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Journal articles on the topic 'Regularisation'

Author: Grafiati

Published: 4 June 2021

Last updated: 7 July 2024

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1

Smit, Monika, Moira Galloway, Mina Vijkhuijs, and Mariska Kromhout. "The ‘Pardon Regulation’: Implementation and outcome of a regularisation programme in the Netherlands." Migration Letters 13, no. 1 (January 15, 2015): 144–58. http://dx.doi.org/10.33182/ml.v13i1.269.

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Regularisation programmes that are intended to legalise the stay of undocumented migrants may provoke public resistance and heated political debates. Governments nevertheless go ahead with such programmes. In the Netherlands, a regularisation programme to settle the legacy of an old Aliens Law, known as the ‘Pardon Regulation’, was implemented in 2007. In this contribution we describe the implementation and outcome of the Pardon Regulation, which led to over 28,000 regularisations. We focus on the question to what extent pitfalls that were experienced in a number of regularisation programmes in other European countries were avoided and intended goals were met.

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2

Kraler, Albert. "Fixing, Adjusting, Regulating, Protecting Human Rights - The Shifting Uses of Regularisations in the European Union." European Journal of Migration and Law 13, no. 3 (2011): 297–316. http://dx.doi.org/10.1163/157181611x587865.

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AbstractAlmost all Member States in the European Union currently make use, or in the past have made use of some form of regularisation of irregular immigrants, although to greatly varying degrees, in different ways and as a rule only reluctantly. A distinct feature of recent regularisations has been the shift towards a humanitarian justification of regularisation measures. In this context, regularisation has become reframed as an issue of the protection of irregular migrants’ human rights. As a result, regularisation has to some extent also been turned from a political tool in managing migration into an issue of international, European and national human rights law. While a human rights framework indeed offers a powerful rationale and at times compelling reasons why states ought to afford a legal status to irregular migrants, I argue that a human rights based approach must always be complemented by pragmatic considerations, as a human rights based justification of regularisation alone will be insufficient to find adequate responses to the changing presence of irregular migrants in the EU, not all of which can invoke human rights based claims to residence.

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3

Fife, Paul C., and Xiao-Ping Wang. "Periodic structures in a van der Waals fluid." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 128, no. 2 (1998): 235–50. http://dx.doi.org/10.1017/s0308210500012762.

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A system of partial differential equations modelling a van der Waals fluid or an elastic medium with nonmonotone pressure-density relation is studied. As the system changes type, regularisations are considered. The existence of one-dimensional periodic travelling waves, with prescribed average density in a certain range, average velocity and wavelength, is proved. They exhibit layer structure when the regularisation parameter is small. Similarities with the Cahn–Hilliard equation are explored.

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4

Liu, Yongshi, Xiaodong Yu, Jianjun Zhao, Changchun Pan, and Kai Sun. "Development of a Robust Data-Driven Soft Sensor for Multivariate Industrial Processes with Non-Gaussian Noise and Outliers." Mathematics 10, no. 20 (October 17, 2022): 3837. http://dx.doi.org/10.3390/math10203837.

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Industrial processes are often nonlinear and multivariate and suffer from non-Gaussian noise and outliers in the process data, which cause significant challenges in data-driven modelling. To address these issues, a robust soft-sensing algorithm that integrates Huber’s M-estimation and adaptive regularisations with multilayer perceptron (MLP) is proposed in this paper. The proposed algorithm, called RAdLASSO-MLP, starts with an initially well-trained MLP for nonlinear data-driven modelling. Subsequently, the residuals of the proposed model are robustified with Huber’s M-estimation to improve the resistance to non-Gaussian noise and outliers. Moreover, a double L1-regularisation mechanism is introduced to minimise redundancies in the input and hidden layers of MLP. In addition, the maximal information coefficient (MIC) index is investigated and used to design the adaptive operator for the L1-regularisation of the input neurons to improve biased estimations with L1-regularisation. Including shrinkage parameters and Huber’s M-estimation parameter, the hyperparameters are determined via grid search and cross-validation. To evaluate the proposed algorithm, simulations were conducted with both an artificial dataset and an industrial dataset from a practical gasoline treatment process. The results indicate that the proposed algorithm is superior in terms of predictive accuracy and robustness to the classic MLP and the regularised soft-sensing approaches LASSO-MLP and dLASSO-MLP.

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5

Magina, Fredrick Bwire, Alphonce Kyessi, and Wilbard Kombe. "The Urban Land Nexus– Challenges and Opportunities of Regularising Informal Settlements: The Case Studies of Dar es Salaam and Mwanza in Tanzania." JOURNAL OF AFRICAN REAL ESTATE RESEARCH 5, no. 1 (June 1, 2020): 32–54. http://dx.doi.org/10.15641/jarer.v5i1.837.

