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Multiscale Analysis and Nonlinear Dynamics
by Heinz Georg Schuster Misha Meyer PesensonSince modeling multiscale phenomena in systems biology and neuroscience is a highly interdisciplinarytask, the editor of the book invited experts in bio-engineering, chemistry, cardiology, neuroscience,computer science, and applied mathematics, to provide their perspectives. Each chapter is a window into the current state of the art in the areas of research discussed and the book is intended for advanced researchers interested in recent developments in these fields. While multiscaleanalysis is the major integrating theme of the book, its subtitle does not call for bridging thescales from genes to behavior, but rather stresses the unifying perspective offered by the conceptsreferred to in the title. It is believed that the interdisciplinary approach adopted here will be beneficial for all the above mentioned fields.
Multiscale Analysis of Viscous Flows in Thin Tube Structures (Advances in Mathematical Fluid Mechanics)
by Konstantin Pileckas Grigory PanasenkoThis book presents the analysis of viscous flows in thin tube structures, and develops a multi-scale method for modeling blood flow. For the reader’s convenience, the authors introduce all necessary notions and theorems from functional analysis and the classical theory of the Navier-Stokes equations. The problems of all asymptotic methods used in the book are explained as well, such as the dimension reduction and the boundary layer method. Through several numerical experiments, readers will discover that the proposed methods are more flexible than the theoretically predicted conditions. Multiscale Analysis of Viscous Flows in Thin Tube Structures will be a valuable resource for a wide range of readers, including applied mathematicians, specialists in bio-engineering, and biophysicists.
Multiscale Cancer Modeling (Chapman & Hall/CRC Mathematical Biology Series)
by Thomas S. Deisboeck Georgios S. StamatakosCancer is a complex disease process that spans multiple scales in space and time. Driven by cutting-edge mathematical and computational techniques, in silico biology provides powerful tools to investigate the mechanistic relationships of genes, cells, and tissues. It enables the creation of experimentally testable hypotheses, the integration of dat
Multiscale Forecasting Models
by Lida Mercedes Barba MaggiThis book presents two new decomposition methods to decompose a time series in intrinsic components of low and high frequencies. The methods are based on Singular Value Decomposition (SVD) of a Hankel matrix (HSVD). The proposed decomposition is used to improve the accuracy of linear and nonlinear auto-regressive models. Linear Auto-regressive models (AR, ARMA and ARIMA) and Auto-regressive Neural Networks (ANNs) have been found insufficient because of the highly complicated nature of some time series. Hybrid models are a recent solution to deal with non-stationary processes which combine pre-processing techniques with conventional forecasters, some pre-processing techniques broadly implemented are Singular Spectrum Analysis (SSA) and Stationary Wavelet Transform (SWT). Although the flexibility of SSA and SWT allows their usage in a wide range of forecast problems, there is a lack of standard methods to select their parameters. The proposed decomposition HSVD and Multilevel SVD are described in detail through time series coming from the transport and fishery sectors. Further, for comparison purposes, it is evaluated the forecast accuracy reached by SSA and SWT, both jointly with AR-based models and ANNs.
Multiscale Methods for Fredholm Integral Equations
by Zhongying Chen Charles A. Micchelli Yuesheng XuThe recent appearance of wavelets as a new computational tool in applied mathematics has given a new impetus to the field of numerical analysis of Fredholm integral equations. This book gives an account of the state of the art in the study of fast multiscale methods for solving these equations based on wavelets. The authors begin by introducing essential concepts and describing conventional numerical methods. They then develop fast algorithms and apply these to solving linear, nonlinear Fredholm integral equations of the second kind, ill-posed integral equations of the first kind and eigen-problems of compact integral operators. Theorems of functional analysis used throughout the book are summarised in the appendix. The book is an essential reference for practitioners wishing to use the new techniques. It may also be used as a text, with the first five chapters forming the basis of a one-semester course for advanced undergraduates or beginning graduates.
