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Construction of Curtis-Phan-Tits system in black box classical groups
Get PDFWe present a polynomial time Monte-Carlo algorithm for finite simple black box classical groups of odd characteristic which constructs all root SL(2,q)-subgroups associated with the nodes of the extended Dynkin diagram of the corresponding algebraic group
NLEVP: A Collection of Nonlinear Eigenvalue Problems. Users' Guide
Get PDFThis is the Users' Guide for NLEVP: a collection of nonlinear eigenvalue problems provided in the form of a MATLAB toolbox. A separate paper describes the collection and its organization
Enzyme kinetics informatics: from instrument to browser
Get PDFA limited number of publicly available resources provide access to enzyme kinetic parameters. These have been compiled through manual data mining of published papers, not from the original, raw experimental data from which the parameters were calculated. This is largely due to the lack of software or standards to support the capture, analysis, storage and dissemination of such experimental data. Introduced here is an integrative system to manage experimental enzyme kinetics data from instrument to browser. The approach is based on two interrelated databases: the existing SABIO- RK database, containing kinetic data and corresponding metadata, and the newly introduced experimental raw data repository, MeMo-RK. Both systems are publicly available by web browser and web service interfaces and are configurable to ensure privacy of unpublished data. Users of this system are provided with the ability to view both kinetic parameters and the experimental raw data from which they are calculated, providing increased confidence in the data. A data analysis and submission tool, the kinetics- wizard, has been developed to allow the experimentalist to perform data collection, analysis and submission to both data resources. The system is designed to be extensible, allowing integration with other manufacturer instruments covering a range of analytical techniques
NLEVP: A Collection of Nonlinear Eigenvalue Problems
Get PDFWe present a collection of 46 nonlinear eigenvalue problems
in the form of a MATLAB toolbox.
The collection contains problems from models of real-life applications
as well as ones constructed specifically to have particular
properties.
A classification is given of polynomial eigenvalue problems
according to their structural properties.
Identifiers based on these and other properties can be used to extract
particular types of problems from the collection.
A brief description of each problem is given.
NLEVP serves both to illustrate the tremendous variety of applicationseigenvalue problems and to provide representative problems for testing,
tuning, and benchmarking of algorithms and codes
Passage-time Computation and Aggregation Strategies for Large Semi-Markov Processes
Get PDFHigh-level semi-Markov modelling paradigms such as semi-Markov stochastic Petri nets and process algebras are used to capture realistic performance models of computer and communication systems but often have the drawback of generating huge underlying semi-Markov processes. Extraction of performance measures such as steady-state probabilities and passage-time distributions therefore relies on sparse matrix�vector operations involving very large transition matrices. Previous studies have shown that exact state-by-state aggregation of semi-Markov processes can be applied to reduce the number of states. This can, however, lead to a dramatic increase in matrix density caused by the creation of additional transitions between remaining states. Our paper addresses this issue by presenting the concept of state space partitioning for aggregation.
We present a new deterministic partitioning method which we term barrier partitioning. We show that barrier partitioning is capable of splitting very large semi-Markov models into a number of partitions such that first passage-time analysis can be performed more quickly and using up to 99% less memory than existing algorithms
Geometric structure in the representation theory of p-adic groups II
Get PDFThis expository note will state the ABP (Aubert-Baum-Plymen) conjecture. The conjecture can be stated at four levels:
1. K-theory of C*-algebras
2. Periodic cyclic homology of finite type algebras
3. Geometric equivalence of finite type algebras
4. Representation theory.
The emphasis in this note will be on representation theory. This is v2
Free central extensions of groups and modular Lie powers of relation modules
No full textThe most prominent special case of our main result is that the free centre-by-(nilpotent of class (c-1))-by-abelian
groups F/[\gamma_c(F'),F] are torsion-free whenever c is divisible by at least two distinct
primes. This is in stark contrast to the case where c is a prime
or c=4, where these relatively free groups contain non-trivial
elements of finite order
A Schur--Pad\'e Algorithm for Fractional Powers of a Matrix
No full textA new algorithm is developed for computing arbitrary real powers of a matrix . The algorithm starts with a Schur decomposition, takes square roots of the triangular factor , evaluates an Pad\'e approximant of at , and squares the result times. The parameters and are chosen to minimize the cost subject to achieving double precision accuracy in the evaluation of the Pad\'e approximant, making use of a result that bounds the error in the matrix Pad\'e approximant by the error in the scalar Pad\'e approximant with argument the norm of the matrix. The Pad\'e approximant is evaluated from the continued fraction representation in bottom-up fashion, which is shown to be numerically stable. In the squaring phase the diagonal and first superdiagonal are computed from explicit formulae for , yielding increased accuracy. Since the basic algorithm is designed for , a criterion for reducing an arbitrary real to this range is developed, making use of bounds for the condition number of the problem. How best to compute for a negative integer is also investigated. In numerical experiments the new algorithm is found to be superior in accuracy and stability to several alternatives, including the use of an eigendecomposition and approaches based on the formula
Local presentability of categories of sheaves of modules
Get PDFWe show that the category of modules over a ring in a Grothendieck topos is monadic, and as a consequence, the category of modules over a ring in a locally finitely presentable topos is locally finitely presentable
Computing combinatorial types of trajectories in Pfaffian Dynamics
Get PDFSuppose that the state space of a dynamical system has a finite partition, and each element of the partition is labelled by a letter of some alphabet. Then every trajectory of the system is naturally labelled by a word in this alphabet. This word is called the combinatorial type of the trajectory. In applications it is important to decide whether among a certain family of trajectories there is at least one trajectory of a given type, or whether all the trajectories in this family have the same type. In this paper we construct algorithms for solving this sort of questions for a wide class of Pfaffian dynamical systems, which have elementary (doubly-exponential) upper complexity bounds