Tabu search for graph partitioning

In this paper, we develop a tabu search procedure for solving the uniform graph partitioning problem. Tabu search, an abstract heuristic search method, has been shown to have promise in solving several NP-hard problems, such as job shop and flow shop scheduling, vehicle routing, quadratic assignment, and maximum satisfiability. We compare tabu search to other heuristic procedures for graph partitioning, and demonstrate that tabu search is superior to other solution approaches for the uniform graph partitioning problem both with respect to solution quality and computational requirements.     

Characteristics of high energy interactions II. Production spectra of Gamma-rays in graphite

Twenty high energy nuclear interactions produced in the graphite units of an emulsion chamber were recorded. The emulsion chamber was exposed to cosmic rays at an atmospheric depth of 10 g cm⁻² for about 7 hr over Hyderabad, India. Fourteen interactions which radiated energyΣ E _r⩾1000 GeV in the form ofγ-rays were analysed in detail. The median energy 〈Σ E _r〉 of the interactions was 1600 GeV. Results concerning the multiplicity, the transverse and longitudinal momentum distributions, and the fractional energy distribution ofγ-rays in these interactions are presented. The average transverse momentum ofπ ⁰—mesons <pt _π ⁰> is found to increase very slowly with the primary energyE ₀ and it can be approximated by the function <pt _π ⁰>=0·238E ₀ ^0.06 .     

Characteristics of high energy interactions I. High energy gamma-ray spectra near the top of the atmosphere

An emulsion chamber was used to study the characteristics of high energy nuclear interactions from the production spectra ofγ-rays. The emulsion chamber, which comprised of two parts, namely the detector and the graphite producer unit, was exposed to cosmic rays for about 7 hr at an atmospheric depth of 10 g cm⁻² at Hyderabad (geomagnetic latitude 7·6°N). 720 electromagnetic cascades due toγ-rays were recorded in the detector. These cascades were classified into three groups; (a)γ-rays from nuclear interactions in the detector (b)γ-rays from nuclear interactions in the producer unit and (c)γ-rays of atmospheric origin. The energies of the cascades were determined using photometric method. The spectra ofγ-rays from groups (a) and (c) were determined and compared with similar spectra obtained at greater atmospheric depths. The spectra were found to obey a power law. The spectrum ofγ-rays of atmospheric origin was found to steepen at high energies,E _r>2200 GeV.     

Optical characterization of the silicon photodiodes for the establishment of national radiometric standards

Optical properties of the silicon photodiodes are investigated in the visible spectral regime. Non-linearity measurement standard was established by using Hamamatsu S1337-11 type windowless silicon photodiode whose non-linearity value was found to be better than 6×10⁻⁵ at photocurrent level of 10⁻⁹ to 10⁻⁴ A. Temperature effects on the spectral responsivity for S1337-11, S1337-1010BQ and S1227-1010BQ type photodiodes were analyzed between 20°C and 40°C at 488.1, 514.7 and 632.8 nm vacuum wavelengths. The spatial uniformities of the responsivity for three type photodiodes are performed with a laser beam having 1 mm diameter by using home made two-axis micro translation system. Results of the reflectance measurements for three elements of reflection-based trap detectors were compared with the predicted values obtained from Fresnel equations.     

Lower bounds for boundary roughness for droplets in Bernoulli percolation

We consider boundary roughness for the ``droplet' created when supercritical two-dimensional Bernoulli percolation is conditioned to have an open dual circuit surrounding the origin and enclosing an area at least l², for large l. The maximum local roughness is the maximum inward deviation of the droplet boundary from the boundary of its own convex hull; we show that for large l this maximum is at least of order l^1/3(logl)^–2/3. This complements the upper bound of order l^1/3(logl)^–2/3 proved in [Al3] for the average local roughness. The exponent 1/3 on l here is in keeping with predictions from the physics literature for interfaces in two dimensions. The research of the first author was supported by NSF grant DMS-9802368. The research of the second author was supported by NSF grants DMS-9802368 and DMS-0103790.Mathematics Subject Classification (2000): Primary 60K35; Secondary 82B20, 82B43     

Analytical computation of the eigenvalues and eigenvectors in DT-MRI

In this paper a noniterative algorithm to be used for the analytical determination of the sorted eigenvalues and corresponding orthonormalized eigenvectors obtained by diffusion tensor magnetic resonance imaging (DT-MRI) is described. The algorithm uses the three invariants of the raw water spin self-diffusion tensor represented by a 3 x 3 positive definite matrix and certain math functions that do not require iteration. The implementation requires a positive definite mask to preserve the physical meaning of the eigenvalues. This algorithm can increase the speed of eigenvalue/eigenvector calculations by a factor of 5-40 over standard iterative Jacobi or singular-value decomposition techniques. This approach may accelerate the computation of eigenvalues, eigenvalue-dependent metrics, and eigenvectors especially when having high-resolution measurements with large numbers of slices and large fields of view.