Quantifying Cellular Pluripotency and Pathway Robustness through Forman-Ricci Curvature

In stem cell biology, cellular pluripotency describes the capacity of a given cell to differentiate into multiple cell types. From a statistical physics perspective, entropy provides a statistical measure of randomness and has been demonstrated as a way to quantitate pluripotency when considering biological gene networks. Furthermore, recent theoretical work has established a relationship between Ricci curvature (a geometric measure of "flatness") and entropy (also related to robustness), which one can exploit to link the geometric quantity of curvature to the statistical quantity of entropy. Therefore, this study seeks to explore Ricci curvature in biological gene networks as a descriptor of pluripotency and robustness among gene pathways. Here, we investigate Forman-Ricci curvature, a combinatorial discretization of Ricci curvature, along with network entropy, to explore the relationship of the two quantities as they occur in gene networks. First, we demonstrate our approach on an experiment of stem cell gene expression data. As expected, we find Ricci curvature directly correlates with network entropy, suggesting Ricci curvature could serve as an indicator for cellular pluripotency much like entropy. Second, we measure Forman-Ricci curvature in a dataset of cancer and non-cancer cells from melanoma patients. We again find Ricci curvature is increased in the cancer state, reflecting increased pluripotency or "stemness". Further, we locally examine curvature on the gene level to identify several genes and gene pathways with known relevance to melanoma. In turn, we conclude Forman-Ricci curvature provides valuable biological information related to pluripotency and pathway functionality. In particular, the advantages of this geometric approach are promising for extension to higher-order topological structures in order to represent more complex features of biological systems.

EEG-Based Emotion Recognition by Exploiting Fused Network Entropy Measures of Complex Networks across Subjects

It is well known that there may be significant individual differences in physiological signal patterns for emotional responses. Emotion recognition based on electroencephalogram (EEG) signals is still a challenging task in the context of developing an individual-independent recognition method. In our paper, from the perspective of spatial topology and temporal information of brain emotional patterns in an EEG, we exploit complex networks to characterize EEG signals to effectively extract EEG information for emotion recognition. First, we exploit visibility graphs to construct complex networks from EEG signals. Then, two kinds of network entropy measures (nodal degree entropy and clustering coefficient entropy) are calculated. By applying the AUC method, the effective features are input into the SVM classifier to perform emotion recognition across subjects. The experiment results showed that, for the EEG signals of 62 channels, the features of 18 channels selected by AUC were significant (p < 0.005). For the classification of positive and negative emotions, the average recognition rate was 87.26%; for the classification of positive, negative, and neutral emotions, the average recognition rate was 68.44%. Our method improves mean accuracy by an average of 2.28% compared with other existing methods. Our results fully demonstrate that a more accurate recognition of emotional EEG signals can be achieved relative to the available relevant studies, indicating that our method can provide more generalizability in practical use.

Research on the Stock Correlation Network Entropy and Its Influencing Factors in the Chinese Interbank Market

The stability of the interbank market is an essential guarantee for the sustainable development of society. Network entropy theory provides a critical research paradigm for the study of the stability of the interbank market. Considering that few scholars have conducted in-depth analysis on the influencing factors of the network entropy’s evolution process, this paper constructs the stock correlation network entropy model in the Chinese interbank market based on the correlation of stock price fluctuation. It focuses on analyzing the influencing factors in the dynamic evolution process of the stock correlation network entropy. In the light of empirical research, we can obtain the following results. First, the interbank market network’s aggregation coefficient, the interbank market network’s centrality, and the bank stock’s return rate play a positive role in the dynamic evolution of stock correlation network entropy in the Chinese interbank market. Second, the bank stock return’s volatility is negatively correlated with its network entropy. To maintain the stability of the financial market, the supervision department can monitor the stability of the interbank market by constructing the stock correlation network entropy.

