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8.282J Introduction to Astronomy (MIT) 8.282J Introduction to Astronomy (MIT)

Description

Introduction to Astronomy provides a quantitative introduction to the physics of the solar system, stars, the interstellar medium, the galaxy, and the universe, as determined from a variety of astronomical observations and models. Introduction to Astronomy provides a quantitative introduction to the physics of the solar system, stars, the interstellar medium, the galaxy, and the universe, as determined from a variety of astronomical observations and models.

Subjects

solar system; stars; interstellar medium; the Galaxy; the Universe; planets; planet formation; star formation; stellar evolution; supernovae; compact objects; white dwarfs; neutron stars; black holes; plusars | binary X-ray sources; star clusters; globular and open clusters; interstellar medium | gas | dust | magnetic fields | cosmic rays; distance ladder; | solar system; stars; interstellar medium; the Galaxy; the Universe; planets; planet formation; star formation; stellar evolution; supernovae; compact objects; white dwarfs; neutron stars; black holes; plusars | binary X-ray sources; star clusters; globular and open clusters; interstellar medium | gas | dust | magnetic fields | cosmic rays; distance ladder; | solar system | solar system | stars | stars | interstellar medium | interstellar medium | the Galaxy | the Galaxy | the Universe | the Universe | planets | planets | planet formation | planet formation | star formation | star formation | stellar evolution | stellar evolution | supernovae | supernovae | compact objects | compact objects | white dwarfs | white dwarfs | neutron stars | neutron stars | black holes | black holes | plusars | binary X-ray sources | plusars | binary X-ray sources | star clusters | star clusters | globular and open clusters | globular and open clusters | interstellar medium | gas | dust | magnetic fields | cosmic rays | interstellar medium | gas | dust | magnetic fields | cosmic rays | distance ladder | distance ladder | galaxies | normal and active galaxies | jets | galaxies | normal and active galaxies | jets | gravitational lensing | gravitational lensing | large scaling structure | large scaling structure | Newtonian cosmology | dynamical expansion and thermal history of the Universe | Newtonian cosmology | dynamical expansion and thermal history of the Universe | cosmic microwave background radiation | cosmic microwave background radiation | big-bang nucleosynthesis | big-bang nucleosynthesis | pulsars | pulsars | binary X-ray sources | binary X-ray sources | gas | gas | dust | dust | magnetic fields | magnetic fields | cosmic rays | cosmic rays | galaxy | galaxy | universe | universe | astrophysics | astrophysics | Sun | Sun | supernova | supernova | globular clusters | globular clusters | open clusters | open clusters | jets | jets | Newtonian cosmology | Newtonian cosmology | dynamical expansion | dynamical expansion | thermal history | thermal history | normal galaxies | normal galaxies | active galaxies | active galaxies | Greek astronomy | Greek astronomy | physics | physics | Copernicus | Copernicus | Tycho | Tycho | Kepler | Kepler | Galileo | Galileo | classical mechanics | classical mechanics | circular orbits | circular orbits | full kepler orbit problem | full kepler orbit problem | electromagnetic radiation | electromagnetic radiation | matter | matter | telescopes | telescopes | detectors | detectors | 8.282 | 8.282 | 12.402 | 12.402 | plusars | plusars | galaxies | galaxies | normal and active galaxies | normal and active galaxies | dynamical expansion and thermal history of the Universe | dynamical expansion and thermal history of the Universe

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8.282J Introduction to Astronomy (MIT) 8.282J Introduction to Astronomy (MIT)

Description

Introduction to Astronomy provides a quantitative introduction to physics of the solar system, stars, interstellar medium, the galaxy, and universe, as determined from a variety of astronomical observations and models.Topics include: planets, planet formation; stars, the Sun, "normal" stars, star formation; stellar evolution, supernovae, compact objects (white dwarfs, neutron stars, and black holes), plusars, binary X-ray sources; star clusters, globular and open clusters; interstellar medium, gas, dust, magnetic fields, cosmic rays; distance ladder; galaxies, normal and active galaxies, jets; gravitational lensing; large scaling structure; Newtonian cosmology, dynamical expansion and thermal history of the Universe; cosmic microwave background radiation; big-bang nucleosynthesis Introduction to Astronomy provides a quantitative introduction to physics of the solar system, stars, interstellar medium, the galaxy, and universe, as determined from a variety of astronomical observations and models.Topics include: planets, planet formation; stars, the Sun, "normal" stars, star formation; stellar evolution, supernovae, compact objects (white dwarfs, neutron stars, and black holes), plusars, binary X-ray sources; star clusters, globular and open clusters; interstellar medium, gas, dust, magnetic fields, cosmic rays; distance ladder; galaxies, normal and active galaxies, jets; gravitational lensing; large scaling structure; Newtonian cosmology, dynamical expansion and thermal history of the Universe; cosmic microwave background radiation; big-bang nucleosynthesis

