scholarly journals Computing Euclidean Steiner trees over segments

2020 ◽  
Vol 8 (3-4) ◽  
pp. 309-325 ◽  
Author(s):  
Ernst Althaus ◽  
Felix Rauterberg ◽  
Sarah Ziegler
Keyword(s):  
Euclidean Plane ◽  
Classical Problem ◽  
Classical Case ◽  
Minimum Length ◽  
Second Phase ◽  
Two Phase ◽  
Math Program ◽  
Steiner Minimum Tree ◽  
Set Of Points ◽  
Selection Of

Abstract In the classical Euclidean Steiner minimum tree (SMT) problem, we are given a set of points in the Euclidean plane and we are supposed to find the minimum length tree that connects all these points, allowing the addition of arbitrary additional points. We investigate the variant of the problem where the input is a set of line segments. We allow these segments to have length 0, i.e., they are points and hence we generalize the classical problem. Furthermore, they are allowed to intersect such that we can model polygonal input. As in the GeoSteiner approach of Juhl et al. (Math Program Comput 10(2):487–532, 2018) for the classical case, we use a two-phase approach where we construct a superset of so-called full components of an SMT in the first phase. We prove a structural theorem for these full components, which allows us to use almost the same GeoSteiner algorithm as in the classical SMT problem. The second phase, the selection of a minimal cost subset of constructed full components, is exactly the same as in GeoSteiner approach. Finally, we report some experimental results that show that our approach is more efficient than the approximate solution that is obtained by sampling the segments.

ON THE STEINER RATIO IN $\mathcal{R}_{n}$

2011 ◽  
Vol 03 (04) ◽  
pp. 473-489
Author(s):  
HAI DU ◽  
WEILI WU ◽  
ZAIXIN LU ◽  
YINFENG XU
Keyword(s):  
Euclidean Space ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Dimensional Euclidean Space ◽  
Minimum Length ◽  
Steiner Ratio ◽  
Line Segments ◽  
Finite Set ◽  
Steiner Minimum Tree ◽  
Set Of Points

The Steiner minimum tree and the minimum spanning tree are two important problems in combinatorial optimization. Let P denote a finite set of points, called terminals, in the Euclidean space. A Steiner minimum tree of P, denoted by SMT(P), is a network with minimum length to interconnect all terminals, and a minimum spanning tree of P, denoted by MST(P), is also a minimum network interconnecting all the points in P, however, subject to the constraint that all the line segments in it have to terminate at terminals. Therefore, SMT(P) may contain points not in P, but MST(P) cannot contain such kind of points. Let [Formula: see text] denote the n-dimensional Euclidean space. The Steiner ratio in [Formula: see text] is defined to be [Formula: see text], where Ls(P) and Lm(P), respectively, denote lengths of a Steiner minimum tree and a minimum spanning tree of P. The best previously known lower bound for [Formula: see text] in the literature is 0.615. In this paper, we show that [Formula: see text] for any n ≥ 2.

IDENTIFYING STEINER MINIMAL TREES ON FOUR POINTS IN SPACE

2009 ◽  
Vol 01 (03) ◽  
pp. 401-411 ◽  
Author(s):  
J. F. WENG ◽  
D. A. THOMAS ◽  
I. MAREELS
Keyword(s):  
Euclidean Space ◽  
Euclidean Plane ◽  
Sufficient Conditions ◽  
Steiner Tree Problem ◽  
Minimum Length ◽  
Minimal Tree ◽  
Steiner Minimal Tree ◽  
Steiner Minimal Trees ◽  
Necessary And Sufficient ◽  
Set Of Points

A Steiner minimal tree is a network with minimum length spanning a given set of points in space. There are several criteria for identifying the Steiner minimal tree on four points in the Euclidean plane. However, it has been proved that the length of the Steiner minimal tree on four points cannot be computed using radicals if the four points lie in Euclidean space. This unsolvability implies that it is unlikely that similar necessary and sufficient conditions exist in the spatial case. Hence, a problem arises: Is it possible to generalize the known planar criteria to space in the sense that they are sufficient to identify Steiner minimal trees on four points in space? This problem is investigated and some sufficient conditions are proved in this paper. These sufficient conditions can help us to solve the general Steiner tree problem on n(> 4) points in Euclidean space.

scholarly journals Selection of quality indicators for nutritional therapy in pediatrics: a cross-sectional study conducted in Brazil

