How Light Enters the Eye

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Refraction of Light

Refraction is the change in direction of a wave due to a change in its speed. This is most commonly seen when a wave passes from one medium to another. Refraction of light is the most commonly seen example, but any type of wave can refract when it interacts with a medium, for example when sound waves pass from one medium into another or when water waves move into water of a different depth.

In optics, refraction occurs when light waves travel from a medium with a given refractive index to a medium with another. At the boundary between the media, the wave's phase velocity is altered, it changes direction, and its wavelength increases or decreases but its frequency remains constant. For example, a light ray will refract as it enters and leaves glass; understanding of this concept led to the invention of lenses and the refracting telescope.

Refraction can be seen when looking into a bowl of water. Air has a refractive index of about 1.0003, and water has a refractive index of about 1.33. If a person looks at a straight object, such as a pencil or straw, which is placed at a slant, partially in the water, the object appears to bend at the water's surface. This is due to the bending of light rays as they move from the water to the air. Once the rays reach the eye, the eye traces them back as straight lines (lines of sight). The lines of sight (shown as dashed lines) intersect at a higher position than where the actual rays originated. This causes the pencil to appear higher and the water to appear shallower than it really is. The depth that the water appears to be when viewed from above is known as the apparent depth. This is an important consideration for spearfishing from the surface because it will make the target fish appear to be in a different place, and the fisher must aim lower to catch the fish.

Refraction is also responsible for rainbows and for the splitting of white light into a rainbow-spectrum as it passes through a glass prism. Glass has a higher refractive index than air and the different frequencies of light travel at different speeds (dispersion), causing them to be refracted at different angles, so that you can see them. The different frequencies correspond to different colors observed.

While refraction allows for beautiful phenomena such as rainbows, it may also produce peculiar optical phenomena, such as mirages and Fata Morgana. These are caused by the change of the refractive index of air with temperature.

Snell's law is used to calculate the degree to which light is refracted when traveling from one medium to another.

Recently some metamaterials have been created which have a negative refractive index. With metamaterials, we can also obtain the total refraction phenomena when the wave impedances of the two media are matched. There is no reflected wave.

Also, since refraction can make objects appear closer than they are, it is responsible for allowing water to magnify objects. First, as light is entering a drop of water, it slows down. If the water's surface is not flat, then the light will be bent into a new path. This round shape will bend the light outwards and as it spreads out, the image you see gets larger.

A useful analogy in explaining the refraction of light would be to imagine a marching band as they march from pavement (a fast medium) into mud (a slower medium) The marchers on the side that runs into the mud first will slow down first. This causes the whole band to pivot slightly toward the normal (make a smaller angle from the normal).

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Laws of reflection

Reflection is the change in direction of a wave front at an interface between two different media so that the wave front returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves.

Reflection of light may be specular (that is, mirror-like) or diffuse (that is, not retaining the image, only the energy) depending on the nature of the interface. Furthermore, if the interface is between dielectric-conductor or dielectric-dielectric media, the phase of the reflected wave may or may not be inverted, respectively.

A mirror provides the most common model for specular light reflection and consists of a glass sheet in front of a metallic coating where the reflection actually occurs. Reflection is enhanced in metals by suppression of wave propagation beyond their skin depths. It is also possible for reflection to occur from the surface of transparent media, such as water or glass. In the diagram, a light ray PO strikes a vertical mirror at point O, and the reflected ray is OQ. By projecting an imaginary line through point O perpendicular to the mirror, known as the normal, we can measure the angle of incidence, θi and the angle of reflection, θr. The law of reflection states that θi = θr, or in other words, the angle of incidence equals the angle of reflection.

In fact, reflection of light may occur whenever light travels from a medium of a given refractive index into a medium with a different refractive index. In the most general case, a certain fraction of the light is reflected from the interface, and the remainder is refracted. Solving Maxwell's equations for a light ray striking a boundary allows the derivation of the Fresnel equations, which can be used to predict how much of the light reflected, how much is refracted in a given situation. Total internal reflection of light from a denser medium occurs if the angle of incidence is above the critical angle. Total internal reflection is used as a means of focussing waves that cannot effectively be reflected by common means. X-ray telescopes are constructed by creating a converging "tunnel" for the waves. As the waves interact at low angle with the surface of this tunnel they are reflected toward the focus point (or toward another interaction with the tunnel surface, eventually being directed to the a detector at the focus). A conventional reflector would be useless as the X-rays would simply pass through the intended reflector. When light reflects off a material denser (with higher refractive index) than the external medium, it undergoes a 180° phase reversal. In contrast, a less dense, lower refractive index material will reflect light in phase. This is an important principle in the field of thin-film optics. Specular reflection at a curved surface forms an image which may be magnified or demagnified; curved mirrors have optical power. Such mirrors may have surfaces that are spherical or parabolic.

