NERCCS 2021:
Fourth Northeast Regional
Conference on Complex Systems

March 31 - April 2, 2021
Abstracts

Online (via Zoom)

Abstracts for NERCCS 2021:
Fourth Northeast Regional Conference on
Complex Systems
Complex Systems Society US Northeast Chapter
Center for Collective Dynamics of Complex Systems
Binghamton University, State University of New YorkMarch 31–April 2, 2021
Online (via Zoom)
https://nerccs2021.github.io/

Contents
I

Invited Talks

1

Erik Bollt: On Geometry of Information Flow for Causal Inference in Complex Systems

2

Alexandra Paxton: From Arguments to Wars and the Scales In-Between: Dynamical
Systems Analyses of Human Conflict

3

II

4

Contributed Talk Session 1

Li Pi, Paul Expert and Ceire Costelloe: CPE spreading patterns from contact networksof patients in 3 urban hospitals: implications for infection prevention and control

5Samin Aref and Zachary Neal: Analyzing coalitions, ideology, and effectiveness in the US
Congress by optimally partitioning signed networks of legislators

6

Guillaume St-Onge, Hanlin Sun, Antoine Allard, Laurent Hébert-Dufresne and Ginestra Bianconi: Bursty exposure on higher-order networks leads to nonlinear infection
kernels7

Pegah Hozhabrierdi, Raymond Zhu, Maduakolam Onyewu and Sucheta Soundarajan:
Network-Based Analysis of Early Pandemic Mitigation Strategies: Solutions, and Future Directions

8

III

9

Contributed Talk Session 2

Mateusz Wilinski and Andrey Lokhov: Scalable Learning of Independent Cascade Dynamics from Partial Observations
10
Dj Passey, Ben Webb, Joseph Wilkes and Joseph Jamieson: Understanding Reservoirs:
Ideal Networks for Replicating Chaos
11
Andreia Sofia Teixeira, Francisco C. Santos, Alexandre P Francisco and Fernando P. Santos: Fairness in multiplayer ultimatum games through degree-based role assignment 12
Gabriele Pisciotta and Giulio Rossetti: A Network Science approach to Instance Matching
13

IV

Contributed Talk Session 3

14

Alfredo Morales, Isabella Loaiza and Sandy Pentland: Modeling Migrant Mobility

iii

15

Ülgen Kilic, Sarah Muldoon and Dane Taylor: Geometrical and topological data analyses
reveal that higher-order structures provide flow channels for neuronal avalanches
16
Andrea Allen, Mariah Boudreau, Nicholas Roberts and Laurent Hebertdufresne: Modeling epidemic interventions with probability generating functions
17
Dylan Morris, Daniel Cooney, Simon Levin, Daniel Rubenstein and Pawel Romanczuk:Social Dilemmas of Sociality in the Presence of Beneficial and Costly Contagion
18

V

Contributed Talk Session 4

19

Denis Patterson and Jonathan Touboul: A Mathematical Model of Neuronal Identitywith Ectopic Domains
20
Eric Peña and Hiroki Sayama: A Life Worth Mentioning: Complexity of Conway’s Gameof Life and Other Notable Life-like Rules
21
Lingqi Meng and Naoki Masuda: Epidemic threshold for metapopulation model networks with a second-order mobility rule
22
Caitrin Hall, Ji Chul Kim, Edward Large and Alexandra Paxton: Differential Coordination Patterns During Human-Metronome Phasing
23

VI

Contributed Talk Session 5

24

Daniel Stroembom and Alice Antia: Anticipation induces polarized collective motion in
attraction based models
25
Zhao Song and Dane Taylor: Asymmetric Coupling of Networks Optimally Accelerates
Collective Dynamics
26
Jan Korbel, Simon Lindner, Rudolf Hanel and Stefan Thurner: Thermodynamics ofstructure-forming systems
27
Virginia Morini, Laura Pollacci and Giulio Rossetti: Towards a Standard Approach for
Echo Chamber Detection: Reddit Case Study28

VII

Contributed Talk Session 6

29

Massimo Stella: Cognitive network science and its links with Education, complex systems
and ways of thinking
30
Shuang Zhang, Feifan Liu and Haoxiang Xia: Understanding Scholars Mobility in Knowledge Embedded Space
31
iv

Tuan Pham, Andrew Alexander, Jan Korbel, Rudolf Hanel and Stefan Thurner: Balanced and fragmented phases in societies with homophily and social balance
32
Elie Alhajjar, Ryan Fameli and Shane Warren: Are Terrorist Networks Just Glorified
Criminal Cells?
33

VIII

Contributed Talk Session 7

34

Mengyuan Sun and Naoki Masuda: COVID-19 impacts on domestic airlines via multilayer network analysis
35
Anca Radulescu: Complex dynamics in networks, templates and mutated systems

36

Bao Huynh, Haimonti Dutta and Dane Taylor: Impact of Community Structure on Consensus Machine Learning
37
Ülgen Kılıç and Sarah Muldoon: Characterization of communities in dynamic functional
networks
38

IX

Contributed Talk Session 8

39

Marina Vegué, Vincent Thibeault, Patrick Desrosiers and Antoine Allard: Dimension
reduction on heterogeneous networks
40
Yiming Che and Changqing Cheng: Active Learning and Relevance Vector Machine in
Efficient Estimate for Basin Stability of Dynamic Networks
41
Chanon Thongprayoon, Lorenzo Livi and Naoki Masuda: Visualizing trajectory of tiedecay temporal networks
42
Vincent Thibeault, Marina Vegué, Antoine Allard and Patrick Desrosiers: Dimension
reduction of high-dimensional dynamics on networks with adaptation
43

X

Poster Session 1

44

Scott Donaldson: Flocc: From Agent-Based Models to Interactive Simulations on theWeb
45
Felipe Xavier Costa and Pedro Pessoa: Entropic dynamics of networks

46

Goktug Islamoglu: Exact Formulation of Ising Model Transitions Between Six Magnetic
Phases [commercial video]
47v

Jun Kataoka, Jayanth Sivakumar, Eric Peña, Yiming Che and Changqing Cheng: Network Reconstruction (Bayesian Sequential Inference of Sparse Network Connectivity)
48
Nicholas Landry and Karen Stengel: The effect of a viral load function on epidemic
dynamics
49
Salvatore Citraro, Massimo Stella and Giulio Rossetti: Towards a multiplex networkmodel of word associations and similarity in the human mind
50
Kazuki Nakajima, Kazuyuki Shudo and Naoki Masuda: Configuration models for hypergraphs preserving local quantities of nodes and hyperedges [commercial video]
51
Stephany Rajeh, Marinette Savonnet, Eric Leclercq and Hocine Cherifi: Correlation ofcommunity-aware and classical centrality measures: Examining the role of network
topology [commercial video]
52
Jake Williams and Diana Solano-Oropeza: The Mixing Law

53Penghang Liu, Tomomi Kito, Naoki Masuda and A. Erdem Sarıyüce: Temporal Motifs
in Patent Opposition and Collaboration Networks [commercial video]
54
Francesca Larosa, Jamie Rickman and Nadia Ameli: Finding the right dam(n) partners
for a just energy transition
55
Daiki Miyagawa, Koki Okamoto and Genki Ichinose: Robustness of football passing networks against cascading failure
56
Luka Blagojević and Aleksandra Alorić: Incremental research - a favoured strategy inthe “publish or perish” environment [commercial video]
57
Mahsa Bagherikalhor and G.Reza Jafari: Abnormal behavior of the Heider balance theory with heterogeneous triads [commercial video]
58
Sriniwas Pandey and Hiroki Sayama: Analyzing Eccentric Behavior of GAB Social Media Users [commercial video]
59
Noha Abdel-Mottaleb, Kashin Sugishita, Naoki Masuda and Qiong Zhang: Bio-Inspired
Water Distribution Network Design
60
Tayeb Jamali, Olha Buchel, Yaneer Bar-Yam and Leila Hedayatifar: A Meta-Population
Movement-Based Epidemic Model for COVID-19 Pandemic
61
Oleg Pavlov and Evangelos Katsamakas: COVID-19 and Financial Sustainability of Academic Institutions
62

vi

Sangeeta Rani Ujjwal, Ulrike Feudel and Ramakrishna Ramaswamy: Intermittent frequency chimeras in modular network of FitzHugh-Nagumo oscillators
63

XI

Poster Session 2

64

Yanchen Liu: approximate network symmetry

65

John Meluso, Laurent Hébert-Dufresne, James Bagrow and Rob Razzante: Masculinity
Contest Cultures and Inclusive Cultures: Insights From a Network Model of Organizational Socialization and Promotion
66
Christopher Diggans, Jeremie Fish and Erik Bollt: Emergent hierarchy through conductancebased node constraints
67
Volkan Saribas, Babek Erdebilli and Ibrahim Yilmaz: MULTICRITERIA SELECTION
AND EVALUATION OF THE LIFESAVING UAVs FOR A DETERMINED AREA
(AEGEAN SEA COASTLINE) IN TURKEY BY COMPARING TODIM&GOALPROGRAMMING (GP) METHOD
68
Ruodan Liu, Masaki Ogura, Elohim Fonseca Dos Reis and Naoki Masuda: Modelingepidemic spreading in Markovian temporal networks with different degrees of concurrency
69
John O’Meara, Ashwin Vaidya and Stephen Essien: Complexity and Curriculum: Examining the Role of Connectivity in a Precalculus Course
70
Estera Boncea, Paul Expert and Ceire Costelloe: Exploring the connectivity of a hospital:
A network analysis of patient movement community structures [commercial video] 71
Fabiano Lemes Ribeiro: On the relation between transversal and longitudinal scaling incities72
Prosenjit Kundu, Chittaranjan Hens, Baruch Barzel and Pinaki Pal: Perfect synchronization in networks of Sakaguchi-Kuramoto oscillators
73
Touria Karite, Adil Khazari and Delfim F. M. Torres: Optimal control problem of variable order fractional systems with Riemann-Liouville derivative
74
Rupam Acharyya, Penghang Liu, A. Erdem Sariyuce and Naoki Masuda: Detecting
Fraudulent Users in Online Marketplaces Using Temporal Motifs
75
Matthew Tomlinson, David Greenwood and Marcin Mucha-Kruczynski: Extreme financial losses and gains: mutually-exciting arrivals or conditional volatility?
76
André Martins: Defining extremism in opinion models [commercial video]

vii

77

Cynthia Siew and Anutra Guru: Longitudinal Subject Fluency Networks of Psychology
and Biology Students
78
Francesco Bertolotti, Angela Locoro and Luca Mari: Emergence of Risk Sensitivity in a
First-principles Agent-based model
79
Andreas Pape and Peter DiCola: A Modular Common Pool Resource Model with Social
Planning
80
Elias Fernández Domingos, Jelena Grujić, Juan Carlos Burguillo, Francisco C. Santos
and Tom Lenaerts: Modeling behavioral experiments on uncertainty and cooperation
with population-based reinforcement learning - Extended Abstract
81
Tong Wu, Matthew McGuire, Sarah Muldoon and David Poulsen: Evolution of brain
networks after traumatic brain injury
82
Xinglong Ju and Feng Liu: Optimizing Wind Farm Efficiency with Self-Adaptivity Mechanism in Evolutionary Algorithm
83
Zachary Boyd and Kayvan Lavassani: Resiliency of Global Medical Equipment Supply
Chains84

viiiPart I

Invited Talks

1

On Geometry of Information Flow for Causal Inference in Complex Systems
Erik Bollt
Department of Mathematics, Clarkson University
ebollt@clarkson.edu
Abstract
Causal inference is perhaps one of the most fundamental concepts in science,
beginning originally from the works of some of the ancient philosophers, throughtoday, but also weaved strongly in current work from statisticians, machine learning
experts, and scientists from many fields. We take the perspective of information
flow, which includes the Nobel prize winning work on Granger-causality, and therecently highly popular transfer entropy, these being probabilistic in nature. We
will briefly describe some examples of our causation entropy principle designed todifferentiate direct versus indirect influences, with applications such as from Earthscience, and neuro science. Our main contribution today will be our newly
developed analysis contrasting geometric interpretation of information flow versus
otherwise usually indicated by positive conditional entropies. The dimensionalityof data intrinsic in an underlying manifold effectively projects into the outcome
space summarizes information flow. Thus contrasting fractal dimensions
conditionally applied to competing explanations of future forecasts shed light on
causality.

2

From Arguments to Wars and the Scales In-Between:
Dynamical Systems Analyses of Human Conflict
Alexandra Paxton
Department of Psychological Sciences, University of Connecticut
alexandra.paxton@uconn.edu
Abstract
A dynamical systems perspective on human interaction might consider theinteraction context—that is, the set of physical and social characteristics in which
the interaction occurs—as a sort of constraint on the emergent dynamics. In thistalk, I consider the impact of conflict as a constraint on human interaction on a
range of spatiotemporal scales.

