- 1-Theoretical concepts and experiments dealing with evolution of molecules in vitro reached a state that allows for direct applications to the design of biomolecules with predefined properties. RNA...
The Origin and Processing of Biological (2009)
Information has several meanings in everyday life. It is important, for example, to distinguish between a statistical notion of information linked to uncertainty and a semantic notion of information...
Evolutionary Biotechnology – From Ideas and Concepts to Experiments and Computer Simulations (2009)
Research on biological evolution entered the realm of science last century with the centennial publications by Charles Darwin and Gregor Mendel. Molecular models for evolution under controlled...
Preface: Dynamics of Evolutionary Processes (2009)
James P. Crutchfield, Peter Schuster
Starting with a brief historical introduction, we review recent results in the theory of evolutionary dynamics, emphasizing new mathematical and simulation methods that promise to provide...
Uniqueness, Continuity, and Existence of Implicit Functions in Constructive Analysis (2009)
Diener, Hannes, Schuster, Peter
We extract a quantitative variant of uniqueness from the usual hypotheses of the implicit functions theorem. This leads not only to an a priori proof of continuity, but also to an alternative, fully...
Jason Noble, Simon Powers, Soichiro Tsuda, Social Learning, Alife Xi, Eva Jablonka, ...
Social learning, the evolution of altruism, and controlling robots with biological cells: Some examples of the work of the
From Self-Organization to Evolution of RNA Molecules: The Origin of Biological Information (2008)
Abstract. Autocatalytic chemical reactions may lead to spatio-temporal patterns if processed under non-equilibrium conditions. The patterns disappear when the conditions change and information stored...
A NILREGULAR ELEMENT PROPERTY (2008)
Thierry Coquand, Henri Lombardi, Peter Schuster
Abstract. An element a of a commutative ring R is nilregular if and only if x is nilpotent whenever ax is nilpotent. More generally, an ideal I of R is nilregular if and only if x is nilpotent...
What is Continuity, Constructively? 1 (2008)
Abstract: The concept of continuity for mappings between metric spaces should coincide with that of uniform continuity in the case of a compact domain, and still give rise to a category. In...
Adjoints, absolute values and polar decompositions (2008)
Douglas Bridges, Fred Richman, Peter Schuster, Communicated William, B. Arveson
Abstract. Various questions about adjoints, absolute values and polar decompositions of operators are addressed from a constructive point of view. The focus is on bilinear forms. Conditions are given...
innovation, discovery, and bricolage Are we doomed to progress to ever increasing complexity? 1
Do Noetherian Modules Have Noetherian Basis Functions? (2008)
Abstract. In Bishop-style constructive algebra it is known that if a module over a commutative ring has a Noetherian basis function, then it is Noetherian. Using countable choice we prove the reverse...
Compactness in apartness spaces (2008)
Douglas Bridges, Hajime Ishihara, Peter Schuster
Abstract. In this note, we establish some results which suggest a possible solution to the problem of finding the right constructive notion of compactness in the context of a...
Commentary Taming combinatorial explosions (2008)
Assembling objects from building blocks by means of predefined combination rules leads to combinatorial explosions. Indeed, it does not matter, how many classes of building blocks or alternatives of...
Magister Rerum Naturalium, Verfasser Thomas Taylor, Studienrichtung A, Molekulare Biologie, Betreuer Prof, Dr. Peter Schuster, ...
Silent gratitude isn’t much use to anyone.
Vorgelegt Der, Fakultät Für Chemie, Mag Michael Wolfinger, Peter Stadler, Ivo Hofacker, ...
Dank an alle, die zum Gelingen dieser Arbeit beigetragen haben:
Copyright © 2000 RNA Society+ RNA folding at elementary step resolution (2008)
Christoph Flamm, Walter Fontana, Ivo L. Hofacker, Peter Schuster
We study the stochastic folding kinetics of RNA sequences into secondary structures with a new algorithm based on the formation, dissociation, and the shifting of individual base pairs. We discuss...
Mag Susanne Rauscher, Molekulare Strukturbiologie, Im Juni, Peter Schuster, Peter Stadler, ...
Dank an alle,
Copyright © 2000 RNA Society+ RNA folding at elementary step resolution (2008)
Christoph Flamm, Walter Fontana, Ivo L. Hofacker, Peter Schuster
We study the stochastic folding kinetics of RNA sequences into secondary structures with a new algorithm based on the formation, dissociation, and the shifting of individual base pairs. We discuss...
Invited Review Hydrogen Bonding: From Small Clusters to Biopolymers (2008)
Peter Schuster, Peter Wolschann
Summary. High quality ab initio computations and molecular spectroscopy of small hydrogen-bonded clusters in the vapor phase provide highly accurate data in general agreement with the theory of...
Chance and Necessity in Evolution: (2008)
Lessons From Rna, Peter Schuster, Walter Fontana
The RNA folding map, understood as the relationship between sequences and secondary structures or shapes, exhibits robust statistical properties summarized by three notions: (1) the notion of a...
RNA Multi-Structure Landscapes - A Study Based on Temperature Dependent Partition Functions (2008)
Sebastian Bonhoeffer, John S. McCaskill, Peter F. Stadler, Peter Schuster
Statistical properties of RNA folding landscapes obtained by the partition function algorithm (McCaskill, 1990) are investigated in detail. The pair correlation of free energies as a function of the...
