Fast numerical algorithms for the computation of invariant tori in Hamiltonian systems

In this paper, we develop numerical algorithms that use small requirements of storage and operations for the computation of invariant tori in Hamiltonian systems (exact symplectic maps and Hamiltonian vector fields). The algorithms are based on the parameterization method and follow closely the proof of the KAM theorem given in [LGJV05] and [FLS07]. They essentially consist in solving a functional equation satisfied by the invariant tori by using a Newton method. Using some geometric identities, it is possible to perform a Newton step using little storage and few operations. In this paper we focus on the numerical issues of the algorithms (speed, storage and stability) and we refer to the mentioned papers for the rigorous results. We show how to compute efficiently both maximal invariant tori and whiskered tori, together with the associated invariant stable and unstable manifolds of whiskered tori. Moreover, we present fast algorithms for the iteration of the quasi-periodic cocycles and the computation of the invariant bundles, which is a preliminary step for the computation of invariant whiskered tori. Since quasi-periodic cocycles appear in other contexts, this section may be of independent interest. The numerical methods presented here allow to compute in a unified way primary and secondary invariant KAM tori. Secondary tori are invariant tori which can be contracted to a periodic orbit. We present some preliminary results that ensure that the methods are indeed implementable and fast. We postpone to a future paper optimized implementations and results on the breakdown of invariant tori.

Generic super-exponential stability of invariant tori in Hamiltonian systems

In this article, we consider solutions starting close to some linearly stable invariant tori in an analytic Hamiltonian system and we prove results of stability for a super-exponentially long interval of time, under generic conditions. The proof combines classical Birkhoff normal forms and a new method to obtain generic Nekhoroshev estimates developed by the author and L. Niederman in another paper. We will mainly focus on the neighbourhood of elliptic fixed points, the other cases being completely similar.

The Role of supply constraints in multiplier analysis

Multiplier analysis based upon the information contained in Leontief's inverse is undoubtedly part of the core of the input-output methodology and numerous applications an extensions have been developed that exploit its informational content. Nonetheless there are some implicit theoretical assumptions whose implications have perhaps not been fully assessed. This is the case of the 'excess capacity' assumption. Because of this assumption resources are available as needed to adjust production to new equilibrium states. In real world applications, however, new resources are scarce and costly. Supply constraints kick in and hence resource allocation needs to take them into account to really assess the effect of government policies. Using a closed general equilibrium model that incorporates supply constraints, we perform some simple numerical exercises and proceed to derive a 'constrained' multiplier matrix that can be compared with the standard 'unrestricted' multiplier matrix. Results show that the effectiveness of expenditure policies hinges critically on whether or not supply constraints are considered.

Opportunities and constraints in schistosomiasis vaccine development: infection characteristics and industry realities

The notes provided in this article relate to two components of the development of vaccines against schistosomiasis: (1) The characteristics of schistosome infections (eg. features of the schistosome life cycle), and the parasite itself, that have implications for vaccination strategies; (2) The characteristics of the biopharmaceutical industry that have implications for product development. As will be seen, these two topic areas are not vastly disparate.

Compositional Constraints in the Extremely GC-poor Genome of Plasmodium falciparum

We have analyzed the compositional properties of coding (protein encoding) and non-coding sequences of Plasmodium falciparum, a unicellular parasite characterized by an extremely AT-rich genome. GC% levels, base and dinucleotide frequencies were studied. We found that among the various factors that contribute to the properties of the sequences analyzed, the most relevant are the compositional constraints which operate on the whole genome

Changes in wage structure in Mexico going beyond the mean: An analysis of differences in distribution, 1987-2008

This paper conducts an empirical analysis of the relationship between wage inequality, employment structure, and returns to education in urban areas of Mexico during the past two decades (1987-2008). Applying Melly’s (2005) quantile regression based decomposition, we find that changes in wage inequality have been driven mainly by variations in educational wage premia. Additionally, we find that changes in employment structure, including occupation and firm size, have played a vital role. This evidence seems to suggest that the changes in wage inequality in urban Mexico cannot be interpreted in terms of a skill-biased change, but rather they are the result of an increasing demand for skills during that period.