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Informal settlements in Tanzania accommodate more than 70% of the urban population. Owing to this, the Tanzanian government has undertaken several initiatives to address the growing size and number of informal settlements. One such initiative is regularisation which addresses security of tenure for residents of these settlements. Most of the people living in informal settlements lack legal land ownership and as a result properties in such settlements have relatively less value and lack security of tenure. Providing security of tenure is believed to encourage investment into informal households and facilitate the provision of urban services. This study aims to evaluate the process of regularisation in three Tanzanian settlements; Magengenu in Dar es Salaam (Tanzania’s largest city), Ibungilo and Isamilo in Mwanza city (the nation’s second largest city). Using qualitative data the paper explores the challenges and opportunities that emerged from regularisation. Findings indicate that the regularisation process has facilitated the issuance of title deeds, increased land value and security of tenure. However, a number of challenges were highlighted during regularisation. These include an over-emphasis on the protection of private rights while undermining public interests, a lack of harmonised cost for regularisation, and prolonged delays in completing the regularisation process. These require policy actions, particularly reviewing the national informal settlements regularisation guidelines, as a way to address the weaknesses emerging from regularisation projects in the studied settlements. We conclude that land regularisation remains an important tool to enhance livable cities and protect long-term public and private interests in land development. In order to achieve this, supportive policy actions are required to support the protection of public interests in land regularisation and harmonise the costs of regularisation.

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6

Bonora, Loriano, Roberto Soldati, and Stav Zalel. "Dirac, Majorana, Weyl in 4D." Universe 6, no. 8 (August 4, 2020): 111. http://dx.doi.org/10.3390/universe6080111.

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This is a review of some elementary properties of Dirac, Weyl and Majorana spinors in 4D. We focus in particular on the differences between massless Dirac and Majorana fermions, on one side, and Weyl fermions, on the other. We review in detail the definition of their effective actions, when coupled to (vector and axial) gauge fields, and revisit the corresponding anomalies using the Feynman diagram method with different regularisations. Among various well known results we stress in particular the regularisation independence in perturbative approaches, while not all the regularisations fit the non-perturbative ones. As for anomalies, we highlight in particular one perhaps not so well known feature: the rigid relation between chiral and trace anomalies.

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7

Valkonen, T. "Regularisation, optimisation, subregularity." Inverse Problems 37, no. 4 (March 16, 2021): 045010. http://dx.doi.org/10.1088/1361-6420/abe4aa.

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8

Venkatesh, Prasana K. "On Tikhonov regularisation." Physica A: Statistical Mechanics and its Applications 284, no. 1-4 (September 2000): 448–60. http://dx.doi.org/10.1016/s0378-4371(00)00203-x.

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9

Laborde, Jean-Marie. "Regularisation numerique d'orbites." Discrete Mathematics 53 (March 1985): 151–55. http://dx.doi.org/10.1016/0012-365x(85)90138-4.

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10

Acquah, Joseph, Francis Benyah, and Jerry S. Y. Kuma. "Regularisation Technique for a Distributed Parameter Identification Problem." Journal of Mathematics Research 11, no. 1 (January 22, 2019): 64. http://dx.doi.org/10.5539/jmr.v11n1p64.

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This paper examined the problem of ill-posedness of solution in identifying parameters from a given groundwater flow model. The solution approach to the problem was attempted by the method of Parameter Transformation coupled with Tikhonov Regularisation with and without Truncation which has not been explored. Convergence of the method was assessed by the L-Curve criterion. Numerical examples were presented to illustrate the efficiency of the proposed Regularisation Technique. Tikhonov Regularisation with Truncation turns to give a more realistic solution estimates when examined numerically, compared to that of Regularisation without Truncation.

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11

Williams, Bryan M., Jianping Zhang, and Ke Chen. "A new image deconvolution method with fractional regularisation." Journal of Algorithms & Computational Technology 10, no. 4 (July 28, 2016): 265–76. http://dx.doi.org/10.1177/1748301816660439.

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Image deconvolution is an important pre-processing step in image analysis which may be combined with denoising, also an important image restoration technique, and prepares the image to facilitate diagnosis in the case of medical images and further processing such as segmentation and registration. Considering the variational approach to this problem, regularisation is a vital component for reconstructing meaningful information and the problem of defining appropriate regularisation is an active research area. An important question in image deconvolution is how to obtain a restored image which has sharp edges where required but also allows smooth regions. Many of the existing regularisation methods allow for one or the other but struggle to obtain good results with both. Consequently, there has been much work in the area of variational image reconstruction in finding regularisation techniques which can provide good quality restoration for images which have both smooth regions and sharp edges. In this paper, we propose a new regularisation technique for image reconstruction in the blind and non-blind deconvolution problems where the precise cause of blur may or may not be known. We present experimental results which demonstrate that this method of regularisation is beneficial for restoring images and blur functions which contain both jumps in intensity and smooth regions.

