High-Precision Entropy Values for Spanning Trees in Lattices

Shrock and Wu have given numerical values for the exponential growth rate of the number of spanning trees in Euclidean lattices. We give a new technique for numerical evaluation that gives much more precise values, together with rigorous bounds on the accuracy. In particular, the new values resolve one of their questions.Comment: 7 pages. Revision mentions alternative approach. Title changed slightly. 2nd revision corrects first displayed equatio

A Remote Sensing Evaluation of Forest Resources in Indiana's Coastal Zone Management Area

No abstract availabl

Propagation of Errors for Matrix Inversion

A formula is given for the propagation of errors during matrix inversion. An explicit calculation for a 2 by 2 matrix using both the formula and a Monte Carlo calculation are compared. A prescription is given to determine when a matrix with uncertain elements is sufficiently nonsingular for the calculation of the covariances of the inverted matrix elements to be reliable.Comment: 18 pages, 4 figures, figure 4 contains two eps file

Life interrupted and life regained? Coping with stroke at a young age

Stroke is a leading cause of disability across the developed world, affecting an increasing number of younger people. In this article, we seek to understand the experience of stroke as a disabling life situation among young people and the strategies that they use to recover and cope. Directed content analysis was conducted from interviews with 17 community-dwelling stroke survivors aged 55 years and younger across the United Kingdom. The sample was drawn from a larger maximum variation sample of stroke survivors. Using the sociological concepts of biographical disruption and biographical repair as a guide, excerpts from the interviews pertaining to aspects of the patients’ life that were interrupted, in addition to how they coped with the changes, were selected and analysed. All individuals described an ‘‘altered sense of self,’’ a theme that included loss of identity, family disruption, and/or loss of valued activities. Individuals sought to adapt their sense of self by seeking external support, by restoring normality, and/or through positive reflection. Despite the adapted self that emerged, most individuals continued to experience impairments. While young stroke survivors adapt to their illness over time, they continue to experience impairments and disruptions in their personal and work lives.Aholistic model of rehabilitation that helps individuals regain the capacity for everyday activities related to work, family life, and leisure can begin to address the emotional ramifications of diseases such as stroke, restore wellness, and work towards minimizing the burden felt by family caregivers and children

Life interrupted and life regained? Coping with stroke at a young age

Stroke is a leading cause of disability across the developed world, affecting an increasing number of younger people. In this article, we seek to understand the experience of stroke as a disabling life situation among young people and the strategies that they use to recover and cope. Directed content analysis was conducted from interviews with 17 community-dwelling stroke survivors aged 55 years and younger across the United Kingdom. The sample was drawn from a larger maximum variation sample of stroke survivors. Using the sociological concepts of biographical disruption and biographical repair as a guide, excerpts from the interviews pertaining to aspects of the patients’ life that were interrupted, in addition to how they coped with the changes, were selected and analysed. All individuals described an ‘‘altered sense of self,’’ a theme that included loss of identity, family disruption, and/or loss of valued activities. Individuals sought to adapt their sense of self by seeking external support, by restoring normality, and/or through positive reflection. Despite the adapted self that emerged, most individuals continued to experience impairments. While young stroke survivors adapt to their illness over time, they continue to experience impairments and disruptions in their personal and work lives.Aholistic model of rehabilitation that helps individuals regain the capacity for everyday activities related to work, family life, and leisure can begin to address the emotional ramifications of diseases such as stroke, restore wellness, and work towards minimizing the burden felt by family caregivers and children

Minimum orbit dimension for local unitary action on n-qubit pure states

The group of local unitary transformations partitions the space of n-qubit quantum states into orbits, each of which is a differentiable manifold of some dimension. We prove that all orbits of the n-qubit quantum state space have dimension greater than or equal to 3n/2 for n even and greater than or equal to (3n + 1)/2 for n odd. This lower bound on orbit dimension is sharp, since n-qubit states composed of products of singlets achieve these lowest orbit dimensions.Comment: 19 page

Influence of molecular weight on the phase behavior and structure formation of branched side-chain hairy-rod polyfluorene in bulk phase.

We report on an experimental study of the self-organization and phase behavior of hairy-rod π -conjugated branched side-chain polyfluorene, poly[9,9-bis(2-ethylhexyl)-fluorene-2,7-diyl]—i.e., poly[2,7–(9,9–bis(2–ethylhexyl)fluorene] (PF2∕6) —as a function of molecular weight (Mn) . The results have been compared to those of phenomenological theory. Samples for which Mn=3–147 kg∕mol were used. First, the stiffness of PF2∕6 , the assumption of the theory, has been probed by small-angle neutron scattering in solution. Thermogravimetry has been used to show that PF2∕6 is thermally stable over the conditions studied. Second, the existence of nematic and hexagonal phases has been phenomenologically identified for lower and higher Mn (LMW, Mn<Mn* and HMW, Mn>Mn* ) regimes, respectively, based on free-energy argument of nematic and hexagonal hairy rods and found to correspond to the experimental x-ray diffraction (XRD) results for PF2∕6 . By using the lattice parameters of PF2∕6 as an experimental input, the nematic-hexagonal transition has been predicted in the vicinity of glassification temperature (Tg) of PF2∕6 . Then, by taking the orientation parts of the free energies into account the nematic-hexagonal transition has been calculated as a function of temperature and Mn and a phase diagram has been formed. Below Tg of 80 °C only (frozen) nematic phase is observed for Mn<Mn*=104 g∕mol and crystalline hexagonal phase for Mn>Mn* . The nematic-hexagonal transition upon heating is observed for the HMW regime depending weakly on Mn , being at 140–165 °C for Mn>Mn* . Third, the phase behavior and structure formation as a function of Mn have been probed using powder and fiber XRD and differential scanning calorimetry and reasonable semiquantitative agreement with theory has been found for Mn≥3 kg∕mol . Fourth, structural characteristics are widely discussed. The nematic phase of LMW materials has been observed to be denser than high-temperature nematic phase of HMW compounds. The hexagonal phase has been found to be paracrystalline in the (ab0) plane but a genuine crystal meridionally. We also find that all these materials including the shortest 10-mer possess the formerly observed rigid five-helix hairy-rod molecular structure

Phase Transitions on Nonamenable Graphs

We survey known results about phase transitions in various models of statistical physics when the underlying space is a nonamenable graph. Most attention is devoted to transitive graphs and trees

Dynamical percolation on general trees

H\"aggstr\"om, Peres, and Steif (1997) have introduced a dynamical version of percolation on a graph $G$. When $G$ is a tree they derived a necessary and sufficient condition for percolation to exist at some time $t$. In the case that $G$ is a spherically symmetric tree, H\"aggstr\"om, Peres, and Steif (1997) derived a necessary and sufficient condition for percolation to exist at some time $t$ in a given target set $D$. The main result of the present paper is a necessary and sufficient condition for the existence of percolation, at some time $t\in D$, in the case that the underlying tree is not necessary spherically symmetric. This answers a question of Yuval Peres (personal communication). We present also a formula for the Hausdorff dimension of the set of exceptional times of percolation.Comment: 24 pages; to appear in Probability Theory and Related Field