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Topic: Information geometry

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	Information geometry - Wikipedia, the free encyclopedia
		The main tenet of information geometry is that many important structures in probability theory, information theory and statistics can be treated as structures in differential geometry by regarding a space of probabilities as a differential manifold endowed with a Riemannian metric and a family of affine connections.
		The Fisher information metric is a Riemannian metric.
		The Fisher information matrix was shown by Cramer and Rao to be a Riemannian metric on the space of probabilities, and became known as Fisher information metric.
	en.wikipedia.org /wiki/Information_geometry (884 words)

	Information Geometry of the EM and em Algorithms for Neural Networks - Amari (ResearchIndex) (Site not responding. Last check: 2007-10-20)
		0.8: Information Geometry on Hierarchical Decomposition of Stochastic..
		15 The geometry of asymptotic inference (context) - Kass - 1989
		15 Dualistic geometry of the manifold of higher-order neurons (context) - Amari - 1991 ACM
	citeseer.ist.psu.edu /amari95information.html (857 words)

	Merlins Geometry Intro
		It was by way of sacred geometry that ancient architects, artists, designers, and builders created structures and works of art that still astonish the viewer by their beauty, their practicality, and their harmonious relationship to their surroundings.
		Instead, sacred geometry is about opening up the self to the experience of geometric form, recognizing the presence of underlying laws in the play of form, and learning to understand the universe in a different and deeper way.
		Geometry was only one of a group of ancient arts with the same broad purpose and approach, and most of the cultures that made use of sacred geometry drew on these other arts as well.
	www.merlinsrealm.com /merlinsrealm002_030.htm (1321 words)

	Digital Governance
		Geometry of Information Flows is a detailed human-centric picture of information flows in a society.
		The aim is to understand the distribution of "information" and "information flows" in the society, instead of focusing solely on enhanced communication.
		Information on how to deal with the government (which government department and who is the responsible officer to whom the query should be addressed).
	www.cddc.vt.edu /digitalgov/gov-geometry2.html (1894 words)

	Basic Terms
		We may think of a line as a "straight" line that we might draw with a ruler on a piece of paper, except that in geometry, a line extends forever in both directions.
		We may think of a line segment as a "straight" line that we might draw with a ruler on a piece of paper.
		A ray is one of the basic terms in geometry.
	www.mathleague.com /help/geometry/basicterms.htm (572 words)

	Z. Shen's preprints on Riemannian Geometry and Finsler Geometry
		Information Geometry studies two (possibly independent) metric and spray structures arising from various models, such as statistical models (exponential family of distributions) with the f-divergence.
		One of the fundamental problems in Riemann geometry is to study the topology of manifolds with certain restrictions on their curvature.
		Finsler geometry is an old area in differential geometry, and developed very slowly in the last 70 years, due to the complexity of Finsler structures.
	www.math.iupui.edu /~zshen/Research/index.html (819 words)

	Are We Cruising a Hypothesis Space?
		This paper is about Information Geometry, a relatively new subject within mathematical statistics that attempts to study the problem of inference by using tools from modern differential geometry.
		On the other hand, physicists may see information geometry as a possible language for the elusive theory of quantum gravity since it is a language already made out of the right ingredients: uncertainty and differential geometry.
		I believe that one of the most promising areas for research in the field of information geometry is the clarification of the role of curvature in statistical inference.
	omega.albany.edu:8008 /cruise.html (2657 words)

	The AFEPack Handbook: Understanding the Library
		For the node(0-dimensional) geometry, the index of the vertex and boundary is the index of the corresponding point.
		The geometry information of a template element is comparatively complete than that of a real element in a triangulation.
		And the numerical quadrature information is also include in the geometry information in the library, though we believe that it can be took out as an independent part.
	www.acm.caltech.edu /~rli/AFEPack/index-4.html (1202 words)

	Information
		Although such an understanding of mathematics and geometry is beyond the scope of primary students, nevertheless, they can, and should, still acquire spatial intuition and knowledge of various geometric concepts.
		The major aim of geometry at these levels is to develop geometric awareness in children.
		Though these three aspects of the geometry curriculum are related and can, and at times should, be taught together, they provide a convenient skeleton on which to base the geometry units of Levels 1 to 4.
	www.nzmaths.co.nz /Geometry/Info/GeoInfo.aspx (2239 words)

	PBL: Real World Geometry Project Information
		They gained an understanding of the history of geometry and came to appreciate the many professionals who employ geometry in their daily work.
		In cooperative groups researched one or more geometry topics and concepts and presented their ideas in a multimedia presentation.
		Geometry unit pre-testadministered during the first week and a post-test administered at the culmination of the unit
	www.wested.org /pblnet/exp_projects/realworld.html (876 words)

	artransforms.com - process - sacred geometry
		The study of sacred geometry, so ably and beautifully presented by Robert Lawlor in his workbook, "Sacred Geometry", and chronicled by Drunvolo Melchisedek in "The Flower of Life" is an ancient practice, dating back thousands of years.
		The study of sacred geometry accesses information held by wisdom traditions, mystery schools, and indigenous sacred circles throughout human time.
		The diagram, created by connecting the centers of all the circles in the form (two rings of 6, and one in the center) is said to function as a blueprint for the crystal structures of all carbon based life.
	www.artransforms.com /process/sacred_geometry.html (692 words)

