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Автор: Grafiati

Опубліковано: 11 вересня 2023

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1

TAN, GUANGHUA, JUN QI, CHUNMING GAO, JIN CHEN, and LIYUAN ZHUO. "SALIENCY-BASED UNSUPERVISED IMAGE MATTING." International Journal of Pattern Recognition and Artificial Intelligence 28, no. 04 (June 2014): 1454001. http://dx.doi.org/10.1142/s0218001414540019.

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Анотація:

Spectral matting is the state-of-the-art matting method and can well solve the highly under-conditioned matte problem without manual intervention. However, it suffers from huge computation cost and inaccurate alpha matte. This paper presents a modified spectral matting method which combines saliency detection algorithm to get a higher accuracy of alpha matte with less computational cost. First, the saliency detection algorithm is used to detect general locations of foreground objects. For saliency detection method, original two-stage scheme is replaced by feedback scheme to get a more suitable saliency map for unsupervised image matting. Next, matting components are obtained through a linear transformation of the smallest eigenvectors of the matting Laplacian matrix. Then, the improved saliency map is used for grouping matting components. Finally, the alpha matte is obtained based on matte cost function. Experiments show that the proposed method outperforms the state-of-the-art methods based on spectral matting both in speed and alpha matte accuracy.

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2

Ju, Tingting, Meifeng Dai, Changxi Dai, Yu Sun, Xiangmei Song, and Weiyi Su. "Applications of Laplacian spectrum for the vertex–vertex graph." Modern Physics Letters B 33, no. 17 (June 18, 2019): 1950184. http://dx.doi.org/10.1142/s0217984919501847.

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Анотація:

Complex networks have attracted a great deal of attention from scientific communities, and have been proven as a useful tool to characterize the topologies and dynamics of real and human-made complex systems. Laplacian spectrum of the considered networks plays an essential role in their network properties, which have a wide range of applications in chemistry and others. Firstly, we define one vertex–vertex graph. Then, we deduce the recursive relationship of its eigenvalues at two successive generations of the normalized Laplacian matrix, and we obtain the Laplacian spectrum for vertex–vertex graph. Finally, we show the applications of the Laplacian spectrum, i.e. first-order network coherence, second-order network coherence, Kirchhoff index, spanning tree, and Laplacian-energy-like.

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3

DING, QINGYAN, WEIGANG SUN, and FANGYUE CHEN. "APPLICATIONS OF LAPLACIAN SPECTRA ON A 3-PRISM GRAPH." Modern Physics Letters B 28, no. 02 (January 8, 2014): 1450009. http://dx.doi.org/10.1142/s0217984914500092.

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In this paper, we calculate the Laplacian spectra of a 3-prism graph and apply them. This graph is both planar and polyhedral, and belongs to the generalized Petersen graph. Using the regular structures of this graph, we obtain the recurrent relationships for Laplacian matrix between this graph and its initial state — a triangle — and further derive the corresponding relationships for Laplacian eigenvalues between them. By these relationships, we obtain the analytical expressions for the product and the sum of the reciprocals of all nonzero Laplacian eigenvalues. Finally we apply these expressions to calculate the number of spanning trees and mean first-passage time (MFPT) and see that the scaling of MFPT with the network size N is N2, which is larger than those performed on some uniformly recursive trees.

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4

Dai, Meifeng, Tingting Ju, Yongbo Hou, Jianwei Chang, Yu Sun, and Weiyi Su. "Coherence analysis of a family of weighted star-composed networks." International Journal of Modern Physics B 33, no. 23 (September 20, 2019): 1950264. http://dx.doi.org/10.1142/s0217979219502643.

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Анотація:

Recently, the study of many kinds of weighted networks has received the attention of researchers in the scientific community. In this paper, first, a class of weighted star-composed networks with a weight factor is introduced. We focus on the network consistency in linear dynamical system for a class of weighted star-composed networks. The network consistency can be characterized as network coherence by using the sum of reciprocals of all nonzero Laplacian eigenvalues, which can be obtained by using the relationship of Laplacian eigenvalues at two successive generations. Remarkably, the Laplacian matrix of the class of weighted star-composed networks can be represented by the Kronecker product, then the properties of the Kronecker product can be used to obtain conveniently the corresponding characteristic roots. In the process of finding the sum of reciprocals of all nonzero Laplacian eigenvalues, the key step is to obtain the relationship of Laplacian eigenvalues at two successive generations. Finally, we obtain the main results of the first- and second-order network coherences. The obtained results show that if the weight factor is 1 then the obtained results in this paper coincide with the previous results on binary networks, otherwise the scalings of the first-order network coherence are related to the node number of attaching copy graph, the weight factor and generation number. Surprisingly, the scalings of the first-order network coherence are independent of the node number of initial graph. Consequently, it will open up new perspectives for future research.

