Related papers: The Lost Art of Mathematical Modelling
During recent years, the renaissance of neural networks as the major machine learning paradigm and more specifically, the confirmation that deep learning techniques provide state-of-the-art results for most of computer vision tasks has been…
Many mathematicians find mathematics aesthetically beautiful and even comparable to art forms such as music or painting. On the other hand, every year a great number of school students leave mathematics with total disillusionment and…
In this review article we explore several recent advances in the quantitative modeling of financial markets. We begin with the Efficient Markets Hypothesis and describe how this controversial idea has stimulated a number of new directions…
The century of complexity has come. The face of science has changed. Surprisingly, when we start asking about the essence of these changes and then critically analyse the answers, the result are mostly discouraging. Most of the answers are…
Algorithmic modeling relies on limited information in data to extrapolate outcomes for unseen scenarios, often embedding an element of arbitrariness in its decisions. A perspective on this arbitrariness that has recently gained interest is…
It is not an exaggeration to say that the recent progress in artificial intelligence technology depends on large-scale and high-quality data. Simultaneously, a prevalent issue exists everywhere: the budget for data labeling is constrained.…
Many biological functions are executed by molecular machines, which consume energy and convert it into mechanical work. Biological machines have evolved to transport cargo, facilitate folding of proteins and RNA, remodel chromatin and…
Lack of methodical support, low level of teachers' awareness of existing effective teaching technologies such as computer modeling does not allow students to form their own individual trajectory for development as well as their competence…
Digital aquaculture leverages advanced technologies and data-driven methods, providing substantial benefits over traditional aquaculture practices. This paper presents a comprehensive review of three interconnected digital aquaculture…
The biologically-inspired swarm paradigm is being used to design self-organizing systems of locally interacting artificial agents. A major difficulty in designing swarms with desired characteristics is understanding the causal relation…
This chapter is an overview of foundational results in the mathematical theory of replicator systems. Its primary aim is to provide a unified framework for the mathematical formalisation of evolutionary processes in the spirit of…
The highest level of mathematics has traditionally been seen as a solitary endeavour, to produce a proof for review and acceptance by research peers. Mathematics is now at a remarkable inflexion point, with new technology radically…
Large language models (LLMs) are limited by substantial computational cost. We introduce a "computational economics" framework that treats an LLM as an internal economy of resource-constrained agents (attention heads and neuron blocks) that…
Ever since the advent of molecular biology in the 1970s, mechanical models have become the dogma in the field, where a "true" understanding of any subject is equated to a mechanistic description. This has been to the detriment of the…
As the amount of economic and other data generated worldwide increases vastly, a challenge for future generations of econometricians will be to master efficient algorithms for inference in empirical models with large information sets. This…
Statistical mechanics is one of the most powerful and elegant tools in the quantitative sciences. One key virtue of statistical mechanics is that it is designed to examine large systems with many interacting degrees of freedom, providing a…
Insufficient performance of optimization approaches for fitting of mathematical models is still a major bottleneck in systems biology. In this manuscript, the reasons and methodological challenges are summarized as well as their impact in…
Many intellectual endeavors require mathematical problem solving, but this skill remains beyond the capabilities of computers. To measure this ability in machine learning models, we introduce MATH, a new dataset of 12,500 challenging…
Mistakes in machine learning practice are commonplace, and can result in a loss of confidence in the findings and products of machine learning. This guide outlines common mistakes that occur when using machine learning, and what can be done…
Mathematical oncology is an interdisciplinary research field where the mathematical sciences meet cancer research. Being situated at the intersection of these two fields makes mathematical oncology highly dynamic, as practicing researchers…