Solving applied general equilibrium models represented as a mixture of linearized and levels equations

General equilibrium moels are usually represented as a system of levels equations (e.g., in North America) or a system of linearized equations (e.g., in Australia). Either representation can be used to obtain accurate solutions. General-purpose software is available in both cases-GAMS or MPS/GE is typically used by levels modellers and GEMPACK by linearizers. Some equations (notably accounting identities) are naturally expressed in the levels while others (especially behavioural equations) are naturally expressed in a linearized form. This paper describes the new GEMPACK facility for solving models represented as a mixture of levels and linearized equations and discusses the advantages to modellers of using such a representation.     

GEMPACK: General-purpose software for applied general equilibrium and other economic modellers

This paper gives a brief overview of a new suite of software designed to make it relatively painless to implement large economic models, especially those in the computable general equilibrium (CGE) class. Whereas in the past a large element in the cost of building these models has been the writing of special-purpose code, the GEMPACK facility described here virtually eliminates the need for tailor-made programs. Moreover, because this facility is accessed via an essentially algebraic language, the GEMPACK computer text file used to implement an economic model provides an easily understood, but exhaustive and definitive, documentation of the model itself — something which only rarely has been available in the past.In this paper the CGE label applies to all numerical applications of general equilibrium (loosely speaking, multisectoral models whose detail gives an exhaustive coverage of the economy, and which recognise balance identities on both the revenue and costs sides of the transactions accounts of explicitly identified representative agents).     

EXTRACTING SECONDARY BIO‐EVENT ARGUMENTS WITH EXTRACTION CONSTRAINTS

This paper describes our bio‐event extraction system developed for the BioNLP 2009 Shared Task 2, with focus on its capability of extracting secondary biological event arguments from literature. Shared Task 2 is particularly interesting because when browsing literature, biologists often need to understand conditions surrounding biological events, which are usually expressed by secondary event arguments (e.g., binding sites). To achieve our goal, we take an approach that extracts n‐ary relations from text using event extraction constraints automatically generated from a training corpus. Event constraints consist of sequences of trigger words and semantic roles which we automatically identify using Conditional Random Fields (CRFs). Unlike most other systems participating in this shared task, our system is light‐weight and relies on neither external resources (e.g., Ontologies and dictionaries) nor natural language processing software (e.g., POS taggers and parsers). The official test results show that our approach performed well on extracting secondary arguments in Task 2, yielding the highest precision at 76.62% and the second highest F‐measure at 43.22%.     

How to divide a territory? A new simple differential formalism for optimization of set functions

In many practical problems, we must optimize a set function, i.e., find a set A for which f(A)→max, where f is a function defined on the class of sets. Such problems appear in design, in image processing, in game theory, etc. Most optimization problems can be solved (or at least simplified) by using the fact that small deviations from an optimal solution can only decrease the value of the objective function; as a result, some derivative must be equal to 0. This approach has been successfully used, e.g., for set functions in which the desired set A is a shape, i.e., a smooth (or piece-wise smooth) surface. In some real-life problems, in particular, in the territorial division problem, the existing methods are not directly applicable. For such problems, we design a new simple differential formalism for optimizing set functions. ©1999 John Wiley & Sons, Inc.     

Multi-Frame Correspondence Estimation Using Subspace Constraints

When a rigid scene is imaged by a moving camera, the set of all displacements of all points across multiple frames often resides in a low-dimensional linear subspace. Linear subspace constraints have been used successfully in the past for recovering 3D structure and 3D motion information from multiple frames (e.g., by using the factorization method of Tomasi and Kanade (1992, International Journal of Computer Vision, 9:137–154)). These methods assume that the 2D correspondences have been precomputed. However, correspondence estimation is a fundamental problem in motion analysis. In this paper we show how the multi-frame subspace constraints can be used for constraining the 2D correspondence estimation process itself.We show that the multi-frame subspace constraints are valid not only for affine cameras, but also for a variety of imaging models, scene models, and motion models. The multi-frame subspace constraints are first translated from constraints on correspondences to constraints directly on image measurements (e.g., image brightness quantities). These brightness-based subspace constraints are then used for estimating the correspondences, by requiring that all corresponding points across all video frames reside in the appropriate low-dimensional linear subspace.The multi-frame subspace constraints are geometrically meaningful, and are {not} violated at depth discontinuities, nor when the camera-motion changes abruptly. These constraints can therefore replace {heuristic} constraints commonly used in optical-flow estimation, such as spatial or temporal smoothness.     

