JabRef References output

Author	Title	Year	Journal/Proceedings	Reftype	DOI/URL
Loris, I. & Verhoeven, C.	An iterative algorithm for sparse and constrained recovery with applications to divergence-free current reconstructions in magneto-encephalography [Abstract] [BibTeX]	2012	Computational Optimization and Applications	article	DOI URL
Abstract: We propose an iterative algorithm for the minimization of a $1$-norm penalized least squares functional, under additional linear constraints. The algorithm is fully explicit: it uses only matrix multiplications with the three matrices present in the problem (in the linear constraint, in the data misfit part and in penalty term of the functional). None of the three matrices must be invertible. Convergence is proven in a finite-dimensional setting. We apply the algorithm to a synthetic problem in magneto-encephalography where it is used for the reconstruction of divergence-free current densities subject to a sparsity promoting penalty on the wavelet coefficients of the current densities. We discuss the effects of imposing zero divergence and of imposing joint sparsity (of the vector components of the current density) on the current density reconstruction.
BibTeX: @article{Loris2011, author = {Ignace Loris and Caroline Verhoeven}, title = {An iterative algorithm for sparse and constrained recovery with applications to divergence-free current reconstructions in magneto-encephalography}, journal = {Computational Optimization and Applications}, year = {2012}, note = {Special Issue on Optimization methods for inverse problems in imaging. Online first.}, url = {http://arxiv.org/abs/1202.3362}, doi = {http://dx.doi.org/10.1007/s10589-012-9482-y} }
Loris, I. & Verhoeven, C.	Iterative algorithms for total variation-like reconstructions in seismic tomography [Abstract] [BibTeX]	2012	International Journal on Geomathematics Vol. 3	article	DOI URL
Abstract: A qualitative comparison of total variation like penalties (total variation, Huber variant of total variation, total generalized variation, is made in the context of global seismic tomography. Both penalized and constrained formulations of seismic recovery problems are treated. A number of simple iterative recovery algorithms applicable to these problems are described. The convergence speed of these algorithms is compared numerically in this setting. For the constrained formulation a new algorithm is proposed and its convergence is proven.
BibTeX: @article{Loris2012, author = {Ignace Loris and Caroline Verhoeven}, title = {Iterative algorithms for total variation-like reconstructions in seismic tomography}, journal = {International Journal on Geomathematics}, year = {2012}, volume = {3}, note = {Online first.}, url = {http://arxiv.org/abs/1203.4451}, doi = {http://dx.doi.org/10.1007/s13137-012-0036-3} }
Loris, I. & Verhoeven, C.	On a generalization of the iterative soft-thresholding algorithm for the case of non-separable penalty [Abstract] [BibTeX]	2011	Inverse Problems Vol. 27, pp. 125007	article	DOI URL
Abstract: An explicit algorithm for the minimization of an $1$ penalized least squares functional, with non-separable $1$ term, is proposed. Each step in the iterative algorithm requires four matrix vector multiplications and a single simple projection on a convex set (or equivalently thresholding). Convergence is proven and a $1/N$ convergence rate is derived for the functional. In the special case where the matrix in the $1$ term is the identity (or orthogonal), the algorithm reduces to the traditional iterative soft-thresholding algorithm. In the special case where the matrix in the quadratic term is the identity (or orthogonal), the algorithm reduces to a gradient projection algorithm for the dual problem. By replacing the projection with a simple proximity operator, other convex non-separable penalties than those based on an $1$-norm can be handled as well.
