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Latent Curve Models: A Structural Equation Perspective
by Kenneth A. Bollen Patrick J. CurranAn effective technique for data analysis in the social sciences The recent explosion in longitudinal data in the social sciences highlights the need for this timely publication. <p><p>Latent Curve Models: A Structural Equation Perspective provides an effective technique to analyze latent curve models (LCMs). This type of data features random intercepts and slopes that permit each case in a sample to have a different trajectory over time. Furthermore, researchers can include variables to predict the parameters governing these trajectories. <p><p>The authors synthesize a vast amount of research and findings and, at the same time, provide original results. The book analyzes LCMs from the perspective of structural equation models (SEMs) with latent variables. While the authors discuss simple regression-based procedures that are useful in the early stages of LCMs, most of the presentation uses SEMs as a driving tool. This cutting-edge work includes some of the authors' recent work on the autoregressive latent trajectory model, suggests new models for method factors in multiple indicators, discusses repeated latent variable models, and establishes the identification of a variety of LCMs.
Latent Factor Analysis for High-dimensional and Sparse Matrices: A particle swarm optimization-based approach (SpringerBriefs in Computer Science)
by Ye Yuan Xin LuoLatent factor analysis models are an effective type of machine learning model for addressing high-dimensional and sparse matrices, which are encountered in many big-data-related industrial applications. The performance of a latent factor analysis model relies heavily on appropriate hyper-parameters. However, most hyper-parameters are data-dependent, and using grid-search to tune these hyper-parameters is truly laborious and expensive in computational terms. Hence, how to achieve efficient hyper-parameter adaptation for latent factor analysis models has become a significant question.This is the first book to focus on how particle swarm optimization can be incorporated into latent factor analysis for efficient hyper-parameter adaptation, an approach that offers high scalability in real-world industrial applications. The book will help students, researchers and engineers fully understand the basic methodologies of hyper-parameter adaptation via particle swarm optimization in latent factor analysis models. Further, it will enable them to conduct extensive research and experiments on the real-world applications of the content discussed.
Latent Markov Models for Longitudinal Data (Chapman & Hall/CRC Statistics in the Social and Behavioral Sciences)
by Francesco Bartolucci Alessio Farcomeni Fulvia PennoniDrawing on the authors' extensive research in the analysis of categorical longitudinal data, this book focuses on the formulation of latent Markov models and the practical use of these models. It demonstrates how to use the models in three types of analysis, with numerous examples illustrating how latent Markov models are used in economics, education, sociology, and other fields. The R and MATLAB routines used for the examples are available on the authors' website.
Latent Variable Modeling Using R: A Step-by-Step Guide
by A. Alexander BeaujeanThis step-by-step guide is written for R and latent variable model (LVM) novices. Utilizing a path model approach and focusing on the lavaan package, this book is designed to help readers quickly understand LVMs and their analysis in R. The author reviews the reasoning behind the syntax selected and provides examples that demonstrate how to analyze data for a variety of LVMs.? Featuring examples applicable to psychology, education, business, and other social and health sciences, minimal text is devoted to theoretical underpinnings. The material is presented without?the use of matrix algebra. As a whole the book prepares readers to write about and interpret LVM results they obtain in R. Each chapter features background information, boldfaced key? terms defined in the glossary, detailed interpretations of R output, descriptions of how to write the analysis of results for publication, a summary, R based practice exercises (with solutions included in the back of the book), and references and related readings. Margin notes help readers better understand LVMs and write their own R syntax. Examples using data from published work across a variety of disciplines demonstrate how to use R syntax for analyzing and interpreting results. R functions, syntax, and the corresponding results appear in gray boxes to help readers quickly locate this material. A unique index helps readers quickly locate R?functions, packages, and datasets. The book and accompanying website at http://blogs.baylor.edu/rlatentvariable/ provides all of the data for the book’s examples and exercises as well as R syntax so readers can replicate the analyses. The book reviews how to enter the data into