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Journal articles on the topic 'Translation invariance'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Mossop, Brian. "‘Intersemiotic translating’." Translation and Interpreting Studies 14, no. 1 (April 5, 2019): 75–94. http://dx.doi.org/10.1075/tis.00031.mos.

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Abstract Should transpositions between language and other sign systems be considered a kind of translation? The answer could be yes if the comparison is made to interlingual translating that features a high degree of variance. Here, however, the question will be whether there are any kinds of intersemiotic transposition that feature a high degree of invariance. Four criteria are suggested for defining invariance-oriented translation, and a variety of possible instances of invariant intersemiotic translation are considered, with special mention of transpositions to and from music.

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2

Cedzich, C., T. Geib, C. Stahl, L. Velázquez, A. H. Werner, and R. F. Werner. "Complete homotopy invariants for translation invariant symmetric quantum walks on a chain." Quantum 2 (September 24, 2018): 95. http://dx.doi.org/10.22331/q-2018-09-24-95.

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We provide a classification of translation invariant one-dimensional quantum walks with respect to continuous deformations preserving unitarity, locality, translation invariance, a gap condition, and some symmetry of the tenfold way. The classification largely matches the one recently obtained (arXiv:1611.04439) for a similar setting leaving out translation invariance. However, the translation invariant case has some finer distinctions, because some walks may be connected only by breaking translation invariance along the way, retaining only invariance by an even number of sites. Similarly, if walks are considered equivalent when they differ only by adding a trivial walk, i.e., one that allows no jumps between cells, then the classification collapses also to the general one. The indices of the general classification can be computed in practice only for walks closely related to some translation invariant ones. We prove a completed collection of simple formulas in terms of winding numbers of band structures covering all symmetry types. Furthermore, we determine the strength of the locality conditions, and show that the continuity of the band structure, which is a minimal requirement for topological classifications in terms of winding numbers to make sense, implies the compactness of the commutator of the walk with a half-space projection, a condition which was also the basis of the general theory. In order to apply the theory to the joining of large but finite bulk pieces, one needs to determine the asymptotic behaviour of a stationary Schrödinger equation. We show exponential behaviour, and give a practical method for computing the decay constants.

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3

Cadieu, Charles, Minjoon Kouh, Anitha Pasupathy, Charles E. Connor, Maximilian Riesenhuber, and Tomaso Poggio. "A Model of V4 Shape Selectivity and Invariance." Journal of Neurophysiology 98, no. 3 (September 2007): 1733–50. http://dx.doi.org/10.1152/jn.01265.2006.

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Object recognition in primates is mediated by the ventral visual pathway and is classically described as a feedforward hierarchy of increasingly sophisticated representations. Neurons in macaque monkey area V4, an intermediate stage along the ventral pathway, have been shown to exhibit selectivity to complex boundary conformation and invariance to spatial translation. How could such a representation be derived from the signals in lower visual areas such as V1? We show that a quantitative model of hierarchical processing, which is part of a larger model of object recognition in the ventral pathway, provides a plausible mechanism for the translation-invariant shape representation observed in area V4. Simulated model neurons successfully reproduce V4 selectivity and invariance through a nonlinear, translation-invariant combination of locally selective subunits, suggesting that a similar transformation may occur or culminate in area V4. Specifically, this mechanism models the selectivity of individual V4 neurons to boundary conformation stimuli, exhibits the same degree of translation invariance observed in V4, and produces observed V4 population responses to bars and non-Cartesian gratings. This work provides a quantitative model of the widely described shape selectivity and invariance properties of area V4 and points toward a possible canonical mechanism operating throughout the ventral pathway.

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4

Manuilov, V., and K. Thomsen. "Extensions of $C^*$-algebras and translation invariant asymptotic homomorphisms." MATHEMATICA SCANDINAVICA 100, no. 1 (March 1, 2007): 131. http://dx.doi.org/10.7146/math.scand.a-15018.

