Transition Constraints Research Articles

Model-based diagnosis-state transition events and constraint equations

Two different approaches to modelbased on-line diagnosis are compared. The DMP method is based on quantitative constraint equations. MIDAS is based on signed directed graphs that are translated into an event graph consisting of the possible state transition events of the process and the failures that they are symptoms of. The methods, which both have been implemented in G2, have been applied to a real-time simulation model of a sterilization process.

A Signal Extraction Approach to the Estimation of Treatment and Control Curves

Abstract Suppose that the response of a group of subjects, which we call the control group, is monitored over time. At a given time after the start of the experiment, the experimenter intervenes and applies a treatment to a subset of the group. We propose a signal extraction approach to the simultaneous estimation of the treatment and control mean response curves, and their rates of change, imposing a smooth transition constraint between the two curves at the time of intervention. By expressing the model in state-space form, we show how to compute the likelihood and the cross-validation function efficiently in O(n) operations together with the response curve estimates and their standard errors. We also show that the curve estimates are solutions to a penalized least squares problem. A small simulation study to assess the performance of the generalized cross-validation and marginal likelihood estimates of the smoothing parameter is carried out, and the methodology in the article is applied to an experiment...

Formal techniques for systems specification and verification

An information system is an agent that keeps its own database, may communicate with other systems through messages and performs some activities. A layered approach is proposed for information systems specification and verification, according to the Infolog model. This formal approach includes five layers: the first two layers are concerned with the specification of safety constraints on the envisaged system database (both static and transition constraints); in the third layer we describe the application-dependent operations by their properties; in the fourth layer we specify a set of liveness and other requirements on the system evolution and we describe its communication behavior; and in the last layer we specify the activities that the system should perform in reaction to trigger events. Each layer should comply with the specification of the previous layer. A unifying, logical framework is proposed supporting the layered approach. The framework includes linear logics for some layers and branching logics for other layers, depending on the type of requirements and constraints relevant in each layer. Both proof-theoretic and model-theoretic techniques are used when introducing the unifying approach.

Objects with roles

The use of object-oriented conceptual models for modeling office applications and information systems is discussed. A model for describing object behavior based on the concept of role is presented. Roles allow one to describe different perspectives for object evolution. For each role, relevant characteristics such as role properties, role states, messages, and role-state transition rules and constraints are defined. The implications of considering several roles in parallel for an object are discussed, and a classification of possible role interactions is given.

Compiling complex database transition triggers

This paper presents a language for specifying database updates, queries and rule triggers, and describes how triggers can be compiled into an efficient mechanism. The rule language allows specification of both state and transition constraints as special cases, but is more general than either. The implementation we describe compiles rules and updates independently of each other. Thus rules can be added or deleted without recompiling any update program and vice versa.

Incorporating theory into database system development

Database systems, like all models, must be constrained to represent just those states and transitions which are possible in the world they model. Database integrity constraints, transition constraints and transaction definitions specify the conformity of a database system to the real world. The enforcement of database system constraints is a difficult problem to solve efficiently; this follows from the large amounts of data involved and the complexity of determining minimum required checks. We present a database system development method in which considerable theoretical support in the form of automated theorem proving is brought to bear on the integrity enforcement problem.

推移律を満足する集団選好の構造化

推移律を満足する集団選好の構造化

SERIATION USING ASYMMETRIC PROXIMITY MEASURES

The data analysis problem of ordering or sequencing a set of objects using an asymmetric proximity function is reviewed, with an emphasis on literature not generally referenced in psychology. In particular, an attempt is made to present some of the more important approaches to the asymmetric seriation task that have been developed independently under a number of different names, for instance, the triangularization of input‐output matrices, minimum feedback arc sets, maximum likelihood paired comparison ranking, majority rule under transitivity constraints, and so on. A simple numerical example that illustrates some of the basic concepts is presented in the course of the discussion.

Note—A Note on Majority Rule under Transitivity Constraints

In a recent paper [Bowman, V. J., C. S. Colantoni. 1973. Majority rule under transitivity constraints. Management Sci. 19 (9, May) 1029–1041.] Bowman and Colantoni have described an optimization model which they relate to problems of majority voting in the theory of social choice. Their optimization model was a linear integer programming problem. The purpose of this note is to indicate that an alternative view may be more useful viz. formulating the problem as a quadratic assignment type. We have discussed this in detail elsewhere [Blin, J. M., K. S. Fu, K. B. Moberg, A. B. Whinston. 1973. Optimization theory and social choice. Proceedings of the Sixth Hawaiian International Conference on Systems Science. Supplement on Urban and Regional Systems: Modelling Analysis and Decision Making. University of Hawaii.] and will limit ourselves here to some brief comments.

Further Comments on Majority Rule Under Transitivity Constraints

In their note [Blin, J. M., A. B. Whinston. 1974. A note on majority rule under transitivity constraints. Management Sci. 20 (11) 1439–1440.], Blin and Whinston indicate that the linear integer programming formulation of the majority voting problem can also be formulated as a quadratic assignment problem. We wish to point out that both of these formulations are a result of the fact that majority decision functions can be linearized over the set of integer solutions to the linear program.

