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1
Nicholls, Sarah Louise. The development of simple mathematical models to describe the mechanical behaviour of a human muscle-tendon complex. Birmingham: University of Birmingham, 1994.
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Aliev, Vagif, and Dmitriy Chistov. Business planning using the Project Expert program (full course). ru: INFRA-M Academic Publishing LLC., 2022. http://dx.doi.org/10.12737/1248243.
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The tutorial uses practical examples to describe the technology of developing and analyzing acceptable investment projects, as well as developing business plans for these projects using the popular Project Expert 7 program.
It is intended for students studying in the areas of "Finance and credit", "Accounting, analysis and audit", "Taxes and taxation", "Crisis management", "Mathematical methods in economics", teachers and graduate students of economic universities, heads of enterprises, organizations and firms involved in the preparation of expertise and implementation of business-plans or preparation of scientifically based recommendations on the acceptability of a ready-made investment project and business plan, including for advanced training courses in the direction of "Development and analysis of investment projects using modern information technologies".
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Dubanov, Aleksandr. Computer simulation in pursuit problems. ru: Publishing Center RIOR, 2022. http://dx.doi.org/10.29039/02102-6.
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Currently, computer simulation in virtual reality systems has a special status. In order for a computer model to meet the requirements of the tasks it models, it is necessary that the mathematical apparatus correctly describe the simulated phenomena.
In this monograph, the simulation of pursuit problems is carried out. An adaptive modeling of the behavior of both pursuers and targets is carried out. An iterative calculation of the trajectories of the participants in the pursuit problem is carried out.
The main attention is paid to the methods of pursuit and parallel rendezvous. These methods are taken as the basis of the study and are modified in the future.
The scientific novelty of the study is the iterative calculation of the trajectories of the participants in the pursuit task when moving at a constant speed, while following the predicted trajectories.
The predicted trajectories form a one-parameter network of continuous lines of the first order of smoothness. The predicted trajectories are calculated taking into account the restrictions on the curvature of the participant in the pursuit problem.
The fact of restrictions on curvature can be interpreted as restrictions on the angular frequency of rotation of the object of the pursuit problem.
Also, the novelty is the calculation of the iterative process of group pursuit of multiple targets, when targets are hit simultaneously or at specified intervals. The calculation of the parameters of the network of predicted trajectories is carried out with a curvature variation in order to achieve the desired temporal effect.
The work also simulates the adaptive behavior of the pursuer and the target. The principle of behavior can be expressed on the example of a pursuer with a simple phrase: "You go to the left - I go to the left." This happens at each iteration step in terms of choosing the direction of rotation. For the purpose, the principle of adaptive behavior is expressed by the phrase: "You go to the left - I go to the right."
The studies, algorithms and models presented in the monograph can be in demand in the design of autonomously controlled unmanned aerial vehicles with elements of artificial intelligence.
The task models in the monograph are supplemented with many animated images, where you can see the research process.
Also, the tasks have an implementation in a computer mathematics system and can be transferred to virtual reality systems if necessary.
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Shabel, Lisa. A Priority and Application: Philosophy of Mathematics in the Modern Period. Edited by Stewart Shapiro. Oxford University Press, 2009. http://dx.doi.org/10.1093/oxfordhb/9780195325928.003.0002.
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The state of modern mathematical practice called for a modern philosopher of mathematics to answer two interrelated questions. Given that mathematical ontology includes quantifiable empirical objects, how to explain the paradigmatic features of pure mathematical reasoning: universality, certainty, necessity. And, without giving up the special status of pure mathematical reasoning, how to explain the ability of pure mathematics to come into contact with and describe the empirically accessible natural world. The first question comes to a demand for apriority: a viable philosophical account of early modern mathematics must explain the apriority of mathematical reasoning. The second question comes to a demand for applicability: a viable philosophical account of early modern mathematics must explain the applicability of mathematical reasoning. This article begins by providing a brief account of a relevant aspect of early modern mathematical practice, in order to situate philosophers in their historical and mathematical context.
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Henderson, Andrea. Introduction. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198809982.003.0001.