Subjects

solar system; stars; interstellar medium; the Galaxy; the Universe; planets; planet formation; star formation; stellar evolution; supernovae; compact objects; white dwarfs; neutron stars; black holes; plusars | binary X-ray sources; star clusters; globular and open clusters; interstellar medium | gas | dust | magnetic fields | cosmic rays; distance ladder; | solar system; stars; interstellar medium; the Galaxy; the Universe; planets; planet formation; star formation; stellar evolution; supernovae; compact objects; white dwarfs; neutron stars; black holes; plusars | binary X-ray sources; star clusters; globular and open clusters; interstellar medium | gas | dust | magnetic fields | cosmic rays; distance ladder; | solar system | solar system | stars | stars | interstellar medium | interstellar medium | the Galaxy | the Galaxy | the Universe | the Universe | planets | planets | planet formation | planet formation | star formation | star formation | stellar evolution | stellar evolution | supernovae | supernovae | compact objects | compact objects | white dwarfs | white dwarfs | neutron stars | neutron stars | black holes | black holes | plusars | binary X-ray sources | plusars | binary X-ray sources | star clusters | star clusters | globular and open clusters | globular and open clusters | interstellar medium | gas | dust | magnetic fields | cosmic rays | interstellar medium | gas | dust | magnetic fields | cosmic rays | distance ladder | distance ladder | galaxies | normal and active galaxies | jets | galaxies | normal and active galaxies | jets | gravitational lensing | gravitational lensing | large scaling structure | large scaling structure | Newtonian cosmology | dynamical expansion and thermal history of the Universe | Newtonian cosmology | dynamical expansion and thermal history of the Universe | cosmic microwave background radiation | cosmic microwave background radiation | big-bang nucleosynthesis | big-bang nucleosynthesis | pulsars | pulsars | binary X-ray sources | binary X-ray sources | gas | gas | dust | dust | magnetic fields | magnetic fields | cosmic rays | cosmic rays | galaxy | galaxy | universe | universe | astrophysics | astrophysics | Sun | Sun | supernova | supernova | globular clusters | globular clusters | open clusters | open clusters | jets | jets | Newtonian cosmology | Newtonian cosmology | dynamical expansion | dynamical expansion | thermal history | thermal history | normal galaxies | normal galaxies | active galaxies | active galaxies | Greek astronomy | Greek astronomy | physics | physics | Copernicus | Copernicus | Tycho | Tycho | Kepler | Kepler | Galileo | Galileo | classical mechanics | classical mechanics | circular orbits | circular orbits | full kepler orbit problem | full kepler orbit problem | electromagnetic radiation | electromagnetic radiation | matter | matter | telescopes | telescopes | detectors | detectors | 8.282 | 8.282 | 12.402 | 12.402

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12.570 Structure and Dynamics of the CMB Region (MIT) 12.570 Structure and Dynamics of the CMB Region (MIT)

Description

The Core Mantle Boundary (CMB) represents one of the most important physical and chemical discontinuities of the deep Earth as it separates the solid state, convective lower mantle from the liquid outer core. In this seminar course, the instructors will examine our current understanding of the CMB region from integrated seismological, mineral physics and geodynamical perspectives. Instructors will also introduce state-of-the-art methodologies that are employed to characterize the CMB region and relevant papers will be discussed in class. Topics will include CMB detection and topography, D'' anisotropy, seismic velocity anomalies (e.g., ultra-low velocity zones), temperature, chemical reactions, phase relations, and mineral fabrications at the core-mantle boundary. These results will be i The Core Mantle Boundary (CMB) represents one of the most important physical and chemical discontinuities of the deep Earth as it separates the solid state, convective lower mantle from the liquid outer core. In this seminar course, the instructors will examine our current understanding of the CMB region from integrated seismological, mineral physics and geodynamical perspectives. Instructors will also introduce state-of-the-art methodologies that are employed to characterize the CMB region and relevant papers will be discussed in class. Topics will include CMB detection and topography, D'' anisotropy, seismic velocity anomalies (e.g., ultra-low velocity zones), temperature, chemical reactions, phase relations, and mineral fabrications at the core-mantle boundary. These results will be i

Subjects

Core Mantle Boundary (CMB) | Core Mantle Boundary (CMB) | deep Earth | deep Earth | lower mantle | lower mantle | outer core | outer core | integrated seismological | integrated seismological | mineral physics and geodynamical perspectives | mineral physics and geodynamical perspectives | CMB detection and topography | CMB detection and topography | D'' anisotropy | D'' anisotropy | seismic velocity anomalies (e.g. | seismic velocity anomalies (e.g. | ultra-low velocity zones) | ultra-low velocity zones) | temperature | temperature | chemical reactions | chemical reactions | phase relations | phase relations | mineral fabrications | mineral fabrications | cmb detection | cmb detection | topography | topography | mineral physics | mineral physics | geodynamical perspectives | geodynamical perspectives | D" Region | D" Region | ultra-low velocity zones | ultra-low velocity zones | partial melting | partial melting | mineral texture | mineral texture | core rigidity zones | core rigidity zones | sedimentation | sedimentation | mantle flow | mantle flow | core mantle coupling | core mantle coupling | geomagnetic field | geomagnetic field

License

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8.282J Introduction to Astronomy (MIT)

Description

Introduction to Astronomy provides a quantitative introduction to the physics of the solar system, stars, the interstellar medium, the galaxy, and the universe, as determined from a variety of astronomical observations and models.