R, specify the LVMs, and obtain and interpret the estimated parameter values. The book opens with the fundamentals of using R including how to download the program, use functions, and enter and manipulate data. Chapters 2 and 3 introduce and then extend path models to include latent variables. Chapter 4 shows readers how to analyze a latent variable model with data from more than one group, while Chapter 5 shows how to analyze a latent variable model with data from more than one time period. Chapter 6 demonstrates the analysis of dichotomous variables, while Chapter 7 demonstrates how to analyze LVMs with missing data. Chapter 8 focuses on sample size determination using Monte Carlo methods, which can be used with a wide range of statistical models and account for missing data. The final chapter examines hierarchical LVMs, demonstrating both higher-order and bi-factor approaches. The book concludes with three Appendices: a review of common measures of model fit including their formulae and interpretation; syntax for other R latent variable models packages; and solutions for each chapter’s exercises. Intended as a supplementary text for graduate and/or advanced undergraduate courses on latent variable modeling, factor analysis, structural equation modeling, item response theory, measurement, or multivariate statistics taught in psychology, education, human development, business, economics, and social and health sciences, this book also appeals to researchers in these fields. Prerequisites include familiarity with basic statistical concepts, but knowledge of R is not assumed.
Latent Variable Modeling with R
by W. Holmes Finch Brian F. FrenchThis book demonstrates how to conduct latent variable modeling (LVM) in R by highlighting the features of each model, their specialized uses, examples, sample code and output, and an interpretation of the results. Each chapter features a detailed example including the analysis of the data using R, the relevant theory, the assumptions underlying the model, and other statistical details to help readers better understand the models and interpret the results. Every R command necessary for conducting the analyses is described along with the resulting output which provides readers with a template to follow when they apply the methods to their own data. The basic information pertinent to each model, the newest developments in these areas, and the relevant R code to use them are reviewed. Each chapter also features an introduction, summary, and suggested readings. A glossary of the text’s boldfaced key terms and key R commands serve as helpful resources. The book is accompanied by a website with exercises, an answer key, and the in-text example data sets. Latent Variable Modeling with R: -Provides some examples that use messy data providing a more realistic situation readers will encounter with their own data. -Reviews a wide range of LVMs including factor analysis, structural equation modeling, item response theory, and mixture models and advanced topics such as fitting nonlinear structural equation models, nonparametric item response theory models, and mixture regression models. -Demonstrates how data simulation can help researchers better understand statistical methods and assist in selecting the necessary sample size prior to collecting data. -www.routledge.com/9780415832458 provides exercises that apply the models along with annotated R output answer keys and the data that corresponds to the in-text examples so readers can replicate the results and check their work. The book opens with basic instructions in how to use R to read data, download functions, and conduct basic analyses. From there, each chapter is dedicated to a different latent variable model including exploratory and confirmatory factor analysis (CFA), structural equation modeling (SEM), multiple groups CFA/SEM, least squares estimation, growth curve models, mixture models, item response theory (both dichotomous and polytomous items), differential item functioning (DIF), and correspondance analysis. ?The book concludes with a discussion of how data simulation can be used to better understand the workings of a statistical method and assist researchers in deciding on the necessary sample size prior to collecting data.? A mixture of independently developed R code along with available libraries for simulating latent models in R are provided so readers can use these simulations to analyze data using the methods introduced in the previous chapters. Intended for use in graduate or advanced undergraduate courses in latent variable modeling, factor analysis, structural equation modeling, item response theory, measurement, or multivariate statistics taught in psychology, education, human development, and social and health sciences, researchers in these fields also appreciate this book’s practical approach. The book provides sufficient conceptual background information to serve as a standalone text.? Familiarity with basic statistical concepts is assumed but basic knowledge of R is not.
