Linear-Time Algorithms for Finding Tucker Submatrices and Lekkerkerker-Boland Subgraphs

Lekkerkerker and Boland characterized the minimal forbidden induced subgraphs for the class of interval graphs. We give a linear-time algorithm to find one in any graph that is not an interval graph. Tucker characterized the minimal forbidden submatrices of binary matrices that do not have the consecutive-ones property. We give a linear-time algorithm to find one in any binary matrix that does not have the consecutive-ones property.Comment: A preliminary version of this work appeared in WG13: 39th International Workshop on Graph-Theoretic Concepts in Computer Scienc

Simple DFS on the Complement of a Graph and on Partially Complemented Digraphs

A complementation operation on a vertex of a digraph changes all outgoing arcs into non-arcs, and outgoing non-arcs into arcs. A partially complemented digraph $\widetilde{G}$ is a digraph obtained from a sequence of vertex complement operations on $G$. Dahlhaus et al. showed that, given an adjacency-list representation of $\widetilde{G}$, depth-first search (DFS) on $G$ can be performed in $O(n + \widetilde{m})$ time, where $n$ is the number of vertices and $\widetilde{m}$ is the number of edges in $\widetilde{G}$. To achieve this bound, their algorithm makes use of a somewhat complicated stack-like data structure to simulate the recursion stack, instead of implementing it directly as a recursive algorithm. We give a recursive $O(n+\widetilde{m})$ algorithm that uses no complicated data-structures

Interval-Like Graphs and Digraphs

We unify several seemingly different graph and digraph classes under one umbrella. These classes are all, broadly speaking, different generalizations of interval graphs, and include, in addition to interval graphs, adjusted interval digraphs, threshold graphs, complements of threshold tolerance graphs (known as `co-TT\u27 graphs), bipartite interval containment graphs, bipartite co-circular arc graphs, and two-directional orthogonal ray graphs. (The last three classes coincide, but have been investigated in different contexts.) This common view is made possible by introducing reflexive relationships (loops) into the analysis. We also show that all the above classes are united by a common ordering characterization, the existence of a min ordering. We propose a common generalization of all these graph and digraph classes, namely signed-interval digraphs, and show that they are precisely the digraphs that are characterized by the existence of a min ordering. We also offer an alternative geometric characterization of these digraphs. For most of the above graph and digraph classes, we show that they are exactly those signed-interval digraphs that satisfy a suitable natural restriction on the digraph, like having a loop on every vertex, or having a symmetric edge-set, or being bipartite. For instance, co-TT graphs are precisely those signed-interval digraphs that have each edge symmetric. We also offer some discussion of future work on recognition algorithms and characterizations

Double Threshold Digraphs

A semiorder is a model of preference relations where each element x is associated with a utility value alpha(x), and there is a threshold t such that y is preferred to x iff alpha(y) - alpha(x) > t. These are motivated by the notion that there is some uncertainty in the utility values we assign an object or that a subject may be unable to distinguish a preference between objects whose values are close. However, they fail to model the well-known phenomenon that preferences are not always transitive. Also, if we are uncertain of the utility values, it is not logical that preference is determined absolutely by a comparison of them with an exact threshold. We propose a new model in which there are two thresholds, t_1 and t_2; if the difference alpha(y) - alpha(x) is less than t_1, then y is not preferred to x; if the difference is greater than t_2 then y is preferred to x; if it is between t_1 and t_2, then y may or may not be preferred to x. We call such a relation a (t_1,t_2) double-threshold semiorder, and the corresponding directed graph G = (V,E) a (t_1,t_2) double-threshold digraph. Every directed acyclic graph is a double-threshold digraph; increasing bounds on t_2/t_1 give a nested hierarchy of subclasses of the directed acyclic graphs. In this paper we characterize the subclasses in terms of forbidden subgraphs, and give algorithms for finding an assignment of utility values that explains the relation in terms of a given (t_1,t_2) or else produces a forbidden subgraph, and finding the minimum value lambda of t_2/t_1 that is satisfiable for a given directed acyclic graph. We show that lambda gives a useful measure of the complexity of a directed acyclic graph with respect to several optimization problems that are NP-hard on arbitrary directed acyclic graphs

Isomorphism of graph classes related to the circular-ones property

We give a linear-time algorithm that checks for isomorphism between two 0-1 matrices that obey the circular-ones property. This algorithm leads to linear-time isomorphism algorithms for related graph classes, including Helly circular-arc graphs, \Gamma-circular-arc graphs, proper circular-arc graphs and convex-round graphs.Comment: 25 pages, 9 figure

Three-dimensional observations of an aperiodic oscillatory gliding behavior in Myxococcus xanthus using confocal interference reflection microscopy