Introduction Global divisors on an algebraic curve (2008)
Discussions Henri Lombardi, Claude Quitté, Peter Schuster
The goal of this note is to give an elementary definition of the divisor class group of an algebraic
Chen, Jian, Off, Morten Kristian, Solheim, Eivind, Schuster, Peter, Hoff, Per Ivar, Ohm, Ole-Jørgen
Aims The recurrence of atrial fibrillation (AF) after pulmonary vein (PV) isolation is still a challenge. We investigated a new approach to treating AF patients by silencing electrical activity in...
Christian M. Reidys, Peter Schuster
A mathematical model for the relation of ribonucleic acid (RNA) sequences and coarse grained three dimensional structures of these RNA molecules is used to investigate optimization processes as they...
landscape paradigms in physics and biology LANDSCAPES AND MOLECULAR EVOLUTION (2007)
Evolution of RNA molecules in vitro is visualized as a hill-climbing process on a fitness landscape that can be derived from molecular properties and functions. The optimization process is shaped by...
Fast Folding and Comparison of RNA Secondary Structures (2007)
The Vienna, Ivo L. Hofacker, Walter Fontana, Peter F. Stadler, L. Sebastian Bonhoeffer, Manfred Tacker, ...
Computer codes for computation and comparison of RNA secondary structures, the Vienna RNA package, are presented, that are based on dynamic programming algorithms and aim at predictions of structures...
Constructive Solutions of Continuous Equations (2007)
Peter Schuster, Helmut Schwichtenberg
We modify some seminal notions from constructive analysis, by providing witnesses for (strictly) positive quantiers occurring in their definitions. For instance, we understand a real number as...
Adjoints, absolute values and polar decompositions (2007)
Douglas Bridges, Fred Richman, Peter Schuster
Abstract. Various questions about adjoints, absolute values and polar decompositions of operators are addressed from a constructive point of view. The focus is on bilinear forms. Conditions are given...
Molecular Insights into Evolution of (2007)
Success and efficiency of Darwinian evolution is based on the dichotomy of genotype and phenotype: The former is the object under variation whereas the latter constitutes the target of selection....
Molecular Insights into Evolution of (2007)
Success and efficiency of Darwinian evolution is based on the dichotomy of genotype and phenotype: The former is the object under variation whereas the latter constitutes the target of selection....
Hydrogen Bonding: From Small Clusters to Biopolymers (2007)
Peter Schuster, Peter Wolschann
sserstoffbrcken aber auch indirekt die Ausbildung von Biopolymerstrukturen, da sie essentiell an der Struktur des flssigen Wassers mitwirken. Die gegenwrtig zur Verfgung stehenden Daten legen nahe,...
Molecular Insights into Evolution (2007)
Evolution of ribonucleic acid (RNA) molecules in the test-tube provides a possibility to study evolutionary optimization and adaptation to the environment on time scales accessible to human...
Undergraduate Research: Experiences from a Three-Year Project (2007)
Schuster, Peter, Birdsong, Charles
There are significant benefits of research for the involved undergraduate student. These include exposure to advanced topics, introduction to research methods, and direct interaction with faculty and...
A Pre-Crash Simulator to Evaluate Vehicle Collision Prediction Algorithms (2007)
Desrosiers, Dana, Birdsong, Charles, Schuster, Peter
This paper describes a software simulator for pre-crash collision predictions. The simulator is a surrogate test bed for evaluating the performance of proposed pre-crash algorithms. It reads data...
Inverse bifurcation analysis: application to simple gene systems (2006)
Lu, James, Engl, Heinz W, Schuster, Peter
Abstract Background Bifurcation analysis has proven to be a powerful method for understanding the qualitative behavior of gene regulatory networks. In addition to the more traditional forward problem...
Research in the Undergraduate Environment (2006)
Birdsong, Charles, Schuster, Peter
The benefits of research experiences for undergraduates are significant. For many faculty, these were the experiences that convinced us to pursue further education and a career in academia. However,...
The fan theorem and unique existence of maxima (2006)
Berger, Josef, Bridges, Douglas, Schuster, Peter
The existence and uniqueness of a maximum point for a continuous real—valued function on a metric space are investigated constructively. In particular, it is shown, in the spirit of reverse...
Test Methods and Results for Sensors in a Pre-Crash Detection System (2006)
Birdsong, Charles, Schuster, Peter, Carlin, John, Kawano, Daniel, Thompson, William
Automobile safety can be improved by anticipating a crash before it occurs and thereby providing additional time to deploy safety technologies. This requires an accurate, fast and robust pre-crash...
Classifying Dini's Theorem (2006)
Berger, Josef, Schuster, Peter
Dini's theorem says that compactness of the domain, a metric space, ensures the uniform convergence of every simply convergent monotone sequence of real-valued continuous functions whose limit is...
A Nilregular Element Property (2006)
Coquand, Thierry, Lombardi, Henri, Schuster, Peter
An element or an ideal of a commutative ring is nilregular if and only if it is regular modulo the nilradical. We prove that if the ring is Noetherian, then every nilregular ideal contains a...
Evaluation of Cost Effective Sensor Combinations for a Vehicle Precrash Detection System (2005)
Carlin, John, Birdsong, Charles, Schuster, Peter, Thompson, William, Kawano, Daniel
The future of vehicle safety will benefit greatly from precrash detection -the ability of a motor vehicle to predict the occurrence of an accident before it occurs. There are many different sensor...
On constructing completions (2005)
Crosilla, Laura, Ishihara, Hajime, Schuster, Peter
The Dedekind cuts in an ordered set form a set in the sense of constructive Zermelo—Fraenkel set theory. We deduce this statement from the principle of refinement, which we distill before from the...