Iteration complexity of an interior-point algorithm for nonlinear p∗-complementarity problems

This paper provides an analysis of the iterative complexity of a predictor-corrector type interior-point algorithm for a class of non-monotone nonlinear complementarity problems, i.e., the nonlinear P?-complementarity problems, which is quite general because it includes as a special case the monotone complementarity problem. At each corrector step, one has to compute an approximate solution of a nonlinear system such that a certain accuracy requirement is satisfied. The proof of the iterative complexity of the proposed algorithm requires that the mapping associated the problem satisfies a scaled Lipschitz condition.     

Possibility theory in constraint satisfaction problems: Handling priority, preference and uncertainty

In classical Constraint Satisfaction Problems (CSPs) knowledge is embedded in a set of hard constraints, each one restricting the possible values of a set of variables. However constraints in real world problems are seldom hard, and CSP's are often idealizations that do not account for the preference among feasible solutions. Moreover some constraints may have priority over others. Lastly, constraints may involve uncertain parameters. This paper advocates the use of fuzzy sets and possibility theory as a realistic approach for the representation of these three aspects. Fuzzy constraints encompass both preference relations among possible instantiations and priorities among constraints. In a Fuzzy Constraint Satisfaction Problem (FCSP), a constraint is satisfied to a degree (rather than satisfied or not satisfied) and the acceptability of a potential solution becomes a gradual notion. Even if the FCSP is partially inconsistent, best instantiations are provided owing to the relaxation of some constraints. Fuzzy constraints are thus flexible. CSP notions of consistency and k-consistency can be extended to this framework and the classical algorithms used in CSP resolution (e.g., tree search and filtering) can be adapted without losing much of their efficiency. Most classical theoretical results remain applicable to FCSPs. In the paper, various types of constraints are modelled in the same framework. The handling of uncertain parameters is carried out in the same setting because possibility theory can account for both preference and uncertainty. The presence of uncertain parameters leads to ill-defined CSPs, where the set of constraints which defines the problem is not precisely known.     

A Closed-Form Solution to Non-Rigid Shape and Motion Recovery

Recovery of three dimensional (3D) shape and motion of non-static scenes from a monocular video sequence is important for applications like robot navigation and human computer interaction. If every point in the scene randomly moves, it is impossible to recover the non-rigid shapes. In practice, many non-rigid objects, e.g. the human face under various expressions, deform with certain structures. Their shapes can be regarded as a weighted combination of certain shape bases. Shape and motion recovery under such situations has attracted much interest. Previous work on this problem (Bregler, C., Hertzmann, A., and Biermann, H. 2000. In Proc. Int. Conf. Computer Vision and Pattern Recognition; Brand, M. 2001. In Proc. Int. Conf. Computer Vision and Pattern Recognition; Torresani, L., Yang, D., Alexander, G., and Bregler, C. 2001. In Proc. Int. Conf. Computer Vision and Pattern Recognition) utilized only orthonormality constraints on the camera rotations (rotation constraints). This paper proves that using only the rotation constraints results in ambiguous and invalid solutions. The ambiguity arises from the fact that the shape bases are not unique. An arbitrary linear transformation of the bases produces another set of eligible bases. To eliminate the ambiguity, we propose a set of novel constraints, basis constraints, which uniquely determine the shape bases. We prove that, under the weak-perspective projection model, enforcing both the basis and the rotation constraints leads to a closed-form solution to the problem of non-rigid shape and motion recovery. The accuracy and robustness of our closed-form solution is evaluated quantitatively on synthetic data and qualitatively on real video sequences.     

Continuous spatial assignment of moving users

Consider a set of servers and a set of users, where each server has a coverage region (i.e., an area of service) and a capacity (i.e., a maximum number of users it can serve). Our task is to assign every user to one server subject to the coverage and capacity constraints. To offer the highest quality of service, we wish to minimize the average distance between users and their assigned server. This is an instance of a well-studied problem in operations research, termed optimal assignment. Even though there exist several solutions for the static case (where user locations are fixed), there is currently no method for dynamic settings. In this paper, we consider the continuous assignment problem (CAP), where an optimal assignment must be constantly maintained between mobile users and a set of servers. The fact that the users are mobile necessitates real-time reassignment so that the quality of service remains high (i.e., their distance from their assigned servers is minimized). The large scale and the time-critical nature of targeted applications require fast CAP solutions. We propose an algorithm that utilizes the geometric characteristics of the problem and significantly accelerates the initial assignment computation and its subsequent maintenance. Our method applies to different cost functions (e.g., average squared distance) and to any Minkowski distance metric (e.g., Euclidean, L ₁ norm, etc.).     

