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Topic: Metric structure

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	20th WCP: Mathematical Models of Spacetime in Contemporary Physics and Essential Issues of the Ontology of Spacetime
		In that way defined geometrical structure of spacetime is substantial, because it is invariant as a pseudo-Riemannian space with affine relationship — all physical events are accidental and fully reducible to the manifestations of the substratum i.
		The Euclidean space and Minkowski's space are the intermediate structures between fundamental mathematical structure — complex space of spinors — and physical spacetime.
		Theories of spacetime in mathematical physics, while considering continua and metric manifolds, cannot explain the difference between time dimension and space dimensions, they are also unable to explain by means of geometry the unidirection of the passage of time, which can be comprehended only by means of thermodynamics.
	www.bu.edu /wcp/Papers/Math/MathGos.htm (2817 words)

	Metre (music) - Wikipedia, the free encyclopedia
		Metric structure includes metre, tempo, and all rhythmic aspects which produce temporal regularity or structure, against which the foreground details or durational patterns are projected (Wittlich 1975, chap.
		The beat level is the metric level at which pulses are heard as the basic time unit of the piece.
		A metric modulation is a modulation from one metric unit or metre to another.
	en.wikipedia.org /wiki/Polymeter (1345 words)

	Tetrahedron Model Postscript
		The particle aspect is what I refer to as the "metric particles", the bosons and field vectors (force carriers) of the forces, such as the photon, the graviton, the IVBs (Intermediate Vector Bosons) of the weak force, and the gluons of the strong force color charges.
		Particles are evidently "knotted" entanglements of electromagnetic energy and metric dimensional structure; the 4x3 fractal pattern in which they exist is apparently the contribution of the three- and four-dimensional structure of space and spacetime.
		The fractal structure of the Universe is thoroughgoing, and it is the resonant mechanism by which the structural imprint of electromagnetic energy and spacetime is transmitted to every level of organized information, including life (through the 4x3 structure of the baryon, alpha particle, carbon, DNA, and the genetic code).
	home.earthlink.net /~johngowan/commentary.html (2732 words)

	Data Capture Interface (DCI) - Overview of the DCI Specification
		The metrics name space is grouped into two layers: one layer to identify a metric class, or metric datum within a metric class, and another layer to identify the available instances for a metric class.
		A derived metric is defined by explicitly encoding the manner of its derivation in the derived metric's DatumId.
		The data structures for the first two types are identical: a variable length byte array called "string" and a "size" field includes the size of the entire structure along with the variable length data and enough padding ensure that the "size" field is always a multiple of 4 bytes in size.
	www.opengroup.org /onlinepubs/009657299/c427-3/chap3.htm (13243 words)

	The Impact Of Decline Upon Weights And Measures
		Metric in the building industry survives because the metre can be discarded in favour of measures that reproduce the very Imperial units metric was intended to replace.
		Metric's inappropriate divisions are compounded by the fact that metric is based on abstract scientific principles which are aloof from everyday uses.
		Metric is workable only by abandoning its standard measures, the metre, kilo and litre, and replacing them with units of different sizes based on human needs and totally unrelated to "wavelengths in a vacuum".
	www.ourcivilisation.com /weight (2415 words)

	Whitehead and Newton on Space and Time Structure
		The metric structure is dependent on, according to the Einsteinian formulation, and is independent of, according to the Whiteheadian formulation, the distribution of matter in the universe.
		The uniform metric structure would serve as a framework in terms of which the self-congruence, or the lack of it, of a measuring standard could be determined.
		The importance of the uniform metric structure to Whitehead is underscored by contrasting it briefly with the variable metric structure in the Einsteinian formulation of GTR.
	www.religion-online.org /showarticle.asp?title=2433 (8917 words)

	Metric tensor (general relativity) - Wikipedia, the free encyclopedia
		The metric captures all the geometric and causal structure of spacetime.
		Mathematically, spacetime is represented by a 4-dimensional differentiable manifold M and the metric is given as a covariant, second-rank, symmetric tensor on M, conventionally denoted by g.
		One of the core ideas of general relativity is that the metric (and the associated geometry of spacetime) is determined by the matter and energy content of spacetime.
	en.wikipedia.org /wiki/Metric_tensor_(general_relativity) (968 words)

