19107527
Investigating DEs with CRACK and related programs
The aim of the package to be described is to try modularizing the investigation of differential equations for which there are no complete algorithms available yet. All, that is available for such problems are algorithms for special situations, e.g. when first integrals with a simple structure exist (e.g. polynomial in first derivatives) or when the problem has infinitesimal symmetries. In all such cases, finally a system of differential equations has to be solved which is overdetermined in the sense that more conditions have to be satisfied than there are unknown functions. To do a variety of such investigations efficiently, like a symmetry analysis, application of symmetries, determination of first integrals, differential factors, equivalent Lagrangians, the strategy is to have one package (CRACK) for simplifying DEs and solving simple DEs as effective as possible and to use this program as the main tool for all the above mentioned investigations. For each investigation there is then only a short program necessary to just formulate the necessary conditions in form of an overdetermined DE-system and to call CRACK to solve this, possibly in a number of successive calls. The examples below shall indicate the range of possible applications.
1220
A comparison of four approaches to the calculation of conservation laws
The paper compares computational aspects of four approaches to compute conservation laws of single differential equations or systems of them, ODEs and PDEs. The only restriction, required by two of the four corresponding computer algebra programs, is that each DE has to be solvable for a leading derivative. Extra constraints may be given. Examples of new conservation laws include non-polynomial expressions, an explicit variable dependence and conservation laws involving arbitrary functions. Examples involve the following equations: Ito, Liouville, Burgers, Kadomtsev-Petviashvili, Karney-Sen-Chu-Verheest, Boussinesq, Tzetzeica, Benney.
1703030
Optimizing GoTools' Search Heuristics using Genetic Algorithms
GoTools is a program which solves life & death problems in the game of Go. This paper describes experiments using a Genetic Algorithm to optimize heuristic weights used by GoTools' tree-search. The complete set of heuristic weights is composed of different subgroups, each of which can be optimized with a suitable fitness function. As a useful side product, an MPI interface for FreePascal was implemented to allow the use of a parallelized fitness function running on a Beowulf cluster. The aim of this exercise is to optimize the current version of GoTools, and to make tools available in preparation of an extension of GoTools for solving open boundary life & death problems, which will introduce more heuristic parameters to be fine tuned.
27429660
Automatic determination of dynamical symmetries of ordinary differential equations
We describe the application of a computer program CRACKSTAR for the exact analytic solution of overdetermined systems of differential equations which result in determining point-, contact- and dynamical symmetries of ordinary differential equations. Examples are discussed.ZusammenfassungWir beschreiben die Anwendung des Computerprogramms CRACKSTAR zur exakten Lösung überbestimmter Differentialgleichungssysteme, die von der Bestimmung von Punkt- und Berührungssymmetrien sowie dynamischer Symmetrien gewöhnlicher Differentialgleichungen herrühren.
45184054
A package for the analytic investigation and exact solution of differential equations
To find exact solutions of differential equations fDEs) one usually performs a variety of tests and ansaetze as e.g. the symmetry ansatz, separation ansatz, ansaetze for first integrals. When carrying through these ideas one h a s to solve overdetermined systems of partial DEs fPDEs). Whereas the formulation of the overdetermined system f o r each ansatz is achieved by different programs we use one program to investigate the overdetermined sys~. This program CRAOKSTAR contains three basic modules for the deooupling of DEs, for the integration of exact DEs and f o r separation. They are explained by examples. With these new a b i l i t i e s i t becomes poss ib le f o r CRACKSTAR to so lve systems of DEs which are sore difficult, i.e. the ansatz to be carried through ma y be less restrictive. An example shows that in this way not only point s y m m e t r i e s b u t a l s o m o r e g e n e r a l d y n a m i c a l s y m m e t r i e s o f o r d i n a r y DEs ( O D E s ) c a n b e d e t e r m i n e d . F o r t h e I n v e s t i g a t i o n o f L l e s ~ t r i e s o f systems of PDEs an interval strategy is applied which reduces the effort f o r GKACKSTM~ c o n s i d e r a b l y . F u r t h e r t w o new c o n c e p t s , a n i n t e g r a l a n s a t z f o r ODEs and a generalized separation ansatz f o r PDEs are described as w e l l a s t h e p r o g r a m s w h i c h g e n e r a t e o v e r d e t e r m i n e d s y s t e m s for e a c h ansatz.