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12

Zhu, Wei, Shangxu Wang, Xu Chang, Hongyu Zhai, Taiming He, and Hezhen Wu. "Tomography with sparseness regularisation for ultrasonic velocity imaging." Journal of Geophysics and Engineering 19, no. 1 (February 2022): 85–105. http://dx.doi.org/10.1093/jge/gxac001.

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Abstract Ultrasonic tomography, which is widely used in the study of the fracturing process of rocks, often exhibits low resolution due to insufficient ray coverage, particularly while evaluating the three-dimensional (3D) fractures. To resolve this issue, we adopted sparseness regularisation in tomography to reconstruct the ultrasonic velocity of rocks. Both numerical and laboratory experiments demonstrate that tomography with sparseness regularisation generates velocity images with clear fracture morphology than that with Tikhonov regularisation. Dynamic monitoring of the fracturing process of a granite slab with two-dimensional (2D) velocity images can reveal the accurate development of the fracturing process. The experiment on the internal structure of tight sandstone after hydraulic fracturing reveals demarcated low-velocity regions in the 3D ultrasonic velocity images of tomography with sparseness regularisation. These low-velocity regions correspond to the positions of the fractures when compared to the X-ray scanning images. Thus, tomography with sparseness regularisation can improve the resolution of ultrasonic velocity images, which can be used to accurately describe the fracture development and strain localisation during rock deformation.

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13

Woods, Luke T., and Zeeshan A. Rana. "Constraints on Optimising Encoder-Only Transformers for Modelling Sign Language with Human Pose Estimation Keypoint Data." Journal of Imaging 9, no. 11 (November 2, 2023): 238. http://dx.doi.org/10.3390/jimaging9110238.

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Supervised deep learning models can be optimised by applying regularisation techniques to reduce overfitting, which can prove difficult when fine tuning the associated hyperparameters. Not all hyperparameters are equal, and understanding the effect each hyperparameter and regularisation technique has on the performance of a given model is of paramount importance in research. We present the first comprehensive, large-scale ablation study for an encoder-only transformer to model sign language using the improved Word-level American Sign Language dataset (WLASL-alt) and human pose estimation keypoint data, with a view to put constraints on the potential to optimise the task. We measure the impact a range of model parameter regularisation and data augmentation techniques have on sign classification accuracy. We demonstrate that within the quoted uncertainties, other than ℓ2 parameter regularisation, none of the regularisation techniques we employ have an appreciable positive impact on performance, which we find to be in contradiction to results reported by other similar, albeit smaller scale, studies. We also demonstrate that the model architecture is bounded by the small dataset size for this task over finding an appropriate set of model parameter regularisation and common or basic dataset augmentation techniques. Furthermore, using the base model configuration, we report a new maximum top-1 classification accuracy of 84% on 100 signs, thereby improving on the previous benchmark result for this model architecture and dataset.

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14

Koch, Lukas. "Post-hoc regularisation of unfolded cross-section measurements." Journal of Instrumentation 17, no. 10 (October 1, 2022): P10021. http://dx.doi.org/10.1088/1748-0221/17/10/p10021.

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Abstract Neutrino cross-section measurements are often presented as unfolded binned distributions in “true” variables. The ill-posedness of the unfolding problem can lead to results with strong anti-correlations and fluctuations between bins, which make comparisons to theoretical models in plots difficult. To alleviate this problem, one can introduce regularisation terms in the unfolding procedure. These suppress the anti-correlations in the result, at the cost of introducing some bias towards the expected shape of the data. This paper discusses a method using simple linear algebra, which makes it is possible to regularise any result that is presented as a central value and a covariance matrix. This “post-hoc” regularisation is generally much faster than repeating the unfolding method with different regularisation terms. The method also yields a regularisation matrix which connects the regularised to the unregularised result, and can be used to retain the full statistical power of the unregularised result when publishing a nicer looking regularised result. In addition to the regularisation method, this paper also presents some thoughts on the presentation of correlated data in general. When using the proposed method, the bias of the regularisation can be understood as a data visualisation problem rather than a statistical one. The strength of the regularisation can be chosen by minimising the difference between the implicitly uncorrelated distribution shown in the plots and the actual distribution described by the unregularised central value and covariance. Aside from minimising the difference between the shown and the actual result, additional information can be provided by showing the local log-likelihood gradient of the models shown in the plots. This adds more information about where the model is “pulled” by the data than just comparing the bin values to the data's central values.

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15

Osborne, M. R., and Tania Prvan. "Applications of L1 regularisation." ANZIAM Journal 52 (October 17, 2011): 866. http://dx.doi.org/10.21914/anziamj.v52i0.3805.

