Related papers: Elaboration on Two Points Raised in ``Classifier T…
This paper continues a series in which we study deficiencies in previously published works concerning fixed point assertions for digital images.
Real-life conjectures do not come with instructions saying whether they they should be proven or, instead, refuted. Yet, as we now know, in either case the final argument produced had better be not just convincing but actually verifiable in…
Expansions of abelian categories are introduced. These are certain functors between abelian categories and provide a tool for induction/reduction arguments. Expansions arise naturally in the study of coherent sheaves on weighted projective…
In this article, we describe various aspects of categorification of the structures appearing in information theory. These aspects include probabilistic models both of classical and quantum physics, emergence of F-manifolds, and motivic…
Expanding upon recent work, a new class of $A$-functions is introduced that can be viewed as an appropriate generalization of the class of regular $A$-functions, the class of structured $A$-functions, and the class of perfect $A$-functions.…
Calibration is a classical notion from the forecasting literature which aims to address the question: how should predicted probabilities be interpreted? In a world where we only get to observe (discrete) outcomes, how should we evaluate a…
It is well-known that biological phenomena are emergent. Emergent phenomena are quite interesting and amazing. However, they are difficult to be understood. Due to this difficulty, we propose a theory to describe emergence based on a…
In contemporary educational systems, academic performance indicators play a central role in institutional evaluation and in the interpretation of student trajectories. However, under conditions of rapid technological change, the inferential…
This text discusses several popular explanatory methods that go beyond the error measurements and plots traditionally used to assess machine learning models. Some of the explanatory methods are accepted tools of the trade while others are…
We prove an improved form of an expectation of Polya and discuss several related questions
In this article, we define the notion of a filtration and then give the basic theorems on initial and progressive enlargements of filtrations.
With information systems becoming larger scale, recommendation systems are a topic of growing interest in machine learning research and industry. Even though progress on improving model design has been rapid in research, we argue that many…
In the recent development in a various disciplines of physics, it is noted the need for including the deformed versions of the exponential functions. In this paper, we consider the deformations which have two purposes: to have them like…
To be usable in practice, interactive theorem provers need to provide convenient and efficient means of writing expressions, definitions, and proofs. This involves inferring information that is often left implicit in an ordinary…
In this work, I use a survey of senior visualization researchers and thinkers to ideate about the notion of progress in visualization research: how are we growing as a field, what are we building towards, and are our existing methods…
This paper will develop a single framework for unifying, simplifying and extending our prior results about axiom systems that retain a partial knowledge of their own consistency, via an axiomatic declaration of self-consistency. Its perhaps…
We show that the space in which scientific, technological and economic developments interplay with each other can be mathematically shaped using pioneering multilayer network and complexity techniques. We build the tri-layered network of…
Adopting the scientific method a theoretical model is proposed as foundation for information science and technology, extending the existing theory of signaling: a fact f becomes known in a physical system only following the success of a…
In this Book we argue that the fruitful interaction of computer vision and belief calculus is capable of stimulating significant advances in both fields. From a methodological point of view, novel theoretical results concerning the…
Neural network-based machine learning is capable of approximating functions in very high dimension with unprecedented efficiency and accuracy. This has opened up many exciting new possibilities, not just in traditional areas of artificial…