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Signs, polynomials, and reaction networks

Many real-world problems are reduced to the study of polynomial equations in the non-negative orthant, and this is in particular the case for models of the abundance of the species in a biochemical reaction network. The polynomial... ver más

31/12/2027

UCPH

2M€

Presupuesto del proyecto: 2M€

Líder del proyecto

KOBENHAVNS UNIVERSITET No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Fecha límite participación Sin fecha límite de participación.

Financiación concedida El organismo HORIZON EUROPE notifico la concesión del proyecto el día 2022-06-16

ERC-2021-COG: ERC CONSOLIDATOR GRANTS Scope:Objectives

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1 Participantes

UCPH

1.78M€ | Lider

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Duración del proyecto: 66 meses Fecha Inicio: 2022-06-16
Fecha Fin: 2027-12-31

Líder del proyecto

KOBENHAVNS UNIVERSITET No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Presupuesto del proyecto 2M€

Fecha límite de participación Sin fecha límite de participación.

Descripción del proyecto Many real-world problems are reduced to the study of polynomial equations in the non-negative orthant, and this is in particular the case for models of the abundance of the species in a biochemical reaction network. The polynomials associated with realistic models are huge, with many parameters and variables, making qualitative analyses, without fixing parameter values, challenging. This results in a mismatch between the needs in biology and the available mathematical tools. The driving aim of this proposal is to narrow the gap by developing novel mathematical theory within applied algebra to ultimately advance in the systematic analysis of biochemical models. Motivated by specific applications in the field of reaction networks, we consider parametrized systems of polynomial equations, and address questions regarding the number of positive solutions, connected components of semi-algebraic sets, and signs of vectors. Specifically, we (1) pursue a generalization of the Descartes' rule of signs to hypersurfaces, to bound the number of negative and of positive connected components of the complement of a hypersurface in the positive orthant, in terms of the signs of the coefficients of the hypersurface; (2) follow a new strategy to prove the Global Attractor Conjecture; and, (3) develop new results to count the number of positive solutions or find parametrizations. The novelty and strength of this proposal resides in the interplay between the advance in the analysis of reaction networks and the development of theory in real algebraic geometry. The research problems are studied in full generality for arbitrary parametrized polynomial systems, but each question has a well-defined purpose, directed to the ultimate goal of having a scanning tool to automatically analyze the models used in systems and synthetic biology. Therefore, this proposal will strengthen the bridge between applied algebra and real-world applications, through the study of reaction networks.

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