	Higher-Order Metrics
		To visualize the effect of higher order metrics, recall that for a second-order metric the locus of points at a fixed distance ds from the origin must be a conic, i.e., an ellipse, hyperbola, or parabola.
		This illustrates how, as the number of sub-light cones goes to infinity, the structure of the manifold goes over to the usual Minkowski pseudometric, except for the discrete null sub-light surfaces which are distributed throughout the interior of the future and past light cones, and which accumulate on the light cones.
		However, with more spatial dimensions the sub-light null structure is subtly less symmetrical, because each null surface represents a discrete cone, which associates two of the trajectories in the xt plane as the sides of a single cone.
	www.mathpages.com /rr/s9-03/9-03.htm (1337 words)

	MTO 7.2: Dissertation Listings
		The broad explanatory context by which accent may be defined is metric theory, for accent is both a determinant and a function of metric structure.
		Metric structure must necessarily be conceived as a genuinely temporal and context-sensitive process in which that which 'measures' is constantly redefined by that which is 'measured'.
		An accent is a structural time-point; it is a time-point which is constituent of the highly specified hierarchy of metric structure.
	www.societymusictheory.org /mto/issues/mto.01.7.2/dis.7.2.html (1790 words)

	PlanetMath: metric space
		formed by these open sets is called the metric topology, and in fact the open sets form a basis for this topology (proof).
		More generally, any normed vector space has an underlying metric space structure; when the vector space is finite dimensional, the resulting metric space is isomorphic to Euclidean space.
		This is version 9 of metric space, born on 2001-10-25, modified 2005-11-28.
	planetmath.org /encyclopedia/Metric.html (195 words)

	The Higgs Field vs the Spacetime Metric
		The IVBs are "metric" particles, composed of the dense metric of the early universe, and they reflect the structure of the spacetime metric from which they are derived - the four bosons of the electroweak unified force correspond in some way to the four dimensions.
		The IVBs are "metric" particles, derived from the spacetime metric.
		Whereas particles retain a complete (gravitational) connection to the spatial metric of the photon, their participation in the creation of that metric is distinctly different from light; photons create the spatial metric by their own intrinsic motion (the entropy drive of free energy).
	home.earthlink.net /~johngowan/higgs.html (3271 words)

	XRadar - Setting up XRadar-config.xml
		This breakdown structure is a hierarchical node tree where the end nodes are values calculated by the various metrics found in the XRadar common xml-database.
		The abbreviation attribute specifies the metric to aggregate.
		When the "metric" element is of type "value", its value element is a calculation that is defined by the elements within.
	xradar.sourceforge.net /installation/xradar-config.html (986 words)

	Fleischer (Site not responding. Last check: 2007-10-13)
		The notion of metric coherence describes the correspondences of varying degree between the accents of the outer and inner metric structure.
		As the outcome a relationship was detected between metric coherence and the understanding of the corresponding interpretation by the listeners.
		Metric weights of higher degree of coherence led to a more convincing interpretation regarding the question in how far the metric structure was expressed properly.
	www.unina2.it /capirelamusica.sun/Fleischer2.htm (293 words)

	R Tsur on Comparative Metrics
		In fact, it is the number of metrical positions rather than the number of syllables that are specified in syllabotonic verse.
		The occurrence of certain metres in certain languages may be determined by a wide variety of factors: the constraints of the specific languages, the aesthetic demand for unity and complexity which I assume (though cannot prove) to be universal, and many accidental factors which may be cultural, historical, or I don't know what.
		Indeed, "hamerube," the most frequent versification structure, is based on a metric foot in which the short unit comes before the first long unit (that is, its weight is in its second half).
	www2.bc.edu /~richarad/lcb/fea/tsurin/compmetrics.html (1825 words)

