Analytic Non-integrability in String Theory

Using analytic techniques developed for Hamiltonian dynamical systems we show that a certain classical string configurations in AdS_5 x X_5 with X_5 in a large class of Einstein spaces, is non-integrable. This answers the question of integrability of string on such backgrounds in the negative. We consider a string localized in the center of AdS_5 that winds around two circles in the manifold X_5.Comment: 14 page

Darboux points and integrability of homogeneous Hamiltonian systems with three and more degrees of freedom

We consider natural complex Hamiltonian systems with $n$ degrees of freedom given by a Hamiltonian function which is a sum of the standard kinetic energy and a homogeneous polynomial potential $V$ of degree $k>2$. The well known Morales-Ramis theorem gives the strongest known necessary conditions for the Liouville integrability of such systems. It states that for each $k$ there exists an explicitly known infinite set \scM_k\subset\Q such that if the system is integrable, then all eigenvalues of the Hessian matrix V''(\vd) calculated at a non-zero \vd\in\C^n satisfying V'(\vd)=\vd, belong to \scM_k. The aim of this paper is, among others, to sharpen this result. Under certain genericity assumption concerning $V$ we prove the following fact. For each $k$ and $n$ there exists a finite set \scI_{n,k}\subset\scM_k such that if the system is integrable, then all eigenvalues of the Hessian matrix V''(\vd) belong to \scI_{n,k}. We give an algorithm which allows to find sets \scI_{n,k}. We applied this results for the case $n=k=3$ and we found all integrable potentials satisfying the genericity assumption. Among them several are new and they are integrable in a highly non-trivial way. We found three potentials for which the additional first integrals are of degree 4 and 6 with respect to the momenta.Comment: 54 pages, 1 figur

Image Features Extraction Using Proportional-Integral Filters

This document aims to demonstrate that features generated as a side effect of using Proportional-Integral filters, with explicit or implicit Euler discretization, could be viable for imaging Machine Learning applications. This thesis delves into how the Proportional-Integral and Super-Twisting filters are defined, how they are discretized with the Forward and Backward Euler method, which results in the need to calculate an error or difference scaled with a step size (discrete derivative), and how these features are used in an image classification problem with two different datasets, using a convex machine learning method (Support Vector Classifier). These results are compared with a commonly used kernel for extracting an image's differences or edges, called the Sobel operator. With the PI and ST robustness and stability in mind and their implicit low-pass filter from their formulation as a continuous output signal, two tests involving adding artificial uniform and Gaussian noise are realized. The features derived from the automatic control algorithms prove to be viable but more valuable in situations where noise exists

Servitization and co-opetition in the pharmaceutical distribution: Back to Basics?

This paper discusses how the pharmaceutical distribution sector has evolved in the past decades and the role of servitization in an ever changing market led by big players. An empirical analysis was conducted on Portuguese and Spanish distributors which enabled the identification of a detailed portfolio of services currently offered by the industry. These companies were compared in terms of current service provision, levels of implementation of added-value services, main reasons for implementation and levels of co-opetion within the sector. Some differences between both countries have been found in terms of their level and reasons for the implementation of value adding services. Major findings refer to the tendency of distributors to further develop their base services provision in the future aiming at achieving increased competitive advantage and loyalty. This raises concerns given that it can be interpreted as a “back to basics” strategy of low differentiation which may not be consistent with long term competitiveness

Integrability of Stochastic Birth-Death processes via Differential Galois Theory

Stochastic birth-death processes are described as continuous-time Markov processes in models of population dynamics. A system of infinite, coupled ordinary differential equations (the so-called master equation) describes the time-dependence of the probability of each system state. Using a generating function, the master equation can be transformed into a partial differential equation. In this contribution we analyze the integrability of two types of stochastic birth-death processes (with polynomial birth and death rates) using standard differential Galois theory. We discuss the integrability of the PDE via a Laplace transform acting over the temporal variable. We show that the PDE is not integrable except for the (trivial) case in which rates are linear functions of the number of individuals