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Let $A$, $B$ be $C^*$-algebras; $A$ separable, $B$ $\sigma$-unital and stable. We introduce a notion of translation invariance for asymptotic homomorphisms from $SA=C_0(\mathsf{R})\otimes A$ to $B$ and show that the Connes-Higson construction applied to any extension of $A$ by $B$ is homotopic to a translation invariant asymptotic homomorphism. In the other direction we give a construction which produces extensions of $A$ by $B$ out of such a translation invariant asymptotic homomorphism. This leads to our main result; that the homotopy classes of extensions coincide with the homotopy classes of translation invariant asymptotic homomorphisms.

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5

Iordan, M. C., C. Baldassano, D. B. Walther, D. M. Beck, and L. Fei-Fei. "Translation Invariance of Natural Scene Categories." Journal of Vision 11, no. 11 (September 23, 2011): 816. http://dx.doi.org/10.1167/11.11.816.

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6

Mignemi, S. "Doubly special relativity and translation invariance." Physics Letters B 672, no. 2 (February 2009): 186–89. http://dx.doi.org/10.1016/j.physletb.2009.01.023.

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7

Iqbal Ali, Agha, and Lawrence M. Seiford. "Translation invariance in data envelopment analysis." Operations Research Letters 9, no. 6 (November 1990): 403–5. http://dx.doi.org/10.1016/0167-6377(90)90061-9.

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8

Paris, J. B., and A. Vencovská. "Translation Invariance and Miller’s Weather Example." Journal of Logic, Language and Information 28, no. 4 (May 13, 2019): 489–514. http://dx.doi.org/10.1007/s10849-019-09291-6.

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9

Cheoi, Kyung Joo, Hyeonyeong Choi, and Jaepil Ko. "Empirical Remarks on the Translational Equivariance of Convolutional Layers." Applied Sciences 10, no. 9 (May 1, 2020): 3161. http://dx.doi.org/10.3390/app10093161.

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In general, convolutional neural networks (CNNs) maintain some level of translational invariance. However, the convolutional layer itself is translational-equivariant. The pooling layers provide some level of invariance. In object recognition, invariance is more important than equivariance. In this paper, we investigate how vulnerable CNNs without pooling or augmentation are to translation in object recognition. For CNNs that are specialized in learning local textures but vulnerable to learning global geometric information, we propose a method to explicitly transform an image into a global feature image and then provide it as an input to neural networks. In our experiments on a modified MNIST dataset, we demonstrate that the recognition accuracy of a conventional baseline network significantly decreases from 98% to less than 60% even in the case of 2-pixel translation. We also demonstrate that the proposed method is far superior to the baseline network in terms of performance improvement.

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10

VYAS, VIBHA S., and PRITI P. REGE. "GEOMETRIC TRANSFORM INVARIANT TEXTURE ANALYSIS WITH MODIFIED CHEBYSHEV MOMENTS BASED ALGORITHM." International Journal of Image and Graphics 09, no. 04 (October 2009): 559–74. http://dx.doi.org/10.1142/s0219467809003587.

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Texture based Geometric invariance, which comprises of rotation scale and translation (RST) invariant is finding application in various areas including industrial inspection, estimation of object range and orientation, shape analysis, satellite imaging, and medical diagnosis. Moments based techniques, apart from being computationally simple as compared to other RST invariant texture operators, are also robust in presence of noise. Zernike moments (ZM) based techniques are one of the well-established methods used for texture identification. As ZM are continuous moments, when discretization is done for implementation, errors are introduced. Error, calculated as difference between theoretically computed values and simulated values is proved to be prominent for fine textures. Therefore, a novel approach to detect RST invariant textures present in image is presented in this paper. This approach calculates discrete Chebyshev moments (CM) of log-polar transformed images to achieve rotation and scale invariance. The image is made translation invariant by shifting it to its centroid. The data is collected as samples from Brodatz and Vistex data sets. Zernike moments and its modifications, along with proposed scheme are applied to the same and Performance evaluation apart from RST invariance is noise sensitivity and redundancy. The performance is also compared with circular Mellin Feature extractors.

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11

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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12

Lev, Vsevolod F. "Translation invariance in groups of prime order." Journal of Number Theory 131, no. 10 (October 2011): 1827–32. http://dx.doi.org/10.1016/j.jnt.2011.03.002.

