The density of critical percolation clusters touching the boundaries of strips and squares

We consider the density of two-dimensional critical percolation clusters, constrained to touch one or both boundaries, in infinite strips, half-infinite strips, and squares, as well as several related quantities for the infinite strip. Our theoretical results follow from conformal field theory, and are compared with high-precision numerical simulation. For example, we show that the density of clusters touching both boundaries of an infinite strip of unit width (i.e. crossing clusters) is proportional to $(\sin \pi y)^{-5/48}\{[\cos(\pi y/2)]^{1/3} +[\sin (\pi y/2)]^{1/3}-1\}$. We also determine numerically contours for the density of clusters crossing squares and long rectangles with open boundaries on the sides, and compare with theory for the density along an edge.Comment: 11 pages, 6 figures. Minor revision

Interferometric scattering enables fluorescence-free electrokinetic trapping of single nanoparticles in free solution

Anti-Brownian traps confine single particles in free solution by closed-loop feedback forces that directly counteract Brownian motion. The extended-duration measurement of trapped objects allows detailed characterization of photophysical and transport properties, as well as observation of infrequent or rare dynamics. However, this approach has been generally limited to particles that can be tracked by fluorescent emission. Here we present the Interferometric Scattering Anti-Brownian ELectrokinetic trap (ISABEL trap), which uses interferometric scattering rather than fluorescence to monitor particle position. By decoupling the ability to track (and therefore trap) a particle from collection of its spectroscopic data, the ISABEL trap enables confinement and extended study of single particles that do not fluoresce, that only weakly fluoresce, or which exhibit intermittent fluorescence or photobleaching. This new technique significantly expands the range of nanoscale objects that may be investigated at the single-particle level in free solution.Comment: Manuscript and SI; videos available upon reques

E5501: phase II study of topotecan sequenced with etoposide/cisplatin, and irinotecan/cisplatin sequenced with etoposide for extensive-stage small-cell lung cancer.

PURPOSE: Sequence-dependent improved efficacy of topoisomerase I followed by topoisomerase 2 inhibitors was assessed in a randomized phase II study in extensive-stage small-cell lung cancer (SCLC). METHODS: Patients with previously untreated extensive-stage SCLC with measurable disease, ECOG performance status of 0-3 and stable brain metastases were eligible. Arm A consisted of topotecan (0.75 mg/m(2)) on days 1, 2 and 3, etoposide (70 mg/m(2)) and cisplatin (20 mg/m(2)) (PET) on days 8, 9 and 10 in a 3-week cycle. Arm B consisted of irinotecan (50 mg/m(2)) and cisplatin (20 mg/m(2)) on days 1 and 8 followed by etoposide (85 mg/m(2) PO bid) on days 3 and 10 (PIE) in a 3-week cycle. RESULTS: We enrolled 140 patients and randomized 66 eligible patients to each arm. Only 54.5 % of all patients completed the planned maximum 6 cycles. There were grade ≥3 treatment-related adverse events in approximately 70 % of the patients on both arms including 6 treatment-related grade 5 events. The overall response rates (CR + PR) were 69.7 % (90 % CI 59.1-78.9, 95 % CI 57.1-80.4 %) for arm A and 57.6 % (90 % CI 46.7-67.9, 95 % CI 44.8-69.7 %) for arm B. The median progression-free survival and overall survival were 6.4 months (95 % CI 5.4-7.5 months) and 11.9 months (95 % CI 9.6-13.7 months) for arm A and 6.0 months (95 % CI 5.4-7.0 months) and 11.0 months (95 % CI 8.6-13.1 months) for arm B. CONCLUSION: Sequential administration of topoisomerase inhibitors did not improve on the historical efficacy of standard platinum-doublet chemotherapy for extensive-stage SCLC

Older persons’ experiences of Reflective STRENGTH‐Giving Dialogues – ‘It\u27s a push to move forward’

Rationale: Experiences of the innovative method Reflective STRENGTH‐Giving Dialogue (STRENGTH), which is grounded in a lifeworld perspective and developed to improve quality of care, is described in this study. Innovative thinking in developing health and social care, which may include digital solutions, is required to ensure a meaningful and dignified life in old age. Aim: The aim of this study was to describe experiences of the intervention Reflective STRENGTH‐Giving Dialogue from the perspective of older persons living with long‐term health problems. Method: Individual qualitative interviews were conducted with 27 older persons who participated in the intervention. The older persons wrote notes from each dialogue in booklets, and the booklets became part of the study data, analysed with a Reflective Lifeworld Research approach. Results: STRENGTH is experienced as an opportunity to reflect upon life and identify small and large life projects. Dialogues that lead to change in thoughts and actions influence the older persons\u27 well‐being, sense of balance, joy and meaning in life. There is an experience of STRENGTH as a starting point and a push to move forward in an effort to experience joy and meaning in life when living with long‐term health problems. Conclusions: STRENGTH has the potential to contribute to quality improvement in person‐centred care and enhance meaning in life for older persons living with long‐term health problems. However, the use of a digital tool in this particular context poses challenges that must be considered

Intertwining caring science, caring practice and caring education from a lifeworld perspective—two contextual examples

This article describes how caring science can be a helpful foundation for caring practice and what kind of learning support that can enable the transformation of caring science into practice. The lifeworld approach is fundamental for both caring and learning. This will be illustrated in two examples from research that show the potential for promoting health and well-being as well as the learning process. One example is from a caring context and the other is from a learning context. In this article, learning and caring are understood as parallel processes. We emphasize that learning cannot be separated from life and thus caring and education is intertwined with caring science and life. The examples illustrate how an understanding of the intertwining can be fruitful in different contexts. The challenge is to implant a lifeworld-based approach on caring and learning that can lead to strategies that in a more profound way have the potential to strengthen the person's health and learning processes

Resolvent Estimates in L^p for the Stokes Operator in Lipschitz Domains

We establish the $L^p$ resolvent estimates for the Stokes operator in Lipschitz domains in $R^d$, $d\ge 3$ for $|\frac{1}{p}-1/2|< \frac{1}{2d} +\epsilon$. The result, in particular, implies that the Stokes operator in a three-dimensional Lipschitz domain generates a bounded analytic semigroup in $L^p$ for (3/2)-\varep < p< 3+\epsilon. This gives an affirmative answer to a conjecture of M. Taylor.Comment: 28 page. Minor revision was made regarding the definition of the Stokes operator in Lipschitz domain

On thin plate spline interpolation

We present a simple, PDE-based proof of the result [M. Johnson, 2001] that the error estimates of [J. Duchon, 1978] for thin plate spline interpolation can be improved by $h^{1/2}$. We illustrate that ${\mathcal H}$-matrix techniques can successfully be employed to solve very large thin plate spline interpolation problem