Subjects

solar system; stars; interstellar medium; the Galaxy; the Universe; planets; planet formation; star formation; stellar evolution; supernovae; compact objects; white dwarfs; neutron stars; black holes; plusars | binary X-ray sources; star clusters; globular and open clusters; interstellar medium | gas | dust | magnetic fields | cosmic rays; distance ladder; | solar system | stars | interstellar medium | the Galaxy | the Universe | planets | planet formation | star formation | stellar evolution | supernovae | compact objects | white dwarfs | neutron stars | black holes | plusars | binary X-ray sources | star clusters | globular and open clusters | interstellar medium | gas | dust | magnetic fields | cosmic rays | distance ladder | galaxies | normal and active galaxies | jets | gravitational lensing | large scaling structure | Newtonian cosmology | dynamical expansion and thermal history of the Universe | cosmic microwave background radiation | big-bang nucleosynthesis | pulsars | binary X-ray sources | gas | dust | magnetic fields | cosmic rays | galaxy | universe | astrophysics | Sun | supernova | globular clusters | open clusters | jets | Newtonian cosmology | dynamical expansion | thermal history | normal galaxies | active galaxies | Greek astronomy | physics | Copernicus | Tycho | Kepler | Galileo | classical mechanics | circular orbits | full kepler orbit problem | electromagnetic radiation | matter | telescopes | detectors | 8.282 | 12.402 | plusars | galaxies | normal and active galaxies | dynamical expansion and thermal history of the Universe

License

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8.282J Introduction to Astronomy (MIT)

Description

Introduction to Astronomy provides a quantitative introduction to the physics of the solar system, stars, the interstellar medium, the galaxy, and the universe, as determined from a variety of astronomical observations and models.

Subjects

solar system; stars; interstellar medium; the Galaxy; the Universe; planets; planet formation; star formation; stellar evolution; supernovae; compact objects; white dwarfs; neutron stars; black holes; plusars | binary X-ray sources; star clusters; globular and open clusters; interstellar medium | gas | dust | magnetic fields | cosmic rays; distance ladder; | solar system | stars | interstellar medium | the Galaxy | the Universe | planets | planet formation | star formation | stellar evolution | supernovae | compact objects | white dwarfs | neutron stars | black holes | plusars | binary X-ray sources | star clusters | globular and open clusters | interstellar medium | gas | dust | magnetic fields | cosmic rays | distance ladder | galaxies | normal and active galaxies | jets | gravitational lensing | large scaling structure | Newtonian cosmology | dynamical expansion and thermal history of the Universe | cosmic microwave background radiation | big-bang nucleosynthesis | pulsars | binary X-ray sources | gas | dust | magnetic fields | cosmic rays | galaxy | universe | astrophysics | Sun | supernova | globular clusters | open clusters | jets | Newtonian cosmology | dynamical expansion | thermal history | normal galaxies | active galaxies | Greek astronomy | physics | Copernicus | Tycho | Kepler | Galileo | classical mechanics | circular orbits | full kepler orbit problem | electromagnetic radiation | matter | telescopes | detectors | 8.282 | 12.402 | plusars | galaxies | normal and active galaxies | dynamical expansion and thermal history of the Universe

License

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6.231 Dynamic Programming and Stochastic Control (MIT) 6.231 Dynamic Programming and Stochastic Control (MIT)

Description

This course covers the basic models and solution techniques for problems of sequential decision making under uncertainty (stochastic control). We will consider optimal control of a dynamical system over both a finite and an infinite number of stages (finite and infinite horizon). We will also discuss some approximation methods for problems involving large state spaces. Applications of dynamic programming in a variety of fields will be covered in recitations. This course covers the basic models and solution techniques for problems of sequential decision making under uncertainty (stochastic control). We will consider optimal control of a dynamical system over both a finite and an infinite number of stages (finite and infinite horizon). We will also discuss some approximation methods for problems involving large state spaces. Applications of dynamic programming in a variety of fields will be covered in recitations.

