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Topic: Fundamental representation

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	Fundamental representation - Wikipedia, the free encyclopedia
		All other irreducible representations of the group can be found in the tensor products of the fundamental representation with many copies of itself.
		For example, the fundamental representation of SO(n) or SU(n) are n-dimensional vector spaces, and the fundamental representation of E8 is 248-dimensional.
		In greater generality it is not expected to happen in the way that all irreducible representations occur as direct summands; rather (at best) as subquotients.
	en.wikipedia.org /wiki/Fundamental_representation (240 words)

	What is a Knowledge Representation?
		A representation's theory of intelligent reasoning is often implicit, but can be made more evident by examining its three components: (i) the representation's fundamental conception of intelligent inference; (ii) the set of inferences the representation sanctions; and (iii) the set of inferences it recommends.
		The result is knowledge representations applied in ways that are uninformed by the inspirations and insights that led to their invention and that are the source of their power.
		We suggest that representation technologies should not be considered as opponents to be overcome, forced to behave in a particular way, but should instead be understood on their own terms and used in ways that rely on the insights that were their original inspiration and source of power.
	www.medg.lcs.mit.edu /ftp/psz/k-rep.html (10517 words)

	[No title]
		Interaction and Representation Mark H. Bickhard Mark H. Bickhard Department of Philosophy 15 University Drive Lehigh University Bethlehem, PA 18015 610-967-6770 mhb0@lehigh.edu Interaction and Representation Mark H. Bickhard Abstract There is a form of representation that is naturally emergent in the organization of interactive systems.
		Representation must be capable of truth value, and something is representational only for that for which it is capable of truth value.
		Representational error emerges as a particular kind of functional error, and, therefore, representation emerges as a particular kind of function - the function of indicating possibilities of further interactive process.
	www.lehigh.edu /~mhb0/interrepascii (7179 words)

	Edit ReflectionsonRepresentation (Site not responding. Last check: 2007-09-17)
		Representations are ''material'', they allow ideas and experience to have an independent existence in an externalized form, they help to capture emergent thought.
		Representations mediate the relation between collaborators and their products, between individuals in a group, between the group and their sponsors and between the group and their users / market.
		When a representation crosses boundaries, there is a loss of meaning (reification) and context, which is counter-balanced by an opportunity for new negotiations, different views and altered meaning.
	www.voght.com /cgi-bin/pywiki/pywiki?edit=ReflectionsonRepresentation (733 words)

	ChildrenFrame
		Roughly, it is the presupposition that representation -- all representation -- is constituted as encodings.
		Any interactive representation of the form "whatever yields this outcome for this interaction will also yield that outcome for that interaction" is unbounded both for the class of environments that might satisfy the indication, and for whatever the class of possible environmental properties are that would support that satisfaction.
		To represent the falseness of a representation seems to require metarepresentation of the primary level representation, and metarepresentation of what it is being taken to represent, tied together by a metarepresentation of the purported representational correspondence between them.
	www.lehigh.edu /~mhb0/childrenframe.html (8654 words)

	Quantum Electrical Metrology
		At present, there is no fundamental representation of current; the representation of current is via the representations of voltage and resistance.
		Though these representations are based on fundamental physical principles and are of high quality, the representation of current is dependent upon them.
		An independent representation of current could provide significant additional confidence in the coherency of the representations of the SI electrical units through closure of the "metrology triangle," V = IR with all measurements based on fundamental constants.
	www.nist.gov /public_affairs/guide/quantum_electrical.htm (3264 words)

	Converted file trb (Site not responding. Last check: 2007-09-17)
		Latta consented to the joint representation after it was challenged by the State at her trial.
		The principal issues raised by the joint representation were whether her consent was knowing and intelligent and, if so, whether a conflict created by joint counsel can nevertheless be so severe that a defendant’s Sixth Amendment right to effective counsel requires a retrial.
		It established in conclusory terms that Latta had been informed of the risks associated with joint representation and that she wished for Studtmann to represent her, but did not develop any record as to what her understanding of those risks was.
	www.state.in.us /judiciary/opinions/archive/03160101.trb.html (4368 words)

	Linear representation of Boolean logic
		If we were only interested in representation theory, then we would represent the individual operations minimally.
		Rather than guessing representations, we use information theoretical ideas to look for a new strategy which might give a 1:1 representation.
		This is a minimal (irreducible) representation, in the sense that it is the smallest representation which satisfies all the conditions.
	www.iu.hio.no /data/QIC/info3/node7.html (848 words)

	Representation on Almondnet (Site not responding. Last check: 2007-09-17)
		So representation is not just about the way the world is presented to...
		Its primary focus is the study of elections and voting systems; but it has a general interest in all matters relating to the theme of representative democracy'.
		Representation refers to the construction in any medium (especially the mass media) of...
	www.blackstoryrecords.co.uk /rnb/representation.html (438 words)

