
	Where results make sense

Topic: Regularization (mathematics)

	Applied and Computational Mathematics (ACM) Seminar
		Because of the substantial variations in the operating parameters and water properties along the channel, the membrane filtration system presents strong nonlinear behaviors that cannot be adequately explained within the framework of the classic membrane filtration theories.
		Mathematical model for the heterogeneous membrane system is first developed.
		Moreover, the use of total variation is of two-fold: it induces regularization in regions where the pixels are observed and induces inpainting in regions where the pixels are missing.
	www.math.nus.edu.sg /~bao/acm/acm.htm (1984 words)

	Regularization - Wikipedia, the free encyclopedia
		The mathematical term regularization has two main meanings, both associated with making a mathematical more 'regular' or smooth.
		In linguistics, regularization is the process of making irregular forms regular (e.g., "oxen" becomes "oxes;" "grew" becomes "growed").
		Regularization is also the act of giving legal residency and identity documents to an illegal alien.
	en.wikipedia.org /wiki/Regularization (121 words)

	Early stopping - Wikipedia, the free encyclopedia
		In machine learning, early stopping is a form of regularization used when a machine learning model (such as a neural network) is trained by on-line gradient descent.
		Overfitting is a phenomenon in which a learning system, such as a neural network gets very good at dealing with one data set at the expense of becoming very bad at dealing with other data sets.
		Early stopping is effectively limiting the used weights in the network and thus imposes a regularization, effectively lowering the VC dimension.
	en.wikipedia.org /wiki/Early_stopping (223 words)

	UBC Mathematics Department - Colloquium (Site not responding. Last check: 2007-11-01)
		In 1989 Engl & Kunisch & Neubauer and Seidman & Vogel developed a regularization theory for non-linear inverse problems where F is a non-linear, differentiable operator.
		The analysis of bounded variation regularization is significantly more involved since the penalization functional is not differentiable.
		Another complication is introduced in the analysis of regularization functionals if for instance the operator F can be decomposed into a continuous and a discontinuous operator.
	www.math.ubc.ca /Dept/Events/colloquia/Scherzer.html (270 words)

	F1308
		Regularization of parameter estimation by adaptive discretization using refinement and coarsening indicators.
		Stability and convergence analysis of Tikhonov regularization for parameter identification in a parabolic equation.
		Regularization by projection with a posteriori discretization level choice for linear and nonlinear ill-posed problems.
	www.sfb013.uni-linz.ac.at /~sfb/publications/F1308.html (3050 words)

	Age of Enlightenment - Wikipedia, the free encyclopedia
		The ideas of Newton, which combined the mathematics of axiomatic proof with the mechanics of physical observation, resulted in a coherent system of verifiable predictions and set the tone for much of what would follow in the century after the publication of his Philosophiae Naturalis Principia Mathematica.
		Sir Isaac Newton's greatest claim to prominence came from a systematic application of algebra to geometry, and synthesizing a workable calculus which was applicable to scientific problems.
		The "Enlightened Despotism" of, for example, Catherine the Great of Russia and Frederick the Great of Prussia (a state within The Holy Roman Empire of the German Nation), is not based on mystical appeals to authority, but on the pragmatic invocation of state power as necessary to hold back chaotic and anarchic warfare and rebellion.
	en.wikipedia.org /wiki/The_Enlightenment (3051 words)

	SISC Volume 23 Issue 6
		Special techniques known as regularization methods are needed to treat these problems in order to control the effect of the noise on the solution.
		This formulation is equivalent to Tikhonov regularization, and we note that it is also a special case of the trust-region subproblem from optimization.
		We analyze the trust-region subproblem in the regularization case and we consider the nontrivial extensions of a recently developed method for general large-scale subproblems that will allow us to handle this case.
	epubs.siam.org /SISC/volume-23/art_37816.html (265 words)

	Brian Spencer
		The long term objective of this research is to develop mathematical models to predict and control morphology development in strained solid films, which are of importance in emerging semiconductor device applications.
		The mathematical challenge of the work is to develop solutions for a nonlinear free boundary problem in which the development of the film shape and composition nonuniformities is coupled to the elastic strain in the material.
		This regularization is a nonlinear singular perturbation, and the connection between the regularized and unregularized behavior has not been firmly established.
	www.math.buffalo.edu /~spencerb/alloyfilm.html (1720 words)

	Sheaf (mathematics) Encyclopedia (Site not responding. Last check: 2007-11-01)
		In mathematics, a sheaf is the basic tool for expressing relationships between small regions of a space and large regions.
		It is still common in some areas of mathematics such as mathematical analysis.
		At this point sheaves had become a mainstream part of mathematics, with use by no means restricted to algebraic topology.
	www.hallencyclopedia.com /topic/Sheaf_(mathematics).html (5563 words)

	Math Department
		Alexandru Tamasan, Department of Mathematics, University of Central Florida
		Jonathan Leto, Department of Mathematics, University of Central Florida
		Copyright(c) 2003, University of Central Florida, Department of Mathematics.
	math.ucf.edu (159 words)