Subjects

dynamic programming | dynamic programming | stochastic control | stochastic control | decision making | decision making | uncertainty | uncertainty | sequential decision making | sequential decision making | finite horizon | finite horizon | infinite horizon | infinite horizon | approximation methods | approximation methods | state space | state space | large state space | large state space | optimal control | optimal control | dynamical system | dynamical system | dynamic programming and optimal control | dynamic programming and optimal control | deterministic systems | deterministic systems | shortest path | shortest path | state information | state information | rollout | rollout | stochastic shortest path | stochastic shortest path | approximate dynamic programming | approximate dynamic programming

License

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12.864 Inference from Data and Models (MIT) 12.864 Inference from Data and Models (MIT)

Description

The course is directed at making scientifically sensible deductions from the combination of observations with dynamics and kinematics represented, generically, as "models". There are two overlapping central themesLinear "inverse" methods and data "assimilation" including regression, singular value decomposition, objective mapping, non-stationary models and data, Kalman filters, adjoint methods ("assimilation") etc.Standard time series analysis, including basic statistics, Fourier methods, spectra, coherence, filtering, etc. The course is directed at making scientifically sensible deductions from the combination of observations with dynamics and kinematics represented, generically, as "models". There are two overlapping central themesLinear "inverse" methods and data "assimilation" including regression, singular value decomposition, objective mapping, non-stationary models and data, Kalman filters, adjoint methods ("assimilation") etc.Standard time series analysis, including basic statistics, Fourier methods, spectra, coherence, filtering, etc.

Subjects

kinematical and dynamical models | kinematical and dynamical models | Basic statistics | Basic statistics | linear algebra | linear algebra | inverse methods | inverse methods | singular value decompositions | singular value decompositions | control theory | control theory | sequential estimation | sequential estimation | Kalman filters | Kalman filters | smoothing algorithms | smoothing algorithms | adjoint/Pontryagin principle methods | adjoint/Pontryagin principle methods | model testing | model testing | stationary processes | stationary processes | Fourier methods | Fourier methods | z-transforms | z-transforms | sampling theorems | sampling theorems | spectra | spectra | multi-taper methods | multi-taper methods | coherences | coherences | filtering | filtering | quantitative combinations of models | quantitative combinations of models

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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12.864 Inference from Data and Models (MIT) 12.864 Inference from Data and Models (MIT)

Description

The course is directed at making scientifically sensible deductions from the combination of observations with dynamics and kinematics represented, generically, as "models". There are two overlapping central themeslinear "inverse" methods and data "assimilation" including regression, singular value decomposition, objective mapping, non-stationary models and data, Kalman filters, adjoint methods ("assimilation") etc.standard time series analysis, including basic statistics, Fourier methods, spectra, coherence, filtering, etc. The course is directed at making scientifically sensible deductions from the combination of observations with dynamics and kinematics represented, generically, as "models". There are two overlapping central themeslinear "inverse" methods and data "assimilation" including regression, singular value decomposition, objective mapping, non-stationary models and data, Kalman filters, adjoint methods ("assimilation") etc.standard time series analysis, including basic statistics, Fourier methods, spectra, coherence, filtering, etc.

Subjects

observation | observation | kinematical models | kinematical models | dynamical models | dynamical models | basic statistics | basic statistics | linear algebra | linear algebra | inverse methods | inverse methods | singular value decompositions | singular value decompositions | control theory | control theory | sequential estimation | sequential estimation | Kalman filters | Kalman filters | smoothing algorithms | smoothing algorithms | adjoint/Pontryagin principle methods | adjoint/Pontryagin principle methods | model testing | model testing | stationary processes | stationary processes | Fourier methods | Fourier methods | z-transforms | z-transforms | sampling theorems | sampling theorems | spectra | spectra | multi-taper methods | multi-taper methods | coherences | coherences | filtering | filtering | quantitative combinations | quantitative combinations | realistic observations | realistic observations | data assimilations | data assimilations | deduction | deduction | regression | regression | objective mapping | objective mapping | time series analysis | time series analysis | inference | inference

License

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18.311 Principles of Applied Mathematics (MIT) 18.311 Principles of Applied Mathematics (MIT)

Description

Discussion of computational and modeling issues. Nonlinear dynamical systems; nonlinear waves; diffusion; stability; characteristics; nonlinear steepening, breaking and shock formation; conservation laws; first-order partial differential equations; finite differences; numerical stability; etc. Applications to traffic problems, flows in rivers, internal waves, mechanical vibrations and other problems in the physical world.Technical RequirementsMATLAB® software is required to run the .m files found on this course site. MATLAB® is a trademark of The MathWorks, Inc. Discussion of computational and modeling issues. Nonlinear dynamical systems; nonlinear waves; diffusion; stability; characteristics; nonlinear steepening, breaking and shock formation; conservation laws; first-order partial differential equations; finite differences; numerical stability; etc. Applications to traffic problems, flows in rivers, internal waves, mechanical vibrations and other problems in the physical world.Technical RequirementsMATLAB® software is required to run the .m files found on this course site. MATLAB® is a trademark of The MathWorks, Inc.

