Complexity analysis of EEG in patients with schizophrenia using fractal dimension

We computed Higuchi's fractal dimension (FD) of resting, eyes closed EEG recorded from 30 scalp locations in 18 male neuroleptic-naive, recent-onset schizophrenia (NRS) subjects and 15 male healthy control (HC) subjects, who were group-matched for age. Schizophrenia patients showed a diffuse reduction of FD except in the bilateral temporal and occipital regions, with the reduction being most prominent bifrontally. The positive symptom (PS) schizophrenia subjects showed FD values similar to or even higher than HC in the bilateral temporo-occipital regions, along with a co-existent bifrontal FD reduction as noted in the overall sample of NRS. In contrast, this increase in FD values in the bilateral temporo-occipital region was absent in the negative symptom (NS) subgroup. The regional differences in complexity suggested by these findings may reflect the aberrant brain dynamics underlying the pathophysiology of schizophrenia and its symptom dimensions. Higuchi's method of measuring FD directly in the time domain provides an alternative for the more computationally intensive nonlinear methods of estimating EEG complexity.

Advances in Nonlinear Complexity Analysis for Partial Differential Equations

1 p. -- [Editorial Material]

Time complexity analysis of the stochastic diffusion search

The Stochastic Diffusion Search algorithm -an integral part of Stochastic Search Networks is investigated. Stochastic Diffusion Search is an alternative solution for invariant pattern recognition and focus of attention. It has been shown that the algorithm can be modelled as an ergodic, finite state Markov Chain under some non-restrictive assumptions. Sub-linear time complexity for some settings of parameters has been formulated and proved. Some properties of the algorithm are then characterised and numerical examples illustrating some features of the algorithm are presented.

Medical image retrieval based on complexity analysis

Texture is one of the most important visual attributes used in image analysis. It is used in many content-based image retrieval systems, where it allows the identification of a larger number of images from distinct origins. This paper presents a novel approach for image analysis and retrieval based on complexity analysis. The approach consists of a texture segmentation step, performed by complexity analysis through BoxCounting fractal dimension, followed by the estimation of complexity of each computed region by multiscale fractal dimension. Experiments have been performed with MRI database in both pattern recognition and image retrieval contexts. Results show the accuracy of the method and also indicate how the performance changes as the texture segmentation process is altered.

Cogeneration design problem Computational complexity analysis and solution through an expert system

Purpose - The purpose of this paper is twofold: to analyze the computational complexity of the cogeneration design problem; to present an expert system to solve the proposed problem, comparing such an approach with the traditional searching methods available.Design/methodology/approach - The complexity of the cogeneration problem is analyzed through the transformation of the well-known knapsack problem. Both problems are formulated as decision problems and it is proven that the cogeneration problem is np-complete. Thus, several searching approaches, such as population heuristics and dynamic programming, could be used to solve the problem. Alternatively, a knowledge-based approach is proposed by presenting an expert system and its knowledge representation scheme.Findings - The expert system is executed considering two case-studies. First, a cogeneration plant should meet power, steam, chilled water and hot water demands. The expert system presented two different solutions based on high complexity thermodynamic cycles. In the second case-study the plant should meet just power and steam demands. The system presents three different solutions, and one of them was never considered before by our consultant expert.Originality/value - The expert system approach is not a "blind" method, i.e. it generates solutions based on actual engineering knowledge instead of the searching strategies from traditional methods. It means that the system is able to explain its choices, making available the design rationale for each solution. This is the main advantage of the expert system approach over the traditional search methods. On the other hand, the expert system quite likely does not provide an actual optimal solution. All it can provide is one or more acceptable solutions.

Complexity analysis of spontaneous brain activity: effects of depression and antidepressant treatment

Magnetoencephalography (MEG) allows the real-time recording of neural activity and oscillatory activity in distributed neural networks. We applied a non-linear complexity analysis to resting-state neural activity as measured using whole-head MEG. Recordings were obtained from 20 unmedicated patients with major depressive disorder and 19 matched healthy controls. Subsequently, after 6 months of pharmacological treatment with the antidepressant mirtazapine 30 mg/day, patients received a second MEG scan. A measure of the complexity of neural signals, the Lempel–Ziv Complexity (LZC), was derived from the MEG time series. We found that depressed patients showed higher pre-treatment complexity values compared with controls, and that complexity values decreased after 6 months of effective pharmacological treatment, although this effect was statistically significant only in younger patients. The main treatment effect was to recover the tendency observed in controls of a positive correlation between age and complexity values. Importantly, the reduction of complexity with treatment correlated with the degree of clinical symptom remission. We suggest that LZC, a formal measure of neural activity complexity, is sensitive to the dynamic physiological changes observed in depression and may potentially offer an objective marker of depression and its remission after treatment.

