We show that if the nearly-linear time solvers for Laplacian matrices and their generalizations can be extended to solve just slightly larger families of linear systems, then they can be used to quickly solve all systems of linear equations over the reals. This result can be viewed either positively or negatively: either we will develop nearly-linear time algorithms for solving all systems of linear equations over the reals, or progress on the families we can solve in nearlylinear time will soon halt.We establish a dichotomy result for the families of linear equations that can be solved in nearlylinear time. If nearly-linear time solvers exist for a slight generalization of the families for which they are currently known, then nearly-linear time solvers exist for all linear systems over the reals.This type of reduction is related to the successful research program of fine-grained complexity, such as the result [WW10] which showed that the existence of a "truly subcubic" time algorithm for All-Pairs Shortest Paths Problem is equivalent to the existence of "truly subcubic" time algorithm for a wide range of other problems. For any constant a ≥ 1, our result establishes for 2-commodity matrices, and several other classes of graph structured linear systems, that we can solve a linear system in a matrix of this type with s nonzeros in time O(s a ) if and only if we can solve linear systems in all matrices with polynomially bounded integer entries in time O(s a ).In the RealRAM model, given a matrix A ∈ R n×n and a vector c ∈ R n , we can solve the linear system Ax = c in O(n ω ) time, where ω is the matrix multiplication constant, for which the best currently known bound is ω < 2.3727 [Str69,Wil12]. Such a running time bound is cost prohibitive for the large sparse matrices often encountered in practice. Iterative methods [Saa03], first order methods [BV04], and matrix sketches [Woo14] can all be viewed as ways of obtaining significantly better performance in cases where the matrices have additional structure.In contrast, when A is an n × n Laplacian matrix with m non-zeros, and polynomially bounded entries, the linear system Ax = c can be solved approximately to -accuracy in O((m + n) log 1/2+o(1) n log (1/ )) time [ST14, CKM + 14]. This result spurred a series of major developments in fast graph algorithms, sometimes referred to as "the Laplacian Paradigm" of designing graph algorithms [Ten10]. The asymptotically fastest known algorithms for Maximum Flow in directed unweighted graphs [Mad13, Mad16], Negative Weight Shortest Paths and Maximum Weight Matchings [CMSV17], Minimum Cost Flows and Lossy Generalized Flows [LS14, DS08] all rely on fast Laplacian linear system solvers.The core idea of the Laplacian paradigm can be viewed as showing that the linear systems that arise from interior point algorithms, or second-order optimization methods, have graph structure, and can be preconditioned and solved using graph theoretic techniques. These techniques could potentially be extended to a range of other problems, provide...

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Japanese macaques on Shodoshima Island habitually form very large rest clusters, in which 50+ or even 100+ individuals huddle together. This behavior is not seen in any other populations of the species. Mean cluster sizes of two groups of Shodoshima monkeys are three and four in summer and 17 and 16 in winter, respectively. A maximum of 137 individuals have been seen to huddle in one cluster. It is difficult to explain the extra large clusters on Shodoshima only as an adaptive behavior against cold, since Shodoshima is relatively warm in the range of habitats for Japanese macaques. Compared with other groups of Japanese macaques, Shodoshima monkeys show: more frequent affinitive interactions, shorter inter-individual distance, more frequent ignoring of exclusion, more frequent aggression, less intense aggression, and more frequent counter-aggression. These characteristics suggest that the Japanese macaques on Shodoshima have relaxed dominant relations. The specific social organization of Shodoshima monkeys may sustain the formation of extra large clusters. Inter-group comparisons suggest that the social structure of Japanese macaques might be highly plastic, and that Shodoshima monkeys have less despotic, more tolerant social relations than typically reported for this species.

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The pore structure of marine-continental transitional shales from the Longtan Formation in Guizhou, China, was investigated using fractal dimensions calculated by the FHH (Frenkel-Halsey-Hill) model based on low-temperature N2 adsorption data. Results show that the overall D 1 (fractal dimension under low relative pressure, P / P 0 ≤ 0.5 ) and D 2 (fractal dimension under high relative pressure, P / P 0 > 0.5 ) values of Longtan shales were relatively large, with average values of 2.7426 and 2.7838, respectively, indicating a strong adsorption and storage capacity and complex pore structure. The correlation analysis of fractal dimensions with specific surface area, average pore size, and maximum gas absorption volume indicates that D 1 can comprehensively characterize the adsorption and storage capacity of shales, while D 2 can effectively characterize the pore structure complexity. Further correlation among pore fractal dimension, shale organic geochemical parameters, and mineral composition parameters shows that there is a significant positive correlation between fractal dimensions and organic matter abundance as well as a complex correlation between fractal dimension and organic matter maturity. Fractal dimensions increase with an increase in clay mineral content and pyrite content but decrease with an increase in quartz content. Considering the actual geological evaluation and shale gas exploitation characteristics, a lower limit for D 1 and upper limit for D 2 should be set as evaluation criteria for favorable reservoirs. Combined with the shale gas-bearing property test results of Longtan shales in Guizhou, the favorable reservoir evaluation criteria are set as D 1 ≥ 2.60 and D 2 ≤ 2.85 . When D 1 is less than 2.60, the storage capacity of the shales is insufficient. When D 2 is greater than 2.85, the shale pore structure is too complicated, resulting in poor permeability and difficult exploitation.

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