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2. Extending error bounds for radial basis function interpolation to measuring the error in higher order Sobolev norms.

Author

Hangelbroek, T. and Rieger, C.

Subjects
*INTERPOLATION spaces, *RADIAL basis functions, *HILBERT space, *INTERPOLATION, *MATHEMATICS
Abstract

Radial basis functions (RBFs) are prominent examples for reproducing kernels with associated reproducing kernel Hilbert spaces (RKHSs). The convergence theory for the kernel-based interpolation in that space is well understood and optimal rates for the whole RKHS are often known. Schaback added the doubling trick [Math. Comp. 68 (1999), pp. 201–216], which shows that functions having double the smoothness required by the RKHS (along with specific, albeit complicated boundary behavior) can be approximated with higher convergence rates than the optimal rates for the whole space. Other advances allowed interpolation of target functions which are less smooth, and different norms which measure interpolation error. The current state of the art of error analysis for RBF interpolation treats target functions having smoothness up to twice that of the native space, but error measured in norms which are weaker than that required for membership in the RKHS. Motivated by the fact that the kernels and the approximants they generate are smoother than required by the native space, this article extends the doubling trick to error which measures higher smoothness. This extension holds for a family of kernels satisfying easily checked hypotheses which we describe in this article, and includes many prominent RBFs. In the course of the proof, new convergence rates are obtained for the abstract operator considered by Devore and Ron in [Trans. Amer. Math. Soc. 362 (2010), pp. 6205–6229], and new Bernstein estimates are obtained relating high order smoothness norms to the native space norm. [ABSTRACT FROM AUTHOR]

Published
2025
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6. Influenza virus infections in patients with malignancies –– characteristics and outcome of the season 2014/15. A survey conducted by the Infectious Diseases Working Party (AGIHO) of the German Society of Haematology and Medical Oncology (DGHO)

Author

Hermann, B., Lehners, N., Brodhun, M., Boden, K., Hochhaus, A., Kochanek, M., Meckel, K., Mayer, K., Rachow, T., Rieger, C., Schalk, E., Weber, T., Schmeier-Jürchott, A., Schlattmann, P., Teschner, D., and von Lilienfeld-Toal, M.

Published
2017
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8. What's new in diagnosis and antimicrobial therapy of febrile neutropenic patients with lung infiltrates?

Author

Rieger, C., Barlow, S., and Maschmeyer, G.

Subjects
Pentamidine isethionate, Palliative treatment, Methicillin, Posaconazole, Caspofungin, Diagnostic imaging, Health care industry
Abstract

Author(s): C. Rieger [sup.1], S. Barlow [sup.1], G. Maschmeyer [sup.2] Author Affiliations: (1) grid.5252.0, 000000041936973X, Department of Hematology and Oncology, Ludwig-Maximilians-University Munich, , Munich, Germany (2) grid.419816.3, 0000000403903563, Department of [...]

Published
2014
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14. P115 - Why underrepresentation costs lives: First results from a high-volume multi-institutional study in Germany about risk factors for mortality in Fournier gangrene.

Author

Rieger, C., Hübers, M., Pfister, D., Schleifer, S., Hirsch, J., Kranz, J., Gerdes, B., Pantea, V., Chachin, A., Träger, M., Glienke, M., Henniges, P., Vetterlein, M.W., Klemm, J., Roghmann, F., Dellino, M., Jany, U., Tylingr, M., Al Assali, K., and Patroi, P.

Subjects
*FOURNIER gangrene, *COST, MORTALITY risk factors
Published
2024
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44. AN INVERSE THEOREM FOR COMPACT LIPSCHITZ REGIONS IN Rd USING LOCALIZED KERNEL BASES.

Author

HANGELBROEK, T., NARCOWICH, F. J., RIEGER, C., and WARD, J. D.

Subjects
INVERSE functions, LIPSCHITZ spaces, KERNEL (Mathematics), RADIAL basis functions, APPROXIMATION algorithms
Abstract

While inverse estimates in the context of radial basis function approximation on boundary-free domains have been known for at least ten years, such theorems for the more important and difficult setting of bounded domains have been notably absent. This article develops inverse estimates for finite dimensional spaces arising in radial basis function approximation and meshless methods. The inverse estimates we consider control Sobolev norms of linear combinations of a localized basis by the Lp norm over a bounded domain. The localized basis is generated by forming local Lagrange functions for certain types of RBFs (namely Matèrn and surface spline RBFs). [ABSTRACT FROM AUTHOR]

Published
2018
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45. Anti-infective vaccination strategies in patients with hematologic malignancies or solid tumors--Guideline of the Infectious Diseases Working Party (AGIHO) of the German Society for Hematology and Medical Oncology (DGHO).

