Qualitative Constraints Research Articles

Henderson Porphyry Molybdenum System, Colorado: II.Decoupling of Introduction and Deposition of Metals during GeochemicalEvolution of Hydrothermal Fluids

Henderson Porphyry Molybdenum System, Colorado: II.Decoupling of Introduction and Deposition of Metals during GeochemicalEvolution of Hydrothermal Fluids

A Set-Theoretical Foundation of Qualitative Reasoning and its Application to the Modeling of Economics and Business Management Problems

The qualitative reasoning (QR) field has developed various representation and reasoning methods for the modeling with incomplete information or incomplete knowledge. While most uncertain reasoning approaches describe uncertain or imprecisely known information as probability distribution functions, qualitative reasoning bases its model specification on qualitative descriptions that are derived from known qualitative system properties. Problems are formulated as sets of qualitative constraints and their analysis is performed by applying a qualitative calculus. This paper presents a general, unifying theory of the various existing qualitative reasoning systems that includes, as special cases, reasoning methods that use representations of qualitative differential equations and qualitative difference equations. Based on set theory, our QR framework describes fundamental concepts such as qualitative models and solutions, and relates them to the quantitative analogues of its underlying quantitative reference system. Our motivation arises from the types of models found in the management sciences. Thus we emphasize the significance of discrete, dynamic models and optimization models in the business management and economics fields, both of which have received less attention in current QR research. Finally, we extend our theoretical framework to include an approach to qualitative optimization.

A NOVEL OPTIMIZATION APPROACH TO THE EFFECTIVE COMPUTATION OF NURBS KNOTS

This paper presents a novel modeling technique and develops an interactive algorithm that facilitates the automatic determination of non-uniform knot vectors as well as other control variables for NURBS curves and surfaces through the unified methodology of energy minimization, variational principle, and numerical techniques. NURBS have become a de facto industry-standard primarily because of their power to represent free-form shapes as well as commonly-used analytic shapes. Although many geometric algorithms have been developed for NURBS, existing techniques primarily concentrate on NURBS control points. Recently, the optimization principle has been widely studied, which affords designers to interactively manipulate NURBS via energy functionals, simulated forces, qualitative and quantitative constraints, etc. The key advantage of energy-based approaches is that they can evolve both the control points and the weights in response to NURBS deformation resulted from the numerical optimization of a set of energy functionals. These energy functionals have the capability to quantify user-centered aesthetic criteria, qualitative constraints, and functional requirements for a large variety of applications in a unified fashion. In this paper, we further augment our NURBS modeling capabilities by incorporating NURBS' non-uniform knot sequence into our shape parameter set intuitively controlled by energy functionals. We also have implemented a software environment that supports a large variety of functionals ranging from simple quadratic energy forms to non-linear curvature-based objective functionals.

Data Sharpening for Nonparametric Inference Subject to Constraints

Data sharpening involves perturbing the data to improve the performance of a statistical method. The versions of it that have been proposed in the past have been for bias reduction in curve estimation, and the amount of perturbation of each datum has been determined by an explicit formula. This article suggests a distance-based form of data sharpening, in which the sum of the distances that data are moved is minimized subject to a constraint imposed on an estimator. The constraint could be one that leads to bias reduction, or to variance or variability reduction, or to a curve estimator being monotone or unimodal. In contrast to earlier versions of the method, in the form presented in this article the amount and extent of sharpening is determined implicitly by a formula that is typically given as the solution of a Lagrange-multiplier equation. Sometimes the solution can be found by Newton–Raphson iteration, although when qualitative constraints are imposed it usually requires quadratic programming or a related method.

Hairy black holes,horizon mass and solitons

Properties of the horizon mass of hairy black holes are discussed withemphasis on certain subtle and initially unexpected features. A keyproperty suggests that hairy black holes may be regarded as `bound states'of ordinary black holes (without hair) and coloured solitons. This model isthen used to predict the qualitative behaviour of the horizon properties ofhairy black holes, to provide a physical `explanation' of their instabilityand to put qualitative constraints on the end-point configurations thatresult from this instability. The available numerical calculations supportthese predictions. Furthermore, the physical arguments are robust andshould also be applicable in more complicated situations where detailednumerical work is yet to be carried out.

