Toward an Algebraic Theory of Systems

We propose the concept of a system algebra with a parallel composition operation and an interface connection operation, and formalize composition-order invariance, which postulates that the order of composing and connecting systems is irrelevant, a generalized form of associativity. Composition-order invariance explicitly captures a common property that is implicit in any context where one can draw a figure (hiding the drawing order) of several connected systems, which appears in many scientific contexts. This abstract algebra captures settings where one is interested in the behavior of a composed system in an environment and wants to abstract away anything internal not relevant for the behavior. This may include physical systems, electronic circuits, or interacting distributed systems. One specific such setting, of special interest in computer science, are functional system algebras, which capture, in the most general sense, any type of system that takes inputs and produces outputs depending on the inputs, and where the output of a system can be the input to another system. The behavior of such a system is uniquely determined by the function mapping inputs to outputs. We consider several instantiations of this very general concept. In particular, we show that Kahn networks form a functional system algebra and prove their composition-order invariance. Moreover, we define a functional system algebra of causal systems, characterized by the property that inputs can only influence future outputs, where an abstract partial order relation captures the notion of "later". This system algebra is also shown to be composition-order invariant and appropriate instantiations thereof allow to model and analyze systems that depend on time

Quantum Rotor Theory of Systems of Spin-2 Bosons

We consider quantum phases of tightly-confined spin-2 bosons in an external field under the presence of rotationally-invariant interactions. Generalizing previous treatments, we show how this system can be mapped onto a quantum rotor model. Within the rotor framework, low-energy excitations about fragmented states, which cannot be accessed within standard Bogoliubov theory, can be obtained. In the spatially extended system in the thermodynamic limit there exists a mean-field ground state degeneracy between a family of nematic states for appropriate interaction parameters. It has been established that quantum fluctuations lift this degeneracy through the mechanism of order-by-disorder and select either a uniaxial or square-biaxial ground state. On the other hand, in the full quantum treatment of the analogous single-spatial mode problem with finite particle number it is known that, due to symmetry restoring fluctuations, there is a unique ground state across the entire nematic region of the phase diagram. Within the established rotor framework we investigate the possible quantum phases under the presence of a quadratic Zeeman field, a problem which has previously received little attention. By investigating wave function overlaps we do not find any signatures of the order-by-disorder phenomenon which is present in the continuum case. Motivated by this we consider an alternative external potential which breaks less symmetry than the quadratic Zeeman field. For this case we do find the phenomenon of order-by-disorder in the fully quantum system. This is established within the rotor framework and with exact diagonalization

On the Functional Integral Theory of Systems with Kinematical Interaction

We propose a systematic way to investigate the low-temperature thermodynamic properties of quantum spin systems subject to the restriction that only a finite number of bosons may occupy a single lattice site. Such a kinematical interaction results in appearance of a temperature dependent chemical potential. Its low-temperature asymptotics is calculated self-consistently using the functional integration technique.Comment: 3 pages (REVTeX), 2 PS figure

Theory of systems with Constraints

Treballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Any: 2014, Tutor: Josep LlosaWe discuss systems subject to constraints. We review Dirac's classical formalism of dealing with such problems and motivate the de nition of objects such as singular and nonsingular Lagrangian, rst and second class constraints, and the Dirac bracket. We show how systems with rst class constraints can be considered to be systems with gauge freedom. We conclude by studing a classical example of systems with constraints, electromagnetic el

A Theory of Systems Evaluation

National Science Foundation Systems Evaluation Grant No. EREC-053549

Universal coalgebra: a theory of systems

In the semantics of programming, finite data types such as finite lists, have traditionally been modelled by initial algebras. Later final coalgebras were used in order to deal with infinite data types. Coalgebras, which are the dual of algebras, turned out to be suited, moreover, as models for certain types of automata and more generally, for (transition and dynamical) systems. An important property of initial algebras is that they satisfy the familiar principle of induction. Such a principle was missing for coalgebras until the work of Aczel (1988) on a theory of non-wellfounded sets, in which he introduced a proof principle nowadays called coinduction. It was formulated in terms of bisimulation, a notion originally stemming from the world of concurrent programming languages (Milner, 1980; Park, 1981). Using the notion of c

Towards a Theory of Systems Engineering Processes: A Principal-Agent Model of a One-Shot, Shallow Process

Systems engineering processes coordinate the effort of different individuals to generate a product satisfying certain requirements. As the involved engineers are self-interested agents, the goals at different levels of the systems engineering hierarchy may deviate from the system-level goals which may cause budget and schedule overruns. Therefore, there is a need of a systems engineering theory that accounts for the human behavior in systems design. To this end, the objective of this paper is to develop and analyze a principal-agent model of a one-shot (single iteration), shallow (one level of hierarchy) systems engineering process. We assume that the systems engineer maximizes the expected utility of the system, while the subsystem engineers seek to maximize their expected utilities. Furthermore, the systems engineer is unable to monitor the effort of the subsystem engineer and may not have a complete information about their types or the complexity of the design task. However, the systems engineer can incentivize the subsystem engineers by proposing specific contracts. To obtain an optimal incentive, we pose and solve numerically a bi-level optimization problem. Through extensive simulations, we study the optimal incentives arising from different system-level value functions under various combinations of effort costs, problem-solving skills, and task complexities

Theory of Systems, Systems Metaphysics and Neoplatonism

Science has been developed from the rational-empirical methods, having as a consequence, the representation of existing phenomena without understanding the root causes. The question which currently has is the sense of the being, and in a simplified way, one can say that the dogmatic religion lead to misinterpretations, the empirical sciences contain the exact rational representations of phenomena. Thus, Science has been able to get rid of the dogmatic religion. The project for the sciences of being looks to return to reality its essential foundations; under the plan of theory of systems necessarily involves a search for the meaning of Reality