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5

KARAMANOS, K., S. I. MISTAKIDIS, T. J. MASSART, and I. S. MISTAKIDIS. "ENTROPY PRODUCTION OF ENTIRELY DIFFUSIONAL LAPLACIAN TRANSFER AND THE POSSIBLE ROLE OF FRAGMENTATION OF THE BOUNDARIES." Fractals 23, no. 03 (July 31, 2015): 1550026. http://dx.doi.org/10.1142/s0218348x15500267.

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Анотація:

The entropy production and the variational functional of a Laplacian diffusional field around the first four fractal iterations of a linear self-similar tree (von Koch curve) is studied analytically and detailed predictions are stated. In a next stage, these predictions are confronted with results from numerical resolution of the Laplace equation by means of Finite Elements computations. After a brief review of the existing results, the range of distances near the geometric irregularity, the so-called "Near Field", a situation never studied in the past, is treated exhaustively. We notice here that in the Near Field, the usual notion of the active zone approximation introduced by Sapoval et al. [M. Filoche and B. Sapoval, Transfer across random versus deterministic fractal interfaces, Phys. Rev. Lett. 84(25) (2000) 5776;1 B. Sapoval, M. Filoche, K. Karamanos and R. Brizzi, Can one hear the shape of an electrode? I. Numerical study of the active zone in Laplacian transfer, Eur. Phys. J. B. Condens. Matter Complex Syst. 9(4) (1999) 739-753.]2 is strictly inapplicable. The basic new result is that the validity of the active-zone approximation based on irreversible thermodynamics is confirmed in this limit, and this implies a new interpretation of this notion for Laplacian diffusional fields.

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6

He, Jiaojiao, Meifeng Dai, Yue Zong, Jiahui Zou, Yu Sun, and Weiyi Su. "Coherence analysis of a class of weighted tree-like polymer networks." Modern Physics Letters B 32, no. 05 (February 20, 2018): 1850064. http://dx.doi.org/10.1142/s0217984918500641.

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Анотація:

Complex networks have elicited considerable attention from scientific communities. This paper investigates consensus dynamics in a linear dynamical system with additive stochastic disturbances, which is characterized as network coherence by the Laplacian spectrum. Firstly, we introduce a class of weighted tree-like polymer networks with the weight factor. Then, we deduce the recursive relationship of the eigenvalues of Laplacian matrix at two successive generations. Finally, we calculate the first- and second-order network coherence quantifying as the sum and square sum of reciprocals of all nonzero Laplacian eigenvalues. The obtained results show that the scalings of first-order coherence with network size obey four laws along with the range of the weight factor and the scalings of second-order coherence with network size obey five laws along with the range of the weight factor.

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7

Dai, Changxi, Meifeng Dai, Tingting Ju, Xiangmei Song, Yu Sun, and Weiyi Su. "Eigentime identity of the weighted (m,n)-flower networks." International Journal of Modern Physics B 34, no. 18 (July 1, 2020): 2050159. http://dx.doi.org/10.1142/s0217979220501593.

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The eigentime identity for random walks on the weighted networks is the expected time for a walker going from a node to another node. Eigentime identity can be studied by the sum of reciprocals of all nonzero Laplacian eigenvalues on the weighted networks. In this paper, we study the weighted [Formula: see text]-flower networks with the weight factor [Formula: see text]. We divide the set of the nonzero Laplacian eigenvalues into three subsets according to the obtained characteristic polynomial. Then we obtain the analytic expression of the eigentime identity [Formula: see text] of the weighted [Formula: see text]-flower networks by using the characteristic polynomial of Laplacian and recurrent structure of Markov spectrum. We take [Formula: see text], [Formula: see text] as example, and show that the leading term of the eigentime identity on the weighted [Formula: see text]-flower networks obey superlinearly, linearly with the network size.

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8

Abanov, Ar, M. Mineev-Weinstein, and A. Zabrodin. "Self-similarity in Laplacian Growth." Physica D: Nonlinear Phenomena 235, no. 1-2 (November 2007): 62–71. http://dx.doi.org/10.1016/j.physd.2007.04.012.

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9

Alekseev, Oleg. "Martingales of stochastic Laplacian growth." Physica D: Nonlinear Phenomena 412 (November 2020): 132629. http://dx.doi.org/10.1016/j.physd.2020.132629.

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10

Liu, Qun. "Spectral analysis for weighted iterated pentagonal graphs and its applications." Modern Physics Letters B 34, no. 28 (June 10, 2020): 2050308. http://dx.doi.org/10.1142/s021798492050308x.

