Applications Of Mathematics In Models Artificial Neural Networks And Arts

The book shows a very original organization addressing in a non traditional way, but with a systematic approach, to who has an interest in using mathematics in the social sciences. The book is divided in four parts: (a) a historical part, written by Vittorio Capecchi which helps us understand the changes in the relationship between mathematics and sociology by analyzing the mathematical models of Paul F. Lazarsfeld, the model of simulation and artificial societies, models of artificial neural network and considering all the changes in scientific paradigms considered; (b) a part coordinated by Pier Luigi Contucci on mathematical models that consider the relationship between the mathematical models that come from physics and linguistics to arrive at the study of society and those which are born within sociology and economics; (c) a part coordinated by Massimo Buscema analyzing models of artificial neural networks; (d) a part coordinated by Bruno D’Amore which considers the relationship between mathematics and art. The title of the book "Mathematics and Society" was chosen because the mathematical applications exposed in the book allow you to address two major issues: (a) the general theme of technological innovation and quality of life (among the essays are on display mathematical applications to the problems of combating pollution and crime, applications to mathematical problems of immigration, mathematical applications to the problems of medical diagnosis, etc.) (b) the general theme of technical innovation and creativity, for example the art and mathematics section which connects to the theme of creative cities. The book is very original because it is not addressed only to those who are passionate about mathematical applications in social science but also to those who, in different societies, are: (a) involved in technological innovation to improve the quality of life; (b) involved in the wider distribution of technological innovation in different areas of creativity (as in the project "Creative Cities Network" of UNESCO).

This volume of research papers comprises the proceedings of the first International Conference on Mathematics of Neural Networks and Applications (MANNA), which was held at Lady Margaret Hall, Oxford from July 3rd to 7th, 1995 and attended by 116 people. The meeting was strongly supported and, in addition to a stimulating academic programme, it featured a delightful venue, excellent food and accommo dation, a full social programme and fine weather - all of which made for a very enjoyable week. This was the first meeting with this title and it was run under the auspices of the Universities of Huddersfield and Brighton, with sponsorship from the US Air Force (European Office of Aerospace Research and Development) and the London Math ematical Society. This enabled a very interesting and wide-ranging conference pro gramme to be offered. We sincerely thank all these organisations, USAF-EOARD, LMS, and Universities of Huddersfield and Brighton for their invaluable support. The conference organisers were John Mason (Huddersfield) and Steve Ellacott (Brighton), supported by a programme committee consisting of Nigel Allinson (UMIST), Norman Biggs (London School of Economics), Chris Bishop (Aston), David Lowe (Aston), Patrick Parks (Oxford), John Taylor (King's College, Lon don) and Kevin Warwick (Reading). The local organiser from Huddersfield was Ros Hawkins, who took responsibility for much of the administration with great efficiency and energy. The Lady Margaret Hall organisation was led by their bursar, Jeanette Griffiths, who ensured that the week was very smoothly run.

This book provides a thorough summary of the means currently available to the investigators of Artificial Intelligence for making criminal behavior (both individual and collective) foreseeable, and for assisting their investigative capacities. The volume provides chapters on the introduction of artificial intelligence and machine learning suitable for an upper level undergraduate with exposure to mathematics and some programming skill or a graduate course. It also brings the latest research in Artificial Intelligence to life with its chapters on fascinating applications in the area of law enforcement, though much is also being accomplished in the fields of medicine and bioengineering. Individuals with a background in Artificial Intelligence will find the opening chapters to be an excellent refresher but the greatest excitement will likely be the law enforcement examples, for little has been done in that area. The editors have chosen to shine a bright light on law enforcement analytics utilizing artificial neural network technology to encourage other researchers to become involved in this very important and timely field of study.

This volume directly addresses the complexities involved in data mining and the development of new algorithms, built on an underlying theory consisting of linear and non-linear dynamics, data selection, filtering, and analysis, while including analytical projection and prediction. The results derived from the analysis are then further manipulated such that a visual representation is derived with an accompanying analysis. The book brings very current methods of analysis to the forefront of the discipline, provides researchers and practitioners the mathematical underpinning of the algorithms, and the non-specialist with a visual representation such that a valid understanding of the meaning of the adaptive system can be attained with careful attention to the visual representation. The book presents, as a collection of documents, sophisticated and meaningful methods that can be immediately understood and applied to various other disciplines of research. The content is composed of chapters addressing: An application of adaptive systems methodology in the field of post-radiation treatment involving brain volume differences in children; A new adaptive system for computer-aided diagnosis of the characterization of lung nodules; A new method of multi-dimensional scaling with minimal loss of information; A description of the semantics of point spaces with an application on the analysis of terrorist attacks in Afghanistan; The description of a new family of meta-classifiers; A new method of optimal informational sorting; A general method for the unsupervised adaptive classification for learning; and the presentation of two new theories, one in target diffusion and the other in twisting theory.

