Marshall W. Bern

Provably good mesh generation

Several versions of the problem of generating triangular meshes for finite-element methods are studied. It is shown how to triangulate a planar point set or a polygonally bounded domain with triangles of bounded aspect ratio, how to triangulate a planar point set with triangles having no obtuse angles, how to triangulate a point set in arbitrary dimension with simplices of bounded aspect ratio, and how to produce a linear-size Delaunay triangulation of a multidimensional point set by adding a linear number of extra points. All the triangulations have size within a constant factor of optimal and run in optimal time O(n log n+k) with input of size n and output of size k. No previous work on mesh generation simultaneously guarantees well-shaped elements and small total size. >

The steiner problem with edge lengths 1 and 2

Abstract The Steiner problem on networks asks for a shortest subgraph spanning a given subset of distinguished vertices. We give a 4 3 -approximation algorithm for the special case in which the underlying network is complete and all edge lengths are either 1 or 2. We also relate the Steiner problem to a complexity class recently defined by Papadimitriou and Yannakakis by showing that this special case is MAX SNP-hard, which may be evidence that the Steiner problem on networks has no polynomial-time approximation scheme.

Surface reconstruction by Voronoi filtering

We give a simple combinatorial algorithm that computes a piecewise-linear approximation of a smooth surface from a finite set of sample points. The algorithm uses Voronoi vertices to remove triangles from the Delaunay triangulation. We prove the algorithm correct by showing that for densely sampled surfaces, where density depends on a local feature size function, the output is topologically valid and convergent (both pointwise and in surface normals) to the original surface. We briefly describe an implementation of the algorithm and show example outputs.

Automatic Quality Assessment of Peptide Tandem Mass Spectra

MOTIVATION A powerful proteomics methodology couples high-performance liquid chromatography (HPLC) with tandem mass spectrometry and database-search software, such as SEQUEST. Such a set-up, however, produces a large number of spectra, many of which are of too poor quality to be useful. Hence a filter that eliminates poor spectra before the database search can significantly improve throughput and robustness. Moreover, spectra judged to be of high quality, but that cannot be identified by database search, are prime candidates for still more computationally intensive methods, such as de novo sequencing or wider database searches including post-translational modifications. RESULTS We report on two different approaches to assessing spectral quality prior to identification: binary classification, which predicts whether or not SEQUEST will be able to make an identification, and statistical regression, which predicts a more universal quality metric involving the number of b- and y-ion peaks. The best of our binary classifiers can eliminate over 75% of the unidentifiable spectra while losing only 10% of the identifiable spectra. Statistical regression can pick out spectra of modified peptides that can be identified by a de novo program but not by SEQUEST. In a section of independent interest, we discuss intensity normalization of mass spectra.

Optimal point placement for mesh smoothing

We study the problem of moving a vertex in an unstructured mesh of triangular, quadrilateral, or tetrahedral elements to optimize the shapes of adjacent elements. We show that many such problems can be solved in linear time using generalized linear programming. We also give efficient algorithms for some mesh smoothing problems that do not fit into the generalized linear programming paradigm.

SecLEACH - A Random Key Distribution Solution for Securing Clustered Sensor Networks

Clustered sensor networks have been shown to increase system throughput, decrease system delay, and save energy. While those with rotating cluster heads, such as LEACH, have also advantages in terms of security, the dynamic nature of their communication makes most existing security solutions inadequate for them. In this paper, we show how random key predistribution, widely studied in the context of flat networks, can be used to secure communication in hierarchical (cluster-based) protocols such as LEACH. To our knowledge, it is the first work that investigates random key predistribution as applied to hierarchical WSNs

Byonic: advanced peptide and protein identification software.

Byonic is the name of a software package for peptide and protein identification by tandem mass spectrometry. This software, which has only recently become commercially available, facilitates a much wider range of search possibilities than previous search software such as SEQUEST and Mascot. Byonic allows the user to define an essentially unlimited number of variable modification types. Byonic also allows the user to set a separate limit on the number of occurrences of each modification type, so that a search may consider only one or two chance modifications such as oxidations and deamidations per peptide, yet allow three or four biological modifications such as phosphorylations, which tend to cluster together. Hence, Byonic can search for tens or even hundreds of modification types simultaneously without a prohibitively large combinatorial explosion. Byonics Wildcard Search allows the user to search for unanticipated or even unknown modifications alongside known modifications. Finally, Byonics Glycopeptide Search allows the user to identify glycopeptides without prior knowledge of glycan masses or glycosylation sites. Curr. Protoc. Bioinform. 40:13.20.1‐13.20.14.

SecLEACH-On the security of clustered sensor networks

Clustered sensor networks have recently been shown to increase system throughput, decrease system delay, and save energy while performing data aggregation. Whereas those with rotating cluster heads, such as LEACH (low-energy adaptive clustering hierarchy), have also advantages in terms of security, the dynamic nature of their communication makes most existing security solutions inadequate for them. In this paper, we investigate the problem of adding security to hierarchical (cluster-based) sensor networks where clusters are formed dynamically and periodically, such as LEACH. For this purpose, we show how random key predistribution, widely studied in the context of flat networks, and μTESLA, a building block from SPINS, can be both used to secure communications in this type of network. We present our solution, and provide a detailed analysis of how different values for the various parameters in such a system impact a hierarchical network in terms of security and energy efficiency. To the best of our knowledge, ours is the first that investigates security in hierarchical WSNs with dynamic cluster formation.

Escape: a target selection technique using visually-cued gestures

Many mobile devices have touch-sensitive screens that people interact with using fingers or thumbs. However, such interaction is difficult because targets become occluded, and because fingers and thumbs have low input resolution. Recent research has addressed occlusion through visual techniques. However, the poor resolution of finger and thumb selection still limits selection speed. In this paper, we address the selection speed problem through a new target selection technique called Escape. In Escape, targets are selected by gestures cued by icon position and appearance. A user study shows that for targets six to twelve pixels wide, Escape performs at a similar error rate and at least 30% faster than Shift, an alternative technique, on a similar task. We evaluate Escapes performance in different circumstances, including different icon sizes, icon overlap, use of color, and gesture direction. We also describe an algorithm that assigns icons to targets, thereby improving Escapes performance.

Deconvolution of mixture spectra from ion-trap data-independent-acquisition tandem mass spectrometry

Data-independent tandem mass spectrometry isolates and fragments all of the molecular species within a given mass-to-charge window, regardless of whether a precursor ion was detected within the window. For shotgun proteomics on complex protein mixtures, data-independent MS/MS offers certain advantages over the traditional data-dependent MS/MS: identification of low-abundance peptides with insignificant precursor peaks, more direct relative quantification, free of biases caused by competing precursors and dynamic exclusion, and faster throughput due to simultaneous fragmentation of multiple peptides. However, data-independent MS/MS, especially on low-resolution ion-trap instruments, strains standard peptide identification programs, because of less precise knowledge of the peptide precursor mass and large numbers of spectra composed of two or more peptides. Here we describe a computer program called DeMux that deconvolves mixture spectra and improves the peptide identification rate by approximately 25%. We compare the number of identifications made by data-independent and data-dependent MS/MS at the peptide and protein levels: conventional data-dependent MS/MS makes a greater number of identifications but is less reproducible from run to run.