When Gravity Fails: Local Search Topology

Local search algorithms for combinatorial search problems frequently encounter a sequence of states in which it is impossible to improve the value of the objective function; moves through these regions, called plateau moves, dominate the time spent in local search. We analyze and characterize plateaus for three different classes of randomly generated Boolean Satisfiability problems. We identify several interesting features of plateaus that impact the performance of local search algorithms. We show that local minima tend to be small but occasionally may be very large. We also show that local minima can be escaped without unsatisfying a large number of clauses, but that systematically searching for an escape route may be computationally expensive if the local minimum is large. We show that plateaus with exits, called benches, tend to be much larger than minima, and that some benches have very few exit states which local search can use to escape. We show that the solutions (i.e., global minima) of randomly generated problem instances form clusters, which behave similarly to local minima. We revisit several enhancements of local search algorithms and explain their performance in light of our results. Finally we discuss strategies for creating the next generation of local search algorithms.Comment: See http://www.jair.org/ for any accompanying file

Probing the Role of the Barrier Layer in Magnetic Tunnel Junction Transport

Magnetic tunnel junctions with a ferrimagnetic barrier layer have been studied to understand the role of the barrier layer in the tunneling process - a factor that has been largely overlooked until recently. Epitaxial oxide junctions of highly spin polarized La0.7Sr0.3MnO3 and Fe3O4 electrodes with magnetic NiMn2O4 (NMO) insulating barrier layers provide a magnetic tunnel junction system in which we can probe the effect of the barrier by comparing junction behavior above and below the Curie temperature of the barrier layer. When the barrier is paramagnetic, the spin polarized transport is dominated by interface scattering and surface spin waves; however, when the barrier is ferrimagnetic, spin flip scattering due to spin waves within the NMO barrier dominates the transport.Comment: 10 pages, 3 figure

Encapsulation of Cs/Sr contaminated clinoptilolite in geopolymers produced from metakaolin

The encapsulation of caesium (Cs) and strontium (Sr) contaminated clinoptilolite in Na and K based metakaolin geopolymers is reported. When Cs or Sr loaded clinoptilolite is mixed with a metakaolin geopolymer paste, the high pH of the activating solution and the high concentration of ions in solution cause ion exchange reactions and dissolution of clinoptilolite with release of Cs and Sr into the geopolymer matrix. The leaching of Cs and Sr from metakaolin-based geopolymer has therefore been investigated. It was found that Na-based geopolymers reduce leaching of Cs compared to K-based geopolymers and the results are in agreement with the hard and soft acids and bases (HSAB) theory. Cs ions are weak Lewis acids and aluminates are a weak Lewis base. During the formation of the geopolymer matrix Cs ions are preferentially bound to aluminate phases and replace Na in the geopolymer structure. Sr uptake by Na-geopolymers is limited to 0.4 mol Sr per mole of Al and any additional Sr is immobilised by the high pH which causes precipitation of Sr as low solubility hydroxide and carbonate phases. There was no evidence of any other phases being formed when Sr or Cs are added to metakaolin geopolymers

Single-Step Quantum Search Using Problem Structure

The structure of satisfiability problems is used to improve search algorithms for quantum computers and reduce their required coherence times by using only a single coherent evaluation of problem properties. The structure of random k-SAT allows determining the asymptotic average behavior of these algorithms, showing they improve on quantum algorithms, such as amplitude amplification, that ignore detailed problem structure but remain exponential for hard problem instances. Compared to good classical methods, the algorithm performs better, on average, for weakly and highly constrained problems but worse for hard cases. The analytic techniques introduced here also apply to other quantum algorithms, supplementing the limited evaluation possible with classical simulations and showing how quantum computing can use ensemble properties of NP search problems.Comment: 39 pages, 12 figures. Revision describes further improvement with multiple steps (section 7). See also http://www.parc.xerox.com/dynamics/www/quantum.htm

Cation-ordering effects in the single layered manganite La(2/3)Sr(4/3)MnO4

We have synthesized epitaxial La(1-x)Sr(1+x)MnO4 (x=1/3) films as random alloys and cation-ordered analogues to probe how cation order affects the properties of a 2D manganite. The films show weak ferromagnetic ordering up to 130 K, although there is a dramatic difference in magnetic anisotropy depending on the cation order. While all films exhibit similar gapped insulator behavior above 130 K, there is a significant difference in the low temperature transport mechanism depending on the cation order. Differences in magnetic anisotropy and low temperature transport are consistent with differences in Mn 3d orbital occupancies. Together this work suggests that cation ordering can significantly alter the Mn 3d orbital ground state in these correlated electron systems.Comment: 4 figure