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Victorian England witnessed a reconception of mathematics as a formal rather than a referential practice—as a means for describing relationships rather than quantities. The value of a mathematical claim lay not in its capacity to describe the world but its internal coherence. Victorian mathematics thus contributed to the development of liberal capitalism by justifying abstraction: liberals proclaimed that formal consistency was the foundation of a rational, equitable order, and marginalist economists insisted that value was not inherent but relational, and made economics a branch of mathematics. Marx, meanwhile, profited from the insights of mathematical formalism even as he resisted its mystification. In its privileging of formal relationships Victorian mathematics redefined all fields around it, even redefining Kantian formalism such that mathematics and art came to share the same virtues: they couldn’t claim to offer truths about the world itself but they insisted that they told a deeper, formal truth.
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Hot or Cold?: Describe and Compare Measurable Attributes. Rosen Publishing Group, 2013.
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Kadunz, Gert, and Adalira Saénz-Ludlow. Semiotics As a Tool for Learning Mathematics: How to Describe the Construction, Visualisation, and Communication of Mathematical Concepts. BRILL, 2016.
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Semiotics As a Tool for Learning Mathematics: How to Describe the Construction, Visualisation, and Communication of Mathematical Concepts. BRILL, 2016.
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Henderson, Andrea. Algebraic Art. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198809982.001.0001.
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Algebraic Art explores the invention of a peculiarly Victorian account of the nature and value of aesthetic form, and it traces that account to a surprising source: mathematics. The nineteenth century was a moment of extraordinary mathematical innovation, witnessing the development of non-Euclidean geometry, the revaluation of symbolic algebra, and the importation of mathematical language into philosophy. All these innovations sprang from a reconception of mathematics as a formal rather than a referential practice—as a means for describing relationships rather than quantities. For Victorian mathematicians, the value of a claim lay not in its capacity to describe the world but its internal coherence. This concern with formal structure produced a striking convergence between mathematics and aesthetics: geometers wrote fables, logicians reconceived symbolism, and physicists described reality as consisting of beautiful patterns. Artists, meanwhile, drawing upon the cultural prestige of mathematics, conceived their work as a “science” of form, whether as lines in a painting, twinned characters in a novel, or wave-like stress patterns in a poem. Avant-garde photographs and paintings, fantastical novels like Flatland and Lewis Carroll’s children’s books, and experimental poetry by Swinburne, Rossetti, and Patmore created worlds governed by a rigorous internal logic even as they were pointedly unconcerned with reference or realist protocols. Algebraic Art shows that works we tend to regard as outliers to mainstream Victorian culture were expressions of a mathematical formalism that was central to Victorian knowledge production and that continues to shape our understanding of the significance of form.
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Budd, Chris. Climate, Chaos and Covid: How Mathematical Models Describe the Universe. World Scientific Publishing Co Pte Ltd, 2022.
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Grekousis, George. Spatial Analysis Theory and Practice: Describe - Explore - Explain Through GIS. University of Cambridge ESOL Examinations, 2020.
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Spatial Analysis Theory and Practice: Describe - Explore - Explain Through GIS. University of Cambridge ESOL Examinations, 2020.
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Biasotti, Silvia, Bianca Falcidieno, Michela Spagnuolo, and Daniela Giorgi. Mathemtcl Tools Shape Analys Descrptn: Mathematical Tools for Shape Analysis and Description. Morgan & Claypool Publishers, 2014.
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Doctor, Bearded. BASIC MATH Describe Count on and Back: Extend Number Sequences, Fun Learn Mathematics for Kids. Independently Published, 2020.
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Thevenot, Catherine, and Pierre Barrouillet. Arithmetic Word Problem Solving and Mental Representations. Edited by Roi Cohen Kadosh and Ann Dowker. Oxford University Press, 2014. http://dx.doi.org/10.1093/oxfordhb/9780199642342.013.043.
