General Time Systems Research Articles

The Relevance of Spatial and Temporal Connections and Relationships for the Formation of a Subtheory of Forensic Forecasting

The article examines the influence of spatial and temporal factors on forming a subtheory of forensic forecasting. The historical analysis of the formation of scientific knowledge about spatial and temporal connections and relationships in the light of the development of the general theory of forensic examination has been carried out. In this regard, the author proposed the term “time correlation of anticipated events” and introduced it into the general time system (from the past to the future) of the time intervals for the occurrence of certain adverse events or phenomena, the so-called precursor events, which by their appearance warn of upcoming events. The author highlights the considerable importance of technological forecasting in organizing human activity since this activity presupposes the future development of various kinds of technologies.

Temporal binding and internal clocks: No evidence for general pacemaker slowing.

The perception of time is distorted by many factors (e.g., arousal, temperature, age etc.), but is it possible that causality would affect our perception of time? We investigate timing changes in the temporal binding effect, which refers to a subjective shortening of the interval between actions and their outcomes. Four experiments investigated whether binding may be due to variations in the rate of an internal clock. Specifically, we asked whether binding reflects changes to a general timing system, or a dedicated clock unique to causal sequences. We developed a novel experimental paradigm (embedded interval estimation procedure) in which participants made temporal judgments of either causal or noncausal intervals, or the duration of an event embedded within that interval. Stimuli and modality were combined factorially, with interval markers and embedded events being either visual or auditory. Although we replicated the temporal binding effect, we found no evidence for commensurate changes to time perception of the embedded event, which suggests that temporal binding is effected by changes to a specific and dedicated, rather than a general clock system. (PsycINFO Database Record

Generalized direct Lyapunov method for the analysis of stability and attraction in general time systems

A generalized direct Lyapunov method is put forward for the study of stability and attraction in general time systems of the following types: the classical dynamical system in the sense of Birkhoff, the general system in the sense of Zubov, the general system in the sense of Seibert, the general system with delay, and the general “input-output” system. For such systems, with the help of generalized Lyapunov functions with respect to two filters, two quasifilters, or two filter bases, necessary and sufficient conditions for stability and attraction are obtained under minimal assumptions about the mathematical structure of the general system.

On feedback controllers

Abstract The two main results are the necessary and sufficient conditions for the existence of a causal and a strongly causal feedback controller which realizes a given behaviour on a given system. The proofs are constructive. If the given system is a discrete event system or an ordinary discrete event system, then a controller could also be a discrete event system or an ordinary discrete event system, respectively. The results are given using an algebraic approach to the modelling of general time systems introduced by the author.

Discrete events and general systems theory

Abstract A new formal approach to the qualitative modelling of general time systems is introduced. The formalism is suitable for general non-deterministic systems with non-numerically valued inputs and outputs, e.g. for discrete event systems. The following basic concepts of systems theory, observability, causality, determinism and interconnections of systems, are defined using an input-output approach to the modelling. The concept of the state is introduced as a secondary one. A general definition of the discrete event systems is given. Some fundamental properties of systems are proved. A real-time extension of the supervisory control problem given by Ramadge and Wonham is formulated. Seven examples are provided.

CHARACTERIZATION OF FINITE STATE AUTOMATA—TOPOLOGICAL APPROACH

This paper deals with the characterization problem or finite state automata. Firstly, two examples of automata are presented, one indicating the existence of some specific class of automata which is on the boundary between finite and infinite automata, and the other as a counterexample to a condition which has been speculated to characterize the finite state automaton class. Secondly, a metric called causal metric is defined for discrete time systems, and the concept of causality of general time systems is topologically characterized for discrete cases. Based on the causal metric another metric is defined on the state spaces of discrete time systems. The compactness of the state spaces with respect to the metric is discussed and this leads us to the theorem: A stationary, causal and finitely observable discrete lime system can be represented by and only by finite automata.

First photoelectron timing error evaluation of a new scintillation detector model

A general timing system model for a scintillation detector developed by Hero et al. (1990) was experimentally evaluated. The detector consists of a scintillator and a photodetector such as a photomultiplier tube (PMT) or an avalanche photodiode. The model uses a Poisson point process to characterize the light output from the scintillator. This timing model was used to simulate a bismuth germanate (BGO) scintillator with a Burle 8575 PMT using first photoelectron timing detection. Evaluation of the model consisted of comparing the root-mean-square error from the simulations with the error from the actual detector system. It is found that the general model compares well with the actual error results for the BGO/8575 PMT detector. >

THE CATEGORY THEORY OF TIME SYSTEMS

In this paper we show a categorical treatment of general time systems using the categorization method presented in our previous paper. Various concepts about general time systems are categorized in the unified framework. Some category theoretical tools for the investigation of such time systems are presented. Using those tools some basic properties of time systems are explored in our framework. In particular, a conceptual equivalence between the causality and the state space representability is proved in the categorical terms. These results show that our method can be a universal tool for a categorization and a categorical treatment of mathematically defined general systems.

Causality invariance of general systems under output feedback transformations

The causality preservation property (CPP) under output feedback transformations, a kind of closedness of causality under the transformations, is introduced as one of the basic system properties about a well-behaved system model. The causality of this paper is the one formulated as past-determinancy in the framework of the mathematical general systems theory. The paper presents a necessary and sufficient condition for a general time system to possess the CPP under the output feedback transformations, and demonstrates the significance of the result by identifying the essential condition which makes a class of linear systems well-posed under the transformations. The paper also discusses the relationship between the feedback transformations and the system inverse transformation, the transformation by interchanging inputs and outputs of a given system. This is of real conceptual significance because it gives a new insight into the feedback transformation. Introducing the auxiliary systems which will be termed ...

Canonical realization of general time systems

The canonical realization of general time systems by dynamical systems is discussed employing the notation and definitions of Takahara and Mesarovic. Previous results are extended to the case of causal, but not necessarily stationary, systems and to stationary, strongly connected systems. Conditions are provided under which a time system is guaranteed to have a canonical representation from within a class of possible realizations.

A Note on Reversibility and Causality of General Time Systems

One of the basic advantages of general systems theory is that it tends to put things into the right perspective, separating those results which are of a global, general nature from others which are solely consequences of particular system features at hand. The problem of representing a general input-output system (which is, in essence, a binary relation between time functions) by some input-output-state system (to be chosen causal, if possible) is one of the central questions of the theory and a number of interesting results have already been achieved [1–9]. Also the investigation of the concepts of observability and controllability [10, 11] of general systems has produced fruitful results. In this paper we shall attempt to tie up the notion of causality with another concept which seems central in general systems theory (as well as in physics and biology) though it has not received too much attention yet in this field, namely the notion of reversibility (see also [12, 20]).

Discrete and Continuous Realizations of General Time Systems

In the theory of general systems an (abstract) system is regarded as a set of input-output pairs [1, 2, 3]. It may be thought of as a set of observations which were collected by an experimenter from an unknown real system. The aims of general system theory consist in the construction of an algebraic model for analysis and description of the internal behavior of the real system. [11]

時間システムの状態空間による表現

時間システムの状態空間による表現

Natural states and past-determinism of general time systems

The concepts of natural state and past-determinism are given for general time systems, i.e., systems whose input-output pairs are ordered pairs of abstract functions defined on a linearly ordered set. It is shown that every general time system has a causal realization; however, only the past-determined systems have causal realizations such that the state can be identified by observing the past input and output over a sufficient inteval of time. Such identifiable states, the natural states, are shown to be unique up to an isomorphism and characterized by equivalence classes of input-output pairs.