Subjects

Nonlinear dynamical systems | Nonlinear dynamical systems | nonlinear waves | nonlinear waves | diffusion | diffusion | stability | stability | characteristics | characteristics | nonlinear steepening | nonlinear steepening | breaking and shock formation | breaking and shock formation | conservation laws | conservation laws | first-order partial differential equations | first-order partial differential equations | finite differences | finite differences | numerical stability | numerical stability | traffic problems | traffic problems | flows in rivers | flows in rivers | internal waves | internal waves | mechanical vibrations | mechanical vibrations

License

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6.243J Dynamics of Nonlinear Systems (MIT) 6.243J Dynamics of Nonlinear Systems (MIT)

Description

This course provides an introduction to nonlinear deterministic dynamical systems. Topics covered include: nonlinear ordinary differential equations; planar autonomous systems; fundamental theory: Picard iteration, contraction mapping theorem, and Bellman-Gronwall lemma; stability of equilibria by Lyapunov's first and second methods; feedback linearization; and application to nonlinear circuits and control systems. This course provides an introduction to nonlinear deterministic dynamical systems. Topics covered include: nonlinear ordinary differential equations; planar autonomous systems; fundamental theory: Picard iteration, contraction mapping theorem, and Bellman-Gronwall lemma; stability of equilibria by Lyapunov's first and second methods; feedback linearization; and application to nonlinear circuits and control systems.

Subjects

nonlinear systems | nonlinear systems | deterministic dynamical systems | deterministic dynamical systems | ordinary differential equations | ordinary differential equations | planar autonomous systems | planar autonomous systems | Picard iteration | Picard iteration | contraction mapping theorem | contraction mapping theorem | Bellman-Gronwall lemma | Bellman-Gronwall lemma | Lyapunov methods | Lyapunov methods | feedback linearization | feedback linearization | nonlinear circuits | nonlinear circuits | control systems | control systems | local controllability | local controllability | volume evolution | volume evolution | system analysis | system analysis | singular perturbations | singular perturbations | averaging | averaging | local behavior | local behavior | trajectories | trajectories | equilibria | equilibria | storage functions | storage functions | stability analysis | stability analysis | continuity | continuity | differential equations | differential equations | system models | system models | parameters | parameters | input/output | input/output | state-space | state-space | 16.337 | 16.337

License

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12.864 Inference from Data and Models (MIT) 12.864 Inference from Data and Models (MIT)

Description

This course covers the fundamental methods used for exploring the information content of observations related to kinematical and dynamical models. This course covers the fundamental methods used for exploring the information content of observations related to kinematical and dynamical models.

Subjects

kinematical and dynamical models | kinematical and dynamical models | Basic statistics | Basic statistics | linear algebra | linear algebra | inverse methods | inverse methods | singular value decompositions | singular value decompositions | control theory | control theory | sequential estimation | sequential estimation | Kalman filters | Kalman filters | smoothing algorithms | smoothing algorithms | adjoint/Pontryagin principle methods | adjoint/Pontryagin principle methods | model testing | model testing | stationary processes | stationary processes | Fourier methods | Fourier methods | z-transforms | z-transforms | sampling theorems | sampling theorems | spectra | spectra | multi-taper methods | multi-taper methods | coherences | coherences | filtering | filtering | quantitative combinations of models | quantitative combinations of models

License

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12.570 Seminar in Geophysics: Thermal and Chemical Evolution of the Earth (MIT) 12.570 Seminar in Geophysics: Thermal and Chemical Evolution of the Earth (MIT)

Description

The main objective of this cross-disciplinary course is to understand the historical development and the current status of ideas and models, to present and question the constraints from the different research fields, and to investigate if and how the different views on mantle flow can be reconciled with the currently available data. The main objective of this cross-disciplinary course is to understand the historical development and the current status of ideas and models, to present and question the constraints from the different research fields, and to investigate if and how the different views on mantle flow can be reconciled with the currently available data.

Subjects

structure | composition | and evolution of Earth's deep interior | structure | composition | and evolution of Earth's deep interior | Seismic imaging | Seismic imaging | geodynamical modeling | geodynamical modeling | nobel gas analyses | nobel gas analyses | mantle convection | mantle convection | geophysics | geophysics | earth science | earth science

License

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12.570 Seminar in Geophysics: Mantle Convection (MIT) 12.570 Seminar in Geophysics: Mantle Convection (MIT)

Description

This cross-disciplinary course aims to understand the historical development and the current status of ideas and models, to present and question the constraints from the different research fields, and to investigate if and how the different views on mantle flow can be reconciled with the currently available data. This cross-disciplinary course aims to understand the historical development and the current status of ideas and models, to present and question the constraints from the different research fields, and to investigate if and how the different views on mantle flow can be reconciled with the currently available data.

