Branching processes and computational collapse of discretized unimodal mappings

In computer simulations of smooth dynamical systems, the original phase space is replaced by machine arithmetic, which is a finite set. The resulting spatially discretized dynamical systems do not inherit all functional properties of the original systems, such as surjectivity and existence of absolutely continuous invariant measures. This can lead to computational collapse to fixed points or short cycles. The paper studies loss of such properties in spatial discretizations of dynamical systems induced by unimodal mappings of the unit interval. The problem reduces to studying set-valued negative semitrajectories of the discretized system. As the grid is refined, the asymptotic behavior of the cardinality structure of the semitrajectories follows probabilistic laws corresponding to a branching process. The transition probabilities of this process are explicitly calculated. These results are illustrated by the example of the discretized logistic mapping.

Object transportation by multiple mobile robots controlled by attractor dynamics: theory and implementation

Dynamical systems theory is used as a theoretical language and tool to design a distributed control architecture for teams of mobile robots, that must transport a large object and simultaneously avoid collisions with (either static or dynamic) obstacles. Here we demonstrate in simulations and implementations in real robots that it is possible to simplify the architectures presented in previous work and to extend the approach to teams of n robots. The robots have no prior knowledge of the environment. The motion of each robot is controlled by a time series of asymptotical stable states. The attractor dynamics permits the integration of information from various sources in a graded manner. As a result, the robots show a strikingly smooth an stable team behaviour.

Fractional Dynamics and Control of Distributed Parameter Systems

Fractional Calculus (FC) goes back to the beginning of the theory of differential calculus. Nevertheless, the application of FC just emerged in the last two decades, due to the progress in the area of chaos that revealed subtle relationships with the FC concepts. In the field of dynamical systems theory some work has been carried out but the proposed models and algorithms are still in a preliminary stage of establishment. Having these ideas in mind, the paper discusses a FC perspective in the study of the dynamics and control of some distributed parameter systems.

A Small World Perspective on Urban Systems

The theory of small-world networks as initiated by Watts and Strogatz (1998) has drawn new insights in spatial analysis as well as systems theory. The theoryâeuro?s concepts and methods are particularly relevant to geography, where spatial interaction is mainstream and where interactions can be described and studied using large numbers of exchanges or similarity matrices. Networks are organized through direct links or by indirect paths, inducing topological proximities that simultaneously involve spatial, social, cultural or organizational dimensions. Network synergies build over similarities and are fed by complementarities between or inside cities, with the two effects potentially amplifying each other according to the âeurooepreferential attachmentâeuro hypothesis that has been explored in a number of different scientific fields (Barabási, Albert 1999; Barabási A-L 2002; Newman M, Watts D, Barabàsi A-L). In fact, according to Barabási and Albert (1999), the high level of hierarchy observed in âeurooescale-free networksâeuro results from âeurooepreferential attachmentâeuro, which characterizes the development of networks: new connections appear preferentially close to nodes that already have the largest number of connections because in this way, the improvement in the network accessibility of the new connection will likely be greater. However, at the same time, network regions gathering dense and numerous weak links (Granovetter, 1985) or network entities acting as bridges between several components (Burt 2005) offer a higher capacity for urban communities to benefit from opportunities and create future synergies. Several methodologies have been suggested to identify such denser and more coherent regions (also called communities or clusters) in terms of links (Watts, Strogatz 1998; Watts 1999; Barabási, Albert 1999; Barabási 2002; Auber 2003; Newman 2006). These communities not only possess a high level of dependency among their member entities but also show a low level of âeurooevulnerabilityâeuro, allowing for numerous redundancies (Burt 2000; Burt 2005). The SPANGEO project 2005âeuro"2008 (SPAtial Networks in GEOgraphy), gathering a team of geographers and computer scientists, has included empirical studies to survey concepts and measures developed in other related fields, such as physics, sociology and communication science. The relevancy and potential interpretation of weighted or non-weighted measures on edges and nodes were examined and analyzed at different scales (intra-urban, inter-urban or both). New classification and clustering schemes based on the relative local density of subgraphs were developed. The present article describes how these notions and methods contribute on a conceptual level, in terms of measures, delineations, explanatory analyses and visualization of geographical phenomena.