PERFORMANCE FUNCTIONS AND SUBLEVEL SETS FOR FREQUENCY DOMAIN DESIGN OF SINGLE LOOP FEEDBACK CONTROL SYSTEMS WITH PLANT UNCERTAINTY

The frequency domain design of control systems involves the fitting of a designable complex function of frequency (e.g., loop transfer function, compensator transfer function) to specification derived constraints in the design space ℂ×ℝ. In the classical Bode approach and its recent modifications the designable function is the loop transfer function, the specifications lead to constraints on the magnitude of the loop transfer function and the constraints have circular cross-sections in ℂ. In more recent design procedures (e.g., H _∞ optimization or QFT) the specifications lead to more complex constraint surfaces in ℂ×ℝ and the design procedure must fit the designable function to these constraints. In this paper we develop explicit representations of some important ℂ×ℝ constraint surfaces encountered in the design of SISO control systems with both non-parametric (unstructured) and parametric plant uncertainty and study the characteristics of their frequency axis cross-sections or level sets: important information use in the fitting process. The results are presented in two systems of co-ordinates (i.e., designable functions): nominal closed loop transfer function T_o(jω) and and nominal open loop transfer function L_o(jω). While the results in T_o co-ordinates are more useful when using mathematical optimization (e.g., H _∞ optimization techniques), the results in L_o co-ordinates have significant advantages of insight and ease of graphical manipulation as demonstrated in QFT. The inclusion of results in both sets of co-ordinates increases their utility for workers in both areas and also reveals some links between these two different approaches. © 1997 by John Wiley & Sons, Ltd.     

On-line Optimal Control of a Class of Discrete Event Systems with Real-Time Constraints

We consider Discrete Event Systems (DES) involving tasks with real-time constraints and seek to control processing times so as to minimize a cost function subject to each task meeting its own constraint. It has been shown that the off-line version of this problem can be efficiently solved by the Critical Task Decomposition Algorithm (CTDA) (Mao et al., IEEE Trans Mobile Comput 6(6):678–688, 2007). In the on-line version, random task characteristics (e.g., arrival times) are not known in advance. To bypass this difficulty, worst-case analysis may be used. This, however, does not make use of probability distributions and results in an overly conservative solution. In this paper, we develop a new approach which does not rely on worst-case analysis but provides a “best solution in probability” efficiently obtained by estimating the probability distribution of sample-path-optimal solutions. We introduce a condition termed “non-singularity” under which the best solution in probability leads to the on-line optimal control. Numerical examples are included to illustrate our results and show substantial performance improvements over worst-case analysis.     

A knowledge server for reasoning about temporal constraints between classes and instances of events

Reasoning with temporal constraints is a ubiquitous issue in many computer science tasks, for which many dedicated approaches have been and are being built. In particular, in many areas, including planning, workflow, guidelines, and protocol management, one needs to represent and reason with temporal constraints between classes of events (e.g., between the types of actions needed to achieve a goal) and temporal constraints between instances of events (e.g., between the specific actions being executed). The temporal constraints between the classes of events must be inherited by the instances, and the consistency of both types of constraints must be checked. In this article, we design a general‐purpose domain‐independent knowledge server dealing with these issues. In particular, we propose a formalism to represent temporal constraints, and we point out two orthogonal parameters that affect the definition of reasoning algorithms operating on them. We then show four algorithms to deal with inheritance and to perform temporal consistency checking (depending on the parameters) and we study their properties. Finally, we report the results we obtained by applying our system to the treatment of temporal constraints in clinical guidelines. © 2004 Wiley Periodicals, Inc. Int J Int Syst 19: 919–947, 2004.     

Real-time Concurrent C: A language for programming dynamic real-time systems

Concurrent C, is a parallel superset of C (and of C++) that provides facilities such as specifying timeouts during process interactions, delaying program execution, accepting messages in a user-specified order, and asynchronous messages that can be used for writing real-time programs. However, Concurrent C does not provide facilities for specifying strict timing constraints, e.g., Concurrent C only ensures that the lower bounds on the specified delay and timeout periods are satisfied. Real-Time Concurrent C extends Concurrent C by providing facilities to specify periodicity or deadline constraints, to seek guarantees that timing constraints will be met, and to perform alternative actions when either the timing constraints cannot be met or the guarantees are not available.In this paper, we will discuss requirements for a real-time programming language, briefly summarize Concurrent C, and motivate and describe the real-time extensions to Concurrent C. We also discuss scheduling and other run-time facilities that have been incorporated to support the real-time extensions. A prototype implementation of Real-Time Concurrent C is nearing completion.     