Subjects

mantle convection | mantle convection | geophysics | geophysics | geodynamics | geodynamics | mantle | mantle | earth | earth | geochemistry | geochemistry | seismology | seismology | stratification | stratification | geodynamical modeling | geodynamical modeling | tomography | tomography | seismic imaging | seismic imaging

License

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MAS.622J Pattern Recognition and Analysis (MIT) MAS.622J Pattern Recognition and Analysis (MIT)

Description

This class deals with the fundamentals of characterizing and recognizing patterns and features of interest in numerical data. We discuss the basic tools and theory for signal understanding problems with applications to user modeling, affect recognition, speech recognition and understanding, computer vision, physiological analysis, and more. We also cover decision theory, statistical classification, maximum likelihood and Bayesian estimation, nonparametric methods, unsupervised learning and clustering. Additional topics on machine and human learning from active research are also talked about in the class. This class deals with the fundamentals of characterizing and recognizing patterns and features of interest in numerical data. We discuss the basic tools and theory for signal understanding problems with applications to user modeling, affect recognition, speech recognition and understanding, computer vision, physiological analysis, and more. We also cover decision theory, statistical classification, maximum likelihood and Bayesian estimation, nonparametric methods, unsupervised learning and clustering. Additional topics on machine and human learning from active research are also talked about in the class.

Subjects

MAS.622 | MAS.622 | 1.126 | 1.126 | pattern recognition | pattern recognition | feature detection | feature detection | classification | classification | probability theory | probability theory | pattern analysis | pattern analysis | conditional probability | conditional probability | bayes rule | bayes rule | random vectors | decision theory | random vectors | decision theory | ROC curves | ROC curves | likelihood ratio test | likelihood ratio test | fisher discriminant | fisher discriminant | template-based recognition | template-based recognition | feature extraction | feature extraction | eigenvector and multilinear analysis | eigenvector and multilinear analysis | linear discriminant | linear discriminant | perceptron learning | perceptron learning | optimization by gradient descent | optimization by gradient descent | support vecotr machines | support vecotr machines | K-nearest-neighbor classification | K-nearest-neighbor classification | parzen estimation | parzen estimation | unsupervised learning | unsupervised learning | clustering | clustering | vector quantization | vector quantization | K-means | K-means | Expectation-Maximization | Expectation-Maximization | Hidden markov models | Hidden markov models | viterbi algorithm | viterbi algorithm | Baum-Welch algorithm | Baum-Welch algorithm | linear dynamical systems | linear dynamical systems | Kalman filtering | Kalman filtering | Bayesian networks | Bayesian networks | decision trees | decision trees | reinforcement learning | reinforcement learning | genetic algorithms | genetic algorithms

License

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6.438 Algorithms for Inference (MIT) 6.438 Algorithms for Inference (MIT)

Description

This is a graduate-level introduction to the principles of statistical inference with probabilistic models defined using graphical representations. The material in this course constitutes a common foundation for work in machine learning, signal processing, artificial intelligence, computer vision, control, and communication. Ultimately, the subject is about teaching you contemporary approaches to, and perspectives on, problems of statistical inference. This is a graduate-level introduction to the principles of statistical inference with probabilistic models defined using graphical representations. The material in this course constitutes a common foundation for work in machine learning, signal processing, artificial intelligence, computer vision, control, and communication. Ultimately, the subject is about teaching you contemporary approaches to, and perspectives on, problems of statistical inference.

Subjects

inference | inference | algorithm | algorithm | graphical model | graphical model | factor graph | factor graph | markov chain | markov chain | Gaussian model | Gaussian model | loopy belief propagation | loopy belief propagation | EM algorithm | EM algorithm | statistical inference | statistical inference | probabilistic graphical model | probabilistic graphical model | Hidden Markov model | Hidden Markov model | linear dynamical systems | linear dynamical systems | Sum-product algorithm | Sum-product algorithm | junction tree algorithm | junction tree algorithm | Forward-backward algorithm | Forward-backward algorithm | Kalman filtering | Kalman filtering | smoothing | smoothing | Variational method | Variational method | mean-field theory | mean-field theory | Min-sum algorithm | Min-sum algorithm | Viterbi algorithm | Viterbi algorithm | parameter estimation | parameter estimation | learning structure | learning structure

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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2.18 Biomolecular Feedback Systems (MIT) 2.18 Biomolecular Feedback Systems (MIT)

Description

This course focuses on feedback control mechanisms that living organisms implement at the molecular level to execute their functions, with emphasis on techniques to design novel systems with prescribed behaviors. Students will learn how biological functions can be understood and designed using notions from feedback control. This course focuses on feedback control mechanisms that living organisms implement at the molecular level to execute their functions, with emphasis on techniques to design novel systems with prescribed behaviors. Students will learn how biological functions can be understood and designed using notions from feedback control.