Multiscale Modeling of Pedestrian Dynamics
by Emiliano Cristiani Benedetto Piccoli Andrea TosinThis book presents mathematical models and numerical simulations of crowd dynamics. The core topic is the development of a new multiscale paradigm, which bridges the microscopic and macroscopic scales taking the most from each of them for capturing the relevant clues of complexity of crowds. The background idea is indeed that most of the complex trends exhibited by crowds are due to an intrinsic interplay between individual and collective behaviors. The modeling approach promoted in this book pursues actively this intuition and profits from it for designing general mathematical structures susceptible of application also in fields different from the inspiring original one. The book considers also the two most traditional points of view: the microscopic one, in which pedestrians are tracked individually and the macroscopic one, in which pedestrians are assimilated to a continuum. Selected existing models are critically analyzed. The work is addressed to researchers and graduate students.
Multiscale Signal Analysis and Modeling
by Ahmed I. Zayed Xiaoping ShenMultiscale Signal Analysis and Modeling presents recent advances in multiscale analysis and modeling using wavelets and other systems. This book also presents applications in digital signal processing using sampling theory and techniques from various function spaces, filter design, feature extraction and classification, signal and image representation/transmission, coding, nonparametric statistical signal processing, and statistical learning theory.
Multistage Separation Processes
by Fouad M. KhouryThe latest edition of a perennial bestseller, Multistage Separation Processes, Fourth Edition provides a clear and thorough presentation of the theoretical foundation, and understanding of the development, evaluation, design, and optimization steps of these processes, from both an academic and industrial perspective. The book's emphasis on starting
Multistage Stochastic Optimization
by Georg Ch. Pflug Alois PichlerMultistage stochastic optimization problems appear in many ways in finance, insurance, energy production and trading, logistics and transportation, among other areas. They describe decision situations under uncertainty and with a longer planning horizon. This book contains a comprehensive treatment of today's state of the art in multistage stochastic optimization. It covers the mathematical backgrounds of approximation theory as well as numerous practical algorithms and examples for the generation and handling of scenario trees. A special emphasis is put on estimation and bounding of the modeling error using novel distance concepts, on time consistency and the role of model ambiguity in the decision process. An extensive treatment of examples from electricity production, asset liability management and inventory control concludes the book.
Multistate Models for the Analysis of Life History Data (Chapman & Hall/CRC Monographs on Statistics and Applied Probability)
by Richard J Cook Jerald F. LawlessMultistate Models for the Analysis of Life History Data provides the first comprehensive treatment of multistate modeling and analysis, including parametric, nonparametric and semiparametric methods applicable to many types of life history data. Special models such as illness-death, competing risks and progressive processes are considered, as well as more complex models. The book provides both theoretical development and illustrations of analysis based on data from randomized trials and observational cohort studies in health research. <P><P>Features <li>Discusses a wide range of applications of multistate models <li>Presents methods for both continuously and intermittently observed life history processes <li>Gives a thorough discussion of conditionally independent censoring and observation processes <li>Discusses models with random effects and joint models for two or more multistate processes <li>Discusses and illustrates software for multistate analysis that is available in R <li>Target audience includes those engaged in research and applications involving multistate models <P><P>Richard Cook is Canada Research Chair in Statistical Methods for Health Research at the University of Waterloo. He has received the Gold Medal of the Statistical Society of Canada and is a Fellow of the American Statistical Association. He collaborates and consults widely on health research and has given many short courses. He and Dr. Lawless previously coauthored the influential book, The Statistical Analysis of Recurrent Events (Springer, 2007). <P><P>Jerald Lawless is Distinguished Professor Emeritus at the University of Waterloo. He is a Fellow of the Royal Society of Canada, a Gold Medal recipient of the Statistical Society of Canada and Fellow of the American Statistical Association. He is a past editor of Technometrics and has collaborated and consulted in numerous areas. He has presented many short courses, with Dr. Cook and individually. <P><P>"The authors of the book are internationally renowned experts in the field of multi-state modeling and have written an extremely clear and comprehensive book on the topic that covers many different aspects, from the fundamental theory to the practical side of analyzing data and interpreting results. The examples are well chosen to represent the most common types of multi-state processes that public health researchers could encounter. The inclusion of software code to illustrate how the models can be fit and interpreted is especially helpful to readers." (Mimi Kim, Albert Einstein College of Medicine)
Multistate Systems Reliability Theory with Applications
by Bent NatvigMost books in reliability theory are dealing with a description of component and system states as binary: functioning or failed. However, many systems are composed of multi-state components with different performance levels and several failure modes. There is a great need in a series of applications to have a more refined description of these states, for instance, the amount of power generated by an electrical power generation system or the amount of gas that can be delivered through an offshore gas pipeline network.This book provides a descriptive account of various types of multistate system, bound-for multistate systems, probabilistic modeling of monitoring and maintenance of multistate systems with components along with examples of applications.Key Features:Looks at modern multistate reliability theory with applications covering a refined description of components and system states.Presents new research, such as Bayesian assessment of system availabilities and measures of component importance.Complements the methodological description with two substantial case studies. Reliability engineers and students involved in the field of reliability, applied mathematics and probability theory will benefit from this book.
