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Example of the natural visibility algorithm (NVG), which generates a network (right side) from a time-series (left side). Dashed lines in the time-series' plot represent the visibility lines.
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In this study, we provide the VisExpA (Visibility Expansion Algorithm), a computational code that implements a recently published method, which allows generating a visibility graph from a complex network instead of a time-series that is currently applicable. The proposed algorithm is applied to a complex network and it uses a node-wise control-attr...
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Citations
... This newly established research field showed a remarkable development, at a multidisciplinary level 4 , when scholars conceptualized 5-7 that transforming a time-series into a graph can produce insights that are not visible by current time-series approaches. In general, studying the topology of a graph instead of the structure of a time-series promotes time-series analysis because it enlarges the embedding of the available information, from a first-order tensor (i.e. the time-series vector) into a second-order tensor (i.e. the graph connectivity matrix) 8 . Within this context, Zhang and Small 7 were the first who constructed graphs from pseudo-periodic time-series, and Yang and Yang 6 applied thresholds to the correlation matrix to convert it into a connectivity matrix. ...
... The visibility algorithm conceptualizes the time-series as a landscape and generates a visibility graph associated with this landscape. The associated (to the time-series) visibility graph is a complex network where complex network analysis can be further applied 8,16 . ...
This paper proposes a new method for converting a time-series into a weighted graph (complex network), which builds on electrostatics in physics. The proposed method conceptualizes a time-series as a series of stationary, electrically charged particles, on which Coulomb-like forces can be computed. This allows generating electrostatic-like graphs associated with time-series that, additionally to the existing transformations, can be also weighted and sometimes disconnected. Within this context, this paper examines the structural similarity between five different types of time-series and their associated graphs that are generated by the proposed algorithm and the visibility graph, which is currently the most popular algorithm in the literature. The analysis compares the source (original) time-series with the node-series generated by network measures (that are arranged into the node-ordering of the source time-series), in terms of a linear trend, chaotic behaviour, stationarity, periodicity, and cyclical structure. It is shown that the proposed electrostatic graph algorithm generates graphs with node-measures that are more representative of the structure of the source time-series than the visibility graph. This makes the proposed algorithm more natural rather than algebraic, in comparison with existing physics-defined methods. The overall approach also suggests a methodological framework for evaluating the structural relevance between the source time-series and their associated graphs produced by any possible transformation.
... 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). ...
... This implies that no other node intermediating the pair (ti,x(ti)) and (tj,x(tj)) is higher and can intersect the visibility line created by nodes (ti,x(ti)) and (tj,x(tj)), as is shown in Figure 2. Therefore, two nodes ni ≡ (ti,x(ti)) and nj ≡ (tj,x(tj)) in the time-series can enjoy a connection (ni,nj) E in the associated visibility graph G(V,E) when they are visible via a visibility line. The visibility algorithm interprets the time-series as a landscape and generates a visibility graph illustrating this landscape in terms of complex network representation, wherein complex network analysis can be further applied [24,32,33]. ...
... The visibility graph is an undirected and unweighted graph model [32,33], wherein network analysis can be applied to examine its topology and hierarchical structure. The network measures used for the analysis of the visibility graph are shown in Table 1, and they were extracted from the sources [34][35][36]. ...
This paper proposes a method for examining chaotic structures in semiconductor or alloy voltage oscillation time-series, and focuses on the case of the TlInTe2 semiconductor. The available voltage time-series are characterized by instabilities in negative differential resistance in the current-voltage characteristic region, and are primarily chaotic in nature. The analysis uses a complex network analysis of the time-series and applies the visibility graph algorithm to transform the available time-series into a graph so that the topological properties of the graph can be studied instead of the source time-series. The results reveal a hybrid lattice-like configuration and a major hierarchical structure corresponding to scale-free characteristics in the topology of the visibility graph, which is in accordance with the default hybrid chaotic and semi-periodic structure of the time-series. A novel conceptualization of community detection based on modularity optimization is applied to the available time-series and reveals two major communities that are able to be related to the pair-wise attractor of the voltage oscillations' phase portrait of the TlInTe2 time-series. Additionally, the network analysis reveals which network measures are more able to preserve the chaotic properties of the source time-series. This analysis reveals metric information that is able to supplement the qualitative phase-space information. Overall, this paper proposes a complex network analysis of the time-series as a method for dealing with the complexity of semiconductor and alloy physics.
... This timely response has led Greece to be currently considered as a successful case in anti-COVID-19 management compared to both the European and global cases [13,16]. At the time that Greece started to attract global attention, the authors of [12] proposed a novel complex network analysis of timeseries, based on the visibility algorithm [25,26], for the study of the Greek COVID-19 infection curve. The authors showed that the evolution of the disease in Greece went through five stages of declining dynamics, where saturation trends (represented by a logarithmic pattern) emerged after the 33rd day (29 April 2020). ...
... Transforming a time-series to a complex network is a modern approach that recently became popular with the emergence of network science in various fields of research [26,38,39]. The most popular method to transform a complex network to a time-series is the visibility graph algorithm that was proposed by [25], which became dominant due to its intuitive conceptualization. ...
