Actions of Polish Groups and Classification Problems

We will discuss in this paper some aspects of a general program whose goal is the development of the theory of definable actions of Polish groups, the structure and classification of their orbit spaces, and the closely related study of definable equivalence relations. This work is motivated by basic foundational questions, like understanding the nature of complete classification of mathematical objects up to some notion of equivalence by invariants, and creating a mathematical framework for measuring the complexity of such classification problems. This theory, which has been growing rapidly over the last few years, is developed within the context of descriptive set theory, which provides the basic underlying concepts and methods. On the other hand, in view of the broad scope of this theory, there are natural interactions of it with other areas of mathematics, such as the theory of topological groups, topological dynamics, ergodic theory and its relationships with the theory of operator algebras, model theory, and recursion theory

On Measuring Non-Recursive Trade-Offs

We investigate the phenomenon of non-recursive trade-offs between descriptional systems in an abstract fashion. We aim at categorizing non-recursive trade-offs by bounds on their growth rate, and show how to deduce such bounds in general. We also identify criteria which, in the spirit of abstract language theory, allow us to deduce non-recursive tradeoffs from effective closure properties of language families on the one hand, and differences in the decidability status of basic decision problems on the other. We develop a qualitative classification of non-recursive trade-offs in order to obtain a better understanding of this very fundamental behaviour of descriptional systems

Permutation entropy and irreversibility in gait kinematic time series from patients with mild cognitive decline and early alzheimer’s dementia

Gait is a basic cognitive purposeful action that has been shown to be altered in late stages of neurodegenerative dementias. Nevertheless, alterations are less clear in mild forms of dementia, and the potential use of gait analysis as a biomarker of initial cognitive decline has hitherto mostly been neglected. Herein, we report the results of a study of gait kinematic time series for two groups of patients (mild cognitive impairment and mild Alzheimer’s disease) and a group of matched control subjects. Two metrics based on permutation patterns are considered, respectively measuring the complexity and irreversibility of the time series. Results indicate that kinematic disorganisation is present in early phases of cognitive impairment; in addition, they depict a rich scenario, in which some joint movements display an increased complexity and irreversibility, while others a marked decrease. Beyond their potential use as biomarkers, complexity and irreversibility metrics can open a new door to the understanding of the role of the nervous system in gait, as well as its adaptation and compensatory mechanismsThis research was funded through the Premio del Ilustre Colegio Profesional de Fisioterapeutas de la Comunidad De Madrid, prize number ICPFM-IX-201

Examining Scientific Writing Styles from the Perspective of Linguistic Complexity

Publishing articles in high-impact English journals is difficult for scholars around the world, especially for non-native English-speaking scholars (NNESs), most of whom struggle with proficiency in English. In order to uncover the differences in English scientific writing between native English-speaking scholars (NESs) and NNESs, we collected a large-scale data set containing more than 150,000 full-text articles published in PLoS between 2006 and 2015. We divided these articles into three groups according to the ethnic backgrounds of the first and corresponding authors, obtained by Ethnea, and examined the scientific writing styles in English from a two-fold perspective of linguistic complexity: (1) syntactic complexity, including measurements of sentence length and sentence complexity; and (2) lexical complexity, including measurements of lexical diversity, lexical density, and lexical sophistication. The observations suggest marginal differences between groups in syntactical and lexical complexity.Comment: 6 figure