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16

Weier, Philippe, Marc Droske, Johannes Hanika, Andrea Weidlich, and Jiří Vorba. "Optimised Path Space Regularisation." Computer Graphics Forum 40, no. 4 (July 2021): 139–51. http://dx.doi.org/10.1111/cgf.14347.

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17

Grasmair, Markus. "Non-convex sparse regularisation." Journal of Mathematical Analysis and Applications 365, no. 1 (May 2010): 19–28. http://dx.doi.org/10.1016/j.jmaa.2009.09.055.

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18

Meek, B. L. "Is standardisation just regularisation?" Computer Standards & Interfaces 7, no. 3 (January 1988): 257–59. http://dx.doi.org/10.1016/0920-5489(88)90087-6.

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19

Olivar de Julián, José Manuel. "The Moroccan Diaspora in Spain." Diaspora Studies 17, no. 2 (March 25, 2024): 180–98. http://dx.doi.org/10.1163/09763457-bja10095.

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Abstract The paper identifies the Moroccan diaspora in Spain, the largest foreign diaspora in that country, and explains the causes for its rapid establishment. After six regularisation processes, which took place between 1985 and 2023, and the ongoing regularisation process in conjunction with family reunification channels, more than 1.3 million Moroccans now live in Spain. This example shows the significant demographic transformations that can result from mass regularisation, the social and political transformations that follow in the host states that enact such measures, and the transformation in external relations with the diaspora’s state of origin.

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20

Fang, Xi-Ming, Fu-Rong Lin, and Chao Wang. "Estimation of a Regularisation Parameter for a Robin Inverse Problem." East Asian Journal on Applied Mathematics 7, no. 2 (May 2017): 325–42. http://dx.doi.org/10.4208/eajam.150216.260117a.

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AbstractWe consider the nonlinear and ill-posed inverse problem where the Robin coefficient in the Laplace equation is to be estimated using the measured data from the accessible part of the boundary. Two regularisation methods are considered — viz. L2 and H1 regularisation. The regularised problem is transformed to a nonlinear least squares problem; and a suitable regularisation parameter is chosen via the normalised cumulative periodogram (NCP) curve of the residual vector under the assumption of white noise, where information on the noise level is not required. Numerical results show that the proposed method is efficient and competitive.

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21

Miguélez, Fausto, and Albert Recio. "Spain: large-scale regularisation and its impacts on labour market and social policy." Transfer: European Review of Labour and Research 14, no. 4 (January 1, 2008): 589–606. http://dx.doi.org/10.1177/102425890801400406.

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Regularisation measures in Spain have formed part of an overall immigration policy that until a few years ago was geared more towards border security than to meeting the demands of the labour market. However, the regularisation campaign in 2005 was different: it enjoyed widespread popular support and sought to combat the informal economy and grant employment rights to immigrants who were in fact working. As a result, the labour market is now better regulated, but efforts to combat segmentation have not been so successful. Furthermore, the regularisation campaigns were inadequately funded, and failed to bring about sufficient improvements in public policies.

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22

Mikkola, S. "A Brief History of Regularisation." Proceedings of the International Astronomical Union 3, S246 (September 2007): 218–27. http://dx.doi.org/10.1017/s1743921308015639.

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AbstractThe various methods for regularisation of the gravitational few-body problem, from the coordinate transformation by the Kustaanheimo-Stiefel method to the more recent methods of algorithmic regularisation, are reviewed. Numerical comparisons of the performance of the methods are presented and future research suggested.

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23

Zheng, Yuhui, Byeungwoo Jeon, Jianwei Zhang, and Yunjie Chen. "Adaptively determining regularisation parameters in non‐local total variation regularisation for image denoising." Electronics Letters 51, no. 2 (January 2015): 144–45. http://dx.doi.org/10.1049/el.2014.3494.

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24

Wysoczański, D., J. Mroczka, and A. G. Polak. "Performance analysis of regularization algorithms used for image reconstruction in computed tomography." Bulletin of the Polish Academy of Sciences: Technical Sciences 61, no. 2 (June 1, 2013): 467–74. http://dx.doi.org/10.2478/bpasts-2013-0046.

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Abstract Computed tomography is one of the most significant diagnostic techniques in medicine. This work is focused on hard-field imaging, where signals take a form of straight rays and the reconstructed image can be presented as a matrix with unknown pixels. Algebraic methods for direct computation of the image have not been used in practice because of the scale of the problem and numerical errors appearing in the solution. The aim of this work was to analyse the performance of direct algebraic algorithms for tomographic image reconstruction including regularisation mechanism such as: generalised regularisation, Tikhonov regularisation, Twomey regularisation and ridge regression (RR), as well as comparing the results with the filtered backprojection (FBP) as the reference method. The performed analyses demonstrated that the regularised algebraic methods are more accurate than the commonly used FBP, and RR appeared the most precise among them. Additionally it was shown that the invariant system matrix (inverted during calculations) can be easily determined by solving the forward problem. Finally, potential directions of further research have been pointed out.

