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Mathematics at the eve of a historic transition in biology [article]

Guo-Wei Wei
2017 arXiv   pre-print
Indeed, algebras, partial differential equations, group theory, and functional analysis underpin the foundation of quantum mechanism.  ...  A century ago physicists and mathematicians worked in tandem and established quantum mechanism.  ...  For example, cryo-EM is one of the most promising techniques for the structure determination of excessively large biomolecules and relies on mathematical algorithms for image analysis and structure reconstruction  ... 
arXiv:1711.02001v1 fatcat:c7glqysunzhw5cgpoabmuscma4

A computer system for analysis and integrated description of regulation of the molecular-genetic system of interferon induction and action

Olga E. Belova, Vitaly A. Likhoshvai, Sergey I. Bazhan, Vladimir A. Kulichkov
1995 Bioinformatics  
The knowledge base incorporates: (i) a reference database containing experimental data on the structural-functional organization of a biological system; (ii) a dynamic mathematical model for analysis of  ...  A new theoretical approach to elaboration of an information-analytical integrated knowledge base containing data on regulation and function of biological systems is presented.  ...  This research was supported, in part, by the Russian Human Genome grant and by a grant from the US Department of Energy, Health Effects and Life Science Research Division.  ... 
doi:10.1093/bioinformatics/11.2.213 fatcat:nni5jwqc3bffxhzax2otv5plji

Page 245 of Cellular and Molecular Life Sciences Vol. 49, Issue 3 [page]

1993 Cellular and Molecular Life Sciences  
a) Through variable feedback mechanisms and a diversity of cooperative reaction steps biological and especially biochemical systems display a highly non-linear kinetic.  ...  Structured analysis; mathematical modelling; stochastic simulation; cell cycle control; tumor biology; calcium oscillations; signal transduction; Structured Biological Modelling. 1 Introduction In biology  ... 

On algorithmic essence of biology
Об алгоритмической сущности биологии

Janusz Zbigniew Uchmanski
2020 Компьютерные исследования и моделирование  
The degree of the mathematization of biology is low, and attempts to mathematize it are limited to the application of mathematical methods used for the description of physical systems.  ...  such biological structures as trees.  ...  On algorithmic essence of biology References  ... 
doi:10.20537/2076-7633-2020-12-3-641-652 fatcat:nmqhgyuqfbgwffkj7msg6uxx2e

Chemistry across scales: from molecules to cells

S. N Yaliraki, M. Barahona
2007 Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences  
The multiscale models integrate the descriptions at different length and time scales by exploiting the idea of mechanical responses.  ...  The methodologies bring together concepts and tools developed in seemingly unrelated areas of mathematics such as algebraic geometry, model reduction, structural graph theory and non-convex optimization  ...  We thank our research groups, especially Joao Costa, Martin Hemberg and Leonid Paramonov, who have contributed directly to the core of this work. We thank Kim Parker for fruitful discussions.  ... 
doi:10.1098/rsta.2007.0015 pmid:17855216 fatcat:jnz2aaahyjdmbiubwkop6melzu

Complex Multicellular Systems and Immune Competition: New Paradigms Looking for a Mathematical Theory [chapter]

Nicola Bellomo, Guido Forni
2008 Current Topics in Developmental Biology  
Finally, the last part is devoted to research perspectives towards the objective of developing a mathematical-biological theory.  ...  A critique is presented of what has already been achieved towards the above target and what is still missing with special focus on multiscale systems.  ...  Conceptual Lines Towards a Biological Mathematical Theory III. From Hartwell's Theory of Modules to Mathematical Structures IV. A Simple Application and Modelling Perspectives V.  ... 
doi:10.1016/s0070-2153(07)81017-9 pmid:18023739 fatcat:7nnstqmnrzfhxf6lzfy7kccjce

Mechanics in biology: cells and tissues

D. Ambrosi, K. Garikipati, E. Kuhl
2009 Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences  
When we first broached the idea of a Theme Issue on 'Mechanics in biology: cells and tissues', we felt the need to collect the state of the art of this fascinating emerging subject.  ...  We thank the authors for their excellent contributions and the Publishing Editor Suzanne Abbott for her support and patience.  ...  A compelling scientific topic is the mathematics of growth and remodelling of soft biological tissues.  ... 
doi:10.1098/rsta.2009.0122 pmid:19657002 fatcat:ojevwv2z6zeydb5fqilxgq7bd4

The Spectrum of Mechanism-oriented Models for Explanations of Biological Phenomena [article]

