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physics - Scale invariance In physics, scale invariance is the feature of physical objects of laws that do not change if the space is magnified, i.e. In mathematics, scale invariance leads to results such as Benford's law, fractals and logarithmic spirals. In cosmology, scale invariance is usually used to describe the near-scale-invariant energy spectrum of the cosmic microwave background - a pattern that is well explained by the theory of inflation. www.physicsdaily.com /physics/Scale_invariance   (92 words)

[No title] An underlying theory with global scale invariance seemed to be a natural explanation of this phenomena, and many theorists were involved in studying the implications of scale invariance1. In general, the quantum failure of a classical symmetry is referred to as an anomaly, and in the case of scale invariance the non-conservation of the scale current is referred to as the trace anomaly, since the vacuum expectation value of the trace of the energy-momentum tensor usually does not vanish. Since the interaction term is not locally scale invariant (local scale invariance would break translational invariance) we cannot absorb the non- trivial contributions to the scale current vertex into a GB pole as we did for the axial-vector current in chapter 3 in order to motivate the form of the one GB coupling. particle.physics.ucdavis.edu /terning/archive/Thesis7   (2840 words)

[No title] Under a translation, the relativity of scales implies that the resolution at which this given structure appears in the new position will a priori be different from the initial one. 18 the property of gauge invariance which, in accordance with Weyl's initial ideas and their development by Dirac [22,23], recovers its initial status of scale invariance. Moreover, our interpretation of gauge invariance yields new insights about the nature of the electric charge, and, when it is combined with the Lorentzian structure of dilations of special scale- relativity, it allows one to obtain new relations between the charges and the masses of elementary particles [ 6,8], as recalled in what follows (Eqs. www.chez.com /etlefevre/rechell/ukmachar.htm   (1624 words)

Scale Dependence and Scale Invariance in Hydrology - Cambridge University Press Whether processes in the natural world are dependent or independent of the scale at which they operate is one of the major issues in hydrologic science. In this volume, leading hydrologists present their views on the role of scale effects in hydrologic phenomena occurring in a range of field settings, from the land surface to deep fractured rock. Scaling of the Richards equation and its application to watershed modeling; 8. www.cambridge.org /catalogue/email.asp?isbn=0521571251   (318 words)

Scale Invariant = Perfect Embedding (No Fear Braiding) = Gravity = Self Aware The geometry of maximum "SCALE INVARIANCE" is dodeca-icosa because the 3D x,y,z coordinates of infinite dodeca-icosa stellation are all simply a power series multiplying GOLDEN MEAN or PHI times itself. SCALE INVARIANCE here means that the pattern held between the waves (which we have been calling MATTER and MIND), can be held even if the form or wave nodes are packed or unpacked into the infinitely small or large. In summary, acheiving scale invariance among waves in all these descriptions, produces the projective geometry of waves which by this processing in fractal recursion, are made into most distributeable or shareable fronts. www.zayra.de /soulcom/scaleinvariant/scaleinvariant.html   (1485 words)

Scale invariance and filling in the missing data However, if we only scale the spatial axes, then the dips represented by the original-size filter (Figure 3dpef) will not be the same as the dips represented by the scaled filter (Figure exp). The filter with scaled axes, shown in Figure exp, does not predict missing values from known ones, so there is no criteria for assigning values to the missing data. In order to move energy between the known and missing traces, we rescale the axes so that the filter is compressed to its original size, as in Figure 3dpef. sepwww.stanford.edu /public/docs/sep104/paper_html/node14.html   (1109 words)

Breakdown of Scale Invariance - Hilarity Ensues | Cosmic Variance Well, Uma’s scale is mostly due to the Bohr radius, r = h-bar^2/(m e^2), where m is the mass of the electron, and e is the charge of the electron. In biology scaling is due to the way that lengths, surface areas and volumes scale. Ken, Daryl, citrine :- On the scaling and physics issues mentioned by many…Yes, transport and diffusion are key processes which produce interesting limitations on scaling… surface area is so important, for example, as is surface tension, in fact…. cosmicvariance.com /2006/03/01/breakdown-of-scale-invariance-hilarity-ensues   (1866 words)