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13

Walter, Gilbert G. "Translation and Dilation Invariance in Orthogonal Wavelets." Applied and Computational Harmonic Analysis 1, no. 4 (September 1994): 344–49. http://dx.doi.org/10.1006/acha.1994.1020.

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14

Candeal, Juan C., Esteban Induráin, and Esteban Oloriz. "Weak Extensive Measurement without Translation-Invariance Axioms." Journal of Mathematical Psychology 42, no. 1 (March 1998): 48–62. http://dx.doi.org/10.1006/jmps.1997.1190.

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15

Qiao Wang and Lenan Wu. "Translation invariance and sampling theorem of wavelet." IEEE Transactions on Signal Processing 48, no. 5 (May 2000): 1471–74. http://dx.doi.org/10.1109/78.839994.

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16

Field, D. J., D. C. Ong, and A. Hayes. "Translation invariance with a contour integration task." Journal of Vision 12, no. 9 (August 10, 2012): 879. http://dx.doi.org/10.1167/12.9.879.

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17

Weber, Eric. "On the translation invariance of wavelet subspaces." Journal of Fourier Analysis and Applications 6, no. 5 (September 2000): 551–58. http://dx.doi.org/10.1007/bf02511546.

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18

TODA, HIROSHI, ZHONG ZHANG, and TAKASHI IMAMURA. "THE DESIGN OF COMPLEX WAVELET PACKET TRANSFORMS BASED ON PERFECT TRANSLATION INVARIANCE THEOREMS." International Journal of Wavelets, Multiresolution and Information Processing 08, no. 04 (July 2010): 537–58. http://dx.doi.org/10.1142/s0219691310003638.

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The useful theorems for achieving perfect translation invariance have already been proved, and based on these theorems, dual-tree complex discrete wavelet transforms with perfect translation invariance have been proposed. However, due to the complication of frequency divisions with wavelet packets, it is difficult to design complex wavelet packet transforms with perfect translation invariance. In this paper, based on the aforementioned theorems, novel complex wavelet packet transforms are designed to achieve perfect translation invariance. These complex wavelet packet transforms are based on the Meyer wavelet, which has the important characteristic of possessing a wide range of shapes. In this paper, two types of complex wavelet packet transforms are designed with the optimized Meyer wavelet. One of them is based on a single Meyer wavelet and the other is based on a number of different shapes of the Meyer wavelets to create good localization of wavelet packets.

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TODA, HIROSHI, ZHONG ZHANG, and TAKASHI IMAMURA. "PERFECT-TRANSLATION-INVARIANT CUSTOMIZABLE COMPLEX DISCRETE WAVELET TRANSFORM." International Journal of Wavelets, Multiresolution and Information Processing 11, no. 04 (July 2013): 1360003. http://dx.doi.org/10.1142/s0219691313600035.

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The theorems, giving the condition of perfect translation invariance for discrete wavelet transforms, have already been proven. Based on these theorems, the dual-tree complex discrete wavelet transform, the 2-dimensional discrete wavelet transform, the complex wavelet packet transform, the variable-density complex discrete wavelet transform and the real-valued discrete wavelet transform, having perfect translation invariance, were proposed. However, their customizability of wavelets in the frequency domain is limited. In this paper, also based on these theorems, a new type of complex discrete wavelet transform is proposed, which achieves perfect translation invariance with high degree of customizability of wavelets in the frequency domain.

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20

TODA, HIROSHI, and ZHONG ZHANG. "PERFECT TRANSLATION INVARIANCE WITH A WIDE RANGE OF SHAPES OF HILBERT TRANSFORM PAIRS OF WAVELET BASES." International Journal of Wavelets, Multiresolution and Information Processing 08, no. 04 (July 2010): 501–20. http://dx.doi.org/10.1142/s0219691310003602.

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It is well known that a Hilbert transform pair of wavelet bases improves the lack of translation invariance of the discrete wavelet transform. However, its shapes and improvement are limited by the difficulty in applying the Hilbert transform pair to a discrete signal. In this paper, novel Hilbert transform pairs of wavelet bases, which are based on a Meyer wavelet and have a wide range of shapes, are proposed to create perfect translation invariance, and their calculation method is designed to apply these wavelet bases to any discrete signal. Therefore, perfect translation invariance is achieved with a wide range of shapes of the Hilbert transform pairs of wavelet bases.