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Arithmetic word problem solving is considered as a testing ground of mathematical achievement, but remains the area of mathematics in which students experience the greatest difficulties. In this chapter, we review recent theoretical and empirical work that could shed light on these difficulties. We first describe the most frequently used classifications of word problems and assess their psychological relevance. Then, we present the main hypotheses concerning the nature of the representations involved in word problems. Some theories assume that problem solving relies on the instantiation of schemas abstracted from recurrently encountered problems of the same relational structure, whereas other theories propose that ad hoc transient mental representations are constructed for each problem encountered. A third part is devoted to the impact of individual differences in calculation, reading comprehension, and more general factors, such as working memory capacity. Finally, we address the issue of enhancing performance in word problem solving.
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Ingram, Jenni. Patterns in Mathematics Classroom Interaction. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198869313.001.0001.
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Classroom interaction has a significant influence on teaching and learning mathematics. It is through interaction that we solve problems, build ideas, make connections, and develop our understanding. This book aims to describe, exemplify, and consider the implications of patterns and structures of mathematics classroom interaction. Drawing on a Conversation Analytic approach, the book examines how the structures of interactions between teachers and students influence, enable, and constrain the mathematics that students are experiencing and learning in school. In particular, the book considers the handling of difficulties or errors and the consequences on both the mathematics students are learning, and the learning of this mathematics. The various roles of silence and the treatment of knowledge and understanding within everyday classroom interactions also reveal the nature of mathematics as it is taught in different classrooms. The book also draws on examples of students explaining, reasoning, and justifying as they interact to examine how the structures of classroom interaction support students to develop these discursive practices. Understanding how these patterns and structures affect students’ experiences in the classroom enables us to use and develop practices that can support students’ learning. This reflexive relationship between these structures of interactions and student actions and learning is central to the issues explored in this book, alongside the implications these may have for teachers’ practice, and students’ learning.
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Bianconi, Ginestra. The Mathematical Definition. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198753919.003.0005.
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This chapter provides the mathematical definition of multilayer networks and it is of fundamental importance for the rest of the book. The mathematical definition of multilayer networks is given in full generality and subsequently applied to specific types of multilayer networks including multiplex networks, multi-slice networks and networks of networks, motivating the discussion with examples and applications. The fundamental terminology used in multilayer networks is here introduced, including replica nodes, supernetworks and the supra-adjacency matrix. Additionally, this chapter describes the most efficient way to store a multilayer network dataset using a Multilayer Network Edgelist. Although this chapter focuses mostly on a matrix formalism to describe multilayer networks, a paragraph is devoted to the tensorial formalism for studying multilayer networks.
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Janiak, Andrew, ed. Space. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780199914104.001.0001.
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This volume chronicles the development of philosophical conceptions of space from early antiquity through the medieval period to the early modern era, ending with Kant. The chapters describe the interactions between philosophy at different moments in history and various other disciplines, especially geometry, optics, and natural science more generally. Figures from the history of mathematics, science, and philosophy are discussed, including Euclid, Plato, Aristotle, Proclus, Ibn al-Haytham, Nicole Oresme, Kepler, Descartes, Newton, Leibniz, Berkeley, and Kant. A series of shorter essays, or Reflections, characterize perspectives on space found in the disciplines of ecology, mathematics, sculpture, neuroscience, cultural geography, art history, and the history of science.
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Gebuis, Titia, and Bert Reynvoet. Number Representations and their Relation with Mathematical Ability. Edited by Roi Cohen Kadosh and Ann Dowker. Oxford University Press, 2014. http://dx.doi.org/10.1093/oxfordhb/9780199642342.013.035.
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In this chapter we review research on the processes that underlie the development of mathematical abilities. It is proposed that numerical deficiencies might arise from domain specific problems. The approximate number system that supports reasoning with non-symbolic numbers, on the one hand, and the symbolic number system on the other hand were put forth as possible candidates. To gain insight into the two different systems, we will describe the development of non-symbolic and symbolic number processing and introduce the two main theories about numerical deficiencies: the approximate number system and the access deficit hypothesis. The paradigms used to study both accounts differ in several ways and are of importance for research on the relation between non-symbolic and symbolic number and mathematical abilities. Then, we will review how the studies investigating both accounts relate to two different sets of developmental models that describe the neural representation of number.
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Healey, Richard. Entanglement. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198714057.003.0003.
