Timed data flow diagrams

Traditional Data Flow Diagrams (DFD\u27s) are the cornerstone of the software development methodology known as Structured Analysis (SA), and they are probably the most widely used specification technique in industry today. DFD\u27s are popular because of their graphical representation and their hierarchical structure. Thus, they are well-suited for users with non-technical backgrounds and are commonly used to depict the static structure of information flow in a system. Numerous attempts to formalize DFD\u27s have appeared in the technical literature. We focus on the Formalized Data Flow Diagrams (FDFD\u27s) developed by Coleman, Wahls, Baker, and Leavens;This dissertation analyzes and extends FDFD\u27s with respect to their usefulness in specifying the qualitative and quantitative properties of real systems. Prior to this dissertation, there existed no well-founded knowledge about the computational power of FDFD\u27s nor any formal model in FDFD\u27s of the timing behavior of real systems;The dissertation is organized as a collection of five independent papers. Briefly, the main results of each paper are as follows: (i) Reduced FDFD\u27s are Turing equivalent. (ii) Stores, persistent flows, tests for empty flows, and infinite domains are not essential for FDFD\u27s. (iii) Subclasses of FDFD\u27s are equivalent to known subclasses of FIFO Petri Nets, immediately furnishing the decidability results for subclasses of FIFO Petri Nets to the corresponding subclasses of FDFD\u27s. (iv) A general stochastic model of time for FDFD\u27s (called Timed Data Flow Diagrams--TDFD\u27s) is defined, allowing not only a description of the relative likelihoods of various execution times, but also descriptions of the possible joint firing behavior of transitions. (v) An aggregation principle can be used for an efficient stochastic analysis of periodic TDFD\u27s with Markovian transition times;The results in this dissertation provide a firm theoretical foundation for further advances in Computer Science and Statistics, leading to practical and expressive tools for the specification and analysis of real systems

Subclasses of Formalized Data Flow Diagrams: Monogeneous, Linear & Topologically Free Choice RDFD\u27s

Formalized Data Flow Diagrams (FDFD\u27s) and, especially, Reduced Data Flow Diagrams (RDFD\u27s) are Turing equivalent (Symanzik and Baker, 1996). Therefore, no decidability problem can be solved for FDFD\u27s in general. However, it is possible to define subclasses of FDFD\u27s for which decidability problems can be answered. In this paper we will define certain subclasses of FDFD\u27s, which we call Monogeneous RDFD\u27s, Linear RDFD\u27s, and Topologically Free Choice RDFD\u27s. We will show that two of these three subclasses of FDFD\u27s can be simulated via isomorphism by the correspondingly named subclasses of FIFO Petri Nets. It is known that isomorphisms between computation systems guarantee the same answers to corresponding decidability problems (e. g., reachability, deadlock, liveness) in the two systems (Kasai and Miller, 1982). This means that problems where it is known that they can (not) be solved for a subclass of FIFO Petri Nets it follows immediately that the same problems can (not) be solved for the correspondingly named subclass of FDFD\u27s

Geographic Variations in Cardiovascular Health in the United States: Contributions of Stateâ and Individualâ Level Factors

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/139063/1/jah3932.pd

Brownian Motions on Metric Graphs

Brownian motions on a metric graph are defined. Their generators are characterized as Laplace operators subject to Wentzell boundary at every vertex. Conversely, given a set of Wentzell boundary conditions at the vertices of a metric graph, a Brownian motion is constructed pathwise on this graph so that its generator satisfies the given boundary conditions.Comment: 43 pages, 7 figures. 2nd revision of our article 1102.4937: The introduction has been modified, several references were added. This article will appear in the special issue of Journal of Mathematical Physics celebrating Elliott Lieb's 80th birthda

Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics

We review the use of an exact renormalization group equation in quantum field theory and statistical physics. It describes the dependence of the free energy on an infrared cutoff for the quantum or thermal fluctuations. Non-perturbative solutions follow from approximations to the general form of the coarse-grained free energy or effective average action. They interpolate between the microphysical laws and the complex macroscopic phenomena. Our approach yields a simple unified description for O(N)-symmetric scalar models in two, three or four dimensions, covering in particular the critical phenomena for the second-order phase transitions, including the Kosterlitz-Thouless transition and the critical behavior of polymer chains. We compute the aspects of the critical equation of state which are universal for a large variety of physical systems and establish a direct connection between microphysical and critical quantities for a liquid-gas transition. Universal features of first-order phase transitions are studied in the context of scalar matrix models. We show that the quantitative treatment of coarse graining is essential for a detailed estimate of the nucleation rate. We discuss quantum statistics in thermal equilibrium or thermal quantum field theory with fermions and bosons and we describe the high temperature symmetry restoration in quantum field theories with spontaneous symmetry breaking. In particular, we explore chiral symmetry breaking and the high temperature or high density chiral phase transition in quantum chromodynamics using models with effective four-fermion interactions.Comment: 178 pages, appears in Physics Report

