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Journal articles on the topic 'Transformation invariance'

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Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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1

Wagner, Jenny. "Generalised model-independent characterisation of strong gravitational lenses." Astronomy & Astrophysics 620 (December 2018): A86. http://dx.doi.org/10.1051/0004-6361/201834218.

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Based on the standard gravitational lensing formalism with its effective, projected lensing potential in a given background cosmology, we investigated under which transformations of the source position and of the deflection angle the observable properties of the multiple images remain invariant. These observable properties are time delay differences, the relative image positions, relative shapes, and magnification ratios. As they only constrain local lens properties, we derive general, local invariance transformations in the areas covered by the multiple images. We show that the known global invariance transformations, for example, the mass-sheet transformation or the source position transformation, are contained in our invariance transformations, when they are restricted to the areas covered by the multiple images and when lens-model-based degeneracies are ignored, like the freedom to add or subtract masses in unconstrained regions without multiple images. Hence, we have identified the general class of invariance transformations that can occur, in particular in our model-independent local characterisation of strong gravitational lenses.

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2

DAS, ASHOK, and MARCELO HOTT. "CHIRAL INVARIANCE OF MASSIVE FERMIONS." Modern Physics Letters A 09, no. 24 (August 10, 1994): 2217–25. http://dx.doi.org/10.1142/s0217732394002070.

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We show that a massive fermion theory, while not invariant under the conventional chiral transformation, is invariant under a m-deformed chiral transformation. These transformations and the associated conserved charges are nonlocal but reduce to the usual transformations and charges when m=0. The m-deformed charges commute with helicity and satisfy the conventional chiral algebra.

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3

Miao, Xu, and Rajesh P. N. Rao. "Learning the Lie Groups of Visual Invariance." Neural Computation 19, no. 10 (October 2007): 2665–93. http://dx.doi.org/10.1162/neco.2007.19.10.2665.

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A fundamental problem in biological and machine vision is visual invariance: How are objects perceived to be the same despite transformations such as translations, rotations, and scaling? In this letter, we describe a new, unsupervised approach to learning invariances based on Lie group theory. Unlike traditional approaches that sacrifice information about transformations to achieve invariance, the Lie group approach explicitly models the effects of transformations in images. As a result, estimates of transformations are available for other purposes, such as pose estimation and visuomotor control. Previous approaches based on first-order Taylor series expansions of images can be regarded as special cases of the Lie group approach, which utilizes a matrix-exponential-based generative model of images and can handle arbitrarily large transformations. We present an unsupervised expectation-maximization algorithm for learning Lie transformation operators directly from image data containing examples of transformations. Our experimental results show that the Lie operators learned by the algorithm from an artificial data set containing six types of affine transformations closely match the analytically predicted affine operators. We then demonstrate that the algorithm can also recover novel transformation operators from natural image sequences. We conclude by showing that the learned operators can be used to both generate and estimate transformations in images, thereby providing a basis for achieving visual invariance.

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4

CHIMENTO, LUIS P., and WINFRIED ZIMDAHL. "DUALITY INVARIANCE AND COSMOLOGICAL DYNAMICS." International Journal of Modern Physics D 17, no. 12 (November 2008): 2229–54. http://dx.doi.org/10.1142/s0218271808013820.

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A duality transformation that interrelates expanding and contracting cosmological models is shown to single out a duality invariant, interacting two-component description of any irrotational, geodesic and shear-free cosmic medium with vanishing three-curvature scalar. We have applied this feature to a system of matter and radiation, to a mixture of dark matter and dark energy, to minimal and conformal scalar fields, and to an enlarged Chaplygin gas model of the cosmic substratum. We have extended the concept of duality transformations to cosmological perturbations and demonstrated the invariance of adiabatic pressure perturbations under these transformations.

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5

Salosin, Evgeny Georgievich. "LORENTZ TRANSFORMATION CHANGE." Globus 8, no. 1(66) (February 4, 2022): 36–40. http://dx.doi.org/10.52013/2658-5197-66-1-9.

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For relativistic velocities, Galileo’s principle of addition of four-dimensional velocities is valid, and not the Lorentz transformation. In this case, it is impossible to write down the law of conservation of energy with Newton’s potential using the Lorentz transformation. And with the proposed transformation it is possible. In addition, the invariance of the wave equation with respect to the Galilean transformation with four-dimensional velocity is obtained. The GR equation is also invariant under the Galileo transformations of the four-vector. This transformation is a more general case of invariance than the Lorentz transformation. Moreover, the Lorentz transformation is contradictory. For a single massive body in general relativity, the Lorentz transformation is not valid, since the metric tensor is not Galilean. Although in the case of SRT such a transformation is possible. Those. the properties of inertial coordinate systems are violated. For a Galilean transformation of a four-vector for a massive body, a Galilean transformation is possible. Moreover, from the Galilean transformations of the four-vector, one can obtain the Lorentz transformation, but with the use of three-dimensional velocity. Three-dimensional speed is limited by the speed of light in real space, where all tricks with its use come from. The 4D speed is unlimited, and there are no coordinate transformation tricks. If you use the transformation between inertial coordinate systems using a limited threedimensional velocity, then tricks arise with the transformation of space and time. If you use unlimited four-dimensional speed, then there are no tricks with a change in space-time. Four-dimensional speed is a more general concept than three-dimensional, and you need to measure the parameters at four-dimensional speed, then there will be no tricks. Thus, measuring time with the help of four-dimensional velocity, we will not get an increase in the muon lifetime.