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Often a pair of quantum systems may be represented mathematically (by a vector) in a way each system alone cannot: the mathematical representation of the pair is said to be non-separable: Schrödinger called this feature of quantum theory entanglement. It would reflect a physical relation between a pair of systems only if a system’s mathematical representation were to describe its physical condition. Einstein and colleagues used an entangled state to argue that its quantum state does not completely describe the physical condition of a system to which it is assigned. A single physical system may be assigned a non-separable quantum state, as may a large number of systems, including electrons, photons, and ions. The GHZ state is an example of an entangled polarization state that may be assigned to three photons.
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Maddy, Penelope. Three Forms of Naturalism. Edited by Stewart Shapiro. Oxford University Press, 2009. http://dx.doi.org/10.1093/oxfordhb/9780195325928.003.0013.
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This article plans to sketch the outlines of the Quinean point of departure, then to describe how Burgess and this article differ from this, and from each other, especially on logic and mathematics. Though this discussion touches on the work of only these three among the many recent “naturalists,” the moral of the story must be that “naturalism,” even restricted to its Quinean and post-Quinean incarnations, is a more complex position, with more subtle variants, than is sometimes supposed.
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Botsford, Louis W., J. Wilson White, and Alan Hastings. Population Dynamics for Conservation. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198758365.001.0001.
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This book is a quantitative exposition of our current understanding of the dynamics of plant and animal populations, with the goal that readers will be able to understand, and participate in the management of populations in the wild. The book uses mathematical models to establish the basic principles of population behaviour. It begins with a philosophical approach to mathematical models of populations. It then progresses from a description of models with a single variable, abundance, to models that describe changes in the abundance of individuals at each age, then similar models that describe populations in terms of the abundance over size, life stage, and space. The book assumes a knowledge of basic calculus, but explains more advanced mathematical concepts such as partial derivatives, matrices, and random signals, as it makes use of them. The book explains the basis of the principles underlying important population processes, such as the mechanism that allow populations to persist, rather than go extinct, the way in which populations respond to variable environments, and the origin of population cycles.The next two chapters focus on application of the principles of population dynamics to manage for the prevention of extinction, as well as the management of fisheries for sustainable, high yields. The final chapter recapitulates how different population behaviors arise in situations with different levels of density dependence and replacement (the potential lifetime reproduction per individual), and how variability arises at different time scales set by a species’ life history.
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Peach, Ken. Science, Research, Development and Scholarship. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198796077.003.0002.
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This chapter defines the domain of science, research, development and scholarship. Science is the established knowledge; research is the process by which the scientific domain is extended. ‘Managing science’ means first ‘managing scientific research’–the process of discovering new facts and phenomena. However, the knowledge itself may not be immediately useful–to become useful requires development. While scholarship is more difficult to define, one way to describe it that it is the systematic accumulation of knowledge about knowledge (of something). This chapter makes the case for science across the whole domain, including ‘blue skies’ research. It also discusses the importance of mathematics and the costs of science.
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Mirowski, Philip, and Edward Nik-Khah. Three Different Modalities of Information in Neoclassical Theory. Oxford University Press, 2017. http://dx.doi.org/10.1093/acprof:oso/9780190270056.003.0008.
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There were eventually three major formats explored by the Cowles economists in their quest to incorporate information into the existing neoclassical model: information as thing, information as inductive index, and information as symbolic computation. We describe the major ways they differed from one another, comparing the inspirational views of Claude Shannon, David Blackwell, and Alan Turing. Further, each came with its own characteristic mathematical formalism, not easily reconciled with prior microeconomics, which tended to be irreducible to the other candidates.
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Zinn-Justin, Jean. From Random Walks to Random Matrices. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198787754.001.0001.
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Theoretical physics is a cornerstone of modern physics and provides a foundation for all modern quantitative science. It aims to describe all natural phenomena using mathematical theories and models and, in consequence, develops our understanding of the fundamental nature of the universe. This book offers an overview of major areas covering the recent developments in modern theoretical physics. Each chapter introduces a new key topic, and develops the discussion in a self-contained manner. At the same time, the selected topics have common themes running throughout the book, which connect the independent discussions. The main themes—renormalization group, fixed points, universality and continuum limit—open and conclude the work. Other important and related themes are path integrals and field integrals, effective field theories, gauge theories, the mathematical structure at the basis of the interactions in fundamental particle physics, including quantization problems and anomalies, stochastic dynamical equations and summation of perturbative series.
