Special Issue "Lie Symmetries at Work in Biology and Medicine"
Deadline for manuscript submissions: 17 December 2020.
Interests: Lie symmetries in classical and quantum mechanics; Lie symmetries in biomathematics; magnetohydrodynamics; bits and pieces of the history of mathematics
Let us ponder those systems of differential equations that are proposed as mathematical models in Life Sciences. Numerical analysis is the most commonly used approach, although arbitrary parameters are in the way, and one has to guess which numbers to replace them with. Indeed, a crunching number approach. One may also look at the asymptotic behavior of solutions. However, to infinity and beyond may dismiss what happens in finite time. Therefore, the next best thing to do is search for Lie symmetries of those systems. They may be trivial, and they may be hidden, but, it is symmetries that allow for both a qualitative and even better quantitative analysis of a model, before going to infinity. This Special Issue invites contributions to show that Lie symmetries are indeed at work in biology and medicine.
V. Torrisi and M.C. Nucci, "Application of Lie group analysis to a mathematical model which describes HIV transmission" in "The Geometrical Study of Differential Equations" (J.A. Leslie and T.P. Hobart, Eds.), A.M.S., Providence (2001) pp. 11-20.
M.C. Nucci, "Using Lie symmetries in epidemiology", Electron. J. Diff. Eqns. Conference 12, pp. 87-101 (2004).
M. Edwards and M.C. Nucci, "Application of Lie group analysis to a core group model for sexually transmitted diseases", J. Nonlinear Math. Phys. 13, pp. 211-230 (2006).
M.C. Nucci and K.M. Tamizhmani, "Lagrangians for biological models", J. Nonlinear Math. Phys. 19, 1250021 (2012).
M.C. Nucci and G. Sanchini, "Symmetries, Lagrangians and Conservation Laws of an Easter Island Population Model", Symmetry 7, pp. 1613-1632 (2015).
Assoc. Prof. Dr. Maria Clara Nucci
Manuscript Submission Information
Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.
Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.
Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.
- Lie symmetries
- Noether symmetries
- Differential equations in Biology and Medicine
The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.
Title: The symmetries of Life
Author: Mario Rasetti
Affiliation: ISI Foundation – Torino, New York
Abstract: Aim of this paper is to argue that in the discussion over the possible existence of a self-consistent scheme for the construction of a virtual ‘machine’ (term which has here a significance analogous to that of the Turing machine, i.e., a formal device which manipulates and evolves ‘states’), able to perform all what living matter – as distinguished from inert matter – can do and inanimate matter cannot, in a formal setting consistent exclusively with the quantum laws, symmetry must play a crucial role. Such symmetry is not simply Lie but bears on more complex, possibly infinite-dimensional algebraic structures. The related theoretical construct - a conceptual framework representing and providing the operational tools of a “Life Machine”, mimicking the features of Life - implies that living matter (and - on equal footing - also intelligence, be it natural or artificial) should be represented by a generalized quantum automaton theory, endowed with a fundamental symmetry. Out of such symmetry, which has deep topological roots, emerges the capacity of the 'objects' of a living world made of quantum entities, to perform complex tasks, e.g., of replicating themselves. The field theoretical automaton that acts as virtual 'life machine' is endowed with the rules of a von Neumann constructor, but quantum and topological & field-theoretical in nature, and its dynamics is constrained by the fundamental symmetry.