An O(T log T) reduction from RAM computations to satisfiability

AbstractA new method is given for obtaining a boolean expression whose satisfiability is equivalent to the existence of an accepting computation of some nondeterministic machine. Although starting from random access machines, this method gives an expression of the same O(T log T) length as the best reduction from general Turing machines

Strong time bounds: Non-computable bounds and a hierarchy theorem

AbstractA RAM program is said to run within a “strong” time bound T if on every sequence of n inputs it terminates within T(n) instruction executions. There are some programs whose execution time in this sense is a non-computable function of n. It is shown that such programs are essential in the sense that some functions can be computed within a non-computable time bound but not within any computable time bound. Nevertheless, strong time bounds are subject to a powerful hierarchy theorem. The condition such as being time constructable which normally applies to the “lower” function in such theorems is replaced by a condition of being the minimum strong time bound for some program

Remarks on separating words

The separating words problem asks for the size of the smallest DFA needed to distinguish between two words of length <= n (by accepting one and rejecting the other). In this paper we survey what is known and unknown about the problem, consider some variations, and prove several new results

Native submerged macrophyte distribution in seasonally-flowing, south-western Australian streams in relation to stream condition

Submerged macrophytes are important structural and biological components of many lowland streams with potential to support ecosystem processes in degraded streams, provided that growth is not excessive. In a low-gradient agricultural landscape, a survey was used to explore associations between submerged macrophyte growth, biodiversity and variables assessing stream condition in seasonally-flowing streams. These variables were sampled across fifty-three reaches on seven adjacent streams in the mediterranean climate region of south-western Australia. Native submerged macrophytes were present in 43 % of sampled reaches, forming two distinct macrophyte assemblages dominated either by Potamogeton spp. together with Otteliaovalifolia, or by Cycnogeton spp. The Potamogeton/Ottelia assemblage was present in degraded reaches with higher light availability and deposition of fine sediments, but did not show excessive growth, even under nutrient-enriched conditions. Conversely, Cycnogeton spp. were associated with shaded conditions and greater flow. Reaches with macrophytes present had significantly higher macroinvertebrate abundance and family richness than those without, although rarefied family richness was similar among reaches with and without submerged macrophytes. The more structurally complex Potamogeton/Ottelia assemblage supported a greater abundance of grazers, shredders and predators than the simpler Cycnogeton spp. In degraded agricultural streams, remnant and colonising populations of submerged macrophytes may compensate for loss of riparian-derived habitat and resources for macroinvertebrates, and thus the food supply for predatory species

About randomised distributed graph colouring and graph partition algorithms

AbstractWe present and analyse a very simple randomised distributed vertex colouring algorithm for arbitrary graphs of size n that halts in time O(logn) with probability 1-o(n-1). Each message containing 1 bit, its bit complexity per channel is O(logn).From this algorithm, we deduce and analyse a randomised distributed vertex colouring algorithm for arbitrary graphs of maximum degree Δ and size n that uses at most Δ+1 colours and halts in time O(logn) with probability 1-o(n-1).We also obtain a partition algorithm for arbitrary graphs of size n that builds a spanning forest in time O(logn) with probability 1-o(n-1). We study some parameters such as the number, the size and the radius of trees of the spanning forest

Australian Group on Antimicrobial Resistance Australian Enterobacteriaceae Sepsis Outcome Programme annual report, 2014

The Australian Group on Antimicrobial Resistance performs regular period-prevalence studies to monitor changes in antimicrobial resistance in selected enteric Gram-negative pathogens. The 2014 survey was the second year to focus on blood stream infections. During 2014, 5,798 Enterobacteriaceae species isolates were tested using commercial automated methods (Vitek 2, BioMérieux; Phoenix, BD) and results were analysed using the Clinical and Laboratory Standards Institute (CLSI) and European Committee on Antimicrobial Susceptibility Testing (EUCAST) breakpoints (January 2015). Of the key resistances, non-susceptibility to the third-generation cephalosporin, ceftriaxone, was found in 9.0%/9.0% of Escherichia coli (CLSI/EUCAST criteria) and 7.8%/7.8% of Klebsiella pneumoniae, and 8.0%/8.0% K. oxytoca. Non-susceptibility rates to ciprofloxacin were 10.4%/11.6% for E. coli, 5.0%/7.7% for K. pneumoniae, 0.4%/0.4% for K. oxytoca, and 3.5%/6.5% in Enterobacter cloacae. Resistance rates to piperacillin-tazobactam were 3.2%/6.8%, 4.8%/7.2%, 11.1%/11.5%, and 19.0%/24.7% for the same 4 species respectively. Fourteen isolates were shown to harbour a carbapenemase gene, 7 blaIMP-4, 3 blaKPC-2, 3 blaVIM-1, 1 blaNDM-4, and 1 blaOXA-181-lke