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Essington, Timothy E. Introduction to Quantitative Ecology. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780192843470.001.0001.
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Modern practice of ecology, conservation, and resource management demands unprecedented levels of quantitative proficiency in mathematical modeling and statistics. This text provides foundational training in the concepts and methods of mathematical and statistical modeling used in ecology, for readers with all levels of quantitative proficiency and confidence. The first chapter presents a generalized approach to develop ecological models and introduces the “describe, explain, and interpret” framework for linking the model world to the real world. Detailed treatment of population models illustrates the myriad ways in which one can develop a model, shows how modeling choices are informed by the ecological question at hand, and emphasizes the epistemology of quantitative techniques. The second part of the book illustrates how to estimate parameters of models from data, and how to use mathematical models combined with statistics to test hypotheses. The third part of the book is devoted to an in-depth development of technical skills to implement models in two common platforms: spreadsheets and the R programming language. The book concludes by demonstrating a quantitative approach to addressing a question that spans density-dependent versus density-independent population models, fitting models to data, evaluating the strength for density dependence using model selection, and evaluating the types of dynamic behaviors that the population might exhibit.
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Blacklock, Mark. Introduction. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198755487.003.0001.
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Introducing the question of why space should be considered to have dimensions, the Introduction proceeds to describe the scope and method of the book. It indicates its intellectual debt to the ideas described by Bruno Latour in We Have Never Been Modern (1993) and its intention to trace ‘quasi-objects’ that disturb the separation of nature and culture. It outlines its frame of reference in the work of scholars of the history of mathematics and late nineteenth-century culture including Joan Richards, Brian Rotman, Mary Poovey, Roger Luckhurst, Jeremy Gray, and Linda Dalrymple Henderson. It describes the historical range of the work, with a focus on the period from 1869 to 1907, outlines the contents of each chapter, and identifies the approach to cultural history of the book as a form of ‘cultural phenomenology’.
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McCann, Kevin S., and Gabriel Gellner, eds. Theoretical Ecology. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198824282.001.0001.
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This book continues the authoritative and established edited series of theoretical ecology books initiated by Robert May which helped pave the way for ecology to become a more robust theoretical science, encouraging the modern biologist to better understand the mathematics behind their theories. This latest instalment in the Theoretical Ecology series builds on the legacy of its predecessors with a completely new set of contributions. Rather than placing emphasis on the historical ideas in theoretical ecology, the editors have encouraged each contribution to: i) synthesize historical theoretical ideas within modern frameworks that have emerged in the last ten to twenty years (e.g., bridging population interactions to whole food webs); ii) describe novel theory that has emerged in the last twenty years from historical empirical areas (e.g., macro-ecology); and iii) cover the booming area of theoretical ecological applications (e.g., disease theory and global change theory). The result is a forward-looking synthesis that will help guide the field through a further decade of development and discovery.
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Holland, John H. 7. Co-evolution and the formation of niches. Oxford University Press, 2014. http://dx.doi.org/10.1093/actrade/9780199662548.003.0007.
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What is a niche? ‘Co-evolution and the formation of niches’ explains that the term ‘niche’ is widely used to describe an important part of the hierarchical organization of complex adaptive systems: local use of signals and resources. Using Markov processes, a mathematical theory of niches can be formed that allows for multiple species with interaction networks that involve loops and recirculation. When realistic niches are considered, the diversity of the niche dwellers stands out. We see a complicated recirculation of resources and signals. How did this complex network of interactions evolve? The short answer is co-evolution through recombination of building blocks, often accompanied by an exaggeration of some of the resulting characteristics.
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Gelman, Andrew, and Deborah Nolan. Statistical thinking in a data science course. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198785699.003.0021.
