VisExpA: Visibility expansion algorithm in the topology of complex networks

Modeling and Forecasting the COVID-19 Temporal Spread in Greece: An Exploratory Approach Based on Complex Network Defined Splines

“…This allows the division of the visibility graph of the COVID-19 infection into connective communities based on the modularity optimization algorithm of [40]. This algorithm is heuristic and separates a complex network into communities, which are dense within (i.e., links inside the communities are the highest possible) and sparse between (i.e., links inside the communities are the highest possible) [12,26,[40][41][42]. Therefore, the most distant nodes within each community can define the knots for applying the spline algorithm.…”

“…This complex-network-based definition (i.e., community detection based on modularity optimization) of the knot vector offers the missing conceptualization to the splines knots, defining them as borderline points of connectivity of the modularity-based communities. According to this approach, the visibility graph of the COVID-19 infection curve is divided into five modularity-based communities, which correspond to the periods Q1 = [1,4] ∪ [9,19], Q2 = [5,8], Q3 = [20,26], Q4 = [27,32], and Q5 = [33,43], as it is shown in Figure 9, where positive integers in these intervals are elements of variable X 1 .…”

“…Consequently, the spline knot vector can be defined by the knots t = (1,4,8,19,26,32,43) in the body of the time-series COVID-19 infection curve. This partition facilitates the application of the spline regression algorithm and comparison of the determination ability of the spline model with the cubic regression models previously shown.…”

“…According to this approach, the visibility graph of the COVID-19 infection curve is divided into five modularity-based communities, which correspond to the periods Q1 = 1,4 ⋃ 9,19 , Q2 = [5,8], Q3 = [20,26], Q4 = [27,32], and Q5 = [33,43], as it is shown in Figure 9, where positive integers in these intervals are elements of variable X1. Consequently, the spline knot vector can be defined by the knots t = (1,4,8,19,26,32,43) in the body of the time-series COVID-19 infection curve. This partition facilitates the application of the spline regression algorithm and comparison of the determination ability of the spline model with the cubic regression models previously shown.…”

Examination of Chaotic Structures in Semiconductor or Alloy Voltage Time-Series: A Complex Network Approach for the Case of TlInTe2

“…As far as the authors know, this approach is here applied for the first time to this kind of material, and is expected to reveal information about the transport phenomena, which in the case of this study regard the current filaments and their connections, and thus to enhance the existence of an electrothermal mechanism. The natural visibility algorithm (NVGA) was proposed by the authors of [24] and conceptualizes a time-series as a landscape [32,33]. In particular, the NVGA considers a time-series as a chain of successive mountains of different heights, whereby an observer standing on each node (time-point) can see in both directions for as far as there is no other node obstructing its visibility (Figure 2).…”