Schuster, Peter, Faerestrand, Svein
The most recent treatment option of medically refractory heart failure includes cardiac resynchronization therapy (CRT) by biventricular pacing in selected patients in NYHA functional class III or IV...
Peter Schuster, Svein Faerestrand
The most recent treatment option of medically refractory heart failure includes cardiac resynchronization therapy (CRT) by biventricular pacing in selected patients in NYHA functional class III or IV...
Products in the category of apartness spaces (2005)
Bridges, Douglas, Ishihara, Hajime, Schuster, Peter, Vîţă, Luminita
Apartness and formal topology (2005)
Erik Palmgren, Erik Palmgren, Peter Schuster, Peter Schuster
The theory of formal spaces and the more recent theory of apartness spaces have a priori not much more in common than that each of them was initiated as a constructive approach to general topology....
zur Erlangung des akademischen Grades (2005)
Vorgelegt Der, Fakultät Für Chemie, Mag Ingrid, G. Abfalter, Peter Stadler, ...
Dank an alle,
Compactness in apartness spaces? (2005)
Bridges, Douglas, Ishihara, Hajime, Schuster, Peter, Vita, Luminita S.
A major problem in the constructive theory of apartness spaces is that of finding a good notion of compactness. Such a notion should (i) reduce to ``complete plus totally bounded'' for uniform spaces...
Schuster, Peter, Matre, Knut, Faerestrand, Svein
Aims To study the feasibility of a new semiautomatic echocardiographic modality called Tissue Synchronization Imaging (TSI) for measurement of the longitudinal left ventricular (LV) movement. Methods...
Schuster, Peter, Faerestrand, Svein, Ohm, Ole-Jorgen, Schouten, Vincent
Objective The rate response of a pacemaker (PM) was compared with the sinus rate in patients during repeated exercise tests, at different settings of the rate response parameters. Methods and...
Strong versus uniform continuity: A constructive round (2004)
Schuster, Peter; Mathematisches Institut, Ludwig-Maximilians- Universität, Theresienstraße 39, 80333 München, Germany ; Peter.Schuster@mathematik.uni-muenchen.de, Bridges, Douglas; Mathematisches Institut, Ludwig-Maximilians-Universität, Theresienstraße 39, 80333 München, Germany And Department Of Mathematics & Statistics, University Of Canterbury, Private B
The notion of apartness has recently shown promise as a means of lifting constructive topology from the restrictive context of metric spaces to more general settings. Extending the point-subset...
Freundschaft und Verwandtschaft als Gegenstand interdisziplinärerer Forschung (2003)
Guichard, Martine, Schlee, Günther, Schuster, Peter, Stichweh, Rudolf, Schmidt, Johannes, Trillmich, Fritz
Networks in Molecular Evolution - A Common Theme at All Levels (2003)
Peter Schuster, Peter F. Stadler
INTRODUCTION N etworks of different kinds and sizes appear at different levels of molecular evolution. Networks have a natural representation as graphs or hypergraphs of various kinds. It is not...
Kinetics of maternal immunity against rabies in fox cubs (Vulpes vulpes) (2002)
Müller, Thomas, Selhorst, Thomas, Schuster, Peter, Vos, Ad, Wenzel, Ulf, Neubert, Andreas
Abstract Background In previous experiments, it was demonstrated that maternal antibodies (maAb) against rabies in foxes ( Vulpes vulpes ) were transferred from the vixen to her offspring. However,...
Networks in molecular evolution (2002)
Peter Schuster, Peter F. Stadler
Networks are a common theme at all levels of molecular evolution: Networks of metastable states and their connecting saddle points determine structure and folding kinetics of biopolymers. Neutral...
Networks in molecular evolution (2002)
Peter Schuster, Peter F. Stadler
Networks are a common theme at all levels of molecular evolution: Networks of metastable states and their connecting saddle points determine structure and folding kinetics of biopolymers. Neutral...
A Toy Model of Chemical Reaction Networks (2002)
Gil Benkö, Peter Stadler, Christoph Flamm, Ivo Hofacker, Peter Schuster, ...
meinen Eltern nicht nur dafür, dass sie diese Arbeit ermöglicht haben Dank an alle, die zum Gelingen dieser Arbeit beigetragen haben:
A testable genotype-phenotype map: Modeling evolution of RNA molecules (2002)
Abstract. Recent experiments and progress in modelling evolution in silico converge towards a coherent view of Darwinian evolution in molecular systems. Conventional population genetics and...
A Constructive Uniform Continuity Theorem (2002)
Ishihara, Hajime, Schuster, Peter
For any mapping on some totally bounded metric space, uniform continuity is derived from the condition that the corresponding inverse image operator preserves the relation ‘two subspaces have...
Networks in molecular evolution (2002)
Peter Schuster, Peter F. Stadler, Chemie Molekulare
etworks of different kinds and sizes appear at different levels of molecular evolution. Networks have a natural representation as graphs or hypergraphs of various kinds. It is not surprising,...
Apartness, topology, and uniformity: a constructive view (2001)
Douglas Bridges, Peter Schuster
Abstract. The theory of apartness spaces, and their relation to topological spaces (in the point—set case) and uniform spaces (in the set—set case), is sketched. New notions of local...
