Trade-offs between driving nodes and time-to-control in complex networks

Abstract Recent advances in control theory provide us with efficient tools to determine the minimum number of driving (or driven) nodes to steer a complex network towards a desired state. Furthermore, we often need to do it within a given time window, so it is of practical importance to understand the trade-offs between the minimum number of driving/driven nodes and the minimum time required to reach a desired state. Therefore, we introduce the notion of actuation spectrum to capture such trade-offs, which we used to find that in many complex networks only a small fraction of driving (or driven) nodes is required to steer the network to a desired state within a relatively small time window. Furthermore, our empirical studies reveal that, even though synthetic network models are designed to present structural properties similar to those observed in real networks, their actuation spectra can be dramatically different. Thus, it supports the need to develop new synthetic network models able to replicate controllability properties of real-world networks.

Download Full-text

Linear impulsive control system with impulse time windows

Journal of Vibration and Control ◽

10.1177/1077546315575465 ◽

2016 ◽

Vol 23 (1) ◽

pp. 111-118 ◽

Cited By ~ 17

Author(s):

Yuming Feng ◽

Junzhi Yu ◽

Chuandong Li ◽

Tingwen Huang ◽

Hangjun Che

Keyword(s):

Impulsive Control ◽

Time Window ◽

Time Windows ◽

Practical Importance ◽

Fixed Time ◽

Small Time ◽

Time Interval ◽

Impulsive Systems ◽

Impulse Time Windows ◽

System States

We formulate the linear impulsive control systems with impulse time windows. Different from the most impulsive systems where the impulses occur at fixed time or when the system states hit a certain hyperplane, the impulse time in the presented systems might be uncertain, but limited to a small time interval, i.e. a time window. Compared with the existing impulsive systems, the systems with impulse time windows is of practical importance. We then study the asymptotic stability of the case of linear systems and obtain several stability criteria. Numerical examples are given to verify the effectiveness of the theoretical results.

Download Full-text

Distance Entropy Cartography Characterises Centrality in Complex Networks

Entropy ◽

10.3390/e20040268 ◽

2018 ◽

Vol 20 (4) ◽

pp. 268 ◽

Cited By ~ 15

Author(s):

Massimo Stella ◽

Manlio De Domenico

Keyword(s):

Complex Networks ◽

Complex Network ◽

Network Models ◽

Closeness Centrality ◽

Network Distance ◽

Synthetic Network ◽

Entropy Information ◽

English Speaking ◽

Path Lengths ◽

Network Encoding

We introduce distance entropy as a measure of homogeneity in the distribution of path lengths between a given node and its neighbours in a complex network. Distance entropy defines a new centrality measure whose properties are investigated for a variety of synthetic network models. By coupling distance entropy information with closeness centrality, we introduce a network cartography which allows one to reduce the degeneracy of ranking based on closeness alone. We apply this methodology to the empirical multiplex lexical network encoding the linguistic relationships known to English speaking toddlers. We show that the distance entropy cartography better predicts how children learn words compared to closeness centrality. Our results highlight the importance of distance entropy for gaining insights from distance patterns in complex networks.

Download Full-text

Modelling community structure and temporal spreading on complex networks

Computational Social Networks ◽

10.1186/s40649-021-00094-z ◽

2021 ◽

Vol 8 (1) ◽

Author(s):

Vesa Kuikka

Keyword(s):

Community Structure ◽

Complex Networks ◽

Community Detection ◽

Network Structure ◽

Network Connectivity ◽

Network Models ◽

Building Blocks ◽

Detection Algorithm ◽

Research Area ◽

Detection Methods

AbstractWe present methods for analysing hierarchical and overlapping community structure and spreading phenomena on complex networks. Different models can be developed for describing static connectivity or dynamical processes on a network topology. In this study, classical network connectivity and influence spreading models are used as examples for network models. Analysis of results is based on a probability matrix describing interactions between all pairs of nodes in the network. One popular research area has been detecting communities and their structure in complex networks. The community detection method of this study is based on optimising a quality function calculated from the probability matrix. The same method is proposed for detecting underlying groups of nodes that are building blocks of different sub-communities in the network structure. We present different quantitative measures for comparing and ranking solutions of the community detection algorithm. These measures describe properties of sub-communities: strength of a community, probability of formation and robustness of composition. The main contribution of this study is proposing a common methodology for analysing network structure and dynamics on complex networks. We illustrate the community detection methods with two small network topologies. In the case of network spreading models, time development of spreading in the network can be studied. Two different temporal spreading distributions demonstrate the methods with three real-world social networks of different sizes. The Poisson distribution describes a random response time and the e-mail forwarding distribution describes a process of receiving and forwarding messages.

Download Full-text

Comparison of Real and Synthetic Network Models of the Western United States with Respect to New Realism Measures

2021 IEEE Power and Energy Conference at Illinois (PECI) ◽

10.1109/peci51586.2021.9435246 ◽

2021 ◽

Author(s):

Sogol Babaeinejadsarookolaee ◽

Jonathan Snodgrass ◽

Sowmya Acharya ◽

Scott Greene ◽

Bernard Lesieutre ◽

...