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Prism

Prism is a transparent optical element with flat, polished surfaces that refract light. The exact angles between the surfaces depend on the application. The traditional geometrical shape is that of a triangular prism with a triangular base and rectangular sides, and in colloquial use "prism" usually refers to this type. Some types of optical prism are not in fact in the shape of geometric prisms. Prisms are typically made out of glass, but can be made from any material that is transparent to the wavelengths for which they are designed.

A prism can be used to break light up into its constituent spectral colors (the colors of the rainbow). Prisms can also be used to reflect light, or to split light into components with different polarizations.

How prisms work

Light changes speed as it moves from one medium to another (for example, from air into the glass of the prism). This speed change causes the light to be refracted and to enter the new medium at a different angle (Huygens principle). The degree of bending of the light's path depends on the angle that the incident beam of light makes with the surface, and on the ratio between the refractive indices of the two media (Snell's law). The refractive index of many materials (such as glass) varies with the wavelength or color of the light used, a phenomenon known as dispersion. This causes light of different colors to be refracted differently and to leave the prism at different angles, creating an effect similar to a rainbow. This effect can be used to separate a beam of white light into its constituent spectrum of colors. Prisms will generally disperse light over a much larger frequency bandwidth than diffraction gratings, making them useful for broad-spectrum spectroscopy. Furthermore, prisms do not suffer from complications arising from overlapping spectral orders, which all gratings have.

Prisms are sometimes used for the internal reflection at the surfaces rather than for dispersion. If light inside the prism hits one of the surfaces at a sufficiently steep angle, total internal reflection occurs and all of the light is reflected. This makes a prism a useful substitute for a mirror in some situations.

Prisms and the nature of light

In Isaac Newton's time, it was believed that white light was colorless, and that the prism itself produced the color. Newton's experiments convinced him that all the colors already existed in the light in a heterogeneous fashion, and that "corpuscles" (particles) of light were fanned out because particles with different colors traveled with different speeds through the prism. It was only later that Young and Fresnel combined Newton's particle theory with Huygen's wave theory to show that color is the visible manifestation of light's wavelength.

Newton arrived at his conclusion by passing the red color from one prism through a second prism and found the color unchanged. From this, he concluded that the colors must already be present in the incoming light — thus, the prism did not create colors, but merely separated colors that are already there. He also used a lens and a second prism to recompose the spectrum back into white light. This experiment has become a classic example of the methodology introduced during the scientific revolution. The results of this experiment dramatically transformed the field of metaphysics, leading to John Locke's primary vs secondary quality distinction.

Newton discussed prism dispersion in great detail in his book Opticks.[1] He also introduced the use of more than one prism to control dispersion. Newton's description of his experiments on prism dispersion was qualitative, and is quite readable. A quantitative description of multiple-prism dispersion was not needed until multiple prism laser beam expanders were introduced in the 1980s.

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SPECTRUM

A spectrum (plural spectra or spectrums) is a condition that is not limited to a specific set of values but can vary infinitely within a continuum. The word saw its first scientific use within the field of optics to describe the rainbow of colors in visible light when separated using a prism; it has since been applied by analogy to many fields. Thus one might talk about the spectrum of political opinion, or the spectrum of activity of a drug, or the autism spectrum. In these uses, values within a spectrum are not necessarily precisely defined numbers as in optics; exact values within the spectrum are not precisely quantifiable. Such use implies a broad range of conditions or behaviors grouped together and studied under a single title for ease of discussion.

In most modern usages of spectrum there is a unifying theme between extremes at either end. Some older usages of the word did not have a unifying theme, but they led to modern ones through a sequence of events set out below. Modern usages in mathematics did evolve from a unifying theme, but this may be difficult to recognize.

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Modern Physics: Special Relativity

Special relativity (SR) (also known as the special theory of relativity or STR) is the physical theory of measurement in inertial frames of reference proposed in 1905 by Albert Einstein (after considerable contributions of Hendrik Lorentz and Henri Poincaré) in the paper "On the Electrodynamics of Moving Bodies". It generalizes Galileo's principle of relativity – that all uniform motion is relative, and that there is no absolute and well-defined state of rest (no privileged reference frames) – from mechanics to all the laws of physics, including both the laws of mechanics and of electrodynamics, whatever they may be. In addition, special relativity incorporates the principle that the speed of light is the same for all inertial observers regardless of the state of motion of the source.