Analyzing dynamic intellectual capital: System-based theory and application

This research report presents an application of systems theory to evaluating intellectual capital (IC) as organization's ability for self-renewal. As renewal ability is a dynamic capability of an organization as a whole, rather than a static asset or an atomistic competence of separate individuals within the organization, it needs to be understood systemically. Consequently, renewal ability has to be measured with systemic methods that are based on a thorough conceptual analysis of systemic characteristics of organizations. The aim of this report is to demonstrate the theory and analysis methodology for grasping companies' systemic efficiency and renewal ability. The volume is divided into three parts. The first deals with the theory of organizations as self-renewing systems. In the second part, the principles of quantitative analysis of organizations are laid down. Finally, the detailed mathematics of the renewal indices are presented. We also assert that the indices produced by the analysis are an effective tool for the management and valuation of knowledge-intensive companies.

Towards input/output-free modelling of linear infinite-dimensional systems in continuous time

This dissertation describes a networking approach to infinite-dimensional systems theory, where there is a minimal distinction between inputs and outputs. We introduce and study two closely related classes of systems, namely the state/signal systems and the port-Hamiltonian systems, and describe how they relate to each other. Some basic theory for these two classes of systems and the interconnections of such systems is provided. The main emphasis lies on passive and conservative systems, and the theoretical concepts are illustrated using the example of a lossless transfer line. Much remains to be done in this field and we point to some directions for future studies as well.

Methods for construction and analysis of computational models in systems biology : applications to the modelling of the heat shock response and the self-assembly of intermediate filaments

Systems biology is a new, emerging and rapidly developing, multidisciplinary research field that aims to study biochemical and biological systems from a holistic perspective, with the goal of providing a comprehensive, system- level understanding of cellular behaviour. In this way, it addresses one of the greatest challenges faced by contemporary biology, which is to compre- hend the function of complex biological systems. Systems biology combines various methods that originate from scientific disciplines such as molecu- lar biology, chemistry, engineering sciences, mathematics, computer science and systems theory. Systems biology, unlike “traditional” biology, focuses on high-level concepts such as: network, component, robustness, efficiency, control, regulation, hierarchical design, synchronization, concurrency, and many others. The very terminology of systems biology is “foreign” to “tra- ditional” biology, marks its drastic shift in the research paradigm and it indicates close linkage of systems biology to computer science. One of the basic tools utilized in systems biology is the mathematical modelling of life processes tightly linked to experimental practice. The stud- ies contained in this thesis revolve around a number of challenges commonly encountered in the computational modelling in systems biology. The re- search comprises of the development and application of a broad range of methods originating in the fields of computer science and mathematics for construction and analysis of computational models in systems biology. In particular, the performed research is setup in the context of two biolog- ical phenomena chosen as modelling case studies: 1) the eukaryotic heat shock response and 2) the in vitro self-assembly of intermediate filaments, one of the main constituents of the cytoskeleton. The range of presented approaches spans from heuristic, through numerical and statistical to ana- lytical methods applied in the effort to formally describe and analyse the two biological processes. We notice however, that although applied to cer- tain case studies, the presented methods are not limited to them and can be utilized in the analysis of other biological mechanisms as well as com- plex systems in general. The full range of developed and applied modelling techniques as well as model analysis methodologies constitutes a rich mod- elling framework. Moreover, the presentation of the developed methods, their application to the two case studies and the discussions concerning their potentials and limitations point to the difficulties and challenges one encounters in computational modelling of biological systems. The problems of model identifiability, model comparison, model refinement, model inte- gration and extension, choice of the proper modelling framework and level of abstraction, or the choice of the proper scope of the model run through this thesis.