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21

Hui, Fan, Yong Liang Wang, and Jin Jiang Li. "Image Denoising Algorithm Based on Dyadic Contourlet Transform." Applied Mechanics and Materials 40-41 (November 2010): 591–97. http://dx.doi.org/10.4028/www.scientific.net/amm.40-41.591.

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This paper constructs a dyadic non-subsampled Contourlet transform for denoising on the image, the transformation has more directional subband, using the non-subsampled filter group for decompositing of direction, so has the translation invariance, eliminated image distortion from Contourlet transform’s lack of translation invariance. Non-subsampled filter reduces noise interference and data redundancy. Using the feature of NSCT translation invariance, multiresolution, multi-direction, and can according to the energy of NSCT in all directions and in all scale, adaptive denoising threshold. Experimental results show that compared to wavelet denoising and traditional Contourlet denoising, the method achieves a higher PSNR value, while preserving image edge details, can effectively reduce the Gibbs distortion, improve visual images.

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22

Dill, Marcus, and Manfred Fahle. "Limited translation invariance of human visual pattern recognition." Perception & Psychophysics 60, no. 1 (January 1998): 65–81. http://dx.doi.org/10.3758/bf03211918.

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23

Lakhno, Viktor D. "Translation invariance and the problem of the bipolaron." Physics-Uspekhi 41, no. 4 (April 30, 1998): 403–6. http://dx.doi.org/10.1070/pu1998v041n04abeh000385.

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24

Ronghui, Liu. "Voltage Flicker Signal Denoising Based on Translation Invariance." Physics Procedia 24 (2012): 375–81. http://dx.doi.org/10.1016/j.phpro.2012.02.055.

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25

Duane, Gregory S., Dongchuan Yu, and Ljupco Kocarev. "Identical synchronization, with translation invariance, implies parameter estimation." Physics Letters A 371, no. 5-6 (November 2007): 416–20. http://dx.doi.org/10.1016/j.physleta.2007.06.059.

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26

Lakhno, Viktor D. "Translation invariance and the problem of the bipolaron." Uspekhi Fizicheskih Nauk 168, no. 4 (1998): 465. http://dx.doi.org/10.3367/ufnr.0168.199804d.0465.

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27

Galluccio, Salvatore, Fedele Lizzi, and Patrizia Vitale. "Translation invariance, commutation relations and ultraviolet/infrared mixing." Journal of High Energy Physics 2009, no. 09 (September 9, 2009): 054. http://dx.doi.org/10.1088/1126-6708/2009/09/054.

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28

Mossop, Brian. "Invariance orientation: Identifying an object for translation studies." Translation Studies 10, no. 3 (May 4, 2016): 329–38. http://dx.doi.org/10.1080/14781700.2016.1170629.

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29

Bertolami, Orfeu, and Luís Guisado. "Noncommutative field theory and violation of translation invariance." Journal of High Energy Physics 2003, no. 12 (December 10, 2003): 013. http://dx.doi.org/10.1088/1126-6708/2003/12/013.

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30

Richthammer, Thomas. "Translation-Invariance of Two-Dimensional Gibbsian Point Processes." Communications in Mathematical Physics 274, no. 1 (June 6, 2007): 81–122. http://dx.doi.org/10.1007/s00220-007-0274-7.

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31

Ziegaus, Christian, and Elmar W. Lang. "Statistical Invariances in Artificial, Natural, and Urban Images." Zeitschrift für Naturforschung A 53, no. 12 (December 1, 1998): 1009–21. http://dx.doi.org/10.1515/zna-1998-1214.

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Abstract To answer the question about the way our visual system processes images it has to work with every day, it is necessary to investigate the statistical structure of these pictures. For this purpose we investigated several ensembles of artificial and real-world greyscale images to find different invariance properties: translation invariance by determining an average pair-correlation function, scale invariance by investigating the power spectrum and the coarse graining of the images, and a new hierarchical invariance recently proposed [D. L. Ruderman, Network 5, 517 (1994)]. The results of our work indicated that the assumption of translational invariance can be taken for granted. Our results concerning the scale invariance are qualitatively the same as those found by Ruderman and others. The deviations of the distributions of the logarithmically transformed images from a Gaussian distribution cannot be seen as clearly as stated by Ruderman. This results from the fact that for a correct determination of the deviations the non-linear transformation must be considered. Depending on the preprocessing of the images the results concerning the hierarchical invariance differed widely. It seems that this new invariance can be confirmed only for logarithmically transformed images.

