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Organising the relevant literature and by letting statistical convergence play the main role in the theory of compactness, a variant of compactness called statistical compactness has been achieved. As in case of sequential compactness, one…
Physics is a field of science that has traditionally used the scientific method to answer questions about why natural phenomena occur and to make testable models that explain the phenomena. Discovering equations, laws and principles that…
We review possible measures of complexity which might in particular be applicable to situations where the complexity seems to arise spontaneously. We point out that not all of them correspond to the intuitive (or "naive") notion, and that…
As the twin movements of open science and open source bring an ever greater share of the scientific process into the digital realm, new opportunities arise for the meta-scientific study of science itself, including of data science and…
A coordinate system is a foundation for every quantitative science, engineering, and medicine. Classical physics and statistics are based on the Cartesian coordinate system. The classical probability and hypothesis testing theory can only…
Supervised machine learning and predictive models have achieved an impressive standard today, enabling us to answer questions that were inconceivable a few years ago. Besides these successes, it becomes clear, that beyond pure prediction,…
Several interdisciplinary areas have appeared at the interface between biological and physical sciences. In this work, we suggest a complex network-based methodology for analyzing the interrelationships between some of these…
The paper discusses the fundamental characteristics distinguishing the natural and social systems from each other. It considers in detail the basic approaches, prospects, and possibilities of constructing mathematical description for social…
Climate statistics is of course a very broad field, along with the many connections and impacts for yet other areas, with a history as long as mankind has been recording temperatures, describing drastic weather events, etc. The important…
Unsolved controversies about uncertainty relations and quantum measurements still persists nowadays. They originate around the shortcomings regarding the conventional interpretation of uncertainty relations. Here we show that the respective…
Understanding realistic complex systems requires confronting significant conceptual, theoretical and experimental limitations rooted in the persistence of views that originated in the mechanics of simple moving bodies. We define the…
Empirical studies of graphs have contributed enormously to our understanding of complex systems. Known today as network science, what was originally a theoretical study of graphs has grown into a more scientific exploration of communities…
Data are invaluable. How can we assess the value of data objectively, systematically and quantitatively? Pricing data, or information goods in general, has been studied and practiced in dispersed areas and principles, such as economics,…
At the heart of causal structure learning from observational data lies a deceivingly simple question: given two statistically dependent random variables, which one has a causal effect on the other? This is impossible to answer using…
This essay, written by a statistician and a climate scientist, describes our view of the gap that exists between current practice in mainstream climate science, and the practical needs of policymakers charged with exploring possible…
Many of life's most fascinating phenomena emerge from interactions among many elements--many amino acids determine the structure of a single protein, many genes determine the fate of a cell, many neurons are involved in shaping our thoughts…
Do different fields of knowledge require different research strategies? A numerical model exploring different virtual knowledge landscapes, revealed two diverging optimal search strategies. Trend following is maximized when the popularity…
Using the known duality between events and states, we establish the fact that there is a duality between quantization of events and measurement of states. With this duality, we will show a generalized system of imprimitivity and a covariant…
The history of data analysis that is addressed here is underpinned by two themes, -- those of tabular data analysis, and the analysis of collected heterogeneous data. "Exploratory data analysis" is taken as the heuristic approach that…
The problem of individualization is recognized as crucial in almost every field. Identifying causes of effects in specific events is likewise essential for accurate decision making. However, such estimates invoke counterfactual…