Knowledge representation and qualitative simulation of salmon redd functioning. Part I: qualitative modeling and simulation

This work aims at representing empirical knowledge of freshwater ecologists on the functioning of salmon redds (spawning areas of salmon) and its impact on mortality of early stages. For this, we use Qsim, a qualitative simulator. In this first part, we provide unfamiliar readers with the underlying qualitative differential equation (QDE) ontology of Qsim: representing quantities, qualitative variables, qualitative constraints, QDE structure. Based on a very simple example taken of the salmon redd application, we show how informal biological knowledge may be represented and simulated using an approach that was first intended to analyze qualitatively ordinary differential equations systems. A companion paper (Part II) gives the full description and simulation of the salmon redd qualitative model. This work was part of a project aimed at assessing the impact of the environment on salmon populations dynamics by the use of models of processes acting at different levels: catchment, river, and redds. Only the latter level is dealt with in this paper.

Reducing variability using bootstrap methods with qualitative constraints

Parametric methods are often attractive for small to moderate samples, since, relative to nonparametric techniques, they reduce variability of a wide range of statistical procedures. However, when sample size is small there is often little empirical evidence to support a particular model, and so, while variance can be reduced, bias may be increased. In theory, smoothing can be used to reduce variability of nonparametric procedures, but the difficulty of choosing the smoothing parameter can be a serious drawback. In the present paper we propose an alternative approach. We suggest implicitly smoothing nonparametric distribution estimates by enforcing the same sort of qualitative constraint that parametric methods attempt to reflect. We show theoretically that such a method produces the same order of variance reduction as explicit smoothing, even when the smoothing parameter for the latter is chosen optimally. Furthermore, we demonstrate numerically that imposing qualitative constraints on distribution estimates, and on the nonparametric bootstrap, does in fact produce important reductions in variability for small sample sizes.

The design of laboratory experiments to produce collisionless shocks of cosmic relevance

Naturally occurring shocks transport energy and accelerate particles throughout the cosmos. The problem of producing collisionless shocks in the laboratory that are of relevance to such cosmic shocks is considered. Such an experiment must meet a number of constraints, several of which can be expressed by algebraic scaling relations. The relations for magnetization, plasma beta, Alfvén Mach number, temperature, magnetic field, and collisionality are described here. Taken together, the limits imposed by these constraints upon possible experiments are specified. The growth of magnetohydrodynamic (MHD) turbulence and the degree of particle acceleration are examined, demonstrating that it is feasible to contemplate studies of such phenomena in the laboratory. Finally, some discussion of how an experiment might meet the other qualitative constraints, and of how a laser might be used to drive the shock, is also included.

Empirical constraints on closure temperatures from a single diffusion coefficient

The elucidation of thermal histories by geochronological and isotopic means is based fundamentally on solid-state diffusion and the concept of closure temperatures. Because diffusion is thermally activated, an analytical solution of the closure temperature (Tc*) can only be obtained if the diffusion coefficient D of the diffusion process is measured at two or more different temperatures. If the diffusion coefficient is known at only one temperature, however, the true closure temperature (Tc*) cannot be calculated analytically because there exist an infinite number of possible (apparent) closure temperatures (T¯c) which can be generated by this single datum. By introducing further empirical constraints to limit the range of possible closure temperatures, however, mathematical analysis of a modified form of the closure temperature equation shows that it is possible to make both qualitative and quantitative estimates of Tc* given knowledge of only one diffusion coefficient DM measured at one temperature TM. Qualitative constraints of the true closure temperature Tc* are obtained from the shapes of curves on a graph of the apparent Tc (T¯c) vs. activation energy E, in which each curve is based on a single diffusion coefficient measurement DM at temperature TM. Using a realistic range of E, the concavity of the curve shows whether TM is less than, approximately equal to, or greater than Tc*. Quantitative estimates are obtained by considering two dimensionless parameters [lnERT^c vs. Tc*/TM] derived from these curves. When these parameters are plotted for known argon diffusion data and for a given diffusion size and cooling rate, it is found that the resultant curves are almost identical for all of the commonly dated K–Ar minerals – biotite, phlogopite, muscovite, hornblende and orthoclase – in spite of differences in their diffusion parameters. A common curve for Ar diffusion can be derived by least-squares fitting of all the Ar diffusion data and provides a way of predicting a “model” closure temperature Tcm from a single diffusion coefficient DM at temperature TM. Preliminary diffusion data for a labradorite lead to a Tcm of 507 ± 17 °C and a corresponding activation energy of about 65 kcal/mol, given a grain size of 200 μm and a cooling rate of 5 °C/Ma. Curves for He diffusion in silicates (augite, quartz and sanidine) also overlap to a significant degree, both among themselves and with the Ar model curve, suggesting that a single model curve may be a good representation of noble gas closure temperatures in silicates. An analogous model curve for a selection of 18O data can also be constructed, but this curve differs from the Ar model curve. A single model curve for cationic species does not appear to exist, however, suggesting that chemical bonding relationships between the ionic size/charge and crystal structure may influence the closure temperatures of diffusing cations. An indication of the degree of overlap among the various curves for Ar, He, 18O and cations is also obtained by considering the dimensionless parameter E/RTc*; for the noble gases and 18O, E/RTc* values for the respective minerals are very similar, whereas for cations, there is significant dispersion. Given these constraints, this may be a potential method of estimating closure temperatures for certain diffusing species when there are limited diffusion data.

