Towards a general theory of extremes for observables of chaotic dynamical systems

In this paper we provide a connection between the geometrical properties of the attractor of a chaotic dynamical system and the distribution of extreme values. We show that the extremes of so-called physical observables are distributed according to the classical generalised Pareto distribution and derive explicit expressions for the scaling and the shape parameter. In particular, we derive that the shape parameter does not depend on the cho- sen observables, but only on the partial dimensions of the invariant measure on the stable, unstable, and neutral manifolds. The shape parameter is negative and is close to zero when high-dimensional systems are considered. This result agrees with what was derived recently using the generalized extreme value approach. Combining the results obtained using such physical observables and the properties of the extremes of distance observables, it is possible to derive estimates of the partial dimensions of the attractor along the stable and the unstable directions of the flow. Moreover, by writing the shape parameter in terms of moments of the extremes of the considered observable and by using linear response theory, we relate the sensitivity to perturbations of the shape parameter to the sensitivity of the moments, of the partial dimensions, and of the Kaplan–Yorke dimension of the attractor. Preliminary numer- ical investigations provide encouraging results on the applicability of the theory presented here. The results presented here do not apply for all combinations of Axiom A systems and observables, but the breakdown seems to be related to very special geometrical configurations.

Supply chain management systems benefits : the expectation-confirmation theory perspective

Organizations adopt a Supply Chain Management System (SCMS) expecting benefits to the organization and its functions. However, organizations are facing mounting challenges to realizing benefits through SCMS. Studies suggest a growing dissatisfaction among client organizations due to an increasing gap between expectations and realization of SCMS benefits. Further, reflecting the Enterprise System studies such as Seddon et al. (2010), SCMS benefits are also expected to flow to the organization throughout its lifecycle rather than being realized all at once. This research therefore proposes to derive a lifecycle-wide understanding of SCMS benefits and realization to derive a benefit expectation management framework to attain the full potential of an SCMS. The primary research question of this study is: How can client organizations better manage their benefit expectations of SCM systems? The specific research goals of the current study include: (1) to better understand the misalignment of received and expected benefits of SCM systems; (2) to identify the key factors influencing SCM system expectations and to develop a framework to manage SCMS benefits; (3) to explore how organizational satisfaction is influenced by the lack of SCMS benefit confirmation; and (4) to explore how to improve the realization of SCM system benefits. Expectation-Confirmation Theory (ECT) provides the theoretical underpinning for this study. ECT has been widely used in the consumer behavior literature to study customer satisfaction, post-purchase behavior and service marketing in general. Recently, ECT has been extended into Information Systems (IS) research focusing on individual user satisfaction and IS continuance. However, only a handful of studies have employed ECT to study organizational satisfaction on large-scale IS. The current study will enrich the research stream by extending ECT into organizational-level analysis and verifying the preliminary findings of relevant works by Staples et al. (2002), Nevo and Chan (2007) and Nevo and Wade (2007). Moreover, this study will go further trying to operationalize the constructs of ECT into the context of SCMS. The empirical findings of the study commence with a content analysis, through which 41 vendor reports and academic reports are analyzed yielding sixty expected benefits of SCMS. Then, the expected benefits are compared with the benefits realized at a case organization in the Fast Moving Consumer Goods industry sector that had implemented a SAP Supply Chain Management System seven years earlier. The study develops an SCMS Benefit Expectation Management (SCMS-BEM) Framework. The comparison of benefit expectations and confirmations highlights that, while certain benefits are realized earlier in the lifecycle, other benefits could take almost a decade to realize. Further analysis and discussion on how the developed SCMS-BEM Framework influences ECT when applied in SCMS was also conducted. It is recommended that when establishing their expectations of the SCMS, clients should remember that confirmation of these expectations will have a long lifecycle, as shown in the different time periods in the SCMS-BEM Framework. Moreover, the SCMS-BEM Framework will allow organizations to maintain high levels of satisfaction through careful mitigation and confirming expectations based on the lifecycle phase. In addition, the study reveals that different stakeholder groups have different expectations of the same SCMS. The perspective of multiple stakeholders has significant implications for the application of ECT in the SCMS context. When forming expectations of the SCMS, the collection of organizational benefits of SCMS should represent the perceptions of all stakeholder groups. The same mechanism should be employed in the measurements of received SCMS benefits. Moreover, for SCMS, there exists interdependence of the satisfaction among the various stakeholders. The satisfaction of decision-makers or the authorized staff is not only driven by their own expectation confirmation level, it is also influenced by the confirmation level of other stakeholders‘ expectations in the organization. Satisfaction from any one particular stakeholder group can not reflect the true satisfaction of the client organization. Furthermore, it is inferred from the SCMS-BEM Framework that organizations should place emphasis on the viewpoints of the operational and management staff when evaluating the benefits of SCMS in the short and middle term. At the same time, organizations should be placing more attention on the perspectives of strategic staff when evaluating the performance of the SCMS in the long term.