PeerJ ◽  
2018 ◽  
Vol 6 ◽  
pp. e4630 ◽  
Author(s):  
Julia Bertoldi ◽  
Aline Ferreira ◽  
Luiza Scancetti ◽  
Patricia Padilha
Keyword(s):  
Quality Indicators ◽  
Oral Intake ◽  
Nutritional Therapy ◽  
Cross Sectional Study ◽  
Second Phase ◽  
Sectional Study ◽  
Alpha Coefficient ◽  
Two Phase ◽  
Cross Sectional ◽  
Selection Of

Background Quality indicators for nutritional therapy (QINT) are important in assessing care and monitoring of resources. Among the 30 indicators proposed by International Life Sciences Institute, Brazil, there is still no evaluation of the most pertinent for Pediatrics. Objective To list the 10 main quality indicators for nutritional therapies (QINTs) for Pediatrics. Methods This was a two-phase cross-sectional study. Firstly, a questionnaire was answered by physicians, nutritionists, nurses, and pharmacists, all with having experience in nutritional therapy (NT) with Pediatrics, in Rio de Janeiro, Brazil. Participants assessed four attributes of QINT by using the Likert scale. A Top 10 ranked QINT list for Pediatrics was established. To verify the consistency of the questionnaire, Cronbach’s Alpha coefficient was calculated. Secondly, the opinions of the participants on the results that were obtained were requested and the percentages of the positive responses were calculated. Results A total of 33 professionals participated in the first phase and 92% (n = 23 of 25) in the second phase approved the results of the selected indicators. Among the Top 10 QINTs, the three main ones were: #1: “Frequency of diarrhea in those patients on enteral nutrition” (mean = 13.194; α = 0.827); #2: “Frequency of dietary nutritional prescriptions upon the hospital discharge of the NT patients” (mean = 12.871; α = 0.822); #3: “Frequency of the NT patients who recovered their oral intake” (mean = 12.839; α = 0.859). Conclusion When considering the consistency and the concordance that were obtained, it can be suggested that the list of Top 10 QINTs as proposed in this study will help in the evaluation of NT quality indicators for Pediatrics.

A Comparison of Tem and Apfim to the Interpretation of Modulated Microstructures

1985 ◽  
Vol 43 ◽  
pp. 70-71
Author(s):  
M.G. Burke ◽  
M.K. Miller
Keyword(s):  
Low Temperature ◽  
Microstructural Characterization ◽  
Superlattice Reflection ◽  
High Volume ◽  
Atom Probe ◽  
Dark Field ◽  
Miscibility Gap ◽  
Second Phase ◽  
Two Phase ◽  
Probe Field

Interpretation of fine-scale microstructures containing high volume fractions of second phase is complex. In particular, microstructures developed through decomposition within low temperature miscibility gaps may be extremely fine. This paper compares the morphological interpretations of such complex microstructures by the high-resolution techniques of TEM and atom probe field-ion microscopy (APFIM).The Fe-25 at% Be alloy selected for this study was aged within the low temperature miscibility gap to form a <100> aligned two-phase microstructure. This triaxially modulated microstructure is composed of an Fe-rich ferrite phase and a B2-ordered Be-enriched phase. The microstructural characterization through conventional bright-field TEM is inadequate because of the many contributions to image contrast. The ordering reaction which accompanies spinodal decomposition in this alloy permits simplification of the image by the use of the centered dark field technique to image just one phase. A CDF image formed with a B2 superlattice reflection is shown in fig. 1. In this CDF micrograph, the the B2-ordered Be-enriched phase appears as bright regions in the darkly-imaging ferrite. By examining the specimen in a [001] orientation, the <100> nature of the modulations is evident.

THE DYNAMIC FRACTURE OF TWO PHASE ALLOYS WITH SECOND PHASE INCLUSIONS

1985 ◽  
Vol 46 (C5) ◽  
pp. C5-251-C5-255
Author(s):  
S. Pytel ◽  
L. Wojnar
Keyword(s):  
Dynamic Fracture ◽  
Second Phase ◽  
Two Phase

Behaviour of air injection nozzles in dissolved air flotation

1995 ◽  
Vol 31 (3-4) ◽  
pp. 25-35 ◽  
Author(s):  
E. M. Rykaart ◽  
J. Haarhoff
Keyword(s):  
Bubble Coalescence ◽  
Second Phase ◽  
Initial Growth ◽  
Two Phase ◽  
Dissolved Air Flotation ◽  
Nozzle Orifice ◽  
Pressure Release ◽  
Air Volume ◽  
Air Flotation ◽  
Dissolved Air