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25

Ma, Liyan, Tieyong Zeng, and Gongyan Li. "Hybrid Variational Model for Texture Image Restoration." East Asian Journal on Applied Mathematics 7, no. 3 (August 2017): 629–42. http://dx.doi.org/10.4208/eajam.090217.300617a.

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AbstractThe hybrid variational model for restoration of texture images corrupted by blur and Gaussian noise we consider combines total variation regularisation and a fractional-order regularisation, and is solved by an alternating minimisation direction algorithm. Numerical experiments demonstrate the advantage of this model over the adaptive fractional-order variational model in image quality and computational time.

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Duignan, Nathan, and Holger R. Dullin. "Regularisation for Planar vector fields." Nonlinearity 33, no. 1 (November 19, 2019): 106–38. http://dx.doi.org/10.1088/1361-6544/ab34d9.

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27

Davies, A. J., L. C. W. Dixon, R. Roy, and P. van der Zee. "Regularisation and the inverse problem." Advances in Engineering Software 30, no. 8 (August 1999): 557–62. http://dx.doi.org/10.1016/s0965-9978(99)00005-8.

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28

Bennett, Terry, Antonio Rodríguez-Ferran, and Harm Askes. "Damage regularisation with inertia gradients." European Journal of Mechanics - A/Solids 31, no. 1 (January 2012): 131–38. http://dx.doi.org/10.1016/j.euromechsol.2011.08.005.

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29

Jack, I., and D. R. T. Jones. "Quadratic divergences and dimensional regularisation." Nuclear Physics B 342, no. 1 (September 1990): 127–48. http://dx.doi.org/10.1016/0550-3213(90)90574-w.

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30

DASS, N. D. HARI. "REGULARISATION OF CHIRAL GAUGE THEORIES." International Journal of Modern Physics B 14, no. 19n20 (August 10, 2000): 1989–2010. http://dx.doi.org/10.1142/s0217979200001138.

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This article gives a review of the topic of regularising chiral gauge theories and is aimed at a general audience. It begins by clarifying the meaning of chirality and goes on to discussing chiral projections in field theory, parity violation and the distinction between vector and chiral field theories. It then discusses the standard model of electroweak interactions from the perspective of chirality. It also reviews at length the phenomenon of anomalies in quantum field theories including the intuitive understanding of anomalies based on the Dirac sea picture as given by Nielsen and Ninomiya. It then raises the issue of a non-perturbative and constructive definition of the standard model as well as the importance of such formulations. The second Nielsen–Ninomiya theorem about the impossibility of regularising chiral gauge theories under some general assumptions is also discussed. After a brief review of lattice regularisation of field theories, it discusses the issue of fermions on the lattice with special emphasis on the problem of species doubling. The implications of these problems to introducing chiral fermions on the lattice as well as the interpretations of anomalies within the lattice formulations and the lattice Dirac sea picture are then discussed. Finally the difficulties of formulating the standard model on the lattice are illustrated through detailed discussions of the Wilson–Yukawa method, the domain wall fermions method and the recently popular Ginsparg–Wilson method.

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31

Bargetz, Christian, and Norbert Ortner. "Kernel identities and vectorial regularisation." Monatshefte für Mathematik 186, no. 2 (July 5, 2017): 201–14. http://dx.doi.org/10.1007/s00605-017-1076-4.

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32

Hai, Dang Dinh, and Dang Dinh Ang. "Regularisation of Abel's integral equation." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 107, no. 1-2 (1987): 165–68. http://dx.doi.org/10.1017/s0308210500029425.

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SynopsisConsider the Abel integral operatorwhere 0 < α < 1. Suppose u is in H1(0, 1) of H1-norm ≦E, and f is an element of L2(0, 1) such that ∥Au – f∥L−2 < ε. We give a regularised approximate solution uβ(f) of the equationwhich satisfiesand can be computed simply by performing some integrations. The preceding error estimate can be sharpened by strengthening regularity conditions on u

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33

Pang, Zhen, Bingqing Lin, and Jiming Jiang. "Regularisation Parameter Selection Via Bootstrapping." Australian & New Zealand Journal of Statistics 58, no. 3 (September 2016): 335–56. http://dx.doi.org/10.1111/anzs.12168.

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34

Kong, Yanfeng, Zhenping Li, and Xiangtuan Xiong. "An Inverse Diffraction Problem: Shape Reconstruction." East Asian Journal on Applied Mathematics 5, no. 4 (November 2015): 342–60. http://dx.doi.org/10.4208/eajam.310315.250915a.