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6

Földiák, Peter. "Learning Invariance from Transformation Sequences." Neural Computation 3, no. 2 (June 1991): 194–200. http://dx.doi.org/10.1162/neco.1991.3.2.194.

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The visual system can reliably identify objects even when the retinal image is transformed considerably by commonly occurring changes in the environment. A local learning rule is proposed, which allows a network to learn to generalize across such transformations. During the learning phase, the network is exposed to temporal sequences of patterns undergoing the transformation. An application of the algorithm is presented in which the network learns invariance to shift in retinal position. Such a principle may be involved in the development of the characteristic shift invariance property of complex cells in the primary visual cortex, and also in the development of more complicated invariance properties of neurons in higher visual areas.

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7

HO, S. H. "ALTERNATIVE CONFORMAL QUANTUM MECHANICS." International Journal of Modern Physics A 26, no. 16 (June 30, 2011): 2735–42. http://dx.doi.org/10.1142/s0217751x11053547.

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We investigate a one-dimensional quantum mechanical model, which is invariant under translations and dilations but does not respect the conventional conformal invariance. We describe the possibility of modifying the conventional conformal transformation such that a scale invariant theory is also invariant under this new conformal transformation.

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8

Alsing, P. M., and G. Milburn. "Lorentz Invariance of Entanglement." Quantum Information and Computation 2, no. 6 (October 2002): 487–512. http://dx.doi.org/10.26421/qic2.6-4.

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We study the transformation of maximally entangled states under the action of Lorentz transformations in a fully relativistic setting. By explicit calculation of the Wigner rotation, we describe the relativistic analog of the Bell states as viewed from two inertial frames moving with constant velocity with respect to each other. Though the finite dimensional matrices describing the Lorentz transformations are non-unitary, each single particle state of the entangled pair undergoes an effective, momentum dependent, local unitary rotation, thereby preserving the entanglement fidelity of the bipartite state. The details of how these unitary transformations are manifested are explicitly worked out for the Bell states comprised of massive spin $1/2$ particles and massless photon polarizations. The relevance of this work to non-inertial frames is briefly discussed.

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9

King, J. R. "Local transformations between some nonlinear diffusion equations." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 33, no. 3 (January 1992): 321–49. http://dx.doi.org/10.1017/s0334270000007074.

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AbstractWe derive local transformations mapping radially symmetric nonlinear diffusion equations with power law or exponential diffusivities into themselves or into other equations of a similar form. Both discrete and continuous transformations are considered. For the cases in which a continuous transformation exists, many additional forms of group-invariant solution may be constructed; some of these solutions may be written in closed form. Related invariance properties of some multidimensional diffusion equations are also exploited.

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10

Dai, Gaole, and Jun Wang. "On Transformation Form-Invariance in Thermal Convection." Materials 16, no. 1 (December 30, 2022): 376. http://dx.doi.org/10.3390/ma16010376.

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Over the past two decades, effective control of physical fields, such as light fields or acoustics fields, has greatly benefited from transforming media. One of these rapidly growing research areas is transformation thermotics, especially embodied in the thermal conductive and radiative modes. On the other hand, transformation media in thermal convection has seldom been studied due to the complicated governing equations involving both fluid motion and heat transfer terms. The difficulty lies in the robustness of form invariance in the Navier–Stokes equations or their simplified forms under coordinate transformations, which determines whether the transformation operations can be executed on thermal convection to simultaneously regulate the flow and thermal fields. In this work, we show that thermal convection in two-dimensional Hele–Shaw cells keeps form-invariance, while its counterpart in general creeping flows or general laminar flows does not. This conclusion is numerically verified by checking the performances of invisible devices made of transformation media in convective environments. We further exploit multilayered structures constituted of isotropic homogeneous natural materials to realize the anisotropic inhomogeneous properties required for transformation media. Our results clarify the long-term confusion about the validation of the transformation method in thermal convection and provide a rigorous foundation and classical paradigm on inspiring various fascinating metadevices in both thermal and flow fields.

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11

HAMMOND, RICHARD T. "THE NECESSITY OF TORSION IN GRAVITY." International Journal of Modern Physics D 19, no. 14 (December 2010): 2413–16. http://dx.doi.org/10.1142/s0218271810018554.

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It is shown that torsion is required for a complete theory of graviation, and that without it, the equations of gravitation violate fundamental laws. In the first case, we are reminded that, in the absence of external forces, the correct conservation law of total angular momentum arises only if torsion, whose origin is intrinsic spin, is included into gravitation. The second case considers the "mass reversal" transformation. It has been known that under a global chiral transformation and "mass to negative mass" transformation, the Dirac equation is invariant. But global transformations violate special relativity, so this transformation must be made local. It is shown that the torsion is the gauge field for this local invariance.

