24,120 research outputs found
Invariants and orthogonal -polynomials associated with
The spaces of invariants and the zonal spherical functions associated with
quantum super 2-shpheres defined by are discussed.
Connection between the zonal spherical functions and orthogonal -polynomials
from the Askey-Wilson scheme is investigated.Comment: AMS-Tex, preprint 18 page
Quantum super spheres and their transformation groups, representations, and little -Jacobi polynomials
Quantum super 2-shpheres and the corresponding quantum super transformation
group are introduced in analogy to the well-known quantum 2-shpheres and
quantum SL(2), connection between little -Jacobi polynomials and the finite
dimensional representations of the quantum super group is formulated, and the
Peter-Weyl theorem is obtained.Comment: AMS-Tex, preprint 18 page
Characterization of Boolean Networks with Single or Bistable States
Many biological systems, such as metabolic pathways, exhibit bistability
behavior: these biological systems exhibit two distinct stable states with
switching between the two stable states controlled by certain conditions. Since
understanding bistability is key for understanding these biological systems,
mathematical modeling of the bistability phenomenon has been at the focus of
researches in quantitative and system biology. Recent study shows that Boolean
networks offer relative simple mathematical models that are capable of
capturing these essential information. Thus a better understanding of the
Boolean networks with bistability property is desirable for both theoretical
and application purposes. In this paper, we describe an algebraic condition for
the number of stable states (fixed points) of a Boolean network based on its
polynomial representation, and derive algorithms for a Boolean network to have
a single stable state or two stable states. As an example, we also construct a
Boolean network with exactly two stable states for the lac operon's
-galactosidase regulatory pathway when glucose is absent based on a
delay differential equation modelComment: Main results of this article appeared as a 4 page abstract in the
ICBBE 2012 Conference Proceeding, pp. 517-52
Structures of Coincidence Symmetry Groups
The structure of the coincidence symmetry group of an arbitrary
-dimensional lattice in the -dimensional Euclidean space is considered by
describing a set of generators. Particular attention is given to the
coincidence isometry subgroup (the subgroup formed by those coincidence
symmetries which are elements of the orthogonal group). Conditions under which
the coincidence isometry group can be generated by reflections defined by
vectors of the lattice will be discussed, and an algorithm to decompose an
arbitrary element of the coincidence isometry group in terms of reflections
defined by vectors of the lattice will be given.Comment: AMS-Latex, preprint 13 page
Multiresolution finite element method based on a new locking-free rectangular Mindlin plate element
A locking-free rectangular Mindlin plate element with a new multi-resolution
analysis (MRA) is proposed and a new finite element method is hence presented.
The MRA framework is formulated out of a mutually nesting displacement subspace
sequence whose basis functions are constructed of scaling and shifting on the
element domain of basic node shape function. The basic node shape function is
constructed by extending the node shape function of a traditional Mindlin plate
element to other three quadrants around the coordinate zero point. As a result,
a new rational MRA concept together with the resolution level (RL) is
constituted for the element. The traditional 4-node rectangular Mindlin plate
element and method is a mono-resolution one and also a special case of the
proposed element and method. The meshing for the monoresolution plate element
model is based on the empiricism while the RL adjusting for the multiresolution
is laid on the rigorous mathematical basis. The analysis clarity of a plate
structure is actually determined by the RL, not by the mesh. Thus, the accuracy
of a plate structural analysis is replaced by the clarity, the irrational MRA
by the rational and the mesh model by the RL that is the discretized model by
the integrated.Comment: 16 pages. arXiv admin note: substantial text overlap with
arXiv:1404.1165, arXiv:1405.677
Indices of Coincidence Isometries of the Hyper Cubic Lattice
The problem of computing the index of a coincidence isometry of the hyper
cubic lattice is considered. The normal form of a rational
orthogonal matrix is analyzed in detail, and explicit formulas for the index of
certain coincidence isometries of are obtained. These formulas
generalize the known results for .Comment: AMS-Latex, preprint 10 page
An Algorithm for Detecting Fixed Points of Boolean Networks
In the applications of Boolean networks to modeling biological systems, an
important computational problem is the detection of the fixed points of these
networks. This is an NP-complete problem in general. There have been various
attempts to develop algorithms to address the computation need for large size
Boolean networks. The existing methods are usually based on known algorithms
and thus limited to the situations where these known algorithms can apply. In
this paper, we propose a novel approach to this problem. We show that any
system of Boolean equations is equivalent to one Boolean equation, and thus it
is possible to divide the polynomial equation system which defines the fixed
points of a Boolean network into subsystems that can be solved easily. After
solving these subsystems and thus reducing the number of states, we can combine
the solutions to obtain all fixed points of the given network. This approach
does not depend on other algorithms and it is straightforward and easy to
implement. We show that our method can handle large size Boolean networks, and
demonstrate its effectiveness by using MAPLE to compute the fixed points of
Boolean networks with hundreds of nodes and thousands of interactions.Comment: A shorter version of this paper appeared in the conference proceeding
of ICME 2013 (Beijing), pp. 670 - 67
Boolean Networks with Multi-Expressions and Parameters
To model biological systems using networks, it is desirable to allow more
than two levels of expression for the nodes and to allow the introduction of
parameters. Various modeling and simulation methods addressing these needs
using Boolean models, both synchronous and asynchronous, have been proposed in
the literature. However, analytical study of these more general Boolean
networks models is lagging. This paper aims to develop a concise theory for
these different Boolean logic based modeling methods. Boolean models for
networks where each node can have more than two levels of expression and
Boolean models with parameters are defined algebraically with examples
provided. Certain classes of random asynchronous Boolean networks and
deterministic moduli asynchronous Boolean networks are investigated in detail
using the setting introduced in this paper. The derived theorems provide a
clear picture for the attractor structures of these asynchronous Boolean
networks.Comment: A version of this paper appeared in IEEE Transactions on
Computational Biology and Bioinformatic
Dynamics of Boolean Networks
Boolean networks are special types of finite state time-discrete dynamical
systems. A Boolean network can be described by a function from an n-dimensional
vector space over the field of two elements to itself. A fundamental problem in
studying these dynamical systems is to link their long term behaviors to the
structures of the functions that define them. In this paper, a method for
deriving a Boolean network's dynamical information via its disjunctive normal
form is explained. For a given Boolean network, a matrix with entries 0 and 1
is associated with the polynomial function that represents the network, then
the information on the fixed points and the limit cycles is derived by
analyzing the matrix. The described method provides an algorithm for the
determination of the fixed points from the polynomial expression of a Boolean
network. The method can also be used to construct Boolean networks with
prescribed limit cycles and fixed points. Examples are provided to explain the
algorithm
Gaussian binomials and the number of sublattices
The purpose of this short communication is to make some observations on the
connections between various existing formulas of counting the number of
sublattices of a fixed index in an -dimensional lattice and their connection
with the Gaussian binomials.Comment: AMS-Latex, preprint 3 page
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