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Topic: Intrinsic volumes

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	Purpose and Philosophy
		In using the volumes, students and instructors may work through the material sequentially as part of a complete learning program, or they may dip directly into material on which they are experiencing difficulty in order to learn from worked exercises and illustrations.
		Volumes in the EE series will include counterexamples in a similar way wherever it is appropriate to clarify the role of critical assumptions in the development of the theory, and to illustrate important cases where results fail.
		The volumes are intended for undergraduate students of econometrics with an introductory knowledge of statistics, for first and second year graduate students of econometrics, and for students and instructors from neighboring disciplines (like statistics, political science, psychology and communications) with interests in econometric methods.
	cowles.econ.yale.edu /econexer/purpose.htm (1968 words)

	Frank Gao's research on intrinsic volumes (Site not responding. Last check: 2007-11-05)
		(with R. Vitale) One of a handful examples where the closed formulae of intrinsic volumes are obtained.
		Intrinsic volumes and polar sets in spherical space.
		The mean of a maximal likelihood estimator associated with Brownian bridges.
	www.webpages.uidaho.edu /~fuchang/IntrinsicVolume.html (82 words)

	eMedicine - Restrictive Lung Disease : Article Excerpt by: Sat Sharma, MD, FRCPC, FACP, FCCP, DABSM
		Background: Restrictive lung diseases are characterized by reduced lung volume, either because of an alteration in lung parenchyma or because of a disease of the pleura, chest wall, or neuromuscular apparatus.
		The volume of FRC is determined by the balance of the inward elastic recoil of the lungs and the outward elastic recoil of the chest wall.
		In cases of intrinsic lung disease, the physiological effects of diffuse parenchymal disorders reduce all lung volumes by the excessive elastic recoil of the lungs, in comparison to the outward recoil forces of the chest wall.
	www.emedicine.com /med/byname/restrictive-lung-disease.htm (604 words)

	Cardiomyopathy - Wikipedia, the free encyclopedia
		An intrinsic cardiomyopathy is weakness in the muscle of the heart that is not due to an identifiable external cause.
		The intrinsic cardiomyopathies are a mixed-bag of disease states, each with their own causes.
		Intrinsic cardiomyopathy has a number of causes including drug and alcohol toxicity, certain infections (including Hepatitis C), and various genetic and idiopathic (i.e., unknown) causes.
	en.wikipedia.org /wiki/Cardiomyopathy (750 words)

	Preservation and Archives Professionals - Bound Volumes
		A volume should be tied so that the bow or knot is positioned across the fore edge (opposite the spine) rather than on the front or back cover, so that the resulting "bump" will not interfere with good shelving practices.
		The volumes should be tied securely (but not so tightly that distortion results), with the tape flat as it wraps around the volume.
		When possible, shelves should be adjusted so that oversize bound materials are stacked no more than three or four volumes high, depending on their thickness, to expedite safe retrieval and reshelving and to avoid the possibility of stacked volumes toppling.
	www.archives.gov /preservation/formats/bound-volumes.html (491 words)

	Alabama Archives: Government Records News - Vol. 4, No.4
		Bound volumes often contain the most valuable historical records found in a community; however, continued use leads to their deterioration and a need to remove them from public access.
		Volumes of intrinsic historical value should be treated separately from those considered for routine commercial binding.
		When volumes are considered for rebinding, the width of the inner margin is of particular importance.
	www.archives.state.al.us /ol_pubs/govrec44.html (1802 words)