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AbstractAn inverse diffraction problem is considered. Both classical Tikhonov regularisation and a slow-evolution-from-the-continuation-boundary (SECB) method are used to solve the ill-posed problem. Regularisation error estimates for the two methods are compared, and the SECB method is seen to be an improvement on the classical Tikhonov method. Two numerical examples demonstrate their feasibility and efficiency.

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35

Simons, S. "Regularisations of convex functions and slicewise suprema." Bulletin of the Australian Mathematical Society 50, no. 3 (December 1994): 481–99. http://dx.doi.org/10.1017/s0004972700013599.

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For a number of years, there has been interest in the regularisation of a given proper convex lower semicontinuous function on a Banach space, defined to be the episum (=inf-convolution) of the function with a scalar multiple of the norm. There is an obvious geometric way of characterising this regularisation as the lower envelope of cones lying above the graph of the original function. In this paper, we consider the more interesting problem of characterising the regularisation in terms of approximations from below, expressing the regularisation as the upper envelope of certain subtangents to the graph of the original function. We shall show that such an approximation is sometimes (but not always) valid. Further, we shall give an extension of the whole procedure in which the scalar multiple of the norm is replaced by a more general sublinear functional. As a by-product of our analysis, we are led to the consideration of two senses stronger than the pointwise sense in which a function on a Banach space can be expressed as the upper envelope of a family of functions. These new senses of suprema lead to some questions in Banach space theorey.

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ARNONE, S., YU A. KUBYSHIN, T. R. MORRIS, and J. F. TIGHE. "A GAUGE INVARIANT REGULATOR FOR THE ERG." International Journal of Modern Physics A 16, no. 11 (April 30, 2001): 1989–2001. http://dx.doi.org/10.1142/s0217751x0100461x.

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A gauge invariant regularisation for dealing with pure Yang-Mills theories within the exact renormalization group approach is proposed. It is based on the regularisation via covariant higher derivatives and includes auxiliary Pauli-Villars fields which amounts to a spontaneously broken SU(N|N) super-gauge theory. We demonstrate perturbatively that the extended theory is ultra-violet finite in four dimensions and argue that it has a sensible limit when the regularization cutoff is removed.

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Engl, Heinz W., and C. W. Groetsch. "A higher order approximation technique for restricted linear least-squares problems." Bulletin of the Australian Mathematical Society 37, no. 1 (February 1988): 121–30. http://dx.doi.org/10.1017/s0004972700004226.

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An essential limitation for the method of weighting for equality constrained linear least-squares problems is the sub-optimality of the attainable convergence rate. In this paper, we propose a method, related to the method of iterated Tikhonov regularisation, that (under suitable conditions) gives rise to convergence rates which are arbitrarily near the optimal rate. As a by-product, we develop the theory of iterated Tikhonov regularisation for equations with unbounded linear operators.

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Anctil, F., and N. Lauzon. "Generalisation for neural networks through data sampling and training procedures, with applications to streamflow predictions." Hydrology and Earth System Sciences 8, no. 5 (October 31, 2004): 940–58. http://dx.doi.org/10.5194/hess-8-940-2004.

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Abstract. Since the 1990s, neural networks have been applied to many studies in hydrology and water resources. Extensive reviews on neural network modelling have identified the major issues affecting modelling performance; one of the most important is generalisation, which refers to building models that can infer the behaviour of the system under study for conditions represented not only in the data employed for training and testing but also for those conditions not present in the data sets but inherent to the system. This work compares five generalisation approaches: stop training, Bayesian regularisation, stacking, bagging and boosting. All have been tested with neural networks in various scientific domains; stop training and stacking having been applied regularly in hydrology and water resources for some years, while Bayesian regularisation, bagging and boosting have been less common. The comparison is applied to streamflow modelling with multi-layer perceptron neural networks and the Levenberg-Marquardt algorithm as training procedure. Six catchments, with diverse hydrological behaviours, are employed as test cases to draw general conclusions and guidelines on the use of the generalisation techniques for practitioners in hydrology and water resources. All generalisation approaches provide improved performance compared with standard neural networks without generalisation. Stacking, bagging and boosting, which affect the construction of training sets, provide the best improvement from standard models, compared with stop-training and Bayesian regularisation, which regulate the training algorithm. Stacking performs better than the others although the benefit in performance is slight compared with bagging and boosting; furthermore, it is not consistent from one catchment to another. For a good combination of improvement and stability in modelling performance, the joint use of stop training or Bayesian regularisation with either bagging or boosting is recommended. Keywords: neural networks, generalisation, stacking, bagging, boosting, stop-training, Bayesian regularisation, streamflow modelling

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Jackson, Yves, Delphine S. Courvoisier, Aline Duvoisin, Giovanni Ferro-Luzzi, Patrick Bodenmann, Pierre Chauvin, Idris Guessous, Hans Wolff, Stéphane Cullati, and Claudine Burton-Jeangros. "Impact of legal status change on undocumented migrants’ health and well-being (Parchemins): protocol of a 4-year, prospective, mixed-methods study." BMJ Open 9, no. 5 (May 2019): e028336. http://dx.doi.org/10.1136/bmjopen-2018-028336.