BibTeX: @article{Loris.Verhoeven2011, author = {Ignace Loris and Caroline Verhoeven}, title = {On a generalization of the iterative soft-thresholding algorithm for the case of non-separable penalty}, journal = {Inverse Problems}, year = {2011}, volume = {27}, pages = {125007}, url = {http://arxiv.org/abs/1104.1087}, doi = {http://dx.doi.org/10.1088/0266-5611/27/12/125007} }
Simons, F.J., Loris, I., Nolet, G., Daubechies, I.C., Voronin, S., Judd, J.S., Vetter, P.A., Charléty, J. & Vonesch, C.	Solving or resolving global tomographic models with spherical wavelets, and the scale and sparsity of seismic heterogeneity [Abstract] [BibTeX]	2011	Geophysical Journal International Vol. 187(2), pp. 969-988	article	DOI URL
Abstract: We propose a class of spherical wavelet bases for the analysis of geophysical models and for the tomographic inversion of global seismic data. Its multiresolution character allows for modeling with an effective spatial resolution that varies with position within the Earth. Our procedure is numerically efficient and can be implemented with parallel computing.We discuss two possible types of discrete wavelet transforms in the angular dimension of the cubed sphere. We discuss benefits and drawbacks of these constructions and apply them to analyze the information present in two published seismic wavespeed models of the mantle, for the statistics and power of wavelet coefficients across scales. The localization and sparsity properties of wavelet bases allow finding a sparse solution to inverse problems by iterative minimization of a combination of the $2$ norm of data fit and the $1$ norm on the wavelet coefficients. By validation with realistic synthetic experiments we illustrate the likely gains of our new approach in future inversions of finite-frequency seismic data and show its readiness for global seismic tomography
BibTeX: @article{Simons.Loris.ea2011, author = {Frederik J. Simons and Ignace Loris and Guust Nolet and Ingrid C. Daubechies and S. Voronin and J. S. Judd and P. A. Vetter and J. Charléty and C. Vonesch}, title = {Solving or resolving global tomographic models with spherical wavelets, and the scale and sparsity of seismic heterogeneity}, journal = {Geophysical Journal International}, year = {2011}, volume = {187}, number = {2}, pages = {969--988}, url = {http://arxiv.org/abs/1104.3151}, doi = {http://dx.doi.org/10.1111/j.1365-246X.2011.05190.x} }
Simons, F.J., Loris, I., Brevdo, E. & Daubechies, I.C.	Wavelets and wavelet-like transforms on the sphere and their application to geophysical data inversion [Abstract] [BibTeX]	2011	Vol. 8138Wavelets and Sparsity~XIV, pp. X1-X15	inproceedings	DOI URL
Abstract: Many flexible parameterizations exist to represent data on the sphere. In addition to the venerable spherical harmonics, we have the Slepian basis, harmonic splines, wavelets and wavelet-like Slepian frames. In this paper we focus on the latter two: spherical wavelets developed for geophysical applications on the cubed sphere, and the Slepian ``tree'', a new construction that combines a quadratic concentration measure with wavelet-like multiresolution. We discuss the basic features of these mathematical tools, and illustrate their applicability in parameterizing large-scale global geophysical (inverse) problems.
BibTeX: @inproceedings{Simons2011, author = {Frederik J. Simons and Ignace Loris and Eugene Brevdo and Ingrid C. Daubechies}, title = {Wavelets and wavelet-like transforms on the sphere and their application to geophysical data inversion}, booktitle = {Wavelets and Sparsity~XIV}, publisher = {SPIE}, year = {2011}, volume = {8138}, pages = {X1--X15}, url = {http://arxiv.org/abs/1109.1718}, doi = {http://dx.doi.org/10.1117/12.892285} }
Loris, I., Douma, H., Nolet, G., Daubechies, I. & Regone, C.	Nonlinear regularization techniques for seismic tomography [Abstract] [BibTeX]	2010	Journal of Computational Physics Vol. 229, pp. 890-905	article	DOI URL
Abstract: The effects of several nonlinear regularization techniques are discussed in the framework of 3D seismic tomography. Traditional, linear, $2$ penalties are compared to so-called sparsity promoting $1$ and $0$ penalties, and a total variation penalty. Which of these algorithms is judged optimal depends on the specific requirements of the scientific experiment. If the correct reproduction of model amplitudes is important, classical damping towards a smooth model using an $2$ norm works almost as well as minimizing the total variation but is much more efficient. If gradients (edges of anomalies) should be resolved with a minimum of distortion, we prefer $1$ damping of Daubechies-4 wavelet coefficients. It has the additional advantage of yielding a noiseless reconstruction, contrary to simple $2$ minimization (`Tikhonov regularization') which should be avoided. In some of our examples, the $0$ method produced notable artifacts. In addition we show how nonlinear $1$ methods for finding sparse models can be competitive in speed with the widely used $2$ methods, certainly under noisy conditions, so that there is no need to shun $1$ penalizations.
