Planar subgraphs without low-degree nodes

We study the following problem: given a geometric graph G and an integer k, determine if G has a planar spanning subgraph (with the original embedding and straight-line edges) such that all nodes have degree at least k. If G is a unit disk graph, the problem is trivial to solve for k = 1. We show that even the slightest deviation from the trivial case (e.g., quasi unit disk graphs or k = 1) leads to NP-hard problems.

Compression of Weighted Graphs

We propose to compress weighted graphs (networks), motivated by the observation that large networks of social, biological, or other relations can be complex to handle and visualize. In the process also known as graph simplication, nodes and (unweighted) edges are grouped to supernodes and superedges, respectively, to obtain a smaller graph. We propose models and algorithms for weighted graphs. The interpretation (i.e. decompression) of a compressed, weighted graph is that a pair of original nodes is connected by an edge if their supernodes are connected by one, and that the weight of an edge is approximated to be the weight of the superedge. The compression problem now consists of choosing supernodes, superedges, and superedge weights so that the approximation error is minimized while the amount of compression is maximized. In this paper, we formulate this task as the 'simple weighted graph compression problem'. We then propose a much wider class of tasks under the name of 'generalized weighted graph compression problem'. The generalized task extends the optimization to preserve longer-range connectivities between nodes, not just individual edge weights. We study the properties of these problems and propose a range of algorithms to solve them, with dierent balances between complexity and quality of the result. We evaluate the problems and algorithms experimentally on real networks. The results indicate that weighted graphs can be compressed efficiently with relatively little compression error.

Three Dimensional Line-Clipping by Systematic Enumeration

Three dimensional clipping is a critical component of the 3D graphics pipeline. A new 3D clipping algorithm is presented in this paper. An efficient 2D clipping routine reported earlier has been used as a submodule. This algorithm uses a new classification scheme for lines of all possible orientations with respect to a rectangular parallelopiped view volume. The performance of this algorithm has been evaluated using exact arithmetic operation counts. It is shown that our algorithm requires less arithmetic operations than the Cyrus-Beck 3D clipping algorithm in all cases. It is also shown that for lines that intersect the clipping volume, our algorithm performs better than the Liang-Barsky 3D clipping algorithm.

Effect of tolerance on the propagation characteristic of a superconducting thin film microstrip delay line

The propagation constant of a superconducting microstrip transmission delay line is evaluated using the spectral domain immitance approach, modelling the superconductor as a surface current having an equivalent surface impedance found through the complex resistive boundary condition. The sensitivity approach is used to study the beta variations with substrate parameters and film characteristics. Results show that the surface impedance does not have much influence on beta sensitivities with respect to epsilon r, W and h. However, it can be observed that the surface impedance plays a crucial role in determining the optimum design.

X-ray diffraction line profile analysis of deformation microstructure in boron modified Ti-6Al-4V alloy

X-ray diffraction line profile analysis (XRDLPA) techniques have been applied to investigate the deformed microstructure of a recently developed boron modified two-phase titanium alloy Ti-6Al-4V. The alloy was hot compressed at 750 degrees C up to 50% height reduction at two different strain rates (10(-3) S-1 and 1 S-1). Microstructural parameters like average domain size, average microstrain within the domain and dislocation density of the two phases were determined using X-ray diffraction line profile analysis. The results indicate an increase in the microstrain and dislocation density for the alpha-phase and decrease for the beta-phase in the case of boron modified alloys as compared to the normal material. Microstructural modifications viz, the grain refinement and the presence of hard, brittle TiB particles in the case of boron modified alloy are held responsible for the observed difference in the dislocation density. (C) 2010 Elsevier Inc. All rights reserved.

