Explaining the causes of infeasibility of Boolean formulas has many practical applications in electronic design automation and formal verification of hardware.Furthermore,a minimum explanation of infeasibility that ex...Explaining the causes of infeasibility of Boolean formulas has many practical applications in electronic design automation and formal verification of hardware.Furthermore,a minimum explanation of infeasibility that excludes all irrelevant information is generally of interest.A smallest-cardinality unsatisfiable subset called a minimum unsatisfiable core can provide a succinct explanation of infea-sibility and is valuable for applications.However,little attention has been concentrated on extraction of minimum unsatisfiable core.In this paper,the relationship between maximal satisfiability and mini-mum unsatisfiability is presented and proved,then an efficient ant colony algorithm is proposed to derive an exact or nearly exact minimum unsatisfiable core based on the relationship.Finally,ex-perimental results on practical benchmarks compared with the best known approach are reported,and the results show that the ant colony algorithm strongly outperforms the best previous algorithm.展开更多
The distribution patterns of mangrove Bruguiera gymnorrhiza population s in southern China are analyzed using the box-counting method of fractal theory. The patterns of B. gymnorrhiza populations could be thought of a...The distribution patterns of mangrove Bruguiera gymnorrhiza population s in southern China are analyzed using the box-counting method of fractal theory. The patterns of B. gymnorrhiza populations could be thought of as fractals as they exhibit self-similarity within the range of scale considered. Their fractal dimensions are not integer but fractional, ranging from 1.04 to 1.51. The unoccupied dimensions change from 0.49 to 0.96. The combined conditions of population density, pattern type and aggregation intensity together influence the values of fractal dimensions of patterns. The box counting is a useful and efficient method to investigate the complexity of patterns. Fractal dimension may be a most desirable and appropriate index for quantifying the horizontal spatial microstructure and fractal behaviors of patterns over a certain range of scales.展开更多
We give estimates of the remainder terms for several conformally-invariant Sobolev-type inequalities on the Heisenberg group. By considering the variations of associated functionals, we give a stability for two dual i...We give estimates of the remainder terms for several conformally-invariant Sobolev-type inequalities on the Heisenberg group. By considering the variations of associated functionals, we give a stability for two dual inequalities: The fractional Sobolev(FS) and Hardy-Littlewood-Sobolev(HLS) inequalities, in terms of distance to the submanifold of extremizers. Then we compare their remainder terms to improve the inequalities in another way. We also compare, in the limit case, the remainder terms of Beckner-Onofri(BO) inequality and its dual logarithmic Hardy-Littlewood-Sobolev(Log-HLS) inequality. Besides, we also list without proof some results for other groups of Iwasawa-type. Our results generalize earlier works on Euclidean spaces of Chen et al.(2013) and Dolbeault and Jankowiak(2014) onto some groups of Heisenberg-type. We worked for "almost"all fractions especially for comparing results, and the stability of HLS is also absolutely new, even for Euclidean case.展开更多
The author reviews some recent developments in Chern-Simons theory on a hyperbolic 3-manifold M with complex gauge group G. The author focuses on the case of G = SL(N, C) and M being a knot complement: M = S^3\ K. The...The author reviews some recent developments in Chern-Simons theory on a hyperbolic 3-manifold M with complex gauge group G. The author focuses on the case of G = SL(N, C) and M being a knot complement: M = S^3\ K. The main result presented in this note is the cluster partition function, a computational tool that uses cluster algebra techniques to evaluate the Chern-Simons path integral for G = SL(N, C). He also reviews various applications and open questions regarding the cluster partition function and some of its relation with string theory.展开更多
基金the National Natural Science Foundation of China (No.60603088)
文摘Explaining the causes of infeasibility of Boolean formulas has many practical applications in electronic design automation and formal verification of hardware.Furthermore,a minimum explanation of infeasibility that excludes all irrelevant information is generally of interest.A smallest-cardinality unsatisfiable subset called a minimum unsatisfiable core can provide a succinct explanation of infea-sibility and is valuable for applications.However,little attention has been concentrated on extraction of minimum unsatisfiable core.In this paper,the relationship between maximal satisfiability and mini-mum unsatisfiability is presented and proved,then an efficient ant colony algorithm is proposed to derive an exact or nearly exact minimum unsatisfiable core based on the relationship.Finally,ex-perimental results on practical benchmarks compared with the best known approach are reported,and the results show that the ant colony algorithm strongly outperforms the best previous algorithm.
基金The paper is supported by grants from the NSFC (No. 39825106 and 39860023).
文摘The distribution patterns of mangrove Bruguiera gymnorrhiza population s in southern China are analyzed using the box-counting method of fractal theory. The patterns of B. gymnorrhiza populations could be thought of as fractals as they exhibit self-similarity within the range of scale considered. Their fractal dimensions are not integer but fractional, ranging from 1.04 to 1.51. The unoccupied dimensions change from 0.49 to 0.96. The combined conditions of population density, pattern type and aggregation intensity together influence the values of fractal dimensions of patterns. The box counting is a useful and efficient method to investigate the complexity of patterns. Fractal dimension may be a most desirable and appropriate index for quantifying the horizontal spatial microstructure and fractal behaviors of patterns over a certain range of scales.
基金supported by National Natural Science Foundation of China(Grant No.11371036)the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.2012000110059)China Scholarship Council(Grant No.201306010009)
文摘We give estimates of the remainder terms for several conformally-invariant Sobolev-type inequalities on the Heisenberg group. By considering the variations of associated functionals, we give a stability for two dual inequalities: The fractional Sobolev(FS) and Hardy-Littlewood-Sobolev(HLS) inequalities, in terms of distance to the submanifold of extremizers. Then we compare their remainder terms to improve the inequalities in another way. We also compare, in the limit case, the remainder terms of Beckner-Onofri(BO) inequality and its dual logarithmic Hardy-Littlewood-Sobolev(Log-HLS) inequality. Besides, we also list without proof some results for other groups of Iwasawa-type. Our results generalize earlier works on Euclidean spaces of Chen et al.(2013) and Dolbeault and Jankowiak(2014) onto some groups of Heisenberg-type. We worked for "almost"all fractions especially for comparing results, and the stability of HLS is also absolutely new, even for Euclidean case.
基金supported by the U.S.Department of Energy(No.DE-SC0009988)
文摘The author reviews some recent developments in Chern-Simons theory on a hyperbolic 3-manifold M with complex gauge group G. The author focuses on the case of G = SL(N, C) and M being a knot complement: M = S^3\ K. The main result presented in this note is the cluster partition function, a computational tool that uses cluster algebra techniques to evaluate the Chern-Simons path integral for G = SL(N, C). He also reviews various applications and open questions regarding the cluster partition function and some of its relation with string theory.
