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PIFISS Potential (Incompressible) Flow & Iterative Solution Software guide
No full textThis is a guide to the contents and scope of the PIFISS software package
Canonical structure and symmetries of the Schlesinger equations
No full textThe Schlesinger equations S (n,m) describe monodromy preserving deformations of order m Fuchsian systems with n + 1 poles. They can be considered as a family of commuting time-dependent Hamiltonian systems on the direct product of n copies of m × m matrix algebras equipped with the standard linear Poisson bracket. In this paper we present a new canonical Hamiltonian formulation of the general Schlesinger equations S (n,m) for all n, m and we compute the action of the symmetries of the Schlesinger equations in these coordinates
Llama: an online microarray linear analysis tool
Get PDFWe have developed a linear modelling tool for analysis of two-colour microarray data that utilises a per-spot linear model to estimate expression differences. Given the design of the experiment, the program combines all relevant data to provide the best estimate of a particular difference in expression between samples. It constructs multiple estimates based on several slides and combines them to get the most precise overall estimates of differential expression. Every effort has been made to make this tool accessible to biologists and it contains many user-friendly option
Metabolic Pathway Modeling by Using the Nearest Neighbor Algorithm
Get PDFA new computational approach was developed for modeling the metabolic pathways. The new approach is featured by combing the knowledge of gene ontology, microarray, and chemical functional group to formulate the enzyme-substrate/product couples in a 1,660 vector space. The nearest neighbor algorithm was used to perform the prediction of the networking relationship occurring in the metabolic pathways. The average overall success rate by jackknife cross-validation tests for the 79 metabolic pathways in the budding yeast system was over 94%, suggesting that the current approach might become a useful tool for studying metabolic pathways and many other networking-related areas
Complex cobordism classes of homogeneous spaces
Get PDFWe consider compact homogeneous spaces of positive Euler characteristic endowed with an invariant almost complex structure and the canonical action of the maximal torus on . We obtain explicit formula for the cobordism class of such manifold through the weights of the action at the identity
fixed point by an action of the quotient group of the Weyl groups for and . In this way we show that the cobordism class for such manifolds can be computed explicitly without information on their cohomology. We also show that formula for cobordism class provides an explicit way for computing the classical Chern numbers for . As a consequence we obtain that the Chern numbers for can be computed without information on cohomology for . As an application we provide an
explicit formula for cobordism classes and characteristic numbers of the flag manifolds , Grassmann manifolds and some particular interesting examples. This paper is going to have continuation in which will be considered the stable complex structures equivariant under given torus action on homogeneous spaces of positive Euler characteristic
On (2+1)-dimensional hydrodynamic type systems possessing pseudopotential with movable singularities
Get PDFA certain class of integrable hydrodynamic type systems with three
independent and N>1 dependent variables is considered. We
choose the existence of a pseudopotential as a criterion of
integrability. It turns out that the class of integrable systems
having pseudopotentials with movable singularities is described by a
functional equation, which can be solved explicitly. This allows
us to construct interesting examples of integrable hydrodynamic
systems for arbitrary N
Optimal Scaling for Random walk Metropolis on spherically constrained target densities
Get PDFWe consider the problem of optimal scaling of the proposal variance
for multidimensional Random walk Metropolis (RWM) algorithms. It is
well known, for a wide range of continuous target densities, that
the optimal scaling of the proposal variance leads to an average
acceptance rate of 0.234. Therefore a natural question is, do
similar results for target densities which have discontinuities? In
the current work, we answer in the affirmative for a class of
spherically constrained target densities. Even though the acceptance
probability is more complicated than for continuous target
densities, the optimal scaling of the proposal variance again leads
to an average acceptance rate of 0.234
Mathematical abilities and mathematical skills
Get PDFThe concept of mathematical abilities is not something that is frequently discussed. At the personal level, however, almost every mathematician and mathematical educator has relatively firm views on the subject. In this document, we summarise less disputed aspects of the highly complex phenomenon and some of its immediate implication for the educational policy
Mathematics under the Microscope
Get PDFIt is an unusual book which casts new and paradoxical light on the nature of mathematics.
The book will be interesting -- perhaps for different reasons -- to school teachers of mathematics and maths majors at universities, to graduate students in mathematics and computer science, to research mathematicians and computer scientists, to philosophers and historians of mathematics, to psychologists and neurophysiologists.
The author attempts to start a dialogue between mathematicians and cognitive scientists. He discusses, from a working mathematician's point of view, the mystery of mathematical intuition: why are certain mathematical concepts are more intuitive than the others? To what extent the "small scale" structure of mathematical concepts and algorithms reflects the workings of the human brain? What are the "elementary particles'' of mathematics which build up the mathematical universe?
One of the principal points of the book is the essential vertical unity of mathematics, the natural integration of its simplest objects and concepts into the complex hierarchy of mathematics as a whole. The same ideas and patterns of thinking can be found in elementary school arithmetic and in the cutting edge mathematical theories. There are no boundaries between "recreational'', "elementary'', "undergraduate'' and "research'' mathematics; the book freely moves throughout the whole range. Nevertheless, the author takes great care of keeping the book as non-technical as possible.
The book is saturated with amusing examples from a wide range of disciplines -- from turbulence to error-correcting codes to logic -- as well as just puzzles and brainteasers. Despite the very serious subject matter, the author's approach is lighthearted and entertaining