Probing the arrangement of hyperplanes

AbstractIn this paper we investigate the combinatorial complexity of an algorithm to determine the geometry and the topology related to an arrangement of hyperplanes in multi-dimensional Euclidean space from the “probing” on the arrangement. The “probing” by a flat means the operation from which we can obtain the intersection of the flat and the arrangement. For a finite set H of hyperplanes in Ed, we obtain the worst-case number of fixed direction line probes and that of flat probes to determine a generic line of H and H itself. We also mention the bound for the computational complexity of these algorithms based on the efficient line probing algorithm which uses the dual transform to compute a generic line of H.We also consider the problem to approximate arrangements by extending the point probing model, which have connections with computational learning theory such as learning a network of threshold functions, and introduce the vertical probing model and the level probing model. It is shown that the former is closely related to the finger probing for a polyhedron and that the latter depends on the dual graph of the arrangement.The probing for an arrangement can be used to obtain the solution for a given system of algebraic equations by decomposing the μ-resultant into linear factors. It also has interesting applications in robotics such as a motion planning using an ultrasonic device that can detect the distances to obstacles along a specified direction

Genome-wide Analyses of the Structural Gene Families Involved in the Legume-specific 5-Deoxyisoflavonoid Biosynthesis of Lotus japonicus

A model legume Lotus japonicus (Regel) K. Larsen is one of the subjects of genome sequencing and functional genomics programs. In the course of targeted approaches to the legume genomics, we analyzed the genes encoding enzymes involved in the biosynthesis of the legume-specific 5-deoxyisoflavonoid of L. japonicus, which produces isoflavan phytoalexins on elicitor treatment. The paralogous biosynthetic genes were assigned as comprehensively as possible by biochemical experiments, similarity searches, comparison of the gene structures, and phylogenetic analyses. Among the 10 biosynthetic genes investigated, six comprise multigene families, and in many cases they form gene clusters in the chromosomes. Semi-quantitative reverse transcriptase–PCR analyses showed coordinate up-regulation of most of the genes during phytoalexin induction and complex accumulation patterns of the transcripts in different organs. Some paralogous genes exhibited similar expression specificities, suggesting their genetic redundancy. The molecular evolution of the biosynthetic genes is discussed. The results presented here provide reliable annotations of the genes and genetic markers for comparative and functional genomics of leguminous plants

The 2nd DBCLS BioHackathon: interoperable bioinformatics Web services for integrated applications

<p>Abstract</p> <p>Background</p> <p>The interaction between biological researchers and the bioinformatics tools they use is still hampered by incomplete interoperability between such tools. To ensure interoperability initiatives are effectively deployed, end-user applications need to be aware of, and support, best practices and standards. Here, we report on an initiative in which software developers and genome biologists came together to explore and raise awareness of these issues: BioHackathon 2009.</p> <p>Results</p> <p>Developers in attendance came from diverse backgrounds, with experts in Web services, workflow tools, text mining and visualization. Genome biologists provided expertise and exemplar data from the domains of sequence and pathway analysis and glyco-informatics. One goal of the meeting was to evaluate the ability to address real world use cases in these domains using the tools that the developers represented. This resulted in i) a workflow to annotate 100,000 sequences from an invertebrate species; ii) an integrated system for analysis of the transcription factor binding sites (TFBSs) enriched based on differential gene expression data obtained from a microarray experiment; iii) a workflow to enumerate putative physical protein interactions among enzymes in a metabolic pathway using protein structure data; iv) a workflow to analyze glyco-gene-related diseases by searching for human homologs of glyco-genes in other species, such as fruit flies, and retrieving their phenotype-annotated SNPs.</p> <p>Conclusions</p> <p>Beyond deriving prototype solutions for each use-case, a second major purpose of the BioHackathon was to highlight areas of insufficiency. We discuss the issues raised by our exploration of the problem/solution space, concluding that there are still problems with the way Web services are modeled and annotated, including: i) the absence of several useful data or analysis functions in the Web service "space"; ii) the lack of documentation of methods; iii) lack of compliance with the SOAP/WSDL specification among and between various programming-language libraries; and iv) incompatibility between various bioinformatics data formats. Although it was still difficult to solve real world problems posed to the developers by the biological researchers in attendance because of these problems, we note the promise of addressing these issues within a semantic framework.</p

