Integral Reduction by Unitarity Method for Two-loop Amplitudes: A Case Study

In this paper, we generalize the unitarity method to two-loop diagrams and use it to discuss the integral bases of reduction. To test out method, we focus on the four-point double-box diagram as well as its related daughter diagrams, i.e., the double-triangle diagram and the triangle-box diagram. For later two kinds of diagrams, we have given complete analytical results in general (4-2\eps)-dimension.Comment: 52 pages, 1 figur

A New Type of Crumb Rubber Asphalt Mixture: A Dry Process Design and Performance Evaluation

To obtain a crumb rubber asphalt mixture with excellent performance, this study combined trans-polyoctenamer rubber (TOR), crumb rubber, and other additives to establish a new type of crumb rubber (CRT). The objective of this study was to design and evaluate the road performance of the new type of crumb rubber asphalt mixture (CRTAM) with a skeleton dense texture through a dry process. First, the skeleton intrusion compact volume method was used to optimize the grading of coarse and fine aggregates, and the design of the CRTAM gradation was carried out through the same and unequal volume replacement grading method. Then, three types of road performance were analyzed: high-temperature stability, low-temperature crack resistance, and water stability. The results showed that 2% and 2.5% CRT met a low-temperature index with equal volume substitution, and the six gradations obtained by unequal volume replacement with 2% CRT complied with the requirements of a skeleton dense texture. When the substitution ratio was 1.5 and 0.5, the high-temperature performance was better. In addition, when the substitution ratio was 0.5, the flexural strain energy density was the highest and the low-temperature performance was the best. Including considerations of economic benefits, it is recommended that the CRT content be 2% and the substitution ratio be 0.5

Improved Algorithms for Clustering with Outliers

Clustering is a fundamental problem in unsupervised learning. In many real-world applications, the to-be-clustered data often contains various types of noises and thus needs to be removed from the learning process. To address this issue, we consider in this paper two variants of such clustering problems, called k-median with m outliers and k-means with m outliers. Existing techniques for both problems either incur relatively large approximation ratios or can only efficiently deal with a small number of outliers. In this paper, we present improved solution to each of them for the case where k is a fixed number and m could be quite large. Particularly, we gave the first PTAS for the k-median problem with outliers in Euclidean space R^d for possibly high m and d. Our algorithm runs in O(nd((1/epsilon)(k+m))^(k/epsilon)^O(1)) time, which considerably improves the previous result (with running time O(nd(m+k)^O(m+k) + (1/epsilon)k log n)^O(1))) given by [Feldman and Schulman, SODA 2012]. For the k-means with outliers problem, we introduce a (6+epsilon)-approximation algorithm for general metric space with running time O(n(beta (1/epsilon)(k+m))^k) for some constant beta>1. Our algorithm first uses the k-means++ technique to sample O((1/epsilon)(k+m)) points from input and then select the k centers from them. Compared to the more involving existing techniques, our algorithms are much simpler, i.e., using only random sampling, and achieving better performance ratios

9-[4-Hydr­oxy-3-(hydroxy­meth­yl)but­yl]guanine monohydrate

In the mol­ecular structure of the title compound, also named penciclovir monohydrate, C10H15N5O3·H2O, the 4-hydr­oxy-3-hydroxy­methyl­but-1-yl group is connected to guanine through an N atom of the imidazole ring. Water mol­ecules stabilize the mol­ecular packing by forming O—H⋯O hydrogen bonds. A three-dimensional network is generated via inter­molecular N—H⋯N, N—H⋯O, O—H⋯N and O—H⋯O hydrogen bonding

Phytoplankton abundance and size-fractionated structure in three contrasting periods in the Pear River Estuary

Phytoplankton abundance, composition and size-fractionated chlorophyll a (micro-, nano- and pico-chl. a) in the Pearl River Estuary (PRE), South China were assessed in three surveys (Aug. 2010, Jan. 2011 and Aug. 2011) to identify key environmental indicators that shape their distribution patterns. Non-metric multidimensional scaling (MDS) showed that the PRE formed three regional clusters that were characterized by a transition from dominant freshwater species to estuarine diatoms in normal summer flow conditions (Aug. 2010). With a reduced river flow in winter (Jan. 2011), the inner estuary was categorized as one group marked by the predominance of the nanoflagellate, Plagioselmis prolonga. This small-sized cryptophyte was first recorded in the PRE and was likely to outcompete other phytoplankton species in turbid or well-mixed waters. During the extreme drought of summer of 2011 (Aug. 2011), the estuarine plume was limited and regional division by MDS was similar to winter patterns, as some marine species were observed in the upper estuary. We considered that the higher phytoplankton density in the summer of 2011 was presumably a combined effect of longer residence time and higher phosphate concentration. With respect to the size-fractionated phytoplankton composition, our results showed that almost half of the chl. a in the estuary was contained in microplankton particles, while the proportion of pico-chl. a increased from the upstream of the PRE towards the estuary boundary (Wanshan Islands). Furthermore, phytoplankton abundance, three size classes of chl. a and environmental factors were explored by principal component regression (PCR) analysis. In three surveys, pico-chl. a was negatively correlated with the first principal component (PCL, positively loaded with salinity and inversely with inorganic nutrients), which indicated a negative influence of the riverine and coastal waters on picophytoplankton and the specific oligotrophic niche of picophytoplankton. Similarly, PC1 was also considered as the key environmental variable basis controlling micro-chl. a in summer of 2010, while in the summer of 2011, zooplankton and copepods were positively associated with phytoplankton abundance, suggesting a resource effect of phytoplankton on zooplankton development

A Unified Framework of FPT Approximation Algorithms for Clustering Problems

In this paper, we present a framework for designing FPT approximation algorithms for many k-clustering problems. Our results are based on a new technique for reducing search spaces. A reduced search space is a small subset of the input data that has the guarantee of containing k clients close to the facilities opened in an optimal solution for any clustering problem we consider. We show, somewhat surprisingly, that greedily sampling O(k) clients yields the desired reduced search space, based on which we obtain FPT(k)-time algorithms with improved approximation guarantees for problems such as capacitated clustering, lower-bounded clustering, clustering with service installation costs, fault tolerant clustering, and priority clustering

4-(8-Hydr­oxy-3-methyl-1,4-dioxo-1,4-dihydro-2-naphth­yl)butanoic acid

In the title compound, C15H14O5, an intramolecular O—H⋯O hydrogen bond occurs. In the crystal, the molecules form inversion dimers linked by pairs of O—H⋯O bonds, which are further linked by C—H⋯O interactions