Proposed visible emission line space solar coronagraph

The outer atmosphere of the sun called the corona has been observed during total solar eclipse for short periods (typically <6 min), from as early as the eighteenth century. In the recent past, space-based instruments have permitted us to study the corona uninterruptedly. In spite of these developments, the dynamic corona and its high temperature (1-2 million K) are yet to be Ally understood. It is conjectured that their dynamic nature and associated energetic events are possible reasons behind the high temperature. In order to study these in detail, a visible emission line space solar coronagraph is being proposed as a payload under the small-satellite programme of the Indian Space Research Organisation. The satellite is named as Aditya-1 and the scientific objectives of this payload are to study: (i) the existence of intensity oscillations for the study of wave-driven coronal heating; (ii) the dynamics and formation of coronal loops and temperature structure of the coronal features; (iii) the origin, cause and acceleration of coronal mass ejections (CMEs) and other solar active features, and (iv) coronal magnetic field topology and three-dimensional structures of CMEs using polarization information. The uniqueness of this payload compared to previously flown space instruments is as follows: (a) observations in the visible wavelength closer to the disk (down to 1.05 solar radii); (b) high time cadence capability (better than two-images per second), and (c) simultaneous observations of at least two spectral windows all the time and three spectral windows for short durations.

New Approximation Algorithms for Minimum Cycle Bases of Graphs

We consider the problem of computing an approximate minimum cycle basis of an undirected non-negative edge-weighted graph G with m edges and n vertices; the extension to directed graphs is also discussed. In this problem, a {0,1} incidence vector is associated with each cycle and the vector space over F-2 generated by these vectors is the cycle space of G. A set of cycles is called a cycle basis of G if it forms a basis for its cycle space. A cycle basis where the sum of the weights of the cycles is minimum is called a minimum cycle basis of G. Cycle bases of low weight are useful in a number of contexts, e.g. the analysis of electrical networks, structural engineering, chemistry, and surface reconstruction. Although in most such applications any cycle basis can be used, a low weight cycle basis often translates to better performance and/or numerical stability. Despite the fact that the problem can be solved exactly in polynomial time, we design approximation algorithms since the performance of the exact algorithms may be too expensive for some practical applications. We present two new algorithms to compute an approximate minimum cycle basis. For any integer k >= 1, we give (2k - 1)-approximation algorithms with expected running time O(kmn(1+2/k) + mn((1+1/k)(omega-1))) and deterministic running time O(n(3+2/k) ), respectively. Here omega is the best exponent of matrix multiplication. It is presently known that omega < 2.376. Both algorithms are o(m(omega)) for dense graphs. This is the first time that any algorithm which computes sparse cycle bases with a guarantee drops below the Theta(m(omega) ) bound. We also present a 2-approximation algorithm with expected running time O(M-omega root n log n), a linear time 2-approximation algorithm for planar graphs and an O(n(3)) time 2.42-approximation algorithm for the complete Euclidean graph in the plane.

Azidothymidine induces apoptosis in mouse myeloma cell line Sp2/0

Azidothymidine (AZT), which has been extensively used as an antiviral agent in the treatment of AIDS, showed strong inhibition of growth of Sp2/0 cells in vitro. AZT-treated cells showed a decrease in viability in a dose-dependent manner. AZT specifically induced typical apoptotic cell death with DNA double-strand cleavage and subsequent formation of apoptotic bodies. The induction of DNA double-strand cleavage into the oligonucleosomal ladder by AZT was protected in the presence of thymidine or uridine. An increase in endonuclease activity from nuclear extract of AZT-treated cells was observed. The enzyme activity was found to be Ca2+- and Mg2+-dependent and was inhibited by zinc acetate. A marked enhancement of PARP activity was observed in AZT-treated cells. These observations show that AZT can trigger both morphological and biochemical changes typical of apoptosis in the mouse myeloma cell line Sp2/0.

Line clipping revisited: Two efficient algorithms based on simple geometric observations

Two new line clipping algorithms, the opposite-corner algorithm and the perpendicular-distance algorithm, that are based on simple geometric observations are presented. These algorithms do not require computation of outcodes nor do they depend on the parametric representations of the lines. It is shown that the opposite-corner algorithm perform consistently better than an algorithm due to Nicholl, Lee, and Nicholl which is claimed to be better than the classic algorithm due to Cohen-Sutherland and the more recent Liang-Barsky algorithm. The pseudo-code of the opposite-corner algorithm is provided in the Appendix.