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IntroductionMigrants without residency permit, known as undocumented, tend to live in precarious conditions and be exposed to an accumulation of adverse determinants of health. Only scarce evidence exists on the social, economic and living conditions-related factors influencing their health status and well-being. No study has assessed the impact of legal status regularisation. The Parchemins study is the first prospective, mixed-methods study aiming at measuring the impact on health and well-being of a regularisation policy on undocumented migrants in Europe.Methods and analysisThe Parchemins study will compare self-rated health and satisfaction with life in a group of adult undocumented migrants who qualify for applying for a residency permit (intervention group) with a group of undocumented migrants who lack one or more eligibility criteria for regularisation (control group) in Geneva Canton, Switzerland. Asylum seekers are not included in this study. The total sample will include 400 participants. Data collection will consist of standardised questionnaires complemented by semidirected interviews in a subsample (n=38) of migrants qualifying for regularisation. The baseline data will be collected just before or during the regularisation, and participants will subsequently be followed up yearly for 3 years. The quantitative part will explore variables about health (ie, health status, occupational health, health-seeking behaviours, access to care, healthcare utilisation), well-being (measured by satisfaction with different dimensions of life), living conditions (ie, employment, accommodation, social support) and economic situation (income, expenditures). Several confounders including sociodemographic characteristics and migration history will be collected. The qualitative part will explore longitudinally the experience of change in legal status at individual and family levels.Ethics and disseminationThis study was approved by the Ethics Committee of Geneva, Switzerland. All participants provided informed consent. Results will be shared with undocumented migrants and disseminated in scientific journals and conferences. Fully anonymised data will be available to researchers.

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Höllmann, M., M. Mehltretter, and C. Heipke. "GEOMETRY-BASED REGULARISATION FOR DENSE IMAGE MATCHING VIA UNCERTAINTY-DRIVEN DEPTH PROPAGATION." ISPRS Annals of Photogrammetry, Remote Sensing and Spatial Information Sciences V-2-2020 (August 3, 2020): 151–59. http://dx.doi.org/10.5194/isprs-annals-v-2-2020-151-2020.

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Abstract. In the present work, an uncertainty-driven geometry-based regularisation for the task of dense stereo matching is presented. The objective of the regularisation is the reduction of ambiguities in the depth reconstruction process, which exist due to the ill-posed nature of this task. Based on cost and uncertainty information computed beforehand, pixels are selected, whose depth information can be determined correctly with a high probability. This depth information assumed to be of high confidence is initially used to construct a triangle mesh, which is interpreted as surface approximation of the imaged scene and allows to propagate the confident depth information of the triangle vertices within local neighbourhoods. The proposed method further computes confidence scores for propagated depth estimates, which are used to fuse this depth information with the previously computed cost information, introducing a regularisation into the data term of global optimisation methods. Furthermore, based on the propagated depth information the local smoothness assumption of global optimisation methods is adjusted. Instead of fronto-parallel planes, the method presumes planes, which are parallel to the propagated depth information. The performance of the proposed regularisation approach is evaluated in combination with a global optimisation method. For a quantitative and qualitative evaluation two commonly employed and well-established stereo datasets are used. The proposed method shows significant improvements in accuracy on both datasets and for two different cost computation methods. Especially in unstructured areas, artefacts in the disparity maps are reduced.

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Lang, Lukas F., Sebastian Neumayer, Ozan Öktem, and Carola-Bibiane Schönlieb. "Template-Based Image Reconstruction from Sparse Tomographic Data." Applied Mathematics & Optimization 82, no. 3 (May 14, 2019): 1081–109. http://dx.doi.org/10.1007/s00245-019-09573-2.

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Abstract We propose a variational regularisation approach for the problem of template-based image reconstruction from indirect, noisy measurements as given, for instance, in X-ray computed tomography. An image is reconstructed from such measurements by deforming a given template image. The image registration is directly incorporated into the variational regularisation approach in the form of a partial differential equation that models the registration as either mass- or intensity-preserving transport from the template to the unknown reconstruction. We provide theoretical results for the proposed variational regularisation for both cases. In particular, we prove existence of a minimiser, stability with respect to the data, and convergence for vanishing noise when either of the abovementioned equations is imposed and more general distance functions are used. Numerically, we solve the problem by extending existing Lagrangian methods and propose a multilevel approach that is applicable whenever a suitable downsampling procedure for the operator and the measured data can be provided. Finally, we demonstrate the performance of our method for template-based image reconstruction from highly undersampled and noisy Radon transform data. We compare results for mass- and intensity-preserving image registration, various regularisation functionals, and different distance functions. Our results show that very reasonable reconstructions can be obtained when only few measurements are available and demonstrate that the use of a normalised cross correlation-based distance is advantageous when the image intensities between the template and the unknown image differ substantially.