3Part II

Contributed Talk Session 1

4

CPE spreading patterns from contact networks of patients in 3 urban hospitals:
implications for infection prevention and control
L Pi1, P Expert2, C Costelloe2
1
Big Data Institute, Li Ka Shing Centre for Health Information and Discovery, University of
Oxford, UK
2
Global Digital Health Unit, Imperial College London, UK.
Healthcare-associated infection (HCAI), defined as infections acquired by patients during caredelivery in a healthcare setting, represents one of the most significant challenges for modern
medicine. HCAI can significantly impact patients' lives, leading to prolonged hospital stays,
long-term disabilities and increased risk of mortality. In a recent modelling study, HCAI was
estimated to cause 22,800 deaths in England and cost the health system an extra £2.1 billion in
2016/2017 [1]. Among nosocomial infection organisms, Carbapenemase-producing
Enterobacteriaceae (CPE), pose nearly the greatest clinical threat, given the high levels of
resistance to carbapenems which are considered as agents of ‘last resort’ against lifethreatening hospital infections. Understanding patterns of CPE infection spreading in hospitals
is therefore crucial to inform infection control protocols to mitigate the presence of CPE in
hospitals. As CPE spreads in healthcare settings through contacts between patients, healthcare
workers, and contaminated environments, we designed a track and trace experiment toreconstruct the contact networks of CPE carriers. We used patient electronic health records of3 urban hospitals from 2015-2018 to i) track microbiologically confirmed CPE carriers and ii)
trace the patients they shared place and time with until their identification using time stamped
ward transfer information. We aggregated the contact network yearly to avoid confounding
seasonal effects and obtain a weighted statistical representation of the contact networks. The
contact networks exhibit a core-periphery structure (Fig 1, left), highlighting the presence of acore set of wards where most carriers-contact interaction occur before being redistributed toperipheral wards. Interestingly, high caseloads are not necessarily associated with core wards,
supporting the mixing and disseminating picture. Using modularity, we identified functional
communities of wards from the whole patient movement network. The contact networks
projected onto the whole patient movement community structure shows a comprehensive
coverage of the hospital. Our findings are robust over time periods and across hospitals. Theyshow that CPE infection can reach virtually all parts of hospitals through first-level contacts.
The methodology is generalisable to any contact transmitted pathogen, e.g. SARS-CoV-2.
They can form the basis for improving infection prevention control strategies.

Figure 1: Structures for Hospital C for year 2. Left: Core (yellow) and periphery (blue) of thecarriers contact network. Right: Functional modules identified from the whole population
movement. Edges used by the contact network in red.
References: [1] Guest, J. F et al. “Modelling the annual nhs costs and outcomes attributable tohealthcare-associated infections in England.” BMJ Open10 (2020)

5

Analyzing coalitions, ideology, and effectiveness in the US Congress by optimallypartitioning signed networks of legislators
Samin Aref1 and Zachary P. Neal2
Max Planck Institute for Demographic Research
aref@demogr.mpg.de
2
Department of Psychology, Michigan State University
zpneal@msu.edu
1

A signed network is one with positive and negative edges, and is k-balanced if the vertices
can be partitioned into k subsets (k-partitioned) such that positive (negative) edges exist within(between) subsets. We analyze signed networks of US Congress from 1979-2018 by solving NPhard problems to optimally partition the legislators into coalitions which minimize the inconsistentedges for k and in general. These signed networks are inferred from bill co-sponsorship data using
a backbone model such that having significantly high (low) co-sponsorships is recorded as a positive (negative) tie. We then investigate the ideological composition and legislative effectiveness ofthese coalitions. Our numerical results show that the collaborative and oppositional patterns of US
Congress are structured by more than two coalitions, in contrast to the traditional two-party categorization which oversimplifies this complex system. After extensive computational experiments, we
focus on the composition of optimal 3-partitions as the most immediate point of departure from thetraditional two-group categorization. The optimal 3-partitions are characterized by a large liberalcoalition and a large conservative coalition, but also include a smaller, ideologically-fluid coalitionof legislators. We observe that in most sessions of the Congress, this third coalition is ideologicallyaligned with the majority party. This group of outsiders tend to push back against members of theirown party and have significantly higher effectiveness in advancing their legislative agenda. Thissuggests that staying out of the partisan divide could enhance legislative effectiveness.
A

1

B

2

5

3
4

1

C

1

5
4

D

2

5

3
4

1

3
4

1

2

5

3
4

Figure 1: (A) An example signed network with negative (positive) edges shown by dotted (solid)lines. (B) Evaluating classic balance using triads: Triad 1-4-5 is unbalanced and triad 1-3-4 isbalanced. Node 2 is disregarded and the macro structure remains unexplored. (C) Evaluating classic balance via 2-partitioning: The 2-partition {{1, 2, 3}, {4, 5}} minimizes the total number of
intra-cluster negative and inter-cluster positive edges to one (edge 4-5). (D) Evaluating generalized balance and clusterability via k-partitioning: The 3-partition {{1, 2, 3}, {4}, {5}} satisfies theconditions of generalized balance.
6

Bursty exposure on higher-order networks leads to nonlinear infection kernels
G. St-Onge 1 , H. Sun 2 , A. Allard 1 , L. Hébert-Dufresne 1,3 , and G. Bianconi 2
1. Université Laval, 2. Queen Mary University of London, 3. University of Vermont
Three properties of human dynamics and disease transmissions are often overlooked in standard
epidemic models: the hypergraph structure of contacts, the burstiness of human behavior, and thecomplex nonlinear relationship between the exposure to infected contacts and the risk of infection.
In this work, we combine these three properties in a hypergraph contagion model, with hyperedges
representing environments where individuals can interact, and where a minimal number of interactions with infected individuals are needed to contract the disease. The central result we obtain isthat bursty exposure, modeled by a power-law distribution of participation time to environments,
can induce a nonlinear relationship between the number of infected participants and the probability
to become infected. We then demonstrate how conventional epidemic wisdom can break down withthe emergence of discontinuous transitions, super-exponential spread, and regimes of hysteresis.
On a theoretical level, this work formally provides a connection between complex contagions basedon nonlinear infection kernels and threshold models. This also allows for a deeper understandingof how higher-order interactions and burstiness affect epidemic spreading. On the epidemiologicallevel, our results challenge a key assumption of most epidemic models and ask: Why assume alinear relationship between the number of infectious contacts and the risk of infection?

α=0

10−2

.5
α

.0
=1

α

=

1.5

10−3

θm (ρ) ∝ ρα

10−4
10−2

10−1

(c) Bifurcation diagram
Stationary prevalence I ∗10−1(b) Temporal evolution
Prevalence I(t)Infection probability θm(a) Infection kernel

10−1

10−2
100

Environment prevalence ρ

0

100

200

Time t × τ̄

300

400

0.75
0.50
0.25
0.00
0.000

0.025

0.050

0.075

0.100

β

Figure 1: Bursty exposure induces contagions with nonlinear infection kernels. We assume that anindividual must have (K = 2) interactions with infected individuals in a hyperedge (environment)
to become infected. Each individual participates a time τ to a hyperedge, distributed according to
P (τ ) ∝ τ −α−1 with τ ∈ [1, ∞). (a) Effective infection probability per participation to a hyperedgeof any size m. The infection probability has a power-law scaling θm (ρ) ∝ ρα if K ≥ α. (b)(c) We study the consequences of nonlinear infection kernels for a SIS-type contagion dynamics on
hypergraphs. The average number of interactions in an environment is proportional to β. (b) Supralinear kernel α > 1 leads to a super-exponential growth for the global prevalence I(t). We adjusted
β to obtain similar prevalence levels. τ̄ is the median participation time associated with P (τ ). (c)The bifurcation diagram in the stationary state (t → ∞) can be continuous or discontinuous with abistable regime. Sub-linear and linear kernels α ≤ 1 lead to a continuous phase transition, and theepidemic threshold βc vanishes for α → 0. Supra-linear kernels α > 1 can lead to a discontinuous
phase transition with a bistable regime.

7

Network-Based Analysis of Early Pandemic Mitigation Strategies: Solutions, and Future
Directions
Pegah Hozhabrierdi, Raymond Zhu, Maduakolam Onyewu and Sucheta Soundarajan
See the full paper published in the Northeast Journal of Complex Systems:
https://orb.binghamton.edu/nejcs/vol3/iss1/3/

8

Part III

Contributed Talk Session 2

9Scalable Learning of Effective Spreading Models on Networks
Mateusz Wilinski1 and Andrey Lokhov1
1

Los Alamos National Laboratory, Los Alamos, 87545 New Mexico, United States of America

Spreading processes on networks play an increasingly important role in modeling infectious
diseases, regulatory networks, marketing and opinion setting. Events like Coronavirus or Cambridge Analytica affair further highlight the need for prediction, optimization, and control ofdiffusion dynamics. To tackle these tasks, it is essential to learn the effective spreading modeland transmission probabilities across the network of interactions. Unfortunately, in most cases
the transmission rates are unknown and need to be inferred from the spreading data. Additionally, it is rarely the case that we have full observation of the dynamics. As a result, typicalmaximum likelihood approach quickly becomes intractable for large network instances.

1.0

inaffected edges
affected edges

0.8
0.6
0.4

­

|αij − αij∗ |®

0% of unobserved nodes
1% of unobserved nodes
5% of unobserved nodes
15% of unobserved nodes
25% of unobserved nodes

αij∗

0.30
0.25
0.20
0.15
0.10
0.05
0.00

0.2
0.0
101

102

105
103
104
number of cascades

106

0.0

0.5
αij

1.0

Figure 1: Left: Average distance between real and estimated transmission parameters αij , for arandom 3-regular graph with N = 100 nodes, as a function of the number of available cascades.
Right: Example of parameters estimation for a random 3-regular graph with N = 100 nodes,
M = 104 cascades and 15% unobserved nodes. Each point represents a different parameter αij .
The red crosses represent edges affected by an unobserved node.
We introduce an efficient algorithm, based on a mean-field approximation and the dynamic
message-passing approach, which is able to reconstruct parameters of the effective spreading
model given only limited information on the activation times of nodes in the network. The
proposed method can be easily generalized to a large class of dynamic models on networks andbeyond. Exemplary results for Independent Cascade model on a random regular graph, areshown in figure 1. Number of cascades refer to the number of observed spreading realisations.
For each simulation we randomly pick unobserved nodes and transmission probabilities. Notethat we analyse a general case, where transmission probability can be different for each edge,
but the method can easily be adjusted to simpler settings. Our algorithm is linear in bothcascade length (number of spreading steps) and size of the network (number of edges), whichmakes it scalable and efficient when dealing with huge empirical networks. Additionally, we
present a scheme to infer the effective model, which is able to approximate marginal activation
probabilities even for settings where message passing is usually inaccurate.

10Understanding Reservoirs: Ideal Networks for Replicating Chaos
J Jamieson, D. Passey, D. Smith, B. Webb, and J. Wilkes
Abstract

Reservoir computers are a machine learning model that, unlike most standard machine learning models, make use of an internal complex network. The effect of network topology on the dynamics of reservoir computers is not well understood. To
investigate this, we trained over one-hundred million reservoir computers to replicate
the chaotic dynamics of the Lorenz attractor. In our experiments, we varied hyperparameters and internal network structure to determine the combinations that produce
the best predictions.
Specifically, we studied how reservoir computer prediction varied with respect tocommon network topologies across a substantial range of hyperparameters. We alsostudied the performance of ”thinned” versions of the standard topologies, by removing
a percent of edges at random.
We found that sparse, e.g. thinned, networks are typically better suited to learn
the dynamics of the Lorenz attractor. Our experiments also revealed an interaction
between the reservoir computer spectral radius parameter (a rescaling of the reservoir
adjacency matrix to produce a desired spectral radius) and the sparsity of the internal
network suggesting that spectral radius and sparsity combine in unexpected ways to
impact reservoir computer predictive ability.
To help interpret our experimental findings, we analyzed the untrained reservoir
dynamical system, studying how reservoir computer fixed points and their stability
vary in response to a training signal. This analysis demonstrated that high spectral
radius and high connectivity reduce the sensitivity of reservoir computers to input data,
making them poorly suited for learning. This analysis offers insight into better designprinciples for reservoir computers and better understanding of the role of network
topology in machine learning.

Figure 1: Complex network models before and after removing 80% of the edges.

11

Fairness in multiplayer ultimatum games through degree-based role assignment
Andreia Sofia Teixeira1,4, Francisco C. Santos1,2, Alexandre P. Francisco1,2, Fernando P. Santos3. (1) INESC-ID,
Lisboa, Portugal, steixeira@inesc-id.pt. (2) Instituto Superior Técnico, Universidade de Lisboa, Portugal (3)Department of Ecology and Evolutionary Biology, Princeton University, Princeton, USA (4) Indiana University
Network Science Institute (IUNI), Indiana University, Bloomington IN, USA

From social contracts to climate agreements, individuals engage in groups that mustcollectively reach decisions with varying levels of equality and fairness. These dilemmas also
pervade Distributed Artificial Intelligence, in domains such as automated negotiation, conflict
resolution or resource allocation. As evidenced by the well-known Ultimatum Game – where a
Proposer has to divide a resource with a Responder – payoff-maximizing outcomes are
frequently at odds with fairness. Eliciting equality in populations of self-regarding agentsrequires judicious interventions. Here we use knowledge about agents’ social networks toassess the impact of a novel fairness mechanism, in the context of Multiplayer Ultimatum
Games. We focus on network-based role assignment and show that preferentially attributing
the role of Proposer to low-connected nodes increases the fairness levels in a population. The!"#

probability that a node j is selected as Proposer is given by 𝑝! = ∑" " !"$ , where 𝛼 controls the$dependence on the degree (see Fig. 1 a)). We evaluate the effectiveness of low-degree Proposer
assignment considering networks with different average connectivity (using the BarabásiAlbert algorithm (BA) of growth and preferential attachment and Dorogotsev-MendesSamukhin (DMS) duplication model), group sizes, and group voting rules - (M) - when
accepting proposals (e.g. majority or unanimity) (see Fig. 1b)). We further show that low-degree
Proposer assignment is efficient, not only optimizing fairness, but also the average payoff levelin the population (see Fig. 1 c)). Finally, we show that stricter voting rules (i.e., imposing an
accepting consensus as requirement for collectives to accept a proposal) attenuates theunfairness that results from situations where hubs are the natural candidates to play as Proposers(see Fig. 1 d)). Our results suggest new routes to use role assignment and voting mechanisms toprevent unfair behaviors from spreading on complex networks.