© by Oldenbourg Wissenschaftsverlag, München From Quasispecies to Universal Grammar (2001)
A. Nowak, Dedicated Prof, Dr. Peter Schuster, M. A. Nowak
The perspective of this paper is to compare mathematical models for the evolutionary dynamics of genomes and languages. The quasispecies equation describes the evolution of genetic sequences under...
A weak countable choice principle (2000)
Douglas Bridges, Fred Richman, Peter Schuster
A weak choice principle is introduced that is implied both by countable choice and by the law of excluded middle. This principle suffices to prove that metric independence is the same as linear...
Discrete Models of Biopolymers (2000)
Peter Schuster, Peter F. Stadler
Discretized models of biopolymer structures can be used not only as approximations of the actual spatial structures but also as a computationally feasible approach to the generic features of the...
RNA folding at elementary step resolution (2000)
Christoph Flamm Walter, Walter Fontana, Ivo L. Hofacker, Peter Schuster
We study the stochastic folding kinetics of RNA sequences into secondary structures with a new algorithm based on the formation, dissociation, and the shifting of individual base pairs. We discuss...
RNA Folding at Elementary Step Resolution (2000)
Christoph Flamm, Walter Fontana, Ivo L. Hofacker, Peter Schuster
We study the stochastic folding kinetics of RNA sequences into secondary structures with a new algorithm based on the formation, dissociation, and the shifting of individual base pairs. We discuss...
RNA Folding at Elementary Step Resolution (2000)
Christoph Flamm, Walter Fontana, Ivo L. Hofacker, Peter Schuster
A algorithm based one three classes of elementary steps for folding RNA sequences into secondary structures is presented. It is formulated as a stochastic process on the discrete confomational space...
Dynamics of Autocatalytic Replicator Networks Based on Higher Order Ligation Reactions (2000)
Peter F. Stadler, Peter Schuster
this paper that the concentrations [A] and [B] of the building blocks are bu#ered, i.e., constant. The crucial step of the replication mechanism is the formation of an intermediate species ABCC which...
Dynamics of Autocatalytic Replicator Networks Based on Higher Order Ligation Reactions (2000)
Peter F. Stadler, Peter Schuster
this paper that the concentrations [A] and [B] of the building blocks are buered, i.e., constant. The crucial step of the replication mechanism is the formation of an intermediate species ABCC which...
Titel auf der Beil.
Chance and Necessity in Evolution: Lessons from RNA (1999)
Peter Schuster, Walter Fontana
The RNA folding map, understood as the relationship between sequences and secondary structures or shapes, exhibits robust statistical properties summarized by three notions: (1) the notion of a...
Chance and Necessity in Evolution: Lessons from RNA (1999)
Peter Schuster And, Peter Schuster, Walter Fontana
The RNA folding map, understood as the relationship between sequences and secondary structures or shapes, exhibits robust statistical properties summarized by three notions: (1) the notion of a...
Chance and Necessity in Evolution: Lessons from RNA (1999)
Peter Schuster And, Peter Schuster, Walter Fontana
The RNA folding map, understood as the relationship between sequences and secondary structures or shapes, exhibits robust statistical properties summarized by three notions: (1) the notion of a...
Chance and Necessity in Evolution: Lessons from RNA (1999)
Peter Schuster And, Peter Schuster, Walter Fontana
The RNA folding map, understood as the relationship between sequences and secondary structures or shapes , exhibits robust statistical properties which are casted into three notions: (1) the notion...
Discrete Models of Biopolymers (1999)
Peter Schuster, Peter F. Stadler
Discretized models of biopolymer structures can be used not only as approximations of the actual spatial structures but also as a computationally feasible approach to the generic features of the...
Replication and Mutation on Neutral Networks (1999)
Christian Reidys, Christian V. Forst, Peter Schuster
. Folding of RNA sequences into secondary structures is viewed as a map that assigns a uniquely defined base pairing pattern to every sequence. This mapping is non-invertible since many sequences...
Topology In Phenotype Space (1999)
Jan Cupal, Peter Schuster, Peter F. Stadler
Introduction The course of biological evolution cannot be understood without the dichotomy of genotype and phenotype. While variation is introduced by mutation or recombination at the genotypic...
Organisms Replace Systems (1999)
Understanding, analysis, and controlled modifications of complex systems represent the utmost challenge for present-day science. Being able to deal successfully with problems created by complex...
Evolution of Molecular Phenotypes - A Physicist's View of Darwin's Principle (1999)
. The power of Darwinian evolution is based on the dichotomy of genotype and phenotype with the former being the object under variation and the latter constituting the target of selection. Only the...
Replication and Mutation on Neutral Networks (1999)
Christian Reidys, Christian V. Forst, Peter Schuster
Folding of RNA sequences into secondary structures is viewed as a map that assigns a uniquely defined base pairing pattern to every sequence. The mapping is non-invertible since many sequences fold...
Dynamics of Autocatalytic Replicator Networks Based on Higher Order Ligation Reaction (1999)
Peter F. Stadler, Peter Schuster
A class of autocatalytic reaction networks based on template depending litigation and higher order...
Alexandra Maier, Ra Maier, Heinz Sklenar, Alexander Renner, Herbert F. Kratky, Er Renner, ...
r the selection of conformers that agree with experimentally determined structures. The continuum model accounts for solvent polarization by means of the electrostatic reaction field. In the case of...
Chance and Necessity in Evolution: Lessons from RNA (1998)
Schuster, Peter, Fontana, Walter
The relationship between sequences and secondary structures or shapes in RNA exhibits robust statistical properties summarized by three notions: (1) the notion of a typical shape (that among all...