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12

Organista, José Orlando, Marek Nowakowski, and H. C. Rosu. "Shape invariance through Crum transformation." Journal of Mathematical Physics 47, no. 12 (December 2006): 122104. http://dx.doi.org/10.1063/1.2397556.

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13

Eichhorn, Ralf, Stefan J. Linz, and Peter Hänggi. "Transformation invariance of Lyapunov exponents." Chaos, Solitons & Fractals 12, no. 8 (June 2001): 1377–83. http://dx.doi.org/10.1016/s0960-0779(00)00120-x.

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14

Even-Tzur, Gilad. "Invariance property of coordinate transformation." Journal of Spatial Science 63, no. 1 (April 21, 2017): 23–34. http://dx.doi.org/10.1080/14498596.2017.1316688.

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15

Bez, H. E. "Conceptual aspects of transformation invariance." Computer-Aided Design 19, no. 9 (November 1987): 475–78. http://dx.doi.org/10.1016/0010-4485(87)90232-6.

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16

Frank, Steven A., and Jordi Bascompte. "Invariance in ecological pattern." F1000Research 8 (December 12, 2019): 2093. http://dx.doi.org/10.12688/f1000research.21586.1.

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Background: The abundance of different species in a community often follows the log series distribution. Other ecological patterns also have simple forms. Why does the complexity and variability of ecological systems reduce to such simplicity? Common answers include maximum entropy, neutrality, and convergent outcome from different underlying biological processes. Methods: This article proposes a more general answer based on the concept of invariance, the property by which a pattern remains the same after transformation. Invariance has a long tradition in physics. For example, general relativity emphasizes the need for the equations describing the laws of physics to have the same form in all frames of reference. Results: By bringing this unifying invariance approach into ecology, we show that the log series pattern dominates when the consequences of processes acting on abundance are invariant to the addition or multiplication of abundance by a constant. The lognormal pattern dominates when the processes acting on net species growth rate obey rotational invariance (symmetry) with respect to the summing up of the individual component processes. Conclusions: Recognizing how these invariances connect pattern to process leads to a synthesis of previous approaches. First, invariance provides a simpler and more fundamental maximum entropy derivation of the log series distribution. Second, invariance provides a simple derivation of the key result from neutral theory: the log series at the metacommunity scale and a clearer form of the skewed lognormal at the local community scale. The invariance expressions are easy to understand because they uniquely describe the basic underlying components that shape pattern.

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17

Pal, Dipan K., and Marios Savvides. "Non-Parametric Transformation Networks for Learning General Invariances from Data." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 4667–74. http://dx.doi.org/10.1609/aaai.v33i01.33014667.

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ConvNets, through their architecture, only enforce invariance to translation. In this paper, we introduce a new class of deep convolutional architectures called Non-Parametric Transformation Networks (NPTNs) which can learn general invariances and symmetries directly from data. NPTNs are a natural generalization of ConvNets and can be optimized directly using gradient descent. Unlike almost all previous works in deep architectures, they make no assumption regarding the structure of the invariances present in the data and in that aspect are flexible and powerful. We also model ConvNets and NPTNs under a unified framework called Transformation Networks (TN), which yields a better understanding of the connection between the two. We demonstrate the efficacy of NPTNs on data such as MNIST with extreme transformations and CIFAR10 where they outperform baselines, and further outperform several recent algorithms on ETH-80. They do so while having the same number of parameters. We also show that they are more effective than ConvNets in modelling symmetries and invariances from data, without the explicit knowledge of the added arbitrary nuisance transformations. Finally, we replace ConvNets with NPTNs within Capsule Networks and show that this enables Capsule Nets to perform even better.

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18

JOGLEKAR, SATISH D., and A. MISRA. "WILSON LOOP AND THE TREATMENT OF AXIAL GAUGE POLES." Modern Physics Letters A 15, no. 08 (March 14, 2000): 541–46. http://dx.doi.org/10.1142/s0217732300000530.

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We consider the question of gauge invariance of the Wilson loop in the light of a new treatment of axial gauge propagator proposed recently based on a finite field-dependent BRS (FFBRS) transformation. We remark that under the FFBRS transformation as the vacuum expectation value of a gauge-invariant observable remains unchanged, our prescription automatically satisfies the Wilson loop criterion. Furthermore, we give an argument for direct verification of the invariance of Wilson loop to O(g4) using the earlier work by Cheng and Tsai. We also note that our prescription preserves the thermal Wilson loop to O(g2).

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19

Heydeman, J., and W. W. Schongs. "Power Invariance Transformation in Power Systems." International Journal of Electrical Engineering & Education 37, no. 2 (April 2000): 180–89. http://dx.doi.org/10.7227/ijeee.37.2.7.

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Many textbooks describe a balanced three-phase circuit by a single-phase equivalent representation. Confusion may arise amongst students regarding per-unit values of line-to-line voltages and phase voltages and, therefore, about the magnitudes of currents and powers. This paper proposes that students must first be taught symmetrical components based on power invariance transformation. A balanced three-phase circuit is to be described only in terms of positive sequence components. In the authors' experience, students understand this approach better and make fewer errors in per-unit calculation than when they use the single-phase equivalent representation.