General theory of stigmergy : modelling stigma semantics

Stigmergy is a biological term used when discussing a sub-set of insect swarm-behaviour describing the apparent organisation seen during their activities. Stigmergy describes a communication mechanism based on environment-mediated signals which trigger responses among the insects. This phenomenon is demonstrated in the behavior of ants and their food gathering process when following pheromone trails, where the pheromones are a form of environment-mediated communication. What is interesting with this phenomenon is that highly organized societies are achieved without an apparent management structure. Stigmergy is also observed in human environments, both natural and engineered. It is implicit in the Web where sites provide a virtual environment supporting coordinative contributions. Researchers in varying disciplines appreciate the power of this phenomenon and have studied how to exploit it. As stigmergy becomes more widely researched we see its definition mutate as papers citing original work become referenced themselves. Each paper interprets these works in ways very specific to the research being conducted. Our own research aims to better understand what improves the collaborative function of a Web site when exploiting the phenomenon. However when researching stigmergy to develop our understanding we discover a lack of a standardized and abstract model for the phenomenon. Papers frequently cited the same generic descriptions before becoming intimately focused on formal specifications of an algorithm, or esoteric discussions regarding sub-facets of the topic. None provide a holistic and macro-level view to model and standardize the nomenclature. This paper provides a content analysis of influential literature documenting the numerous theoretical and experimental papers that have focused on stigmergy. We establish that stigmergy is a phenomenon that transcends the insect world and is more than just a metaphor when applied to the human world. We present from our own research our general theory and abstract model of semantics of stigma in stigmergy. We hope our model will clarify the nuances of the phenomenon into a useful road-map, and standardise vocabulary that we witness becoming confused and divergent. Furthermore, this paper documents the analysis on which we base our next paper: Special Theory of Stigmergy: A Design Pattern for Web 2.0 Collaboration.

Optimal infinite-horizon feedback laws for a general class of constrained discrete-time systems: stability and moving-horizon approximations

Stability results are given for a class of feedback systems arising from the regulation of time-varying discrete-time systems using optimal infinite-horizon and moving-horizon feedback laws. The class is characterized by joint constraints on the state and the control, a general nonlinear cost function and nonlinear equations of motion possessing two special properties. It is shown that weak conditions on the cost function and the constraints are sufficient to guarantee uniform asymptotic stability of both the optimal infinite-horizon and movinghorizon feedback systems. The infinite-horizon cost associated with the moving-horizon feedback law approaches the optimal infinite-horizon cost as the moving horizon is extended.

Distributed optimization in power networks and general multi-agent systems

The dissertation studies the general area of complex networked systems that consist of interconnected and active heterogeneous components and usually operate in uncertain environments and with incomplete information. Problems associated with those systems are typically large-scale and computationally intractable, yet they are also very well-structured and have features that can be exploited by appropriate modeling and computational methods. The goal of this thesis is to develop foundational theories and tools to exploit those structures that can lead to computationally-efficient and distributed solutions, and apply them to improve systems operations and architecture.