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32

Wiskott, Laurenz, and Terrence J. Sejnowski. "Slow Feature Analysis: Unsupervised Learning of Invariances." Neural Computation 14, no. 4 (April 1, 2002): 715–70. http://dx.doi.org/10.1162/089976602317318938.

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Invariant features of temporally varying signals are useful for analysis and classification. Slow feature analysis (SFA) is a new method for learning invariant or slowly varying features from a vectorial input signal. It is based on a nonlinear expansion of the input signal and application of principal component analysis to this expanded signal and its time derivative. It is guaranteed to find the optimal solution within a family of functions directly and can learn to extract a large number of decor-related features, which are ordered by their degree of invariance. SFA can be applied hierarchically to process high-dimensional input signals and extract complex features. SFA is applied first to complex cell tuning properties based on simple cell output, including disparity and motion. Then more complicated input-output functions are learned by repeated application of SFA. Finally, a hierarchical network of SFA modules is presented as a simple model of the visual system. The same unstructured network can learn translation, size, rotation, contrast, or, to a lesser degree, illumination invariance for one-dimensional objects, depending on only the training stimulus. Surprisingly, only a few training objects suffice to achieve good generalization to new objects. The generated representation is suitable for object recognition. Performance degrades if the network is trained to learn multiple invariances simultaneously.

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33

Hameed, Vazeerudeen Abdul. "Orthogonal Moment Invariant Function for Image Processing." Journal of Computational and Theoretical Nanoscience 16, no. 8 (August 1, 2019): 3400–3403. http://dx.doi.org/10.1166/jctn.2019.8299.

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Orthogonal moments are of great importance in image processing due to their high discriminatory capability. Orthogonal moment invariant functions like Legendre moments and Complex Zernike moments are known for high computational complexity and/or they are complex valued. This paper presents a new orthogonal moment function that is real valued. The formulation is appraised to prove that it is computationally less complex when compared to the existing moment functions. The proposed orthogonal moment functions are appraised over their reversible nature to obtain the original data. The new moment functions are also appraised for their discriminating ability through derivations and experiments. Invariance properties such as scaling, translation and rotational invariance are studied over the new formulation to demonstrate the use of the functions over image processing applications that involve invariance to image transformations.

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Liu, Jing Dong, Pak Kwong Chung, and Yanping Duan. "Validity and Reliability of the Chinese Translation of Basic Psychological Needs in Exercise Scale." European Journal of Psychological Assessment 29, no. 1 (March 1, 2013): 51–57. http://dx.doi.org/10.1027/1015-5759/a000120.

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The current study examined some psychometric properties of the Basic Psychological Needs in Exercise Scale (BPNES; Vlachopoulos & Michailidou, 2006 ) in a group of Chinese university students in Hong Kong. A total of 460 undergraduate students were invited to take part in this study. We examined the factorial validity, discriminant validity, nomological validity, internal reliability, and measurement invariance across sex of a Chinese translation of the BPNES. The findings demonstrated that the scale had a good factorial validity and satisfactory internal reliability. Measurement invariance analysis indicated that the factor loadings and factor variance as well as covariance of measurement structure were invariant across male and female participants. Nomological validity was supported by the results of SEM analysis. Overall, the current study provided initial evidence for the validity and reliability of a Chinese translation of BPNES, and suggested that this scale could be used to measure satisfaction of psychological needs in the exercise field of Hong Kong undergraduate students.

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35

Cuong, Hoang, Khalil Sima’an, and Ivan Titov. "Adapting to All Domains at Once: Rewarding Domain Invariance in SMT." Transactions of the Association for Computational Linguistics 4 (December 2016): 99–112. http://dx.doi.org/10.1162/tacl_a_00086.