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20

Bartlett, D. F., and W. F. Edwards. "Invariance of charge to Lorentz transformation." Physics Letters A 151, no. 6-7 (December 1990): 259–62. http://dx.doi.org/10.1016/0375-9601(90)90279-w.

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21

CASTELLANA, MICHELE, and GIOVANNI MONTANI. "BRST SYMMETRY TOWARDS THE GAUSS CONSTRAINT FOR GENERAL RELATIVITY." International Journal of Modern Physics A 23, no. 08 (March 30, 2008): 1218–21. http://dx.doi.org/10.1142/s0217751x08040093.

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Quantization of systems with constraints can be carried on with several methods. In the Dirac's formulation the classical generators of gauge transformations are required to annihilate physical quantum states to ensure their gauge invariance. Carrying on BRST symmetry it is possible to get a condition on physical states which, differently from the Dirac's method, requires them to be invariant under the BRST transformation. Employing this method for the action of general relativity expressed in terms of the spin connection and tetrad fields with path integral methods, we construct the generator of BRST transformation associated with the underlying local Lorentz symmetry of the theory and write a physical state condition following from BRST invariance. The condition we gain differs form the one obtained within Ashtekar's canonical formulation, showing how we recover the latter only by a suitable choice of the gauge fixing functionals. We finally discuss how it should be possible to obtain all the requested physical state conditions associated with all the underlying gauge symmetries of the classical theory using our approach.

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22

Alinea, Allan L., and Takahiro Kubota. "Transformation of primordial cosmological perturbations under the general extended disformal transformation." International Journal of Modern Physics D 30, no. 08 (May 11, 2021): 2150057. http://dx.doi.org/10.1142/s0218271821500577.

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Primordial cosmological perturbations are the seeds that were cultivated by inflation and the succeeding dynamical processes, eventually leading to the current universe. In this work, we investigate the behavior of the gauge-invariant scalar and tensor perturbations under the general extended disformal transformation, namely, [Formula: see text], where [Formula: see text] and [Formula: see text], with [Formula: see text] and [Formula: see text] being a general functional of [Formula: see text]. We find that the tensor perturbation is invariant under this transformation. On the other hand, the scalar curvature perturbation receives a correction due the conformal term only; it is independent of the disformal term at least up to linear order. Within the framework of the full Horndeski theory, the correction terms turn out to depend linearly on the gauge-invariant comoving density perturbation and the first time-derivative thereof. In the superhorizon limit, all these correction terms vanish, leaving only the original scalar curvature perturbation. In other words, it is invariant under the general extended disformal transformation in the superhorizon limit, in the context of full Horndeski theory. Our work encompasses a chain of research studies on the transformation or invariance of the primordial cosmological perturbations, generalizing their results under our general extended disformal transformation.

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23

SAMARSKII, A. A., V. I. MAZHUKIN, P. P. MATUS, V. G. RYCHAGOV, and I. SMUROV. "INVARIANT DIFFERENCE SCHEMES FOR PARABOLIC EQUATIONS WITH TRANSFORMATIONS OF INDEPENDENT VARIABLES." Mathematical Models and Methods in Applied Sciences 09, no. 01 (February 1999): 93–110. http://dx.doi.org/10.1142/s0218202599000075.

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In this paper, invariant difference schemes for nonstationary equations under independent variables transformation constructed and investigated. Under invariance of difference scheme we mean its ability to preserve basic properties (stability, approximation, convergency, etc.) in various coordinate systems. Difference schemes of the second-order approximation that satisfy the invariance property are constructed for equations of parabolic type. Stability and convergency investigation of correspondent difference problems are carried out; a priori estimates in various grid norms are obtained.

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24

Kudari, Medha, Shivashankar S., and Prakash S. Hiremath. "Illumination and Rotation Invariant Texture Representation for Face Recognition." International Journal of Computer Vision and Image Processing 10, no. 2 (April 2020): 58–69. http://dx.doi.org/10.4018/ijcvip.2020040105.

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This article presents a novel approach for illumination and rotation invariant texture representation for face recognition. A gradient transformation is used as illumination invariance property and a Galois Field for the rotation invariance property. The normalized cumulative histogram bin values of the Gradient Galois Field transformed image represent the illumination and rotation invariant texture features. These features are further used as face descriptors. Experimentations are performed on FERET and extended Cohn Kanade databases. The results show that the proposed method is better as compared to Rotation Invariant Local Binary Pattern, Log-polar transform and Sorted Local Gradient Pattern and is illumination and rotation invariant.

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25

Webber, Chris J. S. "Predictions of the Spontaneous Symmetry-Breaking Theory for Visual Code Completeness and Spatial Scaling in Single-Cell Learning Rules." Neural Computation 13, no. 5 (May 1, 2001): 1023–43. http://dx.doi.org/10.1162/08997660151134316.

