3,321 research outputs found
Fractal-cluster theory and thermodynamic principles of the control and analysis for the self-organizing systems
The theory of resource distribution in self-organizing systems on the basis
of the fractal-cluster method has been presented. This theory consists of two
parts: determined and probable. The first part includes the static and dynamic
criteria, the fractal-cluster dynamic equations which are based on the
fractal-cluster correlations and Fibonacci's range characteristics. The second
part of the one includes the foundations of the probable characteristics of the
fractal-cluster system. This part includes the dynamic equations of the
probable evolution of these systems. By using the numerical researches of these
equations for the stationary case the random state field of the one in the
phase space of the , , criteria have been obtained. For the
socio-economical and biological systems this theory has been tested.Comment: 37 pages, 20 figures, 4 table
Partitioning de Bruijn Graphs into Fixed-Length Cycles for Robot Identification and Tracking
We propose a new camera-based method of robot identification, tracking and
orientation estimation. The system utilises coloured lights mounted in a circle
around each robot to create unique colour sequences that are observed by a
camera. The number of robots that can be uniquely identified is limited by the
number of colours available, , the number of lights on each robot, , and
the number of consecutive lights the camera can see, . For a given set of
parameters, we would like to maximise the number of robots that we can use. We
model this as a combinatorial problem and show that it is equivalent to finding
the maximum number of disjoint -cycles in the de Bruijn graph
.
We provide several existence results that give the maximum number of cycles
in in various cases. For example, we give an optimal
solution when . Another construction yields many cycles in larger
de Bruijn graphs using cycles from smaller de Bruijn graphs: if
can be partitioned into -cycles, then
can be partitioned into -cycles for any divisor of
. The methods used are based on finite field algebra and the combinatorics
of words.Comment: 16 pages, 4 figures. Accepted for publication in Discrete Applied
Mathematic
Multicanonical Study of Coarse-Grained Off-Lattice Models for Folding Heteropolymers
We have performed multicanonical simulations of hydrophobic-hydrophilic
heteropolymers with two simple effective, coarse-grained off-lattice models to
study the influence of specific interactions in the models on conformational
transitions of selected sequences with 20 monomers. Another aspect of the
investigation was the comparison with the purely hydrophobic homopolymer and
the study of general conformational properties induced by the "disorder" in the
sequence of a heteropolymer. Furthermore, we applied an optimization algorithm
to sequences with up to 55 monomers and compared the global-energy minimum
found with lowest-energy states identified within the multicanonical
simulation. This was used to find out how reliable the multicanonical method
samples the free-energy landscape, in particular for low temperatures.Comment: 11 pages, RevTeX, 10 Postscript figures, Author Information under
http://www.physik.uni-leipzig.de/index.php?id=2
Fisher information approach to non-equilibrium phase transitions in quantum XXZ spin chain with boundary noise
We investigated quantum critical behaviours in the non-equilibrium steady
state of a spin chain with boundary Markovian noise using the Fisher
information. The latter represents the distance between two infinitesimally
close states, and its superextensive size scaling witnesses a critical
behaviour due to a phase transition, since all the interaction terms are
extensive. Perturbatively in the noise strength, we found superextensive Fisher
information at anisotropy and irrational
irrespective of the order of two non-commuting
limits, i.e. the thermodynamic limit and the limit of sending
to an irrational number via a sequence of rational
approximants. From this result we argue the existence of a non-equilibrium
quantum phase transition with a critical phase . From the
non-superextensivity of the Fisher information of reduced states, we infer that
this non-equilibrium quantum phase transition does not have local order
parameters but has non-local ones, at least at . In the
non-perturbative regime for the noise strength, we numerically computed the
reduced Fisher information which lower bounds the full state Fisher
information, and is superextensive only at . Form the latter
result, we derived local order parameters at in the
non-perturbative case. The existence of critical behaviour witnessed by the
Fisher information in the phase is still an open problem. The
Fisher information also represents the best sensitivity for any estimation of
the control parameter, in our case the anisotropy , and its
superextensivity implies enhanced estimation precision which is also highly
robust in the presence of a critical phase
Knowledge-generating Efficiency in Innovation Systems: The relation between structural and temporal effects
Using time series of US patents per million inhabitants, knowledge-generating
cycles can be distinguished. These cycles partly coincide with Kondratieff long
waves. The changes in the slopes between them indicate discontinuities in the
knowledge-generating paradigms. The knowledge-generating paradigms can be
modeled in terms of interacting dimensions (for example, in
university-industry-government relations) that set limits to the maximal
efficiency of innovation systems. The maximum values of the parameters in the
model are of the same order as the regression coefficients of the empirical
waves. The mechanism of the increase in the dimensionality is specified as
self-organization which leads to the breaking of existing relations into the
more diversified structure of a fractal-like network. This breaking can be
modeled in analogy to 2D and 3D (Koch) snowflakes. The boost of knowledge
generation leads to newly emerging technologies that can be expected to be more
diversified and show shorter life cycles than before. Time spans of the
knowledge-generating cycles can also be analyzed in terms of Fibonacci numbers.
This perspective allows for forecasting expected dates of future possible
paradigm changes. In terms of policy implications, this suggests a shift in
focus from the manufacturing technologies to developing new organizational
technologies and formats of human interaction
Practical implementation of mutually unbiased bases using quantum circuits
The number of measurements necessary to perform the quantum state
reconstruction of a system of qubits grows exponentially with the number of
constituents, creating a major obstacle for the design of scalable tomographic
schemes. We work out a simple and efficient method based on cyclic generation
of mutually unbiased bases. The basic generator requires only Hadamard and
controlled-phase gates, which are available in most practical realizations of
these systems. We show how complete sets of mutually unbiased bases with
different entanglement structures can be realized for three and four qubits. We
also analyze the quantum circuits implementing the various entanglement
classes.Comment: 5 pages, 2 color figures. Comments welcome
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