From one solution of a 3-satisfiability formula to a solution cluster: Frozen variables and entropy

A solution to a 3-satisfiability (3-SAT) formula can be expanded into a cluster, all other solutions of which are reachable from this one through a sequence of single-spin flips. Some variables in the solution cluster are frozen to the same spin values by one of two different mechanisms: frozen-core formation and long-range frustrations. While frozen cores are identified by a local whitening algorithm, long-range frustrations are very difficult to trace, and they make an entropic belief-propagation (BP) algorithm fail to converge. For BP to reach a fixed point the spin values of a tiny fraction of variables (chosen according to the whitening algorithm) are externally fixed during the iteration. From the calculated entropy values, we infer that, for a large random 3-SAT formula with constraint density close to the satisfiability threshold, the solutions obtained by the survey-propagation or the walksat algorithm belong neither to the most dominating clusters of the formula nor to the most abundant clusters. This work indicates that a single solution cluster of a random 3-SAT formula may have further community structures.Comment: 13 pages, 6 figures. Final version as published in PR

Colouring random graphs and maximising local diversity

We study a variation of the graph colouring problem on random graphs of finite average connectivity. Given the number of colours, we aim to maximise the number of different colours at neighbouring vertices (i.e. one edge distance) of any vertex. Two efficient algorithms, belief propagation and Walksat are adapted to carry out this task. We present experimental results based on two types of random graphs for different system sizes and identify the critical value of the connectivity for the algorithms to find a perfect solution. The problem and the suggested algorithms have practical relevance since various applications, such as distributed storage, can be mapped onto this problem.Comment: 10 pages, 10 figure

Inadequate food intake at high temperatures is related to depressed mitochondrial respiratory capacity

Animals, especially ectotherms, are highly sensitive to the temperature of their surrounding environment. Extremely high temperature, for example, induces a decline of average performance of conspecifics within a population, but individual heterogeneity in the ability to cope with elevating temperatures has rarely been studied. In this study, we examined inter-individual variation in feeding ability and consequent growth rate of juvenile brown trout Salmo trutta acclimated to a high temperature (19°C), and investigated the relationship between these metrics of whole-animal performances and among-individual variation in mitochondrial respiration capacity. Food was provided ad libitum yet intake varied ten-fold amongst individuals, resulting in some fish losing weight whilst others continued to grow. Almost half of the variation in food intake was related to variability in mitochondrial capacity: low intake (and hence growth failure) was associated with high leak respiration rates within liver and muscle mitochondria, and a lower coupling of muscle mitochondria. These observations, combined with the inability of fish with low food consumption to increase their intake despite ad libitum food levels, suggest a possible insufficient capacity of the mitochondria for maintaining ATP homeostasis. Individual variation in thermal performance is likely to confer variation in the upper limit of an organism's thermal niche and in turn affect the structure of wild populations in warming environments

Cyclic Response of Reconstituted Low Plasticity Silt

Foundation failures observed over saturated silt-clay mixtures during past earthquakes clearly indicate the need for a profound understanding of the behavior of such soils under seismic loading. Although the mechanisms dominating the response of fine grained soils under seismic loading are known to be different from those of sandy soils, the behavior of low plasticity silt and clay is still under discussion. An experimental research program, still in progress, has been undertaken to investigate the cyclic behavior of low plasticity fine grained soils for developing useful guidelines for the assessment of seismic response. Samples of low plasticity silt, initially consolidated to stress levels above preconsolidation stress, have been tested systemically under monotonic and cyclic loading for isotropic and anisotropic stress conditions. To eliminate the sample variability inherent to the naturally deposited soils and to control the circumstances, the specimens were reconstituted by means of the slurry deposition technique in the study. The preliminary results from cyclic triaxial testing on reconstituted low plasticity silt specimens are presented. The liquefaction susceptibility of the silt was examined via comparisons to the existing empirical criteria in literature

International Law in Ghana: A Study of the Attitudes, Knowledge and use of International Law by Judges and Lawyers