This book offers an introduction to artificial adaptive systems and a general model of the relationships between the data and algorithms used to analyze them. It subsequently describes artificial neural networks as a subclass of artificial adaptive systems, and reports on the backpropagation algorithm, while also identifying an important connection between supervised and unsupervised artificial neural networks. The book’s primary focus is on the auto contractive map, an unsupervised artificial neural network employing a fixed point method versus traditional energy minimization. This is a powerful tool for understanding, associating and transforming data, as demonstrated in the numerous examples presented here. A supervised version of the auto contracting map is also introduced as an outstanding method for recognizing digits and defects. In closing, the book walks the readers through the theory and examples of how the auto contracting map can be used in conjunction with another artificial neural network, the “spin-net,” as a dynamic form of auto-associative memory.

Social (psychological and sociological) systems present considerable difficulties for modellers due to their complexity, multidimensionality, uncertainty and irreducibility. The book proposes that response functions (MRF) be used as a method of constructing purposeful, credible and integrated social systems' models from data and prior knowledge or information. A semi-empirical, or "grey-box", MRF model may be regarded as a trade-off between a knowledge-based model and a "black-box" (empirical) model. It may embody all the existing knowledge on the process (or a part thereof) and, in addition, it relies on parameterised functions, whose parameters are determined from measurements. Observations contain hidden information on the processes under consideration and one of the main purposes of the proposed method is to "extract" and describe these hidden relationships. Parameterisation offers ways to couple qualitative with quantitative analysis. This combination makes it possible to take into account all the phenomena that are not modelled with the required accuracy through prior knowledge. Although only a simplified picture of the processes is modelled, a "grey box" system model provides some insight into the system processes. These processes are featured by chains of causality, highlighting stressors and variables responsive to stressors. The method of response functions is a nonlinear regression method that implies credible models in the sense that they are identifiable and, hopefully, explain system output behaviour satisfactorily. For case studies the authors have selected the problems usually studied by psychologists and sociologists with statistical procedures, such as investigation of variance and discriminant analysis based on the general linear model or one of its multivariate generalisations (structural equation models, etc.); disordered eating and obesity; subjective well-being and alexithymia. An accompanying CD-ROM contains the demonstration versions of three models that are discussed in the various chapters.The Method of Response Functions in Psychology and Sociology is aimed at Mathematical Psychologists; Mathematical Sociologists; Applied Psychologists; Sociologists and Social Practitioners. It will also be suitable for use on undergraduate as well as graduate and postgraduate courses specializing in these areas.

Uniquely focusing on intersections of social problems, multilevel statistical modeling, and causality; the substantively and methodologically integrated chapters of this book clarify basic strategies for developing and testing multilevel linear models (MLMs), and drawing casual inferences from such models. These models are also referred to as hierarchical linear models (HLMs) or mixed models. The statistical modeling of multilevel data structures enables researchers to combine contextual and longitudinal analyses appropriately. But researchers working on social problems seldom apply these methods, even though the topics they are studying and the empirical data call for their use. By applying multilevel modeling to hierarchical data structures, this book illustrates how the use of these methods can facilitate social problems research and the formulation of social policies. It gives the reader access to working data sets, computer code, and analytic techniques, while at the same time carefully discussing issues of causality in such models. This book innovatively: •Develops procedures for studying social, economic, and human development. • Uses typologies to group (i.e., classify or nest) the level of random macro-level factors. • Estimates models with Poisson, binomial, and Gaussian end points using SAS's generalized linear mixed models (GLIMMIX) procedure. • Selects appropriate covariance structures for generalized linear mixed models. • Applies difference-in-differences study designs in the multilevel modeling of intervention studies. •Calculates propensity scores by applying Firth logistic regression to Goldberger-corrected data. • Uses the Kenward-Rogers correction in mixed models of repeated measures. • Explicates differences between associational and causal analysis of multilevel models. • Consolidates research findings via meta-analysis and methodological critique. •Develops criteria for assessing a study's validity and zone of causality. Because of its social problems focus, clarity of exposition, and use of state-of-the-art procedures; policy researchers, methodologists, and applied statisticians in the social sciences (specifically, sociology, social psychology, political science, education, and public health) will find this book of great interest. It can be used as a primary text in courses on multilevel modeling or as a primer for more advanced texts.

Imagine mathematics, imagine with the help of mathematics, imagine new worlds, new geometries, new forms. This volume in the series “Imagine Math” casts light on what is new and interesting in the relationships between mathematics, imagination and culture. The book opens by examining the connections between modern and contemporary art and mathematics, including Linda D. Henderson’s contribution. Several further papers are devoted to mathematical models and their influence on modern and contemporary art, including the work of Henry Moore and Hiroshi Sugimoto. Among the many other interesting contributions are an homage to Benoît Mandelbrot with reference to the exhibition held in New York in 2013 and the thoughts of Jean-Pierre Bourguignon on the art and math exhibition at the Fondation Cartier in Paris. An interesting part is dedicated to the connections between math, computer science and theatre with the papers by C. Bardainne and A. Mondot. The topics are treated in a way that is rigorous but captivating, detailed but very evocative. This is an all-embracing look at the world of mathematics and culture.