Bicriteria Network Design Problems

We study a general class of bicriteria network design problems. A generic problem in this class is as follows: Given an undirected graph and two minimization objectives (under different cost functions), with a budget specified on the first, find a <subgraph \from a given subgraph-class that minimizes the second objective subject to the budget on the first. We consider three different criteria - the total edge cost, the diameter and the maximum degree of the network. Here, we present the first polynomial-time approximation algorithms for a large class of bicriteria network design problems for the above mentioned criteria. The following general types of results are presented. First, we develop a framework for bicriteria problems and their approximations. Second, when the two criteria are the same %(note that the cost functions continue to be different) we present a ``black box'' parametric search technique. This black box takes in as input an (approximation) algorithm for the unicriterion situation and generates an approximation algorithm for the bicriteria case with only a constant factor loss in the performance guarantee. Third, when the two criteria are the diameter and the total edge costs we use a cluster-based approach to devise a approximation algorithms --- the solutions output violate both the criteria by a logarithmic factor. Finally, for the class of treewidth-bounded graphs, we provide pseudopolynomial-time algorithms for a number of bicriteria problems using dynamic programming. We show how these pseudopolynomial-time algorithms can be converted to fully polynomial-time approximation schemes using a scaling technique.Comment: 24 pages 1 figur

Frustrated spin ladder with alternating spin-1 and spin-1/2 rungs

We study the impact of the diagonal frustrating couplings on the quantum phase diagram of a two-leg ladder composed of alternating spin-1 and spin-1/2 rungs. As the coupling strength is increased the system successively exhibits two gapped paramagnetic phases (a rung-singlet and a Haldane-like non-degenerate states) and two ferrimagnetic phases with different ferromagnetic moments per rung. The first two states are similar to the phases studied in the frustrated spin-1/2 ladder, whereas the magnetic phases appear as a result of the mixed-spin structure of the model. A detailed characterization of these phases is presented using density-matrix renormalization-group calculations, exact diagonalizations of periodic clusters, and an effective Hamiltonian approach inspired by the analysis of numerical data. The present theoretical study was motivated by the recent synthesis of the quasi-one-dimensional ferrimagnetic material Fe$^{II}$Fe$^{III}$ (trans-1,4-cyclohexanedicarboxylate) exhibiting a similar ladder structure.Comment: 10 pages, 8 figure

Comparison of pulsar positions from timing and very long baseline astrometry

Pulsar positions can be measured with high precision using both pulsar timing methods and very long baseline interferometry (VLBI). Pulsar timing positions are referenced to a solar-system ephemeris, whereas VLBI positions are referenced to distant quasars. Here, we compare pulsar positions from published VLBI measurements with those obtained from pulsar timing data from the Nanshan and Parkes radio telescopes in order to relate the two reference frames. We find that the timing positions differ significantly from the VLBI positions (and also differ between different ephemerides). A statistically significant change in the obliquity of the ecliptic of 2.16 ± 0.33 mas is found for the JPL ephemeris DE405, but no significant rotation is found in subsequent JPL ephemerides. The accuracy with which we can relate the two frames is limited by the current uncertainties in the VLBI reference source positions and in matching the pulsars to their reference source. Not only do the timing positions depend on the ephemeris used in computing them, but also different segments of the timing data lead to varying position estimates. These variations are mostly common to all ephemerides, but slight changes are seen at the 10 μas level between ephemerides

Luminance-Chrominance-Gradient Based Technique for High Dynamic Range Image Fusion

604-607The High Dynamic Range (HDR) technique involves capturing the same scene multiple times with different exposure values and produces an output image with more dynamic range. Instead of doing all processing in RGB color space, we proposed to do it in Luminance Chrominance Gradient colour space, which results the output images to be more natural and pleasant to perceive with less noise. This experiment was evaluated and analysed with BAR and AEE1 methods and the results are compared. We showed that, our LCGHDR method is computationally efficient and able to remove any colour distortions originated from the RGB color channel

Analysis of bistable and oscillating reaction systems in presence of an external noise

The paper analyses a bistable and an oscillatory reaction system in the presence of an external noise. The analysis of a bistable system shows that in the normal way the inclusion of noise destroys all the deterministic solutions. In other words, the stochastic system does not admit any solution. With imposition of certain restraints it is possible, however, to get stochastic solutions in a certain region of parameter space, which in general shrinks with the extent of noise. The modality of diminishing the region of solutions is different for white and nonwhite noise and has been discussed The paper also evaluates the influence of white and nonwhite noise on the behavior of an oscillating system and illustrates it by considering two case examples. One example indicates the conflicting role of white and nonwhite noise in bringing about the transitions from the oscillatory behavior while the second example shows no influence of white and nonwhite noise on the oscillating solution The implications of the role of noise in analysing bistable and oscillatory systems is discussed