This paper focuses on computing the directional extremal boundary of a union of equal-radius circles. We introduce an efficient algorithm that accurately determines this boundary by analyzing the intersections and dominant relationships among the circles. The algorithm has time complexity of O(n log n).
We challenge the idea that edge insertions are local improvement operations and show that the edge-insertion algorithm must sometimes insert an edge between vertices that are at the farthest combinatorial distance apart, and that this edge must also cross linearly many edges of the triangulation for the algorithm to escape a local optimum and return the optimal triangulation.
An approach to defining quadratic implicit curves is to prescribe two tangent lines and a secant line going through the points of tangency. This paper will show that this method can be generalized to a higher number of tangents, resulting in higher degree curves.
Abstract Background Due to world population ageing and a rise in non-communicable diseases, there is an increased need for rehabilitation services. Rehabilitation nursing in primary health care is an example of an area of high service need that can benefit from more clarity of the role of nurses to optimize rehabilitation interventions for ageing populations. The objective of this scoping review is to describe the role of nurses in the provision of rehabilitation interventions to the ageing population in primary health care. Methods A secondary analysis of a scoping review was carried out following the Preferred Reporting Items for Systematic reviews and Meta-Analyses extension for Scoping Reviews (PRISMA-ScR). Results 68 studies from high- and upper-middle income countries were included and showed that nurses typically had a managerial and clinical role (76%). They worked in multidisciplinary teams in about half of the studies, most often with physical therapists. In total, nurses provided 355 different rehabilitation interventions and mainly assessed person-centered goals and functioning and provided follow-up visits and case management. Nurses had 117 different job titles and little information was available about their educational background and collaboration with other health workers. Conclusion Our scoping review contributes to a better understanding of the key role played by nurses in rehabilitation of the ageing population in primary health care and their collaboration with other health professionals. Matching nurses’ competencies with their level of proficiency is essential to ensure quality rehabilitation care to the ageing population.
This note establishes that every polyhedron that has a Hamiltonian quasigeodesic can be edge-unfolded to a net, and shows that the class of such polyhedra is infinite.
In this paper, a low power ultra‐wideband (UWB) low noise amplifier (LNA) with high and flatvoltage gain is proposed using CS‐CG noise‐cancellation and dual resonancenetwork techniques based on TSMC 180 nm technology. The CS‐CG noise cancellationtechnique reduced the noise figure in 3–10.6 GHz frequency band, and the dualresonance network technique is applied to reach an acceptable input matching. Inorder to reduce the number of inductors, the active inductor is used in thenoise cancellation stage. Also, to control voltage gain and input return loss, aresistor is connected in parallel to channel length modulation resistance of thetransistor in the first stage. The developed LNA circuit provides a high andflat voltage gain of 12.75 dB with 0.65 dB variation, which is the result ofusing two stages common‐source topology. An average noise figure of 2 dB, withits maximum value of 2.3 dB, an IIP3 of −8 dBm are obtained from 3 to 10.6 GHz,respectively. The obtained input and output matching value are better than−10 dB. The layout of proposed LNA occupies an area of 0.55 mm2 including ringpad and this structure consumes 11.56 mW from 1‐V dc supply.
In this short note, we show that cutting cycles of rods is fixed-parameter tractable by reducing the problem to computing a feedback vertex set in a mixed graph.
In this short note, we show that the VC-dimension of the class of $k$-vertex polytopes in $\mathbb R^d$ is at most $8d^2k\log_2k$, answering an old question of Long and Warmuth.
AbstractTo-date systematic testing and comparison of the accuracy of available primer-dimer prediction software has never been conducted, due in part to a lack of tools able to measure the efficacy of Gibbs free energy (ΔG) calculations at predicting dimer formation in PCR. To address this we have developed a novel online tool called PrimerROC (www.primer-dimer.com/roc/), which uses epidemiologically-based Receiver Operating Characteristic (ROC) curves to assess dimer prediction accuracy. Moreover, by integrating PrimerROC with our PrimerDimer prediction software we can determine a ΔG-based dimer-free threshold above which dimer formation is predicted unlikely to occur. Notably, PrimerROC determines this cut-off without any additional information such as salt concentration or annealing temperature, meaning that our PrimerROC method is an assay and condition independent prediction tool. To demonstrate the broad utility of PrimerROC we assessed the performance of seven publically available primer design and dimer analysis tools using a dataset of over 300 primer pairs. We found that our PrimerROC/PrimerDimer software consistently outperforms these other tools and can achieve predictive accuracies greater than 92%. To illustrate its predictive power this method was used in multiplex PCR design to successfully generate four resequencing assays containing up to 126 primers with no observable primer-primer amplification artefacts.
We show that for any $k \geq 0$, there exists a planar graph which is $B_{k+1}$-CPG but not $B_k$-CPG. As a consequence, we obtain that $B_k$-CPG is a strict subclass of $B_{k+1}$-CPG.
We show that the Fréchet distance of two-dimensional parametrised surfaces in a metric space is computable in the bit-model of real computation. An analogous result in the real RAM model for piecewise-linear surfaces has recently been obtained by Nayyeri and Xu (2016).
Following a recent improvement of Cardinal et al. on the complexity of a linear decision tree for $k$-SUM, resulting in $O(n^3 \log^3{n})$ linear queries, we present a further improvement to $O(n^2 \log^2{n})$ such queries.
We give a $O(n)$-time algorithm for determining whether translations of a polyomino with $n$ edges can tile the plane. The algorithm is also a $O(n)$-time algorithm for enumerating all such tilings that are also regular, and we prove that at most $Θ(n)$ such tilings exist.
We prove that for any convex polygon $S$ with at least four sides, or a concave one with no parallel sides, and any $m>0$, there is an $m$-fold covering of the plane with homothetic copies of $S$ that cannot be decomposed into two coverings.
A closed-form solution for the boundary of the flat state of an orthogonal cross section of contiguous surface geometry formed by the intersection of two cylinders of equal radii oriented in dual directions of rotation about their intersecting axes.