Analytical estimation of the correlation dimension of integer lattices

Alzheimer's disease: new insight in assessing of amyloid plaques morphologies using multifractal geometry based on Naive Bayes optimized by random forest algorithm

Alzheimer's disease (AD) is a physical illness, which damages a person's brain; it is the most common cause of dementia. AD can be characterized by the formation of amyloid-beta (Aβ) deposits. They exhibit diverse morphologies that range from diffuse to dense-core plaques. Most of the histological images cannot be described precisely by traditional geometry or methods. Therefore, this study aims to employ multifractal geometry in assessing and classifying amyloid plaque morphologies. The classification process is based on extracting the most descriptive features related to the amyloid-beta (Aβ) deposits using the Naive Bayes classifier. To eliminate the less important features, the Random Forest algorithm has been used. The proposed methodology has achieved an accuracy of 99%, sensitivity of 100%, and specificity of 98.5%. This study employed a new dataset that had not been widely used before.

Correlation dimension in empirical networks

Network correlation dimension governs the distribution of network distance in terms of a power-law model and profoundly impacts both structural properties and dynamical processes. We develop new maximum likelihood methods which allow us robustly and objectively to identify network correlation dimension and a bounded interval of distances over which the model faithfully represents structure. We also compare the traditional practice of estimating correlation dimension by modeling as a power law the fraction of nodes within a distance to a proposed alternative of modeling as a power law the fraction of nodes at a distance. In addition, we illustrate a likelihood ratio technique for comparing the correlation dimension and small-world descriptions of network structure. Improvements from our innovations are demonstrated on a diverse selection of synthetic and empirical networks. We show that the network correlation dimension model accurately captures empirical network structure over neighborhoods of substantial size and span and outperforms the alternative small-world network scaling model. Our improved methods tend to lead to higher estimates of network correlation dimension, implying that prior studies could have produced or utilized systematic underestimates of dimension.

An Extended Correlation Dimension of Complex Networks

Fractal and self-similarity are important characteristics of complex networks. The correlation dimension is one of the measures implemented to characterize the fractal nature of unweighted structures, but it has not been extended to weighted networks. In this paper, the correlation dimension is extended to the weighted networks. The proposed method uses edge-weights accumulation to obtain scale distances. It can be used not only for weighted networks but also for unweighted networks. We selected six weighted networks, including two synthetic fractal networks and four real-world networks, to validate it. The results show that the proposed method was effective for the fractal scaling analysis of weighted complex networks. Meanwhile, this method was used to analyze the fractal properties of the Newman–Watts (NW) unweighted small-world networks. Compared with other fractal dimensions, the correlation dimension is more suitable for the quantitative analysis of small-world effects.

Cortical functional activity in patients with generalized anxiety disorder

BACKGROUND

The neurological correlates of Generalised Anxiety Disorder (GAD) are not well known, however there is evidence of cortical dysregulation in patients with GAD. The aim of the study was to examine cortical functional activity in different cerebral regions in patients with GAD using electroencephalogram (EEG) nonlinear analysis to evaluate its contribution of anxiety severity.

METHODS

The cohorts consisted of 64 patients diagnosed with GAD as classified by the Structured Clinical Interview for the Diagnostic and Statistical Manual of the American Psychiatric Association-IV-TR. Anxiety severity was assessed using the Hamilton Rating Scale for Anxiety (HAMA) severity score, with 7 ≤ scores ≤ 17 indicating mild anxiety as A group (n = 31) and 18 and above indicating moderate-severe anxiety as B group (n = 33). Participants with clinical levels of depression symptoms were excluded. A healthy control group comprising 30 participants was matched for age and gender. Closed eyes EEGs were conducted, and between-group differences on non-linear parameter Correlation Dimension (D2) were analyzed. The association of D2 value with HAMA scores was analyzed using multiple linear stepwise regression.

RESULTS

Compared with the control group, D2 values were increased in anxiety groups (P < .05). For those with mild anxiety, this difference occurred in the left prefrontal regions (P < .05). For those with moderate-severe anxiety, significantly greater D2 values were observed in all of the cerebral regions, especially in the left cerebral regions and right temporal lobe (P < .01). When compared with those with mild anxiety, D2 values were significantly greater for those with moderate-severe anxiety in the right temporal lobe and all left cerebral regions except for left occipital lobe (P < .05). A positive correlation was observed between D2 values and moderate-severe anxiety HAMA scores.

CONCLUSIONS

The increased D2 values were found in the majority of cerebral regions in GAD patients, especially in the left cerebral regions and the right temporal lobe. The increased GAD severity positively correlates to the D2 values in a larger number of cerebral regions. This analysis method can potentially be used as a complementary tool to examine dysfunctional cortical activity in GAD.