Author: Publisher:
ISBN: 9814479454
Category :
Languages : en
Pages :
Book Description
Geometries of Nature, Living Systems and Human Cognition
Author: Geometries of Nature, Living Systems and Human Cognition
Author: Luciano BoiPublisher: World Scientific Publishing Company Incorporated
ISBN: 9789812564740
Category : Science
Languages : en
Pages : 419
Book Description
Intended to provide a study of some mathematical and physical subjects which are at the core of developments in the natural and living sciences. This book aims to show that an accomplished movement of geometrisation has enabled the discovery of a varietyof structures and behaviors in physical reality and in living matter.
New Trends in Geometry
Author: Claudio BartocciPublisher: World Scientific
ISBN: 1908977884
Category : Mathematics
Languages : en
Pages : 328
Book Description
This volume focuses on the interactions between mathematics, physics, biology and neuroscience by exploring new geometrical and topological modelling in these fields. Among the highlights are the central roles played by multilevel and scale-change approaches in these disciplines. The integration of mathematics with physics, as well as molecular and cell biology and the neurosciences, will constitute the new frontier of 21st century science, where breakthroughs are more likely to span across traditional disciplines. Contents:Geometry, Theoretical Physics and Cosmology:The Emergence of Algebraic Geometry in Contemporary Physics (Claudio Bartocci & Ugo Bruzzo)Quantum Gravity and Quantum Geometry (Mauro Carfora)The de Sitter and Anti-de Sitter Universes (Ugo Moschella)Geometry and Topology in Relativistic Cosmology (Jean-Pierre Luminet)The Problem of Space in Neurosciences:Space Coding in the Cerebral Cortex (Leonardo Fogassi)Action and Space Representation (Anna Berti & Alessia Folegatti)The Space Representations in the Brain (Claudio Brozzoli & Alessandro Farnè)The Enactive Constitution of Space (Carrado Sinigaglia & Chiara Brozzo)Geometrical Methods in the Biological Sciences:Causes and Symmetries in Natural Sciences: The Continuum and the Discrete in Mathematical Modelling (Francis Bailly & Giuseppe Longo)Topological Invariants of Geometrical Surfaces and the Protein Folding Problem (Riccardo Broglia)The Geometry of Dense Packing and Biological Structures (Jean-François Sadoc)When Topology and Biology Meet ‘For Life’: The Interactions Between Topological Forms and Biological Functions (Luciano Boi) Readership: Students and researchers in mathematical sciences at graduate level. Keywords:Geometrical Models;Spatial Perception;Mirror Neurons;Quantum Field Theory;String TheoryKey Features:Multidisciplinary approachDistinguished contributors working in different research areasNovel perspectives on the interactions between mathematics and biology
Complexity and Emergence
Author: Sergio AlbeverioPublisher: Springer Nature
ISBN: 3030957039
Category : Mathematics
Languages : en
Pages : 208
Book Description
This book includes contributions about mathematics, physics, philosophy of science, economics and finance and resulted from the Summer School “Complexity and Emergence: Ideas, Methods, with a Special Attention to Economics and Finance” held in Lake Como School of Advanced Studies, on 22–27 July 2018. The aim of the book is to provide useful instruments from the theory of complex systems, both on the theoretical level and the methodological ones, profiting from knowledge and insights from leading experts of different communities. It moves from the volume editors' conviction that to achieve progress in understanding socio-economical as well as ecological problems of our complex word such preparation is needed, together with a critical reconsideration of our basic scientific and economical approach. The potential readers are primarily master and doctorate students of mathematics, information sciences, theoretical physics and economics, as well as research workers in those areas, who want to enlarge their spectrum of knowledge towards the area of complexity and emergence. Since ideas and methods of the theory of complex systems also apply to other areas (from engineering and architecture to biology and medicine, e.g.), students and research workers from those areas will also profit from this book.
Philosophical and Scientific Perspectives on Downward Causation
Author: Michele Paolini PaolettiPublisher: Taylor & Francis
ISBN: 1317271440
Category : Philosophy
Languages : en
Pages : 334
Book Description
Downward causation plays a fundamental role in many theories of metaphysics and philosophy of mind. It is strictly connected with many topics in philosophy, including but not limited to: emergence, mental causation, the nature of causation, the nature of causal powers and dispositions, laws of nature, and the possibility of ontological and epistemic reductions. Philosophical and Scientific Perspectives on Downward Causation brings together experts from different fields—including William Bechtel, Stewart Clark and Tom Lancaster, Carl Gillett, John Heil, Robin F. Hendry, Max Kistler, Stephen Mumford and Rani Lill Anjum —who delve into classic and unexplored lines of philosophical inquiry related to downward causation. It critically assesses the possibility of downward causation given different ontological assumptions and explores the connection between downward causation and the metaphysics of causation and dispositions. Finally, it presents different cases of downward causation in empirical fields such as physics, chemistry, biology and the neurosciences. This volume is both a useful introduction and a collection of original contributions on this fascinating and hotly debated philosophical topic.