Majority Rule Under Transitivity Constraints

In this paper we are concerned with imposing constraints directly on the admissible majority decisions so as to insure transitivity without restricting individual preference orderings. We demonstrate that this corresponds to requiring that majority decisions be confined to the extreme points of a convex polyhedron. Thus, transitive majority decisions can be characterized as basic solutions of a set of linear inequalities. Through the use of a majority decision function (which is not restricted to be linear) it is shown that constrained majority rule is equivalent to an integer programming problem. Some special forms of majority decision functions are studied including the generalized lp norm and an indicator function. Implications of an integer programming solution, including alternate optima and post optimality analysis, are also discussed.

Crosslinking, Filler, or Transition Constraint of Polymer Networks. I

Abstract For a polymer network at equilibrium in solvent, Flory and Rehner related the polymer fraction νr of the swollen volume to the molecular weight Mc of the chains between crosslinks. Their equation is represented below by the function F(νr) with [Mc] denoting the effective mesh weight, i.e., that obtained by physical measurements. Hence the effective crosslinking 1/[Mc]g from swelling measurements νr is given by 1/F(νr).

Crosslinking, filler, or transition constraint of polymer networks. I

AbstractThe basic theory of modulus/swelling is developed to allow for limited extensibility, filler reinforcement or transition effects, and steric hindrance of aligned segments by extended chains or filler particles.Filler forms an effective hard fraction Ch per cubic centimeter of compound with vc a new (compound) index of swelling. For 1/Mc + σ fix points having ratio φ to gum values 1/F0(vr) and with F(vc) replacing the Flory function F(vr): where σ denotes entanglement. Linkage reinforcement φ does not vary with sulfur crosslinking of SBR. Vacuoles invalidate φ from mass‐increment F0(vr)/F(vr) for inert fillers. Then, or for Graphon, with negligible φ ≈ 1: The effective Ch includes rubber stretched hard on Graphon by swelling or trapped inside hard aggregates. Only the right‐hand equation fits normal blacks. In theory, Ch can always be obtained from swollen moduli G by linear slopes (1 + 1.4Ch) relating F(vc) and (1 − C)ρRT/G. For filler fractions C ≥ 0 cm−3 and low strains α = 1.5−2.0 below prestretch the modulus G is given a new basic definition: Here C2* ≈ 0.7 corresponds to Mooney‐Rivlin C2 and the effective crosslinking 1/[Mc] = (ρRT)−1G is equal to (1 − C)(1/Mc + σ) for unswollen prestretched rubber (vr = 1). For higher strains a hypothesis of strain hardening is proposed. This is distinct and opposite in character to the initial prestretch softening (Mullins effect). Nonlinear effects of crosslinks are expressed by a fractional stress‐upturn Ω (1/Mc + σ), effective mesh wieght (1/Mc + σ)−1 − Ω, and hard fraction Ω(1/Mc + σ). For μh characterizing strain hardening up to the prestretch (αh − 1) their contribution is: The sixth‐power refinement has J = j(αb − 1)1/2 with j ≈ 0.4. The hard phase is augmented by filler and grows with increasing strain up to the prestretch.

Crosslinking, filler, or transition constraint of polymer networks. II

AbstractThe theory of Part I is developed by application to filler reinforcement of NR and SBR. For unswollen but prestretched networks it quantifies entire stress–strain curves and applies new concepts of extensibility and strain hardening. Constraint of swelling is expressed by a constant φ, termed linkage reinforcement, and by an effective hard fraction Ch per cubic centimeter of compound. For rubber–filler swelling vc the modified Flory functions F(vc) in part 1 need 3% correction. Then, relative to gum fix points 1/F0(vr): where Ch ≤ 1.15C for filler concentrations C per cubic centimeter of compound. The effective Ch comprises the volume fraction C* of bonded particles and 5–10 Å of surface–bound rubber that has been stretched hard by swelling. When needed, the actual crosslink density and intrinsic linkage reinforcement φ0 can be obtained by dividing by (1 + 2.5Cφ) where Cφ = (C ln φ)/(1 + 2.5C). The case Ch ≤ 1.15C with Graphon or inert fillers is identified and assessed by equations: Results Ch > 1.15C are invalid, but then Ch ≈ 1.15C* ≈ 1.15C, e.g., for carbon blacks. Even Graphon is distinguished from inert fillers at low concentrations C by substantial constraint reinforcement F0(vr)/F(vc) > 1. For prestressed dry rubber a modulus G, network extensibility αb − 1, and upturn coefficient μh express the whole curve; G and μh show identical constraint strength distributions. Network extensibility αb − 1 is the microbreaking strain (prestretch); for pure elastomer it is elongation at break. The relation of stress F to extension ratio α is: where C2* = 0.7 and j = 0.4 from NR/MPC data. Strain‐hardening coefficients h are obtained from μh by the theory given in Part I. Hard modulus components Gh = 0.7 ln (h/h0) vanish as h → h0 (gum) = 110. After high prestresses the residual ln‐(h*/h0) due to strong carbon‐rubber linkages implies Gh* = 0.42 kg/cm2, i.e., ca. 10% of the normal cure crosslinks.