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Анотація:

Deterministic weighted networks have been widely used to model real-world complex systems. In this paper, we study the weighted iterated pentagonal networks. From the construction of the network, we derive recursive relations of all eigenvalues and their multiplicities of its normalized Laplacian matrix from the two successive generations of the weighted iterated pentagonal networks. As applications of spectra of the normalized Laplacian matrix, we study the Kemeny’s constant, the multiplicative degree-Kirchhoff index, and the number of weighted spanning trees and derive their exact closed-form expressions for the weighted iterated pentagonal networks.

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11

Ma, Yue, Zhulou Cao, and Xingqin Qi. "Quasi-Laplacian centrality: A new vertex centrality measurement based on Quasi-Laplacian energy of networks." Physica A: Statistical Mechanics and its Applications 527 (August 2019): 121130. http://dx.doi.org/10.1016/j.physa.2019.121130.

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12

Liu, Jia-Bao, Jing Zhao, and Zheng-Qun Cai. "On the generalized adjacency, Laplacian and signless Laplacian spectra of the weighted edge corona networks." Physica A: Statistical Mechanics and its Applications 540 (February 2020): 123073. http://dx.doi.org/10.1016/j.physa.2019.123073.

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13

Priebe, Carey E., Youngser Park, Joshua T. Vogelstein, John M. Conroy, Vince Lyzinski, Minh Tang, Avanti Athreya, Joshua Cape, and Eric Bridgeford. "On a two-truths phenomenon in spectral graph clustering." Proceedings of the National Academy of Sciences 116, no. 13 (March 8, 2019): 5995–6000. http://dx.doi.org/10.1073/pnas.1814462116.

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Анотація:

Clustering is concerned with coherently grouping observations without any explicit concept of true groupings. Spectral graph clustering—clustering the vertices of a graph based on their spectral embedding—is commonly approached viaK-means (or, more generally, Gaussian mixture model) clustering composed with either Laplacian spectral embedding (LSE) or adjacency spectral embedding (ASE). Recent theoretical results provide deeper understanding of the problem and solutions and lead us to a “two-truths” LSE vs. ASE spectral graph clustering phenomenon convincingly illustrated here via a diffusion MRI connectome dataset: The different embedding methods yield different clustering results, with LSE capturing left hemisphere/right hemisphere affinity structure and ASE capturing gray matter/white matter core–periphery structure.

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14

Lagacé, Jean. "Eigenvalue Optimisation on Flat Tori and Lattice Points in Anisotropically Expanding Domains." Canadian Journal of Mathematics 72, no. 4 (March 7, 2019): 967–87. http://dx.doi.org/10.4153/s0008414x19000130.

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AbstractThis paper is concerned with the maximisation of the $k$-th eigenvalue of the Laplacian amongst flat tori of unit volume in dimension $d$ as $k$ goes to infinity. We show that in any dimension maximisers exist for any given $k$, but that any sequence of maximisers degenerates as $k$ goes to infinity when the dimension is at most 10. Furthermore, we obtain specific upper and lower bounds for the injectivity radius of any sequence of maximisers. We also prove that flat Klein bottles maximising the $k$-th eigenvalue of the Laplacian exhibit the same behaviour. These results contrast with those obtained recently by Gittins and Larson, stating that sequences of optimal cuboids for either Dirichlet or Neumann boundary conditions converge to the cube no matter the dimension. We obtain these results via Weyl asymptotics with explicit control of the remainder in terms of the injectivity radius. We reduce the problem at hand to counting lattice points inside anisotropically expanding domains, where we generalise methods of Yu. Kordyukov and A. Yakovlev by considering domains that expand at different rates in various directions.

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15

Alban-Chacón, Francisco E., Erick A. Lamilla-Rubio, and Manuel S. Alvarez-Alvarado. "A Novel Physical Mechanism to Model Brownian Yet Non-Gaussian Diffusion: Theory and Application." Materials 15, no. 17 (August 23, 2022): 5808. http://dx.doi.org/10.3390/ma15175808.

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In the last years, a few experiments in the fields of biological and soft matter physics in colloidal suspensions have reported “normal diffusion” with a Laplacian probability distribution in the particle’s displacements (i.e., Brownian yet non-Gaussian diffusion). To model this behavior, different stochastic and microscopic models have been proposed, with the former introducing new random elements that incorporate our lack of information about the media and the latter describing a limited number of interesting physical scenarios. This incentivizes the search of a more thorough understanding of how the media interacts with itself and with the particle being diffused in Brownian yet non-Gaussian diffusion. For this reason, a comprehensive mathematical model to explain Brownian yet non-Gaussian diffusion that includes weak molecular interactions is proposed in this paper. Based on the theory of interfaces by De Gennes and Langevin dynamics, it is shown that long-range interactions in a weakly interacting fluid at shorter time scales leads to a Laplacian probability distribution in the radial particle’s displacements. Further, it is shown that a phase separation can explain a high diffusivity and causes this Laplacian distribution to evolve towards a Gaussian via a transition probability in the interval of time as it was observed in experiments. To verify these model predictions, the experimental data of the Brownian motion of colloidal beads on phospholipid bilayer by Wang et al. are used and compared with the results of the theory. This comparison suggests that the proposed model is able to explain qualitatively and quantitatively the Brownian yet non-Gaussian diffusion.

