40,723 research outputs found
On a New Type of Information Processing for Efficient Management of Complex Systems
It is a challenge to manage complex systems efficiently without confronting
NP-hard problems. To address the situation we suggest to use self-organization
processes of prime integer relations for information processing.
Self-organization processes of prime integer relations define correlation
structures of a complex system and can be equivalently represented by
transformations of two-dimensional geometrical patterns determining the
dynamics of the system and revealing its structural complexity. Computational
experiments raise the possibility of an optimality condition of complex systems
presenting the structural complexity of a system as a key to its optimization.
From this perspective the optimization of a system could be all about the
control of the structural complexity of the system to make it consistent with
the structural complexity of the problem. The experiments also indicate that
the performance of a complex system may behave as a concave function of the
structural complexity. Therefore, once the structural complexity could be
controlled as a single entity, the optimization of a complex system would be
potentially reduced to a one-dimensional concave optimization irrespective of
the number of variables involved its description. This might open a way to a
new type of information processing for efficient management of complex systems.Comment: 5 pages, 2 figures, to be presented at the International Conference
on Complex Systems, Boston, October 28 - November 2, 200
Surveying structural complexity in quantum many-body systems
Quantum many-body systems exhibit a rich and diverse range of exotic
behaviours, owing to their underlying non-classical structure. These systems
present a deep structure beyond those that can be captured by measures of
correlation and entanglement alone. Using tools from complexity science, we
characterise such structure. We investigate the structural complexities that
can be found within the patterns that manifest from the observational data of
these systems. In particular, using two prototypical quantum many-body systems
as test cases - the one-dimensional quantum Ising and Bose-Hubbard models - we
explore how different information-theoretic measures of complexity are able to
identify different features of such patterns. This work furthers the
understanding of fully-quantum notions of structure and complexity in quantum
systems and dynamics.Comment: 9 pages, 5 figure
Structural Complexity and Phonon Physics in 2D Arsenenes
In the quest for stable 2D arsenic phases, four different structures have
been recently claimed to be stable. We show that, due to phonon contributions,
the relative stability of those structures differs from previous reports and
depends crucially on temperature. We also show that one of those four phases is
in fact mechanically unstable. Furthermore, our results challenge the common
assumption of an inverse correlation between structural complexity and thermal
conductivity. Instead, a richer picture emerges from our results, showing how
harmonic interactions, anharmonicity and symmetries all play a role in
modulating thermal conduction in arsenenes. More generally, our conclusions
highlight how vibrational properties are an essential element to be carefully
taken into account in theoretical searches for new 2D materials
Maximum Entropy Production Principle for Stock Returns
In our previous studies we have investigated the structural complexity of
time series describing stock returns on New York's and Warsaw's stock
exchanges, by employing two estimators of Shannon's entropy rate based on
Lempel-Ziv and Context Tree Weighting algorithms, which were originally used
for data compression. Such structural complexity of the time series describing
logarithmic stock returns can be used as a measure of the inherent (model-free)
predictability of the underlying price formation processes, testing the
Efficient-Market Hypothesis in practice. We have also correlated the estimated
predictability with the profitability of standard trading algorithms, and found
that these do not use the structure inherent in the stock returns to any
significant degree. To find a way to use the structural complexity of the stock
returns for the purpose of predictions we propose the Maximum Entropy
Production Principle as applied to stock returns, and test it on the two
mentioned markets, inquiring into whether it is possible to enhance prediction
of stock returns based on the structural complexity of these and the mentioned
principle.Comment: 14 pages, 5 figure
Plant structural complexity and mechanical defenses mediate predator-prey interactions in an odonate-bird system.
Habitat-forming species provide refuges for a variety of associating species; these refuges may mediate interactions between species differently depending on the functional traits of the habitat-forming species. We investigated refuge provisioning by plants with different functional traits for dragonfly and damselfly (Odonata: Anisoptera and Zygoptera) nymphs emerging from water bodies to molt into their adult stage. During this period, nymphs experience high levels of predation by birds. On the shores of a small pond, plants with mechanical defenses (e.g., thorns and prickles) and high structural complexity had higher abundances of odonate exuviae than nearby plants which lacked mechanical defenses and exhibited low structural complexity. To disentangle the relative effects of these two potentially important functional traits on nymph emergence-site preference and survival, we conducted two fully crossed factorial field experiments using artificial plants. Nymphs showed a strong preference for artificial plants with high structural complexity and to a lesser extent, mechanical defenses. Both functional traits increased nymph survival but through different mechanisms. We suggest that future investigations attempt to experimentally separate the elements contributing to structural complexity to elucidate the mechanistic underpinnings of refuge provisioning
Categorical invariance and structural complexity in human concept learning
An alternative account of human concept learning based on an invariance measure of the categorical\ud
stimulus is proposed. The categorical invariance model (CIM) characterizes the degree of structural\ud
complexity of a Boolean category as a function of its inherent degree of invariance and its cardinality or\ud
size. To do this we introduce a mathematical framework based on the notion of a Boolean differential\ud
operator on Boolean categories that generates the degrees of invariance (i.e., logical manifold) of the\ud
category in respect to its dimensions. Using this framework, we propose that the structural complexity\ud
of a Boolean category is indirectly proportional to its degree of categorical invariance and directly\ud
proportional to its cardinality or size. Consequently, complexity and invariance notions are formally\ud
unified to account for concept learning difficulty. Beyond developing the above unifying mathematical\ud
framework, the CIM is significant in that: (1) it precisely predicts the key learning difficulty ordering of\ud
the SHJ [Shepard, R. N., Hovland, C. L.,&Jenkins, H. M. (1961). Learning and memorization of classifications.\ud
Psychological Monographs: General and Applied, 75(13), 1-42] Boolean category types consisting of three\ud
binary dimensions and four positive examples; (2) it is, in general, a good quantitative predictor of the\ud
degree of learning difficulty of a large class of categories (in particular, the 41 category types studied\ud
by Feldman [Feldman, J. (2000). Minimization of Boolean complexity in human concept learning. Nature,\ud
407, 630-633]); (3) it is, in general, a good quantitative predictor of parity effects for this large class of\ud
categories; (4) it does all of the above without free parameters; and (5) it is cognitively plausible (e.g.,\ud
cognitively tractable)
Exploiting Structural Complexity for Robust and Rapid Hyperspectral Imaging
This paper presents several strategies for spectral de-noising of
hyperspectral images and hypercube reconstruction from a limited number of
tomographic measurements. In particular we show that the non-noisy spectral
data, when stacked across the spectral dimension, exhibits low-rank. On the
other hand, under the same representation, the spectral noise exhibits a banded
structure. Motivated by this we show that the de-noised spectral data and the
unknown spectral noise and the respective bands can be simultaneously estimated
through the use of a low-rank and simultaneous sparse minimization operation
without prior knowledge of the noisy bands. This result is novel for for
hyperspectral imaging applications. In addition, we show that imaging for the
Computed Tomography Imaging Systems (CTIS) can be improved under limited angle
tomography by using low-rank penalization. For both of these cases we exploit
the recent results in the theory of low-rank matrix completion using nuclear
norm minimization
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