Latent Variable Models and Factor Analysis
by Irini Moustaki Martin Knott David J. BartholomewLatent Variable Models and Factor Analysis provides a comprehensive and unified approach to factor analysis and latent variable modeling from a statistical perspective. This book presents a general framework to enable the derivation of the commonly used models, along with updated numerical examples. Nature and interpretation of a latent variable is also introduced along with related techniques for investigating dependency.This book:Provides a unified approach showing how such apparently diverse methods as Latent Class Analysis and Factor Analysis are actually members of the same family.Presents new material on ordered manifest variables, MCMC methods, non-linear models as well as a new chapter on related techniques for investigating dependency.Includes new sections on structural equation models (SEM) and Markov Chain Monte Carlo methods for parameter estimation, along with new illustrative examples.Looks at recent developments on goodness-of-fit test statistics and on non-linear models and models with mixed latent variables, both categorical and continuous.No prior acquaintance with latent variable modelling is pre-supposed but a broad understanding of statistical theory will make it easier to see the approach in its proper perspective. Applied statisticians, psychometricians, medical statisticians, biostatisticians, economists and social science researchers will benefit from this book.
Latent Variable Models: An Introduction to Factor, Path, and Structural Equation Analysis, Fifth Edition
by A. Alexander Beaujean John C. LoehlinLatent Variable Models: An Introduction to Factor, Path, and Structural Equation Analysis introduces latent variable models by utilizing path diagrams to explain the relationships in the models. This approach helps less mathematically-inclined readers to grasp the underlying relations among path analysis, factor analysis, and structural equation modeling, and to set up and carry out such analyses. This revised and expanded fifth edition again contains key chapters on path analysis, structural equation models, and exploratory factor analysis. In addition, it contains new material on composite reliability, models with categorical data, the minimum average partial procedure, bi-factor models, and communicating about latent variable models. The informal writing style and the numerous illustrative examples make the book accessible to readers of varying backgrounds. Notes at the end of each chapter expand the discussion and provide additional technical detail and references. Moreover, most chapters contain an extended example in which the authors work through one of the chapter’s examples in detail to aid readers in conducting similar analyses with their own data. The book and accompanying website provide all of the data for the book’s examples as well as syntax from latent variable programs so readers can replicate the analyses. The book can be used with any of a variety of computer programs, but special attention is paid to LISREL and R. An important resource for advanced students and researchers in numerous disciplines in the behavioral sciences, education, business, and health sciences, Latent Variable Models is a practical and readable reference for those seeking to understand or conduct an analysis using latent variables.
Latente Klassenanalyse: Eine anwendungsorientierte Einführung mit R (Quantitative Sozialforschung)
by Alice BarthDas Buch bietet eine kompakte, anwendungsorientierte Einführung in die Technik der latenten Klassenanalyse. Grundlagen des Verfahrens sowie Voraussetzungen, praktische Anwendung und Ergebnisinterpretation werden verständlich erläutert. Die Analyse latenter Klassen ist ein statistisches Klassifikationsverfahren, bei dem mehrere kategoriale, manifeste Variablen zu vorher unbeobachteten Gruppen zugeordnet werden. So können z.B. aus einer Vielzahl von Variablen Typologien entwickelt werden. Für die Durchführung der Analysen wird die Open Source-Statistikumgebung R genutzt. Die verwendeten Syntaxbefehle sowie die Ausgabe der Ergebnisse werden erläutert, zusätzlich sind die kommentierte R-Syntax sowie Beispieldaten als elektronisches Zusatzmaterial im GitHub-Repositorium des Buches auf SpringerLink verfügbar. Die in den Beispielen verwendeten Daten haben keine Zugangsbeschränkung und können kostenfrei heruntergeladen werden, um die Analysen selbst nachzuvollziehen.
