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We lay the groundwork for a formal framework that studies scientific theories and can serve as a unified foundation for the different theories within physics. We define a scientific theory as a set of verifiable statements, assertions that can be shown to be true with an experimental test in finite time. By studying the algebra of such objects, we show that verifiability already provides severe constraints. In particular, it requires that a set of physically distinguishable cases is naturally equipped with the mathematical structures (i.e. second-countable Kolmogorov topologies and $sigma$-algebras) that form the foundation of manifold theory, differential geometry, measure theory, probability theory and all the major branches of mathematics currently used in physics. This gives a clear physical meaning to those mathematical structures and provides a strong justification for their use in science. Most importantly it provides a formal framework to incorporate additional assumptions and constrain the search space for new physical theories.
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Conversion of raw data into insights and knowledge requires substantial amounts of effort from data scientists. Despite breathtaking advances in Machine Learning (ML) and Artificial Intelligence (AI), data scientists still spend the majority of their effort in understanding and then preparing the raw data for ML/AI. The effort is often manual and ad hoc, and requires some level of domain knowledge. The complexity of the effort increases dramatically when data diversity, both in form and context, increases. In this paper, we introduce our solution, Augmented Data Science (ADS), towards addressing this human bottleneck in creating value from diverse datasets. ADS is a data-driven approach and relies on statistics and ML to extract insights from any data set in a domain-agnostic way to facilitate the data science process. Key features of ADS are the replacement of rudimentary data exploration and processing steps with automation and the augmentation of data scientist judgment with automatically-generated insights. We present building blocks of our end-to-end solution and provide a case study to exemplify its capabilities.
Generalizing empirical findings to new environments, settings, or populations is essential in most scientific explorations. This article treats a particular problem of generalizability, called transportability, defined as a license to transfer information learned in experimental studies to a different population, on which only observational studies can be conducted. Given a set of assumptions concerning commonalities and differences between the two populations, Pearl and Bareinboim (2011) derived sufficient conditions that permit such transfer to take place. This article summarizes their findings and supplements them with an effective procedure for deciding when and how transportability is feasible. It establishes a necessary and sufficient condition for deciding when causal effects in the target population are estimable from both the statistical information available and the causal information transferred from the experiments. The article further provides a complete algorithm for computing the transport formula, that is, a way of combining observational and experimental information to synthesize bias-free estimate of the desired causal relation. Finally, the article examines the differences between transportability and other variants of generalizability.
Motivated by the application problem of sensor fusion the author introduced the concept of graded set. It is reasoned that in classification problem arising in an information system (represented by information table), a novel set called Granular set naturally arises. It is realized that in any hierarchical classification problem, Granular set naturally arises. Also when the target set of objects forms a graded set the lower and upper approximations of target sets form a graded set. This generalizes the concept of rough set. It is hoped that a detailed theory of granular/ graded sets finds several applications.
The development of artificial general intelligence is considered by many to be inevitable. What such intelligence does after becoming aware is not so certain. To that end, research suggests that the likelihood of artificial general intelligence becoming hostile to humans is significant enough to warrant inquiry into methods to limit such potential. Thus, containment of artificial general intelligence is a timely and meaningful research topic. While there is limited research exploring possible containment strategies, such work is bounded by the underlying field the strategies draw upon. Accordingly, we set out to construct an ontology to describe necessary elements in any future containment technology. Using existing academic literature, we developed a single domain ontology containing five levels, 32 codes, and 32 associated descriptors. Further, we constructed ontology diagrams to demonstrate intended relationships. We then identified humans, AGI, and the cyber world as novel agent objects necessary for future containment activities. Collectively, the work addresses three critical gaps: (a) identifying and arranging fundamental constructs; (b) situating AGI containment within cyber science; and (c) developing scientific rigor within the field.
We present a number of open problems within general relativity. After a brief introduction to some technical mathematical issues and the famous singularity theorems, we discuss the cosmic censorship hypothesis and the Penrose inequality, the uniqueness of black hole solutions and the stability of Kerr spacetime and the final state conjecture, critical phenomena and the Einstein-Yang--Mills equations, and a number of other problems in classical general relativity. We then broaden the scope and discuss some mathematical problems motivated by quantum gravity, including AdS/CFT correspondence and problems in higher dimensions and, in particular, the instability of anti-de Sitter spacetime, and in cosmology, including the cosmological constant problem and dark energy, the stability of de Sitter spacetime and cosmological singularities and spikes. Finally, we briefly discuss some problems in numerical relativity and relativistic astrophysics.
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