Subjects

biomolecular feedback systems | biomolecular feedback systems | systems biology | systems biology | modeling | modeling | feedback | feedback | cell | cell | system | system | control | control | dynamical | dynamical | input/output | input/output | synthetic biology | synthetic biology | techniques | techniques | transcription | transcription | translation | translation | transcriptional regulation | transcriptional regulation | post-transcriptional regulation | post-transcriptional regulation | cellular subsystems | cellular subsystems | dynamic behavior | dynamic behavior | analysis | analysis | equilibrium | equilibrium | robustness | robustness | oscillatory behavior | oscillatory behavior | bifurcations | bifurcations | model reduction | model reduction | stochastic | stochastic | biochemical | biochemical | simulation | simulation | linear | linear | circuit | circuit | design | design | biological circuit design | biological circuit design | negative autoregulation | negative autoregulation | toggle switch | toggle switch | repressilator | repressilator | activator-repressor clock | activator-repressor clock | IFFL | IFFL | incoherent feedforward loop | incoherent feedforward loop | bacterial chemotaxis | bacterial chemotaxis | interconnecting components | interconnecting components | modularity | modularity | retroactivity | retroactivity | gene circuit | gene circuit

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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8.282J Introduction to Astronomy (MIT)

Description

Introduction to Astronomy provides a quantitative introduction to physics of the solar system, stars, interstellar medium, the galaxy, and universe, as determined from a variety of astronomical observations and models.Topics include: planets, planet formation; stars, the Sun, "normal" stars, star formation; stellar evolution, supernovae, compact objects (white dwarfs, neutron stars, and black holes), plusars, binary X-ray sources; star clusters, globular and open clusters; interstellar medium, gas, dust, magnetic fields, cosmic rays; distance ladder; galaxies, normal and active galaxies, jets; gravitational lensing; large scaling structure; Newtonian cosmology, dynamical expansion and thermal history of the Universe; cosmic microwave background radiation; big-bang nucleosynthesis

Subjects

solar system; stars; interstellar medium; the Galaxy; the Universe; planets; planet formation; star formation; stellar evolution; supernovae; compact objects; white dwarfs; neutron stars; black holes; plusars | binary X-ray sources; star clusters; globular and open clusters; interstellar medium | gas | dust | magnetic fields | cosmic rays; distance ladder; | solar system | stars | interstellar medium | the Galaxy | the Universe | planets | planet formation | star formation | stellar evolution | supernovae | compact objects | white dwarfs | neutron stars | black holes | plusars | binary X-ray sources | star clusters | globular and open clusters | interstellar medium | gas | dust | magnetic fields | cosmic rays | distance ladder | galaxies | normal and active galaxies | jets | gravitational lensing | large scaling structure | Newtonian cosmology | dynamical expansion and thermal history of the Universe | cosmic microwave background radiation | big-bang nucleosynthesis | pulsars | binary X-ray sources | gas | dust | magnetic fields | cosmic rays | galaxy | universe | astrophysics | Sun | supernova | globular clusters | open clusters | jets | Newtonian cosmology | dynamical expansion | thermal history | normal galaxies | active galaxies | Greek astronomy | physics | Copernicus | Tycho | Kepler | Galileo | classical mechanics | circular orbits | full kepler orbit problem | electromagnetic radiation | matter | telescopes | detectors | 8.282 | 12.402

License

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12.570 Structure and Dynamics of the CMB Region (MIT)

Description

The Core Mantle Boundary (CMB) represents one of the most important physical and chemical discontinuities of the deep Earth as it separates the solid state, convective lower mantle from the liquid outer core. In this seminar course, the instructors will examine our current understanding of the CMB region from integrated seismological, mineral physics and geodynamical perspectives. Instructors will also introduce state-of-the-art methodologies that are employed to characterize the CMB region and relevant papers will be discussed in class. Topics will include CMB detection and topography, D'' anisotropy, seismic velocity anomalies (e.g., ultra-low velocity zones), temperature, chemical reactions, phase relations, and mineral fabrications at the core-mantle boundary. These results will be i

Subjects

Core Mantle Boundary (CMB) | deep Earth | lower mantle | outer core | integrated seismological | mineral physics and geodynamical perspectives | CMB detection and topography | D'' anisotropy | seismic velocity anomalies (e.g. | ultra-low velocity zones) | temperature | chemical reactions | phase relations | mineral fabrications | cmb detection | topography | mineral physics | geodynamical perspectives | D" Region | ultra-low velocity zones | partial melting | mineral texture | core rigidity zones | sedimentation | mantle flow | core mantle coupling | geomagnetic field

License

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6.243J Dynamics of Nonlinear Systems (MIT)

Description

This course provides an introduction to nonlinear deterministic dynamical systems. Topics covered include: nonlinear ordinary differential equations; planar autonomous systems; fundamental theory: Picard iteration, contraction mapping theorem, and Bellman-Gronwall lemma; stability of equilibria by Lyapunov's first and second methods; feedback linearization; and application to nonlinear circuits and control systems.

Subjects

nonlinear systems | deterministic dynamical systems | ordinary differential equations | planar autonomous systems | Picard iteration | contraction mapping theorem | Bellman-Gronwall lemma | Lyapunov methods | feedback linearization | nonlinear circuits | control systems | local controllability | volume evolution | system analysis | singular perturbations | averaging | local behavior | trajectories | equilibria | storage functions | stability analysis | continuity | differential equations | system models | parameters | input/output | state-space | 16.337

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The transmission electron microscope

Description

This is a third edition of the Electron Microscopy and Analysis textbook, which was published by Taylor and Francis Books UK in 2001 (ISBN 0748409688). It deals with several sophisticated techniques for magnifying images of very small objects by large amounts - especially in a physical science context. Consisting of seven chapters, presented as separate files the resource incorporates questions and answers in each chapter for ease of learning. Equally as relevant for material scientists and bioscientists, this resource is an essential textbook and laboratory manual. The chapter gives insight into the transmission electron microscope technique.