Figure 1: Panel a): Example of probability distribution of degree-based assignment of the role of the proposer. Panelb): Average proposal for different networks, different values of 𝛼 (low (high) 𝛼 means that nodes with low (high)degree are more likely to be the proposers) and different group voting rules (M stands for the minimum group fractionof acceptance necessary for the proposal to be accepted). Panel c): Distributions of average fitness for different
values of 𝛼 and group voting rules. Panel d): Lorenz curves for different values of 𝛼 and group voting rules.

12

A Network Science approach to Instance Matching
Gabriele Pisciotta1 and Giulio Rossetti2
1
2

University of Pisa, Italy g.pisciotta1@studenti.unipi.it
KDD Lab, ISTI-CNR, Italy giulio.rossetti@isti.cnr.it

Nowadays, the use of Knowledge Graphs (KG) as background knowledge is widespreadin Machine Learning. Companies and users continuously create and share Linked Open Data:
as a result it is common that a same real world entity can be described differently by different
KGs. Identifying identity relations is a challenging task, usually called as Instance Matching(IM), that enables inter-linking of different KGs with the aim of supporting the expansion of theknowledge available to ML and Intelligent Agents systems. The IM can be seen as a special
case of the Link Prediction (LP) task, in which the only edge type to be predicted between
individual of different KGs is the owl:sameAs, as shown in Figure 1.
Quoting [2], the IM problem requires to find classifier that effectively discriminate between
matching instances and non-matching instances.
Our Method
Value
Structural
LogicalMixed

Figure 1: Example of matched instances

CODI

F1

P

R

F1

P

R

0.90
0.63
0.92
0.61

0.99
0.72
0.93
0.75

0.85
0.60
0.92
0.53

0.96
0.88
0.97
0.65

0.99
0.95
0.96
0.86

0.93
0.83
0.97
0.54

Table 1: Results for IIMB 2010 [1]Considering the network-based nature of the data, we decided to discard any linguistic feature attached to the entities (usually exploited to address the IM task) and to focus on KGs
topology alone: for each possible edge between the entities coming from KG pairs, discarding those belonging to disjoint classes, we compute: (i) the Jaccard distance between the twoneighbours set, (ii) the Resource Allocation Index , (iii) the Adamic Adar coefficient , (iv) the
Preferential Attachment.
We tested our approach on the IIMB 2010 dataset of the Ontology Evaluation Alignment
Campaign [1] where the task requires to match entities of an original dataset to the ones of its
80 perturbations embedding various kinds of data transformation (including value, structural,logical, and a mixed ones). We applied AdaBoost to a 80-20 training-test split of the edges foreach perturbation sub-task: Table 1 reports the average results for each type of transformationin terms of Precision/Recall and F1. Our results, even with a limited feature set, are in linewith SOTA that leverage linguistic features analysis: moreover, our pure topological approach
appears robust to value and logical transformation, downgrading its performances only whenstructural and mixed transformations are applied.
Concluding, our preliminary work underlines how IM can be successfully tackled without
involving linguistic features related to the textual description of the entities, while focusing
only on Network Science based features. As future works, we plan to extend the experiments
to other datasets enriching the feature set and model definition strategies.
References[1] Jérôme Euzenat et al. “Results of the Ontology Alignment Evaluation Initiative 2010”. In:
Proc. 5th ISWC workshop on ontology matching (OM). 2010, pp. 85–117.
[2] Shu Rong et al. “A Machine Learning Approachfor Instance Matching Based on Simi13
larity Metrics”. In: The Semantic Web – ISWC 2012. 2012, pp. 460–475.

Part IV

Contributed Talk Session 3

14Modeling Migrant Mobility
Alfredo J. Morales, Isabella Loaiza, Alex “Sandy” Pentland
MIT Media Lab
alfredom@mit.edu
Massive migrations have become increasingly prevalent over the last decades. A recent example is the
Venezuelan migration crisis across South America, which particularly affects neighboring countries like
Colombia. It is crucial to map and understand geographic patterns of migration, including spatial mobility
and dynamics over time. The aim of this paper is to uncover mobility and economic patterns of migrantsthat left Venezuela and migrated into Colombia due to the effects of the ongoing social, political andeconomic crisis. We analyze and compare the behavior of two types of migrants: Venezuelan refugees andColombian nationals who used to live in Venezuela and return to their home country. We adapt the gravity
model for human mobility in order to explain migrants’ dispersion across Colombia and analyze patternsof economic integration. This study is a first attempt at analyzing and comparing two kinds of migrant
populations in one destination country, providing unique insight into the processes of mobility andintegration after migration [1]. Findings suggest that migrants and returnees have different drivers behind
their mobility patterns and destination choices (see Figure 1). While migrants are less constrained bydistance and more attracted to larger cities, returnees seem to stay in places where they are from and havesocial networks. We also analyzed the economic integration of these individuals and found that migrants
are less integrated than returnees despite having slightly higher levels of education. We hypothesize thatsuch difference in economic integration is due to the advantages of having pre-existing social networks.
The resolution of the available data does not allow a deeper investigation of the effects of social networks
on the evolution of spatial and economic integration in migrants. However, given the challenges that hostingsocieties face in the context of sudden migrations, these findings highlight their importance for future
research.

Figure 1 Percentage of migrants versus
returnees per department. Dots represent
departments. The x-axis represents therelative number of migrants per department
in 2019. The y-axis represents the relative
number of returnees per department in 2019.
The dot size is proportional to the department
population. The dot color is proportional tothe department distance to Caracas,
Venezuela. The distance has been normalizedby subtracting the average distance anddividing by the standard deviation. Blue
indicates closer to Caracas. Red and green
indicate farther. Scales in Figure. The verticaland horizontal dashed lines show the expected
relative number of migrants or returnees if the
distributions were uniform. The diagonal lineis the identity (x=y). The departments hosting
Bogotá, Medellín and Cali have beenannotated.

[1] Saa, I.L., Novak, M., Morales, A.J. et al. Looking for a better future: modeling migrant mobility.Appl
Netw Sci 5, 70 (2020). https://doi.org/10.1007/s41109-020-00308-9

15

Geometrical and topological data analyses reveal that higher-order
structures provide flow channels for neuronal avalanches
Bengier Ülgen Kılıç1 , Sarah Feldt Muldoon1,2,3 , Dane Taylor1,2
1

Department of Mathematics, University at Buffalo, SUNY, Buffalo, NY
2
3

CDSE Program, University at Buffalo, SUNY, Buffalo, NY

Neuroscience Program, University at Buffalo, SUNY, Buffalo, NY

Neuronal systems exhibit a diversity of dynamical patterns (e.g., excitatory behavior, oscillations, wave propagation), and recent work has developed a broad understanding of how such dynamics relate to network properties
including, for example, modular, geometric, and higher-order structures. Nevertheless, we still lack a mechanistic
understanding of how (micro-scale) neuron dynamics reliably and efficiently organize to enable (large-scale) signal
propagation and neurocomputation at the systems level. Here, we show that higher-order structures provide channels over which neuronal avalanches flow, which can potentially be used by neuronal systems to strike a balance
between local and global signal propagation. To quantitatively study this phenomenon, we leverage mathematical
tools from algebraic topology and geometry [1]. Our work complements prior research that has used topological data
analysis (TDA) to study brain activity at the macroscopic level [2]. Here, we extend prior work [1] to investigate
how neuronal systems balance structural properties (e.g., node degrees, manifold topology, and neighborhood overlap) with dynamical properties (e.g., intrinsic noise, refractory periods, and activation timescale) to yield neuronalavalanches that reliably follow higher-order structures Figure 1. Our model is a simple two-state (xti ∈ {0, 1})
stochastic threshold model with a non-linear responseP function inwhich neuron i fires at time t + 1 with probability
bi
1
t
t
where
R(i)
=
=
0)
=
p(xt+1=1|xiibi ∈Bit n+k − ti , Bi is the set of active neighbors of neuron i at
1+e−CR(i)time step t, C is a constant to tune stochasticity of neuronal responses and ti is an activation threshold for neuron i.

Figure 1: A. We run our experiments on noisy geometric networks that consist of both (i) short-range edges between nodes
that are nearby along a ring manifold and (ii) long-range edges that represent a structural perturbation to the ring manifold.
The top image highlights that there are higher order structures connecting adjacent neighbors. The middle and top images
represent that the noisy geometric network consists of long and short-range edges, and we construct them in a way that issimilar to the Watts-Strogatz small-world model, except that we force the network to be k-regular. B. The top panels depict
distance matrices D, where Dij is a notion of distance that is obtained directly from the dynamics—it is the first activationof the node j for a neuronal cascade that starts from node i. The lower panels depict persistence diagrams that summarize
the topology of the neuronal cascades.. The three panels capture different behaviors that arise for three parameter choices forthe neuron dynamics. From left to right, the neuronal avalanches (i) quickly spread but are not confined to the higher-order
structural channels; (ii) slowly spread down the higher-order structural channels; or (iii) do not spread. C. To support ourcharacterizations of fast, slow and no spreading, we plot the cascade size versus time for the three experiments shown in B.

References[1] Taylor, D., Klimm, F., Harrington, H. et al. Topological data analysis of contagion maps for examining spreading
processes on networks. Nat. Commun. 6, 7723 (2015).
[2] Petri, Giovanni and Expert, Paul and Turkheimer, Federico and Carhart-Harris, Robin and Nutt, David and Hellyer,
Peter J and Vaccarino, Francesco Homological scaffolds of brain functional networks. Journal of The Royal SocietyInterface (11) 101, 20140873 (2014).

16Modeling epidemic interventions with probability generating functions
Andrea Allen1 , Mariah Boudreau1 , Nicholas Roberts1 , and Laurent Hébert-Dufresne1,2
1. Vermont Complex Systems Center, University of Vermont, Burlington, VT, USA
2. Département de Physique, de Génie Physique et d’Optique, Université Laval, Québec, Canada

Infectious diseases, now more than ever, are a critical area of study within the field of public health. Probability generating functions are a common approach used to analyze percolation
models on contact networks,1 which allow for the inclusion of both the stochastic nature of disease spread and the heterogeneous structure of contact networks. One critical limitation of using
percolation models to study epidemics, and the generating function approach more specifically, isthat they integrate over time, precluding us from studying temporal disease dynamics. However,there has been recent work2 which allows for the application of a time varying generating function
approach to study disease spread. We extend this theory to study the effect of public health interventions, such as vaccination, on the population-level disease dynamics. We perform simulationsof disease spread on synthetic contact networks, and find that our results agree with our frameworkacross a range of degree distributions. This agreement validates the use of our model over computationally expensive simulations and paves the way for extensive computational experiments oftime-dependent interventions against emerging epidemics.

Figure 1: Probability distributions for cumulative outbreak size by epidemic generation on a modified
power-law network, validated with simulation results, highlighting the effects of interventions on outbreaksize. Smooth curves depict the analytical distributions, noisy curves show empirical results. Disease transmissibility T was set to T = 0.6, and in the intervention regime, was reduced to T = 0.4 at generation 4. The
non-intervention regime is shown in dark blue, the intervention regime in light blue. The inset plot shows
the network degree distribution, given by pk = k 2 e k/5 .
1 Mark EJ Newman. “Spread of epidemic disease on networks”. In: Physical review E 66.1 (2002), p. 016128.

2 Pierre-André Noël et al. “Time evolution of epidemic disease on finite and infinite networks”. In: Physical Review

E 79.2 (2009), p. 026101.

17

Social Dilemmas of Sociality in the Presence of Beneficial and Costly Contagion
Dylan Morris1,∗ , Daniel Cooney2,∗ , Simon Levin3 , Daniel Rubenstein3 , and Pawel Romanczuk4
1

Department of Ecology and Evolutionary Biology, University of California, Los Angeles
2
Department of Mathematics, University of Pennsylvania, dbcooney@sas.upenn.edu
3
Department of Ecology and Evolutionary Biology, Princeton University
4
Institute for Theoretical Biology, Humboldt University of Berlin

Levels of sociality in nature vary widely from solitary species to the formation of complex animal societies. Increased levels of social interaction can allow for the spread of useful innovations
and beneficial social information, but can also facilitate the spread of harmful infectious disease.
Given the selection pressures that infectious disease impose on a population, it is natural to explore
the ways in which contagion processes may shape the evolution of complex social systems [1].
In this talk, we consider a model for the evolution of sociality strategies in the presence of both abeneficial and costly contagion. We study these dynamics at three timescales: using a susceptibleinfectious-susceptible (SIS) model to describe contagion spread for given sociality strategies, areplicator equation approach to study the changing fractions of resident and mutant strategies, andan adaptive dynamics approach to study the long-time evolution of the resident level of sociality.
We calculate socially-optimal and evolutionarily-stable sociality strategies through the reproduction numbers Ropt and RESS for the good contagion. For a various assumptions on the benefits
and costs of infection, we identify the social dilemma displayed in Figure 1: RESS < Ropt (lessinteraction than optimal) when the bad contagion spreads more readily, while RESS > Ropt (moreinteraction than optimal) when the good contagion spreads more readily. In extreme cases, thisdilemma can result in complete collapse of sociality or reintroduction of harmful disease.

Figure 1: RESS (green) and Ropt (blue) depending on the weight of the good contagion α to CobbDouglas utility when the good contagion spreads less (left) or more (right) than the bad contagion.
References[1] Udiani, O., & Fefferman, N. H. (2020). How disease constrains the evolution of social systems. Proceedings of the Royal Society B, 287(1932), 20201284.
18

Part V

Contributed Talk Session 4

19

A Mathematical Model of Neuronal Identity with Ectopic Domains
Denis Patterson1 and Jonathan Touboul2
1

High Meadows Environmental Institute, Princeton University,
denispatterson@princeton.edu
2
Department of Mathematics, Brandeis University,
jtouboul@brandeis.edu

Recent experiments studying the development of cortical structures in mice have identified
COUP-TF1 as a crucial determinant of both the position and sharpness of the boundary between
the neo and entorhinal cortices. When COUP-TFI is under expressed, neocortex (NC) invades
into territory occupied by the entorhinal cortex (MEC) in wild-type mice, but the sharp boundary
between cortical regions is maintained. However, if COUP-TFI is over-expressed, the boundary
fractures and entorhinal cortex invades the neocortical domain, resulting in mice with ectopic regions of misplaced cortex.
We introduce a novel PDE model based on a Keller-Segel-type chemotaxis mechanism to account for both the sharp cortical boundaries of wild-type mice and the ectopic regions observedin mutant mice. Competition between entorhinal and neocortical progenitor cells is mediated bya gradient of COUP-TF1 across the spatial domain and chemotaxis operators model each cell’saffinity for cells of their own type. We verify the well-posedness of the system and establish necessary conditions for pattern forming Turing bifurcations; we also numerically study the structureof the Turing space and its dependence on model parameters. Numerical simulations show excellent agreement with experimental observations and we present experimental data verifying thedifferential adhesion hypothesis underpinning the model’s phenomenology.