	Boston Review \| The Case for Proportional Representation
		Proportional representation (PR) is based on the principle that any group of like-minded voters should win legislative seats in proportion to its share of the popular vote.
		The advantage of district representation, it is said, is that all areas have someone to hold accountable for district issues.
		Their choice of representation may be influenced by local considerations, and systems can be designed to ensure some geographic representation, but geographic interests are not assumed to be paramount.
	www.bostonreview.net /BR23.1/richie.html (6068 words)

	[No title]
		The spin-1/2 representation is the fundamental representation, in which SU(2) acts on C^2 in the obvious way.
		The fundamental spin-1/2 particles in the Standard Model are the leptons (electron, muon, tau and their corresponding neutrinos) and quarks.
		The "left-handed" one is the fundamental representation, in which SL(2,C) acts on C^2 in the obvious way.
	math.ucr.edu /home/baez/twf_ascii/week109 (2603 words)

	[No title]
		The interplay between the historical and the contemporary, between self-presentation and imposed representation, is fundamental to this discussion.
		The representation of the fl female in Western art has always been heavily governed by prevailing attitudes toward race, gender, and sexuality.
		Posing as the model for a work of art, particularly a photograph, is a type of performance in which the cultural body enacts a signifying role that communicates beyond the artists capabilities and aspirations for the work.
	www.picturingwomen.org /Williams_Willis_Abstract.doc (1004 words)

	Single Electron Tunneling
		For the first, NIST is working on the development of intrinsic standards based on fundamental physical principles, such as the volt, based on the Josephson effect, and the ohm, based on the quantum Hall effect.
		An independent representation of current could provide significant additional confidence in the coherency of the representations of the SI electrical units through closure of the "metrology triangle" V = I R with all measurements based on fundamental constants.
		From a fundamental point of view, the most interesting result was the elucidation of a new mechanism, the "dynamical error." This error can results from the inability of the quantum dot to form the Coulomb blockade quickly enough; research into this mechanism should advance fundamental understanding of Coulomb blockade.
	www.boulder.nist.gov /div814/div817b/whatwedo/set/set.htm (2731 words)

	[No title] (Site not responding. Last check: 2007-09-17)
		* The dimension should be the dimension of the fundamental representation.
		* NF is the dimension of the fundamental representation.
		* NA is the dimension of the adjoint representation.
	www.nikhef.nl /~t68/FORMapplications/Color/Spn.prc (69 words)

	n301/Numbering Systems
		The number f of the representation is called the mantissa and the E is the exponent.
		Recall, the general binary representation of a positive integer is,
		Ex: Find a 16 bit representation of the approximation 1.414 to the square root of 2.
	www.cs.iupui.edu /~aharris/cgi-bin/slideshow/n301/Numbering_Systems.html (672 words)

	MITCHELL v. MULLIGAN
		As the court is well aware, when evaluating an equal protection claim where no fundamental right is infringed and where the claimant is not a member of a suspect (or quasi-suspect) class, the legislation or policy challenged must only be rationally related to a legitimate state interest.
		Unless the accused has acquiesced in such representation, the defense presented is not the defense guaranteed him by the constitution, for, in a very real sense, it is not his defense.
		The fundamental right to self-representation is not "found" in the Sixth Amendment; it is exposed under the Sixth Amendment.
	www.caught.net /prose/mitchell.htm (7337 words)

	Alexandra de Markoff and The SubSpace Project
		These points are covered in The Fundamental Existent in a style available to those who have studied in this field for some time.
		I call each existent a "fundamental existent" or "SubSpace particle", since it is a part of the space we’ve known throughout history (and because I like Star Trek) and "particle" because of its "discrete" nature.
		This axiom defines a relative number as a representation for a measurement of length, from which you can represent the measuring process as an integral part of the abstractions of a physical model.
	www.martinelli.org (1192 words)

	Just WHAT IS ALGEBRAIC THINKING
		It is hoped that by presenting a synthesis of these ideas, educators will make more informed curriculum and instruction decisions about algebraic thinking, and students will be better prepared for and more successful in their secondary mathematics adventures..
		Herbert and Brown (1997): Algebraic thinking is using mathematical symbols and tools to analyze different situations by (1) extracting information from the situation...(2) representing that information mathematically in words, diagrams, tables, graphs, and equations; and (3) interpreting and applying mathematical findings, such as solving for unknowns, testing conjectures, and identifying functional relationships.
		On the other hand, algebra skills that are not understood or connected in logical ways by the learner remain factoids of information that are unlikely to increase true mathematical competence.
	www.math.ucla.edu /~kriegler/pub/algebrat.html (2313 words)

	Web Workshop - Specs & Standards -- VML Basic Types (Site not responding. Last check: 2007-09-17)
		The "fundamental representation" is the highest precision representation that the proposal requires a conforming implementation to maintain; data will be lost if the implementation is not able to represent the data to the precision required.
		There are three possible fundamental representations that the implementation must maintain (i.e., one representation cannot be converted into another without loss of information).
		Implementations are not required to be consistent; however, the integral representation of an angle must not exceed the range of a 32-bit signed integer.
	msdn.microsoft.com /workshop/author/vml/types.asp (3480 words)

