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Topological data analysis has emerged as a powerful tool for extracting the metric, geometric and topological features underlying the data as a multi-resolution summary statistic, and has found applications in several areas where data…
Randomness is one of the important key concepts of statistics. In epidemiology or medical science, we investigate our hypotheses and interpret results through this statistical randomness. We hypothesized by imposing some conditions to this…
Predicting another person's upcoming action to build an appropriate response is a regular occurrence in the domain of motor control. In this review we discuss conceptual and experimental approaches aiming at the neural basis of predicting…
This is an informal paper presenting historical results around the recent paper of the author about Lang's Conjecture and torsion of elliptic curves. This paper also discusses a few aspects of the proof.
In this manuscript we will present a brief overview of the comorbidity concept. We will start by laying its foundations and its definitions and then describing the role that machine learning can hold in mining and defining it. The purpose…
Knowledge graphs typically undergo open-ended growth of new relations. This cannot be well handled by relation extraction that focuses on pre-defined relations with sufficient training data. To address new relations with few-shot instances,…
A joint characterisation of the controllability and observability of a particular kind of discrete system has been developed. The key idea of the procedure can be reduced to a correct choice of the sampling sequence. This freedom, owing to…
We discuss some aspects of the theory of subelliptic estimates.
Some of the most important theoretical and phenomenological aspects of the pinch technique are presented, and several recent developments are briefly reviewed.
A brief discussion is given of the traditional version of the Maximum Entropy Method, including a review of some of the criticism that has been made in regard to its use in statistical inference. Motivated by these questions, a modified…
This is a report about the use and misuse of citation data in the assessment of scientific research. The idea that research assessment must be done using ``simple and objective'' methods is increasingly prevalent today. The ``simple and…
Quantum and classical models for delayed choice entanglement swapping by postselection of measurements are discussed.
These informal notes briefly discuss various aspects of Cantor sets.
The purpose of this paper is to give a survey on the notions of distance between subsets either of a metric space or of a measure space, including definitions, a classification, and a discussion of the best-known distance functions, which…
The purpose of this paper is twofold. First, the definition of new statistical convergence with Fibonacci sequence is given and some fundamental properties of statistical convergence are examined. Second, approximation theory worked as a…
The current research is focusing on the area of Opinion Mining also called as sentiment analysis due to sheer volume of opinion rich web resources such as discussion forums, review sites and blogs are available in digital form. One…
Over the past 50 years many have debated what representation should be used to capture the meaning of natural language utterances. Recently new needs of such representations have been raised in research. Here I survey some of the…
This paper provides the reader with a very brief introduction to some of the theory and methods of text data mining. The intent of this article is to introduce the reader to some of the current methodologies that are employed within this…
The status of stochastic cooling and developments over the years are reviewed with reference to much of the original work. Both theoretical and technological subjects are considered.
These informal notes were prepared in connection with a lecture at a high school mathematics tournament, and provide an overview of some examples of metric spaces and a few of their basic properties.