This theory has a wide range of consequences which have been experimentally verified. Special relativity overthrows Newtonian notions of absolute space and time by stating that time and space are perceived differently by observers in different states of motion. It yields the equivalence of matter and energy, as expressed in the mass-energy equivalence formula E = mc2, where c is the speed of light in a vacuum. The predictions of special relativity agree well with Newtonian mechanics in their common realm of applicability, specifically in experiments in which all velocities are small compared to the speed of light.

The theory is termed "special" because it applies the principle of relativity only to inertial frames. Einstein developed general relativity to apply the principle generally, that is, to any frame, and that theory includes the effects of gravity. Strictly, special relativity cannot be applied in accelerating frames or in gravitational fields.

Special relativity reveals that c is not just the velocity of a certain phenomenon, namely the propagation of electromagnetic radiation (light)—but rather a fundamental feature of the way space and time are unified as spacetime. A consequence of this is that it is impossible for any particle that has mass to be accelerated to the speed of light.

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Resolution - Refutation Proofs

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Programming Paradigms

Computer architecture by discussing function call and return in further depth as well as introducing the swap function in relation to C++ code

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computer architecture function call and returns in relation to C code.

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Computer architecture and the Assembly programming language

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Heap segments and their use in the C programming language

HEap Swgment is a segment of memory claimed by a program. Within the heap, pieces of memory can be used and freed as needed. Depending on usage, heaps can become fragmented as small pieces of memory are used and freed. In formal computer science terms, a heap is the same as a partially ordered tree.

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C programming language and generic stacks

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Programming Paradigms-C language programming by focusing on different forms of stack.

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Linear Dynamical Systems Lecture 20-Observability and State Estimation

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Lecture 19 Controllability and State Transfer and their uses in modern electrical engineering

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Linear Dynamical Systems Lecture 18 -Applications of SVD, Controllability,and State Transfer in Electrical Engineering

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Linear Dynamical Systems Lecture 17-Applications of single value decomposition in LDS and electrical engineering

Singular value decomposition (SVD) is an important factorization of a rectangular real or complex matrix, with several applications in signal processing and statistics. Applications which employ the SVD include computing the pseudoinverse, least squares fitting of data, matrix approximation, and determining the rank, range and null space of a matrix.

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Linear Dynamical Systems Lecture 16- Use of symmetric matrices, quadratic forms, matrix norm, and SVDs in LDS

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Linear Dynamical Systems Lecture 15-Inputs and Outputs of symmetric matrices

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Linear Dynamical Systems Lecture 14- Applications of Jordan Canonical Form in LDS and Electrical Engineering

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Linear Dynamical Systems Lecture 13-generalized eigenvectors, diagonalization, and Jordan canonical form

Jordan normal form (often called Jordan canonical form) shows that a given square matrix M over a field K containing the eigenvalues of M can be transformed into a certain normal form by changing the basis. This normal form is almost diagonal in the sense that its only non-zero entries lie on the diagonal and the superdiagonal. This is made more precise in the Jordan-Chevalley decomposition. One can compare this result with the spectral theorem for normal matrices, which is a special case of the Jordan normal form.

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Linear Dynamical Systems Lecture12-Matrix exponentials,Eigenvectors,and Diagonalization and their uses in LDS

Matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function. Abstractly, the matrix exponential gives the connection between a matrix Lie algebra and the corresponding Lie group.In linear algebra, a square matrix A is called diagonalizable if it is similar to a diagonal matrix, i.e. if there exists an invertible matrix P such that P −1AP is a diagonal matrix. If V is a finite-dimensional vector space, then a linear map T : V → V is called diagonalizable if there exists a basis of V with respect to which T is represented by a diagonal matrix. Diagonalization is the process of finding a corresponding diagonal matrix for a diagonalizable matrix or linear map.

Diagonalizable matrices and maps are of interest because diagonal matrices are especially easy to handle: their eigenvalues and eigenvectors are known and one can raise a diagonal matrix to a power by simply raising the diagonal entries to that same power.

The Jordan-Chevalley decomposition expresses an operator as the sum of its diagonal part and its nilpotent part.

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Linear Dynamical Systems Lecture 11-LaPlace transform use of matrix exponentials

Matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function. Abstractly, the matrix exponential gives the connection between a matrix Lie algebra and the corresponding Lie group.Laplace transform is one of the best known and widely used integral transforms. It is commonly used to produce an easily solvable algebraic equation from an ordinary differential equation. It has many important applications in mathematics, physics, optics, electrical engineering, control engineering, signal processing, and probability theory.