Author

Rieger, C T, Liss, B, Mellinghoff, S, Buchheidt, D, Cornely, O A, Egerer, G, Heinz, W J, Hentrich, M, Maschmeyer, G, and Mayer, K

Subjects
*HEMATOLOGIC malignancies, *VACCINATION, *ANTI-infective agents, *COMMUNICABLE diseases, *ANTINEOPLASTIC agents, *IMMUNOCOMPROMISED patients
Abstract

Infectious complications are a significant cause of morbidity and mortality in patients with malignancies specifically when receiving anticancer treatments. Prevention of infection through vaccines is an important aspect of clinical care of cancer patients. Immunocompromising effects of the underlying disease as well as of antineoplastic therapies need to be considered when devising vaccination strategies. This guideline provides clinical recommendations on vaccine use in cancer patients including autologous stem cell transplant recipients, while allogeneic stem cell transplantation is subject of a separate guideline. The document was prepared by the Infectious Diseases Working Party (AGIHO) of the German Society for Hematology and Medical Oncology (DGHO) by reviewing currently available data and applying evidence-based medicine criteria. [ABSTRACT FROM AUTHOR]

Published
2018
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46. Decision Tree Rating Scales for Workload Estimation: Theme and Variations

Author

Wietwille, W. W, Skipper, J. H, and Rieger, C. A

Subjects
Man/System Technology And Life Support
Abstract

The modified Cooper-Harper (MCH) scale has been shown to be a sensitive indicator of workload in several different types of aircrew tasks. The MCH scale was examined to determine if certain variations of the scale might provide even greater sensitivity and to determine the reasons for the sensitivity of the scale. The MCH scale and five newly devised scales were studied in two different aircraft simulator experiments in which pilot loading was treated as an independent variable. Results indicate that while one of the new scales may be more sensitive in a given experiment, task dependency is a problem. The MCH scale exhibits consistent sensitivity and remains the scale recommended for general use. The results of the rating scale experiments are presented and the questionnaire results which were directed at obtaining a better understanding of the reasons for the relative sensitivity of the MCH scale and its variations are described.

Published
1984

47. Decision tree rating scales for workload estimation: Theme and variations

Author

Wierwille, W. W, Skipper, J. H, and Rieger, C. A

Subjects
Man/System Technology And Life Support
Abstract

The Modified Cooper-Harper (MCH) scale which is a sensitive indicator of workload in several different types of aircrew tasks was examined. The study determined if variations of the scale might provide greater sensitivity and the reasons for the sensitivity of the scale. The MCH scale and five newly devised scales were examined in two different aircraft simulator experiments in which pilot loading was treated as an independent variable. It is indicated that while one of the new scales may be more sensitive in a given experiment, task dependency is a problem. The MCH scale exhibits consistent senstivity and remains the scale recommended for general use. The MCH scale results are consistent with earlier experiments. The rating scale experiments are reported and the questionnaire results which were directed to obtain a better understanding of the reasons for the relative sensitivity of the MCH scale and its variations are described.

Published
1984

48. Toward a theory of distributed word expert natural language parsing

Author

Rieger, C and Small, S

Subjects
Mathematical And Computer Sciences (General)
Abstract

An approach to natural language meaning-based parsing in which the unit of linguistic knowledge is the word rather than the rewrite rule is described. In the word expert parser, knowledge about language is distributed across a population of procedural experts, each representing a word of the language, and each an expert at diagnosing that word's intended usage in context. The parser is structured around a coroutine control environment in which the generator-like word experts ask questions and exchange information in coming to collective agreement on sentence meaning. The word expert theory is advanced as a better cognitive model of human language expertise than the traditional rule-based approach. The technical discussion is organized around examples taken from the prototype LISP system which implements parts of the theory.

Published
1981

49. Distributed problem solving and natural language understanding models

Author

Rieger, C

Subjects
Systems Analysis
Abstract

A theory of organization and control for a meaning-based language understanding system is mapped out. In this theory, words, rather than rules, are the units of knowledge, and assume the form of procedural entities which execute as generator-like coroutines. Parsing a sentence in context demands a control environment in wich experts can ask questions of each other, forward hints and suggestions to each other, and suspend. The theory is a cognitive theory of both language representation and parser control.

Published
1980

50. Artificial intelligence programming languages for computer aided manufacturing

Author

Rieger, C, Samet, H, and Rosenberg, J

Subjects
Computer Programming And Software
Abstract

Eight Artificial Intelligence programming languages (SAIL, LISP, MICROPLANNER, CONNIVER, MLISP, POP-2, AL, and QLISP) are presented and surveyed, with examples of their use in an automated shop environment. Control structures are compared, and distinctive features of each language are highlighted. A simple programming task is used to illustrate programs in SAIL, LISP, MICROPLANNER, and CONNIVER. The report assumes reader knowledge of programming concepts, but not necessarily of the languages surveyed.

Published
1979

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