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This article shows analytically that single-cell learning rules that give rise to oriented and localized receptive fields, when their synaptic weights are randomly and independently initialized according to a plausible assumption of zero prior information, will generate visual codes that are invariant under two-dimensional translations, rotations, and scale magnifications, provided that the statistics of their training images are sufficiently invariant under these transformations. Such codes span different image locations, orientations, and size scales with equal economy. Thus, single-cell rules could account for the spatial scaling property of the cortical simple-cell code. This prediction is tested computationally by training with natural scenes; it is demonstrated that a single-cell learning rule can give rise to simple-cell receptive fields spanning the full range of orientations, image locations, and spatial frequencies (except at the extreme high and low frequencies at which the scale invariance of the statistics of digitally sampled images must ultimately break down, because of the image boundary and the finite pixel resolution). Thus, no constraint on completeness, or any other coupling between cells, is necessary to induce the visual code to span wide ranges of locations, orientations, and size scales. This prediction is made using the theory of spontaneous symmetry breaking, which we have previously shown can also explain the data-driven self-organization of a wide variety of transformation invariances in neurons' responses, such as the translation invariance of complex cell response.

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26

Pestman, Wiebe R. "Creating and classifying measures of linear association by optimization techniques." MATHEMATICA SCANDINAVICA 106, no. 1 (March 1, 2010): 67. http://dx.doi.org/10.7146/math.scand.a-15125.

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The idea of measures of linear association, such as Pearson's correlation coefficient, can be put in a general framework by axiomization. Groups of linear transformations on $\mathsf{R}^n$ can be exploited to create new and classify existing measures according to their invariance properties. Thus invariance under the Euclidean transformation group leads to the class of so-called geometric measures. Similarly, a measure is called algebraic if it is invariant under scalings. Pearson's coefficient is an example of an algebraic measure; it is not geometric. It is proved that, generally, a measure of linear association cannot possibly be both geometric and algebraic. A procedure is developed to convert a geometric measure into an algebraic and vice versa. Thus a kind of a duality between algebraic and geometric measures arises. In this duality measures can be reflexive or not.

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27

Rigolin, Gustavo. "On Lorentz Invariant Complex Scalar Fields." Advances in High Energy Physics 2022 (February 28, 2022): 1–58. http://dx.doi.org/10.1155/2022/5511428.

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We obtain a Lorentz covariant wave equation whose complex wave function transforms under a Lorentz boost according to the following rule, Ψ x ⟶ e i / ℏ f x Ψ x . We show that the spacetime-dependent phase f x is the most natural relativistic extension of the phase associated with the transformation rule for the nonrelativistic Schrödinger wave function when it is subjected to a Galilean transformation. We then generalize the previous analysis by postulating that Ψ x transforms according to the above rule under proper Lorentz transformations (boosts or spatial rotations). This is the most general transformation rule compatible with a Lorentz invariant physical theory whose observables are bilinear functions of the field Ψ x . We use the previous wave equations to describe several physical systems. In particular, we solve the bound state and scattering problems of two particles which interact both electromagnetically and gravitationally (static electromagnetic and gravitational fields). The former interaction is modeled via the minimal coupling prescription while the latter enters via an external potential. We also formulate logically consistent classical and quantum field theories associated with these Lorentz covariant wave equations. We show that it is possible to make those theories equivalent to the Klein-Gordon theory whenever we have self-interacting terms that do not break their Lorentz invariance or if we introduce electromagnetic interactions via the minimal coupling prescription. For interactions that break Lorentz invariance, we show that the present theories imply that particles and antiparticles behave differently at decaying processes, with the latter being more unstable. This suggests a possible connection between Lorentz invariance-breaking interactions and the matter-antimatter asymmetry problem.

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PITMAN, JIM. "Poisson–Dirichlet and GEM Invariant Distributions for Split-and-Merge Transformations of an Interval Partition." Combinatorics, Probability and Computing 11, no. 5 (September 2002): 501–14. http://dx.doi.org/10.1017/s0963548302005163.

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This paper introduces a split-and-merge transformation of interval partitions which combines some features of one model studied by Gnedin and Kerov [12, 11] and another studied by Tsilevich [30, 31] and Mayer-Wolf, Zeitouni and Zerner [21]. The invariance under this split-and-merge transformation of the interval partition generated by a suitable Poisson process yields a simple proof of the recent result of [21] that a Poisson–Dirichlet distribution is invariant for a closely related fragmentation–coagulation process. Uniqueness and convergence to the invariant measure are established for the split-and-merge transformation of interval partitions, but the corresponding problems for the fragmentation–coagulation process remain open.

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29

Sallhofer, Hans. "The Inversion Invariance of the Lorentz Transformation." Zeitschrift für Naturforschung A 52, no. 8-9 (September 1, 1997): 678. http://dx.doi.org/10.1515/zna-1997-8-922.

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30

Gionti, Gabriele, and Andronikos Paliathanasis. "Duality transformation and conformal equivalent scalar–tensor theories." Modern Physics Letters A 33, no. 16 (May 30, 2018): 1850093. http://dx.doi.org/10.1142/s0217732318500931.