In mathematics, it is used for solving differential and integral equations. In physics, it is used for analysis of linear time-invariant systems such as electrical circuits, harmonic oscillators, optical devices, and mechanical systems. In this analysis, the Laplace transform is often interpreted as a transformation from the time-domain, in which inputs and outputs are functions of time, to the frequency-domain, where the same inputs and outputs are functions of complex angular frequency, or radians per unit time. Given a simple mathematical or functional description of an input or output to a system, the Laplace transform provides an alternative functional description that often simplifies the process of analyzing the behavior of the system, or in synthesizing a new system based on a set of specifications.

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Linear Dynamical Systems Lecture 9&10 -Autonomous linear dynamical systems

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Linear Dynamical Systems Lecture 8-Least Norm solutions of undetermined equations

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Linear Dynamical Systems Lecture 7-Regularized least squares and the Gauss-Newton method

Gauss–Newton algorithm is a method used to solve non-linear least squares problems. It can be seen as a modification of Newton's method for finding a minimum of a function. Unlike Newton's method, the Gauss–Newton algorithm can only be used to minimize a sum of squared function values, but it has the advantage that second derivatives, which can be challenging to compute, are not required.Non-linear least squares problems arise for instance in non-linear regression, where parameters in a model are sought such that the model is in good agreement with available observations.The method is due to the renowned mathematician Carl Friedrich Gauss.

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Linear Dynamical Systems Lecture 6-Applications of least squares

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Linear Dynamical Systems Lecture 5- QR Factorization and least squares

The method of least squares is used to solve overdetermined systems. Least squares is often applied in statistical contexts, particularly regression analysis.Least squares can be interpreted as a method of fitting data. The best fit in the least-squares sense is that instance of the model for which the sum of squared residuals has its least value, a residual being the difference between an observed value and the value given by the model. The method was first described by Carl Friedrich Gauss around 1794.[1] Least squares corresponds to the maximum likelihood criterion if the experimental errors have a normal distribution and can also be derived as a method of moments estimator. Regression analysis is available in most statistical software packages.

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Linear Dynamical Systems lecture 4-Orthonormal sets of vectors and QR factorization

In linear algebra, two vectors in an inner product space are orthonormal if they are orthogonal and both of unit length. A set of vectors form an orthonormal set if all vectors in the set are mutually orthogonal and all of unit length. An orthonormal set which forms a basis is called an orthonormal basis.

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Linear Dynamical Systems Lecture 3-Linear algebra

Linear algebra is the branch of mathematics concerned with the study of vectors, vector spaces (also called linear spaces), linear maps (also called linear transformations), and systems of linear equations. Vector spaces are a central theme in modern mathematics; thus, linear algebra is widely used in both abstract algebra and functional analysis. Linear algebra also has a concrete representation in analytic geometry and it is generalized in operator theory. It has extensive applications in the natural sciences and the social sciences, since nonlinear models can often be approximated by linear ones.

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Linear Dynamical Systems Lecture 2 -Linear functions

A linear function is a real or complex function f with the functional equation y=f(x)=m⋅x+b, where m and b are real (or complex) numbers. The equation y=f(x)=m⋅x+b is called (general) linear equation. The graph of a real linear function is a straight line.

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Introduction to Linear Dynamical Systems Lecture 1

Introduction to applied linear algebra and linear dynamical systems, with applications to circuits, signal processing, communications, and control systems. Topics include: Least-squares aproximations of over-determined equations and least-norm solutions of underdetermined equations. Symmetric matrices, matrix norm and singular value decomposition. Eigenvalues, left and right eigenvectors, and dynamical interpretation. Matrix exponential, stability, and asymptotic behavior. Multi-input multi-output systems, impulse and step matrices; convolution and transfer matrix descriptions.

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Convex Optimization II

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Knowledge Based Systems: Logic and Deduction

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Convex Optimization

Convex optimization is a subfield of mathematical optimization. Given a real vector space together with a convex, real-valued function

defined on a convex subset of , the problem is to find the point in for which the number is smallest, i.e., the point such that for all .

The convexity of and make the powerful tools of convex analysis applicable: the Hahn–Banach theorem and the theory of subgradients lead to a particularly satisfying and complete theory of necessary and sufficient conditions for optimality, a duality theory comparable in perfection to that for linear programming, and effective computational methods. Convex optimization has applications in a wide range of disciplines, such as automatic control systems, estimation and signal processing, communications and networks, electronic circuit design, data analysis and modeling, statistics, and finance. Modern computing power has improved the tractability of convex optimization problems to a level roughly equal to that of linear programming.

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Lecture by Professor Stephen Boyd for Convex Optimization II (EE 364B) in the Stanford Electrical Engineering department. Professor Boyd lectures on the localization and cutting-plane methods and then moves into the Analytic center cutting-plane methods.