Figure 1: A: Standard boundary formation in a wild type mouse brain. B-F: Comparison ofmodel solutions (top row) with imaging data from mutant mice brains (bottom row). COUP-TFI
expression levels increase from B to F with the wild type brain shown in panel D.

20

A Life Worth Mentioning
Complexity of Conway’s Game of Life and Other Notable Life-like Rules
Eric Peña & Hiroki Sayama
Center for Collective Dynamics of Complex Systems & Department of Systems Science
Binghamton University, State University of New Yorkeric.pena@binghamton.edu
sayama@binghamton.edu
Cellular automata (CA) have been lauded for their ability to generate complex global patterns
from simple and local rules. The late English mathematician, John Horton Conway, developed his
illustrious Game of Life (Life) CA in 1970 and it has since remained the quintessential CA construction—capable of producing a myriad of complex dynamic patterns and computational universality. Life and several other Life-like rules are usually classified in the same group of aestheticallyand dynamically interesting CA characterized by their complex behaviors. However, a rigorous
quantitative comparison among similarly classified Life-like rules has not been fully established.
We use a modified conditional entropy measure, which considers an information-theoretic distancefrom randomness, as a measure of complexity (∆) for two dimensional (2D) CA patterns. We use
this measure to show that Life naturally aims to minimize density and maximize information content while being the most parsimonious Life-like rule with this feature. That is, Life is capable ofmaintaining a consistent amount of long-lasting complexity with the least number of conditions
compared to other Life-like rules. We also show that the complexity of higher density Life-likerules, which themselves contain the Life rule (i.e., B3/S23), form a distinct density-complexity relationship whereby B356/S23 is proposed as an optimal complexity candidate (Fig.1). Generally,
our results support that Life functions as the basic ingredient for cultivating the balance between
structure and randomness thereby maintaining complexity in 2D CA over many evolutions. This
work highlights the genius of John Horton Conway and his Game of Life—a testament to thetimeless marvel which is certainly a life worth mentioning.

Figure 1: a, Temporal evolution of Life and higher density Life-like rules. b, Density and complexity concave relationship is revealed among Life-like rules that contain Life whereby each rule
is represented with their 95% confidence intervals over 50 simulated runs.

21

Epidemic threshold for metapopulation model networks with a second-order mobility rule
Lingqi Meng1 and Naoki Masuda1,2
Department of Mathematics, University at Buffalo
Computational and Data-Enabled Science and Engineering Program, University at Buffalo
1

2

Metapopulation models have been proven to be powerful for simulating and predicting the
dynamics of disease outbreaks. On a metapopulation network, agents migrate from one subpopulation to another obeying a given mobility rule. How different mobility rules affect epidemic
dynamics occurring on metapopulation model networks has been a much debated topic. However, with regard to the effect of mobility on epidemic dynamics, there are relatively few efforts
on systematic comparison between simple random walks and more complex mobility rules. Here
we study a susceptible-infected-susceptible (SIS) dynamics on metapopulation model networks,
where individual agents obey a parametric second-order Markov chain mobility rule, called thenode2vec, of which we studied diffusion properties in our previous study [1]. We map the secondorder mobility rule of the node2vec to a first-order transition probability matrix among directededges to derive and analyze the expressions of the epidemic threshold for the SIS model and run
numerical simulations for synthetic and empirical networks. We observe that for various networks,
the epidemic threshold increases when the agents less frequently backtrack and visit the common
neighbor(s) of the currently and the last visited subpopulations than when the agents obey the unbiased random walk. However, the amount of change in the epidemic threshold induced by thenode2vec mobility is not as large as the one induced by the change in the diffusion rate.

Figure 1: Epidemic threhold for a Barabási–Albert model network with 100 nodes and 291 edges.
(a) b (i.e., the weight of transiting to a common neighbor of the currently visited subpopulation andthe subpopulation visited in the last step) versus a (i.e., the weight of backtracking). (b) D (i.e.,the diffusion rate) versus b.
References[1] L. Meng, N. Masuda, Analysis of node2vec random walks on networks, P. Roy. Soc. A 476
20200447 (2020).
22Differential Coordination Patterns During Human-Metronome Phasing
Caitrín Hall <caitrin.hall@uconn.edu>, Ji Chul Kim, Edward Large, & Alexandra Paxton
Department of Psychological Sciences, University of Connecticut
One way perception-action coordination (sensorimotor synchronization [SMS]) may bestudied is the coordination of movement with auditory rhythms. The current study assesses
phasing--a musical technique in which two people tap the same rhythm at varying phases byadjusting tempi--to explore how SMS is impacted by situational and personal factors. Building
on a study of professional percussionists, this experiment was designed to evaluate phasing inmusicians and nonmusicians. To ensure that novice participants could complete the experiment,
we simplified the original phasing task in two ways. First, rather than gradually desynchronizing
and resynchronizing with a partner, participants phased with an isochronous metronome. Second,
we narrowed the tempo range to 80-140 beats per minute (bpm). Participants were familiarizedwith phasing via video demonstrations, completed two practice sessions, and then engaged in theexperimental phasing task with a metronome.
One technique to analyze the coordination characteristics of a system is recurrence
quantification analysis (RQA). Coordination research uses RQA to describe potential
nonlinearities of dynamical systems that cannot be captured by linear time series methods. We
used multidimensional recurrence quantification analysis (MdRQA) to compare the nonlinear
dynamics of phasing across tempi, musical experience, and multilingualism. Varying coupling
patterns emerged, though not significantly influenced by linguistic or music experience. Only
38% of trials successfully completed the task (“Compliant Trials”); 41% of trials unsuccessfully
attempted the task (“Noncompliant Trials”). Participants successful at phasing tapped stably nearsynchrony and antiphase, while those unskilled at phasing could not always detect synchrony andwere less attracted to antiphase, as supported by differences in the predictability of the structure(measured in the determinism MdRQA metric) between Compliant and Noncompliant Trials.

Figure. Bar charts: %DET for Compliant Trials (top) and Noncompliant Trials (bottom) for
windows 1 (blue), 2 (yellow), and 3 (green). Pie chart: relative phase range for each window.
23

Part VI

Contributed Talk Session 5

24

Anticipation induces polarized collective motion in attraction based models
Daniel Stroembom and Alice Antia
See the full paper published in the Northeast Journal of Complex Systems:
https://orb.binghamton.edu/nejcs/vol3/iss1/2/

25

Asymmetric Coupling of Networks Optimally Accelerates Collective Dynamics
Zhao Song1 and Dane Taylor1
Department of Mathematics
University at Buffalo, State University of New Yorkzhaosong@buffalo.edu
danet@buffalo.edu
1

Networks are often interconnected with one network wielding greater influence over another,
yet we lack basic insights into the effects of such asymmetry. Studying the convergence rate Re(λ2 )for consensus dynamics, we show that coupling asymmetry can monotonically increase/decrease
Re(λ2 ) or give rise to different types of optima. Symmetry-optimized systems can be counterintuitive: when a fast and slow network are optimally coupled, either one can be more dominant.
We characterize this and other phenomena and provide theoretical support for the optimization ofasymmetrically coupled social, biological, and physical systems.

(B)

(A)

1

6
5

2
3

4

(1 + δ)ω

(1 − δ)ω
1

(C)

6
5

2
3

4

Figure 1: A robust optimum requires that neither layer dominates. (B)-(C) The two columns
represent two different multiplex networks: a toy network (A) and an empirical social network.
They are both 2-layer networks with directed edges within and/or between layers. (B) We plotRe(λ2 ) versus δ for several choices of χ, which is a rate-scaling parameter that tunes the relative
rate of consensus for the two coupled networks. The optima exists only for some values of χ. (C)dWe plot dδRe(λ2 ) versus χ. The colored curves depict different coupled strengths ω. The solidand dash black lines depict our theoretical prediction for the boundary on the range of χ for which
an optimum exists.
26

Thermodynamics of structure-forming systems
Jan Korbel1,2 , Simon David Lindner1,2 , Rudolf Hanel1,2 and Stefan Thurner1,2,3
1Section for the Science of Complex Systems, CeMSIIS, Medical University of Vienna, Vienna,
Austria2
Complexity Science Hub Vienna, Vienna, Austria
3Santa Fe Institute, Santa Fe, NM, USA

Structure-forming systems are ubiquitous in nature, ranging from atoms building molecules
to self-assembly of colloidal amphibolic particles. The understanding of the underlying thermodynamics of such systems remains an important problem. Here we derive the entropy forstructure-forming systems that differs from Boltzmann-Gibbs entropy by a term that explicitly
captures clustered states. For large systems and low concentrations, the approach is equivalent to
the grand-canonical ensemble; for small systems, we find significant deviations. We derive thedetailed fluctuation theorem and Crooks’ work fluctuation theorem for structure-forming systems.
The connection to the theory of particle self-assembly is discussed. We apply the results to several
physical systems. We present the phase diagram for patchy particles described by the Kern-Frenkel
potential. We show that the Curie-Weiss model with molecule structures exhibits a first-order phasetransition.
M
80

60

40

20

Figure 1: Phase diagram for the self-assembly of patchy particles for n = 100 particles. Moredetails are in Ref. [1]References[1] J. Korbel, S. D. Lindner, R. Hanel and S. Thurner, Thermodynamics of structure-forming
systems, Nature Communications 12 (2021) 1127.
27

Towards a Standard Approach for Echo Chamber Detection: Reddit Case Study
Virginia Morini1 , Laura Pollacci2 and Giulio Rossetti1
KDD Lab, ISTI-CNR, Pisa, Italy (virginia.morini, giulio.rossetti)@isti.cnr.it
Department of Computer Science, University of Pisa, Italy laura.pollacci@di.unipi.it
1

2

The rise of Social Networking sites (SNS) has drastically changed how people interact andaccess information. As a side effect, heterogeneity in content and freedom of expression offeredby these platforms have led to the diffusion of alarming phenomena, such as Polarization and Echo
Chambers (ECs). Up to date, researchers have reached no consensus about a standard methodology for ECs detection in a platform-independent way. In this preliminary work, we propose anapproach to identify political ECs on Reddit, easily extendible to other SNS. Based on ECs common definition, such a methodology may be broken down into four key steps.
(i) Firstly, we identify a controversial topic i.e., the debate about Gun Control and Minority Discrimination during the first two and a half years of Donald Trump’s presidency. (ii) Then, sincean ECs key feature is the homogeneous group polarization, we build a model to quantify user’s
polarization degree from posts shared on the platform. For such a purpose, we define our Ground
Truth, selecting strongly polarized subreddits concerning Pro-Trump and Anti-Trump beliefs, andwe leverage Word Embeddings and Long Short-Term Memory architecture to compute posts polarization scores. Our results, shown in Table 1, are in line with SOTA, and, moreover, the model
is quite able to generalize on less polarized sociopolitical topics. (iii) ECs are also strongly characterized by the dense interactions between their members with respect to the overall Network. To
assess this requirement, we define, for each topic, the users’ interaction Network by retrieving all
posts’ comments, and we label users with their average posts polarization score. (iv) Finally, weapply Community Detection algorithms (i.e., Louvain, Infomap and Eva) to extract communities,
evaluating their cohesion both from a topological and ideological point of view.
From preliminary results, as we can see from Figure 1, with Eva we are able to detect potentially
Pro-Trump and Anti-Trump ECs in both sociopolitical topics.
In conclusion, our case study underlines how features shared by most SNS (e.g., the existenceof controversial issues, posts, comments) can be easily leveraged to identify ECs in a standard way.
Consequently, as future work, we plan to extend this case study to other Social Media Services inorder to analyze user behaviour across a wider range of online environments.

Dataset# posts
Test Set
60,000
Gun Control
2,411
Minority Discrimination 4,839

Accuracy
0.843
0.712
0.732

Table 1: Model Accuracy

Figure 1: Discrimination - Echo Chambers
28

Part VII

Contributed Talk Session 6

29

Cognitive network science and its links with Education, complex systems and ways of thinking
Massimo Stella, Department of Computer Science, University of Exeter, UK - ​m.stella@exeter.ac.uk

Cognitive network science is a rising field at the interface of complex networks and psycholinguistics
aimed at representing knowledge in the human mind through conceptual associations between concepts andideas. This contribution focuses on a specific type of cognitive networks combining memory patterns andvalence norms, quantifying how individuals frame and perceive concepts. ​Forma mentis networks (Stella etal., ​PLoS ONE​, 2019) capture the way of thinking of individuals and groups, i.e. their mindset or ​forma
mentis in Latin. Relying on decades of psycholinguistic research, forma mentis networks represent how
ideas are linked in memory via free associations (e.g. reading “math” makes one think of “anxiety”) andhow they are perceived via word valence (e.g. how pleasant “math” is rated by an individual).
Forma mentis networks were successfully used in order to detect key aspects of STEM perceptions in highschool students (N=159) and STEM professionals (N=59) (Stella et al., ​PLoS ONE​, 2019). A cognitive
dissonance was identified in the mindset of students, who framed positively the idea of “science” but thenconcentrated negative emotions of anxiety/stress around “physics” and “maths”. This emotional dichotomy
was absent in researchers. More recent investigations focused on detecting computational thinking (Stella
et al., 2020) and complex systems thinking (Stella, ​IJCE​, 2020), as ways of understanding the world
through data and connections, respectively. Despite being trained in multiple scientific disciplines, students
perceived “computation” and “complexity” as distressing ideas, framed with links to mathematical jargon
but crucially lacking links to real-world discovery. Students’ mindsets around “data”, “model” and“simulations” revealed almost no awareness of numerical modelling and its implications for understanding
our complex world (see Figure 1). On the contrary, STEM experts perceived numerical models as positive
concepts, framed and interpreted as a key way for achieving new knowledge.
The above findings provide concrete evidence that forma mentis networks can provide detailed knowledge
about how students shape their mindsets and ways of thinking around Educational concepts. Comparisonswith professionals or other target groups can provide crucial data-informed evidence for innovative
Educational intervention policies aimed at fostering complex systems and data literacy.