Integrated Temporal Reasoning with Periodic Events

In many areas of Computer Science, including planning, workflows, guidelines, and protocol management, one has to deal with abstract plans, procedures, or schedules involving temporal constraints between classes of actions that have to be repeated at periodic times and may be instantiated in different ways for different executions of the plans (procedures, schedules). In this paper we propose an integrated framework to deal with both qualitative temporal constraints on classes of actions and temporal constraints between instances of actions, in which temporal reasoning is used to amalgamate both types of constraints and to check their consistency. In particular, we consider an expressive formalism to deal with temporal constraints between classes of actions (with special attention to periodic actions) which takes into account different components such as frame times, numeric quantification, periods, and qualitative relations. We define the notions of (contextual) concretization of qualitative temporal constraints between classes and use this notion to formally define the consistency of a knowledge base of temporal constraints between classes and a set of temporal constraints on instances, and to define the algorithm for checking such a consistency. An application for scheduling lessons in a school is shown in an example.

Efficient Processing of Queries and Assertions about Qualitative and Quantitative Temporal Constraints

A critical problem for managers of temporal information is the treatment of assertions and of complex types of queries because in many cases the treatment could involve reasoning on the whole knowledge base of temporal constraints. We propose an efficient approach to this problem. First, we show how different types of queries can be answered (in a complete way) in a time polynomial in the dimension of the query and independently of the dimension of the knowledge base. Second, we provide an efficient (and complete) procedure to deal with sessions of interleaved assertions and queries to the knowledge base. We provide both analytical and experimental evaluations of our approach, and we discuss some application areas.

Imagery Constraints on Quantitative and Qualitative Aspects of Mental Synthesis

Two experiments are reported which explored constraints on the use of imagery in mental synthesis tasks in which subjects generated images of recognisable objects by mentally combining a set of specified shapes. Experiment 1 demonstrated that subjects' naming of imaged constructions is poorer when constructions are derived from sets of concrete-object shapes than from sets of more abstract shapes. This suggests that the semantic properties of the concrete shapes may constrain mental synthesis. In Experiment 2 subjects were given unlimited time to generate multiple imaged patterns from an increasing number of abstract shapes. Number of shapes to be combined had little effect on the number of imaged constructions or on the quality of those constructions as rated by independent judges. In both experiments, drawing the imaged constructions resulted in improved naming of those constructions and appeared to act as a form of external stimulus support that mitigated both qualitative and quantitative constraints on performance.

COBS: qualitatively constrained smoothing via linear programming

Popular smoothing techniques generally have a difficult time accommodating qualitative constraints like monotonicity, convexity or boundary conditions on the fitted function. In this paper, we attempt to bring the problem of constrained spline smoothing to the foreground and describe the details of a constrained B-spline smoothing (COBS) algorithm that is being made available to S-plus users. Recent work of He & Shi (1998) considered a special case and showed that the L1 projection of a smooth function into the space of B-splines provides a monotone smoother that is flexible, efficient and achieves the optimal rate of convergence. Several options and generalizations are included in COBS:it can handle small or large data sets either with user interaction or full automation. Three examples are provided to show how COBS works in a variety of real-world applications.

Computational complexity of relating time points with intervals

Several algebras have been proposed for reasoning about qualitative constraints over the time line. One of these algebras is Vilain's point–interval algebra, which can relate time points with time intervals. Apart from being a stand-alone qualitative algebra, it is also used as a subalgebra in Meiri's approach to temporal reasoning, which combines reasoning about metric and qualitative temporal constraints over both time points and time intervals. While the satisfiability problem for the full point–interval algebra is known to be NP-complete, not much is known about its 4 294 967 296 subclasses. This article completely determines the computational complexity of these subclasses and it identifies all of the maximal tractable subalgebras—five in total.

