Multicriteria Global Minimum Cuts

We consider two multicriteria versions of the global minimum cut problem in undirected graphs. In the k-criteria setting, each edge of the input graph has k non-negative costs associated with it. These costs are measured in separate, non-interchangeable, units. In the AND-version of the problem, purchasing an edge requires the payment of all the k costs associated with it. In the OR-version, an edge can be purchased by paying any one of the k costs associated with it. Given k bounds b₁,b₂,. . . ,b_k, the basic multicriteria decision problem is whether there exists a cut C of the graph that can be purchased using a budget of b_i units of the ith criterion, for 1 ≤ i ≤ k. We show that the AND-version of the multicriteria global minimum cut problem is polynomial for any fixed number k of criteria. The OR-version of the problem, on the other hand, is NP-hard even for k = 2, but can be solved in pseudo-polynomial time for any fixed number k of criteria. It also admits an FPTAS. Further extensions, some applications, and multicriteria versions of two other optimization problems are also discussed.     

Modifying continuous-time random walks to model finite-size particle diffusion in granular porous media

The continuous-time random walk (CTRW) model is useful for alleviating the computational burden of simulating diffusion in actual media. In principle, isotropic CTRW only requires knowledge of the step-size, \(P_l\), and waiting-time, \(P_t\), distributions of the random walk in the medium and it then generates presumably equivalent walks in free space, which are much faster. Here we test the usefulness of CTRW to modelling diffusion of finite-size particles in porous medium generated by loose granular packs. This is done by first simulating the diffusion process in a model porous medium of mean coordination number, which corresponds to marginal rigidity (the loosest possible structure), computing the resulting distributions \(P_l\) and \(P_t\) as functions of the particle size, and then using these as input for a free space CTRW. The CTRW walks are then compared to the ones simulated in the actual media. In particular, we study the normal-to-anomalous transition of the diffusion as a function of increasing particle size. We find that, given the same \(P_l\) and \(P_t\) for the simulation and the CTRW, the latter predicts incorrectly the size at which the transition occurs. We show that the discrepancy is related to the dependence of the effective connectivity of the porous media on the diffusing particle size, which is not captured simply by these distributions. We propose a correcting modification to the CTRW model—adding anisotropy—and show that it yields good agreement with the simulated diffusion process. We also present a method to obtain \(P_l\) and \(P_t\) directly from the porous sample, without having to simulate an actual diffusion process. This extends the use of CTRW, with all its advantages, to modelling diffusion processes of finite-size particles in such confined geometries.     

Compact beam expander with linear gratings

Novel compact beam expanders that could be useful for applications such as providing light to flat panel displays are presented. They are based on a planar configuration in which three spatially linear gratings are recorded on one transparent substrate, so as to expand a narrow incoming beam in two dimensions. We present the design and recording procedures along with results, showing a relatively uniform intensity of the wide output beam. Such expanders can serve for illuminating flat panel displays.     

CT angiography of superior mesenteric artery syndrome

OBJECTIVE: Our purpose was to describe the use of CT angiography and three-dimensional (3D) reconstruction in the diagnosis of superior mesenteric artery syndrome in three patients. CONCLUSION: CT angiography combined with 3D reconstructions is a noninvasive technique that may have a complementary diagnostic role similar to that of angiography in patients with a classic clinical presentation suggestive of superior mesenteric artery syndrome. CT angiography combined with 3D reconstructions should be considered in patients who might otherwise require angiography.     

Computer-originated planar holographic optical elements

We present novel, to our knowledge, methods for the analytical design and recording of planar holographic optical elements in thick materials. The recording of each planar holographic element is done by interference of two aspherical waves that are derived from appropriately designed computer-generated holograms such that the element has the desired grating function for minimizing aberrations and closely fulfills the Bragg condition over its entire area. The design and recording methods are described, along with calculated results of representative elements.     

Compact optical crossbar switch

A novel compact holographic crossbar architecture based on planar optics is presented. It consists of a pair of identical planar holographic elements, a two-dimensional array (N x N) transmission mask, a one-dimensional array (N) of input light sources, and a one-dimensional array (N) of detectors. Each planar element contains two cylindrical holographic lenses, both of which are recorded on a single glass substrate. The design of the overall compact configuration is presented along with experimental results.     

Properties of convergent thalamocortical and intracortical synaptic potentials in single neurons of neocortex

We explored differences in the properties of convergent afferent inputs to single neurons in the barrel area of the neocortex. Thalamocortical slices were prepared from mature mice. Recordings were made from neurons in layer V, and either thalamocortical afferents or horizontal intracortical axons were stimulated. Monosynaptic EPSPs from both sources had latencies shorter than 1.8 msec and low shape variance. Disynaptic thalamocortical IPSPs had latencies longer than 1.8 msec. All neuronal types, as defined by intrinsic firing patterns, received both thalamocortical and intracortical monosynaptic input. The shape parameters (rate of rise and half-width) of monosynaptic EPSPs from the two inputs did not differ significantly. The rate of rise of EPSPs varied considerably across cells, but the rates of rise of thalamocortical and intracortical EPSPs onto single cells were strongly correlated. The relative thresholds for activation of synaptic excitation and inhibition were strikingly different between the two tracts: thalamocortical stimulation induced GABAA-dependent IPSPs at stimulus intensities equal to or less than those required for evoking EPSPs in 35% (24 of 68) of the cells. In contrast, the threshold response to intracortical stimulation was always an EPSP, and only stronger stimuli could generate di- or polysynaptic IPSPs. We suggest that postsynaptic factors may tend to equalize the waveforms of EPSPs from thalamocortical and intracortical synapses onto single neurons. A major difference between the two convergent tracts is that the thalamocortical pathway much more effectively activates feedforward inhibitory circuits than does the horizontal intracortical pathway.     

On-line restricted assignment of temporary tasks with unknown durations

We consider load balancing of temporary tasks on m machines in the restricted assignment model. It is known that the best competitive ratio for this problem is . This bound is not achieved by the greedy algorithm whose competitive ratio is known to be Ω(m2/3). We give an alternative analysis to the greedy algorithm which is better than the known analysis for relatively small values of m. We also show that for a small number of machines, namely m?5, the greedy algorithm is optimal.     

The Stereochemistry of the Cope Rearrangement: Qualitative Theory (OCAMS) and Computation (AM1)

Contrary to common preconceptions, orbital correlation diagrams can be useful for deducing the mechanism and stereochemistry of degenerate sigmatropic rearrangements. The correlation lines have to be drawn between the reactant and the postulated transition state, rather than between the homomeric reactant and product. In the case of the Cope rearrangment, this is done most economically with Orbital Correspondence Analysis in Maximum Symmetry (OCAMS), by drawing correspondence lines between molecular orbitals of the reactant and those of a formal superposition (STS) of alternative transition structures (TS) in a symmetry point group that includes those of both as subgroups. The alternative boat (C_2v) and chair (C_2h) transition structures postulated for the degenerate Cope rearrangement of 1,5-hexadiene are formally combined to an STS of D_2h symmetry. OCAMS then selects its C_2h component, indicating that the pathway via the chair-like transition state is preferred, in agreement with experimental and computational results for both the Cope rearrangement and the isoelectronic Claisen rearrangement. Rearrangement through the less favored boat pathway is shown to arise from a changed electronic configuration in the transition state. Computational evidence is presented showing that the unexpectedly facile rearrangement of polycyclic molecules like semibullvalene and barbaralane, which are constrained to react via the boat pathway, is primarily due to steric and stereoelectronic factors that are explicable in molecular orbital terms, rather than to the incursion of a biradicaloid transition state.