8102710
Degrees of d. c. e. reals
A real α is called a c. e. real if it is the halting probability of a prefix free Turing machine. Equivalently, α is c. e. if it is left computable in the sense that L(α) = {q ∈ ℚ : q ≤ α} is a computably enumerable set. The natural field formed by the c. e. reals turns out to be the field formed by the collection of the d. c. e. reals, which are of the form α—β, where α and β are c. e. reals. While c. e. reals can only be found in the c. e. degrees, Zheng has proven that there are Δ02 degrees that are not even n-c. e. for any n and yet contain d. c. e. reals, where a degree is n-c. e. if it contains an n-c. e. set. In this paper we will prove that every ω-c. e. degree contains a d. c. e. real, but there are ω + 1-c. e. degrees and, hence Δ02 degrees, containing no d. c. e. real. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
1961392
Degrees of Weakly Computable Reals
This paper studies the degrees of weakly computable reals. It is shown that certain types of limit-recursive reals are Turing incomparable to all weakly computable reals except the recursive and complete ones. Furthermore, it is shown that an r.e. Turing degree is array-recursive iff every real in it is weakly computable.
7723209
1-Generic splittings of computably enumerable degrees
Say a set G⊆ω is 1-generic if for any e∈ω, there is a string σ⊂G such that {e}σ(e)↓ or ∀τ⊇σ({e}τ(e)↑). It is known that 0′ can be split into two 1-generic degrees. In this paper, we generalize this and prove that any nonzero computably enumerable degree can be split into two 1-generic degrees. As a corollary, no two computably enumerable degrees bound the same class of 1-generic degrees.
18609322
On the Quotient Structure of Computably Enumerable Degrees Modulo the Noncuppable Ideal
We show that minimal pairs exist in the quotient structure of $\mathcal{R}$ modulo the ideal of noncuppable degrees.
1638130
Bounding computably enumerable degrees in the Ershov hierarchy
Nanyang Technol Univ, Sch Math & Phys Sci, Div Math Sci, Singapore 639798, Singapore. Chinese Acad Sci, Inst Software, Beijing 100080, Peoples R China. Natl Univ Singapore, Dept Math, Singapore 119260, Singapore.
35293254
Quasi-complements of the cappable degrees
Say that a nonzero c. e. degree b is a quasi-complement of a c. e. degree a if a ∩ b = 0 and a ∪ b is high. It is well-known (due to Shore) that each cappable degree has a high quasi-complement. However, by the existence of the almost deep degrees, there are nonzero cappable degrees having no low quasi-complements. In this paper, we prove that any nonzero cappable degree has a low2 quasi-complement. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
7109499
Statistical learning for effective visual information retrieval
For effective retrieval of visual information, statistical learning plays a pivotal role. Statistical learning in such a context faces at least two major mathematical challenges: scarcity of training data, and imbalance of training classes. We present these challenges and outline our methods for addressing them: active learning, recursive subspace co-training, adaptive dimensionality reduction, class-boundary alignment, and quasi-bagging.
13757062
Faster solution to the maximum quartet consistency problem with constraint programming
Evolution is an important sub-area of study in biological science, whereby the evolutionary history, or phylogeny, would shed light on the genetic linkage and the functional correlation for the species under consideration. Many kinds of species data can be deployed for the task and many phylogeny reconstruction methods have been examined in the literature. A quartet approach is to build a local phylogeny for every 4 species, which is called a quartet for these 4 species, and then to assemble a phylogeny for the whole set of species satisfying the topological constraints imposed by these quartets built. In practice, those predicted quartets might not agree each other and the optimization problem, the well-known Maximum Quartet Consistency (MQC) problem, is to construct a phylogeny to satisfy a maximum number of the predicted quartets. An equivalent representation for the MQC problem through searching for a certain ultrametric matrix via Answer Set Programming has recently been proposed. This paper follows the approach and presents a number of optimization techniques to speed up the searching process. The experimental results on both the simulated and real datasets suggest that the new representation combined with Constraint Programming presents a unique perspective to the MQC problem.
2439726
Concept boundary detection for speeding up SVMs
Support Vector Machines (SVMs) suffer from an O(n2) training cost, where n denotes the number of training instances. In this paper, we propose an algorithm to select boundary instances as training data to substantially reduce n. Our proposed algorithm is motivated by the result of (Burges, 1999) that, removing non-support vectors from the training set does not change SVM training results. Our algorithm eliminates instances that are likely to be non-support vectors. In the concept-independent preprocessing step of our algorithm, we prepare nearest-neighbor lists for training instances. In the concept-specific sampling step, we can then effectively select useful training data for each target concept. Empirical studies show our algorithm to be effective in reducing n, outperforming other competing downsampling algorithms without significantly compromising testing accuracy.
22669962
Generic universal switch blocks
A switch block M with W terminals on each side is said to be universal if every set of nets satisfying the dimension constraint (i.e., the number of nets on each side of M is at most W) is simultaneously routable through M (Y.W. Chang et al., 1996). We present an algorithm to construct N-sided universal switch blocks with W terminals on each side. Each of our universal switch blocks has (/sub 2//sup N/)W switches and switch-block flexibility N-1 (i.e., F/sub S/=N-1). We prove that no switch block with less than (/sub 2//sup N/)W switches can be universal. Further, the decomposition property of a universal switch block provides a key insight into its layout implementation with a smaller silicon area. We also compare our universal switch blocks with others of the topology associated with Xilinx XC4000-type FPGAs. Experimental results demonstrate that our universal switch blocks improve routability at the chip level.
8499708
Cooperation models for service oriented multi-agent system
In the paper, the cooperation models for service oriented multi-agent system are formally and rigorously investigated and put forward. According to the service request forces and service offer manners, a number of elementary cooperation models and their atomic communication acts are identified. The rigorous semantics of the communication acts and the cooperation models and their constraints are formally defined and analyzed.