Fractal Geometry, Complex Dimensions and Zeta Functions
Author: Michel L. LapidusPublisher: Springer Science & Business Media
ISBN: 0387352082
Category : Mathematics
Languages : en
Pages : 460
Book Description
Number theory, spectral geometry, and fractal geometry are interlinked in this study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary. The Riemann hypothesis is given a natural geometric reformulation in context of vibrating fractal strings, and the book offers explicit formulas extended to apply to the geometric, spectral and dynamic zeta functions associated with a fractal.
Fractal Geometry, Complex Dimensions and Zeta Functions
Author: Michel LapidusPublisher: Springer Science & Business Media
ISBN: 1461421756
Category : Mathematics
Languages : en
Pages : 583
Book Description
Number theory, spectral geometry, and fractal geometry are interlinked in this in-depth study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary. Throughout Geometry, Complex Dimensions and Zeta Functions, Second Edition, new results are examined and a new definition of fractality as the presence of nonreal complex dimensions with positive real parts is presented. The new final chapter discusses several new topics and results obtained since the publication of the first edition.
What is Geometry?
Author: Giandomenico SicaPublisher: Polimetrica s.a.s.
ISBN: 8876990305
Category : Mathematics
Languages : en
Pages : 270
Book Description
Science
Author: Bertrand ZavidoviquePublisher: World Scientific
ISBN: 9814383287
Category : Science
Languages : en
Pages : 328
Book Description
The book gathers articles that were exposed during the seventh edition of the Workshop ?Data Analysis in Astronomy?. It illustrates a current trend to search for common expressions or models transcending usual disciplines, possibly associated with some lack in the Mathematics required to model complex systems. In that, data analysis would be at the epicentre and a key facilitator of some current integrative phase of Science.It is all devoted to the question of ?representation in Science?, whence its name, IMAGe IN AcTION, and main thrusts Part A: Information: data organization and communication, Part B: System: structure and behaviour, Part C: Data ? System representation. Such a classification makes concepts as ?complexity? or ?dynamics? appear like transverse notions: a measure among others or a dimensional feature among others.Part A broadly discusses a dialogue between experiments and information, be information extracted-from or brought-to experiments. The concept is fundamental in statistics and tailors to the emergence of collective behaviours. Communication then asks for uncertainty considerations ? noise, indeterminacy or approximation ? and its wider impact on the couple perception-action. Clustering being all about uncertainty handling, data set representation appears not to be the only solution: Introducing hierarchies with adapted metrics, a priori pre-improving the data resolution are other methods in need of evaluation. The technology together with increasing semantics enables to involve synthetic data as simulation results for the multiplication of sources.Part B plays with another couple important for complex systems: state vs. transition. State-first descriptions would characterize physics, while transition-first would fit biology. That could stem from life producing dynamical systems in essence. Uncertainty joining causality here, geometry can bring answers: stable patterns in the state space involve constraints from some dynamics consistency. Stable patterns of activity characterize biological systems too. In the living world, the complexity ? i.e. a global measure on both states and transitions ? increases with consciousness: this might be a principle of evolution. Beside geometry or measures, operators and topology have supporters for reporting on dynamical systems. Eventually targeting universality, the category theory of topological thermodynamics is proposed as a foundation of dynamical system understanding.Part C details examples of actual data-system relations in regards to explicit applications and experiments. It shows how pure computer display and animation techniques link models and representations to ?reality? in some ?concrete? virtual, manner. Such techniques are inspired from artificial life, with no connection to physical, biological or physiological phenomena! The Virtual Observatory is the second illustration of the evidence that simulation helps Science not only in giving access to more flexible parameter variability, but also due to the associated data and method storing-capabilities. It fosters interoperability, statistics on bulky corpuses, efficient data mining possibly through the web etc. in short a reuse of resources in general, including novel ideas and competencies. Other examples deal more classically with inverse modelling and reconstruction, involving Bayesian techniques or chaos but also fractal and symmetry.
When Form Becomes Substance
Author: Luciano BoiPublisher: Springer Nature
ISBN: 3030831256
Category : Science
Languages : en
Pages : 607
Book Description
This interdisciplinary volume collects contributions from experts in their respective fields with as common theme diagrams. Diagrams play a fundamental role in the mathematical visualization and philosophical analysis of forms in space. Some of the most interesting and profound recent developments in contemporary sciences, whether in topology, geometry, dynamic systems theory, quantum field theory or string theory, have been made possible by the introduction of new types of diagrams, which, in addition to their essential role in the discovery of new classes of spaces and phenomena, have contributed to enriching and clarifying the meaning of the operations, structures and properties that are at the heart of these spaces and phenomena. The volume gives a closer look at the scope and the nature of diagrams as constituents of mathematical and physical thought, their function in contemporary artistic work, and appraise, in particular, the actual importance of the diagrams of knots, of braids, of fields, of interaction, of strings in topology and geometry, in quantum physics and in cosmology, but also in theory of perception, in plastic arts and in philosophy. The editors carefully curated this volume to be an inspiration to students and researchers in philosophy, phenomenology, mathematics and the sciences, as well as artists, musicians and the general interested audience.