Towards economic and monetary union: changing trends in payment systems for new european members

The objective of this paper is preciselyto study the evolution of payment systems within the accession countries between 1996 and 2003 and compare them with those of the E.U. and the Eurozone countries

Compositional evolution with mass transfer in closed systems

Evolution of compositions in time, space, temperature or other covariates is frequentin practice. For instance, the radioactive decomposition of a sample changes its composition with time. Some of the involved isotopes decompose into other isotopes of thesample, thus producing a transfer of mass from some components to other ones, butpreserving the total mass present in the system. This evolution is traditionally modelledas a system of ordinary di erential equations of the mass of each component. However,this kind of evolution can be decomposed into a compositional change, expressed interms of simplicial derivatives, and a mass evolution (constant in this example). A rst result is that the simplicial system of di erential equations is non-linear, despiteof some subcompositions behaving linearly.The goal is to study the characteristics of such simplicial systems of di erential equa-tions such as linearity and stability. This is performed extracting the compositional differential equations from the mass equations. Then, simplicial derivatives are expressedin coordinates of the simplex, thus reducing the problem to the standard theory ofsystems of di erential equations, including stability. The characterisation of stabilityof these non-linear systems relays on the linearisation of the system of di erential equations at the stationary point, if any. The eigenvelues of the linearised matrix and theassociated behaviour of the orbits are the main tools. For a three component system,these orbits can be plotted both in coordinates of the simplex or in a ternary diagram.A characterisation of processes with transfer of mass in closed systems in terms of stability is thus concluded. Two examples are presented for illustration, one of them is aradioactive decay

Visual management of sags and incidents gathered in distribution substations for power quality management

Monitor a distribution network implies working with a huge amount of data coining from the different elements that interact in the network. This paper presents a visualization tool that simplifies the task of searching the database for useful information applicable to fault management or preventive maintenance of the network

Embedding Emotional Context in Recommender Systems

Emotions are crucial for user's decision making in recommendation processes. We first introduce ambient recommender systems, which arise from the analysis of new trends on the exploitation of the emotional context in the next generation of recommender systems. We then explain some results of these new trends in real-world applications through the smart prediction assistant (SPA) platform in an intelligent learning guide with more than three million users. While most approaches to recommending have focused on algorithm performance. SPA makes recommendations to users on the basis of emotional information acquired in an incremental way. This article provides a cross-disciplinary perspective to achieve this goal in such recommender systems through a SPA platform. The methodology applied in SPA is the result of a bunch of technology transfer projects for large real-world rccommender systems

Dialogic learning and interactive groups: an IMS LD template integrated in runtime systems

Dialogic learning and interactive groups have proved to be a useful methodological approach appliedin educational situations for lifelong adult learners. The principles of this approach stress theimportance of dialogue and equal participation also when designing the training activities. This paperadopts these principles as the basis for a configurable template that can be integrated in runtimesystems. The template is formulated as a meta-UoL which can be interpreted by IMS Learning Designplayers. This template serves as a guide to flexibly select and edit the activities at runtime (on the fly).The meta-UoL has been used successfully by a practitioner so as to create a real-life example, withpositive and encouraging results

Coordination pattern variability provides functional adaptations to constraints in swimming performance.

In a biophysical approach to the study of swimming performance (blending biomechanics and bioenergetics), inter-limb coordination is typically considered and analysed to improve propulsion and propelling efficiency. In this approach, 'opposition' or 'continuous' patterns of inter-limb coordination, where continuity between propulsive actions occurs, are promoted in the acquisition of expertise. Indeed a 'continuous' pattern theoretically minimizes intra-cyclic speed variations of the centre of mass. Consequently, it may also minimize the energy cost of locomotion. However, in skilled swimming performance there is a need to strike a delicate balance between inter-limb coordination pattern stability and variability, suggesting the absence of an 'ideal' pattern of coordination toward which all swimmers must converge or seek to imitate. Instead, an ecological dynamics framework advocates that there is an intertwined relationship between the specific intentions, perceptions and actions of individual swimmers, which constrains this relationship between coordination pattern stability and variability. This perspective explains how behaviours emerge from a set of interacting constraints, which each swimmer has to satisfy in order to achieve specific task performance goals and produce particular task outcomes. This overview updates understanding on inter-limb coordination in swimming to analyse the relationship between coordination variability and stability in relation to interacting constraints (related to task, environment and organism) that swimmers may encounter during training and performance.