Franz Winkler

Johannes Kepler University of Linz

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J. Rafael Sendra

Universidad de Alcalá

Bruno Buchberger

Johannes Kepler University of Linz

L. X. Châu Ngô

Quy Nhon University

Georg Grasegger

Austrian Academy of Sciences

Ekaterina Shemyakova

University of Toledo

Wolfgang Schreiner

Johannes Kepler University of Linz

Christian Mittermaier

Kepler Universitätsklinikum

Erik Hillgarter

Johannes Kepler University of Linz

Marco Antoniotti

University of Milano-Bicocca

Meng Zhou

North China University of Technology

Cooperative Institutions

Johannes Kepler University of Linz

New York University

Courant Institute of Mathematical Sciences

RWTH Aachen University

RISC Software (Austria)

Centre National de la Recherche Scientifique

Lomonosov Moscow State University

Yale University

Cold Spring Harbor Laboratory

Carnegie Mellon University

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A Sense of Life: Computational and Experimental Investigations with Models of Biochemical and Evolutionary Processes

OMICS A Journal of Integrative Biology (2003)

Bud Mishra Raoul-Sam Daruwala Yi Zhou Nadia Ugel Alberto Policriti

We collaborate in a research program aimed at creating a rigorous framework, experimental infrastructure, and computational environment for understanding, experimenting with, manipulating, and modifying a diverse set of fundamental biological processes at multiple scales and spatio-temporal modes. The novelty of our research is based on an approach that (i) requires coevolution of experimental science and theoretical techniques and (ii) exploits a certain universality in biology guided by a parsimonious model of evolutionary mechanisms operating at the genomic level and manifesting at the proteomic, transcriptomic, phylogenic, and other higher levels. Our current program in "systems biology" endeavors to marry largescale biological experiments with the tools to ponder and reason about large, complex, and subtle natural systems. To achieve this ambitious goal, ideas and concepts are combined from many different fields: biological experimentation, applied mathematical modeling, computational reasoning schemes, and large-scale numerical and symbolic simulations. From a biological viewpoint, the basic issues are many: (i) understanding common and shared structural motifs among biological processes; (ii) modeling biological noise due to interactions among a small number of key molecules or loss of synchrony; (iii) explaining the robustness of these systems in spite of such noise; and (iv) cataloging multistatic behavior and adaptation exhibited by many biological processes.

Computational model

Modelling biological systems

Coevolution

Robustness

Biological data

10.1089/153623103322452387

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Citations (6)

Computing by homomorphic images

Texts & monographs in symbolic computation/Texts and monographs in symbolic computation (1996)

Franz Winkler

Chinese remainder theorem

Homomorphic Encryption

Euclidean algorithm

Modulo operation

Modular arithmetic

10.1007/978-3-7091-6571-3_3

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Arithmetic in basic domains

Texts & monographs in symbolic computation/Texts and monographs in symbolic computation (1996)

Franz Winkler

10.1007/978-3-7091-6571-3_2

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Citations (2)

Differential Resultants

ITM Web of Conferences (2018)

Scott McCallum Franz Winkler

We review classical concepts of resultants of algebraic polynomials, and we adapt some of these concepts to objects in diﬀerential algebra, such as linear diﬀerential operators and diﬀerential polynomials.

Stress resultants

10.1051/itmconf/20182001005

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Canonical Reduction Systems in Symbolic Mathematics

Lecture notes in computer science (2009)

Franz Winkler

Symbolic data analysis

10.1007/978-3-642-03564-7_7

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Citations (1)

CASA — A system for Computer Aided Constructive Algebraic geometry

Lecture notes in computer science (1996)

Michal Mňuk Franz Winkler

Constructive

Simplicity

10.1007/3-540-61697-7_31

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Citations (11)

Quantifier elimination in real closed fields

Texts & monographs in symbolic computation/Texts and monographs in symbolic computation (1996)

Franz Winkler

Quantifier elimination

Quantifier (linguistics)

Real number

10.1007/978-3-7091-6571-3_9

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Citations (1)

A p-adic approach to the computation ofGröbner bases

Journal of Symbolic Computation (1988)

Franz Winkler

Congruence relation

Basis (linear algebra)

Natural number

10.1016/s0747-7171(88)80049-x

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Citations (67)

Abstracts of Technical Reports Computer Science Branch, Corporate Research and Development, General Electric Company, Schenectady, NY 12345 (GE)

ACM SIGSAM Bulletin (1987)

Franz Winkler

The unification problem for terms containing associative and commutative functions is of great importance in theorem provers based on the rewriting approach and resolution methods. The complexity of checking whether two such terms are unifiable was known to be NP-hard. It is proved that the problem is NP-complete by describing a nondeterministic polynomial time algorithm for it. It is also shown that if in addition, an associative-commutative function is assumed to be idempotent and/or have an identity, the problem still remains NP-complete.

Associative property

Nondeterministic algorithm

Unification

10.1145/24554.1095562

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Citations (5)

Forever And Ever

Franz Winkler Malia Rosa

Source

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