Shaping space: The possible and the attainable in RNA genotype-phenotype mapping (1998)
Walter Fontana, Peter Schuster
Understanding which phenotypes are accessible from which genotypes is fundamental for understanding the evolutionary process. This notion of accessibility can be used to define a relation of nearness...
Complete Suboptimal Folding of RNA and the Stability of Secondary Structures (1998)
Stefan Wuchty, Walter Fontana, Ivo L. Hofacker, Peter Schuster
An algorithm is presented for generating rigorously all suboptimal secondary structures between the minimum free energy and an arbitrary upper limit. The algorithm is particularly fast in the...
Shaping Space: The Possible and the Attainable in RNA Genotype-Phenotype Mapping (1998)
Walter Fontana And, Walter Fontana, Peter Schuster
Understanding which phenotypes are accessible from which genotypes is fundamental for understanding the evolutionary process. This notion of accessibility can be used to define a relation of nearness...
Complete Suboptimal Folding of RNA and the Stability of Secondary Structures (1998)
Stefan Wuchty, Walter Fontana, Ivo L. Hofacker, Peter Schuster
this paper we describe a fairly simple algorithm which generates all suboptimal folds of a sequence within a desired energy range from the mfe. The idea underlying the algorithm is straightforward,...
Shaping Space: The Possible and the Attainable in RNA Genotype-Phenotype Mapping (1998)
Walter Fontana, Peter Schuster
Understanding which phenotypes are accessible from which genotypes is fundamental for understanding the evolutionary process. This notion of accessibility can be used to define a relation of nearness...
Complete Suboptimal Folding of RNA and the Stability of Secondary Structures (1998)
Stefan Wuchty, Walter Fontana, Ivo L. Hofacker, Peter Schuster
this paper we describe a fairly simple algorithm which generates all suboptimal folds of a sequence within a desired energy range from the mfe. The idea underlying the algorithm is straightforward,...
Shaping Space: The Possible and the Attainable in RNA Genotype-Phenotype Mapping (1998)
Walter Fontana, Peter Schuster, J. Theor Biol, In Press
Understanding which phenotypes are accessible from which genotypes is fundamental for understanding the evolutionary process. This notion of accessibility can be used to define a relation of nearness...
Nature and Evolution of Early Replicons (1998)
Peter Schuster, Peter F. Stadler, Stadler Early
RNA and protein molecules were found to be both templates for replication and specific catalysts for biochemical reactions. RNA molecules, although very difficult to obtain via plausible synthetic...
Shaping Space: The Possible and the Attainable in RNA Genotype-Phenotype Mapping (1998)
Walter Fontana, Peter Schuster, J. Theor Biol, In Press
Understanding which phenotypes are accessible from which genotypes is fundamental for understanding the evolutionary process. This notion of accessibility can be used to define a relation of nearness...
Shaping Space: The Possible and the Attainable in RNA Genotype-Phenotype Mapping (1998)
Walter Fontana, Peter Schuster
Understanding which phenotypes are accessible from which genotypes is fundamental for understanding the evolutionary process. This notion of accessibility can be used to define a relation of nearness...
Nature and Evolution of Early Replicons (1998)
Peter Schuster, Peter F. Stadler, Stadler Early
RNA and protein molecules were found to be both templates for replication and specific catalysts for biochemical reactions. RNA molecules, although very difficult to obtain via plausible synthetic...
Douglas Bridges, Peter Schuster, Fred Richman
A weak choice principle is introduced that is implied both by countable choice and by the law of excluded middle. This principle su ces to prove that metric independence is the same as linear...
Genotypes with phenotypes: Adventures in an RNA toy world (1997)
Evolution has created the complexity of the animate world and deciphering the language of evolution is the key towards understanding nature. The dynamics of evolution is simplified by considering it...
Linear Independence and Choice (1997)
Douglas Bridges, Douglas Bridges, Fred Richman, Fred Richman, Peter Schuster, Peter Schuster
. The notions of linear and metric independence are investigated in relation to the property: if U is a set of m + 1 independentvectors, and X is a set of m independentvectors, then adjoining some...
Structural Constraints and Neutrality in RNA (1997)
Ulrike Göbel, Ulrike G Obel, Peter Schuster, Christian V. Forst
Generic properties of neutral networks of RNA secondary structures can be described by means of random graph theory. The success of this approach is dependent on details of the underlying secondary...
Adjoints, Absolute Values and Polar Decompositions (1997)
Douglas Bridges, Douglas Bridges, Fred Richman, Fred Richman, Peter Schuster, Peter Schuster
. Various questions about adjoints, absolute values and polar decompositions of operators are addressed from a constructive point of view. The focus is on bilinear forms. Conditions are given for the...
Sequence Redundancy in Biopolymers A Study on RNA and Protein Structures (1997)
Peter Schuster And, Peter Schuster, Peter F. Stadler
Mapping sequences onto biopolymer structures is characterized by redundancy since the numbers of sequences exceed the numbers of structures. The degree of Redundancy depends on the notion of...
Autocatalytic Networks with Intermediates I: Irreversible Reactions (1997)
Robert Hecht, Robert Happel, Peter Schuster, Peter F. Stadler
A class of autocatalytic reaction networks based on template dependent replication and specific catalysis is considered. Trimolecular "elementrary steps" of simple replicator dynamics are...
