Introduction to Coding Theory for Flow Equations of Complex Systems Models

The modeling of complex dynamic systems depends on the solution of a differential equations system. Some problems appear because we do not know the mathematical expressions of the said equations. Enough numerical data of the system variables are known. The authors, think that it is very important to establish a code between the different languages to let them codify and decodify information. Coding permits us to reduce the study of some objects to others. Mathematical expressions are used to model certain variables of the system are complex, so it is convenient to define an alphabet code determining the correspondence between these equations and words in the alphabet. In this paper the authors begin with the introduction to the coding and decoding of complex structural systems modeling.

Saint Mathew Law and Bonini Paradox in Textual Theory of Complex Models

The mathematical models of the complex reality are texts belonging to a certain literature that is written in a semi-formal language, denominated L(MT) by the authors whose laws linguistic mathematics have been previously defined. This text possesses linguistic entropy that is the reflection of the physical entropy of the processes of real world that said text describes. Through the temperature of information defined by Mandelbrot, the authors begin a text-reality thermodynamic theory that drives to the existence of information attractors, or highly structured point, settling down a heterogeneity of the space text, the same one that of ontologic space, completing the well-known law of Saint Mathew, of the General Theory of Systems and formulated by Margalef saying: “To the one that has more he will be given, and to the one that doesn't have he will even be removed it little that it possesses.

The theory of functions of a complex variable. [Lectures] New York University, Institute for Mathematics and Mechanics.

"First edition 1948. Second printing 1952."

Elements of the theory of functions of a complex variable with especial reference to the methods of Riemann,

Translation of Elemente der Theorie der Funktionen einer complexen veränderlichen Grösse.

Theory of functions of a complex variable,

Available on demand as hard copy or computer file from Cornell University Library.

Stair builders' guide; a treatise on the construction of straight flight, platform, cylindrical and eliptical [!] stairs, explaining the theory and practice so the average building mechanic may understand it, with examples of work ranging from the simplest to the most complex forms,

Mode of access: Internet.

Theory of functions of a complex variable /

Mode of access: Internet.

The chemistry of the inorganic complex compounds; an introduction to Werner's coordination theory,

Translation of: Chemie der anorganischen komplex Verbindungen.

Examining the strategy development process through the lens of complex adaptive systems theory

The development of strategy remains a debate for academics and a concern for practitioners. Published research has focused on producing models for strategy development and on studying how strategy is developed in organisations. The Operational Research literature has highlighted the importance of considering complexity within strategic decision making; but little has been done to link strategy development with complexity theories, despite organisations and organisational environments becoming increasingly more complex. We review the dominant streams of strategy development and complexity theories. Our theoretical investigation results in the first conceptual framework which links an established Strategic Operational Research model, the Strategy Development Process model, with complexity via Complex Adaptive Systems theory. We present preliminary findings from the use of this conceptual framework applied to a longitudinal, in-depth case study, to demonstrate the advantages of using this integrated conceptual model. Our research shows that the conceptual model proposed provides rich data and allows for a more holistic examination of the strategy development process. © 2012 Operational Research Society Ltd. All rights reserved.

Complex Adaptive On-line Learning System “Theory of Automatic Control"

The controlled from distance teaching (DT) in the system of technical education has a row of features: complication of informative content, necessity of development of simulation models and trainers for conducting of practical and laboratory employments, conducting of knowledge diagnostics on the basis of mathematical-based algorithms, organization of execution collective projects of the applied setting. For development of the process of teaching bases of fundamental discipline control system Theory of automatic control (TAC) the combined approach of optimum combination of existent programmatic instruments of support was chosen DT and own developments. The system DT TAC included: controlled from distance course (DC) of TAC, site of virtual laboratory practical works in LAB.TAC and students knowledge remote diagnostic system d-tester.

Fuzzy Set Theory Approach as the Basis of Analysis of Financial Flows in the Economical Security System

The problems of formalization of the process of matching different management subjects’ functioning characteristics obtained on the financial flows analysis basis is considered. Formal generalizations for gaining economical security system knowledge bases elements are presented. One of feedback directions establishment between knowledge base of the system of economical security and financial flows database analysis is substantiated.