BibTeX: @article{Loris.Douma.ea2009, author = {Loris, I. and Douma, H. and Nolet, G. and Daubechies, I. and Regone, C.}, title = {Nonlinear regularization techniques for seismic tomography}, journal = {Journal of Computational Physics}, year = {2010}, volume = {229}, pages = {890--905}, url = {http://arxiv.org/abs/0808.3472}, doi = {http://dx.doi.org/10.1016/j.jcp.2009.10.020} }
Loris, I. & Verhoeven, C.	Practical error estimates for sparse recovery in linear inverse problems. [Abstract] [BibTeX]	2010		techreport	URL
Abstract: The effectiveness of using model sparsity as a priori information when solving linear inverse problems is studied. We investigate the reconstruction quality of such a method in the non-idealized case and compute some typical recovery errors (depending on the sparsity of the desired solution, the number of data, the noise level on the data, and various properties of the measurement matrix); they are compared to known theoretical bounds and illustrated on a magnetic tomography example.
BibTeX: @techreport{Loris.Verhoeven2010, author = {Ignace Loris and Caroline Verhoeven}, title = {Practical error estimates for sparse recovery in linear inverse problems.}, year = {2010}, url = {http://arxiv.org/abs/0908.3636} }
Brodie, J., Daubechies, I., De Mol, C., Giannone, D. & Loris, I.	Sparse and stable Markowitz portfolios [Abstract] [BibTeX]	2009	Proceedings of the National Academy of Sciences of the USA Vol. 106(30), pp. 12267-12272	article	DOI URL
Abstract: We consider the problem of portfolio selection within the classical Markowitz mean-variance framework, reformulated as a constrained least-squares regression problem. We propose to add to the objective function a penalty proportional to the sum of the absolute values of the portfolio weights. This penalty regularizes (stabilizes) the optimization problem, encourages sparse portfolios (i.e. portfolios with only few active positions), and allows to account for transaction costs. Our approach recovers as special cases the no-short-positions portfolios, but does allow for short positions in limited number. We implement this methodology on two benchmark data sets constructed by Fama and French. Using only a modest amount of training data, we construct portfolios whose out-of-sample performance, as measured by Sharpe ratio, is consistently and significantly better than that of the naive evenly-weighted portfolio which constitutes, as shown in recent literature, a very tough benchmark.
BibTeX: @article{Brodie.Daubechies.ea2009, author = {Brodie, Joshua and Daubechies, Ingrid and De Mol, Christine and Giannone, Domenico and Loris, Ignace}, title = {Sparse and stable Markowitz portfolios}, journal = {Proceedings of the National Academy of Sciences of the USA}, year = {2009}, volume = {106}, number = {30}, pages = {12267--12272}, url = {http://arxiv.org/abs/0708.0046}, doi = {http://dx.doi.org/10.1073/pnas.0904287106} }
Loris, I., Bertero, M., De Mol, C., Zanella, R. & Zanni, L.	Accelerating gradient projection methods for $1$- constrained signal recovery by steplength selection rules [Abstract] [BibTeX]	2009	Applied and Computational Harmonic Analysis Vol. 27, pp. 247-254	article	DOI URL
Abstract: We propose a new gradient projection algorithm that compares favorably with the fastest algorithms available to date for $1$-constrained sparse recovery from noisy data, both in the compressed sensing and inverse problem frameworks. The method exploits a line-search along the feasible direction and an adaptive steplength selection based on recent strategies for the alternation of the well-known Barzilai-Borwein rules. The convergence of the proposed approach is discussed and a computational study on both well-conditioned and ill-conditioned problems is carried out for performance evaluations in comparison with five other algorithms proposed in the literature.
BibTeX: @article{Loris.Bertero.ea2009, author = {Loris, I. and Bertero, M. and De Mol, C. and Zanella, R. and Zanni, L.}, title = {Accelerating gradient projection methods for $1$- constrained signal recovery by steplength selection rules}, journal = {Applied and Computational Harmonic Analysis}, year = {2009}, volume = {27}, pages = {247--254}, url = {http://arxiv.org/abs/0902.4424}, doi = {http://dx.doi.org/10.1016/j.acha.2009.02.003} }
Loris, I.	On the performance of algorithms for the minimization of $1$-penalized functionals [Abstract] [BibTeX]	2009	Inverse Problems Vol. 25, pp. 035008 (16pp)	article	DOI URL
Abstract: The problem of assessing the performance of algorithms used for the minimization of an $1$-penalized least-squares functional, for a range of penalty parameters, is investigated. A criterion that uses the idea of `approximation isochrones' is introduced. Five different iterative minimization algorithms are tested and compared, as well as two warm-start strategies. Both well-conditioned and ill-conditioned problems are used in the comparison, and the contrast between these two categories is highlighted.