Figure 1​: Visual comparison of high school students’ and STEM experts’ mindsets around “model”. Associations
provided by two or more individuals are thicker. Words perceived by students as positive (negative) are highlighted
in cyan (red). Links between positive (positive/negative) words are highlighted in cyan (purple). Larger font-size
indicates higher closeness centrality of a concept.

30

Understanding Scholars Mobility in Knowledge Embedded Space
Shuang Zhang, Feifan Liu, Haoxiang Xia
Institute of Systems Engineering, Dalian University of Technology, Dalian, China
Despite persistent efforts in understanding human mobility in geographical space, little is known
about the spatiotemporal regularity of scholars mobility in virtual knowledge space owing to theinability to track scholars’ overall and fine-grained trajectories in high-dimensional knowledge
space. Only a few studies focus on scholars' research interest evolution and the factors that
influence topic selection. Here, aiming at revealing the characteristics of scholars’ knowledge
exploration behavior and its correlation with academic performance, we study the trajectories of
180,345 highly productive scholars in the Computer Science field (CS), considering their
publication sequence as walks on the two-dimensional scientific domain map constructed bymanifold learning algorithm UMAP based on the semantic proximity of CS papers learned by
Doc2vec. We find that the distributions of the exploration scope and the average step lengths ofscholars are both left-skewed compared with the results of reshuffled or replaced publication
sequence, the visitation frequency of location follows Zipf’s law, and the growth of scholars’
exploration scope and the number of visited locations both present ultraslow diffusive processes.
These results suggest scholars mobility in knowledge space is characterized by subfield constraint,
frequency bias, and proximity bias. Furthermore, we also observe the knowledge boundary effecton the relationship between scholars’ exploration scope and academic performance. With theincrease of scholars’ exploration scope, h-index and the average citations show a trend of firstly
increasing and then decreasing, and publication counts and disruption score remain unchanged
after increasing, implicating over-exploration will not lead to a sustained increase in academic
output and disruption but a decrease in impact. Overall, our study depicts a distinctive portrait ofscholars’ knowledge exploration behavior and can help design scientific policies.

Figure 1. The bounded nature of scholars’ trajectories. a, b. the distribution of scholars’ exploration
scope and step lengths, respectively measured by radius of gyration (rg) and jump lengths. c. Zipf’s
plot showing the visitation frequency fk of the kth most visited location. d,e. rg, number of visited
grids on map versus publication sequence. f. the correlation between rg and academic performance.
31Balanced and fragmented phases in societies with homophily and social balance
T Pham1,2 , A. C. Alexander3 , J. Korbel1,2 , R. Hanel1,2 , S. Thurner1,2,4
1 CeMSIIS, Medical University of Vienna, Spitalgasse 23, A-1090, Vienna, Austria
2 Complexity Science Hub Vienna, Josefstadterstrasse 39, A-1090 Vienna, Austria
3 Department of Mathematics, Princeton University, NJ 08544, Princeton, USA
4 Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA

In the past decades an increasing level of social fragmentation has been observed in societies. We try
to understand this phenomenon with an agent-based model where we use spins to represent G-dimensional
vectors of binary opinions of individuals and use a positive (negative) link weight to represent friendship(enmity), respectively. We take into account the joint effects of (1) homophily—the tendency of people withsimilar opinions to establish positive relations, and (2) social balance—the tendency to establish balanced
triadic relations. These two mechanisms are incorporated in a localized Hamiltonian that minimizes social
stress through the co-evolution of opinions of individuals and their social networks. Specifically, startingfrom a random assignment of opinions for each of N agents, an initial social network is constructed from thesimilarities between pairs of connected agents. The dynamics is iterated in four steps until the system reaches
a steady state: i) we randomly select an agent, i, and within its social neighbourhood a fraction of Q triads is(i)randomly chosen among all possible N∆ triads of node i. The social stress H of i is calculated; ii) one of i’s
opinions is flipped and the weights of all links which are part of the Q selected triads are reevaluated. Now
we re-calculate the stress of i, H 0 ; iii) The update is accepted, if either the stress is reduced, i.e. H 0 < H, or0
in case it increases, with probability e−H +H , otherwise the opinions and network remain unchanged. We
show, for any number of opinions, G, how the likelihood of social fragmentation increases as individuals
care more about social balance. We identify the critical size of the social neighbourhood, Qc , above whichsociety must fragment into communities that are internally cohesive and hostile towards other groups.

135

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Figure 1: Order parameter, f = (n+ − n− )/(n+ + n− ), which measures the level of fragmentation (a) as afunction of q = Q/N∆ and G for K = 32 and N∆ = 360, and (b) as a function of the degree K and G withq = 1/3. Here n+ (n− ) is the number of balanced (unbalance) triangles in the network. A triangle is calledbalanced, if the product of its three link states is positive, and unbalanced, if the product is negative.
References[1] T. Pham, A.C. Alexander, J. Korbel, R. Hanel and S. Thurner, arxiv:2012.11221 (2020).

32

Are Terrorist Networks Just Glorified Criminal Cells?
Elie Alhajjar, Ryan Fameli and Shane Warren
See the full paper published in the Northeast Journal of Complex Systems:
https://orb.binghamton.edu/nejcs/vol3/iss1/1/

33

Part VIII

Contributed Talk Session 7

34

COVID-19 impacts on domestic airlines via multilayer network analysis
Mengyuan J. Sun1 and Naoki Masuda1,2
1. Department of Mathematics, University at Buffalo, Buffalo, USA
2. Computational and Data-Enabled Science and Engineering Program, University at Buffalo, Buffalo, USA

The unprecedented pandemic of COVID-19 has cast a major impact on passenger air transportation due
to restricted traveling policy and health concerns. Because airline companies are constantly opening andshutting down routes to compete with each other, air transportation networks are temporal networks. To
aim to understand such competition, we analyzed an air transportation network data set by month as amulti-layer temporal network in which each layer corresponds to an airline. To examine the possible impactsof COVID-19, we included passenger flight data from January 2015 up to October 2020. The data are fromthe Bureau of Transportation Statistics. We analyzed the four most major domestic airlines, i.e., American
Airlines, United Airlines, Delta Air Lines, and Southwest Airlines. (We analyzed pre-COVID-19 data using
a different network analysis method [1].) The airports present in the flight network of any of the four airlines
are nodes. A pair of airports is adjacent by an edge if and only if there is a direct commercial flight between
them in the month to be analyzed. For simplicity, we assume the network is undirected and unweighted.
Not to our surprise, the number of nodes and that of edges considerably decreased during the COVID-19
pandemic (see Fig. 1(a)). To explore the interactions among the four layers, we measured the normalized
total overlap, which is defined as the fraction of edges that simultaneously exist in a pair of layers of interest.
There was a substantial drop in the normalized total overlap after the start of the COVID-19 pandemic
for most pairs of airlines (see Fig. 1(b)), implying that there were fewer routes operated by two airlines
at the same time. This might be because the airlines chose to shut down competitive routes to decrease
operational costs under the pandemic. Next, we carried out further analysis of the total overlap with theaim of excluding the effect of the decreased number of nodes and edges, which would naturally decrease
the total overlap. For each month, we generated 1000 randomized multi-layer networks using the layer-wise
configuration model, which preserves the degree of each node within each layer and measured the total overlap
for each generated randomized network. Then, we compared the edge overlap for the original multi-layer
network with that for the randomized networks, separately for each month, by calculating the Z score. The
Z score significantly decreased around the COVID-19 period (Fig. 1(c)). To quantify this observation andaccount for the problem of multiple comparisons, we calculated the 5% significance level with the Bonferroni
correction, which is marked by the horizontal dashed lines in Fig. 1(c). For one airline pair, the Z score issignificantly negative during the COVID-19 pandemic but not before. For the other five airline pairs, the Zscore is either insignificant or still significantly positive, but its magnitude considerably dropped (i.e., smaller
total overlap values) during the pandemic in all cases. Therefore, we conclude that the drop in the edge
overlap around June 2020 shown in Fig. 1(b) is not a byproduct of the decrease in the number of the nodes
and edges during the same period. In sum, we suggest that the domestic airline network of the US had
fewer flight overlaps and less direct competition among the airlines during the COVID-19 pandemic. We are
currently measuring other indices that are related to flight route overlaps to try to consolidate this finding.

(a)

(b)

(c)

Figure 1: (a) Number of nodes and edges of the aggregated network. (b) Normalized total overlap between
different pairs of airlines. (c) Z score of the normalized total overlap. In (b) and (c), each line corresponds toa pair of airlines. In (c), the solid line represents 0, and the dashed lines represent the 5% significance level
after the Bonferroni correction.

References[1] K. Sugishita and N. Masuda, Scientific Reports, in press (2021); also available at arXiv:2005.14392.

35

Complex dynamics in networks, templates and mutated systems
Anca Rǎdulescu, Mathematics Department, SUNY New Paltz, radulesa@newpaltz.edu
We explore three directions extending the traditional theory of complex quadratic iterations: (1) complex quadratic
networks; (2) template iterations and (3) mutated iterations. In all three cases, the system’s long-term dynamics ishighly non-trivial, and can be represented by asymptotic sets (Mandelbrot and Julia sets) with specific topologicalsignatures, and with properties far beyond those described in the case of single map iterations.
Network iterations, and applications to brain dynomics [1]. An outstading question in natural complex networks
is how their function depends on the network structure. We use quadratic iterations to develop a new framework
for understanding how dynamic behavior emerges in large networks of nodes. Each node
Examples of network
is viewed symbolically as an integrator of internal and external inputs. The node-wise dyJulia sets for 8 nodes.
namics is driven by a traditional complex quadratic map, with coupling specified by theadjacency matrix Aij and weights gij . Then thePsystem takes the form of an iteration innCn , which acts in each component zk as zk 7→ ( j=1 Akj gkj zj )2 + ck . This theoreticalframework pushes the boundaries of an unexplored field in mathematics, combining theory
and computation in complex dynamics and graph theory. We use the asymptotic behavior of
multi-dimensional orbits (via the topological and fractal structure of Julia and Mandelbrotsets) to quantify dynamic behavior under perturbation of the network architecture. In particular, topological landmarks of Mandelbrot sets can provide valuable clasification criteria
for dynamic networks in neuroscience.
Template iterations, and applications to epigenetics [2]. While single map iterations havebeen often used to represent natural phenomena, a more realistic mathematical framework isthat of time-dependent (non-autonomous) iterations, in which the iterated map may evolvein time. We study the dynamic patterns generated by a pair of complex quadratic functions,fc0 and fc1 , applied according to a general binary symbolic sequence s (which we call
template), in which the “one” positions correspond to iterating the “correct” function fc1 and the “zero” positions
correspond to iterating the “erroneous” function fc0 . Template systems generate new aspects of existing problems in
non-autonomous iterations. Our interest resides in understanding the dependence of the dynamic behavior on the size
and timing of errors (as captured by the complex pair (c0 , c1 ) and by the template s, respectively). We extended theconcepts of Julia and Mandelbrot sets to the case of template iterations, and we study the new topological complexities
introduced by this generalization. For example, the Mandelbrot set can be defined in this context as a parameter subsetof the product space C2 × {0, 1}∞ . The structure of Mandelbrot slices in either subspace, can be efficiently used tounderstand the effects of timing and size of errors in replication systems (such as DNA copying mechanisms).
Mutated iterations, and application to cell differentiation and tumor growth [3]. Copying errors which occur
during mechanisms like cell differentiation, or tumor growth, are highly local, affecting specific genetic loci in the
genome structure. If we use the complex plane C to symbolically represent a cell’s DNA, each point in the plane
corresponds to a single gene. The folding of C through the quadratic map fc1 (z) = z 2 + c1 represents how theemphasis of each gene is recomputed in the replication process, along the specialization path of the cell. This results
each time into a new copy of C, used as template for subsequent replications. We insert local mutations into theiteration, acting as an erroneous function fc0 within a small mutation disk around a mutation center, and continuouslyinterpolating to fc1 within a “transition” annulus around the mutation disk. One can then analyze the asymptotic
trajectory under iterations of the resulting mutated system f . Within this symbolic framework, the prisoner set P(f )of the system can be seen and studied as the set of sustainable genes, active within the chromosome when the cell had
assumed its stable profile, or differentiation.
References[1] Rǎdulescu A, Evans S, 2019. Journal of Complex Networks. 7(3); 315-345.
[2] Rǎdulescu A, Butera K, Williams B, 2021. Journal of Nonlinear Science. 31(22).
[3] Rǎdulescu A, Longbotham A, 2020. ArXiv preprint::2011.14002

36

Impact of Community Structure on Consensus Machine Learning
Bao Huynh1

2

Haimonti Dutta2

Dane Taylor1

1
Department of Mathematics, University at Buffalo, State University of New YorkManagement Science and Systems Department, University at Buffalo, State University of New York

February 12, 2021

Consensus dynamics provides a foundation decentralized machine learning algorithms for data thatare distributed across a cloud compute cluster or across the internet of things. In these and othersettings, one seeks to minimize the time τ required to obtain consensus within some  > 0 marginof error. τ typically depends on the topology of the underlying communication network, and for manyalgorithms τ depends on the second-smallest eigenvalue λ2 ∈ [0, 1] of the network’s normalized Laplacianmatrix L̂: τ ∼ O(λ−12 ). We will discuss our recent work [1] in which we analyze the effect on τ ofnetwork community structure, which can arise when nodes/sensors are spatially clustered into groups,
for example. We study consensus learning over networks drawn from stochastic block models (SBMs), andin particular, heterogeneous models that yield random networks containing communities with different
sizes and densities. Using recently developed random matrix theory techniques for SBMs [2, 3], we analyze
the effects of community structure on λ2 and consensus. Our analysis reveals that there exist two regimesthat are separated by a critical amount of community structure as measured by a community prevalencemeasure (see figure caption). Specifically, above the threshold (∆ > ∆∗1 ), the presence of communities
is a significant bottleneck on consensus and consensus-based machine learning algorithms that causes τto grow exponentially. Below the threshold (∆ < ∆∗1 ), communities have little affect on consensus. Thisobservation establishes an important new connection between decentralized machine learning and the
network-science literature on detectability theory (see e.g., [3] and the references therein). We support
our findings with empirical experiments for decentralized support vector machines (SVM) [4].