	Intrinsic Neurons of Fastigial Nucleus Mediate Neurogenic Neuroprotection against Excitotoxic and Ischemic Neuronal ...
		Intrinsic FN neurons were destroyed by IBO 5 d before FN stimulation or sham stimulation.
		volumes of the focal ischemic infarctions and the extent of cerebellar
		salvage of excitotoxic lesions, intrinsic neurons of the FN, not
	www.jneurosci.org /cgi/content/full/19/10/4142 (7443 words)

	oe magazine - Special Focus - Fiber Gets All Wet (Site not responding. Last check: 2007-11-05)
		The intrinsic sensors that are the focus of this article rely on the interaction between the environment, the fiber, and the light itself to generate information about a specific measurand.
		The stress induces growth of intrinsic and microscopic flaws located on the fiber surface, causing fracture as soon as any flaw grows beyond the critical limit of the material.
		Proof testing involves straining the fiber to destruction to screen out intrinsic flaws -- the higher the proof-test level, the smaller the size of intrinsic flaw that will remain in the surviving fiber and the lower the probability that the fiber will fail under static fatigue.
	oemagazine.com /fromTheMagazine/jul04/fiberwet.html (2374 words)

	Intrinsic \| Information Age
		Intrinsic specialises in enterprise marketing automation, a subset of the fast-growing CRM sector.
		Intrinsic has a presence in France, Spain, Portugal, Belgium, the Netherlands, Australia and the US.
		Intrinsic boasts a blue chip customer base, including Norwich Union, Honda, Thames Water, Lloyds TSB and Sainsbury.
	www.information-age.com /article/2001/march/intrinsic (156 words)

	Coagulation Testing (Part 1): Current Methods and Challenges (IVDT archive, Jul 98)
		The test is performed using a plasma sample, in which the intrinsic pathway is activated by the addition of phospholipid, an activator (ellagic acid, kaolin, or micronized silica), and Ca Formation of the Xase and prothrombinase complexes on the surface of the phospholipid enables prothrombin to be converted into thrombin, with subsequent clot formation.
		The use of reduced sample volumes is attractive, in part, because it implies reduced reagent use—and therefore lower testing costs.
		All whole blood and plasma microanalyzers use ultralow sample volumes in which approximately 50% of the content is cellular and 50% is plasma.
	www.devicelink.com /ivdt/archive/98/07/011.html (3379 words)

	Caltech Multi-Res Modeling Group - Publications
		A central role in this development is played by the intrinsic volumes giving rise to Hadwiger's theorem that all rigid motion invariant measures which are additive and continuous in the limit must be a formed by a linear combination of the intrinsic volumes.
		The inside/outside function of the volume data is progressively transmitted through the use of an adaptive octree,while a local frame based encoding is used for the fine level placement of surface samples.
		In this paper we present a novel approach that utilizes a hierarchy on both the input and the output data.For the generation of a coarse base mesh, we construct a hierarchy of volumes and extract an iso-surface from the coarsest resolution with a standard Marching Cubes algorithm.
	www.multires.caltech.edu /pubs (11796 words)

	eMedicine - Restrictive Lung Disease : Article by Sat Sharma, MD, FRCPC, FACP, FCCP, DABSM
		The presence of bilateral cysts and nodules, with preservation of lung volumes, may suggest a diagnosis of LAM or histiocytosis X. Bibasilar reticular fibrosis with coexisting retraction bronchiectasis indicates end-stage irreversible disease, and ground-glass attenuation may indicate the presence of an active inflammatory process with potential to respond to medical therapy.
		Evidence of nonmuscular diseases of the chest wall and associated deformities of the spinal column and ribs are readily appreciated on chest radiographs.
		The diffusing capacity of lung for carbon monoxide (DLCO) is reduced in all patients with intrinsic lung disorders, and the severity of the reduction does not correlate well with the stage of the disease.
	www.emedicine.com /med/topic2012.htm (6630 words)