Evolutionary Optimization of Biopolymers and Sequence Structure Maps (1997)
Christian Reidys, Stephan Kopp, Peter Schuster
Searching for biopolymers having a predefined function is a core problem of biotechnology, biochemistry and pharmacy. On the level of RNA sequences and their corresponding secondary structures we...
Sequence Redundancy in Biopolymers - A Study on RNA and Protein Structures (1997)
Peter Schuster, Peter F. Stadler
Mapping sequences onto biopolymer structures is characterized by redundancy since the numbers of sequences exceed the numbers of structures. The degree of Redundancy depends on the notion of...
Genotypes with Phenotypes: Adventures in an RNA toy world (1997)
Evolution has created the complexity of the animate world and deciphering the language of evolution is the key towards understanding nature. The dynamics of evolution is simpli ed by considering it...
Walter Fontana, Peter Schuster
Understanding which phenotypes are accessible from which genotypes is fundamental for understanding the evolutionary process. This notion of acessibility can be used to define a relation of nearness...
Leipzig, Univ., Diss., 1996.
Algorithm Independent Properties of RNA Secondary Structure Predictions (1996)
Manfred Tacker, Peter F. Stadler, Ivo L. Hofacker, Peter Schuster
Algorithms predicting RNA secondary structures based on different folding criteria -- minimum free energies (mfe), kinetic folding (kin), maximum matching (mm) -- and different parameter sets are...
ory of - 2 - life on earth. Palaeontologists have discovered rather large and abrupt jumps in structural and functional complexity in the fossil record. Irrespective of this evidence, increasing...
Approximate Scaling Properties of RNA Free Energy Landscapes (1996)
Subbiah Baskaran, Peter F. Stadler, Peter Schuster
RNA free energy landscapes are analyzed by means of "time-series" that are obtained from random walks restricted to excursion sets. The power spectra, the scaling of the jump size...
Analysis of RNA Sequence Structure Maps by Exhaustive Enumeration - I. Neutral Networks (1996)
Walter Grüner, Walter Gr Uner, Robert Giegerich, Dirk Strothmann, Christian Reidys, Jacqueline Weber, ...
Global relations between RNA sequences and secondary structures are understood as mappings from sequence space into shape space. These mappings are investigated by exhaustive folding of all GC and AU...
Exploration of Artificial Landscapes - Based on Random Graphs (1996)
Stephan Kopp, Christian Reidys, Peter Schuster
The mapping of RNA--molecules to secondary structures is a good example to study principles of evolutionary optimization. Instead of using a prediction algorithm which takes into account...
Walter Grüner, Walter Gr Uner, Robert Giegerich, Dirk Strothmann, Christian Reidys, Jacqueline Weber, ...
The relations between RNA sequences and secondary structures are investigated by exhaustive folding of all GC and AU sequences with chain lengths up to 30. The technique of tries is used for economic...
Algorithm Independent Properties of RNA Secondary Structure Predictions (1996)
Manfred Tacker, Peter F. Stadler, Ivo L. Hofacker, Peter Schuster
Algorithms predicting RNA secondary structures based on different folding criteria -- minimum free energies (mfe), kinetic folding (kin), maximum matching (mm) -- and different parameter sets are...
Analysis of RNA Sequence Structure Maps by Exhaustive Enumeration (1996)
Walter Grüner, Walter Gr Uner, Robert Giegerich, Dirk Strohmann, Christian Reidys, Jacqueline Weber, ...
The mapping from RNA sequences to their secondary structures is investigated by exhaustively folding all GC and AU sequences with chain lengths up to 30. We analyse the distribution of secondary...
Combinatorics Of RNA Secondary Structures (1996)
Ivo L. Hofacker, Peter Schuster, Peter F. Stadler
Secondary structures of polynucleotides can be view as a certain class of planar vertex-labeled graphs. We construct recursion formulae enumerating various sub-classes of these graphs as well as...
Palaeontologists have discovered rather large and abrupt jumps in structural and functional complexity in the fossil record. Irrespective of this evidence, increasing complexity in evolution is...
Dynamics of Small Autocatalytic Reaction Networks II : Replication, Mutation and Catalysis (1995)
Peter F. Stadler, Wolfgang Schnabl, Christian Forst, Peter Schuster
. Mutation is introduced into autocatalytic reaction networks. The differential equations obtained are neither of replicator type nor can they be transformed straightway into a linear equation....
Generic Properties of Combinatory Maps - Neutral Networks of RNA Secondary Structures (1995)
Christian Reidys, Peter F. Stadler, Peter Schuster
Random graph theory is used to model relationships between sequences and secondary structures of RNA molecules. Sequences folding into identical structures form neutral networks which percolate...
Dynamics of Small Autocatalytic Reaction Network II: Replication, Mutation and Catalysis (1994)
Stadler, Peter F., Schnabl, Wolfgang, Forst, Christian V., Schuster, Peter
Mutation is introduced into autocatalytic reaction networks. Examples of low dimensional dynamical systems --- n = 2, 3 and 4 --- are discussed and complete qualitative analysis is presented. Error...
Permanence of Sparse Autocatalytic Networks (1994)
Peter F. Stadler, Peter Schuster, Schuster Permanence
Some global dynamical properties of catalytic networks, in particular permanence, are closely related with a directed graph representing the differential equation. It can be shown that for every...
Fast Folding and Comparison of RNA Secondary Structures (The Vienna RNA Package) (1994)
Ivo L. Hofacker, Walter Fontana, Peter F. Stadler, L. Sebastian Bonhoeffer, Manfred Tacker, Peter Schuster
Computer codes for computation and comparison of RNA secondary structures, the Vienna RNA package, are presented, that are based on dynamic programming algorithms and aim at predictions of structures...