BibTeX: @article{Loris2009, author = {Loris, Ignace}, title = {On the performance of algorithms for the minimization of $1$-penalized functionals}, journal = {Inverse Problems}, year = {2009}, volume = {25}, pages = {035008 (16pp)}, url = {http://arxiv.org/abs/0710.4082}, doi = {http://dx.doi.org/10.1088/0266-5611/25/3/035008} }
Daubechies., I., Fornasier, M. & Loris, I.	Accelerated projected gradient method for linear inverse problems with sparsity constraints [Abstract] [BibTeX]	2008	Journal of Fourier Analysis and Applications Vol. 14, pp. 764-792	article	DOI URL
Abstract: Regularization of ill-posed linear inverse problems via $1$ penalization has been proposed for cases where the solution is known to be (almost) sparse. One way to obtain the minimizer of such an $1$ penalized functional is via an iterative soft-thresholding algorithm. We propose an alternative implementation to $1$-constraints, using a gradient method, with projection on $1$-balls. The corresponding algorithm uses again iterative soft-thresholding, now with a variable thresholding parameter. We also propose accelerated versions of this iterative method, using ingredients of the (linear) steepest descent method. We prove convergence in norm for one of these projected gradient methods, without and with acceleration.
BibTeX: @article{Daubechies.Fornasier.ea2008, author = {Ingrid Daubechies. and Massimo Fornasier and Ignace Loris}, title = {Accelerated projected gradient method for linear inverse problems with sparsity constraints}, journal = {Journal of Fourier Analysis and Applications}, year = {2008}, volume = {14}, pages = {764--792}, url = {http://arxiv.org/abs/0706.4297}, doi = {http://dx.doi.org/10.1007/s00041-008-9039-8} }
Loris, I.	L1Packv2: A Mathematica package for minimizing an $1$-penalized functional [Abstract] [BibTeX]	2008	Computer Physics Communications Vol. 179, pp. 895-902	article	DOI URL
Abstract: L1Packv2 is a Mathematica package that contains a number of algorithms that can be used for the minimization of an $1$-penalized least squares functional. The algorithms can handle a mix of penalized and unpenalized variables. Several instructive examples are given. Also, an implementation that yields an exact output whenever exact data are given is provided.
BibTeX: @article{Loris2008, author = {Loris, Ignace}, title = {L1Packv2: A Mathematica package for minimizing an $1$-penalized functional}, journal = {Computer Physics Communications}, year = {2008}, volume = {179}, pages = {895--902}, url = {http://arxiv.org/abs/0710.3728}, doi = {http://dx.doi.org/10.1016/j.cpc.2008.07.010} }
Loris, I., Nolet, G., Daubechies, I. & Dahlen, F.A.	Tomographic inversion using $1$-norm regularization of wavelet coefficients [Abstract] [BibTeX]	2007	Geophysical Journal International Vol. 170(1), pp. 359-370	article	DOI URL
Abstract: We propose the use of $1$ regularization in a wavelet basis for the solution of linearized seismic tomography problems $Am=, allowing for the possibility of sharp discontinuities superimposed on a smoothly varying background. An iterative method is used to find a sparse solution $ that contains no more fine-scale structure than is necessary to fit the data $ to within its assigned errors.