Figure 1: (left) Network sampled from a stochastic block model (SBM) with K = 4 communities of sizes[n1 , n2 , n3 , n4 ] = [40, 80, 150, 400]. The edge probabilities within and between communities are givenby [pin , pout ] = [0.5, 0.02]. (center) Empirical observations of convergence time τ (blue dots) versus
community prevalence ∆ = pin − pout . The red curve is a line of best fit: τ ≈ 0.000087/(0.1 − ∆). The
inset shows τ versus λ2 , and the red line indicates the fit τ ≈ 0.0015/λ2 . (right) Predicted values forb and the third-smallest eigenvalue λ2 . The vertical lines indicate
the second-smallest eigenvalue λ2 of L
two critical values: a spectral bifurcation occurs at ∆∗1 (dashed lines) in that the gap between λ2 andλ2 disappears; τ diverges at ∆∗2 = pin (dotted lines) since the communities become disconnected andλ2 → 0.

References[1] Bao Huynh, Haimonti Dutta, and Dane Taylor. Impact of community structure on consensus machine learning.
arXiv preprint arXiv:2011.01334, 2021.
[2] Tiago P. Peixoto. Eigenvalue spectra of modular networks. Phys. Rev. Lett., 111:098701, Aug 2013.
[3] Dane Taylor, Saray Shai, Natalie Stanley, and Peter J. Mucha. Enhanced detectability of community structure
in multilayer networks through layer aggregation. Phys. Rev. Lett., 116:228301, Jun 2016.
[4] Haimonti Dutta and Nitin Nataraj. GADGET SVM: A gossip-based sub-gradient solver for linear SVMs.
arXiv preprint arXiv:1812.02261, 2018.

37
1

Characterization of communities in dynamic functional networks
Bengier Ülgen Kılıç1 , Sarah Feldt Muldoon1,2,3
1

Department of Mathematics, University at Buffalo, SUNY, Buffalo, NY
2
3

CDSE Program, University at Buffalo, SUNY, Buffalo, NY

Neuroscience Program, University at Buffalo, SUNY, Buffalo, NYGrouping similar functioning parts of a system together is a common but difficult task, and doing so for an
ongoing dynamic system in which the interactions of these parts vary over time, is even more challenging. Dynamic
community detection (DCD) tools for temporal data offer various solutions to this problem. However, how to chosean appropriate DCD algorithm is not always clear, as each algorithm requires making multiple choices about how to(i) model the system, (ii) define a community, and (iii) chose optimal algorithm parameters. Once these assumptions
are made, most methods perform a non-unique stochastic partition-space-scan to find the minima of a quality
function that mathematically describes the community over a domain. Here, we explored the parameter spaces ofa handful of novel-class algorithms for performing community detection in temporal networks– each of which uses
different modeling techniques and community definitions. We test algorithms on simulated neuronal spike train data
to show that the performance of some algorithms can be improved and parameter spaces can be simplified under
specific modeling assumptions extracted from the data. Moreover, algorithms are shown to respond distinct type ofcommunity events in the system differently- some capture but others ignore the particular activity. We conclude thatthe choice of a DCD algorithm must take into consideration the specific properties of the data in order to achieve
optimal performance when performing DCD in real-world systems.

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Figure 1: A. Spike trains of a group of neurons leading to fully synchronous activity and the corresponding network
evolution where each snapshot is obtained by calculating pairwise synchronization within the respective time window. Eachtick indicates a spike and colors represent varying spike rates, whereas node colors correspond to the community assignment(same color within the same time window represents synchronous activity). When dynamic community detection is applied
to such a system, different algorithms yield different results because they each define a ’community’ differently. Nevertheless,these different descriptions tend to spit out similar network partitions in many cases. B. Parameter landscapes of different
community detection algorithms as a function of normalized mutual information. Note that each algorithm utilizes distinct
inputs.

38

Part IX

Contributed Talk Session 8

39

Dimension reduction on heterogeneous networks
Marina Vegué1,2 , Vincent Thibeault1,2 , Patrick Desrosiers1,2,3 and Antoine Allard1,2
1 Département de physique, de génie physique et d’optique, Université Laval, Québec, Canada
2 Centre interdisciplinaire de modélisation mathématique de l’Université Laval, Québec, Canada
3 CERVO Brain Research Center, Québec, Canada

The complexity inherent to large, non-linear dynamical systems of interacting units (ecological communities,
neuronal assemblies, etc.) makes them very difficult to study. One of the big challenges of network science isfinding ways to approximate these systems by systems of reduced dimension, which can be more tractable bothanalytically and computationally [1, 2, 3, 4]. We have addressed this problem for dynamical systems whose unitsinteract through a weighted, directed connectivity matrix. Following the lines of previous work [3, 4], we propose
a two-step method for such a dimension reduction that takes into account the properties of the interaction matrix.
First, units are partitioned into groups of similar connectivity properties. Each group is associated to one linear
observable, that is a weighted average of the node activities within the group. The number of groups thus defines thedimension of the reduced system of observables. Second, we derive a set of conditions that have to be fulfilled forthese observables to properly represent the original system’s behavior, together with a method for approximately
solving them. The result is a reduced interaction matrix and an approximate system of ODEs for the temporal
evolution of the observables which is analogous in form to the original system. We show that the reduced system
can be used to predict some properties of the complete dynamics (such as bifurcation boundaries in the parameter
space) for different types of connectivity structures, including highly heterogeneous networks.

Figure 1: Dimension reduction of a heterogeneous network on 100 nodes with Wilson-Cowan dynamics. From left to right,

different node groupings are shown (1, 2, 3, and 5 groups). Top: Connectivity matrix, reordered according to the different nodegroupings. Bottom: Bifurcation diagram of the observable dynamics for the different groupings (orange: exact dynamics,
blue: approximate, reduced dynamics). The x-axis shows the bifurcation parameter, which controls the overall strength of theconnections in the network. The y-axis shows the observables’ average at equilibrium.

References[1] J. Gao, B. Barzel, and A.-L. Barabási. Universal resilience patterns in complex networks. Nature, 530(7590):307–312,
2016.
[2] J. Jiang, Z.-G. Huang, T. P. Seager, W. Lin, C. Grebogi, A. Hastings, and Y.-C. Lai. Predicting tipping points in mutualistic
networks through dimension reduction. PNAS, 115(4):E639–E647, 2018.
[3] E. Laurence, N. Doyon, L. J. Dubé, and P. Desrosiers. Spectral dimension reduction of complex dynamical networks.
Phys. Rev. X, 9(1):011042, 2019.

40 Threefold way to the dimension reduction of dynamics on[4] V. Thibeault, G. St-Onge, L. J. Dubé, and P. Desrosiers.
networks: An application to synchronization. Phys. Rev. Research, 2:043215, 2020.

Active Learning and Relevance Vector Machine in Efficient Estimate for Basin Stability of
Dynamic Networks
Yiming Che and Changqing Cheng
Department of Systems Science and Industrial Engineering
Binghamton University, State University of New Yorkccheng@binghamton.edu
Abstract

The interconnectivity between constituent nodes gives rise to the cascading failure
in most dynamic networks, such as traffic jam in transportation network and largescale blackout in power grid system. Basin stability (BS) has recently garnered tremendous traction to quantify the reliability of such dynamical systems. In the power grid
network, it quantifies the capability of the grid to regain the synchronous state after being perturbated. It is noted that detection of the most vulnerable node or generator withthe lowest BS or the N-1 reliability is critical towards the optimal decision making on
maintenance. However, the conventional estimation of BS relies on Monte Carlo (MC)method to separate the stable and unstable dynamics originated from the perturbation,
which incurs immense computational cost particularly for large-scale networks. As
BS estimate is in essence a classification problem, we investigate relevance vector machine (RVM) and active learning to locate the boundary of stable dynamics or the basinof attraction in an efficient manner. This novel approach eschews the large number ofsampling points in MC method and reduces over 95% of the simulation cost in theassessment of N-1 reliability of power grid network. The result of experiment on theIEEE 118-Bus system in Fig. 1 demonstrates the effectiveness and efficiency of the
proposed method.

Figure 1: (a) Topology of IEEE 118-Bus system. The red circular nodes are loads
and the square nodes are generators. The color of the generators implies themagnitude of the BS and the size of generator indicates the degree, i.e., the numberof connected edges; (b) comparison of network BS for different generators in theIEEE 118-Bus system using MC method and the proposed approach; (c) the
number of iterations in active learning on each node.

41

Visualizing trajectory of tie-decay temporal networks
Chanon Thongprayoon1 , Lorenzo Livi2 , Naoki Masuda1,3
1

Department of Mathematics, University at Buffalo, SUNY, New York, USA
Departments of Computer Science and Mathematics, University of Manitoba, Manitoba, Canada
3
Computational and Data-Enabled Science and Engineering Program, University at Buffalo, SUNY, New York, USA2

To aid visualization and data analysis of a set of networks, we often map the networks to a low dimensional
vector space (e.g., Euclidean space). This procedure is called network embedding. Generally, when embedding
networks, the (dis)similarity in the in the embedding space is preserved as much as possible. In temporal networks,
the network evolves over time, and it is usually the case that we only obtain discrete events occurring at discrete
times. Using network embedding, we consider the problem of constructing a continuous-time trajectory from discrete
time-stamped events occurring on edges of a network.
We consider embedding of temporal networks, where at least one contact event occurs at time ti (with i =0, 1, . . .) in the network. We represent the network evolution over time with a time-dependent adjacency matrix
B(t) = [bij (t)]. Embedding yields a continuous-time trajectory that represents dynamics of the given temporal
network. We use a tie-decay network model in which the weight of each edge exponentially decays at a rate α(> 0)in the absence of contact events, i.e., bij (t) = e−α(t−tk ) bij (tk ) for any t ∈ [tk , tk+1 ), and bij (tk ) instantly increasesby 1 if there is a contact event between the ith and jth nodes at time tk [1]. To embed the temporal network
into a Euclidean space and determine its trajectory, firstly, we propose to construct a matrix encoding the distance
between pairs of networks at different discrete times, t0 , t1 , · · · , but crucially not for t 6∈ {t0 , t1 , · · · }. Next, we apply
the landmark multidimensional scaling (LMDS) algorithm to the distance matrix [2]. The LMDS, an extension ofmultidimensional scaling (MDS), uses a selected subset of the data points as reference points (i.e., landmarks) tocompute the embedding coordinates of any other data points. In this fashion, we produce trajectories of temporal
networks in continuous time. The trajectories for each of two empirical temporal network data and one synthetic,
periodic input of contact events are shown in Fig. 1. We chose a Laplacian network distance measure. (We also used
two other distance measures; results not shown.) For example, Fig. 1(b) illustrates that the network varies relatively
slowly between t = t350 and t = t400 compared to between t = t50 and t = t100 . As another example, Fig. 1(c)captures periodic nature of the input and suggests that the trajectory approaches a limit cycle, corresponding to
the periodic nature of B(t).

