Forcing Adsorption of a Tethered Polymer by Pulling

We present an analysis of a partially directed walk model of a polymer which at one end is tethered to a sticky surface and at the other end is subjected to a pulling force at fixed angle away from the point of tethering. Using the kernel method, we derive the full generating function for this model in two and three dimensions and obtain the respective phase diagrams. We observe adsorbed and desorbed phases with a thermodynamic phase transition in between. In the absence of a pulling force this model has a second-order thermal desorption transition which merely gets shifted by the presence of a lateral pulling force. On the other hand, if the pulling force contains a non-zero vertical component this transition becomes first-order. Strikingly, we find that if the angle between the pulling force and the surface is beneath a critical value, a sufficiently strong force will induce polymer adsorption, no matter how large the temperature of the system. Our findings are similar in two and three dimensions, an additional feature in three dimensions being the occurrence of a reentrance transition at constant pulling force for small temperature, which has been observed previously for this model in the presence of pure vertical pulling. Interestingly, the reentrance phenomenon vanishes under certain pulling angles, with details depending on how the three-dimensional polymer is modeled

Towards the system-wide implementation of the International Classification of Functioning, Disability and Health in routine practice: Lessons from a pilot study in China

In 2011 the Chinese leadership in rehabilitation, in collaboration with the International Classification of Functioning, Disability and Health (ICF) Research Branch, embarked on an effort towards the system-wide implementation of the ICF in the healthcare system in China. We report here on the lessons learned from the pilot phase of testing the ICF Generic Set, a parsimonious set of 7 ICF categories, which have been shown to best describe functioning across the general population and people with various health conditions, for use in routine clinical practice in China. The paper discusses whether classification and measurement are compatible, what number of ICF categories should be included in data collection in routine practice, and the usefulness of a functioning profile and functioning score in clinical practice and health research planning. In addition, the paper reflects on the use of ICF qualifiers in a rating scale and the particularities of certain ICF categories contained in the ICF Generic Set when used as items in the context of Chinese rehabilitation and healthcare. Finally, the steps required to enhance the utility of system-wide implementation of the ICF in rehabilitation and healthcare services are set out.Chinese Mainland Affairs Offic

Trees with Given Stability Number and Minimum Number of Stable Sets

We study the structure of trees minimizing their number of stable sets for given order $n$ and stability number $\alpha$. Our main result is that the edges of a non-trivial extremal tree can be partitioned into $n-\alpha$ stars, each of size $\lceil \frac{n-1}{n-\alpha} \rceil$ or $\lfloor \frac{n-1}{n-\alpha}\rfloor$, so that every vertex is included in at most two distinct stars, and the centers of these stars form a stable set of the tree.Comment: v2: Referees' comments incorporate

Topological self-similarity on the random binary-tree model

Asymptotic analysis on some statistical properties of the random binary-tree model is developed. We quantify a hierarchical structure of branching patterns based on the Horton-Strahler analysis. We introduce a transformation of a binary tree, and derive a recursive equation about branch orders. As an application of the analysis, topological self-similarity and its generalization is proved in an asymptotic sense. Also, some important examples are presented