Non-Linear Unsteady Aerodynamic Response Approximation Using Multi-Layer Functionals

Non-linear functional representation of the aerodynamic response provides a convenient mathematical model for motion-induced unsteady transonic aerodynamic loads response, that accounts for both complex non-linearities and time-history effects. A recent development, based on functional approximation theory, has established a novel functional form; namely, the multi-layer functional. For a large class of non-linear dynamic systems, such multi-layer functional representations can be realised via finite impulse response (FIR) neural networks. Identification of an appropriate FIR neural network model is facilitated by means of a supervised training process in which a limited sample of system input-output data sets is presented to the temporal neural network. The present work describes a procedure for the systematic identification of parameterised neural network models of motion-induced unsteady transonic aerodynamic loads response. The training process is based on a conventional genetic algorithm to optimise the network architecture, combined with a simplified random search algorithm to update weight and bias values. Application of the scheme to representative transonic aerodynamic loads response data for a bidimensional airfoil executing finite-amplitude motion in transonic flow is used to demonstrate the feasibility of the approach. The approach is shown to furnish a satisfactory generalisation property to different motion histories over a range of Mach numbers in the transonic regime.

Educational Leadership: Exploring the Influence of Managed and Living Systems in Educational Leadership Discourse

A conceptual analysis of educational leadership explored the influence of managed and living systems on 21st century leadership discourse. Drawing on a detailed understanding of managed and living systems theory compiled from the work of Capra (2002), Morgan (1997), Mitchell and Sackney (2009), and Wheatley (2007), this study draws attention to the managed systems systemic concepts of efficiency, control, and standardization, and the living systems concepts of collaboration, shared meaning, change, and interconnection as markers of systems theory that find resonance within leadership literature. Using these systemic concepts as a framework, this study provides important insights into the espousal of managed and living systems concepts within the leadership discourse.

Teoría del caos y la complejidad en la representación de la relación estratégica comunitaria y marketing en los estados financieros

El presente trabajo tiene como finalidad caracterizar conceptos y elementos clave del caos y de la complejidad existente en la relación entre las organizaciones y la comunidad. Esta relación parte de la base de satisfacer las necesidades de los actores involucrados y, así mismo, mejorar el desempeño de cada uno, y contribuir al bienestar de la sociedad y a la perdurabilidad de las empresas. Para alcanzar el objetivo planteado, inicialmente se hace necesario contextualizar conceptos que estarán presentes durante todo el escrito. Por esto se expondrán términos como teoría de la complejidad, teoría del caos, los aspectos más representativos de la relación comunitaria y el marketing y su impacto en las comunidades. La teoría de la complejidad permitirá entender los sistemas como un todo, en donde las relaciones e interacciones de cada una de sus diferentes partes nos conducen a innumerables escenarios posibles. También se buscará entender la importancia de la relación organización-comunidad, ya que la comunidad puede jugar un papel determinante cuando las organizaciones se adaptan a los cambios. Es de suma importancia establecer relaciones estratégicas con la comunidad, entendiendo a la comunidad como un sistema o grupo social con determinadas características, que permitan tanto a las organizaciones como a la misma comunidad entender, comprender y satisfacer eficazmente las necesidades subyacentes y, así, llegar a establecer un entorno de retroalimentación continua y sostenibilidad a lo largo del tiempo. Actualmente, el funcionamiento del mundo ha cambiado en cierta medida, ya que antes la base del conocimiento se centraba en función del orden y la regularidad. Ahora, en cambio, se destaca la creatividad y la dinámica que son causadas por el desorden y la irregularidad presentes en los sistemas. El mundo se plantea como un grupo de innumerables sistemas auto-organizados, donde su funcionamiento puede provocar resultados impredecibles o aleatorios. La materia de complejidad en los sistemas se ha desarrollado por diferentes autores según aproximaciones desde diferentes ramas de la ciencia, como la cibernética, basada en los mecanismos de retroalimentación y control; desde la teoría general de los sistemas, que da énfasis en el dinamismo presente en los sistemas y cómo la organización está presente en su estructura. En el presente proyecto se realizará un estudio de tipo teórico-conceptual: se seleccionarán las bases de datos, fuentes de información y los documentos más representativos o que proporcionen la mayor información posible que permita el completo entendimiento de la investigación y de sus alcances propuestos. Es así que esta investigación busca aportar más elementos dentro de los diferentes estudios que pretenden explicar y mejorar la perdurabilidad de las empresas bajo las diferentes líneas de investigación. A través del tiempo, el GIPE ha ido evolucionando de acuerdo con los resultados de las investigaciones y se ha centrado en cuatro líneas de investigación: Liderazgo, Realidad, Estrategia y Gerencia. El proyecto de investigación “Relación de las organizaciones con el medio y marketing” hace parte de la línea de gerencia y busca identificar oportunidades gerenciales para las organizaciones que las acerquen al conocimiento y manejo de las áreas funcionales (Facultad de Administración, 2013). Además, el proyecto se adentra en las organizaciones en entornos complejos y su relación con la comunidad, y se observa así la organización como un ser vivo que contribuye al bienestar de la sociedad que, finalmente, es lo que garantiza su perdurabilidad.

