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# Topic: Invariant

###### In the News (Mon 19 Aug 19)

 Invariant Invariants are displayed only if the confidence that the invariant did not occur by chance is greater than this. The invariants must all be of the same type and should come from the children of parent_ppt. Actually, this isn't strictly true: we don't have an invariant "a[] is a palindrome" corresponding to "a[] is the reverse of a[]", for instance. groups.csail.mit.edu /pag/daikon/download/jdoc/daikon/inv/Invariant.html   (3711 words)

 Invariant mass - Wikipedia, the free encyclopedia In particle physics, the mathematical combination of a particle's energy and its momentum to give a value for the mass of the particle at rest. The invariant mass is the same for all frames of reference (see Special Relativity). The invariant mass of a system of decay particles is related to the rest mass of the original particle by the following equation: en.wikipedia.org /wiki/Invariant_mass   (127 words)

 PlanetMath: fully invariant subgroup This is a stronger condition than being a characteristic subgroup. See Also: characteristic subgroup, subnormal subgroup, example of fully invariant subgroup This is version 3 of fully invariant subgroup, born on 2002-12-07, modified 2004-03-22. www.planetmath.org /encyclopedia/FullyInvariantSubgroup.html   (68 words)

 Invariant subspace   (Site not responding. Last check: ) In mathematics an invariant subspace of a linear mapping T from a vector space V to itself is a subspace W of V such that The invariant subspace problem concerns the case where V is a Hilbert space over the complex numbers of dimension > 1 and T is a bounded operator. More generally invariant subspaces are defined for of operators (operator algebras group representations) as subspaces invariant for each operator the set. www.freeglossary.com /Invariant_subspace   (263 words)

 Dynamical systems with Invariant manifolds   (Site not responding. Last check: ) An Invariant Manifold is a manifold embedded in a phase space with the property that it is invariant under the flow, i.e. The phase space of many dynamical systems have embedded in them, invariant manifolds whose dimensions are smaller than the dimensions of the entire phase space. The invariant manifold is attracting in the transverse direction if all the periodic orbits embedded in the chaotic attractor are attracting in the transverse direction. mrsec.uchicago.edu /~scvenkat/research/node16.html   (346 words)

 Citations: Smooth Invariant Manifolds and Normal Forms - Bronstein, Ya (ResearchIndex) ....and sufficient condition for the persistence of an invariant manifold is the property that the contraction in directions normal to the manifold is r time exponentially stronger than the contraction within the manifold. ....properties 37 (i) 7.3) has a compact invariant C 1 manifold M B of dimension m that is normally hyperbolic, and (ii) the ow of (7.3) on M is Anosov and transitive. ....of the smooth invariant section theorem are established and used to prove some results on finitely smooth conjugacy of two flows in the neighbourhood of their common smooth invariant submanifold. citeseer.ist.psu.edu /context/548463/0   (915 words)

 Learn more about GNU free documentation license from the online encyclopedia.   (Site not responding. Last check: ) The "Invariant Sections" are certain Secondary Sections whose titles are designated, as being those of Invariant Sections, in the notice that says that the Document is released under this License. If there are multiple Invariant Sections with the same name but different contents, make the title of each such section unique by adding at the end of it, in parentheses, the name of the original author or publisher of that section if known, or else a unique number. Replacing Invariant Sections with translations requires special permission from their copyright holders, but you may include translations of some or all Invariant Sections in addition to the original versions of these Invariant Sections. www.onlineencyclopedia.org /g/gn/gnu_free_documentation_license.html   (2666 words)

 Time-invariant   (Site not responding. Last check: ) He came up with the idea that the laws of nature must be invariant to a change of coordinate systems. Department of Geology The study of geology includes time invariant processes following the laws of physical science but it is tempered by the recognition that these processes occur in a complex framework, the result of previous geologic history. Physics, Invariant Theory, Modular Forms, and Algebraic Geometry Several lecture note sets by Igor Dolgachev in various formats, including DVI and PostScript. www.serebella.com /encyclopedia/article-Time-invariant.html   (340 words)