The DBCLS BioHackathon: standardization and interoperability for bioinformatics web services and workflows. The DBCLS BioHackathon Consortium*

Web services have become a key technology for bioinformatics, since life science databases are globally decentralized and the exponential increase in the amount of available data demands for efficient systems without the need to transfer entire databases for every step of an analysis. However, various incompatibilities among database resources and analysis services make it difficult to connect and integrate these into interoperable workflows. To resolve this situation, we invited domain specialists from web service providers, client software developers, Open Bio* projects, the BioMoby project and researchers of emerging areas where a standard exchange data format is not well established, for an intensive collaboration entitled the BioHackathon 2008. The meeting was hosted by the Database Center for Life Science (DBCLS) and Computational Biology Research Center (CBRC) and was held in Tokyo from February 11th to 15th, 2008. In this report we highlight the work accomplished and the common issues arisen from this event, including the standardization of data exchange formats and services in the emerging fields of glycoinformatics, biological interaction networks, text mining, and phyloinformatics. In addition, common shared object development based on BioSQL, as well as technical challenges in large data management, asynchronous services, and security are discussed. Consequently, we improved interoperability of web services in several fields, however, further cooperation among major database centers and continued collaborative efforts between service providers and software developers are still necessary for an effective advance in bioinformatics web service technologies

Probing a Set of Hyperplanes by Lines and Related Problems

Suppose that for a set H of n unknown hyperplanes in the Euclidean d-dimensional space, a line probe is available which reports the set of intersection points of a query line with the hyperplanes. Under this model, this paper investigates the complexity to find a generic line for H and further to determine the hyperplanes in H . This problem arises in factoring the u-resultant to solve systems of polynomials (e.g., Renegar [12]). We prove that d+1 line probes are sufficient to determine H . Algorithmically, the time complexity to find a generic line and reconstruct H from O(dn) probed points of intersection is important. It is shown that a generic line can be computed in O(dn log n) time after d line probes, and by an additional d line probes, all the hyperplanes in H are reconstructed in O(dn log n) time. This result can be extended to the d-dimensional complex space. Also, concerning the factorization of the u-resultant using the partial derivatives on a generic line, we touch upon reducing the time complexity to compute the partial derivatives of the u-resultant represented as the determinant of a matrix

A Cluster of Genes Encodes the Two Types of Chalcone Isomerase Involved in the Biosynthesis of General Flavonoids and Legume-Specific 5-Deoxy(iso)flavonoids in Lotus japonicus

Leguminous plants produce 5-deoxyflavonoids and 5-deoxyisoflavonoids that play essential roles in legume-microbe interactions. Together with chalcone polyketide reductase and cytochrome P450 2-hydroxyisoflavanone synthase, the chalcone isomerase (CHI) of leguminous plants is fundamental in the construction of these ecophysiologically active flavonoids. Although CHIs of nonleguminous plants isomerize only 6′-hydroxychalcone to 5-hydroxyflavanone (CHIs with this function are referred to as type I), leguminous CHIs convert both 6′-deoxychalcone and 6′-hydroxychalcone to 5-deoxyflavanone and 5-hydroxyflavanone, respectively (referred to as type II). In this study, we isolated multiple CHI cDNAs (cCHI1–cCHI3) from a model legume, Lotus japonicus. In contrast to previous observations, the amino acid sequence of CHI2 was highly homologous to nonleguminous CHIs, whereas CHI1 and CHI3 were the conventional leguminous type. Furthermore, genome sequence analysis revealed that four CHI genes (CHI1–3 and a putative gene, CHI4) form a tandem cluster within 15 kb. Biochemical analysis with recombinant CHIs expressed in Escherichia coli confirmed that CHI1 and CHI3 are type II CHIs and that CHI2 is a type I CHI. The occurrence of both types of CHIs is probably common in leguminous plants, and it was suggested that type II CHIs evolved from an ancestral CHI by gene duplication and began to produce 5-deoxy(iso)flavonoids along with the establishment of the Fabaceae