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The discipline of Synthetic Biology has recently emerged at the interface of biology and engineering. The definition of Synthetic Biology has been dynamic over time ever since, which exemplifies that the field is rapidly moving and comprises a broad range of research areas. In the frame of this Research Topic, we focus on Synthetic Biology approaches that aim at rearranging biological parts/ entities in order to generate novel biochemical functions with inherent metabolic activity. This Research Topic encompasses Pathway Engineering in living systems as well as the in vitro assembly of biomolecules into nano- and microscale bioreactors. Both, the engineering of metabolic pathways in vivo, as well as the conceptualization of bioreactors in vitro, require rational design of assembled synthetic pathways and depend on careful selection of individual biological functions and their optimization. Mathematical modelling has proven to be a powerful tool in predicting metabolic flux in living and artificial systems, although modelling approaches have to cope with a limitation in experimentally verified, reliable input variables. This Research Topic puts special emphasis on the vital role of modelling approaches for Synthetic Biology, i.e. the predictive power of mathematical simulations for (i) the manipulation of existing pathways and (ii) the establishment of novel pathways in vivo as well as (iii) the translation of model predictions into the design of synthetic assemblies.

Metabolic Engineering --- reconstitution --- molecular dynamics simulations --- Membrane Transport Proteins --- Protein Engineering --- Protein scaffolds --- metabolite profiling --- Interaction domains --- Metabolic Modelling --- Starch biosynthesis

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The discipline of Synthetic Biology has recently emerged at the interface of biology and engineering. The definition of Synthetic Biology has been dynamic over time ever since, which exemplifies that the field is rapidly moving and comprises a broad range of research areas. In the frame of this Research Topic, we focus on Synthetic Biology approaches that aim at rearranging biological parts/ entities in order to generate novel biochemical functions with inherent metabolic activity. This Research Topic encompasses Pathway Engineering in living systems as well as the in vitro assembly of biomolecules into nano- and microscale bioreactors. Both, the engineering of metabolic pathways in vivo, as well as the conceptualization of bioreactors in vitro, require rational design of assembled synthetic pathways and depend on careful selection of individual biological functions and their optimization. Mathematical modelling has proven to be a powerful tool in predicting metabolic flux in living and artificial systems, although modelling approaches have to cope with a limitation in experimentally verified, reliable input variables. This Research Topic puts special emphasis on the vital role of modelling approaches for Synthetic Biology, i.e. the predictive power of mathematical simulations for (i) the manipulation of existing pathways and (ii) the establishment of novel pathways in vivo as well as (iii) the translation of model predictions into the design of synthetic assemblies.

Metabolic Engineering --- reconstitution --- molecular dynamics simulations --- Membrane Transport Proteins --- Protein Engineering --- Protein scaffolds --- metabolite profiling --- Interaction domains --- Metabolic Modelling --- Starch biosynthesis

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This volume presents easy-to-understand yet surprising properties obtained using topological, geometric and graph theoretic tools in the areas covered by the Geometry Conference that took place in Mulhouse, France from September 7–11, 2014 in honour of Tudor Zamfirescu on the occasion of his 70th anniversary. The contributions address subjects in convexity and discrete geometry, in distance geometry or with geometrical flavor in combinatorics, graph theory or non-linear analysis. Written by top experts, these papers highlight the close connections between these fields, as well as ties to other domains of geometry and their reciprocal influence. They offer an overview on recent developments in geometry and its border with discrete mathematics, and provide answers to several open questions. The volume addresses a large audience in mathematics, including researchers and graduate students interested in geometry and geometrical problems.

Mathematics. --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Convex geometry. --- Discrete geometry. --- Combinatorics. --- Graph theory. --- Convex and Discrete Geometry. --- Graph Theory. --- Global Analysis and Analysis on Manifolds. --- Graph theory --- Convex domains. --- Convex regions --- Convexity --- Graphs, Theory of --- Theory of graphs --- Extremal problems --- Calculus of variations --- Convex geometry --- Point set theory --- Combinatorial analysis --- Topology --- Discrete groups. --- Global analysis. --- Groups, Discrete --- Infinite groups --- Combinatorics --- Algebra --- Mathematical analysis --- Discrete mathematics --- Convex geometry . --- Geometry, Differential --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Geometry --- Combinatorial geometry

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This book presents state-of-the-art results and methodologies in modern global optimization, and has been a staple reference for researchers, engineers, advanced students (also in applied mathematics), and practitioners in various fields of engineering. The second edition has been brought up to date and continues to develop a coherent and rigorous theory of deterministic global optimization, highlighting the essential role of convex analysis. The text has been revised and expanded to meet the needs of research, education, and applications for many years to come. Updates for this new edition include: · Discussion of modern approaches to minimax, fixed point, and equilibrium theorems, and to nonconvex optimization; · Increased focus on dealing more efficiently with ill-posed problems of global optimization, particularly those with hard constraints; · Important discussions of decomposition methods for specially structured problems; · A complete revision of the chapter on nonconvex quadratic programming, in order to encompass the advances made in quadratic optimization since publication of the first edition. · Additionally, this new edition contains entirely new chapters devoted to monotonic optimization, polynomial optimization and optimization under equilibrium constraints, including bilevel programming, multiobjective programming, and optimization with variational inequality constraint. From the reviews of the first edition: The book gives a good review of the topic. …The text is carefully constructed and well written, the exposition is clear. It leaves a remarkable impression of the concepts, tools and techniques in global optimization. It might also be used as a basis and guideline for lectures on this subject. Students as well as professionals will profitably read and use it.—Mathematical Methods of Operations Research, 49:3 (1999).

Mathematics. --- Operations research. --- Decision making. --- Business mathematics. --- Computers. --- Numerical analysis. --- Mathematical models. --- Calculus of variations. --- Calculus of Variations and Optimal Control; Optimization. --- Numeric Computing. --- Mathematical Modeling and Industrial Mathematics. --- Theory of Computation. --- Operation Research/Decision Theory. --- Business Mathematics. --- Convex functions. --- Convex sets. --- Mathematical optimization. --- Nonlinear programming. --- Programming (Mathematics) --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Sets, Convex --- Convex domains --- Set theory --- Functions, Convex --- Functions of real variables --- Electronic data processing. --- Information theory. --- Operations Research/Decision Theory. --- Arithmetic, Commercial --- Business --- Business arithmetic --- Business math --- Commercial arithmetic --- Finance --- Mathematics --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Communication theory --- Communication --- Cybernetics --- ADP (Data processing) --- Automatic data processing --- Data processing --- EDP (Data processing) --- IDP (Data processing) --- Integrated data processing --- Computers --- Office practice --- Automation --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management --- Management decisions --- Choice (Psychology) --- Problem solving --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic brains --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Computer systems --- Machine theory --- Calculators --- Cyberspace --- Models, Mathematical --- Isoperimetrical problems --- Variations, Calculus of --- Decision making