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We deal with the duality symmetry of the dilaton field in cosmology and specifically with the so-called Gasperini–Veneziano duality transformation. In particular, we determine two conformal equivalent theories to the dilaton field, and we show that under conformal transformations Gasperini–Veneziano duality symmetry does not survive. Moreover, we show that those theories share a common conservation law, of Noetherian kind, while the symmetry vector which generates the conservation law is an isometry only for the dilaton field. Finally, we show that the Lagrangian of the dilaton field is equivalent with the two-dimensional “hyperbolic oscillator” in a Lorentzian space whose O(d, d) invariance is transformed into the Gasperini–Veneziano duality invariance in the original coordinates.

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31

Siahaan, Haryanto M., and Triyanta Triyanta. "On the Napsuciale-Kirchbach Formalism for Spin 3/2 Field Theory." Indonesian Journal of Physics 19, no. 2 (November 3, 2016): 51–54. http://dx.doi.org/10.5614/itb.ijp.2008.19.2.3.

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We consider the newly approach by Napsuciale and Kirchbach as an alternative formalism for spin-3/2 fields. The Feynman rules for interacting case are derived. Gauge invariance property in this formalism is shown from the corresponding invariant Compton scattering amplitude related to gauge transformation of the polarization vector.

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32

Zhang, Feng, Yuru Hu, and Xiangpeng Xin. "Lie Symmetry Analysis, Exact Solutions, and Conservation Laws of Variable-Coefficients Boiti-Leon-Pempinelli Equation." Advances in Mathematical Physics 2021 (November 29, 2021): 1–14. http://dx.doi.org/10.1155/2021/6227384.

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In this article, we study the generalized ( 2 + 1 )-dimensional variable-coefficients Boiti-Leon-Pempinelli (vcBLP) equation. Using Lie’s invariance infinitesimal criterion, equivalence transformations and differential invariants are derived. Applying differential invariants to construct an explicit transformation that makes vcBLP transform to the constant coefficient form, then transform to the well-known Burgers equation. The infinitesimal generators of vcBLP are obtained using the Lie group method; then, the optimal system of one-dimensional subalgebras is determined. According to the optimal system, the ( 1 + 1 )-dimensional reduced partial differential equations (PDEs) are obtained by similarity reductions. Through G ′ / G -expansion method leads to exact solutions of vcBLP and plots the corresponding 3-dimensional figures. Subsequently, the conservation laws of vcBLP are determined using the multiplier method.

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33

Webber, Chris J. S. "Self-Organization of Symmetry Networks: Transformation Invariance from the Spontaneous Symmetry-Breaking Mechanism." Neural Computation 12, no. 3 (March 1, 2000): 565–96. http://dx.doi.org/10.1162/089976600300015718.

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Symmetry networks use permutation symmetries among synaptic weights to achieve transformation-invariant response. This article proposes a generic mechanism by which such symmetries can develop during unsupervised adaptation: it is shown analytically that spontaneous symmetry breaking can result in the discovery of unknown invariances of the data's probability distribution. It is proposed that a role of sparse coding is to facilitate the discovery of statistical invariances by this mechanism. It is demonstrated that the statistical dependences that exist between simple-cell-like threshold feature detectors, when exposed to temporally uncorrelated natural image data, can drive the development of complex-cell-like invariances, via single-cell Hebbian adaptation. A single learning rule can generate both simple-cell-like and complex-cell-like receptive fields.

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34

FAN, HONG-YI, and JI-SUO WANG. "ON THE WEYL ORDERING INVARIANCE UNDER GENERAL n-MODE SIMILAR TRANSFORMATIONS." Modern Physics Letters A 20, no. 20 (June 28, 2005): 1525–32. http://dx.doi.org/10.1142/s0217732305017512.

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We reveal that Weyl ordering of operators is invariant under general n-mode similar transformations. The technique of integration within a Weyl ordered product of operators is employed to prove our statement. Application of this property in obtaining generalized squeezed state via similar transformation is discussed.

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35

Polihronov, J. "Incompressible flows: Relative scale invariance and isobaric polynomial fields." AIP Advances 12, no. 8 (August 1, 2022): 085022. http://dx.doi.org/10.1063/5.0101855.

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This article examines the Bouton–Lie group invariants of the Navier–Stokes equation (NSE) for incompressible fluids. The theory is applied to the general scaling transformation admitted by the NSE: it adds new partial differential equations to the Navier–Stokes system of equations and is used to derive all self-similar solutions. This method can be applied to any differential equation exhibiting scaling invariance. The solutions are found to be based on isobaric polynomials, which can be smooth and nonzero at the initial moment. The non-self-similar velocity and pressure fields in the case of constant viscosity at all scales are studied and also found to be polynomials, nonzero, and smooth at the initial moment; they vanish far away from the origin and are not increasing in time. For a subset of the solutions, the cavitation number is shown to be a conserved quantity; the invariant analysis is extended to higher-dimensioned manifolds for the purpose of finding additional conserved quantities.

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HAMADA, KEN-JI. "CONFORMAL FIELD THEORY ON R × S3 FROM QUANTIZED GRAVITY." International Journal of Modern Physics A 24, no. 16n17 (July 10, 2009): 3073–110. http://dx.doi.org/10.1142/s0217751x0904422x.