The deltaproteobacterium Myxococcus xanthus is a model for bacterial motility and has provided unprecedented insights into bacterial swarming behaviors. Fluorescence microscopy techniques have been invaluable in defining the mechanisms that are involved in gliding motility, but these have almost entirely been limited to two-dimensional (2D) studies, and there is currently no understanding of gliding motility in a three-dimensional (3D) context. We present here the first use of confocal interference reflection microscopy (IRM) to study gliding bacteria, revealing aperiodic oscillatory behavior with changes in the position of the basal membrane relative to the substrate on the order of 90 nm in vitro. First, we use a model planoconvex lens specimen to show how topological information can be obtained from the wavelength-dependent interference pattern in IRM. We then use IRM to observe gliding M. xanthus bacteria and show that cells undergo previously unobserved changes in their adhesion profile as they glide. We compare the wild type with mutants that have reduced motility, which also exhibit the same changes in the adhesion profile during gliding. We find that the general gliding behavior is independent of the proton motive force-generating complex AglRQS and suggest that the novel behavior that we present here may be a result of recoil and force transmission along the length of the cell body following firing of the type IV pili. IMPORTANCE 3D imaging of live bacteria with optical microscopy techniques is a challenge due to the small size of bacterial cells, meaning that previous studies have been limited to observing motility behavior in 2D. We introduce the application of confocal multiwavelength interference reflection microscopy to bacteria, which enables visualization of 3D motility behaviors in a single 2D image. Using the model organism Myxococcus xanthus, we identified novel motility behaviors that are not explained by current motility models, where gliding bacteria exhibit aperiodic changes in their adhesion to an underlying solid surface. We concluded that the 3D behavior was not linked to canonical motility mechanisms and that IRM could be applied to study a range of microbiological specimens with minimal adaptation to a commercial microscope

Use of MMG signals for the control of powered orthotic devices: Development of a rectus femoris measurement protocol

Copyright © 2009 Rehabilitation Engineering and Assistive Technology Society (RESNA). This is an Author's Accepted Manuscript of an article published in Assistive Technology, 21(1), 1 - 12, 2009, copyright Taylor & Francis, available online at: http://www.tandfonline.com/10.1080/10400430902945678.A test protocol is defined for the purpose of measuring rectus femoris mechanomyographic (MMG) signals. The protocol is specified in terms of the following: measurement equipment, signal processing requirements, human postural requirements, test rig, sensor placement, sensor dermal fixation, and test procedure. Preliminary tests of the statistical nature of rectus femoris MMG signals were performed, and Gaussianity was evaluated by means of a two-sided Kolmogorov-Smirnov test. For all 100 MMG data sets obtained from the testing of two volunteers, the null hypothesis of Gaussianity was rejected at the 1%, 5%, and 10% significance levels. Most skewness values were found to be greater than 0.0, while all kurtosis values were found to be greater than 3.0. A statistical convergence analysis also performed on the same 100 MMG data sets suggested that 25 MMG acquisitions should prove sufficient to statistically characterize rectus femoris MMG. This conclusion is supported by the qualitative characteristics of the mean rectus femoris MMG power spectral densities obtained using 25 averages

Changes in Black Carbon Deposition to Antarctica from Two Ice Core Records, A.D. 1850-2000

Continuous flow analysis was based on a steady sample flow and in-line detection of BC and other chemical substances as described in McConnell et al. (2007). In the cold room, previously cut one meter ice core sticks of 3x3cm, are melted continuously on a heated melter head specifically designed to eliminate contamination from the atmosphere or by the external parts of the ice. The melted ice from the most inner part of the ice stick is continuously pumped by a peristaltic pump and carried to a clean lab by Teflon lines. The recorded signal is continuous, integrating a sample volume of about 0.05 mL, for which the temporal resolution depends on the speed of melting, ice density and snow accumulation rate at the ice core drilling site. For annual accumulation derived from the WAIS and Law Dome ice cores, we assumed ~3.1 cm water equivalent uncertainty in each year's accumulation from short scale spatial variability (glaciological noise) which was determined from several measurements of annual accumulation in multiple parallel ice cores notably from the WAIS Divide ice core site (Banta et al., 2008) and from South Pole site (McConnell et al., 1997; McConnell et al., 2000). Refractory black carbon (rBC) concentrations were determined using the same method as in (Bisiaux et al., 2011) and adapted to continuous flow measurements as described by (McConnell et al., 2007). The technique uses a single particle intracavity laser induced incandescence photometer (SP2, Droplet Measurement Technologies, Boulder, Colorado) coupled to an ultrasonic nebulizer/desolvation (CETAC UT5000) Flow Injection Analysis (FIA). All analyses, sample preparation etc, were performed in a class 100 cleanroom using anti contamination "clean techniques". The samples were not acidified