Specifically, the thesis focuses on two concrete areas. The first one is to design distributed rules to manage distributed energy resources in the power network. The power network is undergoing a fundamental transformation. The future smart grid, especially on the distribution system, will be a large-scale network of distributed energy resources (DERs), each introducing random and rapid fluctuations in power supply, demand, voltage and frequency. These DERs provide a tremendous opportunity for sustainability, efficiency, and power reliability. However, there are daunting technical challenges in managing these DERs and optimizing their operation. The focus of this dissertation is to develop scalable, distributed, and real-time control and optimization to achieve system-wide efficiency, reliability, and robustness for the future power grid. In particular, we will present how to explore the power network structure to design efficient and distributed market and algorithms for the energy management. We will also show how to connect the algorithms with physical dynamics and existing control mechanisms for real-time control in power networks.

The second focus is to develop distributed optimization rules for general multi-agent engineering systems. A central goal in multiagent systems is to design local control laws for the individual agents to ensure that the emergent global behavior is desirable with respect to the given system level objective. Ideally, a system designer seeks to satisfy this goal while conditioning each agent’s control on the least amount of information possible. Our work focused on achieving this goal using the framework of game theory. In particular, we derived a systematic methodology for designing local agent objective functions that guarantees (i) an equivalence between the resulting game-theoretic equilibria and the system level design objective and (ii) that the resulting game possesses an inherent structure that can be exploited for distributed learning, e.g., potential games. The control design can then be completed by applying any distributed learning algorithm that guarantees convergence to the game-theoretic equilibrium. One main advantage of this game theoretic approach is that it provides a hierarchical decomposition between the decomposition of the systemic objective (game design) and the specific local decision rules (distributed learning algorithms). This decomposition provides the system designer with tremendous flexibility to meet the design objectives and constraints inherent in a broad class of multiagent systems. Furthermore, in many settings the resulting controllers will be inherently robust to a host of uncertainties including asynchronous clock rates, delays in information, and component failures.

General rules for predicting where a catalytic reaction should occur on metal surfaces: A density functional theory study of C-H and C-O bond breaking/making on flat, stepped, and kinked metal surfaces

To predict where a catalytic reaction should occur is a fundamental issue scientifically. Technologically, it is also important because it can facilitate the catalyst's design. However, to date, the understanding of this issue is rather limited. In this work, two types of reactions, CH4 CH3 + H and CO C + 0 on two transition metal surfaces, were chosen as model systems aiming to address in general where a catalytic reaction should occur. The dissociations of CH4 - CH3 + H and CO --> C + O and their reverse reactions on flat, stepped, and kinked Rh and Pd surfaces were studied in detail. We find the following: First, for the CH4 Ch(3) + H reaction, the dissociation barrier is reduced by similar to0.3 eV on steps and kinks as compared to that on flat surfaces. On the other hand, there is essentially no difference in barrier for the association reaction of CH3 + H on the flat surfaces and the defects. Second, for the CO C + 0 reaction, the dissociation barrier decreases dramatically (more than 0.8 eV on Rh and Pd) on steps and kinks as compared to that on flat surfaces. In contrast to the CH3 + H reaction, the C + 0 association reaction also preferentially occurs on steps and kinks. We also present a detailed analysis of the reaction barriers in which each barrier is decomposed quantitatively into a local electronic effect and a geometrical effect. Our DFT calculations show that surface defects such as steps and kinks can largely facilitate bond breaking, while whether the surface defects could promote bond formation depends on the individual reaction as well as the particular metal. The physical origin of these trends is identified and discussed. On the basis of our results, we arrive at some simple rules with respect to where a reaction should occur: (i) defects such as steps are always favored for dissociation reactions as compared to flat surfaces; and (ii) the reaction site of the association reactions is largely related to the magnitude of the bonding competition effect, which is determined by the reactant and metal valency. Reactions with high valency reactants are more likely to occur on defects (more structure-sensitive), as compared to reactions with low valency reactants. Moreover, the reactions on late transition metals are more likely to proceed on defects than those on the early transition metals.