BibTeX: @article{Loris.Nolet.ea2007, author = {Loris, Ignace and Nolet,Guust and Daubechies, Ingrid and Dahlen, F. A.}, title = {Tomographic inversion using $1$-norm regularization of wavelet coefficients}, journal = {Geophysical Journal International}, year = {2007}, volume = {170}, number = {1}, pages = {359--370}, url = {http://arxiv.org/abs/physics/0608094}, doi = {http://dx.doi.org/10.1111/j.1365-246X.2007.03409.x} }
Khare, A., Loris, I. & Sasaki, R.	Affine Toda-Sutherland systems [BibTeX]	2004	Journal of Physics A-Mathematical and General Vol. 37(5), pp. 1665-1679	article	DOI URL
BibTeX: @article{Khare.Loris.ea2004, author = {Khare, A. and Loris, I. and Sasaki, R.}, title = {Affine Toda-Sutherland systems}, journal = {Journal of Physics A-Mathematical and General}, year = {2004}, volume = {37}, number = {5}, pages = {1665--1679}, url = {http://arxiv.org/abs/hep-th/0309077}, doi = {http://dx.doi.org/10.1088/0305-4470/37/5/013} }
Loris, I. & Sasaki, R.	Quantum and classical eigenfunctions in Calogero and Sutherland systems [BibTeX]	2004	Journal of Physics A-Mathematical and General Vol. 37(1), pp. 211-237	article	DOI URL
BibTeX: @article{Loris.Sasaki2004, author = {Loris, I. and Sasaki, R.}, title = {Quantum and classical eigenfunctions in Calogero and Sutherland systems}, journal = {Journal of Physics A-Mathematical and General}, year = {2004}, volume = {37}, number = {1}, pages = {211--237}, url = {http://arxiv.org/abs/hep-th/0308052}, doi = {http://dx.doi.org/10.1088/0305-4470/37/1/015} }
Loris, I. & Sasaki, R.	Quantum vs classical mechanics: role of elementary excitations [BibTeX]	2004	Physics Letters A Vol. 327(2-3), pp. 152-157	article	DOI URL
BibTeX: @article{Loris.Sasaki2004a, author = {Loris, I. and Sasaki, R.}, title = {Quantum vs classical mechanics: role of elementary excitations}, journal = {Physics Letters A}, year = {2004}, volume = {327}, number = {2-3}, pages = {152--157}, url = {http://arxiv.org/abs/quant-ph/0308040}, doi = {http://dx.doi.org/10.1016/j.physleta.2004.05.015} }
Loris, I.	Bilinear representations of integrable equations [BibTeX]	2002	Theoretical and Mathematical Physics Vol. 133(2), pp. 1549-1556	article	DOI
BibTeX: @article{Loris2002, author = {Loris, I.}, title = {Bilinear representations of integrable equations}, journal = {Theoretical and Mathematical Physics}, year = {2002}, volume = {133}, number = {2}, pages = {1549--1556}, note = {Proceedings of the NEEDS'01 Conference.}, doi = {http://dx.doi.org/10.1023/A:1021103012057} }
Lambert, F., Loris, I. & Springael, J.	Classical Darboux transformations and the KP hierarchy [BibTeX]	2001	Inverse Problems Vol. 17(4), pp. 1067-1074	article	DOI
BibTeX: @article{Lambert.Loris.ea2001, author = {Lambert, F. and Loris, I. and Springael, J.}, title = {Classical Darboux transformations and the KP hierarchy}, journal = {Inverse Problems}, year = {2001}, volume = {17}, number = {4}, pages = {1067--1074}, doi = {http://dx.doi.org/10.1088/0266-5611/17/4/333} }
Lambert, F., Loris, I., Springael, J. & Willox, R.	On the Hirota representation of soliton equations with one tau-function [BibTeX]	2001	Journal of the Physical Society of Japan Vol. 70(3), pp. 605-608	article	DOI
BibTeX: @article{Lambert.Loris.ea2001a, author = {Lambert, F. and Loris, I. and Springael, J. and Willox, R.}, title = {On the Hirota representation of soliton equations with one tau-function}, journal = {Journal of the Physical Society of Japan}, year = {2001}, volume = {70}, number = {3}, pages = {605--608}, doi = {http://dx.doi.org/10.1143/JPSJ.70.605} }
Loris, I.	Dimensional reductions of BKP and CKP hierarchies [BibTeX]	2001	Journal of Physics A-Mathematical and General Vol. 34(16), pp. 3447-3459	article	DOI
BibTeX: @article{Loris2001, author = {Loris, I.}, title = {Dimensional reductions of BKP and CKP hierarchies}, journal = {Journal of Physics A-Mathematical and General}, year = {2001}, volume = {34}, number = {16}, pages = {3447--3459}, doi = {http://dx.doi.org/10.1088/0305-4470/34/16/313} }