A constructive heuristic for the Undirected Rural Postman Problem

This paper describes a constructive heuristic for the well-known Undirected Rural Postman Problem. At each iteration, the procedure inserts a connected component of the required edges and performs a local postoptimization. Computational results on a set of benchmark instances with up to 350 vertices show that the proposed procedure is competitive with the classical Frederickson procedure. Its use is recommended when a high-quality solution is needed in a short amount of time (e.g., in laser plotter applications).     

A Survey of Automated Timetabling

The timetabling problem consists in scheduling a sequence of lectures between teachers and students in a prefixed period of time (typically a week), satisfying a set of constraints of various types. A large number of variants of the timetabling problem have been proposed in the literature, which differ from each other based on the type of institution involved (university or school) and the type of constraints. This problem, that has been traditionally considered in the operational research field, has recently been tackled with techniques belonging also to Artificial Intelligence (e.g., genetic algorithms, tabu search, and constraint satisfaction). In this paper, we survey the various formulations of the problem, and the techniques and algorithms used for its solution.     

Euler Spiral for Shape Completion

In this paper we address the curve completion problem, e.g., the geometric continuation of boundaries of objects which are temporarily interrupted by occlusion. Also known as the gap completion or shape completion problem, this problem is a significant element of perceptual grouping of edge elements and has been approached by using cubic splines or biarcs which minimize total curvature squared (elastica), as motivated by a physical analogy. Our approach is motivated by railroad design methods of the early 1900's which connect two rail segments by transition curves, and by the work of Knuth on mathematical typography. We propose that in using an energy minimizing solution completion curves should not penalize curvature as in elastica but curvature variation. The minimization of total curvature variation leads to an Euler Spiral solution, a curve whose curvature varies linearly with arclength. We reduce the construction of this curve from a pair of points and tangents at these points to solving a nonlinear system of equations involving Fresnel Integrals, whose solution relies on optimization from a suitable initial condition constrained to satisfy given boundary conditions. Since the choice of an appropriate initial curve is critical in this optimization, we analytically derive an optimal solution in the class of biarc curves, which is then used as the initial curve. The resulting interpolations yield intuitive interpolation across gaps and occlusions, and are extensible, in contrast to the scale-invariant version of elastica. In addition, Euler Spiral segments can be used in other applications of curve completions, e.g., modeling boundary segments between curvature extrema or modeling skeletal branch geometry.     

Solution of the input-constrained LQR problem using dynamic programming

The input-constrained LQR problem is addressed in this paper; i.e., the problem of finding the optimal control law for a linear system such that a quadratic cost functional is minimised over a horizon of length N subject to the satisfaction of input constraints. A global solution (i.e., valid in the entire state space) for this problem, and for arbitrary horizon N, is derived analytically by using dynamic programming. The scalar input case is considered in this paper. Solutions to this problem (and to more general problems: state constraints, multiple inputs) have been reported recently in the literature, for example, approaches that use the geometric structure of the underlying quadratic programming problem and approaches that use multi-parametric quadratic programming techniques. The solution by dynamic programming proposed in the present paper coincides with the ones obtained by the aforementioned approaches. However, being derived using a different approach that exploits the dynamic nature of the constrained optimisation problem to obtain an analytical solution, the present result complements the previous methods and reveals additional insights into the intrinsic structure of the optimal solution.     

Error-Free and Best-Fit Extensions of Partially Defined Boolean Functions

In this paper, we address a fundamental problem related to the induction of Boolean logic: Given a set of data, represented as a set of binary “truen-vectors” (or “positive examples”) and a set of “falsen-vectors” (or “negative examples”), we establish a Boolean function (or an extension)f, so thatfis true (resp., false) in every given true (resp., false) vector. We shall further require that such an extension belongs to a certain specified class of functions, e.g., class of positive functions, class of Horn functions, and so on. The class of functions represents our a priori knowledge or hypothesis about the extensionf, which may be obtained from experience or from the analysis of mechanisms that may or may not cause the phenomena under consideration. The real-world data may contain errors, e.g., measurement and classification errors might come in when obtaining data, or there may be some other influential factors not represented as variables in the vectors. In such situations, we have to give up the goal of establishing an extension that is perfectly consistent with the given data, and we are satisfied with an extensionfhaving the minimum number of misclassifications. Both problems, i.e., the problem of finding an extension within a specified class of Boolean functions and the problem of finding a minimum error extension in that class, will be extensively studied in this paper. For certain classes we shall provide polynomial algorithms, and for other cases we prove their NP-hardness.