Phase transitions in diluted negative-weight percolation models

We investigate the geometric properties of loops on two-dimensional lattice graphs, where edge weights are drawn from a distribution that allows for positive and negative weights. We are interested in the appearance of spanning loops of total negative weight. The resulting percolation problem is fundamentally different from conventional percolation, as we have seen in a previous study of this model for the undiluted case. Here, we investigate how the percolation transition is affected by additional dilution. We consider two types of dilution: either a certain fraction of edges exhibit zero weight, or a fraction of edges is even absent. We study these systems numerically using exact combinatorial optimization techniques based on suitable transformations of the graphs and applying matching algorithms. We perform a finite-size scaling analysis to obtain the phase diagram and determine the critical properties of the phase boundary. We find that the first type of dilution does not change the universality class compared to the undiluted case whereas the second type of dilution leads to a change of the universality class.Comment: 8 pages, 7 figure

Analysis of the loop length distribution for the negative weight percolation problem in dimensions d=2 through 6

We consider the negative weight percolation (NWP) problem on hypercubic lattice graphs with fully periodic boundary conditions in all relevant dimensions from d=2 to the upper critical dimension d=6. The problem exhibits edge weights drawn from disorder distributions that allow for weights of either sign. We are interested in in the full ensemble of loops with negative weight, i.e. non-trivial (system spanning) loops as well as topologically trivial ("small") loops. The NWP phenomenon refers to the disorder driven proliferation of system spanning loops of total negative weight. While previous studies where focused on the latter loops, we here put under scrutiny the ensemble of small loops. Our aim is to characterize -using this extensive and exhaustive numerical study- the loop length distribution of the small loops right at and below the critical point of the hypercubic setups by means of two independent critical exponents. These can further be related to the results of previous finite-size scaling analyses carried out for the system spanning loops. For the numerical simulations we employed a mapping of the NWP model to a combinatorial optimization problem that can be solved exactly by using sophisticated matching algorithms. This allowed us to study here numerically exact very large systems with high statistics.Comment: 7 pages, 4 figures, 2 tables, paper summary available at http://www.papercore.org/Kajantie2000. arXiv admin note: substantial text overlap with arXiv:1003.1591, arXiv:1005.5637, arXiv:1107.174

Magnetoresistance behavior of a ferromagnetic shape memory alloy: Ni_1.75Mn_1.25Ga

A negative-positive-negative switching behavior of magnetoresistance (MR) with temperature is observed in a ferromagnetic shape memory alloy Ni_1.75Mn_1.25Ga. In the austenitic phase between 300 and 120 K, MR is negative due to s-d scattering. Curiously, below 120K MR is positive, while at still lower temperatures in the martensitic phase, MR is negative again. The positive MR cannot be explained by Lorentz contribution and is related to a magnetic transition. Evidence for this is obtained from ab initio density functional theory, a decrease in magnetization and resistivity upturn at 120 K. Theory shows that a ferrimagnetic state with anti-ferromagnetic alignment between the local magnetic moments of the Mn atoms is the energetically favoured ground state. In the martensitic phase, there are two competing factors that govern the MR behavior: a dominant negative trend up to the saturation field due to the decrease of electron scattering at twin and domain boundaries; and a weaker positive trend due to the ferrimagnetic nature of the magnetic state. MR exhibits a hysteresis between heating and cooling that is related to the first order nature of the martensitic phase transition.Comment: 17 pages, 5 figures. Accepted in Phys. Rev.

Workshop on computer applications in water management: proceedings of the 1995 workshop

Compiled and edited by L. Ahuja, J. Leppert, K. Rojas, E. Seely.Also published as: Great Plains Agricultural Council publication, no. 154.Includes bibliographical references.Presented at the Workshop on computer applications in water management: proceedings of the 1995 workshop held on May 23-25, 1995 at Colorado State University in Fort Collins, Colorado

Maximum flow and topological structure of complex networks

The problem of sending the maximum amount of flow $q$ between two arbitrary nodes $s$ and $t$ of complex networks along links with unit capacity is studied, which is equivalent to determining the number of link-disjoint paths between $s$ and $t$. The average of $q$ over all node pairs with smaller degree $k_{\rm min}$ is $_{k_{\rm min}} \simeq c k_{\rm min}$ for large $k_{\rm min}$ with $c$ a constant implying that the statistics of $q$ is related to the degree distribution of the network. The disjoint paths between hub nodes are found to be distributed among the links belonging to the same edge-biconnected component, and $q$ can be estimated by the number of pairs of edge-biconnected links incident to the start and terminal node. The relative size of the giant edge-biconnected component of a network approximates to the coefficient $c$. The applicability of our results to real world networks is tested for the Internet at the autonomous system level.Comment: 7 pages, 4 figure

Tracking pulsar dispersion measures using the giant metrewave radio telescope

In this paper, we describe a novel experiment for the accurate estimation of pulsar dispersion measures (DMs) using the Giant Metrewave Radio Telescope. This experiment was carried out for a sample of 12 pulsars, over a period of more than one year (2001 January to 2002 May) with observations about once every fortnight. At each epoch, the pulsar DMs were obtained from simultaneous dual-frequency observations, without requiring any absolute timing information. The DM estimates were obtained from both the single-pulse data streams and from the average profiles. The accuracy of the DM estimates at each epoch is ~1 part in 104 or better, making the data set useful for many different kinds of studies. The time-series of DMs shows significant variations on time-scales of weeks to months for most of the pulsars. An analysis of the mean DM values from these data shows significant deviations from catalogue values (as well as from other estimates in the literature) for some of the pulsars, with PSR B1642-03 showing the most notable differences. From our analysis results it appears that the constancy of pulsar DMs (at the level of 1 in 103 or better) cannot be taken for granted. For PSR B2217+47, we see evidence of a large-scale DM gradient over a 1-yr period, which is modelled as being due to a blob of enhanced electron density sampled by the line of sight. For some pulsars, including pulsars with fairly simple profiles such as PSR B1642-03, we find evidence for small changes in DM values for different frequency pairs of measurement, a result that needs to be investigated in detail. Another interesting result is that we find significant differences in DM values obtained from average profiles and single-pulse data

Network Flows

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Some Recent Advances in Network Flows

The literature on network flow problems is extensive, and over the past 40 years researchers have made continuous improvements to algorithms for solving several classes of problems. However, the surge of activity on the algorithmic aspects of network flow problems over the past few years has been particularly striking. Several techniques have proven to be very successful in permitting researchers to make these recent contributions: (i) scaling of the problem data; (ii) improved analysis of algorithms, especially amortized average case performance and the use of potential functions; and (iii) enhanced data structures. In this survey, we illustrate some of these techniques and their usefulness in developing faster network flow algorithms. Our discussion focuses on the design of faster algorithms from the worst case perspective and we limit our discussion to the following fundamental problems: the shortest path problem, the maximum flow problem, and the minimum cost flow problem. We consider several representative algorithms from each problem class including the radix heap algorithm for the shortest path problem, preflow push algorithms for the maximum flow problem, and the pseudoflow push algorithms for the minimum cost flow problem