Complexity analysis of electroencephalographic data

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Understanding ageing effects using complexity analysis of foot-ground clearance during walking

Ageing influences gait patterns which in turn can affect the balance control of human locomotion. Entropy-based regularity and complexity measures have been highly effective in analysing a broad range of physiological signals. Minimum toe clearance (MTC) is an event during the swing phase of the gait cycle and is highly sensitive to the spatial balance control properties of the locomotor system. The aim of this research was to investigate the regularity and complexity of the MTC time series due to healthy ageing and locomotors' disorders. MTC data from 30 healthy young (HY), 27 healthy elderly (HE) and 10 falls risk (FR) elderly subjects with balance problems were analysed. Continuous MTC data were collected and using the first 500 data points, MTC mean, standard deviation (SD) and entropy-based complexity analysis were performed using sample entropy (SampEn) for different window lengths (m) and filtering levels (r). The MTC SampEn values were lower in the FR group compared to the HY and HE groups for all m and r. The HY group had a greater mean SampEn value than both HE and FR reflecting higher complexity in their MTC series. The mean SampEn values of HY and FR groups were found significantly different for m = 2, 4, 5 and r = (0.1-0.9) × SD, (0.3-0.9) × SD and (0.3-0.9) × SD, respectively. They were also significant difference between HE and FR groups for m = 4-5 and r = (0.3-0.7) × SD, but no significant differences were seen between HY and HE groups for any m and r. A significant correlation of SampEn with SD of MTC was revealed for the HY and HE groups only, suggesting that locomotor disorders could significantly change the regularity or the complexity of the MTC series while healthy ageing does not. These results can be usefully applied to the early diagnosis of common gait pathologies.

Complexity quantification of dense array EEG using sample entropy analysis

n this paper, a time series complexity analysis of dense array electroencephalogram signals is carried out using the recently introduced Sample Entropy (SampEn) measure. This statistic quantifies the regularity in signals recorded from systems that can vary from the purely deterministic to purely stochastic realm. The present analysis is conducted with an objective of gaining insight into complexity variations related to changing brain dynamics for EEG recorded from the three cases of passive, eyes closed condition, a mental arithmetic task and the same mental task carried out after a physical exertion task. It is observed that the statistic is a robust quantifier of complexity suited for short physiological signals such as the EEG and it points to the specific brain regions that exhibit lowered complexity during the mental task state as compared to a passive, relaxed state. In the case of mental tasks carried out before and after the performance of a physical exercise, the statistic can detect the variations brought in by the intermediate fatigue inducing exercise period. This enhances its utility in detecting subtle changes in the brain state that can find wider scope for applications in EEG based brain studies.

Aging reduces complexity of heart rate variability assessed by conditional entropy and symbolic analysis

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Aging reduces complexity of heart rate variability assessed by conditional entropy and symbolic analysis

Increasing age is associated with a reduction in overall heart rate variability as well as changes in complexity of physiologic dynamics. The aim of this study was to verify if the alterations in autonomic modulation of heart rate caused by the aging process could be detected by Shannon entropy (SE), conditional entropy (CE) and symbolic analysis (SA). Complexity analysis was carried out in 44 healthy subjects divided into two groups: old (n = 23, 63 +/- A 3 years) and young group (n = 21, 23 +/- A 2). It was analyzed SE, CE [complexity index (CI) and normalized CI (NCI)] and SA (0V, 1V, 2LV and 2ULV patterns) during short heart period series (200 cardiac beats) derived from ECG recordings during 15 min of rest in a supine position. The sequences characterized by three heart periods with no significant variations (0V), and that with two significant unlike variations (2ULV) reflect changes in sympathetic and vagal modulation, respectively. The unpaired t test (or Mann-Whitney rank sum test when appropriate) was used in the statistical analysis. In the aging process, the distributions of patterns (SE) remain similar to young subjects. However, the regularity is significantly different; the patterns are more repetitive in the old group (a decrease of CI and NCI). The amounts of pattern types are different: 0V is increased and 2LV and 2ULV are reduced in the old group. These differences indicate marked change of autonomic regulation. The CE and SA are feasible techniques to detect alteration in autonomic control of heart rate in the old group.

Time cumulative complexity modeling and analysis for space-based networks

In this paper, the notion of the cumulative time varying graph (C-TVG) is proposed to model the high dynamics and relationships between ordered static graph sequences for space-based information networks (SBINs). In order to improve the performance of management and control of the SBIN, the complexity and social properties of the SBIN's high dynamic topology during a period of time is investigated based on the proposed C-TVG. Moreover, a cumulative topology generation algorithm is designed to establish the topology evolution of the SBIN, which supports the C-TVG based complexity analysis and reduces network congestions and collisions resulting from traditional link establishment mechanisms between satellites. Simulations test the social properties of the SBIN cumulative topology generated through the proposed C-TVG algorithm. Results indicate that through the C-TVG based analysis, more complexity properties of the SBIN can be revealed than the topology analysis without time cumulation. In addition, the application of attack on the SBIN is simulated, and results indicate the validity and effectiveness of the proposed C-TVG and C-TVG based complexity analysis for the SBIN.

On the complexity of solving polytree-shaped limited memory influence diagrams with binary variables

Influence diagrams are intuitive and concise representations of structured decision problems. When the problem is non-Markovian, an optimal strategy can be exponentially large in the size of the diagram. We can avoid the inherent intractability by constraining the size of admissible strategies, giving rise to limited memory influence diagrams. A valuable question is then how small do strategies need to be to enable efficient optimal planning. Arguably, the smallest strategies one can conceive simply prescribe an action for each time step, without considering past decisions or observations. Previous work has shown that finding such optimal strategies even for polytree-shaped diagrams with ternary variables and a single value node is NP-hard, but the case of binary variables was left open. In this paper we address such a case, by first noting that optimal strategies can be obtained in polynomial time for polytree-shaped diagrams with binary variables and a single value node. We then show that the same problem is NP-hard if the diagram has multiple value nodes. These two results close the fixed-parameter complexity analysis of optimal strategy selection in influence diagrams parametrized by the shape of the diagram, the number of value nodes and the maximum variable cardinality.