Language and Culture

Language pervades social life. It is a primary means by which we gain access to the contents of others\u27 minds and establish shared understanding of the reality. Meanwhile, there is an enormous amount of linguistic diversity among human populations. Depending on what counts as a language, there are 3,000 to 10,000 living languages in the world, although a quarter of the world’s languages have fewer than 1,000 speakers and half have fewer than 10,000 (Crystal, 1997). Not surprisingly, a key question in culture and psychology research concerns the role of language in cultural processes. The present chapter focuses on two issues that have received by far the greatest amount of research attention from cultural researchers. First, how does language and human cultures co-evolve? Second, what are the non-linguistic cognitive effects of using a certain language? Does speaking different languages orient individuals to see and experience the external reality differently? The scope of the present chapter does not permit a comprehensive review of all pertinent research; only a selected sample of studies will be used to illustrate the main ideas in the present chapter

Transforming Bell's Inequalities into State Classifiers with Machine Learning

Quantum information science has profoundly changed the ways we understand, store, and process information. A major challenge in this field is to look for an efficient means for classifying quantum state. For instance, one may want to determine if a given quantum state is entangled or not. However, the process of a complete characterization of quantum states, known as quantum state tomography, is a resource-consuming operation in general. An attractive proposal would be the use of Bell's inequalities as an entanglement witness, where only partial information of the quantum state is needed. The problem is that entanglement is necessary but not sufficient for violating Bell's inequalities, making it an unreliable state classifier. Here we aim at solving this problem by the methods of machine learning. More precisely, given a family of quantum states, we randomly picked a subset of it to construct a quantum-state classifier, accepting only partial information of each quantum state. Our results indicated that these transformed Bell-type inequalities can perform significantly better than the original Bell's inequalities in classifying entangled states. We further extended our analysis to three-qubit and four-qubit systems, performing classification of quantum states into multiple species. These results demonstrate how the tools in machine learning can be applied to solving problems in quantum information science

On Self-Injectivity and p-Injectivity

A generalization of injectivity is studied and several properties are developed. Von Neumann regular rings are characterized. Sufficient conditions are given for a ring to admit a strongly regular classical left quotient ring. A nice characterization of strongly regular rings is given. Special direct summands of left self-injective regular and left continuous regular rings are considered