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

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

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

Approach to the Organisational Complexity in Terms of Network and Intellectual Capital Concepts

The viability of the systems depends on the way of adaptation of the internal complexity to the environmental complexity. Under structural aspect, any complex system represents a network. Complexity may be estimated on the basis of density and of the non-redundant character of the network. The capacity of the networks to create and diffuse knowledge is essential. Comparing the change speed of the environment with the knowledge processing speed in the system, we can determine the maximum complexity that can be absorbed. A close image of the internal complexity is the level of the human and structural capital. The external complexity may be expressed by means of the relational capital.requisite variety, endogenous complexity, exogenous complexity, network, intellectual capital

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

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