Jerzy W. Jaromczyk

Relative neighborhood graphs and their relatives

Results of neighborhood graphs are surveyed. Properties, bounds on the size, algorithms, and variants of the neighborhood graphs are discussed. Numerous applications including computational morphology, spatial analysis, pattern classification, and databases for computer vision are described. >

Plant-symbiotic fungi as chemical engineers: multi-genome analysis of the clavicipitaceae reveals dynamics of alkaloid loci

The fungal family Clavicipitaceae includes plant symbionts and parasites that produce several psychoactive and bioprotective alkaloids. The family includes grass symbionts in the epichloae clade (Epichloë and Neotyphodium species), which are extraordinarily diverse both in their host interactions and in their alkaloid profiles. Epichloae produce alkaloids of four distinct classes, all of which deter insects, and some—including the infamous ergot alkaloids—have potent effects on mammals. The exceptional chemotypic diversity of the epichloae may relate to their broad range of host interactions, whereby some are pathogenic and contagious, others are mutualistic and vertically transmitted (seed-borne), and still others vary in pathogenic or mutualistic behavior. We profiled the alkaloids and sequenced the genomes of 10 epichloae, three ergot fungi (Claviceps species), a morning-glory symbiont (Periglandula ipomoeae), and a bamboo pathogen (Aciculosporium take), and compared the gene clusters for four classes of alkaloids. Results indicated a strong tendency for alkaloid loci to have conserved cores that specify the skeleton structures and peripheral genes that determine chemical variations that are known to affect their pharmacological specificities. Generally, gene locations in cluster peripheries positioned them near to transposon-derived, AT-rich repeat blocks, which were probably involved in gene losses, duplications, and neofunctionalizations. The alkaloid loci in the epichloae had unusual structures riddled with large, complex, and dynamic repeat blocks. This feature was not reflective of overall differences in repeat contents in the genomes, nor was it characteristic of most other specialized metabolism loci. The organization and dynamics of alkaloid loci and abundant repeat blocks in the epichloae suggested that these fungi are under selection for alkaloid diversification. We suggest that such selection is related to the variable life histories of the epichloae, their protective roles as symbionts, and their associations with the highly speciose and ecologically diverse cool-season grasses.

Analysis of chameleon sequences and their implications in biological processes.

Chameleon sequences have been implicated in amyloid related diseases. Here we report an analysis of two types of chameleon sequences, chameleon‐HS (Helix vs. Strand) and chameleon‐HE (Helix vs. Sheet), based on known structures in Protein Data Bank. Our survey shows that the longest chameleon‐HS is eight residues while the longest chameleon‐HE is seven residues. We have done a detailed analysis on the local and global environment that might contribute to the unique conformation of a chameleon sequence. We found that the existence of chameleon sequences does not present a problem for secondary structure prediction programs, including the first generation prediction programs, such as Chou–Fasman algorithm, and the third generation prediction programs that utilize evolution information. We have also investigated the possible implication of chameleon sequences in structural conservation and functional diversity of alternatively spliced protein isoforms. Proteins 2007.

An efficient algorithm for the Euclidean two-center problem

We present a new algorithm for the two-center problem: “Given a set <italic>S</italic> of <italic>n</italic> points in the real plane, find two closed discs whose union contains all of the points and the radius of the larger disc is minimized.” An almost quadratic <italic>O</italic>(<italic>n</italic><supscrpt>2</supscrpt>log<italic>n</italic>) solution is given. The previously best known algorithms for the two-center problem have time complexity <italic>O</italic>(<italic>n</italic><supscrpt>2</supscrpt>log<supscrpt>3</supscrpt><italic>n</italic>). The solution is based on a new geometric characterization of the optimal discs and on a searching scheme with so-called lazy evaluation. The algorithm is simple and does not assume general position of the input points. The importance of the problem is known in various practical applications including transportation, station placement, and facility location.

A note on relative neighborhood graphs

<italic>Two new algorithms finding relative neighborhood graph RNG(V) for a set V of n points are presented. The first algorithm solves this problem for input points in (R<supscrpt>2</supscrpt>,L<subscrpt>p</subscrpt>) metric space in time &Ogr;(n α(n,n)) if the Delaunay triangulation DT(V) is given. This time performance is achieved due to attractive and natural application of FIND-UNION data structure to represent so-called elimination forest of edges in DT(V). The second algorithm solves the relative neighborhood graph problem in (R<supscrpt>d</supscrpt>,L<subscrpt>p</subscrpt>), 1 <p<oo, metric space in time &Ogr;(n<supscrpt>2</supscrpt>) when no three points in V form an isosceles triangle. The complexity analysis of this algorithm is based on some general facts pertaining to properties of equilateral triangles in the metric space (R<supscrpt>d</supscrpt>,L<subscrpt>p</subscrpt>).</italic>

Computing convex hull in a floating point arithmetic

Abstract We present an algorithm which is numerically stable and optimal in time and space complexity for constructing the convex hull for a set of points on a plane. In contrast to existing numerically stable algorithms which return only an approximate hull, our algorithm constructs a polygon that is truly convex. The algorithm is simple and easy to implement. We assume a floating point arithmetic as a computation model.

Skewed projections with an application to line stabbing in R3

A new geometrical transform, skewed-projection, is introduced. This transform is applied to design a new algorithm for a common transversal problem for families of polyhedra in <italic>R</italic><supscrpt>3</supscrpt>. The time and space analysis, using Davenport-Schinzel sequences, is given.

The Two-Line Center Problem from a Polar View: A New Algorithm and Data Structure

We present a new algorithm for the two-line center problem (also called unweighted orthogonal L∞-fit problem): “Given a set S of n points in the real plane, find two closed strips whose union contains all of the points and such that the width of the wider strip is minimized.” An almost quadratic O(n2 log2n) solution is given. The previously best known algorithm for this problem has time complexity O(n2log5n) and uses a parametric search methodology. Our solution applies a new geometric structure, anchored lower and upper chains, and is based on examining several constraint versions of the problem. The anchored lower and upper chain structure is of interest by itself and provides a fast response to queries that involve planar configurations of points. The algorithm does not assume the general position of the input data points.

Support for XML markup of image-based electronic editions

Image-based electronic editions enable researchers to view and study in an electronic environment historical manuscript images intricately linked to edition, transcript, glossary and apparatus files. Building image-based electronic editions poses a two-fold challenge. For humanities scholars, it is important to be able to use image and text to successfully encode the desired features of the manuscripts. Computer Scientists must find mechanisms for representing markup in its association both with the images, text and other auxiliary files and for making the representation available for efficient querying. This paper addresses the architecture of one such solution, that uses efficient data structures to store image-based encodings in main memory and on disk.

Numerical stability of a convex hull algorithm for simple polygons

A numerically stable and optimalO(n)-time implementation of an algorithm for finding the convex hull of a simple polygon is presented. Stability is understood in the sense of a backward error analysis. A concept of the condition number of simple polygons and its impact on the performance of the algorithm is discussed. It is shown that if the condition number does not exceed (1+O(ε))/(3ε), then, in floating-point arithmetic with the unit roundoffε, the algorithm produces the vertices of a convex hull for slightly perturbed input points. The relative perturbation does not exceed 3ε(1+O(ε)).