Combining All Pairs Shortest Paths and All Pairs Bottleneck Paths Problems

We introduce a new problem that combines the well known All Pairs Shortest Paths (APSP) problem and the All Pairs Bottleneck Paths (APBP) problem to compute the shortest paths for all pairs of vertices for all possible flow amounts. We call this new problem the All Pairs Shortest Paths for All Flows (APSP-AF) problem. We firstly solve the APSP-AF problem on directed graphs with unit edge costs and real edge capacities in $\tilde{O}(\sqrt{t}n^{(\omega+9)/4}) = \tilde{O}(\sqrt{t}n^{2.843})$ time, where $n$ is the number of vertices, $t$ is the number of distinct edge capacities (flow amounts) and $O(n^{\omega}) < O(n^{2.373})$ is the time taken to multiply two $n$-by-$n$ matrices over a ring. Secondly we extend the problem to graphs with positive integer edge costs and present an algorithm with $\tilde{O}(\sqrt{t}c^{(\omega+5)/4}n^{(\omega+9)/4}) = \tilde{O}(\sqrt{t}c^{1.843}n^{2.843})$ worst case time complexity, where $c$ is the upper bound on edge costs

Optimization of suppression for two-element treatment liners for turbomachinery exhaust ducts

Sound wave propagation in a soft-walled rectangular duct with steady uniform flow was investigated at exhaust conditions, incorporating the solution equations for sound wave propagation in a rectangular duct with multiple longitudinal wall treatment segments. Modal analysis was employed to find the solution equations and to study the effectiveness of a uniform and of a two-sectional liner in attenuating sound power in a treated rectangular duct without flow (M = 0) and with uniform flow of Mach 0.3. Two-segment liners were shown to increase the attenuation of sound as compared to a uniform liner. The predicted sound attenuation was compared with measured laboratory results for an optimized two-segment suppressor. Good correlation was obtained between the measured and predicted suppressions when practical variations in the modal content and impedance were taken into account. Two parametric studies were also completed

Randomness for Free

We consider two-player zero-sum games on graphs. These games can be classified on the basis of the information of the players and on the mode of interaction between them. On the basis of information the classification is as follows: (a) partial-observation (both players have partial view of the game); (b) one-sided complete-observation (one player has complete observation); and (c) complete-observation (both players have complete view of the game). On the basis of mode of interaction we have the following classification: (a) concurrent (both players interact simultaneously); and (b) turn-based (both players interact in turn). The two sources of randomness in these games are randomness in transition function and randomness in strategies. In general, randomized strategies are more powerful than deterministic strategies, and randomness in transitions gives more general classes of games. In this work we present a complete characterization for the classes of games where randomness is not helpful in: (a) the transition function probabilistic transition can be simulated by deterministic transition); and (b) strategies (pure strategies are as powerful as randomized strategies). As consequence of our characterization we obtain new undecidability results for these games

Fault Locking, Block Rotation and Crustal Deformation in the Pacific Northwest

We interpret Global Positioning System (GPS) measurements in the northwestern United States and adjacent parts of western Canada to describe relative motions of crustal blocks, locking on faults and permanent deformation associated with convergence between the Juan de Fuca and North American plates. To estimate angular velocities of the oceanic Juan de Fuca and Explorer plates and several continental crustal blocks, we invert the GPS velocities together with seafloor spreading rates, earthquake slip vector azimuths and fault slip azimuths and rates. We also determine the degree to which faults are either creeping aseismically or, alternatively, locked on the block-bounding faults. The Cascadia subduction thrust is locked mainly offshore, except in central Oregon, where locking extends inland. Most of Oregon and southwest Washington rotate clockwise relative to North America at rates of 0.4-1.0 ° Myr-1. No shear or extension along the Cascades volcanic arc has occurred at the mm/yr level during the past decade, suggesting that the shear deformation extending northward from the Walker Lane and eastern California shear zone south of Oregon is largely accommodated by block rotation in Oregon. The general agreement of vertical axis rotation rates derived from GPS velocities with those estimated from palaeomagnetic declination anomalies suggests that the rotations have been relatively steady for 10-15 Ma. Additional permanent dextral shear is indicated within the Oregon Coast Range near the coast. Block rotations in the Pacific Northwest do not result in net westward flux of crustal material¿the crust is simply spinning and not escaping. On Vancouver Island, where the convergence obliquity is less than in Oregon and Washington, the contractional strain at the coast is more aligned with Juan de Fuca¿North America motion. GPS velocities are fit significantly better when Vancouver Island and the southern Coast Mountains move relative to North America in a block-like fashion. The relative motions of the Oregon, western Washington and Vancouver Island crustal blocks indicate that the rate of permanent shortening, the type that causes upper plate earthquakes, across the Puget Sound region is 4.4 ± 0.3 mm yr-1. This shortening is likely distributed over several faults but GPS data alone cannot determine the partitioning of slip on them. The transition from predominantly shear deformation within the continent south of the Mendocino Triple Junction to predominantly block rotations north of it is similar to changes in tectonic style at other transitions from shear to subduction. This similarity suggests that crustal block rotations are enhanced in the vicinity of subduction zones possibly due to lower resisting stress