 Invariant Character Handling   (Site not responding. Last check: ) Guideline: Implementers may assume that all characters in NCIP messages are invariant characters except the character content of elements with the fixed attribute datatype="string". Besides the space character (which is an invariant character), permitted white space in an NCIP message (other than within elements of "string" datatype) are tab, carriage-return and newline. While none of these are invariant characters, neither may they appear in an NCIP message except where they may be ignored by the XML parser (and the NCIP application). www.cde.state.co.us /ncip/guidelines/ICH.htm   (669 words)

 The Daikon dynamic invariant detector   (Site not responding. Last check: ) An invariant is a property that holds at a certain point or points in a program; these are often seen in assert statements, documentation, and formal specifications. Invariants can be useful in program understanding and a host of other applications. Dynamic invariant detection runs a program, observes the values that the program computes, and then reports properties that were true over the observed executions. pag.csail.mit.edu /daikon   (227 words)

 LMS Proceedings Abstract, paper PLMS 1329   (Site not responding. Last check: ) A theorem of J. Hersch (1970) states that for any smooth metric on $S^2$, with total area equal to $4\pi$, the first non-zero eigenvalue of the Laplace operator acting on functions is less than or equal to 2 (this being the value for the standard round metric). For metrics invariant under the standard $S^1$-action on $S^2$, one can restrict the Laplace operator to the subspace of $S^1$-invariant functions and consider its spectrum there. The corresponding eigenvalues will be called invariant eigenvalues, and the purpose of this paper is to analyse their possible values. www.lms.ac.uk /publications/proceedings/abstracts/p1329a.html   (238 words)

 Invariant   (Site not responding. Last check: ) The variance of a probability distribution is invariant under translations of the real line; hence the variance of a random variable is unchanged by the addition of a constant to it. A loop invariant is a constraint that should be satisfied by everyiteration of a loop. A class invariant is a constraint that should be satisfied byevery method of a class. www.therfcc.org /invariant-32671.html   (387 words)

 Invariant Chain   (Site not responding. Last check: ) Invariant chain (Ii) which trimerizes in the ER, associates with MHC class II molecules and is released from the ER as a nine subunit complex. Here the invariant chain is proteolytically degraded and a peptide from the external protein associates with the MHC II molecule in the channel between the alpha-1 and beta-1 domains. Interaction of MHC class II molecules with the invariant chain: role of the invariant chain (81-90) region. www.cryst.bbk.ac.uk /pps97/assignments/projects/coadwell/007.htm   (209 words)

 The Daikon Invariant Detector User Manual This means that each invariant would be a valid Java expression, if inserted at the correct program point: right after method entry, for method entry invariants; right before method exit, for method exit invariants;, or anywhere in the code, for object invariants. This is a special invariant used internally by Daikon to represent an antecedent invariant in an implication where that antecedent consists of two invariants anded together. Represents the bitwise subset invariant between corresponding elements of two sequences of long; that is, the bits of y[] are a subset of the bits of x[]. pag.csail.mit.edu /daikon/download/doc/daikon.html   (10866 words)

 How to Use the Optional Features of the GFDL - GNU Project - Free Software Foundation (FSF) The idea of invariant sections is that they give you a way to express nontechnical personal opinions about the topic. The classical example of an invariant nontechnical section in a free manual is the GNU Manifesto, which is included in the GNU Emacs Manual. Person B who modifies a manual that was written by person A should not be able to make any of person A's documentation invariant, for that would deny person C the permission to modify it further. www.gnu.org /licenses/fdl-howto-opt.html   (891 words)

 Invariant - Wikipedia, the free encyclopedia invariant (computer science), such as a combination of variables not altered in a program loop The Invariant Society, the undergraduate mathematical society of Oxford University This is a disambiguation page, a list of pages that otherwise might share the same title. en.wikipedia.org /wiki/Invariant   (90 words)