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In this chapter, we describe the philosophy, goals, syllabus, and activities for a course that we have developed in data science course. In this course we integrate topics from computing, statistics, and working with data. This integrated approach addresses many core aspects in statistics training, including statistical thinking, the role of context in addressing a statistical problem, statistical communication through code, and the balance between programming and mathematical approaches to problems. When designing this course, we asked ourselves what our students ought to be able to do computationally. While we do provide a list of technical material, we also considered the broader goals of the course. Examples include plotting on Google Earth and developing a spam filter for unwanted email.
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Frenier, Wayne W., and Murtaza Ziauddin. Formation, Removal, and Inhibition of Inorganic Scale in the Oilfield Environment. Society of Petroleum EngineersRichardson, Texas, USA, 2008. http://dx.doi.org/10.2118/9781555631406.
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Scale buildup can have serious operational consequences. Formation, Removal and Inhibition of Organic Scale in the Oilfield Environment gives an overview of the science and technology of scale formation, removal, and inhibition to a general technical audience, with emphasis placed on the basic chemical and mechanical principles for scale control. Learn about the environment in which damaging scales occur and the technical aspects of scale management from an upstream oil and gas industry perspective. The text and more than 100 illustrations describe aspects of inorganic scales, including the chemical driving forces for scale formation, methods for removing and preventing scale, and the mathematical methods behind engineering guidelines, along with a discussion of best practices and case histories for control of the various types of inorganic deposits.
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Mann, Peter. Coordinates & Constraints. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0006.
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This short chapter introduces constraints, generalised coordinates and the various spaces of Lagrangian mechanics. Analytical mechanics concerns itself with scalar quantities of a dynamic system, namely the potential and kinetic energies of the particle; this approach is in opposition to Newton’s method of vectorial mechanics, which relies upon defining the position of the particle in three-dimensional space, and the forces acting upon it. The chapter serves as an informal, non-mathematical introduction to differential geometry concepts that describe the configuration space and velocity phase space as a manifold and a tangent, respectively. The distinction between holonomic and non-holonomic constraints is discussed, as are isoperimetric constraints, configuration manifolds, generalised velocity and tangent bundles. The chapter also introduces constraint submanifolds, in an intuitive, graphic format.
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Baloh, Robert W. Breuer’s Experiments on the Semicircular Canals and Otolith Organs. Oxford University Press, 2016. http://dx.doi.org/10.1093/med/9780190600129.003.0006.
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After his groundbreaking work in the mid-1860s, Josef Breuer continued to perform experiments on the inner ear balance receptors in animals. He studied the macules of fish, reptiles, and birds and noted that all these creatures had three macules arranged in the planes of the semicircular canals, perpendicular to one another. By contrast, mammals had only two macules located in the utricle (horizontal plane) and saccule (vertical plane), again perpendicular to each other. He developed the concept of “slip” to describe the movement of the otoconial membrane over the underlying sensory epithelium that occurred with linear displacement or gravity. He developed a mathematical model to hypothesize that in humans there was only one combination of responses from the two macules on each side for a single head position in space.
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Mann, Peter. Vector Calculus. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0034.
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This chapter gives a non-technical overview of differential equations from across mathematical physics, with particular attention to those used in the book. It is a common trend in physics and nature, or perhaps just the way numbers and calculus come together, that, to describe the evolution of things, most theories use a differential equation of low order. This chapter is useful for those with no prior knowledge of the differential equations and explains the concepts required for a basic exposition of classical mechanics. It discusses separable differential equations, boundary conditions and initial value problems, as well as particular solutions, complete solutions, series solutions and general solutions. It also discusses the Cauchy–Lipschitz theorem, flow and the Fourier method, as well as first integrals, complete integrals and integral curves.
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Hamilton, John. A Complete Body of Perspective, in all its Branches Teaching to Describe, by Mathematical Rules, the Appearances of Lines, Plain Figures, and Solid ... Uniform, Easy, and General Methods, v 1 of 2. Gale ECCO, Print Editions, 2018.
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Ferrari, Matthew. Using disease dynamics and modeling to inform control strategies in low-income countries. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198789833.003.0008.