A simple two-phase conceptual model is postulated to explain the initial growth of microbubbles after pressure release in dissolved air flotation. During the first phase bubbles merely expand from existing nucleation centres as air precipitates from solution, without bubble coalescence. This phase ends when all excess air is transferred to the gas phase. During the second phase, the total air volume remains the same, but bubbles continue to grow due to bubble coalescence. This model is used to explain the results from experiments where three different nozzle variations were tested, namely a nozzle with an impinging surface immediately outside the nozzle orifice, a nozzle with a bend in the nozzle channel, and a nozzle with a tapering outlet immediately outside the nozzle orifice. From these experiments, it is inferred that the first phase of bubble growth is completed at approximately 1.7 ms after the start of pressure release.

scholarly journals A novel two-phase cycle algorithm for effective cyber intrusion detection in edge computing

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yiguang Gong ◽  
Yunping Liu ◽  
Chuanyang Yin
Keyword(s):  
Intrusion Detection ◽  
Optimal Parameter ◽  
Edge Computing ◽  
Cloud Services ◽  
Second Phase ◽  
Pareto Optimal ◽  
Two Phase ◽  
Multi Objective ◽  
Phase Cycle ◽  
Positive Rate

AbstractEdge computing extends traditional cloud services to the edge of the network, closer to users, and is suitable for network services with low latency requirements. With the rise of edge computing, its security issues have also received increasing attention. In this paper, a novel two-phase cycle algorithm is proposed for effective cyber intrusion detection in edge computing based on a multi-objective genetic algorithm (MOGA) and modified back-propagation neural network (MBPNN), namely TPC-MOGA-MBPNN. In the first phase, the MOGA is employed to build a multi-objective optimization model that tries to find the Pareto optimal parameter set for MBPNN. The Pareto optimal parameter set is applied for simultaneous minimization of the average false positive rate (Avg FPR), mean squared error (MSE) and negative average true positive rate (Avg TPR) in the dataset. In the second phase, some MBPNNs are created based on the parameter set obtained by MOGA and are trained to search for a more optimal parameter set locally. The parameter set obtained in the second phase is used as the input of the first phase, and the training process is repeated until the termination criteria are reached. A benchmark dataset, KDD cup 1999, is used to demonstrate and validate the performance of the proposed approach for intrusion detection. The proposed approach can discover a pool of MBPNN-based solutions. Combining these MBPNN solutions can significantly improve detection performance, and a GA is used to find the optimal MBPNN combination. The results show that the proposed approach achieves an accuracy of 98.81% and a detection rate of 98.23% and outperform most systems of previous works found in the literature. In addition, the proposed approach is a generalized classification approach that is applicable to the problem of any field having multiple conflicting objectives.

scholarly journals Three-Dimensional Analysis of the In Vivo Motion of Implantable Cardioverter Defibrillator Leads

2021 ◽  
Author(s):  
Tamas Szili-Torok ◽  
Jens Rump ◽  
Torsten Luther ◽  
Sing-Chien Yap
Keyword(s):  
Three Dimensional ◽  
Second Phase ◽  
Two Phase ◽  
Maximum Curvature ◽  
Phase Study ◽  
Absolute Curvature ◽  
Icd Leads ◽  
Lead Testing ◽  
Design And Testing

Abstract Better understanding of the lead curvature, movement and their spatial distribution may be beneficial in developing lead testing methods, guiding implantations and improving life expectancy of implanted leads. Objective The aim of this two-phase study was to develop and test a novel biplane cine-fluoroscopy-based method to evaluate input parameters for bending stress in leads based on their in vivo 3D motion using precisely determined spatial distributions of lead curvatures. Potential tensile, compressive or torque forces were not subjects of this study. Methods A method to measure lead curvature and curvature evolution was initially tested in a phantom study. In the second phase using this model 51 patients with implanted ICD leads were included. A biplane cine-fluoroscopy recording of the intracardiac region of the lead was performed. The lead centerline and its motion were reconstructed in 3D and used to define lead curvature and curvature changes. The maximum absolute curvature Cmax during a cardiac cycle, the maximum curvature amplitude Camp and the maximum curvature Cmax@amp at the location of Camp were calculated. These parameters can be used to characterize fatigue stress in a lead under cyclical bending. Results The medians of Camp and Cmax@amp were 0.18 cm−1 and 0.42 cm−1, respectively. The median location of Cmax was in the atrium whereas the median location of Camp occurred close to where the transit through the tricuspid valve can be assumed. Increased curvatures were found for higher slack grades. Conclusion Our results suggest that reconstruction of 3D ICD lead motion is feasible using biplane cine-fluoroscopy. Lead curvatures can be computed with high accuracy and the results can be implemented to improve lead design and testing.