Subjects

electron microscopy | book | analysis | lenses | image formation | contrast | kinematical and dynamical conditions | defects in crystals | specimen preparation | tem | corematerials | ukoer | Engineering | H000

License

Attribution-Share Alike 2.0 UK: England & Wales Attribution-Share Alike 2.0 UK: England & Wales http://creativecommons.org/licenses/by-sa/2.0/uk/ http://creativecommons.org/licenses/by-sa/2.0/uk/

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6.231 Dynamic Programming and Stochastic Control (MIT)

Description

This course covers the basic models and solution techniques for problems of sequential decision making under uncertainty (stochastic control). We will consider optimal control of a dynamical system over both a finite and an infinite number of stages (finite and infinite horizon). We will also discuss some approximation methods for problems involving large state spaces. Applications of dynamic programming in a variety of fields will be covered in recitations.

Subjects

dynamic programming | stochastic control | decision making | uncertainty | sequential decision making | finite horizon | infinite horizon | approximation methods | state space | large state space | optimal control | dynamical system | dynamic programming and optimal control | deterministic systems | shortest path | state information | rollout | stochastic shortest path | approximate dynamic programming

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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12.864 Inference from Data and Models (MIT)

Description

The course is directed at making scientifically sensible deductions from the combination of observations with dynamics and kinematics represented, generically, as "models". There are two overlapping central themesLinear "inverse" methods and data "assimilation" including regression, singular value decomposition, objective mapping, non-stationary models and data, Kalman filters, adjoint methods ("assimilation") etc.Standard time series analysis, including basic statistics, Fourier methods, spectra, coherence, filtering, etc.

Subjects

kinematical and dynamical models | Basic statistics | linear algebra | inverse methods | singular value decompositions | control theory | sequential estimation | Kalman filters | smoothing algorithms | adjoint/Pontryagin principle methods | model testing | stationary processes | Fourier methods | z-transforms | sampling theorems | spectra | multi-taper methods | coherences | filtering | quantitative combinations of models

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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12.864 Inference from Data and Models (MIT)

Description

The course is directed at making scientifically sensible deductions from the combination of observations with dynamics and kinematics represented, generically, as "models". There are two overlapping central themeslinear "inverse" methods and data "assimilation" including regression, singular value decomposition, objective mapping, non-stationary models and data, Kalman filters, adjoint methods ("assimilation") etc.standard time series analysis, including basic statistics, Fourier methods, spectra, coherence, filtering, etc.

Subjects

observation | kinematical models | dynamical models | basic statistics | linear algebra | inverse methods | singular value decompositions | control theory | sequential estimation | Kalman filters | smoothing algorithms | adjoint/Pontryagin principle methods | model testing | stationary processes | Fourier methods | z-transforms | sampling theorems | spectra | multi-taper methods | coherences | filtering | quantitative combinations | realistic observations | data assimilations | deduction | regression | objective mapping | time series analysis | inference

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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18.311 Principles of Applied Mathematics (MIT)

Description

Discussion of computational and modeling issues. Nonlinear dynamical systems; nonlinear waves; diffusion; stability; characteristics; nonlinear steepening, breaking and shock formation; conservation laws; first-order partial differential equations; finite differences; numerical stability; etc. Applications to traffic problems, flows in rivers, internal waves, mechanical vibrations and other problems in the physical world.Technical RequirementsMATLAB® software is required to run the .m files found on this course site. MATLAB® is a trademark of The MathWorks, Inc.

Subjects

Nonlinear dynamical systems | nonlinear waves | diffusion | stability | characteristics | nonlinear steepening | breaking and shock formation | conservation laws | first-order partial differential equations | finite differences | numerical stability | traffic problems | flows in rivers | internal waves | mechanical vibrations

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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2.18 Biomolecular Feedback Systems (MIT)

Description

This course focuses on feedback control mechanisms that living organisms implement at the molecular level to execute their functions, with emphasis on techniques to design novel systems with prescribed behaviors. Students will learn how biological functions can be understood and designed using notions from feedback control.

Subjects

biomolecular feedback systems | systems biology | modeling | feedback | cell | system | control | dynamical | input/output | synthetic biology | techniques | transcription | translation | transcriptional regulation | post-transcriptional regulation | cellular subsystems | dynamic behavior | analysis | equilibrium | robustness | oscillatory behavior | bifurcations | model reduction | stochastic | biochemical | simulation | linear | circuit | design | biological circuit design | negative autoregulation | toggle switch | repressilator | activator-repressor clock | IFFL | incoherent feedforward loop | bacterial chemotaxis | interconnecting components | modularity | retroactivity | gene circuit

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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