Об анатомическом строении членистостебельного растения Annulina Neuburgiana Radczenko

The purpose was to compare two approaches for the acquisition and analysis of dynamic-contrast-enhanced MRI data with respect to differences in the modelling of the arterial input-function (AIF), the dependency of the model parameters on physiological parameters and their numerical stability. Eight hundred tissue concentration curves were simulated for different combinations of perfusion, permeability, interstitial volume and plasma volume based on two measured AIFs and analysed according to the two commonly used approaches. The transfer constants (Approach 1) K (trans) and (Approach 2) k (ep) were correlated with all tissue parameters. K (trans) showed a stronger dependency on perfusion, and k (ep) on permeability. The volume parameters (Approach 1) v (e) and (Approach 2) A were mainly influenced by the interstitial and plasma volume. Both approaches allow only rough characterisation of tissue microcirculation and microvasculature. Approach 2 seems to be somewhat more robust than 1, mainly due to the different methods of CA administration

Symmetric Strategy Improvement

Symmetry is inherent in the definition of most of the two-player zero-sum games, including parity, mean-payoff, and discounted-payoff games. It is therefore quite surprising that no symmetric analysis techniques for these games exist. We develop a novel symmetric strategy improvement algorithm where, in each iteration, the strategies of both players are improved simultaneously. We show that symmetric strategy improvement defies Friedmann's traps, which shook the belief in the potential of classic strategy improvement to be polynomial

Boundary effects on one-particle spectra of Luttinger liquids

We calculate one-particle spectra for a variety of models of Luttinger liquids with open boundary conditions. For the repulsive Hubbard model the spectral weight close to the boundary is enhanced in a large energy range around the chemical potential. A power law suppression, previously predicted by bosonization, only occurs after a crossover at energies very close to the chemical potential. Our comparison with exact spectra shows that the effects of boundaries can partly be understood within the Hartree-Fock approximation.Comment: 4 pages including 4 figures, revised version, to be published in Phys. Rev. B, January 200

Response modes and coordination in a traffic context, an experimental comparison of Chinese and German participants

This paper reports results of laboratory experiments about traffic behavior of participants with different cultural backgrounds. We conducted the minority game as an elementary traffic scenario in which human participants of a German and Chinese subject pool had to choose over 100 periods between a road A and a road B. In each period, the road which was chosen by the minority of players won, these participants got a payoff. The payoff in the majority group was 0. An important observation is that the number of road changes of a participant is negatively correlated with her cumulative payoff. The Chinese participants reacted differently to the payoffs of preceding periods than the German participants

Surface characterization and surface electronic structure of organic quasi-one-dimensional charge transfer salts

We have thoroughly characterized the surfaces of the organic charge-transfer salts TTF-TCNQ and (TMTSF)2PF6 which are generally acknowledged as prototypical examples of one-dimensional conductors. In particular x-ray induced photoemission spectroscopy turns out to be a valuable non-destructive diagnostic tool. We show that the observation of generic one-dimensional signatures in photoemission spectra of the valence band close to the Fermi level can be strongly affected by surface effects. Especially, great care must be exercised taking evidence for an unusual one-dimensional many-body state exclusively from the observation of a pseudogap.Comment: 11 pages, 12 figures, v2: minor changes in text and figure labellin