Group divisible designs with block size 4 and group sizes 4 and 7

In this paper, we consider the existence of group divisible designs (GDDs) with block size $4$ and group sizes $4$ and $7$. We show that there exists a 4-GDD of type $4^t 7^s$ for all but a finite specified set of feasible values for $(t, s)$.Comment: arXiv admin note: substantial text overlap with arXiv:2109.1122

Low temperature shape relaxation of 2-d islands by edge diffusion

We present a precise microscopic description of the limiting step for low temperature shape relaxation of two dimensional islands in which activated diffusion of particles along the boundary is the only mechanism of transport allowed. In particular, we are able to explain why the system is driven irreversibly towards equilibrium. Based on this description, we present a scheme for calculating the duration of the limiting step at each stage of the relaxation process. Finally, we calculate numerically the total relaxation time as predicted by our results and compare it with simulations of the relaxation process.Comment: 11 pages, 5 figures, to appear in Phys. Rev.

Efficiently Clustering Very Large Attributed Graphs

Attributed graphs model real networks by enriching their nodes with attributes accounting for properties. Several techniques have been proposed for partitioning these graphs into clusters that are homogeneous with respect to both semantic attributes and to the structure of the graph. However, time and space complexities of state of the art algorithms limit their scalability to medium-sized graphs. We propose SToC (for Semantic-Topological Clustering), a fast and scalable algorithm for partitioning large attributed graphs. The approach is robust, being compatible both with categorical and with quantitative attributes, and it is tailorable, allowing the user to weight the semantic and topological components. Further, the approach does not require the user to guess in advance the number of clusters. SToC relies on well known approximation techniques such as bottom-k sketches, traditional graph-theoretic concepts, and a new perspective on the composition of heterogeneous distance measures. Experimental results demonstrate its ability to efficiently compute high-quality partitions of large scale attributed graphs.Comment: This work has been published in ASONAM 2017. This version includes an appendix with validation of our attribute model and distance function, omitted in the converence version for lack of space. Please refer to the published versio

GBRDs over groups of orders ≤100 or of order pq with p, q primes

AbstractThere are well-known necessary conditions for the existence of a generalized Bhaskar Rao design over a group G, with block size k=3. It has been conjectured that these necessary conditions are indeed sufficient. We prove that they are sufficient for groups G of order pq where p,q are primes and for groups of all orders ≤100 except possibly 32, 36, 48, 54, 60, 64, 72, 96

Guidelines for initiation of anti-tumour necrosis factor therapy in rheumatoid arthritis: similarities and differences across Europe.

Contains fulltext : 80544.pdf (publisher's version ) (Closed access

Assessing the number of users who are excluded by domestic heating controls

This is the pre-print version of the Article. This Article is also referred to as: "Assessing the 'Design Exclusion' of Heating Controls at a Low-Cost, Low-Carbon Housing Development". - Copyright @ 2011 Taylor & FrancisSpace heating accounts for almost 60% of the energy delivered to housing which in turn accounts for nearly 27% of the total UK's carbon emissions. This study was conducted to investigate the influence of heating control design on the degree of ‘user exclusion’. This was calculated using the Design Exclusion Calculator, developed by the Engineering Design Centre at the University of Cambridge. To elucidate the capability requirements of the system, a detailed hierarchical task analysis was produced, due to the complexity of the overall task. The Exclusion Calculation found that the current design placed excessive demands upon the capabilities of at least 9.5% of the UK population over 16 years old, particularly in terms of ‘vision’, ‘thinking’ and ‘dexterity’ requirements. This increased to 20.7% for users over 60 years old. The method does not account for the level of numeracy and literacy and so the true exclusion may be higher. Usability testing was conducted to help validate the results which indicated that 66% of users at a low-carbon housing development could not programme their controls as desired. Therefore, more detailed analysis of the cognitive demands placed upon the users is required to understand where problems within the programming process occur. Further research focusing on this cognitive interaction will work towards a solution that may allow users to behave easily in a more sustainable manner

Changing shapes in the nanoworld

What are the mechanisms leading to the shape relaxation of three dimensional crystallites ? Kinetic Monte Carlo simulations of fcc clusters show that the usual theories of equilibration, via atomic surface diffusion driven by curvature, are verified only at high temperatures. Below the roughening temperature, the relaxation is much slower, kinetics being governed by the nucleation of a critical germ on a facet. We show that the energy barrier for this step linearly increases with the size of the crystallite, leading to an exponential dependence of the relaxation time.Comment: 4 pages, 5 figures. Accepted by Phys Rev Let