	[No title] (Site not responding. Last check: 2007-11-05)
		Just as happens for volume and area, it can be shown by continuity considerations that the measure $\mu_1$ can be extended to all reasonable solids in ordinary space, for example, to all convex sets and to all polyhedra, convex or non convex.
		The intrinsic volumes are first defined on an orthogonal polytope $P$ whose sides equal $x_1,x_2,\dots, x_n$ by setting $$\mu_k(P) = e_k(x_1,x_2,\dots,x_n),$$ where $ e_x(x_1,x_2,\dots,x_n) $ is the $k$-th elementary symmetric function.
		The answer is clear: such a probability equals the ratio of the volume of $A$ by the volume of $B$.
	www-math.mit.edu /~combin/archive/old/98a.html (17757 words)

	volumes - OneLook Dictionary Search
		volumes : Cambridge International Dictionary of English [home, info]
		volumes : Cambridge Dictionary of American English [home, info]
		Phrases that include volumes: law of combining volumes, available volumes, intrinsic volumes, list of asterix volumes, lung volumes, more...
	www.onelook.com /?w=volumes (114 words)

	The Hindu Business Line : Sell L&T May 200 call
		The May 200 call was active clocking volumes of around 143 contracts.
		Close to 97 per cent of the premium is intrinsic.
		Close to 83 per cent of the premium consists of intrinsic value.
	www.thehindubusinessline.com /2002/05/14/stories/2002051402191300.htm (468 words)

	Viscotek - product profiles
		FIPA measures polymer concentration, molecular weight and intrinsic viscosity of a solution or emulsion reactor sample in less than five minutes.
		The polymer is separated from the low molecular constituents (diluent, additives, monomer, oligomers) by the FIPA column.
		Precision on molecular weight, molecular size and intrinsic viscosity is typically less than 0.3% RSD, which permits excellent feedback for control of the polymerization process.
	www.viscotek.com /fipa.php4 (329 words)

	Influence of expiratory loading and hyperinflation on cardiac output during exercise -- Stark-Leyva et al. 96 (5): 1920 ...
		ERV is the expiratory reserve volume and VC is the vital capacity.
		Mean cardiac output (CO), stroke volume (SV), heart rate (HR), and mean arterial pressure (MAP) are shown for each breathing condition at 3 workloads.
		in higher expiratory pressures at the lower lung volumes (24).
	jap.physiology.org /cgi/content/full/96/5/1920 (5045 words)

	Nonparametric Morphological Estimators in Statistical Image Analysis (Site not responding. Last check: 2007-11-05)
		Specific Minkowski functionals or, equivalently, specific intrinsic volumes are important characteristics in order to describe the morphological structure of binary images.
		A family of nonparametric estimators is investigated for the simultaneous estimation of the vector of all specific intrinsic volumes.
		Using techniques from stochastic geometry like Steiner's polynomial series expansion for the area of the epsilon-neighborhood of polyconvex sets, or the principal kinematic formula of convex geometry, these estimators can be represented by integrals of stationary random fields.
	www.stanford.edu /group/or/seminars/schmidt_041305.html (331 words)

	Introduction to Geometric Probability (Site not responding. Last check: 2007-11-05)
		7.3 An Euler relation for the intrinsic volumes 84
		8.4 The normalization of the intrinsic volumes 100
		9.2 The intrinsic volumes of the unit ball 108
	faculty.uml.edu /dklain/contents.html (74 words)

	AMP MATH VIDEO LIBRARY
		One set of such measures, known as the intrinsic volumes, are quite new and still somewhat mysterious.
		However, they have intriguing probabilistic interpretations and in fact can be shown to form a basis for the space of all continuous invariant measures.
		The most familiar examples of invariant measures are area and volume, which are invariant under the group of rigid motions.
	www.csudh.edu /math/sraianu/amp/video.htm (3075 words)

	Citebase - Intrinsic Volumes of the Brownian Motion Body
		Authors: Gao, Fuchang; Vitale, Richard A. Motivated from Gaussian processes, we derive the intrinsic volumes of the infinite--dimensional Brownian motion body.
		The method is by discretization to a class of orthoschemes.
		Numerical support is offered for a conjecture of Sangwine-Yager, and another conjecture is offered on the rate of decay of intrinsic volume sequences.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:math/0011052 (116 words)

