Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

Aspect] is a simple and practical aspect-oriented extension to Java With just a few new constructs, AspectJ provides support for modular implementation of a range of crosscutting concerns. In AspectJ's dynamic join point model, join points are well-defined points in the execution of the program; pointcuts are collections of join points; advice are special method-like constructs that can be attached to pointcuts; and aspects are modular units of crosscutting implementation, comprising pointcuts, advice, and ordinary Java member declarations. AspectJ code is compiled into standard Java bytecode. Simple extensions to existing Java development environments make it possible to browse the crosscutting structure of aspects in the same kind of way as one browses the inheritance structure of classes. Several examples show that AspectJ is powerful, and that programs written using it are easy to understand.

An overview of AspectJ

The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

1. Ordered Fields, Real Closed Fields.- 2. Semi-algebraic Sets.- 3. Real Algebraic Varieties.- 4. Real Algebra.- 5. The Tarski-Seidenberg Principle as a Transfer Tool.- 6. Hilbert's 17th Problem. Quadratic Forms.- 7. Real Spectrum.- 8. Nash Functions.- 9. Stratifications.- 10. Real Places.- 11. Topology of Real Algebraic Varieties.- 12. Algebraic Vector Bundles.- 13. Polynomial or Regular Mappings with Values in Spheres.- 14. Algebraic Models of C? Manifolds.- 15. Witt Rings in Real Algebraic Geometry.- Index of Notation.

https://hal.archives-ouvertes.fr/hal-00609687/document

Real Algebraic Geometry

http://personal.cimat.mx:8181/~jortega/MaterialDidactico/modestoI10/Proyectos/Blum%20%282005%29AntCol.pdf

Ant colony optimization: Introduction and recent trends

A comprehensive and systematic introduction is presented for the concepts associated with 'modeling', involving the transition from a physical system down to an abstract description of that system in the form of a set of differential and/or difference equations, and basing its treatment of modeling on the mathematics of dynamical systems. Attention is given to the principles of passive electrical circuit modeling, planar mechanical systems modeling, hierarchical modular modeling of continuous systems, and bond-graph modeling. Also discussed are modeling in equilibrium thermodynamics, population dynamics, and system dynamics, inductive reasoning, artificial neural networks, and automated model synthesis.

Continuous System Modeling

Highly computer-oriented text, introducing numerical methods and algorithms along with the applications and conceptual tools Includes homework problems, suggestions for research projects, and open-ended questions at the end of each chapter Written by our successful author who also wrote Continuous System Modeling, a best-selling Springer book first published in the 1991 (sold about 1500 copies)

Continuous System Simulation

A new methodology for the object-oriented description of models consisting of a mixture of continuous and discrete components is presented. The object-oriented paradigm enables the user to describe such models in a modular fashion that permits the reuse of these models independently of the environment in which they are to be embedded. The paper explains the basic mechanisms needed for object-oriented modeling of hybrid systems by means of language constructs available in the object-oriented modeling language Dymola.It then addresses more advanced concepts such as variable structure models containing e.g. ideal electrical switches, ideal diodes and dry friction.

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Object-oriented modeling of hybrid systems

Digital continuous-system simulation languages are discussed. It is demonstrated how sophisticated automated formula manipulation can be used to automatically generate state-space models from an object-oriented description of a physical system. The two major complications, algebraic loops and structural singularities, occur frequently as a consequence of couplings between submodels (objects), and these difficulties can often be dealt with by automated formula manipulation. A software tool, Dymola, in which the various formula manipulation techniques have been implemented, is presented. Dymola is an object-oriented continuous-system modeling language and a model manipulator that can be used to generate models in several simulation languages. >

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Automated formula manipulation supports object-oriented continuous-system modeling

10 Chapter.I: Introduction 16 Chapter.II: Historical Development 23 Chapter.Ill: Usefulness of Combined System Simulation 30 Chapter.IV: Numerical Aspects 53 IV. 1: Structure of the Run-Time Package 53 IV.1.1: Conditions for Changing to Continuous Simulation when Executing Discrete Simulation 54 IV.1.2: Conditions for Changing to Discrete Simulation when Executing Continuous Simulation 54 IV.1.2.1: The Regula-Falsi Iteration Scheme 55 IV.1.2.2: The Generalized Regula-Falsi Iteration Scheme 58 IV.1.2.3: The Inverse Hermite1 Inter¬ polation 60

François E. Cellier

Papers

Continuous System Modeling

Continuous System Simulation

Object-oriented modeling of hybrid systems

Automated formula manipulation supports object-oriented continuous-system modeling

Combined continuous/discrete system simulation by use of digital computers