Efficient Last-iterate Convergence Algorithms in Solving Games

No-regret algorithms are popular for learning Nash equilibrium (NE) in two-player zero-sum normal-form games (NFGs) and extensive-form games (EFGs). Many recent works consider the last-iterate convergence no-regret algorithms. Among them, the two most famous algorithms are Optimistic Gradient Descent Ascent (OGDA) and Optimistic Multiplicative Weight Update (OMWU). However, OGDA has high per-iteration complexity. OMWU exhibits a lower per-iteration complexity but poorer empirical performance, and its convergence holds only when NE is unique. Recent works propose a Reward Transformation (RT) framework for MWU, which removes the uniqueness condition and achieves competitive performance with OMWU. Unfortunately, RT-based algorithms perform worse than OGDA under the same number of iterations, and their convergence guarantee is based on the continuous-time feedback assumption, which does not hold in most scenarios. To address these issues, we provide a closer analysis of the RT framework, which holds for both continuous and discrete-time feedback. We demonstrate that the essence of the RT framework is to transform the problem of learning NE in the original game into a series of strongly convex-concave optimization problems (SCCPs). We show that the bottleneck of RT-based algorithms is the speed of solving SCCPs. To improve the their empirical performance, we design a novel transformation method to enable the SCCPs can be solved by Regret Matching+ (RM+), a no-regret algorithm with better empirical performance, resulting in Reward Transformation RM+ (RTRM+). RTRM+ enjoys last-iterate convergence under the discrete-time feedback setting. Using the counterfactual regret decomposition framework, we propose Reward Transformation CFR+ (RTCFR+) to extend RTRM+ to EFGs. Experimental results show that our algorithms significantly outperform existing last-iterate convergence algorithms and RM+ (CFR+)

Mineralogy and Geochemistry of Late Permian Coals within the Tongzi Coalfield in Guizhou Province, Southwest China

first_pagesettings Open AccessArticle Mineralogy and Geochemistry of Late Permian Coals within the Tongzi Coalfield in Guizhou Province, Southwest China by Baoqing Li 1,*,Xinguo Zhuang 1,Xavier Querol 1,2,Natalia Moreno 2OrcID,Linjian Yang 3,Yunfei Shangguan 1 andJing Li 1 1 Key Laboratory of Tectonics and Petroleum Resources (China University of Geosciences), Ministry of Education, Wuhan 430074, China 2 Institute of Environmental Assessment and Water Research, CSIC, C/Jordi Girona 18–26, 08034 Barcelona, Spain 3 No. 106 Geological Team of Guizhou Province Geology and Mineral Bureau, Zunyi 563000, China * Author to whom correspondence should be addressed. Minerals 2020, 10(1), 44; https://doi.org/10.3390/min10010044 Received: 18 December 2019 / Revised: 29 December 2019 / Accepted: 30 December 2019 / Published: 31 December 2019 (This article belongs to the Collection Minerals in Coal and Coal Combustion Products) Download PDF Browse Figures Abstract The lowermost Late Permian coal seam (C4 Coal) in the Tongzi Coalfield offers an opportunity to investigate the influence of terrigenous detrital materials from the Qianbei Upland on the mineralogical and geochemical patterns of the C4 Coal. The minerals are mainly dominated by pyrite and, to a lesser extent, tobelite, kaolinite, and calcite, along with traces of Al-oxyhydroxide minerals. The various degrees of marine influence may have resulted in the variation in the amount of Fe-sulfides (e.g., pyrite) and elements having Fe-sulfides affinity. Furthermore, the abundant Fe ions involved in the formation of Fe-sulfides were most likely derived from the claystone on the Qianbei Upland. The tobelite identified in the C4 Coal probably originated from the interaction between pre-existing kaolinite and NH4+ from NH3 released from the thermally affected organic matter at least shortly after the highly volatile bituminous stage under NH4+-rich and K+-poor conditions. The terrigenous detrital materials were derived from two possible sediment-region sources—the Qianbei Upland and Kangdian Upland—which is different from Late Permian coals in Western Guizhou Province. The claystone on the Qianbei Upland may have served as parent rock, as indicated by the presence of the Al-oxyhydroxide minerals as well as low SiO2/Al2O3 ratio (0.66 on average) and low quartz content. Meanwhile, the detrital materials from the Kangdian Upland most likely originated from the erosion of the felsic rocks at the uppermost part of the Kangdian Upland, as evidenced by the high Al2O3/TiO2 ratio (36.0 on average) and the strongly negative Eu anomaly (0.61 on average).The authors would like to give their sincere thanks to No. 106 Geological Team of Guizhou Province Geology for assistance during sampling and Institute of Environmental Assessment and Water Research, CSIC, Spain for assistance during the sample analysis. Also, many thanks are given to academic editor and two anonymous reviewers for their valuable comments on the manuscript.Peer reviewe