	Curriculum Vitae of Vladimir Dobrushkin
		Regularization and numerical calculation of singular and hypersingular integrals.
		A new method of regularization and approximate calculation of hypersingular integrals and integro-differential expressions with singularities was proposed.
		Regularization and approximate calculation of the Marchaud's derivative of a two-dimensional integral with sliding singularities.
	www.cfm.brown.edu /people/dobrush/cv.html (2327 words)

	Applied Mathematics: Research Overview
		Their mathematical study seeks to develop generally applicable methods, based on our expanding understanding of matching, multiscale, and regularization concepts.
		Our interests include mathematical methods for studying the hydrodynamical instability of shear flows, transition from laminar flow to turbulence, applications of fractals to turbulence, two-dimensional and quasi-geostrophic turbulence theory and computation, and large-scale nonlinear wave mechanics.
		Mathematical biology is an increasingly large and well-established branch of applied mathematics.
	www.amath.washington.edu /research (1594 words)

	PDE/Applied Math Seminar, University of Maryland, College Park (Site not responding. Last check: 2007-11-01)
		I will discuss some recent progresses on the regularity and symmetry property for the associated Euler-Lagrange system and applications of the approach to some sharp integral inequalities for harmonic functions and a conformally invariant integral equation motivated from Carleman's proof of the isoperimetric inequality in dimension two.
		Leray-type regularizations of the Burgers and the isentropic Euler equations
		This type of regularization was first proposed in 1934 by Leray, who applied it in the context of the incompressible Navier-Stokes equations.
	www.math.umd.edu /research/seminars/pde (1077 words)

	Frank Bauer: Research in Applied Mathematics (Publications)
		In this paper we show that a notion of regularization defined according to what is usually done for ill-posed inverse problems allows to derive learning algorithms which are consistent and provide a fast convergence rate.
		Regularization under the assumption of badly known noise covariance operators is a demanding subject.
		It is done on the basis of a balancing principle for the choice of the regularization parameter, which is new in geoscientific applications.
	www-user.rhrk.uni-kl.de /~fbauer/FBauerPublications.html (1394 words)

	Caltech - Applied & Computational Mathematics
		The aim is to cover the interactions existing between applied mathematics, namely applied and computational harmonic analysis, approximation theory, etc., and statistics and signal processing.
		The mathematical theory of ordinary and partial differential equations, including a discussion of elliptic regularity, maximal principles, solubility of equations.
		The aim of the course is to develop the basic mathematical tools, and to demonstrate these through concrete applications in engineering, finance and physics.
	www.acm.caltech.edu /courses.shtml (1096 words)

	Regularization in Hilbert scales (Site not responding. Last check: 2007-11-01)
		For solving linear ill-posed problems regularization methods are required when the available data include some noise.
		In the present paper regularized approximations are obtained by a general regularization scheme in Hilbert scales which include well-known regularization methods such as the method of Tikhonov regularization and its higher-order forms, spectral methods, asymptotical regularization and iterative regularization methods.
		For both the cases of high- and low-order regularization, we study a priori and a posteriori rules for choosing the regularization parameter and provide order optimal error bounds that characterize the accuracy of the regularized approximations.
	www.iop.org /Select/abstract/-group=issn/0266-5611/21/6/003 (232 words)

	Department of Mathematics - University of Georgia
		The fact that the same Hopf algebra was useful in the study of foliations, renormalization in quantum field theory, and number theory has led to interesting discoveries.
		Mathematical theory and numerical algorithms are developed to for the phase field models.
		Multivariate splines are natural generalizations of splines in one variable, where the piecewise polynomials satisfying smoothness conditions are associated with partitions (such as triangulations and tetrahedral partitions) of a given n-dimensional domain.
	www.math.uga.edu /seminars_conferences/coll_schedule2005-06.html (1633 words)

	Numerical inversion of real-valued Laplace transforms. Regularization method by Vladimir Kryzhniy
		This is due to the fact that zeroes of the inverse Laplace transform of a sum of exponential decays are as informative as its maxima.
		Kryzhniy V.V. On regularization of numerical inversion of Laplace transforms.
		Short discussion on automated choice of regularization parameter might be of interest.
	www-users.cs.umn.edu /~yelena/web/mathmethod.php (920 words)

	Women in Applied Mathematics: Research and Leadership
		The Fredholm equation that is typically used to mathematically describe the blurring of an image by, say, a faulty lens, is an example of a linear ill-posed problem.
		A regularization technique must be used to lessen the effect of noise on the solution.
		In this work we consider a projection-based variant of the well-known Tikhonov regularization method for the solution of large-scale, linear discrete ill-posed problems when the regularization operator is not the identity.
	www.cs.umd.edu /users/oleary/leaderworkshop/abstracts.html (4458 words)