Figure 1: Trajectories of temporal networks. (a) Proximity between students in a primary school. (b) Proximity
between students in a high school. In (a) and (b), the data are from the SocioPatterns Project, and we have set
α = 0.01 and only used the first 501 time points at which the events are recorded. (c) A periodic, synthetic inputof adjacency matrices with 9 nodes that arrive with regular intervals with period four. We set α = 0.04.
References[1] W. Ahmad, M. A. Porter, and M. Beguerisse-Dı́az. arXiv:1805.00193, 2018.
[2] V. De Silva, and J. B. Tenenbaum. Technical Report, Stanford University, 2004. [Online]. Available: http://graphics.stanford.edu/courses/cs468-05-winter/Papers/Landmarks/Silva_landmarks5.pdf

42Dimension reduction of high-dimensional dynamics on networks with adaptation
Vincent Thibeault1,2 , Marina Vegué1,2 , Antoine Allard,1,2 and Patrick Desrosiers1,2,3
1. Département de physique, de génie physique et d’optique, Université Laval, Québec (QC), G1V 0A6, Canada
2. Centre interdisciplinaire de modélisation mathématique de l’Université Laval, Québec (QC), G1V 0A6, Canada
3. CERVO Brain Research Center, Québec (QC), G1J 2G3, Canada

Adaptation is a defining property of complex systems. It is characterized by changes in the structure and the dynamics
of the system according to its environment and its own behavior [1]. For instance, neurons in the brain are connectedby synapses that increase or decrease in strength as a response to neuronal activity. Synaptic plasticity is known
to be an essential mechanism of learning and memory, but its precise role and its global influence on brain activity
remain unclear [2]. From a theoretical standpoint, the impact of adaptation on the neuronal dynamics’ equilibrium
points is hard to predict. This is partly due to the high dimensionality of the dynamical system describing adaptative
neuronal networks. Indeed, in addition to the ordinary differential equations (ODEs) describing the activity of all
neurons (nodes), there is another large set of ODEs governing the evolution of the strength (weight) of all synapses(edges).
Based on our previous works [3-4], we introduce a new dimension reduction framework that systematically yields
a low-dimensional (reduced) adaptative dynamics from a high-dimensional (complete) adaptative dynamics. The
reduced dynamics accurately describes the complete Wilson-Cowan dynamics with three different adaptation rules:
Hebb’s rule, Oja’s rule, and even the biologically plausible Bienenstock-Cooper-Monroe’s (BCM) rule [5]. The WilsonCowan dynamics with the BCM rule exhibits rich bifurcation phenomena that are well predicted by the reduced
adaptative dynamics [FIG. 1]. For instance, our dimension reduction framework captures the emergence of surprisingnonlinear oscillations in the firing rate and the synaptic strength which appear through a supercritical Hopf bifurcation.
Our framework is flexible: we can tune the number of observables as we want to describe adaptative networks withmore modules and heterogeneity. It also unlocks the possibility to perform dynamical analysis on large real networks
which paves the way towards a better understanding of emergent phenomena in the plastic brain.
[1] M. Mitchell, Complexity : A Guided Tour, (Oxford University Press, New York, 2009).
[2] Y. Humeau and D. Choquet, “The next generation of approaches to investigate the link between synaptic plasticity and learning”, Nat.
Neurosci. 22, 1536 (2019).
[3] V. Thibeault, G. St-Onge, L.J. Dubé, and P. Desrosiers , “Threefold way to the dimension reduction of dynamics on networks: An
application to synchronization”, Phys. Rev. Research 2, 043215 (2020).
[4] E. Laurence, N. Doyon, L.J. Dubé, and P. Desrosiers, “Spectral Dimension Reduction of Complex Dynamical Networks”. Phys. Rev. X
9, 011042 (2019).
[5] L. Cooper and M. Bear “The BCM theory of synapse modification at 30: interaction of theory with experiment”, Nat. Rev. Neurosci.
13, 798 (2012).

FIG. 1. Bifurcation diagram of the Wilson-Cowan dynamics with the BCM rule (10 200 ODEs) obtained from its reduced
dynamics (3 ODEs). The firing rate threshold µ is the midpoint of the sigmoidal activation function of the Wilson-Cowan
dynamics and τx is the time scale of the activity while τw is the one for the weights. Figures a-e illustrate the equilibrium pointsof the mean global activity observable X vs. the mean global weight observable W when there is no adaptation and when there
is adaptation for the complete and reduced dynamics. These figures show that the reduced dynamics predicts accurately theequilibrium points in every region of the bifurcation diagram.43
We choose a weighted Erdős-Rényi network with N = 100 and
p = 0.5 as an initial condition for the synaptic dynamics.

Part X

Poster Session 1

44

Flocc: From Agent-Based Models to Interactive Simulations on the Web
Scott Donaldson
See the full paper published in the Northeast Journal of Complex Systems:
https://orb.binghamton.edu/nejcs/vol3/iss1/6/

45

Entropic dynamics of networks
Felipe Xavier Costa and Pedro Pessoa
See the full paper published in the Northeast Journal of Complex Systems:
https://orb.binghamton.edu/nejcs/vol3/iss1/5/

46

Exact Formulation of Ising Model Transitions Between Six Magnetic Phases
Goktug Islamoglu
B.Sc. Civil Engineering, Istanbul Technical University
M.Sc. Occupational Health and Safety, Karadeniz Technical University
In a conventional cellular automaton, a cell’s state is updated in relation to its neighbors. In thiswork the author explores has reversed the cellular automaton’s cell update rule, allowing a celldictate the states of its neighbors1. The rule forces the corners of the Moore neighborhood to
update into von Neumann neighborhood. Author hypothesizes that this is a decimation. By
employing configurations that tune the automaton’s neighborhood based on the cell’s state (bydefault 6-neighborhood tuning is preferred), six magnetic responses are plotted respectively inthe probability range: demagnetization (degaussing), ferrimagnetic, ferromagnetic, paramagnetic,
antiferromagnetic and again paramagnetic. The maximum count of cells with state 1 corresponds
to an evasion curve (inverse of a pursuit curve) that evades the inverse Ising critical temperature.
If tuning is brought to less than 6 neighbors, instead the maximum cell count corresponds toIsing criticality. This is achieved by coupling the system with a p*(1-p) = 1/8 equation(neighborhood average). The first order transition points are the roots of this coupling equation11𝜋𝜋± 2√2, which are exactly representable by trigonometric values of cos 2 ( 8 ) and sin2 ( 8 ). This2is the basis of the trigonometric transformation, when plotted, a cot2x + cotx graph emerges inabsence of any trigonometric functions present in the automaton’s code. Arms of this graph are
the roots given above, and the immediate values outside of first order transition boundary. Bysolving this cotangent equation, the author has come upon a renormalization recursion, thus
reaffirming his hypothesis of renormalization simulating cellular automaton. The recursion
reveals exact equations that correspond to phase transitions unique to each magnetic phase.
cot2x + cotx Output of Cellular Automaton

Value of cot2x + cotx output

3

2,5
2
0.85361,50.14640.853510.14650,50
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49

Cellular Automata Update Count

Keywords: Cellular Automata, Ising Model, Magnetic Phase Transitions
47
1. https://github.com/goktu/ADama/blob/master/cellularautomata.py

Network Reconstruction
Bayesian Sequential Inference of Sparse Network Connectivity
Jun Kataoka, Jayanth Sivakumar, Eric Peña, Yiming Che, Changqing Cheng
Department of Systems Science and Industrial Engineering
Binghamton University, State University of New York
While significant effort has been devoted to the design, control, and optimization of complex
networks, most existing work assumes the network structure is known or is readily available. However, the network topology could be radically altered (e.g., due to an adversarial attack or power
outage) and remain unknown for subsequent analysis. In this work, we propose a novel Bayesiansequential learning algorithm to adaptively reconstruct network connectivity. A sparse Spike-andSlab prior distribution is placed on all edges and the connectivity learned from the reconstructed
nodes will be incorporated to select the next node and will then update the prior knowledge. Central to our approach is that most realistic networks are sparse, in that the degree of each node ismuch smaller compared to the total number of nodes in the network. A sophisticated method ofsequentially selecting nodes is implemented using the between-node expected improvement. The
performance is measured and compared against randomly selecting nodes. Our algorithm is an
improvement over traditional reconstruction efforts when faced with limited data and is robust tovarying levels of noise. That is, our algorithm accurately reconstructs the network with fewer nodes
than the whole network structure. This algorithm has been applied to real network data: IEEE
118-Bus System provided by the Illinois Center for a Smarter Electric Grid (ICSEG) whereby thetime-series for each node has been simulated. The performance of our algorithm compared torandom node selection is shown in Fig. 1. This algorithm has also been applied to the BarabasiAlbert network for m = 1 and m = 2. This study has the potential to significantly scale up thereconstruction algorithms to accommodate massive networks and radically transform the operationof various realistic networked systems including power grid, transportation, and communication
networks particularly in a host of military operation scenarios.

Figure 1: Reconstruction error for the proposed algorithm and random selection for noise levels(a) σ = 0.03, (b) σ = 0.04, and (c) σ = 0.05
48

The effect of time-dependent infectiousness on epidemic dynamics
Nicholas W. Landry1 and Karen L. Stengel2
1

Department of Applied Mathematics, University of Colorado Boulder
nicholas.landry@colorado.edu
2
Department of Computer Science, University of Colorado Boulder
karen.stengel@colorado.edu
Abstract

In contrast to the common assumption in epidemic models that the rate of infection
between individuals is constant, in reality, an individual’s viral load determines theirinfectiousness. We compare the dynamics of an epidemic model with a deterministic,
time-dependent infection rate to that of a standard SIR model with a constant, Markovian rate of infection and healing. We predict the epidemic threshold in terms of contact structure for fully-mixed populations and category-mixed populations. We compare the trajectories of epidemic spread on both fully-mixed and category-mixed populations using both an SIR model and a time-dependent viral load mean-field model.
We find that the reproductive number only depends on the total infectious exposureand the largest eigenvalue of the mixing matrix and that the two are independent ofeach other. We find that when we compare the viral load model to the SIR model, theepidemic peak is delayed but more pronounced. In addition, the specific infection ratefunction has a strong effect on the time dynamics of the epidemic.
Fully mixed

1.0
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1.0
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1.0(t) e4 te t/4, (VL Model)(t) = c, (VL Model)
SIR Model

0.5
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25

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Figure 1: Plot of the infection curves for different population structures and epidemic models,
where the total infection and healing rates are identical for each model.

49

Towards a multiplex network model of word associations and similarity in the human mind
Salvatore Citraro, Department of Computer Science, and ISTI-CNR, Italy - ​salvatore.citraro@phd.unipi.it
Massimo Stella, Department of Computer Science, University of Exeter, UK - ​m.stella@exeter.ac.uk
Giulio Rossetti, Istituto di Scienza e Tecnologie dell’Informazione (ISTI), CNR, Italy - ​giulio.rossetti@isti.cnr.it

This work suggests a unified multiplex network framework enriching network layers of multiple interaction
types (structural layers) together with layers of similarity patterns between nodes (similarity layers). Thisapproach gives emphasis to structural links but it also considers potential features of individual nodes thatare often neglected in network models (Citraro and Rossetti, APN, 2020). We show the benefit ofconsidering similarity in synergy with structure when modelling the human mental lexicon, a cognitive
complex system where conceptual units/words possess features as reflected in language (e.g. frequency,
polysemy or length) and can be associated with each other according to mechanisms like recall frommemory, overlap in meaning or phonological similarities (see also Stella et al., Sci.Rep., 2017).
Building semantic and phonological structural layers in addition to similarity layers spanning vector spaces
across frequency, polysemy and length, we reconstruct a multidimensional representation of the mental
lexicon including 529 English words and available to a population of over 1000 English toddlers between
18 and 36 months. Considering the network metric of conformity (Rossetti et al., IEEE Int.Sys., 2021), we
investigate correlations between structural and similarity layers. Conformity is able to unveil theheterogeneous mixing patterns hidden in complex attributed graphs, and considers the evidence that nodes
with similar characteristics are not divided by long chains. Modelling each node as a vector of its
conformity values w/r/t the single features, we highlight the presence of multiple word clusters that could
not be observed on structural layers only. As reported in Figure 1 (a), conformity identifies 6 clusters of
nodes differing in their tendencies to connect (structurally) with other nodes sharing (similar) features. In
particular, a core of words of short length, high frequency and several meanings is highlighted by thismethodology (Figure 1 (c-e)). This core emerges early on during word development? Figure 1 (b) cansuggest a prevalence of early acquired words, but more statistical tests and analyses are needed to assess
some possible roles of such clusters in the development of children’s mental lexicon.

Figure 1: ​(a) Conformity w/r/t frequency vs. conformity w/r/t length: point colors denote node memberships to acluster -- K-Means as method, k=6 according to the elbow method; (c-e) percentages of feature values within theclusters, e.g., the cluster labeled as C contains only (c) very frequent and (d) short words, and (e) nearly half of themconvey a high number of meanings; (b) distribution of word age of acquisition is also presented for each cluster.

50

Configuration models for hypergraphs preserving local quantities of nodes and hyperedges
Kazuki Nakajima1 , Kazuyuki Shudo1 , and Naoki Masuda2,3
Department of Mathematical and Computing Science, Tokyo Institute of Technology
2
Department of Mathematics, University at Buffalo
3
Computational and Data-Enabled Science and Engineering Program, University at Buffalo
1

Empirical hypergraph data, where unit interactions include those among three or more nodes in general, are increasingly available [1]. By extending a class of configuration models called the dK-series
that are originally proposed for dyadic graphs [2], we propose a family of configuration models for hypergraphs that preserve local properties of the given hypergraph to different extents. The proposed model
specifies the joint degree distributions of nodes in the subgraphs of size dv or less and the joint degree
distributions of hyperedges in the subgraphs of size de or less for the bipartite graph that corresponds to
the given hypergraph. We consider dv ∈ {0, 1, 2, 2.5} and de ∈ {0, 1}.
Figure 1 shows four properties of nodes, i.e., (a) node’s degree distribution (DD), (b) node’s degree correlation (DC), (c) so-called degree-dependent node redundancy coefficient (DRC), and (d) the
distribution of the shortest path length (SPL), for an empirical hypergraph data and the corresponding
configuration models with de = 0. The empirical data is a drug network from the national drug code
directory (NDC-classes) data set with 1,149 nodes and 1,047 hyperedges. The model with dv = 0 only
intends to preserve the number of edges in the original bipartite graph. Therefore, it does not accurately
approximate the four node’s quantities. The model with dv = 1 preserves the node’s degree distributionof the given hypergraph (Fig. 1(a)), as it intends, but not the other three quantities (Fig. 1(b)–(d)). The
model with dv = 2 preserves the node’s degree distribution and roughly preserves the degree correlation(Fig. 1(a)–(b)). The model with dv = 2.5 further captures the abundance of triadic relationships (Fig.
1(c)). Furthermore, as dv increases from 0 to 2.5, the model better approximates the distribution of theshortest path length although the model is not designed to preserve it (Fig. 1(d)). The present family of
configuration models is expected to serve as reference models when one investigates the structure anddynamics of empirical and synthetic hypergraphs.
(b) DC

10−2
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101
102
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103

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node redundancy

Probability

10−1

10

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Empirical
dv = 0dv = 1
dv = 2
dv = 2.5(c) DRC

80
60
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0.6

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100

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−2

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101
102
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103

0.0
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5
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Figure 1: Distributions of node properties for the configuration models for hypergraphs. We set de = 0.
References[1] F. Battiston, G. Cencetti, I. Iacopini, V. Latora, M. Lucas, A. Patania, J. -G. Young, and G. Petri.
Networks beyond pairwise interactions: structure and dynamics. Physics Reports, 874:1–92, 2020.
[2] C. Orsini, M. M. Dankulov, P. Colomer-de Simón, A. Jamakovic, P. Mahadevan, A. Vahdat, K.E.
Bassler, Z. Toroczkai, M. Boguñá, G. Caldarelli, S. Fortunato, and D. Krioukov. Quantifying ran51
domness in real networks. Nature Communications, 6:8627, 2015.

