Related papers: Finding meaningful and workable applied mathematic…
Basic principles of mathematical modeling are reviewed in this book, with the focus on physics and its practical applications, and examples of selected mathematical methods are presented. Most of the models have been imported from physics…
Support for arithmetic in multiple precisions and number formats is becoming increasingly common in emerging high-performance architectures. From a computational scientist's perspective, our goal is to determine how and where we can safely…
Scientific research involves mathematical modelling in the context of an interactive balance between theory, experiment and computation. However, computational methods and tools are still far from being appropriately integrated in the high…
One of the outstanding problems of philosophy of science and mathematics today is whether there is just "one" unique mathematics or the same can be bifurcated into "pure" and "applied" categories. A novel solution for this problem is…
Recent years have seen the dramatic rise of the usage of AI algorithms in pure mathematics and fundamental sciences such as theoretical physics. This is perhaps counter-intuitive since mathematical sciences require the rigorous definitions,…
"I am an industrial mathematician." When asked to identify my profession or academic field of study, this is the most concise answer I can provide. However, this seemingly straightforward statement is commonly greeted by a blank stare or an…
Over the past thirty years or so the authors have been teaching various programming for mathematics courses at our respective Universities, as well as incorporating computer algebra and numerical computation into traditional mathematics…
The standard assumptions that underlie many conceptual and quantitative frameworks do not hold for many complex physical, biological, and social systems. Complex systems science clarifies when and why such assumptions fail and provides…
We claim that human mathematics is only a limited part of the consequences of the chosen basic axioms. Properly human mathematics varies with time but appears to have universal features which we try to analyze. In particular the functioning…
A suite of impressive scientific discoveries have been driven by recent advances in artificial intelligence. These almost all result from training flexible algorithms to solve difficult optimization problems specified in advance by teams of…
The scientific process is a means to turn the results of experiments into knowledge about the world in which we live. Much research effort has been directed toward automating this process. To do this, one needs to formulate the scientific…
The reproduction and replication of research results has become a major issue for a number of scientific disciplines. In computer science and related computational disciplines such as systems biology, the challenges closely revolve around…
We present and discuss a curated selection of recent literature related to the application of quantitative techniques, tools, and topics from mathematics and data science that have been used to analyze the mathematical sciences community.…
Computational scientists are facing a new era where the old ways of developing and reusing code have to be left behind and a few daring steps are to be made towards new horizons. The present work analyzes the needs that drive this change,…
Although the gender gap in academia has narrowed, females are underrepresented within some fields in the USA. Prior research suggests that the imbalances between science, technology, engineering and mathematics fields may be partly due to…
Mathematical information is essential for technical work, but its creation, interpretation, and search are challenging. To help address these challenges, researchers have developed multimodal search engines and mathematical question…
In the quest to align deep learning with the sciences to address calls for rigor, safety, and interpretability in machine learning systems, this contribution identifies key missing pieces: the stages of hypothesis formulation and testing,…
Process science is a highly interdisciplinary field of research. Despite numerous proposals, process science lacks an adequate understanding of the core concepts of the field, including notions such as process, event, and system. A more…
Scientific software often presents very particular requirements regarding usability, which is often completely overlooked in this setting. As computational science has emerged as its own discipline, distinct from theoretical and…
This paper covers two topics: first an introduction to Algorithmic Complexity Theory: how it defines probability, some of its characteristic properties and past successful applications. Second, we apply it to problems in A.I. - where it…