Loris, I.	Solutions of coupled Korteweg-de Vries systems [BibTeX]	2001	Journal of the Physical Society of Japan Vol. 70(3), pp. 662-665	article	DOI
BibTeX: @article{Loris2001a, author = {Loris, I.}, title = {Solutions of coupled Korteweg-de Vries systems}, journal = {Journal of the Physical Society of Japan}, year = {2001}, volume = {70}, number = {3}, pages = {662--665}, doi = {http://dx.doi.org/10.1143/JPSJ.70.662} }
Loris, I.	Recursion operator for a constrained BKP system [BibTeX]	2000	Proceedings of the workshop on Nonlinearity, integrability, and all that: 20 years after NEEDS '79, pp. 325-330	inproceedings
BibTeX: @inproceedings{Loris2000, author = {Loris, Ignace}, title = {Recursion operator for a constrained BKP system}, booktitle = {Proceedings of the workshop on Nonlinearity, integrability, and all that: 20 years after NEEDS '79}, publisher = {World Scientific, Singapore}, year = {2000}, pages = {325--330} }
Loris, I. & Willox, R.	Symmetry reductions of the BKP hierarchy [BibTeX]	1999	Journal of Mathematical Physics Vol. 40(3), pp. 1420-1431	article	DOI
BibTeX: @article{Loris.Willox1999, author = {Loris, I. and Willox, R.}, title = {Symmetry reductions of the BKP hierarchy}, journal = {Journal of Mathematical Physics}, year = {1999}, volume = {40}, number = {3}, pages = {1420--1431}, doi = {http://dx.doi.org/10.1063/1.532812} }
Loris, I.	On reduced CKP equations [BibTeX]	1999	Inverse Problems Vol. 15(4), pp. 1099-1109	article	DOI
BibTeX: @article{Loris1999, author = {Loris, I.}, title = {On reduced CKP equations}, journal = {Inverse Problems}, year = {1999}, volume = {15}, number = {4}, pages = {1099--1109}, doi = {http://dx.doi.org/10.1088/0266-5611/15/4/317} }
Willox, R. & Loris, I.	KP constraints from reduced multi-component hierarchies [BibTeX]	1999	Journal of Mathematical Physics Vol. 40(12), pp. 6501-6525	article	DOI
BibTeX: @article{Willox.Loris1999, author = {Willox, R. and Loris, I.}, title = {KP constraints from reduced multi-component hierarchies}, journal = {Journal of Mathematical Physics}, year = {1999}, volume = {40}, number = {12}, pages = {6501--6525}, doi = {http://dx.doi.org/10.1063/1.533104} }
Willox, R. & Loris, I.	An algebraic description of generalized k-constraints [BibTeX]	1999	Journal of Physics A-Mathematical and General Vol. 32(10), pp. 2027-2036	article	DOI
BibTeX: @article{Willox.Loris1999a, author = {Willox, R. and Loris, I.}, title = {An algebraic description of generalized k-constraints}, journal = {Journal of Physics A-Mathematical and General}, year = {1999}, volume = {32}, number = {10}, pages = {2027--2036}, doi = {http://dx.doi.org/10.1088/0305-4470/32/10/018} }
Loris, I.	Symmetry reductions in the tau-function approach to integrability [BibTeX]	1998	School: Vrije Universiteit Brussel	phdthesis
BibTeX: @phdthesis{Loris1998, author = {Loris, Ignace}, title = {Symmetry reductions in the tau-function approach to integrability}, school = {Vrije Universiteit Brussel}, year = {1998} }
Willox, R., Tokihiro, T., Loris, I. & Satsuma, J.	The fermionic approach to Darboux transformations [BibTeX]	1998	Inverse Problems Vol. 14(3), pp. 745-762	article	DOI
BibTeX: @article{Willox.Tokihiro.ea1998, author = {Willox, R. and Tokihiro, T. and Loris, I. and Satsuma, J.}, title = {The fermionic approach to Darboux transformations}, journal = {Inverse Problems}, year = {1998}, volume = {14}, number = {3}, pages = {745--762}, doi = {http://dx.doi.org/10.1088/0266-5611/14/3/022} }
Loris, I. & Willox, R.	On solutions of constrained Kadomtsev-Petviashvili equations: Grammians [BibTeX]	1997	Journal of Mathematical Physics Vol. 38(10), pp. 5190-5197	article	DOI
BibTeX: @article{Loris.Willox1997, author = {Loris, I. and Willox, R.}, title = {On solutions of constrained Kadomtsev-Petviashvili equations: Grammians}, journal = {Journal of Mathematical Physics}, year = {1997}, volume = {38}, number = {10}, pages = {5190--5197}, doi = {http://dx.doi.org/10.1063/1.531937} }