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Programming Abstractions

The computing environment of tomorrow will not be anything like the stand-alone environment of yesterday. Computing infrastructure is changing drastically, presenting unique opportunities as well as challenges for applications and application scientists. Despite the rapid onset of distributed infrastructure, the majority of scientists still use the same programming methods that they are accustomed to using on isolated computers. On the other hand, the underlying infrastructure does not support seamless extensibility or scaling of applications from desktops to distributed heterogenous resources. An important feature of this theme will be its focus on applications, and thus a consequent "top-down" approach to distributed programming abstractions. In particular, this Theme will examine how scientific applications can be programmed such that they can easily utilise distributed infrastructure, and how computer scientists can help design and implement applications that are shielded from future trends and changes in computing environments. The Theme aims to address these issues by focusing, amongst many others, on the following questions: What are the main barriers to wide-spread distributed High Performance Computing applications? Is there a level at which simple yet powerful programming abstractions can be effective in distributed environments?

Over the course of this theme, there will be a series of correlated workshops and meetings to explore many of these issues. In addition to surveying the status of the field and addressing the high level questions, this theme aims to spawn focussed research groups that will examine in greater detail some of the specific ideas.

Lecture 1

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Special Relativity Lecture

Special relativity (SR) (also known as the special theory of relativity or STR) is the physical theory of measurement in inertial frames of reference proposed in 1905 by Albert Einstein (after considerable contributions of Hendrik Lorentz and Henri Poincaré) in the paper "On the Electrodynamics of Moving Bodies". It generalizes Galileo's principle of relativity – that all uniform motion is relative, and that there is no absolute and well-defined state of rest (no privileged reference frames) – from mechanics to all the laws of physics, including both the laws of mechanics and of electrodynamics, whatever they may be. In addition, special relativity incorporates the principle that the speed of light is the same for all inertial observers regardless of the state of motion of the source.

This theory has a wide range of consequences which have been experimentally verified. Special relativity overthrows Newtonian notions of absolute space and time by stating that time and space are perceived differently by observers in different states of motion. It yields the equivalence of matter and energy, as expressed in the mass-energy equivalence formula E = mc2, where c is the speed of light in a vacuum. The predictions of special relativity agree well with Newtonian mechanics in their common realm of applicability, specifically in experiments in which all velocities are small compared to the speed of light.

The theory is termed "special" because it applies the principle of relativity only to inertial frames. Einstein developed general relativity to apply the principle generally, that is, to any frame, and that theory includes the effects of gravity. Strictly, special relativity cannot be applied in accelerating frames or in gravitational fields.

Special relativity reveals that c is not just the velocity of a certain phenomenon, namely the propagation of electromagnetic radiation (light)—but rather a fundamental feature of the way space and time are unified as spacetime. A consequence of this is that it is impossible for any particle that has mass to be accelerated to the speed of light.

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Searching Game Trees

In combinatorial game theory, a game tree is a directed graph whose nodes are positions in a game and whose edges are moves. The complete game tree for a game is the game tree starting at the initial position and containing all possible moves from each position.


The diagram shows the first two levels, or ply, in the game tree for tic-tac-toe. We consider all the rotations and reflections of positions as being equivalent, so the first player has three choices of move: in the centre, at the edge, or in the corner. The second player has two choices for the reply if the first player played in the centre, otherwise five choices. And so on.

The number of leaf nodes in the complete game tree is called the game tree complexity. It is the number of possible different ways the game can be played. The game tree complexity for tic-tac-toe is 26,830.

Game trees are important in artificial intelligence because one way to pick the best move in a game is to search the game tree using the minimax algorithm or its variants. The game tree for tic-tac-toe is easily searchable, but the complete game trees for larger games like chess are much too large to search. Instead, a chess-playing program searches a partial game tree: typically as many ply from the current position as it can search in the time available.

Two-person games can also be represented as and-or trees. For the first player to win a game, there must exist a winning move for all moves of the second player. This is represented in the and-or tree by using disjunction to represent the first player's alternative moves and using conjunction to represent all of the second player's moves.

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Problem Reduction Search: AND/OR Graphs

Sometimes problems only seem hard to solve. A hard problem may be one that can be reduced to a number of simple problems...and, when each of the simple problems is solved, then the hard problem has been solved. This is the basic intuition behind the method of problem reduction. We will have much more to say about this method of search when we cover problem solving and planning in the second half of the course. At this point, our goal is simply to introduce you to this type of search and illustrate the way in which it differs from state space search.

