Generating semantic maps through multidimensional scaling: linguistic applications and theory

This paper reports on the state-of-the-art in application of multidimensional scaling (MDS) techniques to create semantic maps in linguistic research. MDS refers to a statistical technique that represents objects (lexical items, linguistic contexts, languages, etc.) as points in a space so that close similarity between the objects corresponds to close distances between the corresponding points in the representation. We focus on the use of MDS in combination with parallel corpus data as used in research on cross-linguistic variation. We first introduce the mathematical foundations of MDS and then give an exhaustive overview of past research that employs MDS techniques in combination with parallel corpus data. We propose a set of terminology to succinctly describe the key parameters of a particular MDS application. We then show that this computational methodology is theory-neutral, i.e. it can be employed to answer research questions in a variety of linguistic theoretical frameworks. Finally, we show how this leads to two lines of future developments for MDS research in linguistics.

MATHEMATICAL BASIS FOR ANALYSING SIGNALS REMOVED FROM FROM THE HUMAN CEREBRAL CORTEX USING DOBESHI AND HAAR METHODS

The article presents the results of the study of signals taken from the human cerebral cortex, and presents the mathematical foundations of analysis using the methods of Daubechy and Haar. A comparative analysis of the method of the Daubechy and Haar wavelet transform implemented in MATLAB and developed using the C++ programming language in the course of the study on the example of a recorded audio signal with natural interference is given.

Capillary network formation and structure in a modified discrete mathematical model of angiogenesis

Angiogenesis, as part of cancer development, involves hierarchical complicated events and processes. Multiple studies have revealed the significance of the formation and structure of tumor-induced capillary networks. In this study, a discrete mathematical model of angiogenesis is studied and modified to capture the realistic physics of capillary network formation. Modifications are performed on the mathematical foundations of an existing discrete model of angiogenesis. The main modifications are the imposition of the matrix density effect, implementation of realistic boundary and initial conditions, and improvement of the method of governing equations based on physical observation. Results show that endothelial cells accelerate angiogenesis and capillary formation as they migrate toward the tumor and clearly exhibit the physical concept of haptotactic movement. On the other hand, consideration of blood flow-induced stress leads to a dynamic adaptive vascular network of capillaries which intelligibly reflects the brush border effect . The present modified model of capillary network formation is based on the physical rationale that defines a clear mathematical and physical interpretation of angiogenesis, which is likely to be used in cancer development modeling and anti-angiogenic therapies.

Everything has its Price: Foundations of Cost-Sensitive Learning and its Application in Psychology

Psychology has seen an increase in machine learning (ML) methods. In many applications, observations are classified into one of two groups (binary classification). Off-the-shelf classification algorithms assume that the costs of a misclassification (false-positive or false-negative) are equal. Because this is often not reasonable (e.g., in clinical psychology), cost-sensitive learning (CSL) methods can take different cost ratios into account. We present the mathematical foundations and introduce a taxonomy of the most commonly used CSL methods, before demonstrating their application and usefulness on psychological data, i.e., the drug consumption dataset ($N = 1885$) from the UCI Machine Learning Repository. In our example, all demonstrated CSL methods noticeably reduce mean misclassification costs compared to regular ML algorithms. We discuss the necessity for researchers to perform small benchmarks of CSL methods for their own practical application. Thus, our open materials provide R code, demonstrating how CSL methods can be applied within the mlr3 framework (https://osf.io/cvks7/).