Scale invariance.   (Site not responding. Last check: 2007-10-12) [] show that the class of allowable scale-space kernels can be restricted under weaker conditions, essentially by combining the conditions about linearity, shift invariance, rotational invariance and semi-group structure with scale invariance. It can be shown that for a scale invariant rotationally symmetric semi-group, the Fourier transform of the convolution kernel must be of the form Koenderink and van Doorn [] carried out a closely related study, and showed that derivative operators are natural operators to derive from a scale-space representation given the assumption of scale invariance. www.nada.kth.se /~tony/cern-review/cern-html/node8.html   (216 words)

Invariance and randomness in the Nash program for coalitional games In particular a solution concept for coalitional games that is implemented by a scale invariant equilibrium concept (for example, mixed strategy Nash equilibrium) must be scale invariant. Both are simple corollaries of invariance and they are well understood (especially the first one) by the practitioners of the abstract theory of implementation. By the same token, if a solution is not scale invariant its normative appeal is also very restricted, since an uninformed planner cannot implement it. www.nirdagan.com /research/199801   (806 words)

Xiaofeng Ren: Contours in Natural Images and Scale Invariance As the information about absolute scale is lost in the imaging process, an object at half the distance looks as if having twice the dimensions. Imagine a scale pyramid where the contour C becomes coarser and coarser as we subsample it. is the tangent of C at scale k. www.cs.berkeley.edu /~xren/research/eccv2002   (939 words)

NATURE’S STATISTICAL SYMMETRIES...   (Site not responding. Last check: 2007-10-12) The most intriguing one is "scale-invariance" which describes how spatial statistics collected over a wide range of scales (using wavelets) follow simple power laws with respect to the scale parameter. We use a to denote the scale at which we separate the "fast" and "slow" components and b as a position parameter. The graph of f(x) is plotted in the top panel (a); it is a trace in time of the amount of liquid water in the cloudy atmospheric column above a instrument station in Oklahoma for one day; sampling is done every 20 seconds. members.tripod.com /vismath7/proceedings/davis.htm   (1194 words)

Space, time and string theory The spacetime oscillation spectrum satisfies Lorentz invariance in 26 dimensions, so that these string oscillations on the worldsheet can be classified by the spacetime properties of mass and spin, just like elementary particles. Once again, the goal of conformal invariance is met by demanding that the beta functions vanish. This is a hint that perhaps spacetime geometry is not something fundamental in string theory, but something that emerges in the theory at large distance scales or weak coupling. www.superstringtheory.com /blackh/blackh4a.html   (897 words)

UCLA - Earth and Space Sciences - Didier Sornette, Books This book is an excellent introduction to the concept of scale invariance, which is a growing field of research with wide applications. It describes where and how symmetry under scale transformation (and its various forms of partial breakdown) can be used to analyze solutions of a problem without the need to explicitly solve it. To set the scale of the Japan bubble culminating in 1989-1990, the volume of trading on the Japanese stock markets rose from 231 to 2801 billions of US$ (factor 12) from 1983 to 1989, compared to a growth of 797 to 2016 billions of US$ (factor 2.5) on the US stock markets. www.ess.ucla.edu /faculty/sornette/books.asp   (2425 words)

Physical Scaling and Scale Invariance - Numericana The scale of animals according to Galileo Galilei. French kiddy sensationalism notwithstanding, the performance of creatures having vastly different sizes should not be compared using the linear scaling implied by the above comparison between men and fleas... Taking the above at face value, a jumping creature would be expected to release an energy roughly proportional to its volume (limbs apply a force proportional to the square of the size, along a launching trajectory proportional to the size). home.att.net /~numericana/answer/scaling.htm   (523 words)