Lateral Asymmetry in Animals: Predator-Prey Interactions, Dynamics, and Evolution (Ecological Research Monographs)
by Satoshi Takahashi Michio HoriThis book presents the latest research findings on the laterality of fish and other animals. It describes all aspects of lateral asymmetry, including ecology, morphology, behaviour, dynamics of lefty and righty morphs, genetics and evolution, through field observations, experiments and modeling. Lateral asymmetry in scale-eating cichlids gives a simple and beautiful example of negative frequency-dependent selection and resulting oscillation of lefty and righty morph frequencies. Lateral dimorphism is found not only in scale-eaters but in all orders of fish, shrimps and cuttlefish. Lateral asymmetry interacts between species through "cross-predation." Contrary to fish, lateral asymmetry in snails acts as, in most cases, positive frequency-dependent selection and provides deep insights into speciation. Especially, snakes eating righty snails facilitate speciation of lefty snails.As a collaboration work of field ecologists and theoretical biologists, this book covers a variety of topics on lateral asymmetry, which are consistently related to predation. The topics include behavioral ecology, population dynamics, physiology, evolution, genetics, development, learning and neuroscience, statistics, with the subjects of fish, shrimp, prawn, and crayfish, crab, cuttlefish, and snake and snail. Chapters cover new research results such as cuttlefish laterality dynamics, interaction between laterality of snails and snakes, evolution of laterality genetic system, and statistical analysis of laterality oscillation. Readers will appreciate the simplicity and beauty of lateral asymmetry and its profound impact on ecology and evolution.
Lateral Solutions to Mathematical Problems (AK Peters/CRC Recreational Mathematics Series)
by Desmond MacHaleLateral Solutions to Mathematical Problems offers a fresh approach to mathematical problem solving via lateral thinking. Lateral thinking has long been used informally by good mathematics teachers and lecturers to spice up their material and interest their students in the more artistic aspects of mathematical problem solving. In this book, the author attempts to carry out this process formally, with reference to specific, non-technical problems that are easily understood and explained at an intermediate level.This book is appropriate for interested high school students, undergraduates and postgraduates, looking for relief from technical material and also looking for insight into the methodology of mathematics; for teachers and lecturers looking for a novel approach to course material; and anyone interested in both mathematics and lateral thinking.
Latino Stats
by Idelisse Malavé Esti GiordaniAt a time when politics is seemingly ruled by ideology and emotion and when immigration is one of the most contentious topics, it is more important than ever to cut through the rhetoric and highlight, in numbers, the reality of the broad spectrum of Latino life in the United States. Latinos are both the largest and fastest-growing racial/ethnic group in the country, even while many continue to fight for their status as Americans.Respected movement builder and former leader of the Tides Foundation Idelisse Malavé and her daughter, Celeste Giordani--a communications strategist for the Social Transformation Project--distills the profusion of data, identifying the most telling and engaging facts to assemble a portrait of contemporary Latino life with glimpses of the past and future. From politics and the economy to popular culture, the arts, and ideas about race, gender, and family, Latino Stats both catalogs the inequities that plague Latino communities and documents Latinos' growing power and influence on American life.An essential tool for advocates, educators, and policy makers, Latino Stats will be a go-to guidebook for anyone wanting to raise their awareness and increase their understanding of the complex state of our nation.
Lattice Coding for Signals and Networks
by Ram ZamirUnifying information theory and digital communication through the language of lattice codes, this book provides a detailed overview for students, researchers and industry practitioners. It covers classical work by leading researchers in the field of lattice codes and complementary work on dithered quantization and infinite constellations, and then introduces the more recent results on 'algebraic binning' for side-information problems, and linear/lattice codes for networks. It shows how high dimensional lattice codes can close the gap to the optimal information theoretic solution, including the characterisation of error exponents. The solutions presented are based on lattice codes, and are therefore close to practical implementations, with many advanced setups and techniques, such as shaping, entropy-coding, side-information and multi-terminal systems. Moreover, some of the network setups shown demonstrate how lattice codes are potentially more efficient than traditional random-coding solutions, for instance when generalising the framework to Gaussian networks.
