Unifying hidden-variable problems from quantum mechanics by logics of dependence and independence

We study hidden-variable models from quantum mechanics and their abstractions in purely probabilistic and relational frameworks by means of logics of dependence and independence, which are based on team semantics. We show that common desirable properties of hidden-variable models can be defined in an elegant and concise way in dependence and independence logic. The relationship between different properties and their simultaneous realisability can thus be formulated and proven on a purely logical level, as problems of entailment and satisfiability of logical formulae. Connections between probabilistic and relational entailment in dependence and independence logic allow us to simplify proofs. In many cases, we can establish results on both probabilistic and relational hidden-variable models by a single proof, because one case implies the other, depending on purely syntactic criteria. We also discuss the ‘no-go’ theorems by Bell and Kochen-Specker and provide a purely logical variant of the latter, introducing non-contextual choice as a team-semantical property.     

评《傲慢与偏见》

《傲慢与偏见》是简．奥斯丁最受欢迎的小说。她以一种温和、幽默的方式表达了对爱情和婚姻的看法。在她的眼中经济状况、学识和得体的举止也是决定人们婚姻状况的重要因素。整部书充满了作者的智慧。她的风格也不可避免的受到当时文学思想潮流的影响。     

浅析简·爱的童年对其成年后爱情观的影响

简·爱,夏洛特·勃朗特《简·爱》里的女主人公,在追求爱情的过程中,一直秉承着独立和平等两大原则,她的这种爱情观在很大程度上源于她早期的童年生活。本文将着重从简·爱童年时期的遭遇分析简·爱对爱、独立和平等的渴求。     

基于PB数据库系统的环境独立性研究

本文介绍了一种基于PowerBuilder数据库系统对环境独立的实现方法,以智能教师考核系统为例,表述了该方法的设计思想和运行机理,从而形成了一套完整的切实有效的基于PowerBuilder数据库系统对环境独立的解决方案。     

用归纳法证明基尔霍夫方程组解的存在与唯一性

用数学归纳法证明基尔霍夫方程的个数等于未知电流的个数,方程组的独立性,相容性,从而得出方程组解的存在与唯一性。     

关于数学公理化方法的教学问题

数学中的公理实际上即是关于基本概念的隐定义 ,从逻辑方法上来讲 ,所谓基本概念即是在本系统中不可定义的概念。在公理化方法的教学中 ,不仅要让学生受到数学美的薰陶 ,而且要相信学生也可以自己动手去构建公理系统     

会计确认独立性之必要性研究分析

从会计确认、会计人员的地位、会计性质及相关的经济利益分配等方面,分析了会计确认独立性理论研究的必要性,从法律法规角度,探讨了实施会计确认独立性之必要性。     

On the independence complex of square grids

The enumeration of independent sets of regular graphs is of interest in statistical mechanics, as it corresponds to the solution of hard-particle models. In 2004, it was conjectured by Fendley et al., that for some rectangular grids, with toric boundary conditions, the alternating number of independent sets is extremely simple. More precisely, under a coprimality condition on the sides of the rectangle, the number of independent sets of even and odd cardinality always differ by 1. In physics terms, this means looking at the hard-particle model on these grids at activity −1. This conjecture was recently proved by Jonsson. Here we produce other families of grid graphs, with open or cylindric boundary conditions, for which similar properties hold without any size restriction: the number of independent sets of even and odd cardinality always differ by 0, ±1, or, in the cylindric case, by some power of 2. We show that these results reflect a stronger property of the independence complexes of our graphs. We determine the homotopy type of these complexes using Forman’s discrete Morse theory. We find that these complexes are either contractible, or homotopic to a sphere, or, in the cylindric case, to a wedge of spheres. Finally, we use our enumerative results to determine the spectra of certain transfer matrices describing the hard-particle model on our graphs at activity −1. These results parallel certain conjectures of Fendley et al., proved by Jonsson in the toric case.     

Cores of Simplicial Complexes

We introduce a method to reduce the study of the topology of a simplicial complex to that of a simpler one. Applying this method to complexes arising from graphs, we give topological meaning to classical graph invariants. As a consequence, we answer some questions raised in (Ehrenborg and Hetyei in Eur. J. Comb. 27(6):906–923, 2006) on the independence complex and the dominance complex of a forest and obtain improved algorithms to compute their homotopy types.