Classical Dynamical Systems from q-algebras:"cluster" variables and explicit solutions

A general procedure to get the explicit solution of the equations of motion for N-body classical Hamiltonian systems equipped with coalgebra symmetry is introduced by defining a set of appropriate collective variables which are based on the iterations of the coproduct map on the generators of the algebra. In this way several examples of N-body dynamical systems obtained from q-Poisson algebras are explicitly solved: the q-deformed version of the sl(2) Calogero-Gaudin system (q-CG), a q-Poincare' Gaudin system and a system of Ruijsenaars type arising from the same (non co-boundary) q-deformation of the (1+1) Poincare' algebra. Also, a unified interpretation of all these systems as different Poisson-Lie dynamics on the same three dimensional solvable Lie group is given.Comment: 19 Latex pages, No figure

Hamiltonian flows on null curves

The local motion of a null curve in Minkowski 3-space induces an evolution equation for its Lorentz invariant curvature. Special motions are constructed whose induced evolution equations are the members of the KdV hierarchy. The null curves which move under the KdV flow without changing shape are proven to be the trajectories of a certain particle model on null curves described by a Lagrangian linear in the curvature. In addition, it is shown that the curvature of a null curve which evolves by similarities can be computed in terms of the solutions of the second Painlev\'e equation.Comment: 14 pages, v2: final version; minor changes in the expositio

Binary trees, coproducts, and integrable systems

We provide a unified framework for the treatment of special integrable systems which we propose to call "generalized mean field systems". Thereby previous results on integrable classical and quantum systems are generalized. Following Ballesteros and Ragnisco, the framework consists of a unital algebra with brackets, a Casimir element, and a coproduct which can be lifted to higher tensor products. The coupling scheme of the iterated tensor product is encoded in a binary tree. The theory is exemplified by the case of a spin octahedron.Comment: 15 pages, 6 figures, v2: minor correction in theorem 1, two new appendices adde

Perspectives in the development of hybrid bifunctional antitumour agents

In spite of the development of a large number of novel target-specific antitumour agents, the single-agent therapy is in general not able to provide an effective durable control of the malignant process. The limited efficacy of the available agents (both conventional cytotoxic and novel target-specific) reflects not only the expression of defence mechanisms, but also the complexity of tumour cell alterations and the redundancy of survival pathways, thus resulting in tumour cell ability to survive under stress conditions. A well-established strategy to improve the efficacy of antitumour therapy is the rational design of drug combinations aimed at achieving synergistic effects and overcoming drug resistance. An alternative strategy could be the use of agents designed to inhibit simultaneously multiple cellular targets relevant to tumour growth/survival. Among these novel agents are hybrid bifunctional drugs, i.e. compounds resulting by conjugation of different drugs or containing the pharmocophores of different drugs. This strategy has been pursued using various conventional or target-specific agents (with DNA damaging agents and histone deacetylase inhibitors as the most exploited compounds). A critical overview of the most representative compounds is provided with emphasis on the HDAC inhibitor-based hybrid agents. In spite of some promising results, the actual pharmacological advantages of the hybrid agents remain to be defined. This commentary summarizes the recent advances in this field and highlights the pharmacological basis for a rational design of hybrid bifunctional agents

SME food suppliers versus large retailers: perspectives in the international supply chains

none3noThe market share of international retail chains substantially increased from the beginning of the nineties. The supplier’s market has been adapted to the evolutions of retailers’ market in terms of modified purchasing processes. The concentration of large food retailers has been much faster than the same process among manufacturers. Due to these changes, the requirements towards food industry suppliers grew in number and quality. Thus it is generally true that the nature of the buyer-supplier relationship in retailing has been undergoing dramatic changes. Important literature has described these emerging relationships as "partnerships" or "strategic alliances," as opposed to the traditional "arm's length" type of associations. But these conditions are likely to change especially in the relationships between small and medium suppliers and large retailers. The paper shows how the relationships between suppliers and retailers are experiencing several important changes, above all at international level. In particular, the analysis is focused on the Italian food SME suppliers related with international large retailers. Considering the focus of this paper, in-depth interviews to 28 Italian food SME suppliers have been conducted in early 2007. Results have been analyzed and compared to the retailers’ point of view, resulting from public reports (such as Annual report, CSR report, etc.) to understand retail companies’ approach to SME suppliers. Considering the main topics of such relations and the selection criteria used by retailers, one of the main results of the analysis is that the unbalance of power in the relation is not necessarily a negative condition, as the growth of SME suppliers is stimulated by an improving attitude to operate with large retailers. Retailers reserve a wide space on their shelves to SME references because they contribute to increase the variety of merchandising and ensure a more tight control on the supply chain (traceability). At the same time, the strong pressure on price and the required organizational qualifications lead to a selection process, in which smaller manufacturers seem to be the more vulnerable actors.openC. Pepe; F. Musso; M. RissoC., Pepe; Musso, Fabio; M., Riss

Gaudin Models and Bending Flows: a Geometrical Point of View

In this paper we discuss the bihamiltonian formulation of the (rational XXX) Gaudin models of spin-spin interaction, generalized to the case of sl(r)-valued spins. In particular, we focus on the homogeneous models. We find a pencil of Poisson brackets that recursively define a complete set of integrals of the motion, alternative to the set of integrals associated with the 'standard' Lax representation of the Gaudin model. These integrals, in the case of su(2), coincide wih the Hamiltonians of the 'bending flows' in the moduli space of polygons in Euclidean space introduced by Kapovich and Millson. We finally address the problem of separability of these flows and explicitly find separation coordinates and separation relations for the r=2 case.Comment: 27 pages, LaTeX with amsmath and amssym

Modelling for understanding AND for prediction/classification - the power of neural networks in research

Two articles, Edelsbrunner and, Schneider (2013), and Nokelainen and Silander (2014) comment on Musso, Kyndt, Cascallar, and Dochy (2013). Several relevant issues are raised and some important clarifications are made in response to both commentaries. Predictive systems based on artificial neural networks continue to be the focus of current research and several advances have improved the model building and the interpretation of the resulting neural network models. What is needed is the courage and open-mindedness to actually explore new paths and rigorously apply new methodologies which can perhaps, sometimes unexpectedly, provide new conceptualisations and tools for theoretical advancement and practical applied research. This is particularly true in the fields of educational science and social sciences, where the complexity of the problems to be solved requires the exploration of proven methods and new methods, the latter usually not among the common arsenal of tools of neither practitioners nor researchers in these fields. This response will enrich the understanding of the predictive systems methodology proposed by the authors and clarify the application of the procedure, as well as give a perspective on its place among other predictive approaches