C. Anthony Hunt, Ahmet Erdemir, Feilim Mac Gabhann, William W. Lytton, Edward A. Sander, Mark K. Transtrum, Lealem Mulugeta
2018 arXiv   pre-print
The process starts with knowledge about the phenomenon and continues with explanatory and mathematical descriptions.  ...  To encourage improved semantic and methodological clarity, we describe the spectrum of Mechanism-oriented Models being used to develop explanations of biological phenomena.  ...  Technically, the simulation output is a model of solutions to the relational and mathematical descriptions under particular conditions; and the mathematical descriptions are a model of the mechanistic  ... 
arXiv:1801.04909v1 fatcat:kuiful7fnjdqdl5dy22z2stmgm

Blended and more: instructors organize sensemaking opportunities for mathematical equations in different ways when teaching the same scientific phenomenon

Fang Fang Zhao, Linh Chau, Anita Schuchardt
2021 International Journal of STEM Education  
integration of mathematical and scientific understanding.  ...  The few students who succeed often draw on both their mathematical understanding of the equation and their scientific understanding of the phenomenon.  ...  We would like to thank the Schuchardt/Warfa research group in providing feedback and suggestions on the work.  ... 
doi:10.1186/s40594-021-00280-5 fatcat:5kgwm5btq5hbpkd2ejb5kj756i

Physics in a Beautiful ContextReview of: Physical Biology of the Cell, by PhillipsRob, KondevJane, and TheriotJulie; 2009; 807 pp; Garland Science, Taylor & Francis Group (New York, NY); ISBN 978-0-8153-4163-5

Raquell M. Holmes
2010 CBE - Life Sciences Education  
energy states of biological structures.  ...  The careful attention to explicit descriptions of mathematical principles and notations with numerous easy-to-recognize biological examples has me wanting to delve further into the text and examples.  ... 
doi:10.1187/cbe.10-06-0080 pmcid:PMC2931658 fatcat:xmcafwj7cnhyvjaigw5y2bgmlm

Review of "Contact Mechanics and Friction: Physical Principles and Applications" by Valentin L. Popov

Stanislav N Gorb
2011 Beilstein Journal of Nanotechnology  
Biologists have collected an immense amount of information about the structure of such living micromechanical systems and now find themselves in a situation in which a purely descriptive level of research  ...  It covers an amazingly broad spectrum of topics ranging from atomic scale friction, continuum and structural mechanics, materials science, lubrication, adhesion, capillarity and system dynamics.  ...  Biologists have collected an immense amount of information about the structure of such living micromechanical systems and now find themselves in a situation in which a purely descriptive level of research  ... 
doi:10.3762/bjnano.2.7 fatcat:xy2xmsoqx5henccvu4f74kssc4

PREFACE — CHALLENGING MATHEMATICAL PROBLEMS IN CANCER MODELLING

N. BELLOMO, P. K. MAINI
2007 Mathematical Models and Methods in Applied Sciences  
This literature shows that different mathematical structures correspond to different scalings, and that during the time evolution of cancer tissues the structure of the equations also evolves in time due  ...  This topic was also dealt with in previous issues looking for diffusion limit methods 22,11 and is a crucial step towards multiscale modeling by identifying the correct mathematical description of living  ...  This literature shows that different mathematical structures correspond to different scalings, and that during the time evolution of cancer tissues the structure of the equations also evolves in time due  ... 
doi:10.1142/s0218202507002418 fatcat:kweeqxhncngwpg6l5k6rok73ey

The Spectrum of Mechanism-Oriented Models and Methods for Explanations of Biological Phenomena

C. Hunt, Ahmet Erdemir, William Lytton, Feilim Mac Gabhann, Edward Sander, Mark Transtrum, Lealem Mulugeta
2018 Processes  
The process starts with knowledge about the phenomenon and continues with explanatory and mathematical descriptions.  ...  To encourage improved semantic and methodological clarity, we describe the spectrum of Mechanism-oriented Models being used to develop explanations of biological phenomena.  ...  Labs LLC (L.M.); and the UCSF BioSystems group (C.A.H.).  ... 
doi:10.3390/pr6050056 fatcat:42aalorjyrccxo74lypebzkfju

The Layer-Oriented Approach to Declarative Languages for Biological Modeling

Ivan Raikov, Erik De Schutter, Sean Hill
2012 PLoS Computational Biology  
domains and subdomains of computational biology require that models are structured according to the accepted terminology and classification of that domain.  ...  Our approach uses distinct semantic layers to represent the domain-specific biological concepts and the underlying mathematical formalisms.  ...  Designed and implemented the prototype software: IR.  ... 
doi:10.1371/journal.pcbi.1002521 pmid:22615554 pmcid:PMC3355071 fatcat:pjifixntkjaihcjcy4npqdyvsm

Page 2638 of Mathematical Reviews Vol. , Issue 83f [page]

1983 Mathematical Reviews  
It is conceived to comprise mathematical biology on the one hand and biological mathematics on the other.  ...  Author’s summary: “The mathematical structures underlying the theories of organismic sets, (M,R)-systems and molecular sets are shown to be transformed naturally within the theory of categories and functors  ... 
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