Self-similar stable processes arising from high-density limits of occupation times of particle systems

We extend results on time-rescaled occupation time fluctuation limits of the $(d,\alpha, \beta)$-branching particle system $(0<\alpha \leq 2, 0<\beta \leq 1)$ with Poisson initial condition. The earlier results in the homogeneous case (i.e., with Lebesgue initial intensity measure) were obtained for dimensions $d>\alpha / \beta$ only, since the particle system becomes locally extinct if $d\le \alpha / \beta$. In this paper we show that by introducing high density of the initial Poisson configuration, limits are obtained for all dimensions, and they coincide with the previous ones if $d>\alpha/\beta$. We also give high-density limits for the systems with finite intensity measures (without high density no limits exist in this case due to extinction); the results are different and harder to obtain due to the non-invariance of the measure for the particle motion. In both cases, i.e., Lebesgue and finite intensity measures, for low dimensions ($d<\alpha(1+\beta)/\beta$ and $d<\alpha(2+\beta)/(1+\beta)$, respectively) the limits are determined by non-L\'evy self-similar stable processes. For the corresponding high dimensions the limits are qualitatively different: ${\cal S}'(R^d)$-valued L\'evy processes in the Lebesgue case, stable processes constant in time on $(0,\infty)$ in the finite measure case. For high dimensions, the laws of all limit processes are expressed in terms of Riesz potentials. If $\beta=1$, the limits are Gaussian. Limits are also given for particle systems without branching, which yields in particular weighted fractional Brownian motions in low dimensions. The results are obtained in the setup of weak convergence of S'(R^d)$-valued processes.Comment: 28 page

Fluctuation limits of strongly degenerate branching systems

Functional limit theorems for scaled fluctuations of occupation time processes of a sequence of critical branching particle systems in $\R^d$ with anisotropic space motions and strongly degenerated splitting abilities are proved in the cases of critical and intermediate dimensions. The results show that the limit processes are constant measure-valued Wienner processes with degenerated temporal and simple spatial structures.Comment: 15 page

Feasibility study of multidisciplinary oncology rounds by videoconference for surgeons in remote locales

BACKGROUND: This study was undertaken to assess the feasibility of using videoconferencing to involve community-based surgeons in interactive, multidisciplinary oncology rounds so they may benefit from the type of community of practice that is usually only available in academic cancer centres. METHODS: An existing videoconference service provider with sites across Ontario was chosen and the series was accredited. Indirect needs assessment involved examining responses to a previously conducted survey of provincial surgeons; interviewing three cancer surgeons from different regions of Ontario; and by analyzing an online portfolio of self-directed learning projects. Direct needs assessment involved a survey of surgeons at videoconference-enabled sites. A surgical, medical and radiation oncologist plus a facilitator were scheduled to guide discussion for each session. A patient scenario developed by the discussants was distributed to participants one week prior to each session. RESULTS: Direct and indirect needs assessment confirmed that breast cancer and colorectal cancer topics were of greatest importance to community surgeons. Six one-hour sessions were offered (two breast, two colorectal, one gynecologic and one lung cancer). A median of 22 physicians and a median of eight sites participated in each session. The majority of respondents were satisfied with the videoconference format, presenters and content. Many noted that discussion prompted reflection on practice and that current practice would change. CONCLUSIONS: This pilot study demonstrated that it is possible to engage remote surgeons in multidisciplinary oncology rounds by videoconference. Continued assessment of videoconferencing is warranted but further research is required to develop frameworks by which to evaluate the benefits of telehealth initiatives