... Therefore, two time-series nodes can enjoy a connection in the associated visibility graph if they are visible through a visibility line [25]. The visibility algorithm conceptualizes the time-series as a landscape and produces a visibility graph associated with this landscape [26]. The associated (to the time-series) visibility graph is a complex network where complex network analysis can be further applied [12,26]. ...
Within the complex framework of anti-COVID-19 health management, where the criteria of diagnostic testing, the availability of public-health resources and services, and the applied anti-COVID-19 policies vary between countries, the reliability and accuracy in the modeling of temporal spread can prove to be effective in the worldwide fight against the disease. This paper applies an exploratory time-series analysis to the evolution of the disease in Greece, which currently suggests a success story of COVID-19 management. The proposed method builds on a recent conceptualization of detecting connective communities in a time-series and develops a novel spline regression model where the knot vector is determined by the community detection in the complex network. Overall, the study contributes to the COVID-19 research by proposing a free of disconnected past-data and reliable framework of forecasting, which can facilitate decision-making and management of the available health resources.
... Therefore, this paper advances current quantitative approaches by building on complex network analysis of time-series to transform the COVID-19 infection curve to a complex network. To do so, the visibility graph algorithm is applied [23], which is a non-parametric approach able to provide structural insights of the time-series and to transform it to a complex network that is a tensor of higher dimension in comparison to the series [22,24]. The association with the time-series visibility graph is detected for communities based on the modularity optimization algorithm [25], aiming to develop a partition of the time-series and therefore to interpret their significance in accordance with the anti-COVID-19 policies applied by the Greek state. ...
... In geometric terms, a visibility line can be drawn between two time-series' nodes ni, nj V whether no other intermediating node nk≡(tk, x(tk)) obstructs their visibility [23,24], namely, no other intermediary node is so high as to intersect the visibility line created by this pair of nodes ( Figure 2). Therefore, two time-series' nodes can enjoy a connection in the associated visibility graph if they are visible through a visibility line [23]. ...
... Therefore, two time-series' nodes can enjoy a connection in the associated visibility graph if they are visible through a visibility line [23]. The visibility algorithm conceptualizes the time-series as a landscape and produces a visibility graph associated with this landscape [24]. The associated (to the time-series) visibility graph is a complex network where complex network analysis can be further applied [23,24]. ...
Within the context of Greece promising a success story in the fight against the disease, this paper proposes a novel method for studying the evolution of the Greek COVID-19 infection curve in relation to the anti-COVID-19 policies applied to control the pandemic. Based on the ongoing spread of COVID-19 and the insufficient data for applying classic time-series approaches, the analysis builds on the visibility graph algorithm to study the Greek COVID-19 infection curve as a complex network. By using the modularity optimization algorithm, the generated visibility graph is divided into communities defining periods of different connectivity in the time-series body. These periods reveal a sequence of different typologies in the evolution of the disease, starting with a power pattern, where a second order polynomial (U-shaped) pattern intermediates, being followed by a couple of exponential patterns, and ending up with a current logarithmic pattern revealing that the evolution of the Greek COVID-19 infection curve tends towards saturation. In terms of Gaussian modeling, this successive compression of the COVID-19 infection curve into five parts implies that the pandemic in Greece is about to reach the second (decline) half of the bell-shaped distribution. The network analysis also illustrates stability of hubs and instability of medium and low-degree nodes, implying a low probability of meeting maximum (infection) values in the future and high uncertainty in the variability of other values below the average. The overall approach contributes to the scientific research by proposing a novel method for the structural decomposition of a time-series into periods, which allows removing from the series the disconnected past-data facilitating better forecasting, and provides insights of good policy and decision-making practices and management that may help other countries improve their performance in the war against COVID-19.
... This timely response have led Greece to be currently considered as a successful case in anti-COVID-19 management, comparatively both to the European and the global cases (Roser and Ritchie, 2020; Xu et al., 2020). At the time that Greece started attracting the global attention, Tsiotas and Magafas (2020) proposed a novel complex network analysis of time-series, based on the visibility algorithm (Lacasa et al., 2008;Tsiotas and Charakopoulos, 2020), for the study of the Greek COVID-19 infection curve. The authors showed that the evolution of the disease in Greece went through five stages of declining dynamics, where saturation trends (represented by a logarithmic pattern) emerged after the 33 rd day (29/04/2020). ...
... Transforming a time-series to a complex network is a modern approach that became recently popular, with the emergence of network science in various fields of research (Barabasi, 2016;Tsiotas and Charakopoulos, 2020). The most popular method to transform a complex network to a time-series is the visibility graph algorithm, which was proposed by Lacasa et al. (2008) and became dominant due to its intuitive conceptualization. ...
... Therefore, two time-series nodes can enjoy a connection in the associated visibility graph if they are visible through a visibility line (Lacasa et al., 2008). The visibility algorithm conceptualizes the time-series as a landscape and produces a visibility graph associated to this landscape (Tsiotas and Charakopoulos, 2020). The associated (to the time-series) visibility graph is a complex network where complex network analysis can be further applied (Tsiotas and Charakopoulos, 2020;Tsiotas and Magafas, 2020). ...