Keyword(s):

United States ◽

Network Models ◽

Western United States ◽

Synthetic Network ◽

New Realism

Download Full-text

Anagen Effluvium after Therapeutic Scalp Surgery: Unreported Phenomenon

Skin Appendage Disorders ◽

10.1159/000513087 ◽

2021 ◽

Vol 7 (4) ◽

pp. 311-314

Author(s):

Leticia Arsie Contin ◽

Leopoldo Duailibe Nogueira Santos ◽

Ivan José Netto Pereira ◽

Vanessa Barreto Rocha

Keyword(s):

Hair Loss ◽

Spontaneous Recovery ◽

Case Reports ◽

Practical Importance ◽

Transient Ischemia ◽

Melanocytic Nevi ◽

Scarring Alopecia ◽

Anagen Hair ◽

Time Required

Introduction: Many procedures are performed on the scalp, such as excision of pilar and sebaceous cysts, melanocytic nevi, and reduction surgery for scarring alopecia, among others. In hair transplants, telogen effluvium is often reported 3 months after surgery; however, hair loss usually happens much earlier, around second week after the procedure, not compatible with the time required for hair to enter telogen and exogenous phases in normal conditions. Case Reports: We report 3 cases of anagen hair loss 4 weeks after surgeries, with perilesional trichoscopy suggesting anagen effluvium, with typical signs such as black dots and exclamation hairs. Discussion: There are only a few reports about hair loss around operated areas. The cause of this postoperative anagen effluvium is probably a transient ischemia. Conclusion: The practical importance of this phenomenon is to properly orient patients because most of the hair will be lost, since 85% of them are anagens, and also will have spontaneous recovery in the next 3 months.

Download Full-text

Can Habitat Quality Index Measured Using the InVEST Model Explain Variations in Bird Diversity in an Urban Area?

Sustainability ◽

10.3390/su13105747 ◽

2021 ◽

Vol 13 (10) ◽

pp. 5747

Author(s):

Dehuan Li ◽

Wei Sun ◽

Fan Xia ◽

Yixuan Yang ◽

Yujing Xie

Keyword(s):

Habitat Quality ◽

Quality Index ◽

Empirical Studies ◽

Species Abundance ◽

Diversity Indices ◽

Local Scale ◽

Data Availability ◽

Bird Diversity ◽

Invest Model ◽

Trade Offs

Biodiversity maintenance is a crucial ecosystem service. Due to time limits and data availability, assessing biodiversity using indicators or models has become a hot topic in recent decades. However, whether some proposed indicators can explain biodiversity well at the local scale is still unclear. This study attempted to test whether the habitat quality index (HQI) as measured using the integrated valuation of ecosystem services and trade-offs (InVEST) model could explain variations in bird diversity in New Jiangwan Town, a rapidly urbanized region of Shanghai, China. The relationships from 2002 to 2013 among HQI and the two diversity indices, species richness and species abundance, were analyzed using Fisher’s exact test and gray correlation analysis. No significant association was found. Habitat connectivity was then integrated to develop a new combined indicator of habitat quality and connectivity index (HQCI). The associations between HQCI and the two diversity indices were improved significantly. The results indicated that connectivity may be an important factor explaining the diversity of certain species at a local scale. More empirical studies should be conducted to provide scientific evidence relating habitat quality to biodiversity.

Download Full-text

Friendship paradox in growth networks: analytical and empirical analysis

Applied Network Science ◽

10.1007/s41109-021-00391-6 ◽

2021 ◽

Vol 6 (1) ◽

Author(s):

Sergei P. Sidorov ◽

Sergei V. Mironov ◽

Alexey A. Grigoriev

Keyword(s):

Real World ◽

Preferential Attachment ◽

Empirical Studies ◽

Mean Field ◽

Network Models ◽

Average Degree ◽

Closure Model ◽

Triadic Closure ◽

Attachment Mechanism ◽

Over Time

AbstractMany empirical studies have shown that in social, citation, collaboration, and other types of networks in real world, the degree of almost every node is less than the average degree of its neighbors. This imbalance is well known in sociology as the friendship paradox and states that your friends are more popular than you on average. If we introduce a value equal to the ratio of the average degree of the neighbors for a certain node to the degree of this node (which is called the ‘friendship index’, FI), then the FI value of more than 1 for most nodes indicates the presence of the friendship paradox in the network. In this paper, we study the behavior of the FI over time for networks generated by growth network models. We will focus our analysis on two models based on the use of the preferential attachment mechanism: the Barabási–Albert model and the triadic closure model. Using the mean-field approach, we obtain differential equations describing the dynamics of changes in the FI over time, and accordingly, after obtaining their solutions, we find the expected values of this index over iterations. The results show that the values of FI are decreasing over time for all nodes in both models. However, for networks constructed in accordance with the triadic closure model, this decrease occurs at a much slower rate than for the Barabási–Albert graphs. In addition, we analyze several real-world networks and show that their FI distributions follow a power law. We show that both the Barabási–Albert and the triadic closure networks exhibit the same behavior. However, for networks based on the triadic closure model, the distributions of FI are more heavy-tailed and, in this sense, are closer to the distributions for real networks.