scholarly journals A Decade in Trying to Increase Hand Hygiene—Finally Success

2020 ◽  
Vol 41 (S1) ◽  
pp. s93-s94
Author(s):  
Linda Huddleston ◽  
Sheila Bennett ◽  
Christopher Hermann
Keyword(s):  
Hand Hygiene ◽  
Hand Hygiene Compliance ◽  
Compliance Rate ◽  
Bloodstream Infections ◽  
Central Line ◽  
Second Phase ◽  
Two Phase ◽  
Hygiene Compliance ◽  
Tract Infections ◽  
The Voice

Background: Over the past 10 years, a rural health system has tried 10 different interventions to reduce hospital-associated infections (HAIs), and only 1 intervention has led to a reduction in HAIs. Reducing HAIs is a goal of nearly all hospitals, and improper hand hygiene is widely accepted as the main cause of HAIs. Even so, improving hand hygiene compliance is a challenge. Methods: Our facility implemented a two-phase longitudinal study to utilize an electronic hand hygiene reminder system to reduce HAIs. In the first phase, we implemented an intervention in 2 high-risk clinical units. The second phase of the study consisted of expanding the system to 3 additional clinical areas that had a lower incidence of HAIs. The hand hygiene baseline was established at 45% for these units prior to the voice reminder being turned on. Results: The system gathered baseline data prior to being turned on, and our average hand hygiene compliance rate was 49%. Once the voice reminder was turned on, hand hygiene improved nearly 35% within 6 months. During the first phase, there was a statistically significant 62% reduction in the average number of HAIs (catheter associated urinary tract infections (CAUTI), central-line–acquired bloodstream infections (CLABSIs), methicillin-resistant Staphylococcus aureus (MRSA), multidrug-resistant organisms (MDROs), and Clostridiodes difficile experienced in the preliminary units, comparing 12 months prior to 12 months after turning on the voice reminder. In the second phase, hand hygiene compliance increased to >65% in the following 6 months. During the second phase, all HAIs fell by a statistically significant 60%. This was determined by comparing the HAI rates 6 months prior to the voice reminder being turned on to 6 months after the voice reminder was turned on. Conclusions: The HAI data from both phases were aggregated, and there was a statistically significant reduction in MDROs by 90%, CAUTIs by 60%, and C. difficile by 64%. This resulted in annual savings >$1 million in direct costs of nonreimbursed HAIs.Funding: NoneDisclosures: None

CLIL as a pathway for cross-curricular and translingual classroom practices: A comparative quantitative study on Scottish and Spanish teachers’ views

2021 ◽  
pp. 136216882110324
Author(s):  
Xabier San Isidro
Keyword(s):  
Conceptual Framework ◽  
Quantitative Study ◽  
Classroom Practice ◽  
Classroom Practices ◽  
Research Tool ◽  
Second Phase ◽  
Integrated Learning ◽  
Two Phase ◽  
Pilot Testing ◽  
Final Questionnaire

Despite the numerous attempts to characterize Content and Language Integrated Learning (CLIL), the specialized literature has shown a dearth of cross-contextual studies on how stakeholders conceptualize classroom practice. This article presents the results of a two-phase comparative quantitative study on teachers’ views on CLIL design, implementation and results in two different contexts, Scotland ( n = 127) and Spain ( n = 186). The first phase focused on the creation, pilot-testing and validation of the research tool. The second phase consisted in administering the final questionnaire and analysing the results. The primary goals were (1) to ascertain whether practitioners’ perceptions on CLIL effects and classroom practices match the topics addressed by research; and (2) to analyse and compare teachers’ views in the two contexts. The study offers interesting insights into the main challenges in integrating language and content. Besides providing a conceptual framework for identifiable classroom practice, findings revealed that both cohorts shared broadly similar perceptions, although the Spanish respondents showed more positive views and significantly higher support for this approach.

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