	Small SCSI Disk May Seem to Have Zero Cylinders in Windows 2000
		Although the geometry information is used primarily for older programs and does not for most purposes affect Windows 2000, the code that writes partition tables and signatures on basic disks does so by referring to the disk geometry.
		If you create the FT set while one geometry is in effect, and a member disk fails while it is in a different geometry state, it may not be possible to re-create a partition of the correct size to fill the roll of the failed disk by using the same hardware.
		If the apparent geometry of a boot disk changes for any other reason, it is likely that booting from that disk would not work until you restore the apparent geometry to its original state.
	support.microsoft.com /?kbid=258281 (1156 words)

	History of Geometry
		The geometry of Babylon (in Mesopotamia) and Egypt was mostly experimentally derived rules used by the engineers of those civilizations.
		His major work in geometry is "Synagoge" or the "Collection" (in 8 Books), a handbook on a wide variety of topics: arithmetic, mean proportionals, geometrical paradoxes, regular polyhedra, the spiral and quadratrix, trisection, honeycombs, semiregular solids, minimal surfaces, astronomy, and mechanics.
		is considered the father of both descriptive geometry in "Geometrie descriptive" (1799); and differential geometry in "Application de l'Analyse a la Geometrie" (1800) where he introduced the concept of lines of curvature on a surface in 3-space.
	geometryalgorithms.com /history.htm (2539 words)

	Information Geometry
		One very nice thing about information geometry is that it gives us very strong tools for proving results about statistical models, simply by considering them as well-behaved geometrical objects.
		Thus, for instance, it's basically a tautology to say that a manifold is not changing much in the vicinity of points of low curvature, and changing greatly near points of high curvature.
		Kazushi Ikeda, "Information Geometry of Interspike Intervals in Spiking Neurons",
	cscs.umich.edu /~crshalizi/notebooks/info-geo.html (795 words)

	Fractal Geometry
		He is the key Chaotician of our times, and before we begin our journey into the geometry of chaos, we must first understand his story.
		But Mandelbrot conceived and developed a new fractal geometry of nature based on the fourth dimension and Complex numbers which is capable of describing mathematically the most amorphous and chaotic forms of the real world.
		Mandelbrot discovered that the fourth dimension of fractal forms includes an infinite set of fractional dimensions which lie between the zero and first dimension, the first and second dimension and the second and third dimension.
	www.fractalwisdom.com /FractalWisdom/fractal.html (2550 words)

	The Geometry of Information Retrieval
		The Geometry of Information Retrieval (C.J. van Rijsbergen)
		Information retrieval, IR, the science of extracting information from any potential source, can be viewed in a number of ways: logical, probabilistic and vector space models are some of the most important.
		In this book, the author, one of the leading researchers in the area, shows how these views can be reforged in the same framework used to formulate the general principles of quantum mechanics.
	ir.dcs.gla.ac.uk /GeometryOfIR (158 words)

	Geometry
		It manages all rendering information such as a collection of states and the data for a model.
		During instantiation the geometry is set including vertex, normal, color and texture information.
		The location of the geometry is based on the location of all this node's parents.
	www.jmonkeyengine.com /doc/com/jme/scene/Geometry.html (1781 words)

	Livine/Terno Geometry from Information
		By proposing a way how the geometric concepts arise from the pregeometric information (I hope this word isn't overloaded to much?) in the spin networks this point is clarified, and the precise additional information/assumptions needed to get geometry becomes visible.
		Indeed just as the correlations in QFT contain all the information about the theory and describes the dynamics of the matter degrees of freedom, we expect in a quantum gravity theory that the correlations contained in a quantum state to fully describe the geometry of the quantum space-time defined by that state.
		Now it may be that the least information of a system accurs along the geodesic.
	www.physicsforums.com /showthread.php?t=117710 (1159 words)

	ThinkQuest : Library Search
		Whether you are a student taking geometry now, a student that has already had geometry, or a teacher, if you said yes to the first question, then you are in the majority.
		An extensive history of mathematics is at your fingertips, from Babylonian cuneiforms to advances in Egyptian geometry, from Mayan numbers to contemporary theories of axiomatical mathematics.
		Concepts are presented in the areas of geometry, algebra, and trigonometry.
	www.thinkquest.org /library/search.html?search_text=geometry (1112 words)