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16

Abanov, Ar, M. Mineev-Weinstein, and A. Zabrodin. "Multi-cut solutions of Laplacian growth." Physica D: Nonlinear Phenomena 238, no. 17 (August 2009): 1787–96. http://dx.doi.org/10.1016/j.physd.2009.06.001.

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17

Mahanta, Abhigyan, Idweep Jyoti Gogoi, and A. Bharali. "A note on the generalized adjacency, Laplacian and signless Laplacian spectra of the weighted edge corona networks." Physica A: Statistical Mechanics and its Applications 581 (November 2021): 126241. http://dx.doi.org/10.1016/j.physa.2021.126241.

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18

SUZUKI, Yasuhiro, Shishir PUROHIT, Satoshi OHDACHI, Satoshi YAMAMOTO, and Kazunobu NAGASAKI. "New tomographic reconstruction technique based on Laplacian eigenfunction." Plasma Science and Technology 22, no. 10 (August 20, 2020): 102002. http://dx.doi.org/10.1088/2058-6272/aba185.

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19

Ieta, Adrian, Zdenek Kucerovsky, and William D. Greason. "Laplacian approximation of Warburg distribution." Journal of Electrostatics 63, no. 2 (February 2005): 143–54. http://dx.doi.org/10.1016/j.elstat.2004.10.001.

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20

BEJANCU, AUREL. "A NEW APPROACH FOR SPACE-TIME-MATTER THEORY." International Journal of Geometric Methods in Modern Physics 10, no. 04 (March 6, 2013): 1350004. http://dx.doi.org/10.1142/s0219887813500047.

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Анотація:

This is the first paper in a series of three papers on a new approach for space-time-matter (STM) theory. The main purpose of this approach is to replace the Levi-Civita connection on the space-time from the classical Kaluza–Klein theory by what we call the Riemannian horizontal connection on the general Kaluza–Klein space. This is done by a development of a 4D tensor calculus whose geometrical objects live in a 5D space. The 4D tensor calculus and the Riemannian horizontal connection enable us to define in a 5D space some 4D differential operators: horizontal differential, horizontal gradient, horizontal divergence and horizontal Laplacian, which have a great role in the presentation of the STM theory in a covariant form. Finally, we introduce and study the horizontal electromagnetic tensor field, the horizontal Ricci tensor and the horizontal Einstein gravitational tensor field, which replace the well-known tensor fields from the classical Kaluza–Klein theory.

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21

KALINAY, PAVOL, LADISLAV ŠAMAJ, and IGOR TRAVĚNEC. "SURVIVAL PROBABILITY (HEAT CONTENT) AND THE LOWEST EIGENVALUE OF DIRICHLET LAPLACIAN." International Journal of Modern Physics B 25, no. 15 (June 20, 2011): 1993–2007. http://dx.doi.org/10.1142/s0217979211101004.

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Анотація:

We study the survival probability of a particle diffusing in a two-dimensional domain, bounded by a smooth absorbing boundary. The short-time expansion of this quantity depends on the geometric characteristics of the boundary, whilst its long-time asymptotics is governed by the lowest eigenvalue of the Dirichlet Laplacian defined on the domain. We present a simple algorithm for calculation of the short-time expansion for an arbitrary "star-shaped" domain. The coefficients are expressed in terms of powers of boundary curvature, integrated around the circumference of the domain. Based on this expansion, we look for a Padé interpolation between the short-time and the long-time behavior of the survival probability, i.e., between geometric characteristics of the boundary and the lowest eigenvalue of the Dirichlet Laplacian.

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22

Gazzina, Stefano, Mario Grassi, Enrico Premi, Maura Cosseddu, Antonella Alberici, Silvana Archetti, Roberto Gasparotti, et al. "Education modulates brain maintenance in presymptomatic frontotemporal dementia." Journal of Neurology, Neurosurgery & Psychiatry 90, no. 10 (June 10, 2019): 1124–30. http://dx.doi.org/10.1136/jnnp-2019-320439.