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Existing work on domain adaptation for statistical machine translation has consistently assumed access to a small sample from the test distribution (target domain) at training time. In practice, however, the target domain may not be known at training time or it may change to match user needs. In such situations, it is natural to push the system to make safer choices, giving higher preference to domain-invariant translations, which work well across domains, over risky domain-specific alternatives. We encode this intuition by (1) inducing latent subdomains from the training data only; (2) introducing features which measure how specialized phrases are to individual induced sub-domains; (3) estimating feature weights on out-of-domain data (rather than on the target domain). We conduct experiments on three language pairs and a number of different domains. We observe consistent improvements over a baseline which does not explicitly reward domain invariance.

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36

Yoshida, Yuji. "Weighted Quasi-Arithmetic Means and the Domain Translations." Journal of Advanced Computational Intelligence and Intelligent Informatics 16, no. 1 (January 20, 2012): 148–53. http://dx.doi.org/10.20965/jaciii.2012.p0148.

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The monotonicity of the weighted quasi-arithmetic means is discussed from the viewpoint of utility functions and weighting functions. Observing the indices given by utility functions and weighting functions, we find that these indices give similarmonotonicity for the weighted quasi-arithmetic means, and this paper investigates the reason using the direct domain translation adapted to the weighted quasi-arithmetic means. Further, general domain translations are introduced and they are discussed in relation to these indices. Some examples are given for the domain translations and as a special case the translation invariance is presented, and a lot of examples with various utility functions and weighting functions are shown, and their indices and the translated forms are derived.

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Adams, R., J. Young, and S. Gedney. "Compressing H2 Matrices for Translationally Invariant Kernels." Applied Computational Electromagnetics Society 35, no. 11 (February 5, 2021): 1392–93. http://dx.doi.org/10.47037/2020.aces.j.351165.

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H2 matrices provide compressed representations of the matrices obtained when discretizing surface and volume integral equations. The memory costs associated with storing H2 matrices for static and low-frequency applications are O(N). However, when the H2 representation is constructed using sparse samples of the underlying matrix, the translation matrices in the H2 representation do not preserve any translational invariance present in the underlying kernel. In some cases, this can result in an H2 representation with relatively large memory requirements. This paper outlines a method to compress an existing H2 matrix by constructing a translationally invariant H2 matrix from it. Numerical examples demonstrate that the resulting representation can provide significant memory savings.

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38

Mabrouk, Mohamed Ben Ridha. "Translation invariance when utility streams are infinite and unbounded." International Journal of Economic Theory 7, no. 4 (November 14, 2011): 317–29. http://dx.doi.org/10.1111/j.1742-7363.2011.00168.x.

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39

Aparicio, Juan, Jesus T. Pastor, and Fernando Vidal. "The directional distance function and the translation invariance property." Omega 58 (January 2016): 1–3. http://dx.doi.org/10.1016/j.omega.2015.04.012.

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40

Torres, Rafael, Pierre Pellat-Finet, and Yezid Torres. "Fractional convolution, fractional correlation and their translation invariance properties." Signal Processing 90, no. 6 (June 2010): 1976–84. http://dx.doi.org/10.1016/j.sigpro.2009.12.016.

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41

Bastys, A. "Translation Invariance of Orthogonal Multiresolution Analyses of L2(R)." Applied and Computational Harmonic Analysis 9, no. 2 (September 2000): 128–45. http://dx.doi.org/10.1006/acha.2000.0311.

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42

Lazzeretti, Paolo. "Invariance of molecular response properties under a coordinate translation." International Journal of Quantum Chemistry 114, no. 20 (March 14, 2014): 1364–92. http://dx.doi.org/10.1002/qua.24662.

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43

Du, Wenliao, Shuangyuan Wang, Xiaoyun Gong, Hongchao Wang, Xingyan Yao, and Michael Pecht. "Translation Invariance-Based Deep Learning for Rotating Machinery Diagnosis." Shock and Vibration 2020 (August 11, 2020): 1–16. http://dx.doi.org/10.1155/2020/1635621.

