On the number of rectangulations of a planar point set

AbstractWe investigate the number of different ways in which a rectangle containing a set of n noncorectilinear points can be partitioned into smaller rectangles by n (nonintersecting) segments, such that every point lies on a segment. We show that when the relative order of the points forms a separable permutation, the number of rectangulations is exactly the (n+1)st Baxter number. We also show that no matter what the order of the points is, the number of guillotine rectangulations is always the nth Schröder number, and the total number of rectangulations is O(20n/n4)

A computational approach for genome-wide mapping of splicing factor binding sites

A computational method is presented for genome-wide mapping of splicing factor binding sites that considers both the genomic environment and evolutionary conservation

An Integrative Method for Accurate Comparative Genome Mapping

We present MAGIC, an integrative and accurate method for comparative genome mapping. Our method consists of two phases: preprocessing for identifying “maximal similar segments,” and mapping for clustering and classifying these segments. MAGIC's main novelty lies in its biologically intuitive clustering approach, which aims towards both calculating reorder-free segments and identifying orthologous segments. In the process, MAGIC efficiently handles ambiguities resulting from duplications that occurred before the speciation of the considered organisms from their most recent common ancestor. We demonstrate both MAGIC's robustness and scalability: the former is asserted with respect to its initial input and with respect to its parameters' values. The latter is asserted by applying MAGIC to distantly related organisms and to large genomes. We compare MAGIC to other comparative mapping methods and provide detailed analysis of the differences between them. Our improvements allow a comprehensive study of the diversity of genetic repertoires resulting from large-scale mutations, such as indels and duplications, including explicitly transposable and phagic elements. The strength of our method is demonstrated by detailed statistics computed for each type of these large-scale mutations. MAGIC enabled us to conduct a comprehensive analysis of the different forces shaping prokaryotic genomes from different clades, and to quantify the importance of novel gene content introduced by horizontal gene transfer relative to gene duplication in bacterial genome evolution. We use these results to investigate the breakpoint distribution in several prokaryotic genomes

Using hyperbolic tangents in integer factoring

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1980.MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERINGBibliography: leaf 45.by Ron Yair Pinter.M.S

Optimal Placement for River Routing

Programs for integrated circuit layout typically have two phases: placement and routing. The router should produce as efficient a layout as possible, but of course the quality of the routhing depends heavily on the quality of the placement. On the other hand, the placement procedure ideally should know the quality of a routing before it routes the wires. In this talk we present an optimal solution for a practical, common version of this placement and routing problem. River routing is the problem of connecting in order a set of terminals a1,...,an on a line to another set b1,...,bn across a rectangular channel. Since the terminals are located on modules, the modules must be placed relative to one another before routing. This placement problem arises frequently in design systems like bristle-blocks where stretch lines through a module can effectively break it into several chunks, each of which must be placed separately. In this talk, we shall present concise necessary and sufficient conditions for wirability which are applied to reduce the optimal placement problem to the graph-theoretic single-source-longest-paths problems. By exploiting the special structure of graphs that arise from the placement problem for rectilinear wiring, an optimal solution may be determined in linear time