This work collects the contributions presented at the INdAM Workshop “Mathematical modeling and Analysis of degradation and restoration in Cultural Heritage – MACH2019” held in Rome in March 2019. The book is focused on mathematical modeling and simulation techniques with the aim of improving the current strategies of conservation and restoration in cultural heritage, sharing different experiences and approaches. The main topics are: corrosion and sulphation of materials, damage and fractures, stress in thermomechanical systems, contact and adhesion problems, phase transitions and reaction-diffusion models, restoration techniques, additive manufacturing. The final goal is to build a permanent bridge between the experts in cultural heritage and the mathematical community. The work is addressed to experts in cultural heritage and to mathematicians.

This book collects contributions presented at the INdAM Workshop "Mathematical modeling and Analysis of degradation and restoration in Cultural Heritage–MACH2021", held in Rome, Italy in September 2021. The book is focused on mathematical modeling and simulation techniques with the aim of improving the current strategies of conservation and restoration in cultural heritage, sharing different experiences and approaches. The main topics are corrosion and sulphation of materials, damage and fractures, stress in thermomechanical systems, contact and adhesion problems, and phase transitions.

The sheer computing power of modern information technology is changing the face of research not just in science, technology and mathematics, but in humanities and cultural studies too. Recent decades have seen a major shift both in attitudes and deployment of computers, which are now vital and highly effective tools in disciplines where they were once viewed as elaborate typewriters. This revealing volume details the vast array of computing applications that researchers in the humanities now have recourse to, including the dissemination of scholarly information through virtual ‘co-laboratories’, data retrieval, and the modeling of complex processes that contribute to our natural and cultural heritage. One key area covered in this book is the versatility of computers in presenting images and graphics, which is transforming the analysis of data sets and archaeological reconstructions alike. The papers published here are grouped into three broad categories that cover mathematical and computational methods, research developments in information systems, and a detailed portrayal of ongoing work on documenting, restoring and presenting cultural monuments including the temples in Pompeii and the Banteay Chhmar temples of the Angkorian period in present-day Cambodia. Originally presented at a research workshop in Heidelberg, Germany, they reflect the rapidly developing identity of computational humanities as an interdisciplinary field in its own right, as well as demonstrating the breadth of perspectives in this young and vibrant research area.

Transformations: Mathematical Approaches to Culture Change focuses on the application of contemporary mathematical techniques to the study of culture change and formulates problems in archaeology, anthropology, and historiography in such a way that they are susceptible to treatment of a mathematical kind. Mathematical models, extending from the almost purely quantitative methods of physics to the purely verbal conceptual explanations, are described. Emphasis is placed on catastrophe theoretic models that exemplify the use of soft mathematics in situations in which the use of hard quantitative models is not possible. Comprised of 21 chapters, this book begins with an overview of the role of mathematics in theoretical archaeology, followed by a discussion on two general categories of mathematical methods that seem to be suitable for modeling cultural transformations: methods of dynamical systems theory and methods that give greater emphasis on discrete entities and the structural relations or patterns among them. Subsequent chapters deal with the use of mathematics in history; morphogenesis in biological and social systems; simulation of the growth of hierarchies; and logistic trends in Southwest population growth. A reconstruction of political units in the Valley of Mexico during the Toltec period is also presented. This monograph will be of interest to archaeologists, anthropologists, historians, biologists, sociologists, and mathematicians.

This book provides insights into the state of the art of digital cultural heritage using computer graphics, image processing, computer vision, visualization and reconstruction, virtual and augmented reality and serious games. It aims at covering the emergent approaches for digitization and preservation of Cultural Heritage, both in its tangible and intangible facets. Advancements in Digital Cultural Heritage research have been abundant in recent years covering a wide assortment of topics, ranging from visual data acquisition, pre-processing, classification, analysis and synthesis, 3D modelling and reconstruction, semantics and symbolic representation, metadata description, repository and archiving, to new forms of interactive and personalized presentation, visualization and immersive experience provision via advanced computer graphics, interactive virtual and augmented environments, serious games and digital storytelling. Different aspects pertaining to visual computing with regard to tangible (books, images, paintings, manuscripts, uniforms, maps, artefacts, archaeological sites, monuments) and intangible (e.g. dance and performing arts, folklore, theatrical performances) cultural heritage preservation, documentation, protection and promotion are covered, including rendering and procedural modelling of cultural heritage assets, keyword spotting in old documents, drone mapping and airborne photogrammetry, underwater recording and reconstruction, gamification, visitor engagement, animated storytelling, analysis of choreographic patterns, and many more. The book brings together and targets researchers from the domains of computing, engineering, archaeology and the arts, and aims at underscoring the potential for cross-fertilization and collaboration among these communities.

This volume constitutes selected and revised papers presented during the Third International Conference on Trandisciplinary Multispectral Modelling and Cooperation for the Preservation of Cultural Heritage, TMM_CH 2023, held in Athens, Greece, in March 2023. The 17 full papers and 17 short papers presented in ths volume were thoroughly reviewed and selected from 416 submissions. The papers are organized in topical sections on ​scientific innovations in the diagnosis and preservation of cultural heritage; digital heritage a holistic approach; preservation, reuse and reveal of cultural heritage through sustainable bidding and land management, rural and urban development to recapture the world in crisis through culture.

Modeling Students’ Mathematical Modeling Competencies offers welcome clarity and focus to the international research and professional community in mathematics, science, and engineering education, as well as those involved in the sciences of teaching and learning these subjects.