Self-avoiding walks and connective constants

The connective constant $\mu(G)$ of a quasi-transitive graph $G$ is the asymptotic growth rate of the number of self-avoiding walks (SAWs) on $G$ from a given starting vertex. We survey several aspects of the relationship between the connective constant and the underlying graph $G$. $\bullet$ We present upper and lower bounds for $\mu$ in terms of the vertex-degree and girth of a transitive graph. $\bullet$ We discuss the question of whether $\mu\ge\phi$ for transitive cubic graphs (where $\phi$ denotes the golden mean), and we introduce the Fisher transformation for SAWs (that is, the replacement of vertices by triangles). $\bullet$ We present strict inequalities for the connective constants $\mu(G)$ of transitive graphs $G$, as $G$ varies. $\bullet$ As a consequence of the last, the connective constant of a Cayley graph of a finitely generated group decreases strictly when a new relator is added, and increases strictly when a non-trivial group element is declared to be a further generator. $\bullet$ We describe so-called graph height functions within an account of "bridges" for quasi-transitive graphs, and indicate that the bridge constant equals the connective constant when the graph has a unimodular graph height function. $\bullet$ A partial answer is given to the question of the locality of connective constants, based around the existence of unimodular graph height functions. $\bullet$ Examples are presented of Cayley graphs of finitely presented groups that possess graph height functions (that are, in addition, harmonic and unimodular), and that do not. $\bullet$ The review closes with a brief account of the "speed" of SAW.Comment: Accepted version. arXiv admin note: substantial text overlap with arXiv:1304.721

Effects of functional transient receptor potential channels on adipogenesis and proliferation in human preadipocytes

BACKGROUND: Preadipocytes are extensively used as a type of proliferative cell culture model to investigate proliferation and differentiation of adipocytes and lipodystrophy (eg obesity)-related metabolic dysfunctions and disorders. However, cell biology is not well understood in human preadipocytes. The present study was to investigate the ...published_or_final_versionThe 17th Medicial Research Conference, Department of Medicine, The University of Hong Kong, 14 January 2012. In Hong Kong Medical Journal, 2012, v. 18 n. 1, suppl. 1, p. 24, abstract no. 3

Effects of functional transient receptor potential channels on proliferation and migration in human cardiac c-kit+ cells

Poster PresentationINTRODUCTION: Human adult c-kit+ cardiac stem cell are characterised by the expression of c-kit in the absence of lineage markers such as Nkx2.5. They are self-renewing, clonogenic and multipotent, giving rise to a minimum of three differentiated cell types: myocytes, smooth muscle, and endothelial vascular cells. These cells, although not specifically programmed for myocardial differentiation, have been shown to improve cardiac function in a myocardial injury/reconstitution assay. However, cell biology is not fully understood. The present study was to investigate the expression of transient receptor potential (TRP) channels in hum…published_or_final_versio

Functional expression of transient receptor potential channels in human preadipocytes

published_or_final_versionThe 16th Medical Resarch Conference (MRC), The University of Hong Kong, Hong Kong, China, 22 January 2011. In Hong Kong Medical Journal, 2011, v. 17, suppl. 1, p. 32, abstract no. 4

On the Elevated Temperature Thermal Stability of Nanoscale Mn-Ni-Si Precipitates Formed at Lower Temperature in Highly Irradiated Reactor Pressure Vessel Steels.

Atom probe tomography (APT) and scanning transmission electron microscopy (STEM) techniques were used to probe the long-time thermal stability of nm-scale Mn-Ni-Si precipitates (MNSPs) formed in intermediate and high Ni reactor pressure vessel steels under high fluence neutron irradiation at ≈320 °C. Post irradiation annealing (PIA) at 425 °C for up to 57 weeks was used to determine if the MNSPs are: (a) non-equilibrium solute clusters formed and sustained by radiation induced segregation (RIS); or, (b) equilibrium G or Γ2 phases, that precipitate at accelerated rates due to radiation enhanced diffusion (RED). Note the latter is consistent with both thermodynamic models and x-ray diffraction (XRD) measurements. Both the experimental and an independently calibrated cluster dynamics (CD) model results show that the stability of the MNSPs is very sensitive to the alloy Ni and, to a lesser extent, Mn content. Thus, a small fraction of the largest MNSPs in the high Ni steel persist, and begin to coarsen at long times. These results suggest that the MNSPs remain a stable phase, even at 105 °C higher than they formed at, thus are most certainly equilibrium phases at much lower service relevant temperatures of ≈290 °C

Regenerative-Relational Tritangtu: Sundanese Triadic Transformation Model

 Tritangtu atau pola pikir tritunggal merupakan kosmologi masyarakat Sunda dan Minang yang terdiri dari tiga entitas (pola tiga). Tritangtu sebagai kearifan lokal juga melatarbelakangi struktur mental pelaku kreatif dalam membuat karya baik berupa pertunjukan, nilai filosofi artefak mau- pun produk budaya lainnya di masyarakat Indonesia. Penelitian ini menggunakan metode etnografi dengan teknik pengumpulan data observasi partisipasi, wawancara mendalam dan dokumentasi. Obyek penelitian ini adalah praktik pelaku kreatif di bidang desain di Bandung. Hasil penelitian ini menunjukkan adanya transformasi tritangtu Sunda dari struktur yang tetap menjadi struktur dinamis. Perubahan struktur ini ditentukan oleh relasi antar struktur pembentuk unsur desain de- ngan segmentasi pasar global. Peminjaman penanda identitas Sunda khususnya budaya rakyat atau tradisi masa lalu merupakan upaya regeneratif dalam usahanya untuk harmonisasi pola tiga dalam menghadapi dan memenangkan persaingan pasar bebas di Indonesia.

Clubroot (Plasmodiophora brassicae Woronin): an agricultural and biological challenge worldwide

Clubroot disease and the causal microbe Plasmodiophora brassicae offer abundant challenges to agriculturists and biological scientists. This microbe is well fitted for the environments which it inhabits. Plasmodiophora brassicae exists in soil as microscopic well protected resting spores and then grows actively and reproduces while shielded inside the roots of host plants. The pathogen is active outside the host for only short periods. Consequently, scientific studies are made challenging by the biological context of the host and pathogen and the technology required to investigate and understand that relationship. Controlling clubroot disease is a challenge for farmers, crop consultants and plant pathology practitioners because of the limited options which are available. Full symptom expression happens solely in members of the Brassicaceae family. Currently, only a few genes expressing strong resistance to P. brassicae are known and readily available. Agrochemical control is similarly limited by difficulties in molecule formulation which combines efficacy with environmental acceptability. Manipulation of husbandry encouraging improvements in soil structure, texture, nutrient composition and moisture content can reduce populations of P. brassicae. Integrating such strategies with rotation and crop management will reduce but not eliminate this disease. There are indications that forms of biological competition may be mobilised as additions to integrated control strategies. The aim of this review is to chart key themes in the development of scientific biological understanding of this host-pathogen relationship by offering signposts to grapple with clubroot disease which devastates crops and their profitability. Particular attention is given to the link between soil and nutrient chemistry and activity of this microbe