Immune Networks Modeled by Replicator Equations (1994)
Peter F. Stadler, Peter Schuster, Alan S. Perelson
In order to evaluate the role of idiotypic networks in the operation of the immune system a number of mathematical models have been formulated. Here we examine a class of B-cell models in which cell...
Statistics of RNA Melting Kinetics (1993)
Manfred Tacker, Walter Fontana, Peter F. Stadler, Peter Schuster
We present and study the behavior of a simple kinetic model for the melting of RNA secondary structures, given that those structures are known. The model is then used as a map that assigns structure...
RNA Folding and Combinatory Landscapes (1993)
Walter Fontana, Peter F. Stadler, Thomas Griesmacher, Ivo L. Hofacker, Manfred Tacker, ...
In this paper we view the folding of polynucleotide (RNA) sequences as a map that assigns to each sequence a minimum free energy pattern of base pairings, known as secondary structure. Considering...
Landscapes - Complex Optimization Problems and Biopolymer Structures (1993)
Peter Schuster, Peter F. Stadler
The evolution of RNA molecules in replication assays, viroids and RNA viruses can be viewed as an adaptation process on a 'fitness' landscape. The dynamics of evolution is hence tightly...
Elektronische und magnetische Eigenschaften ultradünner fcc-Kobalt-Schichtsysteme. (1992)
Mikroreprod. eines Ms. Getr. Zählung : graph. Darst.
Wolfgang Schnabl, Peter F. Stadler, Christian Forst, Peter Schuster, W. Schnabl Chaotic
Two chaotic attractors observed in Lotka-Volterra equations of dimension n = 3 are shown to represent two di#erent cross-sections of one and the same chaotic regime. The strange attractor is studied...
Thesis (doctoral)--Rheinisch-Westfälische Technische Hochschule Aachen, 1980.
Strukturen und Tendenzen im Recht der staatlichen Wirtschaftsunternehmen Frankreichs. (1972)
Thèse, Francfort, 1972.
Düsseldorf, Univ., Med. Fak., Diss. 1972.
Thesis (doctoral)--Technische Universität Clausthal, 1970.
Thesis (doctoral)--Technische Hochschule Darmstadt, 1965.
Kinetics of maternal immunity against rabies in fox cubs (Vulpes vulpes)
Müller, Thomas, Selhorst, Thomas, Schuster, Peter, Vos, Ad, Wenzel, Ulf, Neubert, Andreas
Schuster, Peter, Faerestrand, Svein
The most recent treatment option of medically refractory heart failure includes cardiac resynchronization therapy (CRT) by biventricular pacing in selected patients in NYHA functional class III or IV...
Kinetics of maternal immunity against rabies in fox cubs (Vulpes vulpes)
Müller, Thomas, Selhorst, Thomas, Schuster, Peter, Vos, Ad, Wenzel, Ulf, Neubert, Andreas
Schuster, Peter, Faerestrand, Svein
The most recent treatment option of medically refractory heart failure includes cardiac resynchronization therapy (CRT) by biventricular pacing in selected patients in NYHA functional class III or IV...
Replication and Mutation on Neutral Networks: Updated Version 2000
Christian Reidys, Christian V. Forst, Peter Schuster
Folding of RNA sequences into secondary structures is viewed as a map that assigns a uniquely defined base pairing pattern to every sequence. The mapping is non-invertible since many sequences fold...
Molecular Insights into Evolution of Phenotypes
Success and efficiency of Darwinian evolution is based on the dichotomy of genotype and phenotype: The former is the object under variation whereas the latter constitutes the target of selection....
RNA Folding at Elementary Step Resolution
Christoph Flamm, Walter Fontana, Ivo L. Hofacker, Peter Schuster
We study the stochastic folding kinetics of RNA sequences into secondary structures with a new algorithm based on the formation, dissociation, and the shifting of individual base pairs. We discuss...
Dynamics of Autocatalytic Replicator Networks Based on Higher Order Ligation Reactions
Peter F. Stadler, Peter Schuster
A class of autocatalytic reaction networks based on template dependent ligation and higher order catalysis is analyzed. Apart from an irreversible ligation reaction we consider only reversible...
Chance and Necessity in Evolution: Lessons from RNA
Peter Schuster, Walter Fontana
The RNA folding map, understood as the relationship between sequences and secondary structures or shapes, exhibits robust statistical properties summarized by three notions: (1) the notion of a...
Nature and Evolution of Early Replicons
Peter Schuster, Peter F. Stadler
RNA and protein molecules were found to be both templates for replication and specific catalysts for biochemical reactions. RNA molecules, although very difficult to obtain via plausible synthetic...
Complete Suboptimal Folding of RNA and the Stability of Secondary Structures
Stefan Wuchty, Walter Fontana, Ivo L. Hofacker, Peter Schuster
An algorithm is presented for generating rigorously all suboptimal secondary structures between the minimum free energy and an arbitrary upper limit. The algorithm performs particularly well in the...
Replication and Mutation on Neutral Networks
Christian Reidys, Christian V. Forst, Peter Schuster
Folding of RNA sequences into secondary structures is viewed as a map that assigns a uniquely defined base pairing pattern to every sequence. This mapping is non-invertible since many sequences fold...