Multivariable Analysis
by Mitchell H. KatzNow in its third edition, this highly successful text has been fully revised and updated with expanded sections on cutting-edge techniques including Poisson regression, negative binomial regression, multinomial logistic regression and proportional odds regression. As before, it focuses on easy-to-follow explanations of complicated multivariable techniques. It is the perfect introduction for all clinical researchers. It describes how to perform and interpret multivariable analysis, using plain language rather than complex derivations and mathematical formulae. It focuses on the nuts and bolts of performing research, and prepares the reader to set up, perform and interpret multivariable models. Numerous tables, graphs and tips help to demystify the process of performing multivariable analysis. The text is illustrated with many up-to-date examples from the medical literature on how to use multivariable analysis in clinical practice and in research.
Multivariable Calculus (Pure and Applied Mathematics #64)
by Lawrence J. Corwin Robert J. Szczarba<p>Classroom-tested and lucidly written, Multivariable Calculus gives a thorough and rigorous treatment of differential and integral calculus of functions of several variables. Designed as a junior-level textbook for an advanced calculus course, this book covers a variety of notions,including continuity , differentiation, multiple integrals, line and surface integrals, differential forms, and infinite series. <p>Numerous exercises and examples throughout the book facilitate the student's understanding of important concepts. The level of rigor in this textbook is high; virtually every result is accompanied by a proof. To accommodate teachers' individual needs, the material is organized so that proofs can be deemphasized or even omitted. Linear algebra for n-dimensional Euclidean space is developed when required for the calculus; for example, linear transformations are discussed for the treatment of derivatives. <p>Featuring a detailed discussion of differential forms and Stokes' theorem, <i>Multivariable Calculusis</i> an excellent textbook for junior-level advanced calculus courses and it is also useful for sophomores who have a strong background in single-variable calculus. A two-year calculus sequence or a one-year honor calculus course is required for the most successful use of this textbook. Students will benefit enormously from this book's systematic approach to mathematical analysis, which will ultimately prepare them for more advanced topics in the field.</p>
Multivariable Calculus: Early Transcendentals
by Michael Sullivan Kathleen MirandaMichael Sullivan and Kathleen Miranda have written a contemporary calculus textbook that instructors will respect and students can use. Consistent in its use of language and notation, Sullivan/Miranda’s Calculus offers clear and precise mathematics at an appropriate level of rigor. The authors help students learn calculus conceptually, while also emphasizing computational and problem-solving skills. The book contains a wide array of problems including engaging challenge problems and applied exercises that model the physical sciences, life sciences, economics, and other disciplines. Algebra-weak students will benefit from marginal annotations that help strengthen algebraic understanding, the many references to review material, and extensive practice exercises. Strong media offerings include interactive figures and online homework. Sullivan/Miranda’s Calculus has been built with today’s instructors and students in mind.
Multivariable Calculus with Applications (Undergraduate Texts In Mathematics)
by Maria Shea Terrell Peter D. LaxThis text in multivariable calculus fosters comprehension through meaningful explanations. Written with students in mathematics, the physical sciences, and engineering in mind, it extends concepts from single variable calculus such as derivative, integral, and important theorems to partial derivatives, multiple integrals, Stokes’ and divergence theorems. Students with a background in single variable calculus are guided through a variety of problem solving techniques and practice problems. Examples from the physical sciences are utilized to highlight the essential relationship between calculus and modern science. The symbiotic relationship between science and mathematics is shown by deriving and discussing several conservation laws, and vector calculus is utilized to describe a number of physical theories via partial differential equations. Students will learn that mathematics is the language that enables scientific ideas to be precisely formulated and that science is a source for the development of mathematics.