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The incidence infectious disease is inherently dynamic in time and space. Mathematical models that account for the dynamic processes that give rise to fluctuations in disease incidence are powerful tools in disease management and control. We describe the use of dynamic models for surveillance, evaluation and prediction of disease control efforts in low-income countries. Dynamic models can help to anticipate trends owing to intrinsic (e.g., herd immunity) or extrinsic (e.g., seasonality) forces that may confound efforts to isolate the impact of specific interventions. Infectious disease dynamics are frequently nonlinear, meaning that future outcomes are difficult to predict through simple extrapolation of present conditions. Thus, dynamic models can help to explore the potential consequences of proposed interventions. These projections can alert managers to the potential for unintended consequences of control and help to define effect sizes for the design of conventional studies of the impact of interventions.
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Walker, James C. G. Numerical Adventures with Geochemical Cycles. Oxford University Press, 1991. http://dx.doi.org/10.1093/oso/9780195045208.001.0001.
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The dynamic, evolving Earth, and the mathematical representation of its geochemical changes are the subject of this timely, helpful handbook. Global warming, changes in the ocean, and the effects of fossil fuel combustion are just a few of the phenomena that make the development of geochemical models critical. But what computational methods will help to accurately carry out this task? This new text teaches the methodology of computational simulation of environmental change. The author presents interesting applications of his methods to describe the response of the ocean and atmosphere to the infusion of pollutants, the effect of evaporation on seawater composition, climate change, and many other aspects of the Earth's evolving ecosystem. He also presents simple approaches for solving non-linear systems, calculating isotope ratios, and dealing with chains of identical reservoirs. With creative programs that can be executed on any personal computer, Walker offers earth scientists the techniques necessary to address the key problems in their field.
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Kruschke, John K., and Wolf Vanpaemel. Bayesian Estimation in Hierarchical Models. Edited by Jerome R. Busemeyer, Zheng Wang, James T. Townsend, and Ami Eidels. Oxford University Press, 2015. http://dx.doi.org/10.1093/oxfordhb/9780199957996.013.13.
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Bayesian data analysis involves describing data by meaningful mathematical models, and allocating credibility to parameter values that are consistent with the data and with prior knowledge. The Bayesian approach is ideally suited for constructing hierarchical models, which are useful for data structures with multiple levels, such as data from individuals who are members of groups which in turn are in higher-level organizations. Hierarchical models have parameters that meaningfully describe the data at their multiple levels and connect information within and across levels. Bayesian methods are very flexible and straightforward for estimating parameters of complex hierarchical models (and simpler models too). We provide an introduction to the ideas of hierarchical models and to the Bayesian estimation of their parameters, illustrated with two extended examples. One example considers baseball batting averages of individual players grouped by fielding position. A second example uses a hierarchical extension of a cognitive process model to examine individual differences in attention allocation of people who have eating disorders. We conclude by discussing Bayesian model comparison as a case of hierarchical modeling.
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Khailov, Evgenii, Nikolai Grigorenko, Ellina Grigorieva, and Anna Klimenkova. Controlled Lotka-Volterra systems in the modeling of biomedical processes. LCC MAKS Press, 2021. http://dx.doi.org/10.29003/m2448.978-5-317-06681-9.
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This book is devoted to a consistent presentation of the recent results obtained by the authors related to controlled systems created based on the Lotka-Volterra competition model, as well as to theoretical and numerical study of the corresponding optimal control problems. These controlled systems describe various modern methods of treating blood cancers, and the optimal control problems stated for such systems, reflect the search for the optimal treatment strategies. The main tool of the theoretical analysis used in this book is the Pontryagin maximum principle - a necessary condition for optimality in optimal control problems. Possible types of the optimal blood cancer treatment - the optimal controls - are obtained as a result of analytical investigations and are confirmed by corresponding numerical calculations. This book can be used as a supplement text in courses of mathematical modeling for upper undergraduate and graduate students. It is our believe that this text will be of interest to all professors teaching such or similar courses as well as for everyone interested in modern optimal control theory and its biomedical applications.