Loris, I. & Willox, R.	KP symmetry reductions and a generalized constraint [BibTeX]	1997	Journal of Physics A-Mathematical and General Vol. 30(19), pp. 6925-6938	article	DOI
BibTeX: @article{Loris.Willox1997a, author = {Loris, I. and Willox, R.}, title = {KP symmetry reductions and a generalized constraint}, journal = {Journal of Physics A-Mathematical and General}, year = {1997}, volume = {30}, number = {19}, pages = {6925--6938}, doi = {http://dx.doi.org/10.1088/0305-4470/30/19/027} }
Loris, I. & Willox, R.	On solutions of constrained KP equations [BibTeX]	1997	Journal of Mathematical Physics Vol. 38(1), pp. 283-291	article	DOI
BibTeX: @article{Loris.Willox1997b, author = {Loris, I. and Willox, R.}, title = {On solutions of constrained KP equations}, journal = {Journal of Mathematical Physics}, year = {1997}, volume = {38}, number = {1}, pages = {283--291}, doi = {http://dx.doi.org/10.1063/1.531843} }
Loris, I. & Willox, R.	Bilinear form and solutions of the $k$-constrained Kadomtsev-Petviashvili hierarchy [BibTeX]	1997	Inverse Problems Vol. 13(2), pp. 411-420	article	DOI
BibTeX: @article{Loris.Willox1997c, author = {Loris, I. and Willox, R.}, title = {Bilinear form and solutions of the $k$-constrained Kadomtsev-Petviashvili hierarchy}, journal = {Inverse Problems}, year = {1997}, volume = {13}, number = {2}, pages = {411--420}, doi = {http://dx.doi.org/10.1088/0266-5611/13/2/014} }
Loris, I. & Willox, R.	Recent results on dimensional reductions of the Kadomtsev-Petviashvili equation [BibTeX]	1997	Proceedings of the Fourth National Conference on Theoretical and Applied Mechanics, pp. 27-30	inproceedings
BibTeX: @inproceedings{Loris.Willox1997d, author = {Loris, Ignace and Willox, Ralph}, title = {Recent results on dimensional reductions of the Kadomtsev-Petviashvili equation}, booktitle = {Proceedings of the Fourth National Conference on Theoretical and Applied Mechanics}, year = {1997}, pages = {27--30} }
Pelinovsky, D., Springael, J., Lambert, F. & Loris, I.	On modified NLS, Kaup and NLBq equations: differential transformations and bilinearization [BibTeX]	1997	Journal of Physics A-Mathematical and General Vol. 30(24), pp. 8705-8717	article	DOI
BibTeX: @article{Pelinovsky.Springael.ea1997, author = {Pelinovsky, D. and Springael, J. and Lambert, F. and Loris, I.}, title = {On modified NLS, Kaup and NLBq equations: differential transformations and bilinearization}, journal = {Journal of Physics A-Mathematical and General}, year = {1997}, volume = {30}, number = {24}, pages = {8705--8717}, doi = {http://dx.doi.org/10.1088/0305-4470/30/24/029} }
Willox, R., Loris, I. & Gilson, C.R.	Binary Darboux transformations for constrained KP hierarchies [BibTeX]	1997	Inverse Problems Vol. 13(3), pp. 849-865	article	DOI
BibTeX: @article{Willox.Loris.ea1997, author = {Willox, R. and Loris, I. and Gilson, C. R.}, title = {Binary Darboux transformations for constrained KP hierarchies}, journal = {Inverse Problems}, year = {1997}, volume = {13}, number = {3}, pages = {849--865}, doi = {http://dx.doi.org/10.1088/0266-5611/13/3/019} }
Loris, I., Lambert, F. & Willox, R.	New ways of applying the Hirota method in soliton theory [BibTeX]	1996	Journal of Technical Physics Vol. 37, pp. 519-522	article
BibTeX: @article{Loris.Lambert.ea1996, author = {Loris, I. and Lambert, F. and Willox, R.}, title = {New ways of applying the Hirota method in soliton theory}, journal = {Journal of Technical Physics}, year = {1996}, volume = {37}, pages = {519--522}, note = {Proceedings of the Conference on Nonlinear Dynamics, Chaotic and Complex Systems (NDCCS'95), Zakopane, Poland.} }
Loris, I. & Willox, R.	Soliton solutions of Wronskian form to the nonlocal Boussinesq equation [BibTeX]	1996	Journal of the Physical Society of Japan Vol. 65(2), pp. 383-388	article	DOI
BibTeX: @article{Loris.Willox1996, author = {Loris, I. and Willox, R.}, title = {Soliton solutions of Wronskian form to the nonlocal Boussinesq equation}, journal = {Journal of the Physical Society of Japan}, year = {1996}, volume = {65}, number = {2}, pages = {383--388}, doi = {http://dx.doi.org/10.1143/JPSJ.65.383} }