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Conformal algebra on R × S3 derived from quantized gravitational fields is examined. The model we study is a renormalizable quantum theory of gravity in four dimensions described by a combined system of the Weyl action for the traceless tensor mode and the induced Wess–Zumino action managing nonperturbative dynamics of the conformal factor in the metric field. It is shown that the residual diffeomorphism invariance in the radiation+ gauge is equal to the conformal symmetry, and the conformal transformation preserving the gauge-fixing condition that forms a closed algebra quantum mechanically is given by a combination of naive conformal transformation and a certain field-dependent gauge transformation. The unitarity issue of gravity is discussed in the context of conformal field theory. We construct physical states by solving the conformal invariance condition and calculate their scaling dimensions. It is shown that the conformal symmetry mixes the positive-metric and the negative-metric modes and thus the negative-metric mode does not appear independently as a gauge invariant state at all.

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Abreu, Everton M. C., Rafael L. Fernandes, Albert C. R. Mendes, Jorge Ananias Neto, and Mario Jr Neves. "Duality and gauge invariance of non-commutative spacetime Podolsky electromagnetic theory." Modern Physics Letters A 32, no. 03 (January 11, 2017): 1750019. http://dx.doi.org/10.1142/s0217732317500195.

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The interest in higher derivative field theories has its origin mainly in their influence concerning the renormalization properties of physical models and to remove ultraviolet divergences. In this paper, we have introduced the non-commutative (NC) version of the Podolsky theory and we investigated the effect of the non-commutativity over its original gauge invariance property. We have demonstrated precisely that the non-commutativity spoiled the primary gauge invariance of the original action under this primary gauge transformation. After that we have used the Noether dualization technique to obtain a dual and gauge invariant action. We have demonstrated that through the introduction of a Stueckelberg field in this NC model, we can also recover the primary gauge invariance. In this way, we have accomplished a comparison between both methods.

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BONINI, MARISA. "WILSON RENORMALIZATION GROUP FOR GAUGE THEORIES." International Journal of Modern Physics A 16, no. 11 (April 30, 2001): 1847–59. http://dx.doi.org/10.1142/s0217751x01004517.

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The Wilson renormalization group formulation of gauge theories is reviewed. In particular, the fine tuning procedure needed to recover the gauge invariance broken by the infrared cutoff is discussed. When the cutoff is larger than any physical scale, this procedure determines the finite non-invariant couplings of the ultraviolet action. These couplings are used to build up a local field transformation which allows to write a BRS invariant ultraviolet action.

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39

Carruthers, Isaac M., Diego A. Laplagne, Andrew Jaegle, John J. Briguglio, Laetitia Mwilambwe-Tshilobo, Ryan G. Natan, and Maria N. Geffen. "Emergence of invariant representation of vocalizations in the auditory cortex." Journal of Neurophysiology 114, no. 5 (November 2015): 2726–40. http://dx.doi.org/10.1152/jn.00095.2015.

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An essential task of the auditory system is to discriminate between different communication signals, such as vocalizations. In everyday acoustic environments, the auditory system needs to be capable of performing the discrimination under different acoustic distortions of vocalizations. To achieve this, the auditory system is thought to build a representation of vocalizations that is invariant to their basic acoustic transformations. The mechanism by which neuronal populations create such an invariant representation within the auditory cortex is only beginning to be understood. We recorded the responses of populations of neurons in the primary and nonprimary auditory cortex of rats to original and acoustically distorted vocalizations. We found that populations of neurons in the nonprimary auditory cortex exhibited greater invariance in encoding vocalizations over acoustic transformations than neuronal populations in the primary auditory cortex. These findings are consistent with the hypothesis that invariant representations are created gradually through hierarchical transformation within the auditory pathway.

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40

Qiu, Dong, and Weiquan Zhang. "Convexity Invariance of Fuzzy Sets under the Extension Principles." Journal of Function Spaces and Applications 2012 (2012): 1–13. http://dx.doi.org/10.1155/2012/849104.

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We discuss the convexity invariance of fuzzy sets under the extension principles. Particularly, we give a necessary and sufficient condition for a mapping to be an inverse *-convex transformation, and also obtain some sufficient conditions for a mapping to be an *-convex transformation. Two applications are given to illustrate the obtained results. Finally, we give some applications of the main results to the hyperstructure convexity invariance of type 2 fuzzy sets under hyperalgebra operations, and to the convexity invariance of fuzzy numbers under basic arithmetic operations.

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41

Razina, O. V., P. Yu Tsyba, and N. T. Suikimbayeva. "Application of the form invariance transformations of the scalar cosmological model in inflation theory." Journal of Physics: Conference Series 2090, no. 1 (November 1, 2021): 012054. http://dx.doi.org/10.1088/1742-6596/2090/1/012054.

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Abstract In this work, it is shown that the equations of motion of the scalar field for spatially flat, homogeneous, and isotropic space-time Friedmann-Robertson-Walker have a form-invariance symmetry, which is arising from the form invariance transformation. Form invariance transformation is defined by linear function ρ = n 2 ρ in general case. It is shown the method of getting potential and the scalar field for the power law scale factor. The initial model is always stable at exponent of the scale factor α > 1, but stability of the transformation model depends on index n. Slow roll parameters and spectral induces is obtained and at large α they agree with Planck observation data.