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Harrison, Roger G., Paul W. Todd, Scott R. Rudge, and Demetri P. Petrides. Bioseparations Science and Engineering. Oxford University Press, 2015. http://dx.doi.org/10.1093/oso/9780195391817.001.0001.
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Designed for undergraduates, graduate students, and industry practitioners, Bioseparations Science and Engineering fills a critical need in the field of bioseparations. Current, comprehensive, and concise, it covers bioseparations unit operations in unprecedented depth. In each of the chapters, the authors use a consistent method of explaining unit operations, starting with a qualitative description noting the significance and general application of the unit operation. They then illustrate the scientific application of the operation, develop the required mathematical theory, and finally, describe the applications of the theory in engineering practice, with an emphasis on design and scaleup. Unique to this text is a chapter dedicated to bioseparations process design and economics, in which a process simular, SuperPro Designer® is used to analyze and evaluate the production of three important biological products. New to this second edition are updated discussions of moment analysis, computer simulation, membrane chromatography, and evaporation, among others, as well as revised problem sets. Unique features include basic information about bioproducts and engineering analysis and a chapter with bioseparations laboratory exercises. Bioseparations Science and Engineering is ideal for students and professionals working in or studying bioseparations, and is the premier text in the field.
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Kaiser, David, ed. "Well, Doc, You're In". The MIT Press, 2022. http://dx.doi.org/10.7551/mitpress/13952.001.0001.
Full textAbstract:
The life and work of Freeman Dyson—renowned scientist, visionary, and iconoclast—and his particular way of thinking about deep questions. Freeman Dyson (1923–2020)—renowned scientist, visionary, and iconoclast—helped invent modern physics. Not bound by disciplinary divisions, he went on to explore foundational topics in mathematics, astrophysics, and the origin of life. General readers were introduced to Dyson's roving mind and heterodox approach in his 1979 book Disturbing the Universe, a poignant autobiographical reflection on life and science. “Well, Doc, You're In” (the title quotes Richard Feynman's remark to Dyson at a physics conference) offers a fresh examination of Dyson's life and work, exploring his particular way of thinking about deep questions that range from the nature of matter to the ultimate fate of the universe. The chapters—written by leading scientists, historians, and science journalists, including some of Dyson's colleagues—trace Dyson's formative years, his budding interests and curiosities, and his wide-ranging work across the natural sciences, technology, and public policy. They describe Dyson's innovations at the intersection of quantum theory and relativity, his novel nuclear reactor design (and his never-realized idea of a spacecraft powered by nuclear weapons), his years at the Institute for Advanced Study, and his foray into cosmology. In the coda, Dyson's daughter Esther reflects on growing up in the Dyson household. “Well, Doc, You're In” assesses Dyson's successes, blind spots, and influence, assembling a portrait of a scientist's outsized legacy. Contributors Jeremy Bernstein, Robbert Dijkgraaf, Esther Dyson, George Dyson, Ann Finkbeiner, Amanda Gefter, Ashutosh Jogalekar, David Kaiser, Caleb Scharf, William Thomas
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Shagrir, Oron. The Nature of Physical Computation. Oxford University Press, 2022. http://dx.doi.org/10.1093/oso/9780197552384.001.0001.
Full textAbstract:
Computing systems are everywhere today. Even the brain is thought to be a sort of computing system. But what does it mean to say that a given organ or system computes? What is it about laptops, smartphones, and nervous systems that they are deemed to compute, and why does it seldom occur to us to describe stomachs, hurricanes, rocks, or chairs that way? The book provides an extended argument for the semantic view of computation, which states that semantic properties are involved in the nature of computing systems. Laptops, smartphones, and nervous systems compute because they are accompanied by representations. Stomachs, hurricanes, and rocks, for instance, which do not have semantic properties, do not compute. The first part of the book argues that the linkage between the mathematical theory of computability and the notion of physical computation is weak. Theoretical notions such as algorithms, effective procedure, program, and automaton play only a minor role in identifying physical computation. The second part of the book reviews three influential accounts of physical computation and argues that while none of these accounts is satisfactory, each of them highlights certain key features of physical computation. The final part of the book develops and argues for a semantic account of physical computation and offers a characterization of computational explanations.