Springael, J., Hu, X.B. & Loris, I.	Bilinear characterization of higher order Ito-equations [BibTeX]	1996	Journal of the Physical Society of Japan Vol. 65(5), pp. 1222-1226	article	DOI
BibTeX: @article{Springael.Hu.ea1996, author = {Springael, J. and Hu, X. B. and Loris, I.}, title = {Bilinear characterization of higher order Ito-equations}, journal = {Journal of the Physical Society of Japan}, year = {1996}, volume = {65}, number = {5}, pages = {1222--1226}, doi = {http://dx.doi.org/10.1143/JPSJ.65.1222} }
Willox, R., Loris, I. & Springael, J.	The nlBq-hierarchy as a $pq=C$ reduction of the KP-hierarchy [BibTeX]	1996	Proceedings of the Workshop``Non-linear Physics, Theory and Experiment", pp. 321-329	inproceedings
BibTeX: @inproceedings{Willox.Loris.ea1996, author = {Willox, R. and Loris, I. and Springael, J.}, title = {The nlBq-hierarchy as a $pq=C$ reduction of the KP-hierarchy}, booktitle = {Proceedings of the Workshop``Non-linear Physics, Theory and Experiment"}, publisher = {World Scientific, Singapore}, year = {1996}, pages = {321--329} }
Willox, R. & Loris, I.	Symmetry constraints of the KP hierarchy and a nonlocal Boussinesq equation [BibTeX]	1996	Vol. 2VII International Conference Symmetry Methods in Physics, pp. 603-609	inproceedings
BibTeX: @inproceedings{Willox.Loris1996, author = {Willox, R. and Loris, I.}, title = {Symmetry constraints of the KP hierarchy and a nonlocal Boussinesq equation}, booktitle = {VII International Conference Symmetry Methods in Physics}, publisher = {Joint Institute for Nuclear Research}, year = {1996}, volume = {2}, pages = {603--609} }
Lambert, F., Loris, I., Springael, J. & Willox, R.	A direct bilinearization scheme based on the use of partition polynomials [BibTeX]	1995	Proceedings of the NEEDS'94 workshop at Los Alamos NL, pp. 102-111	inproceedings
BibTeX: @inproceedings{Lambert.Loris.ea1995, author = {Lambert, F. and Loris, I. and Springael, J. and Willox, R.}, title = {A direct bilinearization scheme based on the use of partition polynomials}, booktitle = {Proceedings of the NEEDS'94 workshop at Los Alamos NL}, publisher = {World Scientific, Singapore}, year = {1995}, pages = {102--111} }
Willox, R., Loris, I. & Springael, J.	Bilinearization of the nonlocal Boussinesq equation [BibTeX]	1995	Journal of Physics A-Mathematical and General Vol. 28(20), pp. 5963-5972	article	DOI
BibTeX: @article{Willox.Loris.ea1995, author = {Willox, R. and Loris, I. and Springael, J.}, title = {Bilinearization of the nonlocal Boussinesq equation}, journal = {Journal of Physics A-Mathematical and General}, year = {1995}, volume = {28}, number = {20}, pages = {5963--5972}, doi = {http://dx.doi.org/10.1088/0305-4470/28/20/024} }
Lambert, F., Loris, I., Springael, J. & Willox, R.	On a direct bilinearization method - Kaup's higher-order water-wave equation as a modified nonlocal Boussinesq equation [BibTeX]	1994	Journal of Physics A-Mathematical and General Vol. 27(15), pp. 5325-5334	article	DOI
BibTeX: @article{Lambert.Loris.ea1994, author = {Lambert, F. and Loris, I. and Springael, J. and Willox, R.}, title = {On a direct bilinearization method - Kaup's higher-order water-wave equation as a modified nonlocal Boussinesq equation}, journal = {Journal of Physics A-Mathematical and General}, year = {1994}, volume = {27}, number = {15}, pages = {5325--5334}, doi = {http://dx.doi.org/10.1088/0305-4470/27/15/028} }
Loris, I.	Rechtstreekse bilinearisatie van solitonsystemen: Een systematische aanpak met veralgemeende Bell-polynomen [BibTeX]	1994	School: Vrije Universiteit Brussel	mastersthesis
BibTeX: @mastersthesis{Loris1994, author = {Loris, Ignace}, title = {Rechtstreekse bilinearisatie van solitonsystemen: Een systematische aanpak met veralgemeende Bell-polynomen}, school = {Vrije Universiteit Brussel}, year = {1994} }

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