Download Full-text

Postsynaptic Receptive Field Size and Spike Threshold Determine Encoding of High-Frequency Information Via Sensitivity to Synchronous Presynaptic Activity

Journal of Neurophysiology ◽

10.1152/jn.90814.2008 ◽

2009 ◽

Vol 101 (3) ◽

pp. 1160-1170 ◽

Cited By ~ 26

Author(s):

Jason W. Middleton ◽

André Longtin ◽

Jan Benda ◽

Leonard Maler

Keyword(s):

High Frequency ◽

Time Window ◽

Pyramidal Cells ◽

Spike Trains ◽

Small Time ◽

Field Size ◽

Recent Experimental Data ◽

Neuron Models ◽

High Frequency Signal ◽

Unit Spike

Parallel sensory streams carrying distinct information about various stimulus properties have been observed in several sensory systems, including the visual system. What remains unclear is why some of these streams differ in the size of their receptive fields (RFs). In the electrosensory system, neurons with large RFs have short-latency responses and are tuned to high-frequency inputs. Conversely, neurons with small RFs are low-frequency tuned and exhibit longer-latency responses. What principle underlies this organization? We show experimentally that synchronous electroreceptor afferent (P-unit) spike trains selectively encode high-frequency stimulus information from broadband signals. This finding relies on a comparison of stimulus-spike output coherence using output trains obtained by either summing pairs of recorded afferent spike trains or selecting synchronous spike trains based on coincidence within a small time window. We propose a physiologically realistic decoding mechanism, based on postsynaptic RF size and postsynaptic output rate normalization that tunes target pyramidal cells in different electrosensory maps to low- or high-frequency signal components. By driving realistic neuron models with experimentally obtained P-unit spike trains, we show that a small RF is matched with a postsynaptic integration regime leading to responses over a broad range of frequencies, and a large RF with a fluctuation-driven regime that requires synchronous presynaptic input and therefore selectively encodes higher frequencies, confirming recent experimental data. Thus our work reveals that the frequency content of a broadband stimulus extracted by pyramidal cells, from P-unit afferents, depends on the amount of feedforward convergence they receive.

Download Full-text

Markov chains in small time intervals

Journal of Applied Probability ◽

10.2307/3213331 ◽

1981 ◽

Vol 18 (3) ◽

pp. 747-751

Author(s):

Stig I. Rosenlund

Keyword(s):

Markov Chain ◽

Markov Chains ◽

Transition Probability ◽

Small Time ◽

Exact Order ◽

Time Intervals ◽

Continuous Parameter ◽

Minimum Number

For a time-homogeneous continuous-parameter Markov chain we show that as t → 0 the transition probability pn,j (t) is at least of order where r(n, j) is the minimum number of jumps needed for the chain to pass from n to j. If the intensities of passage are bounded over the set of states which can be reached from n via fewer than r(n, j) jumps, this is the exact order.

Download Full-text

Multiple biological mechanisms result in correlations between pre- and post-mating traits that differ among versus within individuals and genotypes

Proceedings of The Royal Society B Biological Sciences ◽

10.1098/rspb.2018.0951 ◽

2018 ◽

Vol 285 (1885) ◽

pp. 20180951 ◽

Cited By ~ 4

Author(s):

Cristina Tuni ◽

Chang S. Han ◽

Niels J. Dingemanse

Keyword(s):

Empirical Studies ◽

Genetic Correlations ◽

Reproductive Traits ◽

Fertilization Success ◽

Male Quality ◽

Biological Mechanisms ◽

Environmental Correlations ◽

Ejaculate Size ◽

Trade Offs ◽

The Hierarchical Structure

Reproductive traits involved in mate acquisition (pre-mating traits) are predicted to covary with those involved in fertilization success (post-mating traits). Variation in male quality may give rise to positive, and resource allocation trade-offs to negative, covariances between pre- and post-mating traits. Empirical studies have yielded mixed results. Progress is hampered as researchers often fail to appreciate that mentioned biological mechanisms can act simultaneously but at different hierarchical levels of biological variation: genetic correlations may, for example, be negative due to genetic trade-offs but environmental correlations may instead be positive due to individual variation in resource acquisition. We measured pre-mating (aggression, body weight) and post-mating (ejaculate size) reproductive traits in a pedigreed population of southern field crickets ( Gryllus bimaculatus ). To create environmental variation, crickets were raised on either a low or a high nymphal density treatment. We estimated genetic and environmental sources of correlations between pre- and post-mating traits. We found positive genetic correlations between pre- and post-mating traits, implying the existence of genetic variation in male quality. Over repeated trials of the same individual (testing order), positive changes in one trait were matched with negative changes in other traits, suggesting energy allocating trade-offs within individuals among days. These findings demonstrate the need for research on pre- and post-mating traits to consider the hierarchical structure of trait correlations. Only by doing so was our study able to conclude that multiple mechanisms jointly shape phenotypic associations between pre- and post-mating traits in crickets.

Download Full-text