Covering many points with a small-area box

Let $P$ be a set of $n$ points in the plane. We show how to find, for a given integer $k>0$, the smallest-area axis-parallel rectangle that covers $k$ points of $P$ in $O(nk^2 \log n+ n\log^2 n)$ time. We also consider the problem of, given a value $\alpha>0$, covering as many points of $P$ as possible with an axis-parallel rectangle of area at most $\alpha$. For this problem we give a probabilistic $(1-\varepsilon)$-approximation that works in near-linear time: In $O((n/\varepsilon^4)\log^3 n \log (1/\varepsilon))$ time we find an axis-parallel rectangle of area at most $\alpha$ that, with high probability, covers at least $(1-\varepsilon)\mathrm{\kappa^*}$ points, where $\mathrm{\kappa^*}$ is the maximum possible number of points that could be covered

Phase transition in a super superspin glass

We here confirm the occurrence of spin glass phase transition and extract estimates of associated critical exponents of a highly monodisperse and densely compacted system of bare maghemite nanoparticles. This system has earlier been found to behave like an archetypal spin glass, with e.g. a sharp transition from paramagnetic to non-equilibrium behavior, suggesting that this system undergoes a spin-glass phase transition at a relatively high temperature, $T_g$ $\sim$ 140 K.Comment: 4 pages, 3 figure

Effect of catalytic conditions on the synthesis of new aconitate esters

Sugar cane is a crop which generates large amounts of biomass and a juice rich in highvalue natural molecules. After extracting sugar from the juice, the recovering of various compounds such as organic acids contained in molasses could contribute to increase the competivity of the sugar industry. Therefore, according to the biorefinery approach, we propose to study the chemical conversion of one of these acids, the aconitic acid, by esterification reactions. A new series of aconitate esters have been synthesized by combining aconitic acid and alcohols from natural origin. The effects of experimental conditions have been investigated and have shown that the type of catalysis has a significant effect on the selectivity. Kinectics have thus been performed to determine the best conditions to synthetize enriched compositions in esters. Homogeneous catalysis generates the highest yield in triester. Heterogeneous catalysis(macroporous resins) is prefered for the production of monoesters while catalysis assisted by ionic liquid is adapted to prepare mainly diesters. Green indicators have been discussed according to the calculations performed. The resulting polyfunctional esters are totally biosourced molecules and have a great potential as bioproducts for different applications

Relationship of Staff Engagement and Perception of Safety Scores with Patient Outcomes

Purpose/Objective: The purpose of this study is to explore clinical nurses’ perception of engagement and patient safety along with evaluate the correlation between engagement and perception of patient safety to patient outcomes. Background/Significance: Studies have shown evidence that there is a relationship between higher RN job satisfaction and/or a positive patient safety culture and patient outcomes; but limited studies exist showing a statistically significant relationship. Furthermore, limited studies have been conducted exploring perceptions of nurses and whether there is a relationship between perceptions and actual outcomes. Methodology/Data Analysis: The exploratory component of clinical nurses’ perceptions of engagement and patient safety will involve a nontraditional qualitative descriptive research design with focus group led by staff nurse unit-based practice council (UBPC) chairs and thematic analysis. The correlational component consists of parametric statistical analysis of readily available National Database of Nursing Quality Indicators RN Satisfaction scores, Agency for Healthcare Research and Quality Hospital Survey of Patient Safety Culture scores, and patient outcomes data from 2012, 2014, and 2016. Finding/Implications: Findings included statistically significant negative relationships between RN satisfaction and patient falls (r= -0.577, p=0.049) and statistically significant positive relationships between RN satisfaction and perception of patient safety (r=0.756, p=0.004). The implications for practice suggest that the more engaged nurses are, the higher the perception of various patient safety measures which corresponds to a lower fall rate. Thematic analysis of the focus group discussions revealed what nurses themselves perceive as staff engagement and patient safety. Discussion: By keeping staff engaged and patient safety-centered and focusing on what nurses themselves perceive as elements of staff engagement and patient safety, leaders can potentially positively affect patient outcomes. Having nurses themselves work collaboratively to identify how they affect patient outcomes through a deeper understanding, translates to a stronger safety culture and enhanced patient care

Spanning trees crossing few barriers

We consider the problem of finding low-cost spanning trees for sets of n points in the plane, where the cost of a spanning tree is defined as the total number of intersections of tree edges with a given set of m barriers. We obtain the following results: (i) if the barriers are possibly intersecting line segments, then there is always a spanning tree of cost O(min(m2,m SQRT(n))); (ii) if the barriers are disjoint line segments, then there is always a spanning tree of cost O(m); (iii) if the barriers are disjoint convex objects, then there is always a spanning tree of cost O(n + m). All our bounds are worst-case optimal

Melting of Quasi-Two-Dimensional Charge Stripes in La5/3Sr1/3NiO4

Commensurability effects for nickelates have been studied by the first neutron experiments on La5/3Sr1/3NiO4. Upon cooling, this system undergoes three successive phase transitions associated with quasi-two-dimensional (2D) commensurate charge and spin stripe ordering in the NiO$_2$ planes. The two lower temperature phases (denoted as phase II and III) are stripe lattice states with quasi-long-range in-plane charge correlation. When the lattice of 2D charge stripes melts, it goes through an intermediate glass state (phase I) before becoming a disordered liquid state. This glass state shows short-range charge order without spin order, and may be called a "stripe glass" which resembles the hexatic/nematic state in 2D melting.Comment: 10 pages, RevTex, 4 figures available on request to [email protected]

Approximating the Maximum Overlap of Polygons under Translation

Let $P$ and $Q$ be two simple polygons in the plane of total complexity $n$, each of which can be decomposed into at most $k$ convex parts. We present an $(1-\varepsilon)$-approximation algorithm, for finding the translation of $Q$, which maximizes its area of overlap with $P$. Our algorithm runs in $O(c n)$ time, where $c$ is a constant that depends only on $k$ and $\varepsilon$. This suggest that for polygons that are "close" to being convex, the problem can be solved (approximately), in near linear time

Shortcuts for the Circle

Let C be the unit circle in R^2. We can view C as a plane graph whose vertices are all the points on C, and the distance between any two points on C is the length of the smaller arc between them. We consider a graph augmentation problem on C, where we want to place k >= 1 shortcuts on C such that the diameter of the resulting graph is minimized. We analyze for each k with 1 <= k <= 7 what the optimal set of shortcuts is. Interestingly, the minimum diameter one can obtain is not a strictly decreasing function of k. For example, with seven shortcuts one cannot obtain a smaller diameter than with six shortcuts. Finally, we prove that the optimal diameter is 2 + Theta(1/k^(2/3)) for any k