Lattice Basis Reduction: An Introduction to the LLL Algorithm and Its Applications (Chapman & Hall Pure and Applied Mathematics)
by Murray R. BremnerFirst developed in the early 1980s by Lenstra, Lenstra, and Lovasz, the LLL algorithm was originally used to provide a polynomial-time algorithm for factoring polynomials with rational coefficients. It very quickly became an essential tool in integer linear programming problems and was later adapted for use in cryptanalysis. This book provides an i
Lattice Boltzmann Method
by A. A. MohamadLattice Boltzmann Method introduces the lattice Boltzmann method (LBM) for solving transport phenomena - flow, heat and mass transfer - in a systematic way. Providing explanatory computer codes throughout the book, the author guides readers through many practical examples, such as: flow in isothermal and non-isothermal lid driven cavities;flow over obstacles;forced flow through a heated channel;conjugate forced convection; andnatural convection.Diffusion and advection-diffusion equations are discussed with applications and examples, and complete computer codes accompany the coverage of single and multi-relaxation-time methods. Although the codes are written in FORTRAN, they can be easily translated to other languages, such as C++. The codes can also be extended with little effort to multi-phase and multi-physics, if the reader knows the physics of the problem. Readers with some experience of advanced mathematics and physics will find Lattice Boltzmann Method a useful and easy-to-follow text. It has been written for those who are interested in learning and applying the LBM to engineering and industrial problems and it can also serve as a textbook for advanced undergraduate or graduate students who are studying computational transport phenomena.
Lattice Boltzmann Method: Fundamentals and Engineering Applications with Computer Codes
by A. A. MohamadThis book introduces readers to the lattice Boltzmann method (LBM) for solving transport phenomena – flow, heat and mass transfer – in a systematic way. Providing explanatory computer codes throughout the book, the author guides readers through many practical examples, such as:• flow in isothermal and non-isothermal lid-driven cavities;• flow over obstacles;• forced flow through a heated channel;• conjugate forced convection; and• natural convection.Diffusion and advection–diffusion equations are discussed, together with applications and examples, and complete computer codes accompany the sections on single and multi-relaxation-time methods. The codes are written in MatLab. However, the codes are written in a way that can be easily converted to other languages, such as FORTRANm Python, Julia, etc. The codes can also be extended with little effort to multi-phase and multi-physics, provided the physics of the respective problem are known.The second edition of this book adds new chapters, and includes new theory and applications. It discusses a wealth of practical examples, and explains LBM in connection with various engineering topics, especially the transport of mass, momentum, energy and molecular species.This book offers a useful and easy-to-follow guide for readers with some prior experience with advanced mathematics and physics, and will be of interest to all researchers and other readers who wish to learn how to apply LBM to engineering and industrial problems. It can also be used as a textbook for advanced undergraduate or graduate courses on computational transport phenomena
Lattice Gas Methods For Partial Differential Equations
by Gary DoolenAlthough the idea of using discrete methods for modeling partial differential equations occurred very early, the actual statement that cellular automata techniques can approximate the solutions of hydrodynamic partial differential equations was first discovered by Frisch, Hasslacher, and Pomeau. Their description of the derivation, which assumes the validity of the Boltzmann equation, appeared in the Physical Review Letters in April 1986. It is the intent of this book to provide some overview of the directions that lattice gas research has taken from 1986 to early 1989.
Lattice Models for Fluctuating Hydrodynamics in Granular and Active Matter (Springer Theses)
by Alessandro ManacordaThis book investigates the common nature of granular and active systems, which is rooted in their intrinsic out-of-equilibrium behavior, with the aim of finding minimal models able to reproduce and predict the complex collective behavior observed in experiments and simulations. Granular and active matter are among the most studied systems in out-of-equilibrium statistical physics. The book guides readers through the derivation of a fluctuating hydrodynamic description of granular and active matter by means of controlled and transparent mathematical assumptions made on a lattice model. It also shows how a macroscopic description can be provided from microscopic requirements, leading to the prediction of collective states such as cooling, swarming, clustering and the transitions among them. The analytical and numerical results shed new light on the physical connection between the local, microscopic properties of few particles and the macroscopic collective motion of the whole system.