Timed data flow diagrams

Traditional Data Flow Diagrams (DFD's) are the cornerstone of the software development methodology known as "Structured Analysis" (SA), and they are probably the most widely used specification technique in industry today. DFD's are popular because of their graphical representation and their hierarchical structure. Thus, they are well-suited for users with non-technical backgrounds and are commonly used to depict the static structure of information flow in a system. Numerous attempts to formalize DFD's have appeared in the technical literature. We focus on the Formalized Data Flow Diagrams (FDFD's) developed by Coleman, Wahls, Baker, and Leavens;This dissertation analyzes and extends FDFD's with respect to their usefulness in specifying the qualitative and quantitative properties of real systems. Prior to this dissertation, there existed no well-founded knowledge about the computational power of FDFD's nor any formal model in FDFD's of the timing behavior of real systems;The dissertation is organized as a collection of five independent papers. Briefly, the main results of each paper are as follows: (i) Reduced FDFD's are Turing equivalent. (ii) Stores, persistent flows, tests for empty flows, and infinite domains are not essential for FDFD's. (iii) Subclasses of FDFD's are equivalent to known subclasses of FIFO Petri Nets, immediately furnishing the decidability results for subclasses of FIFO Petri Nets to the corresponding subclasses of FDFD's. (iv) A general stochastic model of time for FDFD's (called Timed Data Flow Diagrams--TDFD's) is defined, allowing not only a description of the relative likelihoods of various execution times, but also descriptions of the possible joint firing behavior of transitions. (v) An aggregation principle can be used for an efficient stochastic analysis of periodic TDFD's with Markovian transition times;The results in this dissertation provide a firm theoretical foundation for further advances in Computer Science and Statistics, leading to practical and expressive tools for the specification and analysis of real systems.</p

Stochastic Analysis of Periodic Timed Data Flow Diagrams with Markovian Transition Times

Timed (or Stochastic) Data Flow Diagrams (TDFD's or SDFD's) introduced in Symanzik and Baker (1996d) are an extension of the Formalized Data Flow Diagrams, defined in Leavens et al. (1996). This extension allows us to assess the quantitative behavior (e. g., performance, throughput, average load of a bubble, etc.) as well as the qualitative behavior (e. g., deadlock, reachability, termination, finiteness, liveness, etc.), eventually depending on different types of transition times, for the system modeled through the TDFD. In this paper, we consider Markovian transition times for the consumption of in--flow items and for the production of items on the out--flow. Moreover, we require the TDFD to be periodic and irreducible and it must have a finite reachability set. For these models, we have been able to apply an aggregation principle of Schassberger (1984), extended for periodic Markov chains by Woo (1993), to efficiently determine stationary probabilities, expected waiting times, and limiting process probabilities.© Copyright 1996 by Jürgen Symanzik. All rights reserved.</p

STOCHASTIC ANALYSIS OF PERIODIC TIMED DATA FLOW DIAGRAMS WITH MARKOVIAN TRANSITION TIMES

Timed (or Stochastic) Data Flow Diagrams (TDFD&apos;s or SDFD&apos;s) introduced in [SB96b] are an extension of the Formalized Data Flow Diagrams, defined in [LWBL96]. This extension allows us to assess the quantitative behavior (e. g., performance, throughput, average load of a bubble, etc.) as well as the qualitative behavior (e. g., deadlock, reachability, termination, niteness, liveness, etc.), eventually depending on different types of transition times, for the system modeled through the TDFD. In this paper, we consider Markovian transition times for the consumption of in-flow items and for the production of items on the out-flow. Moreover, we require the TDFD to be periodic and irreducible and it must have a finite reachability set. For these models, we have been able to apply an aggregation principle of [Sch84], extended for periodic Markov chains by [Woo93], to efficiently determine stationary probabilities, expected waiting times, and limiting process probabilities