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Анотація:

ObjectiveCognitively engaging lifestyles have been associated with reduced risk of conversion to dementia. Multiple mechanisms have been advocated, including increased brain volumes (ie, brain reserve) and reduced disease progression (ie, brain maintenance). In cross-sectional studies of presymptomatic frontotemporal dementia (FTD), higher education has been related to increased grey matter volume. Here, we examine the effect of education on grey matter loss over time.MethodsTwo-hundred twenty-nine subjects at-risk of carrying a pathogenic mutation leading to FTD underwent longitudinal cognitive assessment and T1-weighted MRI at baseline and at 1 year follow-up. The first principal component score of the graph-Laplacian Principal Component Analysis on 112 grey matter region-of-interest volumes was used to summarise the grey matter volume (GMV). The effects of education on cognitive performances and GMV at baseline and on the change between 1 year follow-up and baseline (slope) were tested by Structural Equation Modelling.ResultsHighly educated at-risk subjects had better cognition and higher grey matter volume at baseline; moreover, higher educational attainment was associated with slower loss of grey matter over time in mutation carriers.ConclusionsThis longitudinal study demonstrates that even in presence of ongoing pathological processes, education may facilitate both brain reserve and brain maintenance in the presymptomatic phase of genetic FTD.

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23

Sokolov, Arseny A., Peter Zeidman, Adeel Razi, Michael Erb, Philippe Ryvlin, Marina A. Pavlova, and Karl J. Friston. "Asymmetric high-order anatomical brain connectivity sculpts effective connectivity." Network Neuroscience 4, no. 3 (January 2020): 871–90. http://dx.doi.org/10.1162/netn_a_00150.

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Bridging the gap between symmetric, direct white matter brain connectivity and neural dynamics that are often asymmetric and polysynaptic may offer insights into brain architecture, but this remains an unresolved challenge in neuroscience. Here, we used the graph Laplacian matrix to simulate symmetric and asymmetric high-order diffusion processes akin to particles spreading through white matter pathways. The simulated indirect structural connectivity outperformed direct as well as absent anatomical information in sculpting effective connectivity, a measure of causal and directed brain dynamics. Crucially, an asymmetric diffusion process determined by the sensitivity of the network nodes to their afferents best predicted effective connectivity. The outcome is consistent with brain regions adapting to maintain their sensitivity to inputs within a dynamic range. Asymmetric network communication models offer a promising perspective for understanding the relationship between structural and functional brain connectomes, both in normalcy and neuropsychiatric conditions.

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24

MALIK, R. P. "TOPOLOGICAL FEATURES IN NON-ABELIAN GAUGE THEORY." Modern Physics Letters A 14, no. 28 (September 14, 1999): 1937–49. http://dx.doi.org/10.1142/s0217732399002017.

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We discuss the BRST cohomology and exhibit a connection between the Hodge decomposition theorem and the topological properties of a two-dimensional free non-Abelian gauge theory (having no interaction with matter fields). The topological nature of this theory is encoded in the vanishing of the Laplacian operator when equations of motion are exploited. We obtain two sets of topological invariants with respect to BRST and co-BRST charges on the two-dimensional compact manifold and show that the Lagrangian density of the theory can be expressed as the sum of terms that are BRST and co-BRST invariants. Thus, this theory captures together some of the salient features of both Witten and Schwarz type of topological field theories.

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25

Krichever, I., M. Mineev-Weinstein, P. Wiegmann, and A. Zabrodin. "Laplacian growth and Whitham equations of soliton theory." Physica D: Nonlinear Phenomena 198, no. 1-2 (November 2004): 1–28. http://dx.doi.org/10.1016/j.physd.2004.06.003.

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26

Butturini, A., and E. Ejarque. "Technical Note: Dissolved organic matter fluorescence – a finite mixture approach to deconvolve excitation-emission matrices." Biogeosciences Discussions 10, no. 3 (March 8, 2013): 4711–32. http://dx.doi.org/10.5194/bgd-10-4711-2013.

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Анотація:

Abstract. The analysis of the shape of excitation-emission matrices (EEMs) is a relevant tool for exploring the origin, transport and fate of dissolved organic matter (DOM) in aquatic ecosystems. Within this context, the decomposition of EEMs is acquiring a notable relevance. A simple mathematical algorithm that automatically deconvolves single EEM is described, creating new possibilities for the comparison of DOM fluorescence properties and EEMs that are very different from each other. A mixture model approach is adopted to decompose complex surfaces into sub-peaks. The laplacian operator and the Nelder–Mead optimization algorithm are implemented to individuate and automatically locate potential peaks in the EEM landscape. A small heterogeneous data set of 21 EEMs from a human-impacted Mediterranean river is used to describe the model application and to illustrate a strategy that optimises the search for the optimal output.

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27

Jalan, Sarika, and Jayendra N. Bandyopadhyay. "Random matrix analysis of network Laplacians." Physica A: Statistical Mechanics and its Applications 387, no. 2-3 (January 2008): 667–74. http://dx.doi.org/10.1016/j.physa.2007.09.026.

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28

Butturini, A., and E. Ejarque. "Technical Note: Dissolved organic matter fluorescence – a finite mixture approach to deconvolve excitation-emission matrices." Biogeosciences 10, no. 9 (September 6, 2013): 5875–87. http://dx.doi.org/10.5194/bg-10-5875-2013.