Multivariable Calculus with Mathematica
by Robert P. Gilbert Michael Shoushani Yvonne OuMultivariable Calculus with Mathematica is a textbook addressing the calculus of several variables. Instead of just using Mathematica to directly solve problems, the students are encouraged to learn the syntax and to write their own code to solve problems. This not only encourages scientific computing skills but at the same time stresses the complete understanding of the mathematics. Questions are provided at the end of the chapters to test the student’s theoretical understanding of the mathematics, and there are also computer algebra questions which test the student’s ability to apply their knowledge in non-trivial ways. Features Ensures that students are not just using the package to directly solve problems, but learning the syntax to write their own code to solve problems Suitable as a main textbook for a Calculus III course, and as a supplementary text for topics scientific computing, engineering, and mathematical physics Written in a style that engages the students’ interest and encourages the understanding of the mathematical ideas
Multivariable Calculus with MATLAB®
by Ronald L. Lipsman Jonathan M. RosenbergThis comprehensive treatment of multivariable calculus focuses on the numerous tools that MATLAB#65533; brings to the subject, as it presents introductions to geometry, mathematical physics, and kinematics. Covering simple calculations with MATLAB#65533;, relevant plots, integration, and optimization, the numerous problem sets encourage practice with newly learned skills that cultivate the reader's understanding of the material. Significant examples illustrate each topic, and fundamental physical applications such as Kepler's Law, electromagnetism, fluid flow, and energy estimation are brought to prominent position. Perfect for use as a supplement to any standard multivariable calculus text, a "mathematical methods in physics or engineering" class, for independent study, or even as the class text in an "honors" multivariable calculus course, this textbook will appeal to mathematics, engineering, and physical science students. MATLAB#65533; is tightly integrated into every portion of this book, and its graphical capabilities are used to present vibrant pictures of curves and surfaces. Readers benefit from the deep connections made between mathematics and science while learning more about the intrinsic geometry of curves and surfaces. With serious yet elementary explanation of various numerical algorithms, this textbook enlivens the teaching of multivariable calculus and mathematical methods courses for scientists and engineers.
Multivariable Dynamic Calculus on Time Scales
by Svetlin G. Georgiev Martin BohnerThis book offers the reader an overview of recent developments of multivariable dynamic calculus on time scales, taking readers beyond the traditional calculus texts. Covering topics from parameter-dependent integrals to partial differentiation on time scales, the book's nine pedagogically oriented chapters provide a pathway to this active area of research that will appeal to students and researchers in mathematics and the physical sciences. The authors present a clear and well-organized treatment of the concept behind the mathematics and solution techniques, including many practical examples and exercises.
Multivariate Analysemethoden: Eine anwendungsorientierte Einführung
by Klaus Backhaus Bernd Erichson Sonja Gensler Rolf Weiber Thomas WeiberWir leben in einer Welt der Daten. Daten allein aber sind wertlos, wenn wir nicht in der Lage sind, aus ihnen Informationen zu gewinnen. Um Informationen aus Daten zu extrahieren, sind Methoden der multivariaten Datenanalyse unerlässlich.Dieses Buch bietet eine leicht verständliche Einführung in die wichtigsten Methoden der multivariaten Datenanalyse. Es ist anwendungsorientiert, erfordert nur wenige Kenntnisse in Mathematik und Statistik, demonstriert die Verfahren mit numerischen Beispielen und veranschaulicht jede Methode anhand eines ausführlichen Fallbeispiels. Für Interessierte werden im Einführungskapitel für alle Verfahren relevante statistische Grundlagen aufgefrischt. Für die 16. Auflage wurden alle Kapitel inkl. Fallbeispielen neu gefasst und mit der aktuellen Version von IBM SPSS gerechnet. Neue, für die anwendungsorientierten Nutzer sinnvolle Auswertungsoptionen wurden ergänzt.Der InhaltEinführung in die empirische Datenanalyse – Regressionsanalyse – VarianzanalyseDiskriminanzanalyse – Logistische Regression – Kontingenzanalyse – FaktorenanalyseClusteranalyse – Conjoint-AnalyseDas Buch wurde 2015 vom Berufsverband Deutscher Markt- und Sozialforscher (BVM) als das Lehrbuch ausgezeichnet, das die deutsche Marktforschungspraxis in den letzten Jahrzehnten nachhaltig geprägt hat. Es ist auch in Englisch und Chinesisch erschienen.Auf der Webseite www.multivariate-methods.info werden weitere Materialien (bspw. Excel-Beispiele, R Code) angeboten, durch die sich die Verfahren noch besser erschließen und vertiefen lassen. Interaktive Flashcards helfen den eigenen Lernfortschritt zu kontrollieren. Mit der Springer Nature Flashcards-App können Sie exklusive Inhalte nutzen und Ihr Wissen testen.