High-efficiency Algorithm for the Most Unfavourable Load Case Combinations of Multilayered Frame-Type Wharf Structure

The wharf, which was built in the Three Gorges Reservoir of China, is constructed as a layered frame-type structure for adapting to large water level fluctuations that exceed 30 m. These large fluctuations cause the frame-type structure to exhibit a considerably higher number of load case combinations than traditional marine high-piled wharfs. To estimate the most adverse combined internal force and the corresponding unfavourable load case combinations of significant components for multilayered frame-type wharf structures in the Three Gorges Reservoir of China, a high-efficiency algorithm is developed in this study. This algorithm can skilfully transform the computational mode of load case combinations into a matrix operations process by computer programming. By applying the proposed algorithm, the number of load case combinations for eight significant components of frame-type wharf, including piles, columns, beams, braces and berthing components, are resolved to a total of 21 from the original quantity of more than six billion. This high-efficiency algorithm can provide powerful technical support for evaluating the bearing capability of multilayered frame-type wharfs in the Three Gorges Reservoir of China

Investigation into the Application of Construction and Demolition Waste in Urban Roads

The recycling and reuse of waste materials is a topic of global concern and great international interest for those interested in sustainable development and protecting the environment. In recent decades, global production of construction and demolition waste (C&D waste) has significantly increased and became a worldwide problem. This research proposes to evaluate the feasibility of using aggregate from recycled C&D waste for urban road embankment applications based on the Sanhuan road construction project in eastern Xi’an. An extensive suite of laboratory and field compaction tests were carried out to determine the physical properties and engineering characteristics of the C&D waste. The effect of curing on the strength of the C&D waste was investigated using unconfined compression strength (UCS), California bearing ratio (CBR), and deflection tests. The results show that the C&D waste has the characteristics of high strength and significant stability after simple treatment and further suggest that the use of these materials for paving urban road embankments is feasible. This study is of value for the reasonable and effective promotion of using C&D waste recycled materials in road subgrade applications

In situ inhibitor synthesis and screening by fluorescence polarization: an efficient approach for accelerating drug discovery

Target-directed dynamic combinatorial chemistry has emerged as a useful tool for hit identification, but has not been widely used, in part due to challenges associated with analyses involving complex mixtures. We describe an operationally simple alternative: in situ inhibitor synthesis and screening (ISISS), which links high-throughput bioorthogonal synthesis with screening for target binding by fluorescence. We exemplify the ISISS method by showing how coupling screening for target binding by fluorescence polarization with the reaction of acyl-hydrazides and aldehydes led to the efficient discovery of a potent and novel acylhydrazone-based inhibitor of human prolyl hydroxylase 2 (PHD2), a target for anemia treatment, with equivalent in vivo potency to an approved medicine

In situ inhibitor synthesis and screening by fluorescence polarization: an efficient approach for accelerating drug discovery

Target-directed dynamic combinatorial chemistry has emerged as a useful tool for hit identification, but has not been widely used, in part due to challenges associated with analyses involving complex mixtures. We describe an operationally simple alternative: in situ inhibitor synthesis and screening (ISISS), which links high-throughput bioorthogonal synthesis with screening for target binding by fluorescence. We exemplify the ISISS method by showing how coupling screening for target binding by fluorescence polarization with the reaction of acyl-hydrazides and aldehydes led to the efficient discovery of a potent and novel acylhydrazone-based inhibitor of human prolyl hydroxylase 2 (PHD2), a target for anemia treatment, with equivalent in vivo potency to an approved medicine