A detailed characterization of complex networks using Information Theory

Understanding the structure and the dynamics of networks is of paramount importance for many scientific fields that rely on network science. Complex network theory provides a variety of features that help in the evaluation of network behavior. However, such analysis can be confusing and misleading as there are many intrinsic properties for each network metric. Alternatively, Information Theory methods have gained the spotlight because of their ability to create a quantitative and robust characterization of such networks. In this work, we use two Information Theory quantifiers, namely Network Entropy and Network Fisher Information Measure, to analyzing those networks. Our approach detects non-trivial characteristics of complex networks such as the transition present in the Watts-Strogatz model from k-ring to random graphs; the phase transition from a disconnected to an almost surely connected network when we increase the linking probability of Erdős-Rényi model; distinct phases of scale-free networks when considering a non-linear preferential attachment, fitness, and aging features alongside the configuration model with a pure power-law degree distribution. Finally, we analyze the numerical results for real networks, contrasting our findings with traditional complex network methods. In conclusion, we present an efficient method that ignites the debate on network characterization.

A detailed characterization of complex networks using Information Theory

Understanding the structure and the dynamics of networks is of paramount importance for many scientific fields that rely on network science. Complex network theory provides a variety of features that help in the evaluation of network behavior. However, such analysis can be confusing and misleading as there are many intrinsic properties for each network metric. Alternatively, Information Theory methods have gained the spotlight because of their ability to create a quantitative and robust characterization of such networks. In this work, we use two Information Theory quantifiers, namely Network Entropy and Network Fisher Information Measure, to analyzing those networks. Our approach detects non-trivial characteristics of complex networks such as the transition present in the Watts-Strogatz model from k-ring to random graphs; the phase transition from a disconnected to an almost surely connected network when we increase the linking probability of Erdős-Rényi model; distinct phases of scale-free networks when considering a non-linear preferential attachment, fitness, and aging features alongside the configuration model with a pure power-law degree distribution. Finally, we analyze the numerical results for real networks, contrasting our findings with traditional complex network methods. In conclusion, we present an efficient method that ignites the debate on network characterization.

The biphasic and age-dependent impact of Klotho on hallmarks of aging and skeletal muscle function

Aging is accompanied by disrupted information flow, resulting from accumulation of molecular mistakes. These mistakes ultimately give rise to debilitating disorders including skeletal muscle wasting, or sarcopenia. To derive a global metric of growing 'disorderliness' of aging muscle, we employed a statistical physics approach to estimate the state parameter, entropy, as a function of genes associated with hallmarks of aging. Escalating network entropy reached an inflection point at old age, while structural and functional alterations progressed into oldest-old age. To probe the potential for restoration of molecular 'order' and reversal of the sarcopenic phenotype, we systemically overexpressed the longevity protein, Klotho, via AAV. Klotho overexpression modulated genes representing all hallmarks of aging in old and oldest-old mice, but pathway enrichment revealed directions of changes were, for many genes, age-dependent. Functional improvements were also age-dependent. Klotho improved strength in old mice, but failed to induce benefits beyond the entropic tipping point.

Microcanonical and Canonical Ensembles for fMRI Brain Networks in Alzheimer’s Disease

This paper seeks to advance the state-of-the-art in analysing fMRI data to detect onset of Alzheimer’s disease and identify stages in the disease progression. We employ methods of network neuroscience to represent correlation across fMRI data arrays, and introduce novel techniques for network construction and analysis. In network construction, we vary thresholds in establishing BOLD time series correlation between nodes, yielding variations in topological and other network characteristics. For network analysis, we employ methods developed for modelling statistical ensembles of virtual particles in thermal systems. The microcanonical ensemble and the canonical ensemble are analogous to two different fMRI network representations. In the former case, there is zero variance in the number of edges in each network, while in the latter case the set of networks have a variance in the number of edges. Ensemble methods describe the macroscopic properties of a network by considering the underlying microscopic characterisations which are in turn closely related to the degree configuration and network entropy. When applied to fMRI data in populations of Alzheimer’s patients and controls, our methods demonstrated levels of sensitivity adequate for clinical purposes in both identifying brain regions undergoing pathological changes and in revealing the dynamics of such changes.