Scale invariance and universality of economic fluctuations   (Site not responding. Last check: 2007-10-12) One reason for this interest-is that economic systems are examples of complex interacting systems for which a huge amount of data exist, and it is possible that economic time series viewed from a different perspective might yield new results. This manuscript is a brief summary of a talk that was designed to address the question of whether two of the pillars of the field of phase transitions and critical phenomena - scale invariance and universality - call be useful in guiding research on economics. We shall see that while scale :invariance has been tested for many years, universality is relatively less frequently discussed. amaral.chem-eng.northwestern.edu /Publications/Papers/Stanley-2000-PhysicaA-283-31.html   (317 words)

RR-5143 : Kernel methods and scale invariance using the triangular kernel Titre français : Méthodes à noyaux et invariance par échelle à l'aide du noyau triangulaire The study in (Sahbi and Fleuret, 2002) reported scale invariance for support vector machines (SVM) and the current work is an extension for support vector regression (SVR) and kernel principal component analysis (KPCA). Experiments are conducted in several cases showing the scale invariance and the good performance in real pattern recognition problems including shape description, face detection and recognition. www.inria.fr /rrrt/rr-5143.html   (333 words)

Global Scaling: New Term for Implosion? Scale Invariance.. The pure principle is clearly that Golden Mean ratio is the key wave mechanic to enable scale invariance (soulinvitation.com/scaleinvariant), perfected recursion, self embedding (soulinvitation.com/embedability), perfected nesting, AND THEREFORE - perfect compression- perfect fusion (soulinvitation.com/fusion), perfect collapse (soulinvitation.com/collapse). The Global Scaling movement is correct to propose that capacitors arranged in the geometry of Golden Mean ratio fabricate gravity from voltage, and voltage from gravity. Harmonic inclusiveness (same as non-destructive charge compression and genetic diversity and scale invariance / "Global Scaling") -perfected by Golden Ratio - defines the vitality of everything that lives- as well known in the medicine of EKG (soulinvitation.com/dardik). www.zayra.de /soulcom/globalscaling   (3611 words)

Xiaofeng Ren: A Scale-Invariant Image Representation: the CDT Graph The constrained Delaunay triangulation (CDT) is a variant of of the standard Delaunay Triangulation in which a set of user-specified edges (in our case, the edges in the piecewise linear approximation) must lie in the triangulation. Figure 1: a scale-invariant representation: (a) an object at two scales; (b) the Constrained Delaunay Triangulation (CDT) graph, based on a piecewise linear approximation of low-level edges (G-edges, in fl). The internal structure of the object is independent of scale. www.cs.berkeley.edu /~xren/research/cdtgraph   (899 words)

Scale-Invariance   (Site not responding. Last check: 2007-10-12) Although crucial for obtaining meaningful spatial statistics, even of the standard Gaussian variety (e.g., in climate diagnostics), the importance of establishing stationarity -statistical invariance under translation- is often overlooked. Comparing the spectral responses of different instruments to natural LWC variability, we find scale breaks (characteristic scales separating two distinct power law regimes) that are spurious, being traceable to well-documented idiosyncrasies of the Johnson-Williams probe and Forward Scattering Spectrometer Probes (FSSPs). In data from the King probe, we find no such artifacts; all spectra are of the scale-invariant form k^beta with exponents beta in the range 1.1 to 1.7, depending on the flight and how much weight is given to the different k's in the adopted sampling, averaging and regression strategy. climate.gsfc.nasa.gov /~marshak/Pubs/LW.Part1.html   (486 words)

Perturbations in bouncing cosmologies: dynamical attractor vs scale invariance   (Site not responding. Last check: 2007-10-12) For bouncing cosmologies such as the ekpyrotic/cyclic scenarios we show that it is possible to make predictions for density perturbations which are independent of the details of the bouncing phase. The resulting spectrum is not scale invariant and thus incompatible with experimental data. This can be explicitly shown in synchronous gauge where, contrary to what happens in the commonly used Newtonian gauge, all perturbations remain small going towards the bounce and the existence of the attractor is manifest. hep.bu.edu /abstracts/nicolis-feb-05.html   (148 words)