 NIPS Workshop: Learning of invariant representations   (Site not responding. Last check: ) The purpose of this workshop is to focus on unsupervised learning models that attempt to represent features of the environment which are invariant or insensitive to variations such as position, size, or other factors. For example, priming of object shape is invariant with respect to position and size (Biederman 2001), and neurons in the visual cortex, beginning with complex cells and progressing up to neurons in IT, code for shape features independent of position (Hubel & Wiesel 1962; Hasselmo & Rolls 1989). Some of the approaches to learning invariant representations involve sparse coding as well as methods beyond this classical concept such as temporal coherence. www.ini.unizh.ch /~koerding/learninvariant   (541 words)

 Larch/C++ Reference Manual - Class Invariants   (Site not responding. Last check: ) The formalization of this interpretation of invariants is that the invariant states a theory that is true of all assigned objects of the appropriate type in all visible states. An invariant involving data members of an object of a class is asserted to hold for those data members in all assigned objects of that class in all visible states [Poetzsch-Heffter97]. An invariant involving static or global variables is asserted to hold for those variables whenever they are assigned in visible states. www.cs.iastate.edu /~leavens/larchc++manual/lcpp_137.html   (1317 words)

 Electromagnetic Invariant and its Application for Non-Destructive Testing of Moisture Content Paper is deal with the problems of developing of non-destructive instant monitoring of moisture of granular materials, such as grain, soil, sand, milled ores of minerals, building materials, grinded coal with applying of high-frquency method. With the help of the theory of electromagnetic invariant the analytical expressions for calculation of this equivalent circuit are obtained. Thus, with the help of electromagnetic invariant the analytical expressions permitting to calculate physical properties of particles and interparticle space of GM on integrated parameters of GM volume are obtained. www.ndt.net /article/wcndt00/papers/idn539/idn539.htm   (1221 words)

 Invariant Measures   (Site not responding. Last check: ) Several of the statistical measures we have met are invariant measures, which is to say that the value of the measure does not vary with, for example, the position of the region in the image, or perhaps its orientation or scale. While area does vary with scale (and thus closeness of the camera to the object, for example), compactness  as defined above is invariant with respect to scale as well as position and orientation. 55) are invariant with respect to scaling, rotation and translation. www.cs.cf.ac.uk /Dave/Vision_lecture/node37.html   (160 words)

 Doug's Expositions   (Site not responding. Last check: ) This invariant distinguishes between a cube and a regular tetrahedron, so there is no geometric dissection between the two. The idea of the Dehn invariant is quite simple: Attach an energy to each edge of a polyhedron based on the length of the edge and the dihedral angle such that the alterations made to edges under geometric decomposition do not affect the total energy. Polyhedra are equidecomposable with their mirror images as the Dehn invariants are the same, edge by edge. www.math.columbia.edu /~zare/dehninvstuff.html   (897 words)

 Invariant Chain Targets HLA Class II Molecules to Acidic Endosomes Containing Internalized Influenza Virus -- Lamb et ... The role of the HLA class II-associated invariant chain in the intracellular trafficking of HLA-DR molecules was examined in a transient expression system using HeLa cells. These findings provide direct evidence that the invariant chain targets class II molecules to an acidic endosomal compartment and that this compartment, long suspected to be the site of antigen processing, is the site where class II molecules interact with natural antigen. Invariant chain induces B cell maturation in a process that is independent of its chaperonic activity www.pnas.org /cgi/content/abstract/88/14/5998   (1171 words)

 AGT 3 (2003) Paper 22 (Abstract) On the rho invariant for manifolds with boundary A priori the rho-invariant is an invariant of the Riemannian structure and a representation of the fundamental group. We show, however, that the dependence on the metric is only very mild: it is independent of the metric in the interior and the dependence on the metric on the boundary is only up to its pseudo--isotopy class. www.maths.warwick.ac.uk /agt/AGTVol3/agt-3-22.abs.html   (204 words)