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42

SUGI, T., DEJEY, and R. S. RAJESH. "GEOMETRIC ATTACK RESISTANT ROBUST IMAGE WATERMARKING SCHEME." International Journal of Information Acquisition 09, no. 01 (March 2013): 1350008. http://dx.doi.org/10.1142/s0219878913500083.

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A new watermarking approach based on affine Legendre moment invariants (ALMIs) and local characteristic regions (LCRs) which allows watermark detection and extraction under affine transformation attacks is presented in this paper. It is a non-blind watermarking scheme. Original image color image is converted into HSV color space and divided into four parts. LCR is constructed and a set of affine invariants are derived on LCRs based on Legendre moments for each part. These invariants can be used for estimating the affine transform coefficients on the LCRs. ALMIs are used for watermark embedding, detection and extraction as they provide synchronization and invariant feature which is necessary for a robust watermarking scheme. The proposed scheme shows resistance to geometric distortion, cropping, filtering, compression, and additive noise than the existing ALMI based scheme [Alghoniemy, M. and Tewfik, A. H. [2004] "Geometric invariance in image watermarking," IEEE Trans. Image Process13(2), 145–153] and affine geometric moment invariant (AGMI) based scheme [Seo, J. S. and Yoo, C. D. [2006] "Image watermarking based on invariant regions of scale-space representation," IEEE Trans. Signal Process. 54(4), 1537–1549].

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Rawat, Seema. "CPT Invariance of Quaternion Dirac equation." International Journal for Research in Applied Science and Engineering Technology 10, no. 1 (January 31, 2022): 961–66. http://dx.doi.org/10.22214/ijraset.2022.39956.

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Abstract: In this paper the invariance of Quaternion Dirac equation under Lorentz Transformation, Charge conjugation, Parity transformation and Time reversal operation has been discussed successfully. The invariance under the combined operation of Charge conjugation, Parity and Time reversal (CPT) has also been discussed and expression for C, P, T and combined CPT operators have been obtained in terms of quaternions. Invariance condition for electric and magnetic field has also been obtained. It has been concluded that the Quaternion Dirac equation dominates over ordinary Dirac equation because of the advantage of algebra of quaternions.

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44

Rensink, R. A. "The Invariance of Visual Search to Geometric Transformation." Journal of Vision 4, no. 8 (August 1, 2004): 178. http://dx.doi.org/10.1167/4.8.178.

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45

Kiiranen, K., and V. Rosenhaus. "Gauge invariance as the Lie-Backlund transformation group." Journal of Physics A: Mathematical and General 21, no. 13 (July 7, 1988): L681—L684. http://dx.doi.org/10.1088/0305-4470/21/13/002.

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Elliffe, Martin C. M., Edmund T. Rolls, Néstor Parga, and Alfonso Renart. "A recurrent model of transformation invariance by association." Neural Networks 13, no. 2 (March 2000): 225–37. http://dx.doi.org/10.1016/s0893-6080(99)00096-9.

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47

Shen, Jian Qi. "Generalized Edwards Transformation and Principle of Permutation Invariance." International Journal of Theoretical Physics 47, no. 3 (October 30, 2007): 751–64. http://dx.doi.org/10.1007/s10773-007-9499-7.

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48

Cui, Jing, Nilanjan Ray, Scott T. Acton, and Zongli Lin. "An affine transformation invariance approach to cell tracking." Computerized Medical Imaging and Graphics 32, no. 7 (October 2008): 554–65. http://dx.doi.org/10.1016/j.compmedimag.2008.06.004.

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49

Bhutani, O. P., and K. Vijayakumar. "On certain new and exact solutions of the Emden-Fowler equation and Emden equation via invariant variational principles and group invariance." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 32, no. 4 (April 1991): 457–68. http://dx.doi.org/10.1017/s0334270000008535.

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AbstractAfter formulating the alternate potential principle for the nonlinear differential equation corresponding to the generalised Emden-Fowler equation, the invariance identities of Rund [14] involving the Lagrangian and the generators of the infinitesimal Lie group are used for writing down the first integrals of the said equation via the Noether theorem. Further, for physical realisable forms of the parameters involved and through repeated application of invariance under the transformation obtained, a number of exact solutions are arrived at both for the Emden-Fowler equation and classical Emden equations. A comparative study with Bluman-Cole and scale-invariant techniques reveals quite a number of remarkable features of the techniques used here.

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50

DASTIDAR, T. K. RAI, and KRISHNA RAI DASTIDAR. "LOCAL GAUGE INVARIANCE OF RELATIVISTIC QUANTUM MECHANICS AND CLASSICAL RELATIVISTIC FIELDS." Modern Physics Letters A 10, no. 25 (August 20, 1995): 1843–46. http://dx.doi.org/10.1142/s0217732395001988.

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We extend our earlier work1 to demonstrate that all free matter fields (Bose as well as Fermi, massive as well as massless), that transform like Φ→TΦ under a local Abelian gauge transformation T= exp (–iβ) with β an arbitrary function of space and time, are governed by field equations that are invariant under such local gauge transformations.

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