Spanning trees short or small

We study the problem of finding small trees. Classical network design problems are considered with the additional constraint that only a specified number $k$ of nodes are required to be connected in the solution. A prototypical example is the $k$MST problem in which we require a tree of minimum weight spanning at least $k$ nodes in an edge-weighted graph. We show that the $k$MST problem is NP-hard even for points in the Euclidean plane. We provide approximation algorithms with performance ratio $2\sqrt{k}$ for the general edge-weighted case and $O(k^{1/4})$ for the case of points in the plane. Polynomial-time exact solutions are also presented for the class of decomposable graphs which includes trees, series-parallel graphs, and bounded bandwidth graphs, and for points on the boundary of a convex region in the Euclidean plane. We also investigate the problem of finding short trees, and more generally, that of finding networks with minimum diameter. A simple technique is used to provide a polynomial-time solution for finding $k$-trees of minimum diameter. We identify easy and hard problems arising in finding short networks using a framework due to T. C. Hu.Comment: 27 page

Serological diagnosis of pulmonary aspergillosis

Methods for the preparation of antigens from clinically isolated cultures of Aspergillus were standardized. Sera from 25 suspected cases of pulmonary aspergillosis were tested against antigens prepared by us, from 4 strains of A. fumigatus and one strain of A. flavus, using the Ouchterlony double diffusion and immunoelectrophoretic techniques. Of the 25 sera tested, 18 reacted positively with antigens of A.fumigatus, one with A.flavus and 2 with both these species. Antigens of two non-pathogenic Aspergilli included in the study failed to react with any of the sera. Our antigen preparations gave more numerous as well as sharper precipitin lines than the commercial Bencard antigens which were used for comparison. Moreover, mycelial antigens from 48 to 96 h old cultures revealed precipitin lines comparable to that of the routine, 4 week old culture filtrate antigens, thus suggesting that the incubation period for obtaining antigens could be cut down considerably

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

Population eruption of sunset shell Siliqua radiata (Linnaeus, 1758) along Versova beach in Mumbai

Sudden population eruption of Siliqua radiata during monsoon months (June-August 2008) was observed along Versova beach in Mumbai. Relationship between shell length (SL) and total weight (TW) was TW = 0.0001137 * SL 2.67922, shell length (SL) and meat weight (MW) was MW = 0.0000237 * SL 2.91756. S. radiata had isometric growth. The average density was estimated as 14 per square meter and the biomass was 153 g.m-2. The proportion of meat was 60%. Analysis of meat showed high amount of heavy metals namely copper, cadmium and arsenic

Understanding the Anomalous Diffusion of Water in Aqueous Electrolytes Using Machine Learned Potentials

The diffusivity of water in aqueous cesium iodide solutions is larger than that in neat liquid water, and vice versa for sodium chloride solutions. Such peculiar ion-specific behavior, called anomalous diffusion, is not reproduced in typical force field-based molecular dynamics (MD) simulations due to inadequate treatment of ion-water interactions. Herein, this hurdle is tackled using machine learned atomic potentials (MLPs) trained on data from density functional theory calculations. MLP-based atomistic MD simulations of aqueous salt solutions reproduce experimentally determined thermodynamic, structural, dynamical, and transport properties, including their varied trends of water diffusivities across salt concentration. This enables an examination of their intermolecular structure to unravel the microscopic underpinnings of the distinction in their transport. While both ions in CsI solutions contribute to faster diffusion of water molecules, the competition between the heavy retardation by Na-ions and slight acceleration by Cl-ions in NaCl solutions reduces their water diffusivity.Comment: 23 pages, 5 figure

Advanced photovoltaic power systems using tandem GaAs/GaSb concentrator modules

In 1989, Boeing announced the fabrication of a tandem gallium concentrator solar cell with an energy conversion efficiency of 30 percent. This research breakthrough has now led to panels which are significantly smaller, lighter, more radiation resistant, and potentially less expensive than the traditional silicon flat plate electric power supply. The new Boeing tandem concentrator (BTC) module uses an array of lightweight silicone Fresnel lenses mounted on the front side of a light weight aluminum honeycomb structure to focus sunlight onto small area solar cells mounted on a thin back plane. This module design is shown schematically. The tandem solar cell in this new module consists of a gallium arsenide light sensitive cell with a 24 percent energy conversion efficiency stacked on top of a gallium antimonide infrared sensitive cell with a conversion efficiency of 6 percent. This gives a total efficiency 30 percent for the cell-stack. The lens optical efficiency is typically 85 percent. Discounting for efficiency losses associated with lens packing, cell wiring, and cell operating temperature still allows for a module efficiency of 22 percent which leads to a module power density of 300 Watts/sq. m. This performance provides more than twice the power density available from a single crystal silicon flat plate module and at least four times the power density available from amorphous silicon modules. The fact that the lenses are only 0.010 ft. thick and the aluminum foil back plane is only 0.003 ft. thick leads to a very lightweight module. Although the cells are an easy to handle thickness of 0.020 ft., the fact that they are small, occupying one-twenty-fifth of the module area, means that they add little to the module weight. After summing all the module weights and given the high module power, we find that we are able to fabricate BTC modules with specific power of 100 watts/kg

Fractal Formation Of A Y-Ba-Cu-O Thin-Film On Srtio3

Fractal formation has been observed after thermal annealing of the rf-sputtered Y-Ba-Cu-O thin film on SrTiO3 substrate. Through energy-dispersive x-ray analysis, it was found that the composition of the fractal was YBa2Cu3Ox and the surrounding film composition was Y2Ba2Cu3Ox. The fractal dimensions D ranging from 1.26 to 1.65 were obtained using the standard sandbox method with different thresholds

Tandem concentrator solar cells with 30 percent (AMO) power conversion efficiency

Very high efficiency concentrator solar panels are envisioned as economical and reliable electrical power subsystems for space based platforms of the future. GaAs concentrator cells with very high efficiencies and good sub-bandgap transmissions can be fabricated on standard wafers. GaSb booster cell development is progressing very well; performance characteristics are still improving dramatically. Consistent GaAs/GaSb stacked cell AMO efficiencies greater than 30 percent are expected