While international law is widely accepted and applied within Western nations, in many developing countries its relevance is often questioned and its implementation constrained and haphazard. Consequently, some developing states are bound by treaties at the international level while simultaneously depriving subjects of international law of the benefit of those same treaties at the domestic level. The awareness and application of international law by domestic lawyers and judges is a crucial aspect of rectifying this problem. The article reports the results of our study which sought to ascertain the attitudes of Ghanaian superior court judges and practising lawyers toward international law. The article will assess the degree to which lawyers use international law in their legal submissions and whether this is viewed positively or negatively by the bench. The article will also consider the manner in which Ghanaian superior court judges interpret and apply international law. Finally, the degree of knowledge of international law held by the respondents will be explored.This is an Author Accepted Manuscript of an article published by Edinburgh University Press in African Journal of International and Comparative Law The Version of Record is available online at: http://www.euppublishing.com/doi/abs/10.3366/ajicl.2023.044

Focused Local Search for Random 3-Satisfiability

A local search algorithm solving an NP-complete optimisation problem can be viewed as a stochastic process moving in an 'energy landscape' towards eventually finding an optimal solution. For the random 3-satisfiability problem, the heuristic of focusing the local moves on the presently unsatisfiedclauses is known to be very effective: the time to solution has been observed to grow only linearly in the number of variables, for a given clauses-to-variables ratio $\alpha$ sufficiently far below the critical satisfiability threshold $\alpha_c \approx 4.27$. We present numerical results on the behaviour of three focused local search algorithms for this problem, considering in particular the characteristics of a focused variant of the simple Metropolis dynamics. We estimate the optimal value for the ``temperature'' parameter $\eta$ for this algorithm, such that its linear-time regime extends as close to $\alpha_c$ as possible. Similar parameter optimisation is performed also for the well-known WalkSAT algorithm and for the less studied, but very well performing Focused Record-to-Record Travel method. We observe that with an appropriate choice of parameters, the linear time regime for each of these algorithms seems to extend well into ratios $\alpha > 4.2$ -- much further than has so far been generally assumed. We discuss the statistics of solution times for the algorithms, relate their performance to the process of ``whitening'', and present some conjectures on the shape of their computational phase diagrams.Comment: 20 pages, lots of figure

Behavior of heuristics and state space structure near SAT/UNSAT transition

We study the behavior of ASAT, a heuristic for solving satisfiability problems by stochastic local search near the SAT/UNSAT transition. The heuristic is focused, i.e. only variables in unsatisfied clauses are updated in each step, and is significantly simpler, while similar to, walksat or Focused Metropolis Search. We show that ASAT solves instances as large as one million variables in linear time, on average, up to 4.21 clauses per variable for random 3SAT. For K higher than 3, ASAT appears to solve instances at the ``FRSB threshold'' in linear time, up to K=7.Comment: 12 pages, 6 figures, longer version available as MSc thesis of first author at http://biophys.physics.kth.se/docs/ardelius_thesis.pd

Exponentially hard problems are sometimes polynomial, a large deviation analysis of search algorithms for the random Satisfiability problem, and its application to stop-and-restart resolutions

A large deviation analysis of the solving complexity of random 3-Satisfiability instances slightly below threshold is presented. While finding a solution for such instances demands an exponential effort with high probability, we show that an exponentially small fraction of resolutions require a computation scaling linearly in the size of the instance only. This exponentially small probability of easy resolutions is analytically calculated, and the corresponding exponent shown to be smaller (in absolute value) than the growth exponent of the typical resolution time. Our study therefore gives some theoretical basis to heuristic stop-and-restart solving procedures, and suggests a natural cut-off (the size of the instance) for the restart.Comment: Revtex file, 4 figure

The effect of copper upon the development of bacteria in sea water and the isolation of specific bacteria

Copper is used extensively in the eradication of various types of disease-producing microorganisms, especially fungi, as well as other organisms which are a nuisance to water supplies, such as algae and certain animal forms. It is also known that traces of copper are essential for the growth of many of the lower forms of life. The extensive literature on the relation of copper to microbial development is largely limited to the above two phenomena. Comparatively little is known, however, of the effect of copper upon a mixed microbiological population consisting of many organisms with different metabolic processes. It is known, for example, that the growth of plants in certain soils, as peats, will respond markedly to the application of small amounts of copper (5). The development of fungi in copper-free media has been suggested as a means of determining the concentration of copper in a given soil; this method is based upon the response of A. niger to the presence of small amounts of available copper (3)