.. Scale invariance - Enpsychlopedia length scales (or energies) are multiplied by a common factor. To give a trivial example for the object feature, the mass of the ball divided by the third power of its radius is independent of the radius i.e. In cosmology, scale invariance is usually used to describe the near-scale-invariant energy spectrum of the cosmic microwave background - a pattern that is reasonably well explained by the paradigm of cosmic inflation. www.psychcentral.com /psypsych/Scale_invariance   (158 words)

Re: Scale invariance   (Site not responding. Last check: 2007-10-12) A flat >power spectrum is white noise, which has very little large-> > > scale >power but lots of small-scale power. For me power would just be the value of the power spectrum at a particular wave number or scale. Hence to me a flat power spectrum would have the same "power value" at all scales. www.lns.cornell.edu /spr/2001-06/msg0033428.html   (345 words)

A Jet is a Jet, Big or Small: Scale Invariance of Black Hole Jets Starting from the physical conditions in the accretion disk (such as the magnetic field strength and particle density, see Figure 2), it is then possible to predict how bright a jet from a fl hole of given mass and accretion rate will be. In a stunning confirmation of the scale invariance hypothesis, they discovered that all the active fl holes in the sample followed a simple linear correlation that the scientists called "fundamental plane" of fl hole activity. That is, if one plots the mass, radio luminosity, and X-ray luminosity for every fl hole in their sample, all the plotted points will lie in a well defined plane (see Figure 3). www.mpa-garching.mpg.de /new-home/HIGHLIGHT/2003/highlight0308_e.html   (716 words)

Scale invariance and universality of force networks in static granular matter : Nature Scale invariance and universality of force networks in static granular matter Here we report that molecular dynamics simulations of realistic granular packings reveal scale invariance of clusters of particles interacting by means of relatively strong forces. Despite visual variation, force networks for various values of the confining pressure and other parameters have identical scaling exponents and scaling function, thereby determining a universality class. www.nature.com /nature/journal/v439/n7078/abs/nature04549.html   (301 words)

Transformation invariance An important class of priors arises from the requirement of transformation invariance. Again, the improper prior must be understood as the limit of a proper prior extending several orders of magnitude around the values of interest. to be positive because, traditionally, variables which are believed to satisfy this invariance are associated with positively defined quantities. www.roma1.infn.it /~dagos/rpp/node33.html   (267 words)

UCLA - Earth and Space Sciences - Didier Sornette, Publications: Discrete Scale Invariance & Complex Exponents W.-X. Zhou and D. Sornette, Discrete scale invariance in fractals and multifractal measures, Phys. Johansen, D. Sornette and A.E. Hansen, Punctuated vortex coalescence and discrete scale invariance in two-dimensional turbulence, Physica D 138, Issue 3-4, pp. Johansen and D. Sornette, Evidence of discrete scale invariance by canonical averaging, Int. www.ess.ucla.edu /faculty/sornette/pub_discrete.asp   (821 words)

Line Drawing Recognition System. Version 1   (Site not responding. Last check: 2007-10-12) This system is trained for invariant recognition of a class of line drawing objects. Note that the training for scale invariance consisted of just two exemplars from each category. Still the system demonstrates robust generalization and scale and distortion invariance. www.stanford.edu /~dil/invariance/SystemSourceRel1.html   (334 words)

CiteULike: Scale Invariance in Global Terrorism   (Site not responding. Last check: 2007-10-12) This property is robust, even when we restrict our analysis to events from a single type of weapon or events within major industrialized nations. We also find that the distribution of event sizes has changed very little over the past 37 years, suggesting that scale invariance is an inherent feature of global terrorism. We also find that the distribution of event sizes has changed very little over the past 37 years, suggesting that scale invariance is an inherent feature of global terrorism.}, author = {Clauset, Aaron and Young, Maxwell }, citeulike-article-id = {229190}, comment = {Fascinating. www.citeulike.org /user/michmill/article/229190   (429 words)

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