The taxonomic relevance of flower colour for Epimedium (Berberidaceae), with morphological and nomenclatural notes for five species from China

Morphological variations, particularly flower colour, could be considered as an evolutionarily and ornamentally significant taxonomic criterion for Epimedium. Our extensive field investigation based on population studies revealed abundant intraspecific variations in flower colour. Five species, (i.e., E. acuminatum Franch., E. leptorrhizum Stearn, E. pauciflorum K.C.Yen, E. mikinorii Stearn, and E. glandulosopilosum H.R.Liang) were found to possess polymorphic flower colour, which is first described and illustrated here. Moreover, all these species were found to be polymorphic in other diagnostic characters, such as the type of rhizome, the number and arrangement of stem-leaves, and/or their indumentum, which have not been adequately described in previous studies. Therefore, their morphological descriptions have been complemented and/or revised. We also provide notes on the morphology and nomenclature for each species. Additionally, a key to the species in China has been provided. The present study could serve as a basis for understanding their taxonomy and helping their utilisation as an ornamental plant

Structural load monitoring of floating mooring column and its application on optimal regulation for water conveyance system operation of sea shiplock

Due to the sea water intrusion and the development trend of using large-scale ships, more stringent requirements are put forward for the safety of water delivery process and the mooring equipment operation for the sea shiplock. The maximum loads for the mooring equipment of sea shiplock, i.e., floating mooring column (FMC), are generally occurred at the end of water delivery. The superimposed effect of turbulent flow and marine corrosive environment can accelerate the failure of the floating mooring column structure for the sea shiplock, which leads to the safety incidents, including the structural damage of FMC and the breakage of mooring lines for the ship, etc. The safety of the FMC is mostly influenced by three factors, including the ship’s tonnage, the water flow environment of the locked room, and the lock operation technologies; among these, the water flow environment can be considered the most significant. In practice, because the mooring load of an FMC due to water delivery from the shiplock is very complicated, there is currently no mature approach to condition monitoring. This investigation aims to address a large sea shiplock, and the optimal regulation approach for water delivery of shiplock is established based on a load monitoring methodology for FMCs. The detection accuracy of the FMC mooring loads is controlled by simulation verification with errors less than 10%. During the optimized water delivery process, the exerted loads on the FMCs are noticeably reduced to be lower than the maximum design rating. The innovative approach is essentially based on an inversion calculation of the load response model for obtaining the mooring loads of FMCs, with the monitored load results used to regulate and optimize the water delivery process of the shiplocks. The research results can fill a part of the research gap of FMC mooring load condition monitoring method in shiplock water delivery, and provide technical support for the safety of shiplock water delivery process and mooring equipment operation

A Curve Shaped Description of Large Networks, with an Application to the Evaluation of Network Models

BACKGROUND: Understanding the structure of complex networks is a continuing challenge, which calls for novel approaches and models to capture their structure and reveal the mechanisms that shape the networks. Although various topological measures, such as degree distributions or clustering coefficients, have been proposed to characterize network structure from many different angles, a comprehensive and intuitive representation of large networks that allows quantitative analysis is still difficult to achieve. METHODOLOGY/PRINCIPAL FINDINGS: Here we propose a mesoscopic description of large networks which associates networks of different structures with a set of particular curves, using breadth-first search. After deriving the expressions of the curves of the random graphs and a small-world-like network, we found that the curves possess a number of network properties together, including the size of the giant component and the local clustering. Besides, the curve can also be used to evaluate the fit of network models to real-world networks. We describe a simple evaluation method based on the curve and apply it to the Drosophila melanogaster protein interaction network. The evaluation method effectively identifies which model better reproduces the topology of the real network among the given models and help infer the underlying growth mechanisms of the Drosophila network. CONCLUSIONS/SIGNIFICANCE: This curve-shaped description of large networks offers a wealth of possibilities to develop new approaches and applications including network characterization, comparison, classification, modeling and model evaluation, differing from using a large bag of topological measures