5950046
A theory of Gaussian belief functions
Abstract A Gaussian belief function can be intuitively described as a Gaussian distribution over a hyperplane, whose parallel subhyperplanes are the focal elements. This paper elaborates on the idea of Dempster and Shafer and formally represents a Gaussian belief function as a wide-sense inner product and a linear functional over a variable space, and as their duals over a hyperplane in a sample space. By adapting Dempster's rule to the continuous case, it derives a rule of combination and proves its equivalence to its geometric description by Dempster. It illustrates by examples how mixed knowledge involving linear equations, multivariate Gaussian distributions, and partial ignorance can be represented and combined as Gaussian belief functions.
14735447
Representing asymmetric decision problems using coarse valuations
A valuation-based system approach to knowledge representation has shown its advantages in improving computational efficiency and in allowing many decision models including belief networks. This study applies the Dempster-Shafer theory of belief functions and extends its framework to allow coarse valuations, which admit incomplete specification of probabilities and utilities and, therefore, are more flexible in representing asymmetric decision problems. It presents an algorithm for making inferences and decisions in systems using coarse valuations. It shows that a coarse valuation-based system provides a most natural and compact representation of decision problems.
2807804
Continual Queries for Internet Scale Event-Driven Information Delivery
We introduce the concept of continual queries, describe the design of a distributed event-driven continual query system-OpenCQ, and outline the initial implementation of OpenCQ on top of the distributed interoperable information mediation system DIOM. Continual queries are standing queries that monitor update of interest and return results whenever the update reaches specified thresholds. In OpenCQ, users may specify to the system the information they would like to monitor (such as the events or the update thresholds they are interested in). Whenever the information of interest becomes available, the system immediately delivers it to the relevant users; otherwise, the system continually monitors the arrival of the desired information and pushes it to the relevant users as it meets the specified update thresholds. In contrast to conventional pull-based data management systems such as DBMSs and Web search engines, OpenCQ exhibits two important features: it provides push-enabled, event-driven, content-sensitive information delivery capabilities; and it combines pull and push services in a unified framework. By event-driven we mean that the update events of interest to be monitored are specified by users or applications. By content-sensitive, we mean the evaluation of the trigger condition happens only when a potentially interesting change occurs. By push-enabled, we mean the active delivery of query results or triggering of actions without user intervention.
10550445
Fuzzy Bayesian Networks - A General Formalism for Representation, Inference and Learning with Hybrid Bayesian Networks
This paper proposes a general formalism for representation, inference and learning with general hybrid Bayesian networks in which continuous and discrete variables may appear anywhere in a directed acyclic graph. The formalism fuzzifies a hybrid Bayesian network into two alternative forms: the first form replaces each continuous variable in the given directed acyclic graph (DAG) by a partner discrete variable and adds a directed link from the partner discrete variable to the continuous one. The mapping between two variables is not crisp quantization but is approximated (fuzzified) by a conditional Gaussian (CG) distribution. The CG model is equivalent to a fuzzy set but no fuzzy logic formalism is employed. The conditional distribution of a discrete variable given its discrete parents is still assumed to be multinomial as in discrete Bayesian networks. The second form only replaces each continuous variable whose descendants include discrete variables by a partner discrete variable and adds a directed link from that partner discrete variable to the continuous one. The dependence between the partner discrete variable and the original continuous variable is approximated by a CG distribution, but the dependence between a continuous variable and its continuous and discrete parents is approximated by a conditional Gaussian regression (CGR) distribution. Obviously, the second form is a finer approximation, but restricted to CGR models, and requires more complicated inference and learning algorithms. This results in two general approximate representations of a general hybrid Bayesian networks, which are called here the fuzzy Bayesian network (FBN) form-I and form-II. For the two forms of FBN, general exact inference algorithms exists, which are extensions of the junction tree inference algorithm for discrete Bayesian networks. Learning fuzzy Bayesian networks from data is different from learning purely discrete Bayesian networks because not only all the newly converted discrete variables are latent in the data, but also the number of discrete states for each of these variables and the CG or CGR distribution of each continuous variable given its partner discrete parents or both continuous and discrete parents have to be determined.
24660543
A note on the lower bounds of signed domination number of a graph
Abstract Let G = (V, E) be a graph. For a function f : V → {−1, 1}, the weight of f is w(f) = Σv ∈ V f(v). For a vertex v in V, we define f[v] = Σu∈N[v] f(u). A signed dominating function of G is a function f : V → {−1, 1} such that f[v] ⩾ 1 for all v ∈ V. The signed domination number γs(G) of G is the minimum weight of a signed dominating function on G. A signed dominating function of a weight γs(G) we call a γs-function of G. In this paper, we study the signed domination problem of general graph, and obtain some lower bounds of the signed domination number of a graph, and show that these lower bounds are sharp, and extend a result in Dunbar et al. (1995).
3249877
Dual Laplacian editing for meshes
Recently, differential information as local intrinsic feature descriptors has been used for mesh editing. Given certain user input as constraints, a deformed mesh is reconstructed by minimizing the changes in the differential information. Since the differential information is encoded in a global coordinate system, it must somehow be transformed to fit the orientations of details in the deformed surface, otherwise distortion will appear. We observe that visually pleasing deformed meshes should preserve both local parameterization and geometry details. We propose to encode these two types of information in the dual mesh domain due to the simplicity of the neighborhood structure of dual mesh vertices. Both sets of information are nondirectional and nonlinearly dependent on the vertex positions. Thus, we present a novel editing framework that iteratively updates both the primal vertex positions and the dual Laplacian coordinates to progressively reduce distortion in parametrization and geometry. Unlike previous related work, our method can produce visually pleasing deformations with simple user interaction, requiring only the handle positions, not local frames at the handles.
14344981
Mutation operators for Object-Z specification
As a powerful means of measuring a test set, mutation testing has been applied to program-based testing for a long time. However, with the development of formal specification technique, the formal specifications also play an important role in software testing. For measuring the quality of the specification-based test cases, researchers provide some mutation operators for the logic predicates. With the emergence of the object-oriented formal specifications, these mutation operators cannot completely model the faults arise in an object-oriented specification and from the misunderstanding of the specification. This paper investigates the faults that may occur in the object-oriented specifications, and gives a set of mutation operators for the Object-Z specifications to model these faults. These mutation operators provide an approach to measuring specification-based test cases and validating the Object-Z specifications.