Sampling grid colourings with fewer colours

We provide an optimally mixing Markov chain for 6-colourings of the square grid. Furthermore, this implies that the uniform distribution on the set of such colourings has strong spatial mixing. 4 and 5 are now the only remaining values of k for which it is not known whether there exists a rapidly mixing Markov chain for k-colourings of the square grid

Rapid Mixing for Lattice Colorings with Fewer Colors

We provide an optimally mixing Markov chain for 6-colorings of the square lattice on rectangular regions with free, fixed, or toroidal boundary conditions. This implies that the uniform distribution on the set of such colorings has strong spatial mixing, so that the 6-state Potts antiferromagnet has a finite correlation length and a unique Gibbs measure at zero temperature. Four and five are now the only remaining values of q for which it is not known whether there exists a rapidly mixing Markov chain for q-colorings of the square lattice.Comment: Appeared in Proc. LATIN 2004, to appear in JSTA

Counting Complex Disordered States by Efficient Pattern Matching: Chromatic Polynomials and Potts Partition Functions

Counting problems, determining the number of possible states of a large system under certain constraints, play an important role in many areas of science. They naturally arise for complex disordered systems in physics and chemistry, in mathematical graph theory, and in computer science. Counting problems, however, are among the hardest problems to access computationally. Here, we suggest a novel method to access a benchmark counting problem, finding chromatic polynomials of graphs. We develop a vertex-oriented symbolic pattern matching algorithm that exploits the equivalence between the chromatic polynomial and the zero-temperature partition function of the Potts antiferromagnet on the same graph. Implementing this bottom-up algorithm using appropriate computer algebra, the new method outperforms standard top-down methods by several orders of magnitude, already for moderately sized graphs. As a first application, we compute chromatic polynomials of samples of the simple cubic lattice, for the first time computationally accessing three-dimensional lattices of physical relevance. The method offers straightforward generalizations to several other counting problems.Comment: 7 pages, 4 figure

Recommended practices for wind farm data collection and reliability assessment for O&M optimization

The paper provides a brief overview of the aims and main results of IEA Wind Task 33. IEA Wind Task 33 was an expert working group with a focus on data collection and reliability assessment for O & M optimization of wind turbines. The working group started in 2012 and finalized the work in 2016. The complete results of IEA Wind Task 33 are described in the expert group report on recommended practices for "Wind farm data collection and reliability assessment for O & M optimization" which will be published by IEA Wind in 2017. This paper briefly presents the background of the work, the recommended process to identify necessary data, and appropriate taxonomies structuring and harmonizing the collected entries. Finally, the paper summarizes the key findings and recommendations from the IEA Wind Task 33 work

Increased GABA concentrations in type 2 diabetes mellitus are related to lower cognitive functioning

Type 2 diabetes mellitus is associated with accelerated cognitive decline. The underlying pathophysiological mechanisms still remain to be elucidated although it is known that insulin signaling modulates neurotransmitter activity, including inhibitory γ-aminobutyric acid (GABA) and excitatory glutamate (Glu) receptors. Therefore, we examined whether levels of GABA and Glu are related to diabetes status and cognitive performance. Forty-one participants with type 2 diabetes and 39 participants without type 2 diabetes underwent detailed cognitive assessments and 3-Tesla proton MR spectroscopy. The associations of neurotransmitters with type 2 diabetes and cognitive performance were examined using multivariate regression analyses controlling for age, sex, education, BMI, and percentage gray/white matter ratio in spectroscopic voxel. Analysis revealed higher GABA+ levels in participants with type 2 diabetes, in participants with higher fasting blood glucose levels and in participants with higher HbA(1c) levels, and higher GABA+ levels in participants with both high HbA(1c) levels and less cognitive performance. To conclude, participants with type 2 diabetes have alterations in the GABAergic neurotransmitter system, which are related to lower cognitive functioning, and hint at the involvement of an underlying metabolic mechanism