Sensitivity analysis of the greedy heuristic for binary knapsack problems

Greedy heuristics are a popular choice of heuristics when we have to solve a large variety of NP -hard combinatorial problems. In particular for binary knapsack problems, these heuristics generate good results. If some uncertainty exists beforehand regarding the value of any one element in the problem data, sensitivity analysis procedures can be used to know the tolerance limits within which the value may vary will not cause changes in the output. In this paper we provide a polynomial time characterization of such limits for greedy heuristics on two classes of binary knapsack problems, namely the 0-1 knapsack problem and the subset sum problem. We also study the relation between algorithms to solve knapsack problems and algorithms to solve their sensitivity analysis problems, the conditions under which the sensitivity analysis of the heuristic generates bounds for the toler-ance limits for the optimal solutions, and the empirical behavior of the greedy output when there is a change in the problem data.

A new study of muons in air showers by NBU air shower array

The North Bengal University (NBU) air shower array has been in operation in conjunction with two muon magnetic spectrographs. The array incorporates 21 particle density sampling detectors around the magnetic spectrographs covering an area of 900 sq m. The layout of the array is based on the arrangement of detectors in a square symmetry. The array set up on the ground level is around a 10 m high magnetic spectrograph housing. This magnetic spectrograph housing limits the zenith angular acceptance of the incident showers to a few degrees. Three hundred muons in the fitted showers of size range 10 to the 4th power to 10 to the 5th power particles have so far been scanned and the momenta determined in the momentum range 2 - 440 GeV/c. More than 1500 recorded showers are now in the process of scanning and fitting. A lateral distribution of muons of energy greater than 300 MeV in the shower size range 10 to the 5th power to 7 x 10 to the 5th power has been obtained

Internal magnetic fields in thin ZnSe epilayers

Strain induced spin-splitting is observed and characterized using pump-probe Kerr rotation spectroscopy in n-ZnSe epilayers grown on GaAs substrates. The spin-splitting energies are mapped out as a function of pump-probe separation, applied voltage, and temperature in a series of samples of varying epilayer thicknesses and compressive strain arising from epilayer-substrate lattice mismatch. The strain is independently quantified using photoluminescence and x-ray diffraction measurements. We observe that the magnitude of the spin splitting increases with applied voltage and temperature, and is highly crystal direction dependent, vanishing along [1 1-bar 0].Comment: 9 pages, 3 figure

Planar Two-particle Coulomb Interaction: Classical and Quantum Aspects

The classical and quantum aspects of planar Coulomb interactions have been studied in detail. In the classical scenario, Action Angle Variables are introduced to handle relativistic corrections, in the scheme of time-independent perturbation theory. Complications arising due to the logarithmic nature of the potential are pointed out. In the quantum case, harmonic oscillator approximations are considered and effects of the perturbations on the excited (oscillator) states have been analysed. In both the above cases, the known 3+1-dimensional analysis is carried through side by side, for a comparison with the 2+1-dimensional (planar) results.Comment: LaTex, Figures on request, e-mail:<[email protected]

A new study of shower age distribution in near vertical showers by EAS air shower array

The air shower array has been developed since it started operation in 1931. The array covering an area of 900 sq m now incorporates 21 particle density sampling detectors around two muon magnetic spectrographs. The air showers are detected in the size range 10 to the 4th power to 10 to the 6th power particles. A total of 11000 showers has so far been detected. Average values of shower age have been obtained in various shower size ranges to study the dependence of shower age on shower size. The core distance dependence of shower age parameter has also been analyzed for presentation

Pairwise Balanced Designs From Cyclic PBIB Designs

A pairwise balanced designs was constructed using cyclic partially balanced incomplete block designs with either (λ1 – λ2) = 1 or (λ2 – λ1) = 1. This method of construction of Pairwise balanced designs is further generalized to construct it using cyclic partially balanced incomplete block design when |(λ1 – λ2)| = p. The methods of construction of pairwise balanced designs was supported with examples. A table consisting parameters of Cyclic PBIB designs and its corresponding constructed pairwise balanced design is also included

Current-Induced Polarization and the Spin Hall Effect at Room Temperature

Electrically-induced electron spin polarization is imaged in n-type ZnSe epilayers using Kerr rotation spectroscopy. Despite no evidence for an electrically-induced internal magnetic field, current-induced in-plane spin polarization is observed with characteristic spin lifetimes that decrease with doping density. The spin Hall effect is also observed, indicated by an electrically-induced out-of-plane spin polarization with opposite sign for spins accumulating on opposite edges of the sample. The spin Hall conductivity is estimated as 3 +/- 1.5 Ohms**-1 m**-1/|e| at 20 K, which is consistent with the extrinsic mechanism. Both the current-induced spin polarization and the spin Hall effect are observed at temperatures from 10 K to 295 K.Comment: 5 pages, 4 figure

Interplay of disorder and geometrical frustration in doped Gadolinium Gallium Garnet

The geometrically-frustrated, triangular antiferromagnet GGG exhibits a rich mix of short-range order and isolated quantum states. We investigate the effects of up to 1% Neodymium substitution for Gallium on the ac magnetic response at temperatures below 1 K in both the linear and nonlinear regimes. Substitutional disorder actually drives the system towards a more perfectly frustrated state, apparently compensating for the effect of imperfect Gadolinium/Gallium stoichiometry, while at the same time more closely demarcating the boundaries of isolated, coherent clusters composed of hundreds of spins. Optical measurements of the local Nd environment substantiate the picture of an increased frustration index with doping.Comment: 5 pages, 5 figure

Effect of microstructural parameters,micro texture and matrix strain on the Charpy impact properties of low carbon HSLA steel containing MnS inclusions

Low-carbon micro-alloyed steel containing coarse MnS inclusions was subjected to different thermo-mechanical processing routes to evaluate the effect of microstructure on its Charpy impact properties over a range of temperatures. MnS inclusions were found to deteriorate the upper shelf energy (USE) of the steel but its effect on the impact transition temperature was not as detrimental as that due to the presence of TiN particles. MnS inclusions were responsible for the initiation of micro-voids; however, the propagation of the cracks from these depends on the effective grain size and the strength of the matrix. An increase in the density of dislocations and low-angle boundaries enhances the strength and the strain-hardening ability of the ferrite matrix. This helps in retarding the growth of micro-voids, thereby reducing USE and promoting cleavage crack propagation resulting in an increase in its impact transition temperature. Refinement of effective grain size, on the other hand, increases the crack propagation resistance and therefore, improves the low-temperature toughness of the steel. Finish rolling of the steel just above the Ar3 temperature (austenite to ferrite transformation start temperature) or a simple normalizing treatment of the as-rolled plates at a low austenitization temperature is recommended from the point of view of higher impact toughness and lower impact transition temperature