Desenvolupament, implementació i aplicació de noves metodologies per a l'estudi de la reactivitat química i de les propietats òptiques no lineals

El coneixement de la superfície d'energia potencial (PES) ha estat essencial en el món de la química teòrica per tal de discutir tant la reactivitat química com l'estructura i l'espectroscòpia molecular. En el camp de la reactivitat química es hem proposat continuar amb el desenvolupament de nova metodologia dins el marc de la teoria del funcional de la densitat conceptual. En particular aquesta tesis es centrarà en els següents punts: a) El nombre i la naturalesa dels seus punts estacionaris del PES poden sofrir canvis radicals modificant el nivell de càlcul utilitzats, de tal manera que per estar segurs de la seva naturalesa cal anar a nivells de càlcul molt elevats. La duresa és una mesura de la resistència d'un sistema químic a canviar la seva configuració electrònica, i segons el principi de màxima duresa on hi hagi un mínim o un màxim d'energia trobarem un màxim o un mínim de duresa, respectivament. A l'escollir tot un conjunt de reaccions problemàtiques des del punt de vista de presència de punts estacionaris erronis, hem observat que els perfils de duresa són més independents de la base i del mètode utilitzats, a més a més sempre presenten el perfil correcte. b) Hem desenvolupat noves expressions basades en les integracions dels kernels de duresa per tal de determinar la duresa global d'una molècula de manera més precisa que la utilitzada habitualment que està basada en el càlcul numèric de la derivada segona de l'energia respecte al número d'electrons. c) Hem estudiat la validesa del principis de màxima duresa i de mínima polaritzabiliat en les vibracions asimètriques en sistemes aromàtics. Hem trobat que per aquests sistemes alguns modes vibracionals incompleixen aquests principis i hem analitzat la relació d'aquest l'incompliment amb l'efecte de l'acoblament pseudo-Jahn-Teller. A més a més, hem postulat tot un conjunt de regles molt senzilles que ens permetien deduir si una molècula compliria o no aquests principis sense la realització de cap càlcul previ. Tota aquesta informació ha estat essencial per poder determinar exactament quines són les causes del compliment o l'incompliment del MHP i MPP. d) Finalment, hem realitzat una expansió de l'energia funcional en termes del nombre d'electrons i de les coordenades normals dintre del conjunt canònic. En la comparació d'aquesta expansió amb l'expansió de l'energia del nombre d'electrons i del potencial extern hem pogut recuperar d'una altra forma diferent tot un conjunt de relacions ja conegudes entre alguns coneguts descriptors de reactivitat del funcional de la densitat i en poden establir tot un conjunt de noves relacions i de nous descriptors. Dins del marc de les propietats moleculars es proposa generalitzar i millorar la metodologia pel càlcul de la contribució vibracional (Pvib) a les propietats òptiques no lineals (NLO). Tot i que la Pvib no s'ha tingut en compte en la majoria dels estudis teòrics publicats de les propietats NLO, recentment s'ha comprovat que la Pvib de diversos polímers orgànics amb altes propietats òptiques no lineals és fins i tot més gran que la contribució electrònica. Per tant, tenir en compte la Pvib és essencial en el disseny dels nous materials òptics no lineals utilitzats en el camp de la informàtica, les telecomunicacions i la tecnologia làser. Les principals línies d'aquesta tesis sobre aquest tema són: a) Hem calculat per primera vegada els termes d'alt ordre de Pvib de diversos polímers orgànics amb l'objectiu d'avaluar la seva importància i la convergència de les sèries de Taylor que defineixen aquestes contribucions vibracionals. b) Hem avaluat les contribucions electròniques i vibracionals per una sèrie de molècules orgàniques representatives utilitzant diferents metodologies, per tal de poder de determinar quina és la manera més senzilla per poder calcular les propietats NLO amb una precisió semiquantitativa.