	About My works
		Recently, not only new ingredients in mathematics have enriched it's content, but also applications in fields such as chemistry, physics, neural network, finance, economic, mechanical system, communication, electronic engineering, medical imaging and so on, which always use least squares to measure the discrepancies between their model and observations, broaden it's context.
		Ill-posed means the parameter to be reconstructed does not depend on the observation in a stable way, So regularization methods have to be used in order to compute a stable approximation of the parameter in the presence of data noise.
		However, choice of regularization term depend on the definition of the admissible parameter set.
	www.columbia.edu /~zw2109/researchinterest.html (316 words)

	Weekly Calendar (Site not responding. Last check: 2007-11-01)
		TV regularization entails adding a term to the least-squares objective functional which penalizes total variation of the solution; this term formally appears as (a scalar times) the L-1 norm of the gradient.
		The advantage of this regularization is that it improves the conditioning of the optimization problem while not penalizing discontinuities in the solution, which is important in applications.
		The main drawback with TV regularization is that with it, the optimization problem becomes nonquadratic, so that mathematical and numerical analysis are both more involved.
	www-math.bgsu.edu /oldcalendars/1998-02-09.html (480 words)

	MATHEMATICS AND COMPUTATION IN IMAGING SCIENCE AND INFORMATION PROCESSING - IMS
		Mathematics is probably the least understood (and appreciated) among the hard sciences by the general public.
		My conviction is that if the public is more aware of the "usefulness" and "ubiquity" of mathematics, not only will the public image of mathematics improve, but it'll also provide the public with the necessary understanding to make informed political decisions regarding how society should invest in its technological future.
		Highlighted are mathematical views of machine and human vision, and various modern mathematical tools in image analysis and processing, including regularization and inverse problems, variational optimization, and geometric and nonlinear PDEs.
	www.ims.nus.edu.sg /Programs/imgsci/abstracts.htm (12544 words)

	Regularization in Statistics (Site not responding. Last check: 2007-11-01)
		The ambition of the proposed workshop is to bring together researchers working on all aspects of regularization relevant to statistical data analysis.
		In applied statistics, regularization - often identified as ``penalty-based methods'', ``soft thresholding'' - is associated primarily with nonparametric regression and density estimation, often referred to rather imprecisely as ``smoothing''.
		In applications, regularization offers a unifying perspective on many diverse ill-posed inverse problems, a wide range of problems concerned with recovering information from indirect and usually noisy measurements, arising in geophysics, stereology, tomography, climatology and econometrics.
	www.birs.ca /workshops/2003/03w5089 (299 words)

	CU-Denver Department of Mathematics Events
		In this talk, a direct relationship is established between the radius of the Kantorovich ball guaranteeing the convergence of Newton's method and the regularization parameter.
		This radius of convergence increases with the choice of the regularization parameter.
		A homotopy method in the regularization parameter is employed to improve numerical performance of Newton's method applied to these problems.
	www-math.cudenver.edu /events/QueryEvent.php?eid=308 (103 words)

	The Department of Computational & Applied Mathematics at Rice University
		Formulation and solution of mathematical models in management, economics, engineering and science applications in which one seeks to minimize or maximize an objective function subject to constraints including models in linear, nonlinear and integer programming; basic solution methods for these optimization models; problem solving using a modeling language and optimization software.
		Direct methods for large, sparse linear systems; regularization of ill-conditioned least squares problems; backward error analysis of basic algorithms for linear equations and least squares, condition estimation.
		Study of the minimization of functions of variables that are either unconstrained, subject to equality constraints, subject to inequality constraints, or subject to both equality and inequality constraints.
	www.caam.rice.edu /caam_courses.html (1519 words)

	REDUCE Bibliography
		The application of adiabatic regularization to calculations of cosmological interest.
		Representations of unusual mathematical structures in scientific applications of symbolic computation.
		Memorandum 368, Department of Applied Mathematics, Twente University of Technology, The Netherlands, December 1981.
	www.reduce-algebra.com /bibliography.htm (7590 words)

	SINUM Volume 34 Issue 3
		The objective of the paper is to present a method, called the sequential regularization method (SRM), for the nonstationary incompressible Navier--Stokes equations from the viewpoint of regularization of differential-algebraic equations (DAEs), and to provide a way to apply a DAE method to partial differential-algebraic equations (PDAEs).
		It is proved that its convergence rate is $O(\epsilon^m)$, where $m$ is the number of the SRM iterations and $\epsilon$ is the regularization parameter.
		Unlike other regularizations or pseudocompressibility methods in the Navier--Stokes context, the regularization parameter $\epsilon$ in the SRM need not be very small and the regularized problem in the sequence may be essentially nonstiff in time direction for any $\epsilon$.
	epubs.siam.org /SINUM/volume-34/art_27052.html (266 words)

	Elegant Mathematics Ltd.
		Elegant Mathematics Ltd. is the leading company, which is specialized in the development of the numeric software for different industrial problems.
		Several successful approaches for numerical comutation of direct and inverse scaterring problems are available from Elegant Mathematics Ltd. Using our algorithms we can find a distribution of substance and their penetrate coefficients in the valume if only few emitters and targets on the surface are available.
		In many industrial problems the mathematical model of the preparation is so complicated that is impossible to build a reliable model and to find a numeric solution.
	www.elegant-mathematics.com (2093 words)

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