Hosein Masoomy

The centrality measures, like betweenness b and degree k in complex networks remain fundamental quantities helping to classify them. It is realized from Barthelemy's paper [Eur. Phys. J. B 38, 163 (2004)] that the maximal b−k exponent for the scale-free (SF) networks is ηmax=2, belonging to SF trees, based on which one concludes δ≥γ+12, where γ and...

Outbreaks are complex multi-scale processes that are impacted not only by cellular dynamics and the ability of pathogens to effectively reproduce and spread, but also by population-level dynamics and the effectiveness of mitigation measures. A timely exchange of information related to the spread of novel pathogens, stay-at-home orders, and other me...

Outbreaks are complex multi-scale processes that are impacted not only by cellular dynamics and the ability of pathogens to effectively reproduce and spread, but also by population-level dynamics and the effectiveness of mitigation measures. A timely exchange of information related to the spread of novel pathogens, stay-at-home orders, and other co...

A well-known class of nonstationary self-similar time series is the fractional Brownian motion (fBm) considered to model ubiquitous stochastic processes in nature. Due to noise and trends superimposed on data and even sample size and irregularity impacts, the well-known computational algorithm to compute the Hurst exponent (H) has encountered super...

Review of Homology Theory: Simplex and Simplicial Complex Chain Groups Cycle Groups Boundary Groups Homology Groups Betti Numbers (Topological Invariant) Persistent Homology: Persistent Homology (PH) Pipeline PH-based Analysis of Data Sets PH for Time Series Analysis PH for Filed Analysis PH for Point Cloud Analysis PH for Network Analysis

Data Types: Time Series (Signal) Field (Image) Point Cloud Network (Graph) Methods for Reconstruction of Data Sets of Different Types: Time Delay Embedding (TDE) Recurrent Plot (RP) Visibility Graph (VG) State Space (SS) Correlation Network (CN) Recurrent Network (RN) Excursion Sets (ES)

A well-known class of non-stationary self-similar time series is the fractional Brownian motion (fBm) considered to model ubiquitous stochastic processes in nature. In this paper, we study the homology groups of high-dimensional point cloud data (PCD) constructed from synthetic fBm data. We covert the simulated fBm series to a PCD, a subset of unit...

Topological data analysis is a new branch of computational science that considers abstract concepts in algebraic topology and uses well-defined matrix analysis in linear algebra, as well as using optimal computational algorithms to extract large-scale structures from high-dimensional data that represent the main characteristics of the data from a g...

The problem of betweenness centrality remains a fundamental unsolved problem in complex networks. After a pioneering work by Barthelemy, it has been well-accepted that the maximal betweenness-degree ($b$-$k$) exponent for scale-free (SF) networks is $\eta_{\text{max}}=2$, belonging to scale-free trees (SFTs), based on which one concludes $\delta\ge...

In this paper, we employ the persistent homology (PH) technique to examine the topological properties of fractional Gaussian noise (fGn). We develop the weighted natural visibility graph algorithm, and the associated simplicial complexes through the filtration process are quantified by PH. The evolution of the homology group dimension represented b...

In this study, we investigated cancer cellular networks in the context of gene interactions and their associated patterns in order to recognize the structural features underlying this disease. We aim to propose that the quest of understanding cancer takes us beyond pairwise interactions between genes to a higher-order construction. We characterize...

The Persistent Homology (PH), as the main part of Topological Data Analysis (TDA) is introduced. The application of this method on feature extraction from the weighted version of Visibility Graph (VG) of fractional Gaussian noise (fGn) time series is shown, as well. For an illustration of the capability of this powerful topological tool, we show th...

How the topological invariants (Betti numbers) of complex networks evolve when their intrinsic parameter varies? Random Network: Erdos-Renyi (ER) model Small World Network: Watts-Strogatz (WS) model Scale-Free Network: Barabasi-Albert (BA) model

In this study, we investigated cancer cellular networks in the context of gene interactions and their associated patterns in order to recognize the structural features underlying this disease. We aim to propose that the quest of understanding cancer takes us beyond pairwise interactions between genes to a higher-order construction. We characterize...

Schizophrenia is one of the mental disorders studied in the field of neuroscience. The physiological origin of this disorder is the difference in the way the anatomical connections of different brain regions are compared. This structural difference manifests itself in the functional difference of the brain in the form of a functional network. Study...

In this paper, we utilize persistent homology technique to examine the topological properties of the visibility graph constructed from fractional Gaussian noise (fGn). We develop the weighted natural visibility graph algorithm and the standard network in addition to the global properties in the context of topology, will be examined. Our results dem...

In this talk I explain how topological tools, in particular the Persistent Homology (PH) method can be used to study biological datasets. Practically, we applied this mathematical method on Gene Regulatory Network (GRN) to discover interaction patterns of the agents from homological viewpoints. (https://ccnsd.ir/research_projects/cancer-project/)

Applying topological data analysis (TDA) tools to estimate the correlation of fractional Gaussian noise (fGn) signals (stationary self-similar time series), expressed by the Hurst exponent, based on the zeroth homology group (connectivity).

In this paper, relying on computational approaches based on topological data analysis, and applying the computational algorithm in order to derive topological invariants such as Betti numbers, we present a new method for computing scaling exponents of time series. Our results indicate that the maximum value of 0-Betti has scaling behavior with resp...