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Анотація:

Abstract. The analysis of the shape of excitation-emission matrices (EEMs) is a relevant tool for exploring the origin, transport and fate of dissolved organic matter (DOM) in aquatic ecosystems. Within this context, the decomposition of EEMs is acquiring a notable relevance. A simple mathematical algorithm that automatically deconvolves individual EEMs is described, creating new possibilities for the comparison of DOM fluorescence properties and EEMs that are very different from each other. A mixture model approach is adopted to decompose complex surfaces into sub-peaks. The laplacian operator and the Nelder-Mead optimisation algorithm are implemented to individuate and automatically locate potential peaks in the EEM landscape. The EEMs of a simple artificial mixture of fluorophores and DOM samples collected in a Mediterranean river are used to describe the model application and to illustrate a strategy that optimises the search for the optimal output.

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29

Cafiero, Raffaele, Alessandro Vespignani, Stefano Zapperi, and Luciano Pietronero. "Universality and Scale Invariant Dynamics in Laplacian Fractal Growth." International Journal of Modern Physics B 11, no. 30 (December 10, 1997): 3595–619. http://dx.doi.org/10.1142/s0217979297001805.

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Анотація:

The individuation of the scale invariant dynamics in Laplacian fractal growth processes, like diffusion-limited aggregation (DLA), is an important problem whose solution would clarify some crucial issues concerning the origin of fractal properties and the identification of universality classes for such models. Here, we develop a real space renormalization group scheme to study the dynamic evolution of DLA in a restricted space of relevant parameters. In particular, we investigate the effect of a sticking probability P s and an effective noise reduction parameter S. The renormalization equations flow towards an attractive fixed point corresponding to the scale invariant DLA dynamics ([Formula: see text], S*≃2.0). The existence of a non-trivial fixed point value for S, shows that noise is spontaneously generated by the DLA growth process, and that screening, which is at the origin of fractal properties, persists at all scales.

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30

Tabbone, S. A., L. Alonso, and D. Ziou. "Behavior of the Laplacian of Gaussian Extrema." Journal of Mathematical Imaging and Vision 23, no. 1 (July 2005): 107–28. http://dx.doi.org/10.1007/s10851-005-4970-7.

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31

Kostadinova, E. G., R. Banka, J. L. Padgett, C. D. Liaw, L. S. Matthews, and T. W. Hyde. "Fractional Laplacian spectral approach to turbulence in a dusty plasma monolayer." Physics of Plasmas 28, no. 7 (July 2021): 073705. http://dx.doi.org/10.1063/5.0047649.

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32

Dai, Meifeng, Junjie Shen, Lingfei Dai, Tingting Ju, Yongbo Hou, and Weiyi Su. "Generalized adjacency and Laplacian spectra of the weighted corona graphs." Physica A: Statistical Mechanics and its Applications 528 (August 2019): 121285. http://dx.doi.org/10.1016/j.physa.2019.121285.

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33

Ma, Tinghuai, Lu Li, Sai Ji, Xin Wang, Yuan Tian, Abdullah Al-Dhelaan, and Mznah Al-Rodhaan. "Optimized Laplacian image sharpening algorithm based on graphic processing unit." Physica A: Statistical Mechanics and its Applications 416 (December 2014): 400–410. http://dx.doi.org/10.1016/j.physa.2014.09.026.

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34

SUZUKI, Kosuke, Sadayoshi MURAKAMI, Satoshi OHDACHI, Hiroshi IDEI, Kengoh KURODA, Ryuya IKEZOE, and Takumi ONCHI. "MHD Equilibrium Reconstruction Using the Visible Light Tomographic Method with Laplacian Eigenfunction." Plasma and Fusion Research 16 (July 5, 2021): 2402090. http://dx.doi.org/10.1585/pfr.16.2402090.

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35

Chang, Joon-Hyuk. "Complex laplacian probability density function for noisy speech enhancement." IEICE Electronics Express 4, no. 8 (2007): 245–50. http://dx.doi.org/10.1587/elex.4.245.

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36

Zhang, Zhongzhi, Shuigeng Zhou, Yi Qi, and Jihong Guan. "Topologies and Laplacian spectra of a deterministic uniform recursive tree." European Physical Journal B 63, no. 4 (June 2008): 507–13. http://dx.doi.org/10.1140/epjb/e2008-00262-2.

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37

Zheng, Jinde, Junsheng Cheng, and Yu Yang. "Multiscale Permutation Entropy Based Rolling Bearing Fault Diagnosis." Shock and Vibration 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/154291.