Within the complex framework of anti-COVID-19 health management, where the criteria of diagnostic testing, the availability of public-health resources and services, and the applied anti-COVID-19 policies vary between countries, the reliability and the accuracy in the modeling of temporal spread can be proven effective in the worldwide fight against the disease. This paper applies an exploratory time-series analysis to the evolution of the disease in Greece, which currently suggests a success story of COVID-19 management. The proposed method builds on a recent conceptualization of detecting connective communities in a time-series and develops a novel spline regression model where the knot vector is determined by the community detection in the complex network. Overall, the study contributes to the COVID-19 research by proposing a free of disconnected past-data and reliable framework of forecasting, which can facilitate decision-making and management of the available health resources.
... This timely response have led Greece to be currently considered as a successful case in anti-COVID-19 management, comparatively both to the European and the global cases (Roser and Ritchie, 2020; Xu et al., 2020). At the time that Greece started attracting the global attention, Tsiotas and Magafas (2020) proposed a novel complex network analysis of time-series, based on the visibility algorithm (Lacasa et al., 2008;Tsiotas and Charakopoulos, 2020), for the study of the Greek COVID-19 infection curve. The authors showed that the evolution of the disease in Greece went through five stages of declining dynamics, where saturation trends (represented by a logarithmic pattern) emerged after the 33 rd day (29/04/2020). ...
... Transforming a time-series to a complex network is a modern approach that became recently popular, with the emergence of network science in various fields of research (Barabasi, 2016;Tsiotas and Charakopoulos, 2020). The most popular method to transform a complex network to a time-series is the visibility graph algorithm, which was proposed by Lacasa et al. (2008) and became dominant due to its intuitive conceptualization. ...
... Therefore, two time-series nodes can enjoy a connection in the associated visibility graph if they are visible through a visibility line (Lacasa et al., 2008). The visibility algorithm conceptualizes the time-series as a landscape and produces a visibility graph associated to this landscape (Tsiotas and Charakopoulos, 2020). The associated (to the time-series) visibility graph is a complex network where complex network analysis can be further applied (Tsiotas and Charakopoulos, 2020;Tsiotas and Magafas, 2020). ...
Within the complex framework of anti-COVID-19 health management, where the criteria of diagnostic testing, the availability of public-health resources and services, and the applied anti-COVID-19 policies vary between countries, the reliability and the accuracy in the modeling of temporal spread can be proven effective in the worldwide fight against the disease. This paper applies an exploratory time-series analysis to the evolution of the disease in Greece, which currently suggests a success story of COVID-19 management. The proposed method builds on a recent conceptualization of detecting connective communities in a time-series and develops a novel spline regression model where the knot vector is determined by the community detection in the complex network. Overall, the study contributes to the COVID-19 research by proposing a free of disconnected past-data and reliable framework of forecasting, which can facilitate decision-making and management of the available health resources.
... Therefore, this paper advances current quantitative approaches by building on complex network analysis of time-series to transform the COVID-19 infection-curve to a complex network. To do so, the visibility graph algorithm is applied (Lacasa et al., 2008), which is a nonparametric approach able to provide structural insights of the time-series and to transform it to a complex network that is a tensor of higher dimension in comparison to the series (Box et al., 2015;Tsiotas and Charakopoulos, 2020). The associated to the time-series visibility graph is detected for communities, based on the modularity optimization algorithm (Blondel et al., 2008), aiming to develop a partition of the time-series and therefore to interpret their significance in accordance with the anti-COVID-19 policies applied by the Greek state. ...
... where x(t i ) and x(t j ) express the numeric values of the time-series nodes and t i , t j their timereference points. In a network mapped according to the visibility algorithm, each node is visible at least by its nearest (left and right) neighbors (Gao et al., 2017;Tsiotas and Charakopoulos, 2020). ...
Within the context that Greece promises a success story in the fight against the disease, this paper proposes a novel method to study the evolution of the Greek COVID-19 infection-curve in relation to the anti-COVID-19 policies applied to control the pandemic. Based on the ongoing spreading of COVID-19 and the insufficient data for applying classic time-series approaches, the analysis builds on the visibility graph algorithm to study the Greek COVID-19 infection-curve as a complex network. By using the modularity optimization algorithm, the generated visibility graph is divided into communities defining periods of different connectivity in the time-series body. These periods reveal a sequence of different typologies in the evolution of the disease, starting with a power pattern, where a second order polynomial (U-shaped) pattern intermediates, being followed by a couple of exponential patterns, and ending up with a current logarithmic pattern revealing that the evolution of the Greek COVID-19 infection-curve tends into saturation. The network analysis also illustrates stability of hubs and instability of medium and low-degree nodes, implying a low probability to meet maximum (infection) values at the future and high uncertainty in the variability of other values below the average. The overall approach contributes to the scientific research by proposing a novel method for the structural decomposition of a time-series into periods, which allows removing from the series the disconnected past-data facilitating better forecasting, and provides insights of good policy and decision-making practices and management that may help other countries improve their performance in the war against COVID-19.