Multivariate Analysemethoden: Eine anwendungsorientierte Einführung
by Klaus Backhaus Bernd Erichson Sonja Gensler Rolf Weiber Thomas WeiberWir leben in einer Welt der Daten. Daten allein aber sind wertlos, wenn wir nicht in der Lage sind, aus ihnen Informationen zu gewinnen. Um Informationen aus Daten zu extrahieren, sind Methoden der multivariaten Datenanalyse unerlässlich.Dieses Buch bietet eine leicht verständliche Einführung in die wichtigsten Methoden der multivariaten Datenanalyse. Es ist anwendungsorientiert, erfordert nur wenige Kenntnisse in Mathematik und Statistik, demonstriert die Verfahren mit numerischen Beispielen und veranschaulicht jede Methode anhand eines ausführlichen Fallbeispiels. Für Interessierte werden im Einführungskapitel für alle Verfahren relevante statistische Grundlagen aufgefrischt. Für die 17. Auflage wurden alle Kapitel überprüft und mit der aktuellen Version von IBM SPSS gerechnet.Der InhaltEinführung in die empirische Datenanalyse – Regressionsanalyse – Varianzanalyse – Diskriminanzanalyse – Logistische Regression – Kontingenzanalyse – Faktorenanalyse – Clusteranalyse – Conjoint-AnalyseDas Buch wurde 2015 vom Berufsverband Deutscher Markt- und Sozialforscher (BVM) als das Lehrbuch ausgezeichnet, das die deutsche Marktforschungspraxis in den letzten Jahrzehnten nachhaltig geprägt hat. Es ist auch in Englisch und Chinesisch erschienen.Auf der Webseite www.multivariate-methods.info werden weitere Materialien (bspw. Excel-Beispiele, R Code) angeboten, durch die sich die Verfahren noch besser erschließen und vertiefen lassen. Interaktive Flashcards helfen den eigenen Lernfortschritt zu kontrollieren. Mit der Springer Nature Flashcards-App können Sie exklusive Inhalte nutzen und Ihr Wissen testen.
Multivariate Analysis: An Application-Oriented Introduction
by Klaus Backhaus Bernd Erichson Sonja Gensler Rolf Weiber Thomas WeiberData can be extremely valuable if we are able to extract information from them. This is why multivariate data analysis is essential for business and science. This book offers an easy-to-understand introduction to the most relevant methods of multivariate data analysis. It is strictly application-oriented, requires little knowledge of mathematics and statistics, demonstrates the procedures with numerical examples and illustrates each method via a case study solved with IBM’s statistical software package SPSS. Extensions of the methods and links to other procedures are discussed and recommendations for application are given. An introductory chapter presents the basic ideas of the multivariate methods covered in the book and refreshes statistical basics which are relevant to all methods.For the 2nd edition, all chapters were checked and calculated using the current version of IBM SPSS.ContentsIntroduction to empirical data analysisRegression analysisAnalysis of varianceDiscriminant analysisLogistic regression Contingency analysisFactor analysisCluster analysisConjoint analysisThe original German version is now available in its 17th edition. In 2015, this book was honored by the Federal Association of German Market and Social Researchers as “the textbook that has shaped market research and practice in German-speaking countries”. A Chinese version is available in its 3rd edition.On the website www.multivariate-methods.info, the authors further analyze the data with Excel and R and provide additional material to facilitate the understanding of the different multivariate methods. In addition, interactive flashcards are available to the reader for reviewing selected focal points. Download the Springer Nature Flashcards App and use exclusive content to test your knowledge.