The typical problem that is used to illustrate problem reduction search is the Tower of Hanoi problem because this problem has a very elegant solution using this method. The story that is typically quoted to describe the Tower of Hanoi problem describes the specific problem faced by the priests of Brahmah. Just in case you didn't decide to read this story, the gist of it is that 64 size ordered disks occupy one of 3 pegs and must be transferred to one of the other pegs. But, only one disk can be moved at a time; and a larger disk may never be placed on a smaller disk.

Rather than deal with the 64 disk problem faced by the priests, we will consider only three disks...the minimum required to make the problem mildly interesting and useful for our purpose here...namely to illustrate problem reduction search. The figure below shows the state space associated with a 3-disk Tower of Hanoi Problem. The problem involves moving from a state where the disks are stacked on one of the pegs and moving them so that they end up stacked on a different peg. In this case, we will consider the state at the top of the figure the starting state. In this case all three disks are on the left-most peg. And we will consider the state at the bottom right to be the goal state. In this state the three disks are now all stacked on the right-most peg.

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Heuristic Search A* and Beyond

Heuristic algorithm or simply a heuristic is an algorithm that gives up finding the optimal solution for an improvement in run time.

Two fundamental goals in computer science are finding algorithms with provably good run times and with provably good or optimal solution quality. A heuristic is an algorithm that abandons one or both of these goals; for example, it usually finds pretty good solutions, but there is no proof the solutions could not get arbitrarily bad; or it usually runs reasonably quickly, but there is no argument that this will always be the case.

For instance, say you are packing odd-shaped items into a box. Finding a perfect solution is a hard problem: there is essentially no way to do it without trying every possible way of packing them. What most people do, then, is "put the largest items in first, then fit the smaller items into the spaces left around them." This will not necessarily be perfect packing, but it will usually give a packing that is pretty good. It is an example of a heuristic solution.

Many commercial anti-virus scanners use heuristic signatures to look for specific attributes and characteristics for detecting viruses and other forms of malware.

Judea Pearl states that heuristic methods are based upon intelligent search strategies for computer problem solving, using several alternative approaches.

Often, one can find specially crafted problem instances where the heuristic will in fact produce very bad results or run very slowly; however, such pathological instances might never occur in practice because of their special structure. Therefore, the use of heuristics is very common in real world implementations. For many practical problems, a heuristic algorithm may be the only way to get good solutions in a reasonable amount of time. There is a class of general heuristic strategies called metaheuristics, which often use randomized search for example. They can be applied to a wide range of problems, but good performance is never guaranteed.

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Programming Paradigms

A programming paradigm is a fundamental style of computer programming. (Compare with a methodology, which is a style of solving specific software engineering problems).

A programming language can support multiple paradigms. For example programs written in C++ or Object Pascal can be purely procedural, or purely object-oriented, or contain elements of both paradigms. Software designers and programmers decide how to use those paradigm elements.

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In object-oriented programming, programmers can think of a program as a collection of interacting objects, while in functional programming a program can be thought of as a sequence of stateless function evaluations. When programming computers or systems with many processors, process-oriented programming allows programmers to think about applications as sets of concurrent processes acting upon logically shared data structures.

Just as different groups in software engineering advocate different methodologies, different programming languages advocate different programming paradigms. Some languages are designed to support one particular paradigm (Smalltalk supports object-oriented programming, Haskell supports functional programming), while other programming languages support multiple paradigms (such as Object Pascal, C++, C#, Visual Basic, Common Lisp, Scheme, Python, Ruby and Oz).

Many programming paradigms are as well known for what techniques they forbid as for what they enable. For instance, pure functional programming disallows the use of side-effects; structured programming disallows the use of the goto statement. Partly for this reason, new paradigms are often regarded as doctrinaire or overly rigid by those accustomed to earlier styles. Avoiding certain techniques can make it easier to prove theorems about a program's correctness—or simply to understand its behavior.

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Introduction to Robotics Lecture 16

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Introduction to Robotics Lecture 15

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Introduction to Robotics Lecture 14

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Introduction to Robotics Lecture 13

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Introduction to Robotics Lecture 12

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Introduction to Robotics Lecture 11

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Introduction to Robotics Lecture 10

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Introduction to Robotics Lecture 9

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Introduction to Robotics Lecture 8

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Introduction to Robotics lecture 7

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Introduction to Robotics Lecture 6

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Introduction to Robotics Lecture 5

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Introduction to Robotics

Robotics is the science and technology of robots, their design, manufacture, and application. Robotics requires a working knowledge of electronics, mechanics and software, and is usually accompanied by a large working knowledge of many subjects. A person working in the field is a roboticist.