Shaping Space: The Possible and the Attainable in RNA Genotype-Phenotype Mapping
Walter Fontana, Peter Schuster
Understanding which phenotypes are accessible from which genotypes is fundamental for understanding the evolutionary process. This notion of accessibility can be used to define a relation of nearness...
Sequence Redundancy in Biopolymers: A Study on RNA and Protein Structures
Peter Schuster, Peter F. Stadler
Mapping sequences onto biopolymer structures is characterized by redundancy since the numbers of sequences exceed the numbers of structures. The degree of Redundancy depends on the notion of...
Genotypes with Phenotypes: Adventures in an RNA Toy World
Evolution has created the complexity of the animate world and deciphering the language of evolution is the key toward understanding nature. The dynamics of evolution is simplified by considering it...
Continuity in Evolution: On the Nature of Transition
Walter Fontana, Peter Schuster
To distinguish continuous from discontinuous evolutionary change, a relation of nearness between phenotypes is needed. Such a relation is based on the probability of one phenotype being accessible...
Landscapes and Molecular Evolution
Evolution of RNA molecules in vitro is visualized as a hill-climbing process on a fitness landscape that can be derived from molecular properties and functions. The optimization process is shaped by...
Autocatalytic Networks with Intermediates I: Irreversible Reactions
Robert Hecht, Robert Happel, Peter Schuster, Peter F. Stadler
A class of autocatalytic reaction networks based on template dependent replication and specific catalysis is considered. Trimolecular "elementary strps" of simple replicator dynamics are resolved...
Algorithmic Independence Properties of RNA Secondary Structure Predictions
Manfred Tacker, Peter F. Stadler, Ivo L. Hofacker, Peter Schuster
Algorithms predicting RNA secondary structures based on different folding criteria---minimum free energy (mfe), kinetic folding (kin), maximum matching (mm)---and different parameter sets are studied...
Analysis of RNA Sequence Structure Maps by Exhaustive Enumeration
Walter Gruner, Robert Giegerich, Dirk Strothmann, Christian Reidys, Jacqueline Weber, Ivo L. Hofacker, ...
Global relations between RNA sequences and secondary structures are understood as mappings from sequence space into shape space. These mappings are investigated by exhaustive folding of all GC and AU...
Approximate Scaling Properties of RNA Free Energy Landscapes
Subbiah Baskaran, Peter F. Stadler, Peter Schuster
RNA free energy landscapes are analyzed by means of "time-series" that are obtained from random walks restricted to excursion sets. The power spectra, the scaling of the jump size distribution, and...
Generic Properties of Combinatory Maps: Neutral Networks of RNA Secondary Structures
Christian Reidys, Peter F. Stadler, Peter Schuster
Random graph theory is used to model relationships between sequences and secondary structure of RNA molecules. Sequences folding into identical structures form neutral networks which percolate...
Permanence of Sparse Autocatalytic Networks
Peter F. Stadler, Peter Schuster
Some global dynamical properties of catalytic networks, in particular permanence, are closely related with a directed graph representing the differential equation. It can be shown that for every...
Combinatorics of RNA Secondary Structures
Ivo L. Hofacker, Peter Schuster, Peter F. Stadler
Secondary structures of polynucleotides can be view as a certain class of planar vertex-labeled graphs. We construct recursion formulae enumerating various sub-classes of these graphs as well as...
Dynamics of Small Autocatalytic Reaction Networks II: Replication, Mutation and Catalysis
Peter F. Stadler, Wolfgang Schnabl, Christian V. Forst, Peter Schuster
Mutation is introduced into autocatalytic reaction networks. The differential equations obtained are neither of replicator type nor can they be transformed straightway into a linear equation....
Landscapes Complex Optimization Problems and Biopolymer Structures
Peter Schuster, Peter F. Stadler
The evolution of RNA molecules in replication assays, viroids and RNA viruses can be viewed as an adaptation process on a ``fitness'' landscape. The dynamics of evolution is hence tightly linked to...
Immune Networks Modeled by Replicator Equations
Peter F. Stadler, Peter Schuster, Alan S. Perelson
In order to evaluate the role of idiotypic networks in the operation of the immune system a number of mathematical models have been formulated. Here we examine a class of B-cell models in which cell...
From Sequences to Shapes and Back: A Case Study in RNA Secondary Structures
Peter Schuster, Walter Fontana, Peter F. Stadler, Ivo L. Hofacker
RNA folding is viewed as a map assigning secondary structures to sequences. At fixed chain length the number of sequences exceeds by far the number of structures. Frequencies of structures are highly...
Fast Folding and Comparison of RNA Secondary Structures
Ivo L. Hofacker, Walter Fontana, Peter F. Stadler, L. Sebastian Bonhoeffer, Manfred Tacker, Peter Schuster
Computer codes for computation and comparison of RNA secondary structures, the {\tt Vienna RNA package}, are presented, that are based on dynamic programming algorithms and aim at predictions of...
Statistics of RNA Melting Kinectics
Manfred Tacker, Walter Fontana, Peter F. Stadler, Peter Schuster
We present and study the behavior of a simple kinetic model for the melting of RNA secondary structures, given that those structures are known. The model is then used as a map that assigns structure...
A minimal and self-consistent in silico cell model based on macromolecular interactions
Flamm, Christoph, Endler, Lukas, Müller, Stefan, Widder, Stefanie, Schuster, Peter
A self-consistent minimal cell model with a physically motivated schema for molecular interaction is introduced and described. The genetic and metabolic reaction network of the cell is modelled by...