On a Linear Program for Minimum-Weight Triangulation

Minimum-weight triangulation (MWT) is NP-hard. It has a polynomial-time constant-factor approximation algorithm, and a variety of effective polynomial- time heuristics that, for many instances, can find the exact MWT. Linear programs (LPs) for MWT are well-studied, but previously no connection was known between any LP and any approximation algorithm or heuristic for MWT. Here we show the first such connections: for an LP formulation due to Dantzig et al. (1985): (i) the integrality gap is bounded by a constant; (ii) given any instance, if the aforementioned heuristics find the MWT, then so does the LP.Comment: To appear in SICOMP. Extended abstract appeared in SODA 201

A robust optimization approach for active and reactive power management in smart distribution networks using electric vehicles

YesThis paper presents a robust framework for active and reactive power management in distribution networks using electric vehicles (EVs). The method simultaneously minimizes the energy cost and the voltage deviation subject to network and EVs constraints. The uncertainties related to active and reactive loads, required energy to charge EV batteries, charge rate of batteries and charger capacity of EVs are modeled using deterministic uncertainty sets. Firstly, based on duality theory, the max min form of the model is converted to a max form. Secondly, Benders decomposition is employed to solve the problem. The effectiveness of the proposed method is demonstrated with a 33-bus distribution network

Epigenetic modelling of former, current and never smokers

BACKGROUND: DNA methylation (DNAm) performs excellently in the discrimination of current and former smokers from never smokers, where AUCs > 0.9 are regularly reported using a single CpG site (cg05575921; AHRR). However, there is a paucity of DNAm models which attempt to distinguish current, former and never smokers as individual classes. Derivation of a robust DNAm model that accurately distinguishes between current, former and never smokers would be particularly valuable to epidemiological research (as a more accurate smoking definition vs. self-report) and could potentially translate to clinical settings. Therefore, we appraise 4 DNAm models of ternary smoking status (that is, current, former and never smokers): methylation at cg05575921 (AHRR model), weighted scores from 13 CpGs created by Maas et al. (Maas model), weighted scores from a LASSO model of candidate smoking CpGs from the literature (candidate CpG LASSO model), and weighted scores from a LASSO model supplied with genome-wide 450K data (agnostic LASSO model). Discrimination is assessed by AUC, whilst classification accuracy is assessed by accuracy and kappa, derived from confusion matrices. RESULTS: We find that DNAm can classify ternary smoking status with reasonable accuracy, including when applied to external data. Ternary classification using only DNAm far exceeds the classification accuracy of simply assigning all classes as the most prevalent class (63.7% vs. 36.4%). Further, we develop a DNAm classifier which performs well in discriminating current from former smokers (agnostic LASSO model AUC in external validation data: 0.744). Finally, across our DNAm models, we show evidence of enrichment for biological pathways and human phenotype ontologies relevant to smoking, such as haemostasis, molybdenum cofactor synthesis, body fatness and social behaviours, providing evidence of the generalisability of our classifiers. CONCLUSIONS: Our findings suggest that DNAm can classify ternary smoking status with close to 65% accuracy. Both the ternary smoking status classifiers and current versus former smoking status classifiers address the present lack of former smoker classification in epigenetic literature; essential if DNAm classifiers are to adequately relate to real-world populations. To improve performance further, additional focus on improving discrimination of current from former smokers is necessary. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1186/s13148-021-01191-6

A Novel Approach for Ellipsoidal Outer-Approximation of the Intersection Region of Ellipses in the Plane

In this paper, a novel technique for tight outer-approximation of the intersection region of a finite number of ellipses in 2-dimensional (2D) space is proposed. First, the vertices of a tight polygon that contains the convex intersection of the ellipses are found in an efficient manner. To do so, the intersection points of the ellipses that fall on the boundary of the intersection region are determined, and a set of points is generated on the elliptic arcs connecting every two neighbouring intersection points. By finding the tangent lines to the ellipses at the extended set of points, a set of half-planes is obtained, whose intersection forms a polygon. To find the polygon more efficiently, the points are given an order and the intersection of the half-planes corresponding to every two neighbouring points is calculated. If the polygon is convex and bounded, these calculated points together with the initially obtained intersection points will form its vertices. If the polygon is non-convex or unbounded, we can detect this situation and then generate additional discrete points only on the elliptical arc segment causing the issue, and restart the algorithm to obtain a bounded and convex polygon. Finally, the smallest area ellipse that contains the vertices of the polygon is obtained by solving a convex optimization problem. Through numerical experiments, it is illustrated that the proposed technique returns a tighter outer-approximation of the intersection of multiple ellipses, compared to conventional techniques, with only slightly higher computational cost

Life Cycle Assessment of Municipal Waste Management System (Case Study: Karaj, Iran)

LCA has been defined as a tool for evaluating the environmental burdens and potential impacts that can be applied to municipal solid waste management systems for determine the optimum municipal solid waste (MSW) management strategy.To investigate the Waste Management system strategyof Karaj City we used LCA method. Three scenarios were defined and compared based on environmental burden include water pollution, air pollution, consumed energy and waste residues.. For each of these scenarios, an ecological indicator was achieved from checklist values. From the environmental point of view, results show that recycling is one of the best alternatives for Waste Management. Furthermore, composting has an important role in alleviating the load of pollutants and energy usage in the Waste Management system. ©JASEMKeywords: Waste Management system, LCA, Kara