Chordal Bipartite Graphs with High Boxicity

The boxicity of a graph G is defined as the minimum integer k such that G is an intersection graph of axis-parallel k-dimensional boxes. Chordal bipartite graphs are bipartite graphs that do not contain an induced cycle of length greater than 4. It was conjectured by Otachi, Okamoto and Yamazaki that chordal bipartite graphs have boxicity at most 2. We disprove this conjecture by exhibiting an infinite family of chordal bipartite graphs that have unbounded boxicity.

Some results on the reconstruction problems. p-claw-free, chordal, and p4-reducible graphs

A claw is an induced subgraph isomorphic to K-1,K-3. The claw-point is the point of degree 3 in a claw. A graph is called p-claw-free when no p-cycle has a claw-point on it. It is proved that for p greater than or equal to 4, p-claw-free graphs containing at least one chordless p-cycle are edge reconstructible. It is also proved that chordal graphs are edge reconstructible. These two results together imply the edge reconstructibility of claw-free graphs. A simple proof of vertex reconstructibility of P-4-reducible graphs is also presented. (C) 1995 John Wiley and Sons, Inc.

Irreversibility line and the hierarchy of weak links in Bi2Sr2CaCu2O8+?

The irreversibility line for H?c in a single crystal specimen of Bi2Sr2CaCu2O8+? (Bi2212) has been determined via vanishing of hysteresis in isothermal dc magnetization measurements. The hysteresis loops (H?c) in Bi2212 appear to show signatures of two-component magnetic response in several temperature regions where the temperature dependence of irreversibility field charges sharply. It is proposed that the observed behavior may be a consequence of existence of weak links of varying strength in Bi2212

The existence of homeomorphic subgraphs in chordal graphs

We establish conditions for the existence, in a chordal graph, of subgraphs homeomorphic to K-n (n greater than or equal to 3), K-m,K-n (m,n greater than or equal to 2), and wheels W-r (r greater than or equal to 3). Using these results, we develop a simple linear time algorithm for testing planarity of chordal graphs. We also show how these results lead to simple polynomial time algorithms for the Fixed Subgraph Homeomorphism problem on chordal graphs for some special classes of pattern graphs.

Off-line signature verification using genetically optimized weighted features

This paper is concerned with off-line signature verification. Four different types of pattern representation schemes have been implemented, viz., geometric features, moment-based representations, envelope characteristics and tree-structured Wavelet features. The individual feature components in a representation are weighed by their pattern characterization capability using Genetic Algorithms. The conclusions of the four subsystems teach depending on a representation scheme) are combined to form a final decision on the validity of signature. Threshold-based classifiers (including the traditional confidence-interval classifier), neighbourhood classifiers and their combinations were studied. Benefits of using forged signatures for training purposes have been assessed. Experimental results show that combination of the Feature-based classifiers increases verification accuracy. (C) 1999 Pattern Recognition Society. Published by Elsevier Science Ltd. All rights reserved.

Acyclic Edge-Coloring of Planar Graphs

A proper edge-coloring with the property that every cycle contains edges of at least three distinct colors is called an acyclic edge-coloring. The acyclic chromatic index of a graph G, denoted. chi'(alpha)(G), is the minimum k such that G admits an acyclic edge-coloring with k colors. We conjecture that if G is planar and Delta(G) is large enough, then chi'(alpha) (G) = Delta (G). We settle this conjecture for planar graphs with girth at least 5. We also show that chi'(alpha) (G) <= Delta (G) + 12 for all planar G, which improves a previous result by Fiedorowicz, Haluszczak, and Narayan Inform. Process. Lett., 108 (2008), pp. 412-417].