895386
Size Reduction and Partial Decoupling of Systems of Equations
A method is presented that reduces the number of terms of systems of linear equations (algebraic, ordinary and partial differential equations). As a byproduct these systems have a tendency to become partially decoupled and are more likely to be factorizable or integrable. A variation of this method is applicable to nonlinear systems. Modifications to improve efficiency are given and examples are shown. This procedure can be used in connection with the computation of the radical of a differential ideal (differential Grobner basis).
15117189
Global Biclustering of Microarray Data
We consider the problem of simultaneously clustering genes and conditions of a gene expression data matrix. A bicluster is defined as a subset of genes that show similar behavior within a subset of conditions. Finding biclusters can be useful for revealing groups of genes involved in the same molecular process as well as groups of conditions where this process takes place. Previous work either deals with local, bicluster-based criteria or assumes a very specific structure of the data matrix (e.g. checkerboard or block-diagonal) (Ryan et al., 2005). In contrast, our goal is to find a set of flexibly arranged biclusters which is optimal in regard to a global objective function. As this is a NP-hard combinatorial problem, we describe several techniques to obtain approximate solutions. We benchmarked our approach successfully on the Alizadeh B-cell lymphoma data set (Alizadeh et al., 2000)
35587806
Ein Fuzzy geregeltes optisches Meßsystem zur Messung von 3D-Verformungn
Es wird ein optischer Mesplatz zur beruhrungslosen Verformungsmessung an Proben aus Polymerschaum vorgestellt. Dabei werden zwei bewahrte optische Mesmethoden, ein als digitale Specklephotographie bezeichnetes Korrelationsverfahren und das Projektionsstreifenverfahren miteinander kombiniert, um das dreidimensionale Verschiebungsvektorfeld auf der Probenoberflache zu ermitteln. Grose Dehnungen fuhren bei der Verwendung der digitalen Specklephotographie zu Dekorrelationen, die die Anwendbarkeit des Mesverfahrens beschranken. Durch die Verarbeitung von Vorinformationen und den Einsatz von Fuzzylogik ist es gelungen, den Anwendungsbereich fur beide Mesverfahren zu erweitern.
41947706
Secure Communication in Distributed Ada
This document describes an implementation of secure communication for distributed applications in Ada 95. It explains the basics of cryptography and introduces the problem of key exchange. After a brief description of distributed systems in Ada 95, the modular structure of the implementation and the way it handles key distribution is presented.
43214033
Ein neuer Ansatz zur Lösung der Phasenentfaltungsproblematik
Ein durch eine harmonische Intensitatsverteilung beschreibbares Streifenmuster soll ausgewertet werden. Dabei mus fur jeden Punkt des Musters die Phasenlage bestimmt werden. Mit auto-matischen Phasenauswertemethoden last sich im allgemeinen die Phase nur im sich periodisch fortsetzenden Werteintervall [−π, π] bestimmen (Sagezahnbild). Das Zusammensetzen zur Gesamtphase wird als Phasenentfaltung bezeichnet. Die Anwendung des Streifenprojektions-verfahrens [Breu93] zur Konturbestimmung von Schaumstoffoberflachen in Kombination mit der Phasenshifttechnik fuhrt zu einem Sagezahnbild, dessen automatische Entfaltung bei Anwendung von ublichen Methoden zu erheblichen Fehlern fuhrt. Oftmals ist nur eine interaktive Phasenkorrektur durch den Benutzer moglich. Mit Hilfe der Fuzzy-Logik kann man das menschliche Expertenwissen in einer vom Computer verarbeitbaren Form fur die automatische Phasenentfaltung zur Verfugung stellen.
1643372
Fault Tolerance by Transparent Replication for Distributed Ada 95
This paper presents the foundations of RAPIDS ("Replicated Ada Partitions In Distributed Systems"), an implementation of the Distributed Systems Annex E incorporating the transparent replication of partitions in distributed Ada 95 applications. RAPIDS is a replication manager for semi-active replication based on a piecewise deterministic computation model. It guarantees replica consistency for arbitrary Ada 95 partitions despite the inherent non-determinism of multitasking, offering k-resilient partitions. The RAPIDS prototype is implemented for the GNAT compiler and evolved from its PCS, Garlic.