3,910,822 research outputs found
Are galaxy distributions scale invariant? A perspective from dynamical systems theory
Unless there is evidence for fractal scaling with a single exponent over
distances .1 <= r <= 100 h^-1 Mpc then the widely accepted notion of scale
invariance of the correlation integral for .1 <= r <= 10 h^-1 Mpc must be
questioned. The attempt to extract a scaling exponent \nu from the correlation
integral n(r) by plotting log(n(r)) vs. log(r) is unreliable unless the
underlying point set is approximately monofractal. The extraction of a spectrum
of generalized dimensions \nu_q from a plot of the correlation integral
generating function G_n(q) by a similar procedure is probably an indication
that G_n(q) does not scale at all. We explain these assertions after defining
the term multifractal, mutually--inconsistent definitions having been confused
together in the cosmology literature. Part of this confusion is traced to a
misleading speculation made earlier in the dynamical systems theory literature,
while other errors follow from confusing together entirely different
definitions of ``multifractal'' from two different schools of thought. Most
important are serious errors in data analysis that follow from taking for
granted a largest term approximation that is inevitably advertised in the
literature on both fractals and dynamical systems theory.Comment: 39 pages, Latex with 17 eps-files, using epsf.sty and a4wide.sty
(included) <[email protected]
Global entrainment of transcriptional systems to periodic inputs
This paper addresses the problem of giving conditions for transcriptional
systems to be globally entrained to external periodic inputs. By using
contraction theory, a powerful tool from dynamical systems theory, it is shown
that certain systems driven by external periodic signals have the property that
all solutions converge to a fixed limit cycle. General results are proved, and
the properties are verified in the specific case of some models of
transcriptional systems. The basic mathematical results needed from contraction
theory are proved in the paper, making it self-contained
Rerepresenting and Restructuring Domain Theories: A Constructive Induction Approach
Theory revision integrates inductive learning and background knowledge by
combining training examples with a coarse domain theory to produce a more
accurate theory. There are two challenges that theory revision and other
theory-guided systems face. First, a representation language appropriate for
the initial theory may be inappropriate for an improved theory. While the
original representation may concisely express the initial theory, a more
accurate theory forced to use that same representation may be bulky,
cumbersome, and difficult to reach. Second, a theory structure suitable for a
coarse domain theory may be insufficient for a fine-tuned theory. Systems that
produce only small, local changes to a theory have limited value for
accomplishing complex structural alterations that may be required.
Consequently, advanced theory-guided learning systems require flexible
representation and flexible structure. An analysis of various theory revision
systems and theory-guided learning systems reveals specific strengths and
weaknesses in terms of these two desired properties. Designed to capture the
underlying qualities of each system, a new system uses theory-guided
constructive induction. Experiments in three domains show improvement over
previous theory-guided systems. This leads to a study of the behavior,
limitations, and potential of theory-guided constructive induction.Comment: See http://www.jair.org/ for an online appendix and other files
accompanying this articl
Well-posedness and Stability for Interconnection Structures of Port-Hamiltonian Type
We consider networks of infinite-dimensional port-Hamiltonian systems
on one-dimensional spatial domains. These subsystems of
port-Hamiltonian type are interconnected via boundary control and observation
and are allowed to be of distinct port-Hamiltonian orders .
Wellposedness and stability results for port-Hamiltonian systems of fixed order
are thereby generalised to networks of such. The abstract
theory is applied to some particular model examples.Comment: Submitted to: Control Theory of Infinite-Dimensional System. Workshop
on Control Theory of Infinite-Dimensional Systems, Hagen, January 2018.
Operator Theory: Advances and Applications. (32 pages, 5 figures
<i>H</i><sub>2</sub> and mixed <i>H</i><sub>2</sub>/<i>H</i><sub>â</sub> Stabilization and Disturbance Attenuation for Differential Linear Repetitive Processes
Repetitive processes are a distinct class of two-dimensional systems (i.e., information propagation in two independent directions) of both systems theoretic and applications interest. A systems theory for them cannot be obtained by direct extension of existing techniques from standard (termed 1-D here) or, in many cases, two-dimensional (2-D) systems theory. Here, we give new results towards the development of such a theory in H2 and mixed H2/Hâ settings. These results are for the sub-class of so-called differential linear repetitive processes and focus on the fundamental problems of stabilization and disturbance attenuation
Bifurcation Phenomena in Two-Dimensional Piecewise Smooth Discontinuous Maps
In recent years the theory of border collision bifurcations has been
developed for piecewise smooth maps that are continuous across the border, and
has been successfully applied to explain nonsmooth bifurcation phenomena in
physical systems. However, many switching dynamical systems have been found to
yield two-dimensional piecewise smooth maps that are discontinuous across the
border. The theory for understanding the bifurcation phenomena in such systems
is not available yet. In this paper we present the first approach to the
problem of analysing and classifying the bifurcation phenomena in
two-dimensional discontinuous maps, based on a piecewise linear approximation
in the neighborhood of the border. We explain the bifurcations occurring in the
static VAR compensator used in electrical power systems, using the theory
developed in this paper. This theory may be applied similarly to other systems
that yield two-dimensional discontinuous maps
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