Lattice Path Combinatorics and Special Counting Sequences: From an Enumerative Perspective
by Chunwei SongThis book endeavors to deepen our understanding of lattice path combinatorics, explore key types of special sequences, elucidate their interconnections, and concurrently champion the author's interpretation of the “combinatorial spirit”.The author intends to give an up-to-date introduction to the theory of lattice path combinatorics, its relation to those special counting sequences important in modern combinatorial studies, such as the Catalan, Schröder, Motzkin, Delannoy numbers, and their generalized versions. Brief discussions of applications of lattice path combinatorics to symmetric functions and connections to the theory of tableaux are also included. Meanwhile, the author also presents an interpretation of the "combinatorial spirit" (i.e., "counting without counting", bijective proofs, and understanding combinatorics from combinatorial structures internally, and more), hoping to shape the development of contemporary combinatorics.Lattice Path Combinatorics and Special Counting Sequences: From an Enumerative Perspective will appeal to graduate students and advanced undergraduates studying combinatorics, discrete mathematics, or computer science.
Lattice QCD for Nuclear Physics
by Huey-Wen Lin Harvey B. MeyerWith ever increasing computational resources and improvements in algorithms, new opportunities are emerging for lattice gauge theory to address key questions in strongly interacting systems, such as nuclear matter. Calculations today use dynamical gauge-field ensembles with degenerate light up/down quarks and the strange quark and it is possible now to consider including charm-quark degrees of freedom in the QCD vacuum. Pion masses and other sources of systematic error, such as finite-volume and discretization effects, are beginning to be quantified systematically. Altogether, an era of precision calculation has begun and many new observables will be calculated at the new computational facilities. The aim of this set of lectures is to provide graduate students with a grounding in the application of lattice gauge theory methods to strongly interacting systems and in particular to nuclear physics. A wide variety of topics are covered, including continuum field theory, lattice discretizations, hadron spectroscopy and structure, many-body systems, together with more topical lectures in nuclear physics aimed a providing a broad phenomenological background. Exercises to encourage hands-on experience with parallel computing and data analysis are included.
Lattice Quantum Chromodynamics
by Michael Günther Francesco Knechtli Michael PeardonThis book provides an overview of the techniques central to lattice quantum chromodynamics, including modern developments. The book has four chapters. The first chapter explains the formulation of quarks and gluons on a Euclidean lattice. The second chapter introduces Monte Carlo methods and details the numerical algorithms to simulate lattice gauge fields. Chapter three explains the mathematical and numerical techniques needed to study quark fields and the computation of quark propagators. The fourth chapter is devoted to the physical observables constructed from lattice fields and explains how to measure them in simulations. The book is aimed at enabling graduate students who are new to the field to carry out explicitly the first steps and prepare them for research in lattice QCD.
Lattice Sums Then and Now
by J. M. Borwein M. L. Glasser R. C. Mcphedran J. G. Wan I J. ZuckerThe study of lattice sums began when early investigators wanted to go from mechanical properties of crystals to the properties of the atoms and ions from which they were built (the literature of Madelung's constant). A parallel literature was built around the optical properties of regular lattices of atoms (initiated by Lord Rayleigh, Lorentz and Lorenz). For over a century many famous scientists and mathematicians have delved into the properties of lattices, sometimes unwittingly duplicating the work of their predecessors. Here, at last, is a comprehensive overview of the substantial body of knowledge that exists on lattice sums and their applications. The authors also provide commentaries on open questions, and explain modern techniques which simplify the task of finding new results in this fascinating and ongoing field. Lattice sums in one, two, three, four and higher dimensions are covered.