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Анотація:

A new rolling bearing fault diagnosis approach based on multiscale permutation entropy (MPE), Laplacian score (LS), and support vector machines (SVMs) is proposed in this paper. Permutation entropy (PE) was recently proposed and defined to measure the randomicity and detect dynamical changes of time series. However, for the complexity of mechanical systems, the randomicity and dynamic changes of the vibration signal will exist in different scales. Thus, the definition of MPE is introduced and employed to extract the nonlinear fault characteristics from the bearing vibration signal in different scales. Besides, the SVM is utilized to accomplish the fault feature classification to fulfill diagnostic procedure automatically. Meanwhile, in order to avoid a high dimension of features, the Laplacian score (LS) is used to refine the feature vector by ranking the features according to their importance and correlations with the main fault information. Finally, the rolling bearing fault diagnosis method based on MPE, LS, and SVM is proposed and applied to the experimental data. The experimental data analysis results indicate that the proposed method could identify the fault categories effectively.

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38

El-Nabulsi, Rami Ahmad, and Waranont Anukool. "Casimir effect associated with fractional laplacian and fractal dimensions." Physica E: Low-dimensional Systems and Nanostructures 146 (January 2023): 115552. http://dx.doi.org/10.1016/j.physe.2022.115552.

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39

Weislogel, M. M., Y. Chen, and D. Bolleddula. "A better nondimensionalization scheme for slender laminar flows: The Laplacian operator scaling method." Physics of Fluids 20, no. 9 (September 2008): 093602. http://dx.doi.org/10.1063/1.2973900.

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40

Bouziane, A., C. Taplamacioglu, K. Hidaka, and R. T. Waters. "Non-Laplacian ion trajectories in mutually interacting corona discharges." Journal of Physics D: Applied Physics 30, no. 13 (July 7, 1997): 1913–21. http://dx.doi.org/10.1088/0022-3727/30/13/013.

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41

Gandolfi, Giovanni, Balakrishna S. Haridasu, Stefano Liberati, and Andrea Lapi. "Looking for Traces of Nonminimally Coupled Dark Matter in the X-COP Galaxy Clusters Sample." Astrophysical Journal 952, no. 2 (July 20, 2023): 105. http://dx.doi.org/10.3847/1538-4357/acd755.

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Анотація:

Abstract We look for possible evidence of a nonminimal coupling (NMC) between dark matter (DM) and gravity using data from the X-COP compilation of galaxy clusters. We consider a theoretically motivated NMC that may dynamically arise from the collective behavior of the coarse-grained DM field (e.g., via Bose–Einstein condensation) with averaging/coherence length L NMC. In the Newtonian limit, the NMC modifies the Poisson equation by a term L NMC 2 ∇ 2 ρ proportional to the Laplacian of the DM density itself. We show that this term, when acting as a perturbation over the standard Navarro–Frenk–White (NFW) profile of cold DM particles, can yield DM halo density profiles capable of correctly fitting galaxy clusters’ pressure profiles with an accuracy comparable to and, in some cases, even better than the standard cold DM NFW profile. We also show that the observed relation between the NMC length scale and the virial mass found in Gandolfi et al. for late-type galaxies is consistent with the relation we find in the current work, suggesting that the previously determined power-law scaling law holds up to galaxy cluster mass scales.

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42

DING, J. R., F. WANG, and B. X. LIU. "LOCAL SCALING PROPERTIES OF FRACTALS OBSERVED IN Ni-Zr ALLOY FILMS." Modern Physics Letters B 04, no. 17 (September 20, 1990): 1111–18. http://dx.doi.org/10.1142/s0217984990001409.

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Wavelet transform was performed based on the fractals observed in Ni-Zr alloy films during ion irradiation. The mass distribution measure and the Laplacian potential gradient measure were used to study the local scaling properties of the ion-induced fractals. The strength of singularities at each point was calculated according to the wavelet transform. The densities of the strength of singularities were also deduced and compared with the f-α spectra yielded by multifractal analysis. The results showed that the ion-induced fractals had a wide range of strength of singularities.

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43

Wang, Guangbin, Ying Lv, Tengqiang Wang, Xiaohui Wang, and Huanke Cheng. "Mass Laplacian Discriminant Analysis and Its Application in Gear Fault Diagnosis." Shock and Vibration 2020 (August 3, 2020): 1–13. http://dx.doi.org/10.1155/2020/8826419.

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Fault diagnosis is essentially the identification of multiple fault modes. How to extract sensitive features and improve diagnostic accuracy is the key to fault diagnosis. In this paper, a new manifold learning method (Mass Laplacian Discriminant Analysis, MLDA) is proposed. Firstly, it is assumed that each data point in the space is a point with mass, and the mass is defined as the number of data points in a certain area. Then, the idea of universal gravitation is introduced to calculate the virtual universal gravitation between data points. Based on the Laplace eigenmaps algorithm, the gravitational Laplacian matrix between the same kind of data and the heterogeneous data is obtained, and the discriminant function is constructed by the ratio of the virtual gravitation between the heterogeneous data and the virtual gravitation between the similar data; the projection function with the largest discriminant function value is the optimal feature mapping function. Finally, based on the mapping function, the eigenvalues of the training data and the test data are calculated, and the softmax algorithm is used to classify the test data. Experiments on gear fault diagnosis show that this method has higher diagnostic accuracy than other manifold learning algorithms.

