A study of placement algorithms through trial interchange of logic modules

Based on trial interchanges, this paper develops three algorithms for the solution of the placement problem of logic modules in a circuit. A significant decrease in the computation time of such placement algorithms can be achieved by restricting the trial interchanges to only a subset of all the modules in a circuit. The three algorithms are simulated on a DEC 1090 system in Pascal and the performance of these algorithms in terms of total wirelength and computation time is compared with the results obtained by Steinberg, for the 34-module backboard wiring problem. Performance analysis of the first two algorithms reveals that algorithms based on pairwise trial interchanges (2 interchanges) achieve a desired placement faster than the algorithms based on trial N interchanges. The first two algorithms do not perform better than Steinberg's algorithm1, whereas the third algorithm based on trial pairwise interchange among unconnected pairs of modules (UPM) and connected pairs of modules (CPM) performs better than Steinberg's algorithm, both in terms of total wirelength (TWL) and computation time.

Excitation and relaxation energies of trans-stilbene: Confined singlet, triplet, and charged bipolarons

The π-electronic excitations and excited-state geometries of trans-stilbene (tS) are found by combining exact solutions of the Pariser-Parr-Pople (PPP) model and semiempirical Parametric Method 3 (PM3) calculations. Comprehensive comparisons with tS spectra are obtained and related to the fluorescence and topological alternation of poly(paraphenylenevinylene) (PPV). The one-photon absorption and triplet of tS correspond, respectively, to singlet and triplet bipolarons confined to two phenyls, while the tS2- ground state is a confined charged bipolaron. Independent estimates of the relaxation energy between vertical and adiabatic excitation show the bipolaron binding energy to depend on both charge and spin, as expected for interacting π electrons in correlated or molecular states. Complete configuration interaction within the PPP model of tS accounts for the singlet-triplet gap, for the fine-structure constants and triplet-triplet spectra, for two-photon transitions and intensities, and for one-photon spectra and the radiative lifetime, although the relative position of nearly degenerate covalent and ionic singlets is not resolved. The planar PM3 geometry and low rotational barrier of tS agree with resolved rotational and vibrational spectra in molecular beams. PM3 excitation and relaxation energies for tS bipolarons are consistent with experiment and with PPP results. Instead of the exciton model, we interpret tS excitations in terms of states that are localized on each ring or extended over an alternating chain, as found exactly in Hückel theory, and find nearly degenerate transitions between extended and localized states in the singlet, triplet, and dianion manifolds. The large topological alternation of the extended system increases the ionicity and interchanges the order of the lowest one- and two-photon absorption of PPV relative to polyenes.

Revisiting the earthquake sources in the Himalaya: Perspectives on past seismicity

The similar to 2500 km-long Himalaya plate boundary experienced three great earthquakes during the past century, but none of them generated any surface rupture. The segments between the 1905-1934 and the 1897-1950 sources, known as the central and Assam seismic gaps respectively, have long been considered holding potential for future great earthquakes. This paper addresses two issues concerning earthquakes along the Himalaya plate boundary. One, the absence of surface rupture associated with the great earthquakes, vis-a-vis the purported large slip observed from paleoseismological investigations and two, the current understanding of the status of the seismic gaps in the Central Himalaya and Assam, in view of the paleoseismological and historical data being gathered. We suggest that the ruptures of earthquakes nucleating on the basal detachment are likely to be restricted by the crustal ramps and thus generate no surface ruptures, whereas those originating on the faults within the wedges promote upward propagation of rupture and displacement, as observed during the 2005 Kashmir earthquake, that showed a peak offset of 7 m. The occasional reactivation of these thrust systems within the duplex zone may also be responsible for the observed temporal and spatial clustering of earthquakes in the Himalaya. Observations presented in this paper suggest that the last major earthquake in the Central Himalaya occurred during AD 1119-1292, rather than in 1505, as suggested in some previous studies and thus the gap in the plate boundary events is real. As for the Northwestern Himalaya, seismically generated sedimentary features identified in the 1950 source region are generally younger than AD 1400 and evidence for older events is sketchy. The 1897 Shillong earthquake is not a decollement event and its predecessor is probably similar to 1000 years old. Compared to the Central Himalaya, the Assam Gap is a corridor of low seismicity between two tectonically independent seismogenic source zones that cannot be considered as a seismic gap in the conventional sense. (C) 2011 Elsevier B.V. All rights reserved.

Revisiting the Fourier transform on the Heisenberg group

A recent theorem of S. Alesker, S. Artstein-Avidan and V. Milman characterises the Fourier transform on R-n as essentially the only transform on the space of tempered distributions which interchanges convolutions and pointwise products. In this note we study the image of the Schwartz space on the Heisenberg group under the Fourier transform and obtain a similar characterisation for the Fourier transform on the Heisenberg group.