Time Petri nets for modelling civil litigation

This paper aims to study how Petri nets can be used to model explicit, qualitative time constraints. After discussing some models devoted to temporal reasoning and some previous works about Petri nets and legal systems, the different ways to attach time constraints to Petri nets are discussed. We propose using time windows attached to transitions: such a window is the interval during which the corresponding event (represented by a transition) can occur. The studied example is an action between a plaintiff and a defendant: the corresponding Petri net is proposed. We then show some temporal properties that can be verified using the usual Petri nets methods. So, it is possible to guarantee that no constraint violation will occur.

Orders of magnitude reasoning applied in selecting shield

Orders of magnitude reasoning in artificial intelligence (AI) and qualitative algebra are discussed and applied in selecting shield in this paper. It includes basic quantitative calculation, qualitative constraint and principle of orders of magitude reasoning. The method has potential prospects in dealing with the engineering problems.

Experimental Analysis of Numeric and Symbolic ConstraintSatisfaction Techniques for Temporal Reasoning

Many temporal applications like planning and scheduling can be viewed as special cases of the numeric and symbolic temporal constraint satisfaction problem. Thus we have developed a temporal model, TemPro, based on the interval Algebra, to express such applications in term of qualitative and quantitative temporal constraints. TemPro extends the interval algebra relations of Allen to handle numeric information. To solve a constraint satisfaction problem, different approaches have been developed. These approaches generally use constraint propagation to simplify the original problem and backtracking to directly search for possible solutions. The constraint propagation can also be used during the backtracking to improve the performance of the search. The objective of this paper is to assess different policies for finding if a TemPro network is consistent. The main question we want to answer here is ’’how much constraint propagation is useful‘‘ for finding a single solution for a TemPro constraint graph. For this purpose, we have experimented by randomly generating large consistent networks for which either arc and/or path consistency algorithms (AC-3, AC-7 and PC-2) were applied. The main result of this study is an optimal policy combining these algorithms either at the symbolic (Allen relation propagation) or at the numerical level.

Extending constraint logic programming for temporal reasoning

In recent years, several constraintdbased temporal reasoning frameworks have been proposed. They consider temporal points or intervals as domain elements linked by temporal constraints. Temporal reasoning in these systems is based on constraint propagation. In this paper, we argue that a language based on constraint propagation can be a suitable tool for expressing and reasoning about temporal problems. We concentrate on Constraint Logic Programming (CLP) which is a powerful programming paradigm combining the advantages of Logic Programming and the efficiency of constraint solving. However, CLP presents some limitations in dealing with temporal reasoning. First, it uses an “arc consistency” propagation algorithm which is embedded in the inference engine, cannot be changed by the user, and is too weak in many temporal frameworks. Second, CLP is not able to deal with qualitative temporal constraints. We present a general meta CLP architecture which maintains the advantages of CLP, but overcomes these two main limitations. Each architectural level is a finite domain constraint solver (CLP(FD)) that reasons about constraints of the underlying level. Based on this conceptual architecture, we extend the CLP(FD) language and we specialize the extension proposed on Vilain and Kautz’s Point Algebra, on Allen’s Interval Algebra and on the STP framework by Dechter, Meiri and Pearl. In particular, we show that we can cope effectively with disjunctive constraints even in an intervaldbased framework.

Hierarchical constraint satisfaction of multilateral trade matching in commodity auction markets

A commodity auction market provides a trading intermediary whose role is to find optimal trade matching between buyers and sellers that satisfies their trading constraints. Some commodity auction markets utilize forms of electronic trading intermediary systems in order to improve the efficiency and effectiveness of trading of huge volumes of transactions during short periods of time. Previous research works on electronic trading intermediary systems focus on the maximization of the trade volume obtained by satisfying mainly price and quantity constraints. The principal restriction of these approaches is that the heterogeneity of the commodity is ignored or at least not significantly considered. The objective of the study in this paper is to propose a computable mechanism of trading inter-mediaries for commodity auction markets, supporting not only ordinary trading constraints of prices and quantities but also other qualitative and quantitative constraints on the commodity properties and trading conditions.

Negotiation in Constraint-Based Design

A design problem usually involves multiple perspectives, each with own set of constraints that may interact. The objective of this paper is to develop a methodology to assist in negotiation of constraints from multiple perspectives. The proposed approach is based on qualitative reasoning that provides each perspective with negotiation information for making design decisions. A qualitative constraint network is used to characterize the qualitative and quantitative relationship between design variables. It provides means for tracking dependencies among perspectives for a set of constraints and determines the impact of design changes. When a conflict occurs, effective negotiation strategies are generated. A negotiation procedure for an ill-structured negotiation process is presented. The effectiveness of the negotiation process is improved with the procedure proposed. A valve design problem illustrates the concepts discussed in the paper.