Quantum transition state theory and solving a first order master equation for complex reactions numerically

The field of chemical kinetics is an exciting and active field. The prevailing theories make a number of simplifying assumptions that do not always hold in actual cases. Another current problem concerns a development of efficient numerical algorithms for solving the master equations that arise in the description of complex reactions. The objective of the present work is to furnish a completely general and exact theory of reaction rates, in a form reminiscent of transition state theory, valid for all fluid phases and also to develop a computer program that can solve complex reactions by finding the concentrations of all participating substances as a function of time. To do so, the full quantum scattering theory is used for deriving the exact rate law, and then the resulting cumulative reaction probability is put into several equivalent forms that take into account all relativistic effects if applicable, including one that is strongly reminiscent of transition state theory, but includes corrections from scattering theory. Then two programs, one for solving complex reactions, the other for solving first order linear kinetic master equations to solve them, have been developed and tested for simple applications.

Modeling security and cooperation in wireless networks using game theory

This research involves the design, development, and theoretical demonstration of models resulting in integrated misbehavior resolution protocols for ad hoc networked devices. Game theory was used to analyze strategic interaction among independent devices with conflicting interests. Packet forwarding at the routing layer of autonomous ad hoc networks was investigated. Unlike existing reputation based or payment schemes, this model is based on repeated interactions. To enforce cooperation, a community enforcement mechanism was used, whereby selfish nodes that drop packets were punished not only by the victim, but also by all nodes in the network. Then, a stochastic packet forwarding game strategy was introduced. Our solution relaxed the uniform traffic demand that was pervasive in other works. To address the concerns of imperfect private monitoring in resource aware ad hoc networks, a belief-free equilibrium scheme was developed that reduces the impact of noise in cooperation. This scheme also eliminated the need to infer the private history of other nodes. Moreover, it simplified the computation of an optimal strategy. The belief-free approach reduced the node overhead and was easily tractable. Hence it made the system operation feasible. Motivated by the versatile nature of evolutionary game theory, the assumption of a rational node is relaxed, leading to the development of a framework for mitigating routing selfishness and misbehavior in Multi hop networks. This is accomplished by setting nodes to play a fixed strategy rather than independently choosing a rational strategy. A range of simulations was carried out that showed improved cooperation between selfish nodes when compared to older results. Cooperation among ad hoc nodes can also protect a network from malicious attacks. In the absence of a central trusted entity, many security mechanisms and privacy protections require cooperation among ad hoc nodes to protect a network from malicious attacks. Therefore, using game theory and evolutionary game theory, a mathematical framework has been developed that explores trust mechanisms to achieve security in the network. This framework is one of the first steps towards the synthesis of an integrated solution that demonstrates that security solely depends on the initial trust level that nodes have for each other.^

Equitable representation in councils: theory and an application to the United Nations Security Council

We analyze democratic equity in council voting games (CVGs). In a CVG, a voting body containing all members delegates decision-making to a (time-varying) subset of its members, as describes, e.g., the relationship between the United Nations General Assembly and the United Nations Security Council (UNSC). We develop a theoretical framework for analyzing democratic equitability in CVGs at both the country and region levels, and for different assumptions regarding preference correlation. We apply the framework to evaluate the equitability of the UNSC, and the claims of those who seek to reform it. We find that the individual permanent members are overrepresented by between 21.3 times (United Kingdom) and 3.8 times (China) from a country-level perspective, while from a region perspective Eastern Europe is the most heavily overrepresented region with more than twice its equitable representation, and Africa the most heavily underrepresented. Our equity measures do not preclude some UNSC members from exercising veto rights, however.

Assessing and reducing vulnerability to climate change: Moving from theory to practical decision-support

As climate change continues to impact socio-ecological systems, tools that assist conservation managers to understand vulnerability and target adaptations are essential. Quantitative assessments of vulnerability are rare because available frameworks are complex and lack guidance for dealing with data limitations and integrating across scales and disciplines. This paper describes a semi-quantitative method for assessing vulnerability to climate change that integrates socio-ecological factors to address management objectives and support decision-making. The method applies a framework first adopted by the Intergovernmental Panel on Climate Change and uses a structured 10-step process. The scores for each framework element are normalized and multiplied to produce a vulnerability score and then the assessed components are ranked from high to low vulnerability. Sensitivity analyses determine which indicators most influence the analysis and the resultant decision-making process so data quality for these indicators can be reviewed to increase robustness. Prioritisation of components for conservation considers other economic, social and cultural values with vulnerability rankings to target actions that reduce vulnerability to climate change by decreasing exposure or sensitivity and/or increasing adaptive capacity. This framework provides practical decision-support and has been applied to marine ecosystems and fisheries, with two case applications provided as examples: (1) food security in Pacific Island nations under climate-driven fish declines, and (2) fisheries in the Gulf of Carpentaria, northern Australia. The step-wise process outlined here is broadly applicable and can be undertaken with minimal resources using existing data, thereby having great potential to inform adaptive natural resource management in diverse locations.