	Representation
		A representation and reasoning system is composed of a language to communicate with a computer, a way to assign meaning to the language, and procedures to compute answers given input in the language.
		Important questions include the tradeoffs between representational adequacy, fidelity, and computational cost, how to make plans and construct explanations in dynamic environments, and how best to represent default and probabilistic information." In addition to the helpful Pointers, be sure to follow the links to Subareas at the bottom of their pages for additional information.
		The concepts that we discuss -- the representation of knowledge and the reasoning processes that bring knowledge to life -- are central to the entire field of artificial intelligence.
	www.aaai.org /AITopics/html/repr.html (2927 words)

	Notes Renormalization Group Equations (Site not responding. Last check: 2007-09-17)
		irreducible representations are all one dimensional and are described by their charge
		The sum in (2) is over the number of fermions in the fundamental representation.
		Each family has a fermion in the fundamental and a fermion in the anti-fundamental, explaining the apparent factor-of-two discrepency.
	draal.physics.wisc.edu /Notes/RenormalizationGroupEquations (133 words)

	Luboš Motl's reference frame: Littlest Higgs model & deconstruction
		A Lie algebra of SU(M) coincides with the adjoint representation, which is the tensor product of the fundamental and the anti-fundamental representation (with the trace removed, which is a comment I had to add because of a picky reader who forced me to write SU properly instead of U).
		For large grand unified groups, the exact representations for the Higgses would typically be huge, and full mechanisms to break the symmetry are hard to find.
		This fundamental Planck scale, the size of the smallest meaningful fl holes whose lifetime is comparable to their size, may be reduced in models with large and warped extra dimensions.
	motls.blogspot.com /2005/03/littlest-higgs-model-deconstruction.html (6670 words)

	Why Spin(0,8)?
		Therefore, although the conventional linear vector representation of D3 is 6-dimensional, you could (and I do) say that D3 has a NONlinear 4-dimensional representation due to conformal transformations, and I see a triality among: two D3 4-dim half-spinor representations and one D3 NONlinear conformal (sort of vector-like) 4-dim representation.
		The 240 elements of the orbit of the permutation group S7 of the 7 imaginaries of the octonion algebra correspond to the discrete octonionic algebra representation of the 240 vertices near the origin of the 8-dimensional E8 spacetime lattice.
		the discrete octonionic algebra representation of a second set of 240 vertices near the origin of the 8-dimensional fermion antiparticle -half-spinor E8 lattice (The Witting polytope is self-dual, and the second set of 240 vertices form another 4-complex-dimensional (8-real-dimensional) Witting polytope that is dual to the first Witting polytope.).
	www.valdostamuseum.org /hamsmith/why8.html (3810 words)

	Workshop on Knowledge Representation in Biomedicine (Site not responding. Last check: 2007-09-17)
		This Workshop is the first of this kind, organized by the recently founded Special Interest Group "Formal (Bio-)Medical Knowledge Representation" of the American Medical Informatics Association (AMIA).
		Despite recent advances in using formal languages for biomedical concept representation, many fundamental issues (ontological basis, expressivity, scalability) remain unresolved.
		The goal is to analyze in which aspects (theoretical) KR research can be used for a new generation of biomedical concept systems.
	www.coling.uni-freiburg.de /pub/krmed2004 (175 words)

	ReflectionsonRepresentation (Site not responding. Last check: 2007-09-17)
		Ad hoc sketches, informal qualitative models, senario construction, concept maps, rule sets, structured text all serve as representation, reflecting the expectations and experience of their creators, they connect collaboration to future use.
		Henry Seiler, in "Managed business rules: A repository-based approach" PC AI July / August 1999 16-19, http://www.rulemachines.com/brs/whitepaper.htm talks of business and code developers interaction around business rules (a BO) and gives the roles and architecture of a rule object repository.
		Reusing a proven structure to capture key elements is a powerful representation method.
	www.voght.com /cgi-bin/pywiki/pywiki?ReflectionsonRepresentation (662 words)

	[No title]
		The most common type of spinor is the Dirac spinor which is a member of the fundamental representation of the complexified Clifford algebra C(p, q), into which Spin(p, q) can be embedded.
		In even dimensions, this representation is reducible when taken as a representation of Spin(p, q), and can be decomposed into two representations called the left-handed and right-handed Weyl spinor representations.
		The fundamental class is the canonical generator of the nonvanishing homology group on a topological manifold.
	www.geocities.com /jefferywinkler/beyondstandardmodel9.html (3355 words)

	[No title]
		My `guess' is representation independence: Our action has to be dimensionless and the dimension must be representation independent.
		In SU(3) and up in the fundamental representation a determinant term would not have the correct dimension (but this could maybe be fixed?).
		But again, the representation in which you take the trace can be completely compensated for by changing these factor out front in an appropriate way.
	www.math.niu.edu /~rusin/known-math/01_incoming/yang (1032 words)

	CHAPTER 1
		This is a representation of a horse because it resembles a horse.
		Crane answers that mental representation is fundamental (and he seems to think the distinction is absolute)
		X may resemble Y without X being a representation of Y. Resemblance is symmetrical, representation is not.
	www.nd.edu /~lstubenb/C1.html (600 words)

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