The structure of a robot is usually mostly mechanical and can be called a kinematic chain (its functionality being similar to the skeleton of the human body). The chain is formed of links (its bones), actuators (its muscles) and joints which can allow one or more degrees of freedom. Most contemporary robots use open serial chains in which each link connects the one before to the one after it. These robots are called serial robots and often resemble the human arm. Some robots, such as the Stewart platform, use closed parallel kinematic chains. Other structures, such as those that mimic the mechanical structure of humans, various animals and insects, are comparatively rare. However, the development and use of such structures in robots is an active area of research (e.g. biomechanics). Robots used as manipulators have an end effector mounted on the last link. This end effector can be anything from a welding device to a mechanical hand used to manipulate the environment. ISO 10248 defines a robotic application on the industrial field.
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Introduction to robotics which covers topics such as Spatial Descriptions, Forward Kinematics, Inverse Kinematics, Jacobians, Dynamics, Motion Planning and Trajectory Generation, Position and Force Control, and Manipulator Design.

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Machine Learning lecture 20

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Machine Learning Lecture 4 |

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Machine Learning lecture 3

This course provides a broad introduction to machine learning and statistical pattern recognition. Topics include supervised learning, unsupervised learning, learning theory, reinforcement learning and adaptive control. Recent applications of machine learning, such as to robotic control, data mining, autonomous navigation, bioinformatics, speech recognition, and text and web data processing are also discussed.

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Machine Learning lecture 2

Linerar regression,gradient descent,normal equations

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Machine Learning lecture

Machine learning is concerned with the design and development of algorithms and techniques that allow computers to "learn". At a general level, there are two types of learning: inductive, and deductive. Inductive machine learning methods extract rules and patterns out of massive data sets.

The major focus of machine learning research is to extract information from data automatically, by computational and statistical methods. Hence, machine learning is closely related not only to data mining and statistics, but also theoretical computer science.

Lecture 1

Machine learning algorithms are organized into a taxonomy, based on the desired outcome of the algorithm. Common algorithm types include:

Supervised learning — in which the algorithm generates a function that maps inputs to desired outputs. One standard formulation of the supervised learning task is the classification problem: the learner is required to learn (to approximate) the behavior of a function which maps a vector into one of several classes by looking at several input-output examples of the function.

Unsupervised learning — An agent which models a set of inputs: labeled examples are not available.

Semi-supervised learning — which combines both labeled and unlabeled examples to generate an appropriate function or classifier.

Reinforcement learning — in which the algorithm learns a policy of how to act given an observation of the world. Every action has some impact in the environment, and the environment provides feedback that guides the learning algorithm.

Transduction — similar to supervised learning, but does not explicitly construct a function: instead, tries to predict new outputs based on training inputs, training outputs, and test inputs which are available while training.

Leaning to learn — in which the algorithm learns its own inductive bias based on previous experience.

The computational analysis of machine learning algorithms and their performance is a branch of theoretical computer science known as computational learning theory.

This course provides a broad introduction to machine learning and statistical pattern recognition. Topics include supervised learning, unsupervised learning, learning theory, reinforcement learning and adaptive control. Recent applications of machine learning, such as to robotic control, data mining, autonomous navigation, bioinformatics, speech recognition, and text and web data processing are also discussed.

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Artificial Intelligence:Informed State Space Search

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Artificial Intelligence-Searching with Costs

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Artificial Intelligence-Problem Solving by Search

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Index Properties and Classification of Soils

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Sampling and Non - Intrusive Methods

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Introduction to Subsurface Exploration

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Fluid Mechanics

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Artificial Intelligence

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Sediment Transport and Deposition

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The New Food Wars: Globalization GMOs and Biofuels

The New Food Wars: Globalization GMOs and Biofuels

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Advanced Concepts of Gravity

Advanced Concepts of Gravity

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Weathering

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Metamorphic Rocks

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Sedimentary Rocks

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Igneous Rocks lecture

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Origin And Types of Soils

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Origin And Types of Rocks

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Chemical Characteristics of Minerals

Minerals may be classified according to chemical composition. They are here categorized by anion group. The list below is in approximate order of their abundance in the Earth's crust. The list follows the Dana classification system.

Silicate class

The largest group of minerals by far are the silicates (most rocks are ≥95% silicates), which are composed largely of silicon and oxygen, with the addition of ions such as aluminium, magnesium, iron, and calcium. Some important rock-forming silicates include the feldspars, quartz, olivines, pyroxenes, amphiboles, garnets, and micas.

