Related papers: Open Problems in Mathematical Biology
The study of biological cells in terms of mesoscopic, nonequilibrium, nonlinear, stochastic dynamics of open chemical systems provides a paradigm for other complex, self-organizing systems with ultra-fast stochastic fluctuations, short-time…
We propose a static and a dynamic approach to model biological signaling networks, and show how each can be used to answer relevant biological questions. For this we use the two different mathematical tools of Propositional Logic and…
Motivated by the results of recent laboratory experiments (Yoshida et al. Nature, 424, 303-306 (2003)) as well as many earlier field observations that evolutionary changes can take place in ecosystems over relatively short ecological time…
Computational biology is on the verge of a paradigm shift in its research practice - from a data-based (computational) paradigm to an information-based (cognitive) paradigm. As in the other research fields, this transition is impeded by…
Bacterial growth presents many beautiful phenomena that pose new theoretical challenges to statistical physicists, and are also amenable to laboratory experimentation. This review provides some of the essential biological background,…
Examining individual components of cellular systems has been successful in uncovering molecular reactions and interactions. However, the challenge lies in integrating these components into a comprehensive system-scale map. This difficulty…
Practicing mathematicians often assume that mathematical claims, when they are true, have good reasons to be true. Such a state of affairs is "unreasonable", in Wigner's sense, because basic results in computational complexity suggest that…
With increased access to data and the advent of computers, the use of statistical tools and numerical simulations is becoming commonplace for ecologists. These approaches help improve our understanding of ecological phenomena and their…
The massive data sets from today's particle physics experiments present a variety of challenges amenable to the tools developed by the statistics community. From the real-time decision of what subset of data to record on permanent storage,…
Mathematical software systems are becoming more and more important in pure and applied mathematics in order to deal with the complexity and scalability issues inherent in mathematics. In the last decades we have seen a cambric explosion of…
We present a game of interacting agents which mimics the complex dynamics found in many natural and social systems. These agents modify their strategies periodically, depending on their performances using genetic crossover mechanisms,…
This paper makes a number of connections between life and various facets of genetic and evolutionary algorithms research. Specifically, it addresses the topics of adaptation, multiobjective optimization, decision making, deception, and…
Machine learning is increasingly recognized as a promising technology in the biological, biomedical, and behavioral sciences. There can be no argument that this technique is incredibly successful in image recognition with immediate…
Empirical studies of graphs have contributed enormously to our understanding of complex systems. Known today as network science, what was originally a theoretical study of graphs has grown into a more scientific exploration of communities…
This essay considers the special character of mathematical reasoning, and draws on observations from interactive theorem proving and the history of mathematics to clarify the nature of formal and informal mathematical language. It proposes…
A challenge in global change biology is to predict how species will respond to future environmental change and to manage these responses. To make such predictions and management actions robust to novel futures, we need to accurately…
We present a list of open questions in mathematical physics. After a historical introduction, a number of problems in a variety of different fields are discussed, with the intention of giving an overall impression of the current status of…
One of the greatest research challenges of this century is to understand the neural basis for how behavior emerges in brain-body-environment systems. To this end, research has flourished along several directions but have predominantly…
The implications of large-scale coherence in biological systems and possible links to quantum theory are only beginning to be explored. Whether quantum-like coherent phenomena are relevant, or even possible at all, at the high temperatures…
Every scientific endeavour consists of (at least) two components: A hypothesis on the one hand and data on the other. There is always a more or less abstract level - some theory, a set of concepts, certain relations of ideas - and a…