776929
Trees of extremal connectivity index
The connectivity index w"@a(G) of a graph G is the sum of the weights (d(u)d(v))^@a of all edges uv of G, where @a is a real number (@a 0), and d(u) denotes the degree of the vertex u. Let T be a tree with n vertices and k pendant vertices. In this paper, we give sharp lower and upper bounds for w"1(T). Also, for -1=<@a<0, we give a sharp lower bound and a upper bound for w"@a(T).
653966
Fan-Type Theorem for Long Cycles Containing a Specified Edge
In this paper, we prove that if G is 3-connected noncomplete graph of order n satisfying min{max{d(u),d(v)}:d(u,v)=2}=μ, then for each edge e, G has a cycle containing e of length at least min{n,2μ}, unless G is a spanning subgraph of Kμ + Kcn−μ or K3+(lKμ−2∪Ks), where n=l(μ−2)+s+3,1≤s≤μ−2.
45781537
Lower bounds on the signed k-subdomination number of graphs
17120587
Combination methods in microarray analysis
Microarray technology and experiment can produce thousands or tens of thousands of gene expression measurements in a single cellular mRNA sample. Selecting a list of informative differential genes from these measurement data has been the central problem for microarray analysis. Many methods to identify informative genes have been proposed in the past. However, due to the complexity of biological systems, each proposed method seems to perform nicely in a particular data set or specific experiment. It remains a great challenge to come up with a selection method for a wider spectrum of experiments and a broader variety of data sets. In this paper, we take the approach of method combination using data fusion and rank-score graph which have been used successfully in other application domains such as information retrieval, pattern recognition and tracking, and molecular similarity search. Our method combination is efficient and flexible and can be extended to become a general learning system for microarray gene expression analysis.
267445
Biological Nomenclatures: A Source of Lexical Knowledge and Ambiguity
There has been increased work in developing automated systems that involve natural language processing (NLP) to recognize and extract genomic information from the literature. Recognition and identification of biological entities is a critical step in this process. NLP systems generally rely on nomenclatures and ontological specifications as resources for determining the names of the entities, assigning semantic categories that are consistent with the corresponding ontology, and assignment of identifiers that map to well-defined entities within a particular nomenclature. Although nomenclatures and ontologies are valuable for text processing systems, they were developed to aid researchers and are heterogeneous in structure and semantics. A uniform resource that is automatically generated from diverse resources, and that is designed for NLP purposes would be a useful tool for the field, and would further database interoperability. This paper presents work towards this goal. We have automatically created lexical resources from four model organism nomenclature systems (mouse, fly, worm, and yeast), and have studied performance of the resources within an existing NLP system, GENIES. Using nomenclatures is not straightforward because issues concerning ambiguity, synonymy, and name variations are quite challenging. In this paper we focus mainly on ambiguity. We determined that the number of ambiguous gene names within the individual nomenclatures, across the four nomenclatures, and with general English ranged from 0%-10.18%, 1.187%-20.30%, and 0%-2.49% respectively. When actually processing text, we found the rate of ambiguous occurrences (not counting ambiguities stemming from English words) to range from 2.4%-32.9% depending on the organisms considered.
17436749
Feature Transformation and Multivariate Decision Tree Induction
Univariate decision trees (UDT's) have inherent problems of replication, repetition, and fragmentation. Multivariate decision trees (MDT's) have been proposed to overcome some of the problems. Close examination of the conventional ways of building MDT's, however, reveals that the fragmentation problem still persists. A novel approach is suggested to minimize the fragmentation problem by separating hyperplane search from decision tree building. This is achieved by feature transformation. Let the initial feature vector be x, the new feature vector after feature transformation T is y, i.e., y = T(x). We can obtain an MDTb y (1) building a UDT on y; and (2) replacing new features y at each node with the combinations of initial features x. We elaborate on the advantages of this approach, the details of T, and why it is expected to perform well. Experiments are conducted in order to confirm the analysis, and results are compared to those of C4.5, OC1, and CART.
16386059
A Monotonic Measure for Optimal Feature Selection
Feature selection is a problem of choosing a subset of relevant features. In general, only exhaustive search can bring about the optimal subset. With a monotonic measure, exhaustive search can be avoided without sacrificing optimality. Unfortunately, most error- or distancebased measures are not monotonic. A new measure is employed in this work that is monotonic and fast to compute. The search for relevant features according to this measure is guaranteed to be complete but not exhaustive. Experiments are conducted for verification.