of the second harmonic intensity has been controlled within 5%. (c) 2006 Elsevier Ltd. All rights reserved.

Bertso transformation with pattern-based sampling

This paper presents a method to generate new melodies, based on conserving the semiotic structure of a template piece. A pattern discovery algorithm is applied to a template piece to extract significant segments: those that are repeated and those that are transposed in the piece. Two strategies are combined to describe the semiotic coherence structure of the template piece: inter-segment coherence and intra-segment coherence. Once the structure is described it is used as a template for new musical content that is generated using a statistical model created from a corpus of bertso melodies and iteratively improved using a stochastic optimization method. Results show that the method presented here effectively describes a coherence structure of a piece by discovering repetition and transposition relations between segments, and also by representing the relations among notes within the segments. For bertso generation the method correctly conserves all intra and inter-segment coherence of the template, and the optimization method produces coherent generated melodies.

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.

Improving Content Delivery Efficiency through Multi-Layer Mobile Edge Adaptation

This paper presents a novel architecture for optimizing the HTTP-based multimedia delivery in multi-user mobile networks. This proposal combines the usual client-driven dynamic adaptation scheme DASH-3GPP with network-assisted adaptation capabilities, in order to maximize the overall Quality of Experience. The foundation of this combined adaptation scheme is based on two state of the art technologies. On one hand, adaptive HTTP streaming with multi-layer encoding allows efficient media delivery and improves the experienced media quality in highly dynamic channels. Additionally, it enables the possibility to implement network-level adaptations for better coping with multi-user scenarios. On the other hand, mobile edge computing facilitates the deployment of mobile services close to the user. This approach brings new possibilities in modern and future mobile networks, such as close to zero delays and awareness of the radio status. The proposal in this paper introduces a novel element, denoted as Mobile Edge-DASH Adaptation Function, which combines all these advantages to support efficient media delivery in mobile multi-user scenarios. Furthermore, we evaluate the performance enhancements of this content- and user context-aware scheme through simulations of a mobile multimedia scenario.

Reversible Resistance Switching Effect in Amorphous Ge1Sb4Te7 Thin Films without Phase Transformation

We demonstrate a reversible resistance switching effect that does not rely on amorphous-crystalline phase transformation in a nanoscale capacitor-like cell using Ge1Sb4Te7 films as the working material. The polarity and amplitude of the applied electric voltage switches the cell resistance between low- and high-resistance states, as revealed in the current-voltage characteristics of the film by conductive atomic force microscopy (CAFM). This reversible SET/RESET switching effect is induced by voltage pulses and their polarity. The change of electrical resistance due to the switching effect is approximately two orders of magnitude.