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Discriminative feature extraction is a challenge for data-driven fault diagnosis. Although deep learning algorithms can automatically learn a good set of features without manual intervention, the lack of domain knowledge greatly limits the performance improvement, especially for nonstationary and nonlinear signals. This paper develops a multiscale information fusion-based stacked sparse autoencoder fault diagnosis method. The autoencoder takes advantage of the multiscale normalized frequency spectrum information obtained by dual-tree complex wavelet transform as input. Accordingly, the multiscale normalized features guarantee the translational invariance for signal characteristics, and the stacked sparse autoencoder benefits the unsupervised feature learning and ensures accurate and stable diagnosis performance. The developed method is performed on motor bearing vibration signals and worm gearbox vibration signals, respectively. The results confirm that the developed method can accommodate changing working conditions, be free of manual feature extraction, and perform better than the existing intelligent diagnosis methods.

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44

Yang, G. G., and P. Healey. "Optical quadratic associative memory with translation and scale invariance." Optics Communications 89, no. 2-4 (May 1992): 183–88. http://dx.doi.org/10.1016/0030-4018(92)90156-l.

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45

GHOSH, SUBIR. "SPACETIME SYMMETRIES IN NONCOMMUTATIVE GAUGE THEORY: A HAMILTONIAN ANALYSIS." Modern Physics Letters A 19, no. 33 (October 30, 2004): 2505–17. http://dx.doi.org/10.1142/s0217732304014963.

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We study spacetime symmetries in noncommutative (NC) gauge theory in the (constrained) Hamiltonian framework. The specific example of NC CP(1) model, posited in Ref. 9, has been considered. Subtle features of Lorentz invariance violation in NC field theory were pointed out in Ref. 13. Out of the two — observer and particle — distinct types of Lorentz transformations, symmetry under the former, (due to the translation invariance), is reflected in the conservation of energy and momentum in NC theory. The constant tensor θμν (the noncommutativity parameter) destroys invariance under the latter. In this paper we have constructed the Hamiltonian and momentum operators which are the generators of time and space translations respectively. This is related to the observer Lorentz invariance. We have also shown that the Schwinger condition and subsequently the Poincaré algebra is not obeyed and that one cannot derive a Lorentz covariant dynamical field equation. These features signal a loss of the Particle Lorentz symmetry. The basic observations in the present work will be relevant in the Hamiltonian study of a generic noncommutative field theory.

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Zhang, Rong Guo, Lei Dong, Qi Rui Ge, and Xiao Jun Liu. "Level Set Prior Shape Model in Face Recognition." Applied Mechanics and Materials 687-691 (November 2014): 3901–4. http://dx.doi.org/10.4028/www.scientific.net/amm.687-691.3901.

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Combining level set image segmentation with the prior shape information, we proposed an improved prior shape model in face recognition. Firstly, we introduced a local tensile invariant to X and Y direction and a shear invariant based on the shape statistics. Then, shape energy term with rotation, scale, shear and translation invariance was reconstructed in level set C-V model. The new model considers global and local image change and makes face contour evolving stably. Experimental results demonstrate that our model can segment obscured face images effectively.

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Gluzman, Simon. "Nonlinear Approximations to Critical and Relaxation Processes." Axioms 9, no. 4 (October 28, 2020): 126. http://dx.doi.org/10.3390/axioms9040126.

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We develop nonlinear approximations to critical and relaxation phenomena, complemented by the optimization procedures. In the first part, we discuss general methods for calculation of critical indices and amplitudes from the perturbative expansions. Several important examples of the Stokes flow through 2D channels are brought up. Power series for the permeability derived for small values of amplitude are employed for calculation of various critical exponents in the regime of large amplitudes. Special nonlinear approximations valid for arbitrary values of the wave amplitude are derived from the expansions. In the second part, the technique developed for critical phenomena is applied to relaxation phenomena. The concept of time-translation invariance is discussed, and its spontaneous violation and restoration considered. Emerging probabilistic patterns correspond to a local breakdown of time-translation invariance. Their evolution leads to the time-translation invariance complete (or partial) restoration. We estimate the typical time extent, amplitude and direction for such a restorative process. The new technique is based on explicit introduction of origin in time as an optimization parameter. After some transformations, we arrive at the exponential and generalized exponential-type solutions (Gompertz approximants), with explicit finite time scale, which is only implicit in the initial parameterization with polynomial approximation. The concept of crash as a fast relaxation phenomenon, consisting of time-translation invariance breaking and restoration, is advanced. Several COVID-related crashes in the time series for Shanghai Composite and Dow Jones Industrial are discussed as an illustration.