Lattice-Based Public-Key Cryptography in Hardware (Computer Architecture and Design Methodologies)
by Ingrid Verbauwhede Sujoy Sinha RoyThis book describes the efficient implementation of public-key cryptography (PKC) to address the security challenges of massive amounts of information generated by the vast network of connected devices, ranging from tiny Radio Frequency Identification (RFID) tags to powerful desktop computers. It investigates implementation aspects of post quantum PKC and homomorphic encryption schemes whose security is based on the hardness of the ring-learning with error (LWE) problem. The work includes designing an FPGA-based accelerator to speed up computation on encrypted data in the cloud computer. It also proposes a more practical scheme that uses a special module called recryption box to assist homomorphic function evaluation, roughly 20 times faster than the implementation without this module.
Laura Bassi and Science in 18th Century Europe: The Extraordinary Life and Role of Italy's Pioneering Female Professor
by Monique FrizeThis book presents the extraordinary story of a Bolognese woman of the settecento. Laura Maria Caterina Bassi (1711-1778) defended 49 Theses at the University of Bologna on April 17, 1732 and was awarded a doctoral degree on May 12 of the same year. Three weeks before her defense, she was made a member of the Academy of Sciences in Bologna. On June 27 she defended 12 additional Theses. Several of the 61 Theses were on physics and other science topics. Laura was drawn by the philosophy of Newton at a time when most scientists in Europe were still focused on Descartes and Galen. This last set of Theses was to encourage the University of Bologna to provide a lectureship to Laura, which they did on October 29, 1732. Although quite famous in her day, Laura Bassi is unfortunately not remembered much today. This book presents Bassi within the context of the century when she lived and worked, an era where no women could attend university anywhere in the world, and even less become a professor or a member of an academy. Laura was appointed to the Chair of experimental physics in 1776 until her death. Her story is an amazing one. Laura was a mother, a wife and a good scientist for over 30 years. She made the transition from the old science to the new very early on in her career. Her work was centered on real problems that the City of Bologna needed to solve. It was an exciting time of discovery and she was at the edge of it all the way.
Laws and Explanations; Theories and Modal Possibilities (Synthese Library #410)
by Arnold KoslowThe book has two parts: In the first, after a review of some seminal classical accounts of laws and explanations, a new account is proposed for distinguishing between laws and accidental generalizations (LAG). Among the new consequences of this proposal it is proved that any explanation of a contingent generalization shows that the generalization is not accidental. The second part involves physical theories, their modality, and their explanatory power. In particular, it is shown that (1) Each theory has a theoretical implication structure associated with it, such that there are new physical modal operators on these structures and also special modal entities that are in these structures. A special subset of the physical modals, the nomic modals are associated with the laws of theories. (2) The familiar idea that theories always explain laws by deduction of them has to be seriously modified in light of the fact that there are a host of physical theories (including for example, Newtonian Classical mechanics, Hamiltonian, and Lagrangian theory, and probability theory) that we believe are schematic (they do not have any truth value). Nevertheless, we think that there is a kind of non-deductive explanation and generality that they achieve by subsumtion under a schema.
Lazare and Sadi Carnot
by Raffaele Pisano Charles C. GillispieLazare Carnot was the unique example in the history of science of someone who inadvertently owed the scientific recognition he eventually achieved to earlier political prominence. He and his son Sadi produced work that derived from their training as engineering and went largely unnoticed by physicists for a generation or more, even though their respective work introduced concepts that proved fundamental when taken up later by other hands. There was, moreover, a filial as well as substantive relation between the work of father and son. Sadi applied to the functioning of heat engines the analysis that his father had developed in his study of the operation of ordinary machines. Specifically, Sadi's idea of a reversible process originated in the use his father made of geometric motions in the analysis of machines in general. This unique book shows how the two Carnots influenced each other in their work in the fields of mechanics and thermodynamics, and how future generations of scientists have further benefited from their work.