Structural and chemical embrittlement of grain boundaries by impurities: A general theory and first-principles calculations for copper

First-principles calculations of the Sigma 5(310)[001] symmetric tilt grain boundary in Cu with Bi, Na, and Ag substitutional impurities provide evidence that in the phenomenon of Bi embrittlement of Cu grain boundaries electronic effects do not play a major role; on the contrary, the embrittlement is mostly a structural or "size" effect. Na is predicted to be nearly as good an embrittler as Bi, whereas Ag does not embrittle the boundary in agreement with experiment. While we reject the prevailing view that "electronic" effects (i.e., charge transfer) are responsible for embrittlement, we do not exclude the role of chemistry. However, numerical results show a striking equivalence between the alkali metal Na and the semimetal Bi, small differences being accounted for by their contrasting "size" and "softness" (defined here). In order to separate structural and chemical effects unambiguously if not uniquely, we model the embrittlement process by taking the system of grain boundary and free surfaces through a sequence of precisely defined gedanken processes; each of these representing a putative mechanism. We thereby identify three mechanisms of embrittlement by substitutional impurities, two of which survive in the case of embrittlement or cohesion enhancement by interstitials. Two of the three are purely structural and the third contains both structural and chemical elements that by their very nature cannot be further unraveled. We are able to take the systems we study through each of these stages by explicit computer simulations and assess the contribution of each to the net reduction in intergranular cohesion. The conclusion we reach is that embrittlement by both Bi and Na is almost exclusively structural in origin; that is, the embrittlement is a size effect.

B-spline methods in R-matrix theory for scattering in two-electron systems

The use of B-spline basis sets in R-matrix theory for scattering processes has been investigated. In the present approach a B-spline basis is used for the description of the inner region, which is matched to the physical outgoing wavefunctions by the R-matrix. Using B-splines, continuum basis functions can be determined easily, while pseudostates can be included naturally. The accuracy for low-energy scattering processes is demonstrated by calculating inelastic scattering cross sections for e colliding on H. Very good agreement with other calculations has been obtained. Further extensions of the codes to quasi two-electron systems and general atoms are discussed as well as the application to (multi) photoionization.

A general framework for Business Process Modelling (BPM) based on Formal Temporal Theory with an application to Hospital Patient flows

Existing Workflow Management Systems (WFMSs) follow a pragmatic approach. They often use a proprietary modelling language with an intuitive graphical layout. However the underlying semantics lack a formal foundation. As a consequence, analysis issues, such as proving correctness i.e. soundness and completeness, and reliable execution are not supported at design level. This project will be using an applied ontology approach by formally defining key terms such as process, sub-process, action/task based on formal temporal theory. Current business process modelling (BPM) standards such as Business Process Modelling Notation (BPMN) and Unified Modelling Language (UML) Activity Diagram (AD) model their constructs with no logical basis. This investigation will contribute to the research and industry by providing a framework that will provide grounding for BPM to reason and represent a correct business process (BP). This is missing in the current BPM domain, and may result in reduction of the design costs and avert the burden of redundant terms used by the current standards. A graphical tool will be introduced which will implement the formal ontology defined in the framework. This new tool can be used both as a modelling tool and at the same time will serve the purpose of validating the model. This research will also fill the existing gap by providing a unified graphical representation to represent a BP in a logically consistent manner for the mainstream modelling standards in the fields of business and IT. A case study will be conducted to analyse a catalogue of existing ‘patient pathways’ i.e. processes, of King’s College Hospital NHS Trust including current performance statistics. Following the application of the framework, a mapping will be conducted, and new performance statistics will be collected. A cost/benefits analysis report will be produced comparing the results of the two approaches.

Adaptive general predictive controller for nonlinear systems

A nonlinear general predictive controller (NLGPC) is described which is based on the use of a Hammerstein model within a recursive control algorithm. A key contribution of the paper is the use of a novel, one-step simple root solving procedure for the Hammerstein model, this being a fundamental part of the overall tuning algorithm. A comparison is made between NLGPC and nonlinear deadbeat control (NLDBC) using the same one-step nonlinear components, in order to investigate NLGPC advantages and disadvantages.