Private industrial project management: a systems-based case study

The technique of linear responsibility analysis is used for a retrospective case study of a private industrial development consisting of an extension to existing buildings to provide a warehouse, services block and packing line. The organizational structure adopted on the project is analysed using concepts from systems theory which are included in Walker's theoretical model of the structure of building project organizations (Walker, 1981). This model proposes that the process of building provision can be viewed as systems and subsystems which are differentiated from each other at decision points. Further to this, the subsystems can be viewed as the interaction of managing system and operating system. Using Walker's model, a systematic analysis of the relationships between the contributors gives a quantitative assessment of the efficacy of the organizational structure used. The causes of the client's dissatisfaction with the outcome of the project were lack of integration and complexity of the managing system. However, there was a high level of satisfaction with the completed project and this is reflected by the way in which the organization structure corresponded to the model's propositions.

A conventionally managed project: a systems based case study

The technique of linear responsibility analysis is used for a retrospective case study of a private development consisting of an extension to an existing building to provide a wholesale butchery facility. The project used a conventionally organized management process. The organization structure adopted on the project is analysed using concepts from the systems theory, which are included in Walkers theoretical model of the structure of building project organizations. This model proposes that the process of building provision can be viewed as systems and sub-systems that are differentiated from each other at decision points. Further to this, the sub-systems can be viewed as the interaction of managing system and operating system. Using Walkers model, a systematic analysis of the relationships between the contributors gives a quantitative assessment of the efficiency of the organizational structure used. The project's organization structure diverged from the models propositions resulting in delay to the project's completion and cost overrun but the client was satisfied with the project functionally.

A project managed by a multi disciplinary practice: a systems based case study.

The technique of linear responsibility analysis is used for a retrospective case study of a private industrial development consisting of an engineering factory and offices. A multi-disciplinary professional practice was used to manage and design the project. The organizational structure adopted on the project is analysed using concepts from systems theory which are included in Walker's theoretical model of the structure of building project organizations (Walker, 1981). This model proposes that the process of buildings provision can be viewed as systems and sub-systems which are differentiated form each other at decision points. Further to this, the sub-systematic analysis of the relationship between the contributors gives a quantitative assessment of the efficiency of the organizational structure used. There was a high level of satisfaction with the completed project and this is reflected by the way in which the organization structure corresponded to the model's proposition. However, the project was subject to string environmental forces which the project organization was not capable of entirely overcoming.

An analysis of the management of a public sector project: a systems-based case study

The management of a public sector project is analysed using a model developed from systems theory. Linear responsibility analysis is used to identify the primary and key decision structure of the project and to generate quantitative data regarding differentiation and integration of the operating system, the managing system and the client/project team. The environmental context of the project is identified. Conclusions are drawn regarding the project organization structure's ability to cope with the prevailing environmental conditions. It is found that the complexity of the managing system imposed on the project was unable to achieve this and created serious deficiencies in the outcome of the project.