Effects of culling on badger abundance : implications for tuberculosis control

Culling is often considered as a tool for controlling wildlife diseases that can also infect people or livestock. Culling European badgers Meles meles can cause both positive and negative effects on the incidence of bovine tuberculosis (TB) in cattle. One factor likely to influence the outcome of different badger culling strategies for cattle TB is the reduction in badger population density achieved. However, this reduction is difficult to measure because badgers, being nocturnal and fossorial, are difficult to count. Here, we use indices of badger abundance to measure the population impacts of two culling strategies tested in Britain. The densities of badger setts and latrines recorded before culling were correlated with the densities of badgers captured on initial culls, suggesting that both were indices of actual badger abundance. Widespread 'proactive' culling was associated with a 73% reduction in the density of badger latrines, a 69% reduction in the density of active burrows and a 73% reduction in the density of road killed badgers. This population reduction was achieved by a coordinated effort entailing widespread and repeated trapping over several years. However, this strategy caused only modest reductions in cattle TB incidence in culled areas and elevated incidence in neighbouring unculled areas. Localized 'reactive' culling caused a 26% reduction in latrine density, a 32% reduction in active burrow density and a 10% reduction in the density of road killed badgers, but apparently increased the incidence of cattle TB. These results indicate that the relationship between badger population reduction and TB transmission to cattle is strongly non linear, probably because culling prompts changes in badger behaviour that influence transmission rates. These findings raise serious questions about the capacity of badger culling to contribute to the control of cattle TB in Britain

Potential barrier lowering and electrical transport at the LaAlO3_{3}/SrTiO3_{3} heterointerface

Using a combination of vertical transport measurements across and lateral transport measurements along the LaAlO$_{3}$/SrTiO$_{3}$ heterointerface, we demonstrate that significant potential barrier lowering and band bending are the cause of interfacial metallicity. Barrier lowering and enhanced band bending extends over 2.5 nm into LaAlO$_{3}$ as well as SrTiO$_{3}$. We explain origins of high-temperature carrier saturation, lower carrier concentration, and higher mobility in the sample with the thinnest LaAlO$_{3}$ film on a SrTiO$_{3}$ substrate. Lateral transport results suggest that parasitic interface scattering centers limit the low-temperature lateral electron mobility of the metallic channel.Comment: 10 pages, 3 figures, and 1 tabl

Exhaustive enumeration unveils clustering and freezing in random 3-SAT

We study geometrical properties of the complete set of solutions of the random 3-satisfiability problem. We show that even for moderate system sizes the number of clusters corresponds surprisingly well with the theoretic asymptotic prediction. We locate the freezing transition in the space of solutions which has been conjectured to be relevant in explaining the onset of computational hardness in random constraint satisfaction problems.Comment: 4 pages, 3 figure

The Peculiar Phase Structure of Random Graph Bisection

The mincut graph bisection problem involves partitioning the n vertices of a graph into disjoint subsets, each containing exactly n/2 vertices, while minimizing the number of "cut" edges with an endpoint in each subset. When considered over sparse random graphs, the phase structure of the graph bisection problem displays certain familiar properties, but also some surprises. It is known that when the mean degree is below the critical value of 2 log 2, the cutsize is zero with high probability. We study how the minimum cutsize increases with mean degree above this critical threshold, finding a new analytical upper bound that improves considerably upon previous bounds. Combined with recent results on expander graphs, our bound suggests the unusual scenario that random graph bisection is replica symmetric up to and beyond the critical threshold, with a replica symmetry breaking transition possibly taking place above the threshold. An intriguing algorithmic consequence is that although the problem is NP-hard, we can find near-optimal cutsizes (whose ratio to the optimal value approaches 1 asymptotically) in polynomial time for typical instances near the phase transition.Comment: substantially revised section 2, changed figures 3, 4 and 6, made minor stylistic changes and added reference

Landscape of solutions in constraint satisfaction problems

We present a theoretical framework for characterizing the geometrical properties of the space of solutions in constraint satisfaction problems, together with practical algorithms for studying this structure on particular instances. We apply our method to the coloring problem, for which we obtain the total number of solutions and analyze in detail the distribution of distances between solutions.Comment: 4 pages, 4 figures. Replaced with published versio