 Polynomial Invariants The ideal polynomial invariant would yield a unique polynomial for each isotopic class that is consistant through each projection of the class. Unfortunately, it did not distinguish between a knot and its mirror image, and thus assumed that all knots were achiral. The Bracket Polynomial recognizes the regularly isotopic projections of an isotopic class as the members of the same isotopic class, but the Bracket Polynomial is not an isotopy invariant because it is not invariant under the first Reidemeister Move. library.thinkquest.org /12295/data/Invariants/Data.html   (493 words)

 INVARIANT SETS FOR WINDOWS This book deals with the visualization and exploration of invariant sets (fractals, strange attractors, resonance structures, patterns etc.) for various kinds of nonlinear dynamical systems. In Part II, the invariant sets presented in Part I are investigated from the theoretical perspective. The invariant sets of dynamical systems with one, one-and-a-half and two degrees of freedom, as well as those of two-dimensional maps, are discussed. www.worldscibooks.com /chaos/4220.html   (208 words)

 Peter Kovesi For example, if edge significance could be measured in a way that was invariant to image illumination and contrast, higher-level image processing operations could be conducted with much greater confidence. However, despite their importance, little attention has been paid to the need for invariant quantities in low-level vision for tasks such as feature detection or feature matching. These invariant quantities are developed from representations of the image in the frequency domain. www.csse.uwa.edu.au /~pk/Research/research.html   (821 words)

 Invariants The Invariant Society was founded in 1936 to 'promote interest in all branches of Mathematics'. We also organize a few social events, which everybody with an interest in Mathematics is invited to attend, details to be found on the termcard; we also publish a magazine, the 'Invariant'. All speaker meetings take place at the Mathematical Institute (on the corner of St. Giles' and Keble Road) unless another venue is given in the termcard, and begin at 8.15 p.m. users.ox.ac.uk /~invar   (208 words)

 StInG: Stanford Invariant Generator There are numerous applications for this sort of invariant discovery in the traditional domains of program analysis and more recently in the non-traditional domain of reasoning about biological system models, and analyzing process models. An invariant is a forced condition on a location. Invariants provide a convenient way of adding something common in the guards of transitions. www-cs-students.stanford.edu /~srirams/Software/sting.html   (1611 words)

 IHES PREPRINT M/03/50   (Site not responding. Last check: ) Invariant manifolds are fixed points for this equation, and slow invariant manifolds are Lyapunov stable fixed points. A collection of methods for construction of slow invariant manifolds is presented, in particular, the Newton method subject to incomplete linearization is the analogue of KAM methods for dissipative systems. The systematic use of thermodynamics structures and of the quasi-chemical representation allow to construct approximations which are in concordance with physical restrictions. www.ihes.fr /PREPRINTS/M03/Resu/resu-M03-50.html   (196 words)

 Sorting It All Out : Comparison confusion: INVARIANT vs. ORDINAL The invariant culture's direct ancestor is the invariant locale. I have explained the exact purpose of the invariant locale, and that is NOT it. Further comments that find to be inappopriate the intended purpose and use of the invariant locale's collation behavior (to use the DEFAULT collation table used by half of the locales in Windows) will not be accepted. blogs.msdn.com /michkap/archive/2004/12/29/344136.aspx   (2212 words)

 Alteration of a Single Hydrogen Bond between Class II Molecules and Peptide Results in Rapid Degradation of Class II ...   (Site not responding. Last check: ) Invariant chain protects class II histocompatibility antigens from binding intact polypeptides in the endoplasmic reticulum. Invariant chain cleavage and peptide loading in major histocompatibility complex class II vesicles. Kinetics of the reactions between the invariant chain (85-99) peptide and proteins of the murine class II MHC. www.jem.org /cgi/content/full/188/11/2139   (6631 words)

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