Multivariate Analysis: An Application-Oriented Introduction
by Klaus Backhaus Rolf Weiber Bernd Erichson Thomas Weiber Sonja GenslerData can be extremely valuable if we are able to extract information from them. This is why multivariate data analysis is essential for business and science. This book offers an easy-to-understand introduction to the most relevant methods of multivariate data analysis. It is strictly application-oriented, requires little knowledge of mathematics and statistics, demonstrates the procedures with numerical examples and illustrates each method via a case study solved with IBM’s statistical software package SPSS. Extensions of the methods and links to other procedures are discussed and recommendations for application are given. An introductory chapter presents the basic ideas of the multivariate methods covered in the book and refreshes statistical basics which are relevant to all methods.ContentsIntroduction to empirical data analysisRegression analysisAnalysis of varianceDiscriminant analysisLogistic regression Contingency analysisFactor analysisCluster analysisConjoint analysisThe original German version is now available in its 16th edition. In 2015, this book was honored by the Federal Association of German Market and Social Researchers as “the textbook that has shaped market research and practice in German-speaking countries”. A Chinese version is available in its 3rd edition.On the website www.multivariate-methods.info, the authors further analyze the data with Excel and R and provide additional material to facilitate the understanding of the different multivariate methods. In addition, interactive flashcards are available to the reader for reviewing selected focal points. Download the Springer Nature Flashcards App and use exclusive content to test your knowledge.
Multivariate Analysis (Wiley Series in Probability and Statistics)
by Kanti V. Mardia John T. Kent Charles C. TaylorMultivariate Analysis Comprehensive Reference Work on Multivariate Analysis and its Applications The first edition of this book, by Mardia, Kent and Bibby, has been used globally for over 40 years. This second edition brings many topics up to date, with a special emphasis on recent developments. A wide range of material in multivariate analysis is covered, including the classical themes of multivariate normal theory, multivariate regression, inference, multidimensional scaling, factor analysis, cluster analysis and principal component analysis. The book also now covers modern developments such as graphical models, robust estimation, statistical learning, and high-dimensional methods. The book expertly blends theory and application, providing numerous worked examples and exercises at the end of each chapter. The reader is assumed to have a basic knowledge of mathematical statistics at an undergraduate level together with an elementary understanding of linear algebra. There are appendices which provide a background in matrix algebra, a summary of univariate statistics, a collection of statistical tables and a discussion of computational aspects. The work includes coverage of: Basic properties of random vectors, copulas, normal distribution theory, and estimation Hypothesis testing, multivariate regression, and analysis of variance Principal component analysis, factor analysis, and canonical correlation analysis Discriminant analysis, cluster analysis, and multidimensional scaling New advances and techniques, including supervised and unsupervised statistical learning, graphical models and regularization methods for high-dimensional data Although primarily designed as a textbook for final year undergraduates and postgraduate students in mathematics and statistics, the book will also be of interest to research workers and applied scientists.
Multivariate Analysis, Design of Experiments, and Survey Sampling (Statistics: A Series of Textbooks and Monographs)
by Subir Ghosh"Describes recent developments and surveys important topics in the areas of multivariate analysis, design of experiments, and survey sampling. Features the work of nearly 50 international leaders."
Multivariate Analysis for Neuroimaging Data
by Atsushi KawaguchiThis book describes methods for statistical brain imaging data analysis from both the perspective of methodology and from the standpoint of application for software implementation in neuroscience research. These include those both commonly used (traditional established) and state of the art methods. The former is easier to do due to the availability of appropriate software. To understand the methods it is necessary to have some mathematical knowledge which is explained in the book with the help of figures and descriptions of the theory behind the software. In addition, the book includes numerical examples to guide readers on the working of existing popular software. The use of mathematics is reduced and simplified for non-experts using established methods, which also helps in avoiding mistakes in application and interpretation. Finally, the book enables the reader to understand and conceptualize the overall flow of brain imaging data analysis, particularly for statisticians and data-scientists unfamiliar with this area. The state of the art method described in the book has a multivariate approach developed by the authors’ team. Since brain imaging data, generally, has a highly correlated and complex structure with large amounts of data, categorized into big data, the multivariate approach can be used as dimension reduction by following the application of statistical methods. The R package for most of the methods described is provided in the book. Understanding the background theory is helpful in implementing the software for original and creative applications and for an unbiased interpretation of the output. The book also explains new methods in a conceptual manner. These methodologies and packages are commonly applied in life science data analysis. Advanced methods to obtain novel insights are introduced, thereby encouraging the development of new methods and applications for research into medicine as a neuroscience.