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44

Vandembroucq, Damien, and Stéphane Roux. "Laplacian transfer across a rough interface: numerical resolution in the conformal plane." Physica A: Statistical Mechanics and its Applications 357, no. 1 (November 2005): 97–102. http://dx.doi.org/10.1016/j.physa.2005.05.068.

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45

Zhan, Choujun, Guanrong Chen, and Lam F. Yeung. "On the distributions of Laplacian eigenvalues versus node degrees in complex networks." Physica A: Statistical Mechanics and its Applications 389, no. 8 (April 2010): 1779–88. http://dx.doi.org/10.1016/j.physa.2009.12.005.

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46

Huang, Wei, Hongpo Fu, Yu Li, and Weiguo Zhang. "A Gaussian-multivariate Laplacian mixture distribution based robust cubature Kalman filter." Measurement 213 (May 2023): 112732. http://dx.doi.org/10.1016/j.measurement.2023.112732.

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47

ZHANG, CHI, YUXIN LIU, LIN YUAN, and XIAOXU HOU. "THE ESTIMATION OF RESPIRATION RATE BASED ON THE AMPLIFICATION OF RESPIRATION MOTION IN VIDEO." Journal of Mechanics in Medicine and Biology 21, no. 05 (April 22, 2021): 2140011. http://dx.doi.org/10.1142/s021951942140011x.

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Standard instrument for the clinical diagnosis of sleep apnea is large and based on invasive method, which is not comfortable and not suitable for daily inspection. A video-based measurement method for the respiration rate (RR) is therefore proposed, which is meaningful to the home diagnosis of sleep apnea. We proposed a novel method for the visualization and calculation of RR from a video containing a sleeping person. The video was decomposed by spatio-temporal Laplacian pyramid method into multiresolution image sequences, which were filtered by an infinite-impulse-response bandpass filter to extract the respiration movement in the video. The respiration movement was amplified, and fused into the original video. On the other hand, the signal intensity of the filtering results was compared between layers of Laplacian pyramid to identify the layer with the strongest movement caused by respiration. A morphological calculation was conducted on the image reshaped from the filtered results in this layer, to find the region of interest (ROI) with most significant movement of respiration. The image intensity in the ROI was spatially averaged into a one-dimensional signal, of which the frequency domain was analyzed to obtain RR. The ROI and the calculation results for RR were visualized on the video with enhanced respiration movement. Ten videos lasting 30–60[Formula: see text]s were recorded by a general webcam. The respiration movement of the subject was successfully extracted and amplified, no matter the posture was supine or side lying. The thoracic and abdominal parts were generally identified as ROI in all postures. RR was calculated by the frequency domain analysis for the averaged image intensity in ROI with the error no more than 1 time per minute, and further, as well as ROI, was fused into the amplified video. The region of respiration movement and RR is calculated by the noncontact method, and well visualized in a video. The method provides a novel screening tool for the population suspected of sleep apnea, and is meaningful to the home diagnosis of sleep illness.

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48

Matignon, D. "Diffusive representations for fractional Laplacian: systems theory framework and numerical issues." Physica Scripta T136 (October 2009): 014009. http://dx.doi.org/10.1088/0031-8949/2009/t136/014009.

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49

Ratcliffe, C. P. "DAMAGE DETECTION USING A MODIFIED LAPLACIAN OPERATOR ON MODE SHAPE DATA." Journal of Sound and Vibration 204, no. 3 (July 1997): 505–17. http://dx.doi.org/10.1006/jsvi.1997.0961.

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50

Li, Xuequn, Shuming Zhou, Guanqin Lian, Gaolin Chen, and Jiafei Liu. "Heterogeneity of social network based on degree sequence and community." International Journal of Modern Physics B 32, no. 30 (December 10, 2018): 1850331. http://dx.doi.org/10.1142/s0217979218503319.

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As we know, the scale-free property of networks implies that there are a great deal of nodes with low degree and a few with high degree in networks. In this paper, we mainly stick to the analysis of the heterogeneity of social networks. Heterogeneity measure of degree sequence based on Laplacian centrality (HLC) and degree ratio (HDR) and local neighborhood (HLN) are presented. Furthermore, heterogeneities of community based on the size, edge abundant degree and density of community are explored, respectively. The heterogeneity measures of community are empirically analyzed in the real-world network in terms of these three indices, i.e., size, edge abundant degree and density of community.

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