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Joseph, R., F. Courbin, J. L. Starck, and S. Birrer. "Sparse Lens Inversion Technique (SLIT): lens and source separability from linear inversion of the source reconstruction problem." Astronomy & Astrophysics 623 (February 25, 2019): A14. http://dx.doi.org/10.1051/0004-6361/201731042.

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Strong gravitational lensing offers a wealth of astrophysical information on the background source it affects, provided the lensed source can be reconstructed as if it was seen in the absence of lensing. In the present work, we illustrate how sparse optimisation can address the problem. As a first step towards a full free-form-lens-modelling technique, we consider linear inversion of the lensed source under sparse regularisation and joint deblending from the lens light profile. The method is based on morphological component analysis, assuming a known mass model. We show with numerical experiments that representing the lens and source light using an undecimated wavelet basis allows us to reconstruct the source and to separate it from the foreground lens at the same time. Both the source and lens light have a non-analytic form, allowing for the flexibility needed in the inversion to represent arbitrarily small and complex luminous structures in the lens and source. In addition, sparse regularisation avoids over-fitting the data and does not require the use of an adaptive mesh or pixel grid. As a consequence, our reconstructed sources can be represented on a grid of very small pixels. Sparse regularisation in the wavelet domain also allows for automated computation of the regularisation parameter, thus minimising the impact of the arbitrary choice of initial parameters. Our inversion technique for a fixed mass distribution can be incorporated into future lens-modelling techniques iterating over the lens mass parameters.

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GOVINDARAJAN, T. R., SEÇKIN KÜRKÇÜOǦLU, and MARCO PANERO. "NONLOCAL REGULARISATION OF NONCOMMUTATIVE FIELD THEORIES." Modern Physics Letters A 21, no. 24 (August 10, 2006): 1851–63. http://dx.doi.org/10.1142/s021773230602113x.

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We study noncommutative field theories, which are inherently nonlocal, using a Poincaré-invariant regularisation scheme which yields an effective, nonlocal theory for energies below a cutoff scale. After discussing the general features and the peculiar advantages of this regularisation scheme for theories defined in noncommutative spaces, we focus our attention on the particular case when the noncommutativity parameter is inversely proportional to the square of the cutoff, via a dimensionless parameter η. We work out the perturbative corrections at one-loop order for a scalar theory with quartic interactions, where the signature of noncommutativity appears in η-dependent terms. The implications of this approach, which avoids the problems related to uv–ir mixing, are discussed from the perspective of the Wilson renormalisation program. Finally, we remark about the generality of the method, arguing that it may lead to phenomenologically relevant predictions, when applied to realistic field theories.

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Reuter, M., and W. Dittrich. "Regularisation schemes for the Casimir effect." European Journal of Physics 6, no. 1 (January 1, 1985): 33–40. http://dx.doi.org/10.1088/0143-0807/6/1/005.

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Panis, S., and J. P. Cosmas. "Motion estimation with object based regularisation." Electronics Letters 32, no. 10 (1996): 872. http://dx.doi.org/10.1049/el:19960598.

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Barcelos-Neto, J., and C. Farina de Souza. "Dimensional regularisation in the axial model." Journal of Physics G: Nuclear and Particle Physics 15, no. 5 (May 1, 1989): 555–59. http://dx.doi.org/10.1088/0954-3899/15/5/009.

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Young, R. D., D. B. Leinweber, and A. W. Thomas. "Finite-range regularisation and chiral extrapolation." Nuclear Physics B - Proceedings Supplements 141 (April 2005): 233–37. http://dx.doi.org/10.1016/j.nuclphysbps.2004.12.035.

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del Aguila, F., M. Pérez-Victoria, and J. Santiago. "Discrete regularisation of localised kinetic terms." Nuclear Physics B - Proceedings Supplements 135 (October 2004): 295–99. http://dx.doi.org/10.1016/j.nuclphysbps.2004.09.032.

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Pineda, Antonio, and Joan Soto. "The Lamb shift in dimensional regularisation." Physics Letters B 420, no. 3-4 (February 1998): 391–96. http://dx.doi.org/10.1016/s0370-2693(97)01537-2.

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Johannes, Jan, Sébastien Van Bellegem, and Anne Vanhems. "Iterative regularisation in nonparametric instrumental regression." Journal of Statistical Planning and Inference 143, no. 1 (January 2013): 24–39. http://dx.doi.org/10.1016/j.jspi.2012.07.010.

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