	Moment-entropy inequalities, Erwin Lutwak, Deane Yang, Gaoyong Zhang
		Bourgain, J. and Milman, V. New volume ratio properties for convex symmetric bodies in $R^n$.
		Klain, D. Star valuations and dual mixed volumes.
		Lutwak, E. Centroid bodies and dual mixed volumes.
	projecteuclid.org /getRecord?id=euclid.aop/1079021463 (257 words)

	European Surgical Procedure Volumes
		Key factors include acceptance of innovative technologies, the aging population, patient demand for improved quality of life, and surgical procedures receiving reimbursement code listing.
		European open and laparoscopic surgical procedure volumes forecasts presented in this dynamic report from Medtech Insight cover the years 2005 through 2011.
		Exhibit 10-2: Intrinsic Sphincter Deficiency Correction, Procedure Volumes Forecast, by Country and Type, 2005-2011
	www.medtechinsight.com /ReportA612.html (1243 words)

	Rick Vitale - Intrinsic volumes and Gaussian random processes
		Rick Vitale - Intrinsic volumes and Gaussian random processes
		We describe the extension of intrinsic volumes to a sub-class of compact, convex subsets of Hilbert space.
		This is effected by the use of Gaussian measure and, in fact, provides a link with several questions of interest in probability theory.
	www.cms.math.ca /Events/summer98/s98-abs/node45.html (67 words)

	[No title]
		His most significant work is on valuations (additive functionals) on convex bodies and it has remodeled a central part of convex geometry.
		Group invariant valuations were studied since Dehn's solution of Hilbert's third problem, with later contributions by Blaschke and others, and culminating in Hadwiger's celebrated characterization theory for the intrinsic volumes.
		The approach is via representation theory of the general linear group and involves a surprising application of D-modules.
	www.emis.de /ECM3/prizes.html (1854 words)

	Abstract: Statistics Dept Seminars (Site not responding. Last check: 2007-11-05)
		Intrinsic volumes are renormalized versions of the classic quermassintegrals, which play an important role in the theory of convex bodies, notably in the Steiner volume formula and in a celebrated characterization theorem of Hadwiger.
		More recently, they have been seen to have a remarkable connection with Gaussian processes.
		Among these, I will discuss, as time permits: extension of intrinsic volumes to infinite dimensional convex bodies, bounds and estimates for Gaussian processes, Ito-Nisio oscillation and Gaussian fl holes, the Wills functional, and the Brownian motion body.
	www.stat.yale.edu /seminars/PastSeminars/2000-01/Vitale.html (107 words)

	Euler's Formula
		Shows that the Euler characteristic can be viewed (along with e.g.
		volume and surface area) as one of the fundamental translation-invariant functions on unions of convex sets.
		The valuation-based proof is from section 5.2; the other key sections related to the Euler characteristic are 3.2 (showing that the characteristic is well defined for simplicial complexes) and 7.3 (generalizing Euler's formula to other intrinsic volumes).
	www.ics.uci.edu /~eppstein/junkyard/euler/refs.html (1096 words)

	Electronic Communications in Probability - Vol. 8 (2003)
		A closed formula for the mean of a maximum likelihood estimator associated with the Brownian bridge is obtained; the exact relation with that of the Brownian motion is established.
		Gao, F. and Vitale, R.A. Intrinsic volumes of the Brownian motion body.
		Tsirel'son, B.S. A geometric approach to maximum likelihood estimation for infinite--dimensional Gaussian location I. Theory Prob.
	www.math.washington.edu /~ejpecp/ECP/viewarticle.php?id=1647 (105 words)

	AV #81387 - Video Cassette - Introduction to Geometric Probability (Site not responding. Last check: 2007-11-05)
		Gian-Carlo Rota lectures in this video on invariant measure, from the familiar measures of area and volume to new invariat measures such as intrinsic volumes.
		A link between intrinsic volumes and the Euler characteristic is noted.
		Last modified on August 17, 2006 by av@sfsu.edu
	www.sfsu.edu /~avitv/avcatalog/81387.htm (63 words)

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