Related papers: The FORM project
This text surveys different probabilistic aspects of a model which is used to describe the evolution of an object that falls apart randomly as time passes. Each point of view yields useful techniques to establish properties of such random…
Neutrino physics is now poised to move into the precision regime. Active attempts are under way to commence the era of precision neutrino measurement science which will surely widen the horizon of our knowledge about neutrinos. A number of…
In this introductory chapter of the Special Issue entitled `The Structure and Evolution of Stars', we highlight the recent major progress made in our understanding in the physics that governs stellar interiors. In so doing, we combine…
The physical models of a successful unified theory about the Universe must operate in different phase of matter evolution and different fields of physics. The attempts to build such wide range theory as a bunch of theories developed for…
The past few years have seen dramatic breakthroughs and spectacular and puzzling discoveries in astrophysics and cosmology. In many cases, the new observations can only be explained with the introduction of new fundamental physics. Here we…
New thinking needs to emerge about how to reform publishing along lines that best meet two perennial needs of scientific communication. This paper discusses a model that addresses these two needs with respect to physics. Given the…
A form of the Laplace transform is reviewed as a paradigm for an entire class of fractional functional transforms. Various of its properties are discussed. Such transformations should be useful in application to differential/integral…
Transformers play a central role in the inner workings of large language models. We develop a mathematical framework for analyzing Transformers based on their interpretation as interacting particle systems, which reveals that clusters…
Quantum mechanics, one of the most successful theories in the history of science, was created to account for physical systems not describable by classical physics. Though it is consistent with all experiments conducted thus far, many of its…
In this course, I talk about the source of mathematical constructivism and its role in the future development of theoretical physics. I describe what physical constructivism is and why it is necessary for the penetration of exact methods of…
The ongoing rapid expansion of the Internet greatly increases the necessity of effective recommender systems for filtering the abundant information. Extensive research for recommender systems is conducted by a broad range of communities…
Complex systems throughout Nature display structures and functions that are built and maintained, at least in part, by optimal energies flowing through them--not specific, ideal values, rather ranges in energy rate density below which…
This paper presents a comprehensive survey of research works on the topic of form understanding in the context of scanned documents. We delve into recent advancements and breakthroughs in the field, highlighting the significance of language…
This review is an introduction to theoretical models and mathematical calculations for biological evolution, aimed at physicists. The methods in the field are naturally very similar to those used in statistical physics, although the…
The observational evidence for the recent acceleration of the universe demonstrates that canonical theories of cosmology and particle physics are incomplete---if not incorrect---and that new physics is out there, waiting to be discovered. A…
Recently, much attention has been focused on the replicability of scientific results, causing scientists, statisticians, and journal editors to examine closely their methodologies and publishing criteria. Experimental particle physicists…
In this contribution we discuss the future of the global long-baseline neutrino oscillation program. The case is made that our current lack of understanding of neutrino-nucleus interactions is a serious challenge which will need to be met…
We present an overview of how certain computational tools currently interact with mathematical practice, and reflect on the implications for research mathematics in the short to medium term, as the field navigates the emerging age of AI and…
I first comment on some recent advances in computing equipment for CPU-intensive numerical simulations, and on possible developments in the near future. I then discuss some particularly important and yet unsolved problems in dynamics and…
Critically growing problems of fundamental science organisation and content are analysed with examples from physics and emerging interdisciplinary fields. Their origin is specified and new science structure (organisation and content) is…