	Mass-metric gravity is scalar (Site not responding. Last check: 2007-10-13)
		Weakest of the known forces of nature, it is still responsible for the long-range structure of the universe in which we live.
		Each observer perceives his surroundings according to his own "metric", by which is meant that he uses standard meter sticks and a standard clock to describe events he observes.
		These tend to be metric theories, which agree with GR that gravity actually distorts the metric structure of empty space.
	mass-metricgravity.net (2137 words)

	5.1 Quantum field theory on a differentiable manifold
		One could conventionally split the spacetime metric into two terms: one to be considered a background, which gives a metric structure to spacetime; the other to be treated as a fluctuating quantum field.
		In all versions of ordinary quantum field theory, the metric of spacetime plays an essential role in the construction of the basic theoretical tools (creation and annihilation operators, canonical commutation relations, gaussian measures, propagators...); these tools cannot be used in quantum field over a manifold.
		Technically, the difficulty due to the absence of a background metric is circumvented in loop quantum gravity by defining the quantum theory as a representation of a Poisson algebra of classical observables which can be defined without using a background metric.
	relativity.livingreviews.org /Articles/lrr-1998-1/node9.html (482 words)

	PlanetMath: Riemannian manifold
		Indeed, it is possible to define a Riemannian structure on a manifold
		should be called local coordinate components of a metric tensor, where as “Riemannian metric” should refer to the distance function defined above.
		Cross-references: distance, rectifiable curves, infimum, distance metric, coordinate chart, atlas, manifold, riemannian structure, matrix, fix, smooth functions, components, vector fields, frame, 1-forms, coframe, open subset, local coordinates, function, global sections, sheaf, cotangent bundle, positive definite, symmetric, bilinear form, point, field, type, tensor
	planetmath.org /encyclopedia/MetricTensor.html (237 words)

	UK metric association - metric is a proper system
		The systematic structure of metric has a number of features.
		Metric is based on the principle that all measurable phenomena covered by the system - pretty well everything in the known natural world!
		As for all metric measures, all we need to do is move the decimal point.
	www.metric.org.uk /why/system.htm (549 words)

	Reuven Tsur and Yehosheva Bentov
		The structure of the third foot is similar, but one full vowel is missing; as a result, the smallest units of identical structure are the hemistichs that constitute a symmetrical stich.
		In quotes (2) and (3), the performer must pay attention to the metric pattern, in which the alternating feet are not identical in structure: in addition to the alternation of short and long vowels in a foot, two types of feet (a complex and a simple one) alternate as well.
		The structure of the second strophe is similar to the structure of the first strophe, only the branches rhyme on a different ending; then it ends again with a girdle, whose prosodic structure is again identical with the prosodic structure of the guide; and so forth, up to 5-7 strophes.
	www.tau.ac.il /~tsurxx/TsurBentovEng._b2.html (10158 words)

	Combined metric structure and motion recovery (Site not responding. Last check: 2007-10-13)
		Using the coupled self-calibration algorithm described in Section 6.3.1 it is possible to recover the metric structure of the different subsequences.
		Once the metric structure of the subsequences has been recovered, the pose of the camera can also be determined for the viewpoints observing only planar points.
		Finally, it becomes possible to align the structure and motion recovered for the separate subsequences based on common points.
	www.cs.unc.edu /~marc/tutorial/node73.html (186 words)

	Structure and motion
		In this section the relation between the views and the correspondences between the features will be used to retrieve the structure of the scene and the motion of the camera.
		Once the structure and motion has been determined for the whole sequence, the results can be refined through a projective bundle adjustment.
		Finally, a metric bundle adjustment is carried out to obtain an optimal estimation of the structure and motion.
	www.cs.unc.edu /~marc/tutorial/node60.html (274 words)

	Computing Papers on Metric (Site not responding. Last check: 2007-10-13)
		Navigation in a hypertext is affected by (Check all that apply) a) The structure of the hyperdocument b) The Navigation aids provided by the hypertext system c) The browsing strategy employed by the user d) The size of a node e) The birds-eye view f) Unique Anchors #5.
		One way to de ne a Metric is to pick certain Pn, and to de ne a simiproperties P1 larity between two objects x and y as the degree to which P1 x is s...
		This paper presents a method for learning a distance Metric from relative comparison such as A is closer to B than A is to C.
	computing.breinestorm.net /Metric (2803 words)