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Eickenberg, Michael, Ryan J. Rowekamp, Minjoon Kouh, and Tatyana O. Sharpee. "Characterizing Responses of Translation-Invariant Neurons to Natural Stimuli: Maximally Informative Invariant Dimensions." Neural Computation 24, no. 9 (September 2012): 2384–421. http://dx.doi.org/10.1162/neco_a_00330.

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The human visual system is capable of recognizing complex objects even when their appearances change drastically under various viewing conditions. Especially in the higher cortical areas, the sensory neurons reflect such functional capacity in their selectivity for complex visual features and invariance to certain object transformations, such as image translation. Due to the strong nonlinearities necessary to achieve both the selectivity and invariance, characterizing and predicting the response patterns of these neurons represents a formidable computational challenge. A related problem is that such neurons are poorly driven by randomized inputs, such as white noise, and respond strongly only to stimuli with complex high-order correlations, such as natural stimuli. Here we describe a novel two-step optimization technique that can characterize both the shape selectivity and the range and coarseness of position invariance from neural responses to natural stimuli. One step in the optimization is finding the template as the maximally informative dimension given the estimated spatial location where the response could have been triggered within each image. The estimates of the locations that triggered the response are updated in the next step. Under the assumption of a monotonic relationship between the firing rate and stimulus projections on the template at a given position, the most likely location is the one that has the largest projection on the estimate of the template. The algorithm shows quick convergence during optimization, and the estimation results are reliable even in the regime of small signal-to-noise ratios. When we apply the algorithm to responses of complex cells in the primary visual cortex (V1) to natural movies, we find that responses of the majority of cells were significantly better described by translation-invariant models based on one template compared with position-specific models with several relevant features.

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MELJANAC, S., and A. SAMSAROV. "SCALAR FIELD THEORY ON κ-MINKOWSKI SPACE–TIME AND TRANSLATION AND LORENTZ INVARIANCE." International Journal of Modern Physics A 26, no. 07n08 (March 30, 2011): 1439–68. http://dx.doi.org/10.1142/s0217751x11051536.

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We investigate the properties of κ-Minkowski space–time by using representations of the corresponding deformed algebra in terms of undeformed Heisenberg–Weyl algebra. The deformed algebra consists of κ-Poincaré algebra extended with the generators of the deformed Weyl algebra. The part of deformed algebra, generated by rotation, boost and momentum generators, is described by the Hopf algebra structure. The approach used in our considerations is completely Lorentz covariant. We further use an advantage of this approach to consistently construct a star product, which has a property that under integration sign, it can be replaced by a standard pointwise multiplication, a property that was since known to hold for Moyal but not for κ-Minkowski space–time. This star product also has generalized trace and cyclic properties, and the construction alone is accomplished by considering a classical Dirac operator representation of deformed algebra and requiring it to be Hermitian. We find that the obtained star product is not translationally invariant, leading to a conclusion that the classical Dirac operator representation is the one where translation invariance cannot simultaneously be implemented along with hermiticity. However, due to the integral property satisfied by the star product, noncommutative free scalar field theory does not have a problem with translation symmetry breaking and can be shown to reduce to an ordinary free scalar field theory without nonlocal features and tachyonic modes and basically of the very same form. The issue of Lorentz invariance of the theory is also discussed.

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Kokkinos, Constantinos M., and Angelos Markos. "The Big Five Questionnaire for Children (BFQ-C)." European Journal of Psychological Assessment 33, no. 2 (March 2017): 129–33. http://dx.doi.org/10.1027/1015-5759/a000273.

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Abstract. The purpose of the present study was to examine measurement invariance of the Greek translation of the Big Five Questionnaire for Children (BFQ-C) across different sex and age groups using multigroup confirmatory factor analysis with a sample of 1,103 Greek preadolescents. Results supported measurement invariance across sex. Evidence of configural and metric, but not scalar or strict invariance, was found across age. Implications for personality assessment with the Greek BFQ-C scale are discussed.

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