	Geometry Objects (Site not responding. Last check: 2007-10-20)
		The design of geometry objects in FEMLAB supports explicit hybrid geometry modeling in all dimensions, that is, both solid modeling and boundary modeling is possible, and the different approaches can be combined.
		The crucial information of the geometry objects is the description of these boundaries, together with information on the up and down, or left and right, subdomain of each boundary.
		The geometry objects have the following properties, where n is the space dimension, that is, 1, 2, or 3, and pc, pr, and pt are the maximum degree of rational Bézier curves, rectangular patches and triangular patches, respectively.
	www-math.cudenver.edu /~jmandel/doc/refman/comman10.htm (985 words)

	Information Geometry from the Perspective of Affine Differential Geometry
		Information Geometry from the Perspective of Affine Differential Geometry
		Since the resulting dualistic structure does not require a priori the existence of a metric on the ambient space, this approach may elucidate some fundamental issues in classical information geometry, and generate significant insight in the geometric relations (e.g., conformal, conformal-projective, and projective) among various statistical (sub)manifolds.
		This one-and-a-half day forum will review basic concepts of affine differential geometry, survey the current results in hypersurface realization of statistical manifolds, and define open problems, in both theory and application, that can be tackled by formulating them as problems in affine hypersurface theory.
	venus.kyy.nitech.ac.jp /~matsuzoe/affine/affine-RIKEN.html (337 words)

	Neighbourhoods of Randomness and the Information Geometry of the Mckay Bivariate Gamma 3-manifold -- from Mathematica ...
		Neighbourhoods of Randomness and the Information Geometry of the Mckay Bivariate Gamma 3-manifold -- from Mathematica Information Center
		Neighbourhoods of Randomness and the Information Geometry of the Mckay Bivariate Gamma 3-manifold
		Using Mathematica, without which the computations would have been prohibitively tedious, we derived also the information geometry of the 3-manifold of Mckay bivariate gamma distributions, which can provide a metrization of departures from randomness and independence for bivariate processes.
	library.wolfram.com /infocenter/Conferences/4998 (167 words)

	Amazon.com: Geometry: Books: Ray Jurgensen,Richard G. Brown (Site not responding. Last check: 2007-10-20)
		The book is thorough and teaches Geometry in the way that it should be taught, with a rich mathematical foundation and many opportunities for students of all abilities to learn to think criticlly.
		Students who learn with this book will not only have learned geometry but will have honed their critical thinking skills and be well prepared for subsequent math and science courses and for the various standardized tests that they are required to take.
		In the age of watered down school textbooks, Jurgenson's Geometry is the exception.
	www.amazon.com /Geometry-Ray-Jurgensen/dp/0395977274 (1301 words)

	Geometry Algorithm Web Sites
		Web sites are rapidly becoming a useful source for information about geometry algorithms.
		- this used to be a significant center of computational geometry work from 1991-1998 when it lost its funding, and it is now closed with no staff.
		Has many links for applications of computational geometry to: design and manufacturing, graphics and visualization, information systems, medicine and biology, physical sciences, robotics, and other applications.
	geometryalgorithms.com /websites.htm (1552 words)

	1024 Cylinder Limit, How Windows NT Gets Drive Geometry
		These translated or logical parameters are called "apparent geometry." The physical geometry is called "actual geometry." A drive parameter table has reserved areas for the apparent geometry.
		If neither drive parameter tables nor Interrupt 13H information is available (which is typically the case with disks attached to second and subsequent controllers), then ATDISK calls the IDENTIFY command to ask the disk directly what its parameters are.
		IDENTIFY data is the last choice for geometry information, as it describes the raw disk.
	support.microsoft.com /?kbid=98080 (753 words)

	Geometry Expressions -- Home -- Interactive Symbolic Geometry
		Geometry Expressions can be used as a stand-alone program or in conjunction with your favorite algebra system via MathML input and output.
		I believe this is precisely the type of intuitive computing that would be well-received by students and a real aid to their understanding of many mathematical topics.
		For a glimpse of Geometry Expressions in action, take a look at one of our Flash Demos.
	www.geometryexpressions.com /index.php (241 words)

	trueSpace Geometry Export Converter
		If this checkbox is enabled (checkmarked) then the geometry will be repositioned so that it is sitting flush with the top of the Z plane (the horizontal plane).
		Higher values will make the geometry appear more smooth regardless of how angular the data may be whereas smaller values will make the data appear more faceted.
		If this checkbox is enabled (checkmarked, which is the default) then hierarchy information will be output to the file, else the geometry will be output with no hierarchy.
	www.okino.com /conv/exp_cob.htm (555 words)

	Okino IGES 5.3 Geometry Import Converter
		This complex geometry import converter reads in IGES 5.3 ASCII files including the most used NURBS entities, their related trim curve information, geometry hierarchy connectivity and polygonal data.
		In general only about a quarter of the specification is used for translation of 3D polygonal and NURB geometry while the remainder of the specification is not applicable (B-Rep geometry, 2d entities such as lines, hatch symbols, text entities, etc).
		All of the major 3d geometry entities, such as tabulated surface, surface of revolution, parametric spline surface and all NURB entities are imported and converted to clean and legal trimmed NURB patches.
	www.okino.com /conv/imp_iges.htm (3233 words)

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