Carbonate class

The carbonate minerals consist of those minerals containing the anion (CO3)2- and include calcite and aragonite (both calcium carbonate), dolomite (magnesium/calcium carbonate) and siderite (iron carbonate). Carbonates are commonly deposited in marine settings when the shells of dead planktonic life settle and accumulate on the sea floor. Carbonates are also found in evaporitic settings (e.g. the Great Salt Lake, Utah) and also in karst regions, where the dissolution and reprecipitation of carbonates leads to the formation of caves, stalactites and stalagmites. The carbonate class also includes the nitrate and borate minerals.

Sulfate class

Sulfates all contain the sulfate anion, SO42-. Sulfates commonly form in evaporitic settings where highly saline waters slowly evaporate, allowing the formation of both sulfates and halides at the water-sediment interface. Sulfates also occur in hydrothermal vein systems as gangue minerals along with sulfide ore minerals. Another occurrence is as secondary oxidation products of original sulfide minerals. Common sulfates include anhydrite (calcium sulfate), celestine (strontium sulfate), barite (barium sulfate), and gypsum (hydrated calcium sulfate). The sulfate class also includes the chromate, molybdate, selenate, sulfite, tellurate, and tungstate minerals.

Oxide class

Oxides are extremely important in mining as they form many of the ores from which valuable metals can be extracted. They also carry the best record of changes in the Earth's magnetic field. They commonly occur as precipitates close to the Earth's surface, oxidation products of other minerals in the near surface weathering zone, and as accessory minerals in igneous rocks of the crust and mantle. Common oxides include hematite (iron oxide), magnetite (iron oxide), chromite (iron chromium oxide), spinel (magnesium aluminium oxide - a common component of the mantle), ilmenite (iron titanium oxide), rutile (titanium dioxide), and ice (hydrogen oxide). The oxide class includes the oxide and the hydroxide minerals.

Halide class

The halides are the group of minerals forming the natural salts and include fluorite (calcium fluoride), halite (sodium chloride), sylvite (potassium chloride), and sal ammoniac (ammonium chloride). Halides, like sulfates, are commonly found in evaporitic settings such as playa lakes and landlocked seas such as the Dead Sea and Great Salt Lake. The halide class includes the fluoride, chloride, bromide and iodide minerals.

Sulfide class

Many sulfide minerals are economically important as metal ores. Common sulfides include pyrite (iron sulfide - commonly known as fools' gold), chalcopyrite (copper iron sulfide), pentlandite (nickel iron sulfide), and galena (lead sulfide). The sulfide class also includes the selenides, the tellurides, the arsenides, the antimonides, the bismuthinides, and the sulfosalts (sulfur and a second anion such as arsenic).

Phosphate class

The phosphate mineral group actually includes any mineral with a tetrahedral unit AO4 where A can be phosphorus, antimony, arsenic or vanadium. By far the most common phosphate is apatite which is an important biological mineral found in teeth and bones of many animals. The phosphate class includes the phosphate, arsenate, vanadate, and antimonate minerals.

Element class

The elemental group includes metals and intermetallic elements (gold, silver, copper), semi-metals and non-metals (antimony, bismuth, graphite, sulfur). This group also includes natural alloys, such as electrum (a natural alloy of gold and silver), phosphides, silicides, nitrides and carbides (which are usually only found naturally in a few rare meteorites).

Organic class

The organic mineral class includes biogenic substances in which geological processes have been a part of the genesis or origin of the existing compound. Minerals of the organic class include various oxalates, mellitates, citrates, cyanates, acetates, formates, hydrocarbons and other miscellaneous species. Examples include whewellite, moolooite, mellite, fichtelite, carpathite, evenkite and abelsonite.

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Crystallography and Optical Properties

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Physical Properties of Minerals

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Remote Sensing in Engineering Geology

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Geologic Maps and Stratigraphic Sections

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Geologic Structures

Structural geology is the study of the three dimensional distribution of rock bodies and their planar or folded surfaces, and their internal fabrics.

Structural geology includes features of and overlaps with facets of geomorphology, metamorphism and geotechnical studies. By studying the three dimensional structure of rocks and regions, inferences on tectonic history, past geological environments and deformation events can be made. These can be fixed in time using stratigraphical controls as well as geochronology, to determine when the structural features formed.

More formally stated it is the branch of geology that deals with the geological processes through which the application of a force results in the transformation of a shape, arrangement or internal fabric of the rock into another shape, arrangement or internal fabric. Petroleum structural geologists can interpret prospect or basin scale geology using several techniques. These techniques include the interpretation of surface data, well data, remote sensing data and seismic data. Many structural geologists now use 2D/3D geological modelling software in order to integrate these varied datasets.

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Introduction to Engineering Geology

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