	Poetic Rhythm
		Thus, the perception-oriented theory of metre performs a small Copernican revolution, and instead in the verse structure, it places the constraints in the reader's "rhythmic competence": the utmost limit of rhythmicality is the reader's ability or willingness to perform the verse line rhythmically.
		Rather than in verse structure, the constraint for acceptability in versification is placed in the reader's "rhythmic competence", his ability or willingness to perform the verse line rhythmically, that is, in a way that both metric pattern and the linguistic stress pattern should be accessible to awareness at one and the same time.
		Moreover, when alternative mappings of stress pattern to metric pattern are possible in a verse line, some highly experienced readers may prefer a mapping that involves a stress maximum in the seventh position to some other, perfectly "metrical" mapping under the stress-maximum theory.
	www.tau.ac.il /~tsurxx/Synopsis.html (4632 words)

	The Continuous Structure, Metric Properties and Ordering Relations of Time
		A metric space is an ordered pair (A,a) where A is a non-empty set and a is a function from the set A x A of all ordered pairs (x,y) of elements x and y of A into the set R of all real numbers, such that
		Note that there is a complete structural symmetry between the set of all instants later than any given instant and the set of all instants earlier than that instant.
		These are isometric metric spaces and they are also isomorphic as ordered sets, the ordering relation 'later than' of either set corresponding to the ordering relation 'earlier than' in the other set.
	home.att.net /~zei/TMKelso/time.htm (1923 words)

	Cinemetrics
		In principle, what we know about the metric structure of Intolerance from having watched this film and having read about it is enough to get a good sense of what Griffith was trying to achieve.
		We know that Griffith cross-cuts four stories from four ages; that towards the end of the film the back-and-forth between its stories tends to quicken its pace; and that this quickening is reinforced by the fact that individual shots tend to become shorter and shorter.
		One question the timing and counting allows to address is whether or not the average shot length changes depending on the type of the story Griffith deals with and on the epoch in which it is set, in other words, if there is a correlation between cutting rates and subject matter.
	www.cinemetrics.lv /tsivian.php (1135 words)

	INI : Abstracts : MAAW01 : Model Theory for Metric Structures
		A metric structure is a many-sorted structure with each sort a metric space, which for convenience is assumed to have finite diameter.
		This leads to a new formalism for the logic of metric structures in which the operations of sup and inf play a central role.
		The purpose of this tutorial is to present this logic for metric structures, and to show a few of its application areas, with emphasis on probability spaces and certain linear spaces from functional analysis.
	www.newton.cam.ac.uk /programmes/MAA/Abstract1/berenstein.html (451 words)

	Musical Terms - Rhythm (Site not responding. Last check: 2007-10-13)
		Such groups are commonly of two or three units (or their compounds, such as four or six), the arrangement of the pulse into groups is the metre of a composition, and the rate of pulses is its tempo.
		In some 20th-century music, composers have sought to avoid regular rhythmic structures in order to achieve a more flexible rhythm; in some cases their methods have been influenced by folk music lacking a regular metric structure.
		Rhythm, as a fundamental element - no music can exist other than in time - has a part to play in many other aspects of music: it is an important element in melody, it affects the progression of harmony, and has a role in such matters as texture, timbre and ornamentation.
	w3.rz-berlin.mpg.de /cmp/g_rhythm.html (253 words)

	Lipschitz Algebras (Site not responding. Last check: 2007-10-13)
		This suggests another reason why the theory of Lipschitz spaces was slow to develop: metric structure is finer, and therefore deeper, than topological or measure structure.
		In fact, derivations provide a point of view from which metric structure is seen as a kind of first-order differentiability property.
		It is natural that the functional-analytic versions of topological and measure structure would be understood first, but it is also clear that differentiability is destined to play a central role too.
	www.math.wustl.edu /~nweaver/publications/p25.html (600 words)

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