Local convergence of quasi-Newton methods under metric regularity

We consider quasi-Newton methods for generalized equations in Banach spaces under metric regularity and give a sufficient condition for q-linear convergence. Then we show that the well-known Broyden update satisfies this sufficient condition in Hilbert spaces. We also establish various modes of q-superlinear convergence of the Broyden update under strong metric subregularity, metric regularity and strong metric regularity. In particular, we show that the Broyden update applied to a generalized equation in Hilbert spaces satisfies the Dennis–Moré condition for q-superlinear convergence. Simple numerical examples illustrate the results.

Convergence analysis and validation of low cost distance metrics for computational cost reduction of the Iterative Closest Point algorithm

The Iterative Closest Point algorithm (ICP) is commonly used in engineering applications to solve the rigid registration problem of partially overlapped point sets which are pre-aligned with a coarse estimate of their relative positions. This iterative algorithm is applied in many areas such as the medicine for volumetric reconstruction of tomography data, in robotics to reconstruct surfaces or scenes using range sensor information, in industrial systems for quality control of manufactured objects or even in biology to study the structure and folding of proteins. One of the algorithm’s main problems is its high computational complexity (quadratic in the number of points with the non-optimized original variant) in a context where high density point sets, acquired by high resolution scanners, are processed. Many variants have been proposed in the literature whose goal is the performance improvement either by reducing the number of points or the required iterations or even enhancing the complexity of the most expensive phase: the closest neighbor search. In spite of decreasing its complexity, some of the variants tend to have a negative impact on the final registration precision or the convergence domain thus limiting the possible application scenarios. The goal of this work is the improvement of the algorithm’s computational cost so that a wider range of computationally demanding problems from among the ones described before can be addressed. For that purpose, an experimental and mathematical convergence analysis and validation of point-to-point distance metrics has been performed taking into account those distances with lower computational cost than the Euclidean one, which is used as the de facto standard for the algorithm’s implementations in the literature. In that analysis, the functioning of the algorithm in diverse topological spaces, characterized by different metrics, has been studied to check the convergence, efficacy and cost of the method in order to determine the one which offers the best results. Given that the distance calculation represents a significant part of the whole set of computations performed by the algorithm, it is expected that any reduction of that operation affects significantly and positively the overall performance of the method. As a result, a performance improvement has been achieved by the application of those reduced cost metrics whose quality in terms of convergence and error has been analyzed and validated experimentally as comparable with respect to the Euclidean distance using a heterogeneous set of objects, scenarios and initial situations.

Breaking the silence ceiling: how gender violence became into a social problem in Spain through media and politics

This research presents the explanatory model of the process of reconstruction of the ʺsocial problemʺ of Intimate Partner Violence (I.P.V) in Spain during last five years, with special attention to the role of media in this process. Using a content analysis of the three more diffused general newspapers, a content analysis of the minutes of the Parliament, and the statistics of the police reports and murders, from January of 1997 to December of 2001, it observes the relationship between the evolution of the incidence of Intimate Partner Violence (I.P.V) (measured by the number of deaths and the number of police reports) and the evolution of stories about this topic in press. It also studies the interconnection of the two previous variables with the political answer to the problem (measured by the interventions on the I.P.V. in the Senate and in the Congress). Data shows that, even though police reports have increased due to the contribution of politics and media, I.P.V murders keep on growing up.

Gender portrayals in food commercials: a content analysis of Spanish television advertisements

Content analysis of media messages from a gender perspective has a long tradition. In the particular field of advertising, most of the researches have been focused on generic samples of advertisements or on the advertising traditionally associated to a masculine or a feminine audience. However, few authors have analyzed gender contents in food advertising, in spite of the close relationship between gender structures and the social processes of food purchase and preparation. Thus, gender representations in food advertising broadcast in Spanish television are analyzed in this article. The main results obtained show clear gender differences. For example, there is a clear predominance of masculine voices over and a more balanced situation regarding protagonists. Besides, feminine protagonists are more frequently located indoors, portrayed as attractive women and connected to advertising claims related to beauty or to the healthy qualities of the product.

Rigorous Design of Complex Distillation Columns Using Process Simulators and the Particle Swarm Optimization Algorithm

We present a derivative-free optimization algorithm coupled with a chemical process simulator for the optimal design of individual and complex distillation processes using a rigorous tray-by-tray model. The proposed approach serves as an alternative tool to the various models based on nonlinear programming (NLP) or mixed-integer nonlinear programming (MINLP) . This is accomplished by combining the advantages of using a commercial process simulator (Aspen Hysys), including especially suited numerical methods developed for the convergence of distillation columns, with the benefits of the particle swarm optimization (PSO) metaheuristic algorithm, which does not require gradient information and has the ability to escape from local optima. Our method inherits the superstructure developed in Yeomans, H.; Grossmann, I. E.Optimal design of complex distillation columns using rigorous tray-by-tray disjunctive programming models. Ind. Eng. Chem. Res.2000, 39 (11), 4326–4335, in which the nonexisting trays are considered as simple bypasses of liquid and vapor flows. The implemented tool provides the optimal configuration of distillation column systems, which includes continuous and discrete variables, through the minimization of the total annual cost (TAC). The robustness and flexibility of the method is proven through the successful design and synthesis of three distillation systems of increasing complexity.

The Conservation of our Built Heritage, in Particular Statues in Aberdeen, Evaluated Through a Social and Historical Context and Their Impact, Through the Use of 3D Scanning

Cultural heritage sites all over the world are at risk due to aggressive urban expansion, development, wars and general obsolescence. Not all objects are recorded in detail although they may have social and historical significance. For example more emphasis is placed on the recording of castles and palaces than on crofters’ cottages or tenement blocks, although their history can be just as rich. This paper will investigate the historic fabric of Aberdeen through the use of digital scanning, supported by a range of media including old photographs and paintings. Dissemination of social heritage through visualisations will be explored and how this can aid the understanding of space within the city or specific area. Focus will be given to the major statues/monuments within the context of the city centre, exploring their importance in their environment. In addition studying why many have been re-located away from their original site, the reasons why, and how we have perhaps lost some of the social and historical importance of why that monument was first located there. It will be argued that Digital Media could be utilised for much more than re-creation and re-presentation of physical entities. Digital scanning, in association with visualisation tools, is used to capture the essence of both the cultural heritage and the society that created or used the sites in association with visualisation tools and in some way re-enacting the original importance placed upon the monument in its original location, through adoption of BIM Heritage.