The analysis of multidimensional searching in quad-trees

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Exponential Time Complexity of Weighted Counting of Independent Sets

We consider weighted counting of independent sets using a rational weight x: Given a graph with n vertices, count its independent sets such that each set of size k contributes x^k. This is equivalent to computation of the partition function of the lattice gas with hard-core self-repulsion and hard-core pair interaction. We show the following conditional lower bounds: If counting the satisfying assignments of a 3-CNF formula in n variables (#3SAT) needs time 2^{\Omega(n)} (i.e. there is a c>0 such that no algorithm can solve #3SAT in time 2^{cn}), counting the independent sets of size n/3 of an n-vertex graph needs time 2^{\Omega(n)} and weighted counting of independent sets needs time 2^{\Omega(n/log^3 n)} for all rational weights x\neq 0. We have two technical ingredients: The first is a reduction from 3SAT to independent sets that preserves the number of solutions and increases the instance size only by a constant factor. Second, we devise a combination of vertex cloning and path addition. This graph transformation allows us to adapt a recent technique by Dell, Husfeldt, and Wahlen which enables interpolation by a family of reductions, each of which increases the instance size only polylogarithmically.Comment: Introduction revised, differences between versions of counting independent sets stated more precisely, minor improvements. 14 page

Formation of hot tear under controlled solidification conditions

Aluminum alloy 7050 is known for its superior mechanical properties, and thus finds its application in aerospace industry. Vertical direct-chill (DC) casting process is typically employed for producing such an alloy. Despite its advantages, AA7050 is considered as a "hard-to-cast" alloy because of its propensity to cold cracking. This type of cracks occurs catastrophically and is difficult to predict. Previous research suggested that such a crack could be initiated by undeveloped hot tears (microscopic hot tear) formed during the DC casting process if they reach a certain critical size. However, validation of such a hypothesis has not been done yet. Therefore, a method to produce a hot tear with a controlled size is needed as part of the verification studies. In the current study, we demonstrate a method that has a potential to control the size of the created hot tear in a small-scale solidification process. We found that by changing two variables, cooling rate and displacement compensation rate, the size of the hot tear during solidification can be modified in a controlled way. An X-ray microtomography characterization technique is utilized to quantify the created hot tear. We suggest that feeding and strain rate during DC casting are more important compared with the exerted force on the sample for the formation of a hot tear. In addition, we show that there are four different domains of hot-tear development in the explored experimental window-compression, microscopic hot tear, macroscopic hot tear, and failure. The samples produced in the current study will be used for subsequent experiments that simulate cold-cracking conditions to confirm the earlier proposed model.This research was carried out within the Materials innovation institute (www.m2i.nl) research framework, project no. M42.5.09340

Nucleation of Al3Zr and Al3Sc in aluminum alloys: from kinetic Monte Carlo simulations to classical theory

Zr and Sc precipitate in aluminum alloys to form the compounds Al3Zr and Al3Sc which for low supersaturations of the solid solution have the L12 structure. The aim of the present study is to model at an atomic scale this kinetics of precipitation and to build a mesoscopic model based on classical nucleation theory so as to extend the field of supersaturations and annealing times that can be simulated. We use some ab-initio calculations and experimental data to fit an Ising model describing thermodynamics of the Al-Zr and Al-Sc systems. Kinetic behavior is described by means of an atom-vacancy exchange mechanism. This allows us to simulate with a kinetic Monte Carlo algorithm kinetics of precipitation of Al3Zr and Al3Sc. These kinetics are then used to test the classical nucleation theory. In this purpose, we deduce from our atomic model an isotropic interface free energy which is consistent with the one deduced from experimental kinetics and a nucleation free energy. We test di erent mean-field approximations (Bragg-Williams approximation as well as Cluster Variation Method) for these parameters. The classical nucleation theory is coherent with the kinetic Monte Carlo simulations only when CVM is used: it manages to reproduce the cluster size distribution in the metastable solid solution and its evolution as well as the steady-state nucleation rate. We also find that the capillary approximation used in the classical nucleation theory works surprisingly well when compared to a direct calculation of the free energy of formation for small L12 clusters.Comment: submitted to Physical Review B (2004