Stochastic perturbations to dynamical systems: a response theory approach

Using the formalism of the Ruelle response theory, we study how the invariant measure of an Axiom A dynamical system changes as a result of adding noise, and describe how the stochastic perturbation can be used to explore the properties of the underlying deterministic dynamics. We first find the expression for the change in the expectation value of a general observable when a white noise forcing is introduced in the system, both in the additive and in the multiplicative case. We also show that the difference between the expectation value of the power spectrum of an observable in the stochastically perturbed case and of the same observable in the unperturbed case is equal to the variance of the noise times the square of the modulus of the linear susceptibility describing the frequency-dependent response of the system to perturbations with the same spatial patterns as the considered stochastic forcing. This provides a conceptual bridge between the change in the fluctuation properties of the system due to the presence of noise and the response of the unperturbed system to deterministic forcings. Using Kramers-Kronig theory, it is then possible to derive the real and imaginary part of the susceptibility and thus deduce the Green function of the system for any desired observable. We then extend our results to rather general patterns of random forcing, from the case of several white noise forcings, to noise terms with memory, up to the case of a space-time random field. Explicit formulas are provided for each relevant case analysed. As a general result, we find, using an argument of positive-definiteness, that the power spectrum of the stochastically perturbed system is larger at all frequencies than the power spectrum of the unperturbed system. We provide an example of application of our results by considering the spatially extended chaotic Lorenz 96 model. These results clarify the property of stochastic stability of SRB measures in Axiom A flows, provide tools for analysing stochastic parameterisations and related closure ansatz to be implemented in modelling studies, and introduce new ways to study the response of a system to external perturbations. Taking into account the chaotic hypothesis, we expect that our results have practical relevance for a more general class of system than those belonging to Axiom A.

Effective theory for trapped few-fermion systems

We apply the general principles of effective field theories to the construction of effective interactions suitable for few- and many-body calculations in a no-core shell model framework. We calculate the spectrum of systems with three and four two-component fermions in a harmonic trap. In the unitary limit, we find that three-particle results are within 10% of known semianalytical values even in small model spaces. The method is very general, and can be readily extended to other regimes, more particles, different species (e.g., protons and neutrons in nuclear physics), or more-component fermions (as well as bosons). As an illustration, we present calculations of the lowest-energy three-fermion states away from the unitary limit and find a possible inversion of parity in the ground state in the limit of trap size large compared to the scattering length. Furthermore, we investigate the lowest positive-parity states for four fermions, although we are limited by the dimensions we can currently handle in this case.

Analytic perturbation theory for bound states in the transfer matrix spectrum of weakly correlated lattice ferromagnetic spin systems

We consider general d-dimensional lattice ferromagnetic spin systems with nearest neighbor interactions in the high temperature region ('beta' << 1). Each model is characterized by a single site apriori spin distribution taken to be even. We also take the parameter 'alfa' = ('S POT.4') - 3 '(S POT.2') POT.2' > 0, i.e. in the region which we call Gaussian subjugation, where ('S POT.K') denotes the kth moment of the apriori distribution. Associated with the model is a lattice quantum field theory known to contain a particle of asymptotic mass -ln 'beta' and a bound state below the two-particle threshold. We develop a 'beta' analytic perturbation theory for the binding energy of this bound state. As a key ingredient in obtaining our result we show that the Fourier transform of the two-point function is a meromorphic function, with a simple pole, in a suitable complex spectral parameter and the coefficients of its Laurent expansion are analytic in 'beta'.

Characterization of Stability Region for General Autonomous Nonlinear Dynamical Systems

The existing characterization of stability regions was developed under the assumption that limit sets on the stability boundary are exclusively composed of hyperbolic equilibrium points and closed orbits. The characterizations derived in this technical note are a generalization of existing results in the theory of stability regions. A characterization of the stability boundary of general autonomous nonlinear dynamical systems is developed under the assumption that limit sets on the stability boundary are composed of a countable number of disjoint and indecomposable components, which can be equilibrium points, closed orbits, quasi-periodic solutions and even chaotic invariant sets.