2125782
On the bounded domination number of tournaments
Abstract In a simple digraph, a star of degree t is a union of t edges with a common tail. The k -domination number γ k (G) of digraph G is the minimum number of stars of degree at most k needed to cover the vertex set. We prove that γ k (T)=⌈n/(k+1)⌉ when T is a tournament with n⩾14k lg k vertices. This improves a result of Chen, Lu and West. We also give a short direct proof of the result of E. Szekeres and G. Szekeres that every n -vertex tournament is dominated by at most lg n− lg lg n+2 vertices.
12575856
On avoidable and unavoidable claws
Abstract A claw of degree k is a directed tree consisting of k paths emerging from a common root. We prove that every claw of order n with degree less than 19 50 n appears in every n -vertex tournament. We also construct avoidable claws with degree approaching 11 23 n . Thus for large n , the maximum λ such that every claw with degree λn appears in every n -vertex tournament satisfies λ ⩽ 11 23 . This improves earlier bounds.
11770982
The strong Hall property and symmetric chain orders
Abstract Let G =( X , Y ; E ) be a bipartite graph with | X |⩾| Y |. For A ⊆ X , write φ ( A )=| A |−| N ( A )| and for a ⩽| X |, define φ(a)= max {φ(A) | A⊆X, |A|=a} . The graph G is said to have the strong Hall property if φ ( a )+ φ ( b )⩽| X |−| Y | for all nonnegative integers a and b with a + b ⩽| X |. We shall prove that any unimodal and self-dual poset with the strong Hall property is a symmetric chain order. This result will also be used to show that the inversion poset S 5 is a symmetric chain order.
39506333
GEOTHER: A Geometry Theorem Prover
35725775
A simple method for implicitizing rational curves and surfaces
Abstract This paper presents a simple method for converting rational parametric equations of curves and surfaces into implicit equations. The method proceeds via writing out the implicit polynomial F of estimated degree with indeterminate coefficients u i , substituting the rational expressions for the given parametric curve or surface into F to yield a rational expression g / h in the parameter s (or s and t ), equating the coefficients of g in terms of s (and t ) to 0 to generate a sparse, partially triangular system of linear equations in u i with constant coefficients, and finally solving the linear system for u i . If a nontrivial solution is found, then an implicit polynomial is obtained; otherwise, one repeats the same process, increasing the degree of F . Our experiments show that this simple method is efficient. It performs particularly well in the presence of base points and may detect the dependency of parameters incidentally.
20528314
Anticipation Model for Sequential Learning of Complex Sequences
One of the fundamental aspects of human intelligence is the ability to process temporal information (Lashley, 1951). Learning and reproducing temporal sequences are closely associated with our ability to perceive and generate body movements, speech and language, music, etc. A considerable body of neural network literature is devoted to temporal pattern generation (see Wang, 2001, for a recent review). These models generally treat a temporal pattern as a sequence of discrete patterns, called a temporal sequence. Most of the models are based on either multilayer perceptrons with backpropagation training or the Hopfield model of associative recall. The basic idea for the former class of models is to view a temporal sequence as a set of associations between consecutive components, and learn these associations as input-output transformations (Jordan, 1986; Elman, 1990; Mozer, 1993). To deal with temporal dependencies beyond consecutive components, part of the input layer is used to keep a trace of history, behaving as short-term memory (STM). Similarly, for temporal recall based on the Hopfield associative memory, a temporal sequence is viewed as associations between consecutive components. These associations are stored in extended versions of the Hopfield model that includes some time delays (Sompolinsky & Kanter, 1986; Buhmann & Schulten, 1987; Heskes & Gielen, 1992). To deal with longer temporal dependencies, high-order networks have been proposed (Guyon et al., 1988).
8554279
High level verification of control intensive systems using predicate abstraction
Predicate abstraction has been widely used for model checking hardware/software systems. However, for control intensive systems, existing predicate abstraction techniques can potentially result in a blowup of the size of the abstract model. We deal with this problem by retaining important control variables in the abstract model. By this method we avoid having to introduce an unreasonable number of predicates to simulate the behavior of the control variables. We also show how to improve predicate abstraction by extracting useful information from a high level representation of hardware/software systems. This technique works by first extracting relevant branch conditions. These branch conditions are used to invalidate spurious abstract counterexamples through a new counterexample-based lazy refinement algorithm. Experimental results are included to demonstrate the effectiveness of our methods.
16801655
A Hybird Image Retrieval System with User's Relevance Feedback Using Neurocomputing
This paper aims at developing a hybrid scheme for intelligent image retrieval using neural nets. Each item in an image database is indexed by a visual feature vector, which is extracted using color moments and discrete cosine transform coefficients. Query is characterized by a set of semantic labels, which are predefined by system designers and associated with domain concerns. The proposed hybrid image retrieval (HIR) system utilizes the image content features as the system input, and the semantic labels as its output. To compensate the deficiency of semantics modelling, an on-line user’s relevance feedback is applied to improve the retrieval performance of the HIR system. The neural net acts like a pattern association memory bank that maps the low-level feature vectors to their corresponding semantic labels. During the retrieval process, the weights of the neural net are updated by an interactive user’s relevance feedback technique, where the feedback signal comprise the neural net actual output, semantic labels provided by users and the given query. A prototype HIR system is implemented and evaluated using an artificial image database. Experimental results demonstrate that our proposed techniques are promising.