Servitization and Co-opetition in pharmaceutical industry

Purpose: The present paper aims at providing an outlook of the portfolio of services developed by the pharmaceutical distribution in Spain and Portugal by looking at the different types and levels of implementation. This paper also provides the research framework that is currently the base for the ongoing data collection, exploring the rationale behind the implementation of different types of services and co-opetitive relationships in relation to the pursuit of profit, the creation of barriers with competitors and the reinforcement of customer loyalty. The impact of these factors on the intention to increase the delivery of services in the future will also be analysed. Design/methodology/approach: In order to address the research framework presented, a quantitative research methodology is suggested through the use of web-based questionnaires. After the identification and categorization of services in this industry, a questionnaire was developed in order to measure the presence of the identified services and their impact on the pursuit of profit, the creation of competitive advantages the improvement of customer loyalty, willingness to further develop these services and co-opetitive relationships. The sample includes Portuguese and Spanish pharmaceutical cooperatives and private companies, operating as wholesalers. Findings: The empirical data is currently being collected therefore the present paper provides solely the analysis of the pharmaceutical industry in both countries and the classification of the services offered in this industry which was used as the basis to develop the questionnaire. The paper discusses how the pharmaceutical distribution sector has evolved in the past decades and how the concentration process has changed the rules of the market owned by big players who are taking the lead. Additionally, the portfolio of new services that have recently been developed throughout the industry are identified. Some differences between both countries have been found mainly in IT services. The recent establishment of second degree cooperatives generates new perspectives to the suggested influence of co-opetitive relationships. Originality/value: The present paper is part of an ongoing research project which aims at providing both theoretical and practical implications: 1) The analysis of pharmaceutical wholesalers from a servitization perspective; 2) Application of Baines et al. (2013) classification to the pharmaceutical sector; 3) The adaptation and measurement of co-opetitive relationships within the servitization delivery; 4) Development of instruments to measure the level of implementation and the type of services which can be used in the future to make compared studies in other countries

Chaos around Holographic Regge Trajectories

Using methods of Hamiltonian dynamical systems, we show analytically that a dynamical system connected to the classical spinning string solution holographically dual to the principal Regge trajectory is non-integrable. The Regge trajectories themselves form an integrable island in the total phase space of the dynamical system. Our argument applies to any gravity background dual to confining field theories and we verify it explicitly in various supergravity backgrounds: Klebanov-Strassler, Maldacena-Nunez, Witten QCD and the AdS soliton. Having established non-integrability for this general class of supergravity backgrounds, we show explicitly by direct computation of the Poincare sections and the largest Lyapunov exponent, that such strings have chaotic motion.Comment: 28 pages, 5 figures. V3: Minor changes complying to referee's suggestions. Typos correcte

A list of all integrable 2D homogeneous polynomial potentials with a polynomial integral of order at most 4 in the momenta

We searched integrable 2D homogeneous polynomial potential with a polynomial first integral by using the so-called direct method of searching for first integrals. We proved that there exist no polynomial first integrals which are genuinely cubic or quartic in the momenta if the degree of homogeneous polynomial potentials is greater than 4.Comment: 22 pages, no figures, to appear in J. Phys. A: Math. Ge

On some exceptional cases in the integrability of the three-body problem

We consider the Newtonian planar three--body problem with positive masses $m_1$, $m_2$, $m_3$. We prove that it does not have an additional first integral meromorphic in the complex neighborhood of the parabolic Lagrangian orbit besides three exceptional cases $\sum m_i m_j/(\sum m_k)^2= 1/3$, $2^3/3^3$, $2/3^2$ where the linearized equations are shown to be partially integrable. This result completes the non-integrability analysis of the three-body problem started in our previous papers and based of the Morales-Ramis-Ziglin approach.Comment: 7 page