Related papers: About the Study of the $n$-dimensional Boolean Cub…
Quantum computing is a rapidly evolving field encompassing various disciplines such as physics, mathematics, computer engineering, and computer science. Teaching quantum computing in a concise and effective manner can be challenging,…
In this era of incessant advancements in quantum computing, bridging the gap between quantum algorithms' hardware requisites and available devices has become crucial. A prime focus in this context is the Software and System Level support…
Given the importance of integrating of explainability into machine learning, at present, there are a lack of pedagogical resources exploring this. Specifically, we have found a need for resources in explaining how one can teach the…
Identifying a coupled dynamical system out of many plausible candidates, each of which could serve as the underlying generator of some observed measurements, is a profoundly ill posed problem that commonly arises when modelling real world…
Causality is a fundamental part of the scientific endeavour to understand the world. Unfortunately, causality is still taboo in much of psychology and social science. Motivated by a growing number of recommendations for the importance of…
It is shown by the author in 2017 that for the union of N orthants in the n-dimensional space there exists an efficient and systematic way to find the exact value, using a suitable partial order relation construction. In this paper our…
With a growing interest in quantum technology globally, there is an increasing need for accessing relevant physical systems for education and research. In this paper we introduce a commercially available on-site quantum computer utilizing…
The amount of visual communication we are facing is rapidly increasing, and skills to process, understand, and generate visual representations are in high demand. Especially students focusing on computer graphics and visualization can…
In this article, we continue our study on universal learning machine by introducing new tools. We first discuss boolean function and boolean circuit, and we establish one set of tools, namely, fitting extremum and proper sampling set. We…
Relations between the decision tree complexity and various other complexity measures of Boolean functions is a thriving topic of research in computational complexity. It is known that decision tree complexity is bounded above by the cube of…
An algebraic structure related to discrete zero curvature equations is established. It is used to give an approach for generating master symmetries of first degree for systems of discrete evolution equations and an answer to why there exist…
Methods of high-dimensional probability play a central role in applications for statistics, signal processing theoretical computer science and related fields. These lectures present a sample of particularly useful tools of high-dimensional…
Backdoors and backbones of Boolean formulas are hidden structural properties. A natural goal, already in part realized, is that solver algorithms seek to obtain substantially better performance by exploiting these structures. However, the…
Knowledge of quantum mechanical systems is becoming more important for many science and engineering students who are looking to join the emerging quantum workforce. To better prepare a wide range of students for these careers, we must seek…
The VirtualCube system is a 3D video conference system that attempts to overcome some limitations of conventional technologies. The key ingredient is VirtualCube, an abstract representation of a real-world cubicle instrumented with RGBD…
Condensed mathematics, developed by Clausen and Scholze over the last few years, is a new way of studying the interplay between algebra and geometry. It replaces the concept of a topological space by a more sophisticated but better-behaved…
We present a general method for analysing novel computational substrates to determine which of their parameters can be manipulated to exhibit the complete set of 2-input boolean logical operations. We demonstrate this approach with an…
Advances in molecular technologies underlie an enormous growth in the size of data sets pertaining to biology and biomedicine. These advances parallel those in the deep learning subfield of machine learning. Components in the differentiable…
Multilayered artificial neural networks are becoming a pervasive tool in a host of application fields. At the heart of this deep learning revolution are familiar concepts from applied and computational mathematics; notably, in calculus,…
Contact Boolean algebras are one of the main algebraic tools in region-based theory of space. T. Ivanova provided strong motivations for the study of merely semilattices with a contact relation. Another significant motivation for…