Correlation of community-aware and classical centrality measures: Examining the role of
network topology
Stephany Rajeh1 , Marinette Savonnet1 , Eric Leclercq1 , Hocine Cherifi1
1

Computer Science Department - University of Burgundy, Dijon, FranceThis work investigates the relationship between community-aware centrality measures, classical centrality measures, and network topology. Artificial networks with controlled mesoscopic
properties and real-world networks originating from various domains are used in the experiments.
Kendall’s Tau correlation quantifies the interactions between ten classical centrality measures andtheir corresponding community-aware version based on intra-community links (local measures)and inter-community links (global measures)[1, 2]. Results show that the mixing parameter isthe most influential mesoscopic property in artificial networks. Global community-aware centrality measures exhibit low correlation with classical centrality measures in networks with a strong
community structure, while local community-aware centralities show high correlation. One observes the inverse in networks with a weak community structure. Furthermore, correlation values
are relatively insensitive to the degree distribution’s exponent variations and the community size
distribution. Simple linear regression between the real-world networks’ topological features andthe mean correlation between classical and community-aware centralities is computed. Results
confirm the influence of the community structure strength. Furthermore, it appears that density,transitivity, and efficiency are the most significant macroscopic features affecting the mean correlation between classical and local community-aware centrality measures.

Figure 1: Left: Kendall’s Tau correlation between classical (x-axis) and community-aware (y-axis)
centrality measures. Right: Mean correlation versus mixing parameter of 50 real-world networks.
References[1] N. Gupta, A. Singh and H. Cherifi. Community-based immunization strategies for epidemic
control. IEEE COMSNETS (2015), doi: 10.1109/COMSNETS.2015.7098709[2] Ghalmane, Z, et al. Centrality in Complex Networks with Overlapping Community Structure.
Sci Rep 9, 10133 (2019), doi: https://doi.org/10.1038/s41598-019-46507-y
52

The Mixing Law
Jake Ryland Williams1 and Diana Solano-Oropeza2
Departments of 1 Information Science and 2 Physics, Drexel University{jw3477, ds3367}@drexel.edu
For text, Zipf’s Law (ZL) is the existence of a harmonic relationship in the usage of a document’s vocabulary. So f (rw ) ∝ rw−1 means each word, w, is ordered by a positive integer rank rw
that is equal to its waiting time between appearances (in a shuffling of the document). However,documents exhibit variation in the scaling exponent, and so ZL is often weakened as f (rw ) ∝ rw−θ
for some θ ≥ 0. Moreover, while smaller samples of text generally uphold ZL with θ ≈ 1, larger
samples are known to exhibit words at higher ranks/lower frequencies that deviate far from ZL.In
these circumstances, a scaling break is said to occur at some critical rank b, after which a sec−(θ+µ)
when
ond, more-severe scaling emerges, i.e., f (rw ) ∝ rw−θ for rw < b, but then f (rw ) ∝ rw
rw ≥ b, for some different value µ > 0. Text-mixing was proposed to explain this non-ZL variation at large ranks and exhibited explanatory power in sampling experiments. But that work’s
formalism excluded a functional relationship, which we propose as the Mixing Law (ML).
Define text mixing mathematically for a setof k documents D = {di }ki=1 by assuming each−θiover a vocabupholds ZL as f (rw | di ) ∝ rw,iulary of Ni = |di | words via a scaling exponent
θi . The goal is to simplify
Pk the mixture frequencies: f (rw | D) =i=1 f (rw | di ). This ischallenged by variation in each word’s ranks
across the documents, i.e., the distribution of{rw,i }ki=1 (local ranks). Now, ZL constrains thevariation in exponents {θi }ki=1 so that there exists θ with θi ≈ θ ≈ 1 across D. If for each
Figure 1: Perplexity ratios for hN i & N meaword w of mixture-rank (global rank) rw one
sured by corpus (numer) and regression (demodels P (rw | Ni ) as the chance a documentnom) on samples of 35 documents by decile.
di ∈ D of size Ni = |di | contains w, then:Small/large deciles (1–3/7–10) of a synthetic corf (rw | D) ∝ rw−θ · P (rw | hN i), models thepus (orange) are fragmentations/agglomerations
mixture frequencies (using hN i to denote cenof real documents (blue), taken from deciles 4–7.
trality for D’s vocabulary sizes).
Provided the
mixture’s vocabulary has size
PN
N , let HN = r=1 r−1 be the N th harmonic number, so that hri = HNN averages mixture ranks.
Then θ ≈ 1 − HN−1 approximates the replication rate for Simon’s model from the strong form of
ZL over N harmonics. We propose approximating the ML’s form and role as:
"
i#

− hN
−1
hri
−
1−H
hri
(
)
f (rw | D) ≈ rw−θ · P (rw | hN i) ∝ r|w {z N }· 1 − 1 +rw
Zipf’s Law |{z}
Mixing Law

53

Temporal Motifs in Patent Opposition and Collaboration Networks
Penghang Liu1 , Tomomi Kito2 , Naoki Masuda1 , Ahmet Erdem Sarıyüce1
1

University at Buffalo, 2 Waseda University

Patents are intellectual properties that often reflect innovative activities of companies and organizations. Many studies have investigated the citations among the patents, but only a few addressed therelations between the patent owners. We use patent data from Orbis IP database [1] to analyze theadversarial and collaborative relations among the companies, where the former is formed by thepatent opposition, a legal activity in which a company challenges the validity of a patent, and thelatter is implied by the co-ownership of patents by multiple companies. Characterizing the patent
oppositions, collaborations, and the interplay between them is important for understanding how
innovation happens. Temporality is an important aspect in this context as the order and frequencyof oppositions and collaborations are key to identify and characterize complex relations among
companies.
In this study, we construct a two-layer temporal network to model the patent oppositions andcollaborations among the companies from 1980 to 2018. We utilize temporal motifs [2] to analyze
the oppositions and collaborations from structural and temporal perspectives. We have three main
findings. First, the opposition layer contains significantly more wedge motifs than the triangle
motifs (see Table 1), which is coherent with the structural balance theory [3] since oppositions arenegative relations. Second, if a company receives a burst of oppositions, it is likely to be a large
company which is attacked by small companies, and if a company files a burst of oppositions, it
is usually a large company targeting other large companies. Third, the companies with collaborations in the past are likely to oppose the same company or be opposed by the same company. In
summary, our analysis discovers underlying business relations in the patent data, which we believe
will advance the studies in business strategy and management.

449.81147.60166.12

26.43

16.75

Table 1: Temporal motifs in patent oppositions with their Z scores. Nodes represent companies
and the edges are the patent oppositions. The numbers on the edges denote the temporal order ofthe oppositions. A higher Z score indicates a more significantly overrepresented pattern.
References[1] T. Kito, N. Moriya, and J. Yamanoi Japanese Economic Review, vol. 72, p. 145–166, 2021.
[2] P. Liu, V. Guarrasi, and A. E. Sarıyüce Preprint arXiv:2005.11817, 2020.
[3] D. Cartwright and F. Harary Psychological review, vol. 63, no. 5, pp. 277–293, 1956.

54

Finding the right dam(n) partners for a just energy transition
Francesca Larosa, Jamie Rickman and Nadia Ameli
Supporting the transition towards a carbon neutral global economy requires the conversion of ourenergy systems to fully renewable sources. Over the past decades, solar and wind technologies havewitnessed growth in investment and capacity and their role is expected to increase in the future.
However, hydropower remains the primary renewable energy technology by capacity andgeneration accounting for approximately 60% of international investment flows in renewableenergy. In particular, hydropower is at core of several developing countries’ energy systems, where
it provides the base for energy security.
Currently we have limited understanding of the investment architecture of hydropower, as the focus
on increasing the financial flows for the transition has diverted attention away from who is
operating in this space and how.
Our study responds to thiscrucial policy question byasking how a just transition canbe accelerated around the world
through improving access tofinance for hydropower. We
explore which investment
models and co-investment
patterns have drivenhydropower deployment overthe past century (1903-2020).
First, we detect how different
actors co-mobilised the capitalneeded for hydropower projects
at global level building abipartite network of project
financing investments. Second,
we zoom into the most criticalinvestors who hold the project
finance landscape together,allowing capital to flow from developed to developing nations and we reveal the community
structure that shapes the landscape for hydropower finance. Finally, we investigate investors’
facilitator role in the investment chain and assess their ability to activate public-private partnerships(PPPs) over time.
Our results show that public and international institutions are the critical actors driving hydrofinance through multilateral and bilateral financing mechanisms and global PPPs. These investors
interact both within and across distant communities allowing finance to reach the most vulnerable
areas. They integrate climate objectives into their development goals by mandate, enhancing
economic prosperity and sustainable growth, while also boosting clean and affordable energy
sources. This virtuous investment cycle is enabled by the diversity of partnerships activated byinternational institutions, who pave the road for banks and private actors across multiple countries.
As one of the biggest challenges in sustainable energy transitions is likely to be in developing
countries, our effort serves as a policy base to ensure equitable access and effective capital
allocation for hydropower, the principal energy source in these regions. A strong investment
architecture and channels will accelerate sustainable power deployment while leaving room for new
technologies in the energy transition.

55

Robustness of football passing networks against cascading failure
Daiki Miyagawa1∗ , Koki Okamoto1 , and Genki Ichinose1
1

Department of Mathematical and Systems Engineering, Shizuoka University,
3-5-1 Johoku, Naka-ku, Hamamatsu, 432-8561, Japan∗miyagawa.daiki@shizuoka.ac.jp

robust ness

Existing real-world systems are often represented by networks. On a network, one unit of therelevant quantity is transmitted between every pair of nodes at each time step. Examples are theﬂow of packets over the Internet or the ﬂow of electricity in power grids. When those quantities
are transmitted between a pair of nodes through a link, loads occur depending on the amount of
quantities. If loads exceed nodes’ capacities, the nodes collapse. Then, the loads of those failure
nodes are redistributed to other nodes. This collapse of nodes and the redistribution of loads will
be repeated until the capacities of every node become larger than the loads. These succeedingcollapses of nodes are called a cascading failure. In this study, we consider cascading failures infootball passing networks. Passing in football can be regarded as a network because the ball ispassed between players (nodes). As the amount of passes increases, fatigue of players increases
and their performances suffer. When this situation happens, other players try to make up for theloads. However, when the performances of some players decrease one after another because of
fatigue, passing the ball temporarily does not work. We regard this situation as a cascading failure
in a football passing network. Constructing a robust passing network may be related to the victory
in a game. To this end, we explore the robustness of football passing networks against cascading
failures.
Using the match data of J1 League (the top division league in
1
Japan) in 2019, we constructed one passing network per team for amatch. We simulated cascading failures on these networks. In thesimulations, a single node with the highest loads is selected and0.5
removed (load attack). Here we show the results of the simulationsvs Mat sum ot ovs Tosu
conducted with Yokohama F.Marinos as typical examples. In the0year we analyzed, the team aimed at high ball possession. The blue
1
1.5
2
capacit y rat eline in Fig. 1 indicates the case that the team made many passes
among players in the game (vs Matsumoto Yamaga F.C.). Thisshows that the network keeps high robustness against cascading Figure 1: Network robustfailures in the intermediate capacity rate, meaning that all players ness of Yokohama F.Marinos
relatively equally conducted passes in the game. On the other hand, against cascading failures.
in the other case (vs Sagan Tosu), the passing networks are fragile
against load attacks (green line in Fig. 1). In this game, passes were perhaps concentrated to somespeciﬁc players. In such a case, if the opponent team marks those players, it may be difﬁcult topass the ball among team members. Our results indicate that even though Yokohama aims at highpossession, the quality of their passing networks against cascading failures changes according to
opponents’ defensive tactics.
56

Incremental research - a favoured strategy in the “publish or perish” environment
Luka Blagojević1 and Aleksandra Alorić2
1
2

Department of Network and Data Science, Central European University, Vienna, Austria
Center for the Study of Complex Systems, Institute of Physics Belgrade, Belgrade, Serbia

To venture into a new research direction and risk slow progress and productivity gaps, or incrementally refine your previous research agenda and have a steady research output is just an academics’ version of a long “to explore or exploit” dilemma researched in various disciplines fromcomputer science to management. Motivated by empirical results [1] that find physicists acrossdifferent subfields explore with caution and note stronger exploitation among younger researchers,
this paper sets to investigate whether seniors’ exploration is only a consequence of survivor bias,
or riskiness of exploration and productivity pressures on researchers’ drive them to exploitation
strategies. With a stylised agent-based model we investigate agents with a fixed propensity for exploration and show that even with a mild risk (a paper on a new topic only takes twice as long as anincremental research paper) fraction of exploiters increases, and the effect is even stronger if there
is productivity related rate of leaving academia (Fig. 1). Dominant exploitation strategies as theconsequence have smaller knowledge diversity which is why we ought to find systemic incentives
that favour exploration. This is somewhat easier now with the abundance of empirical data, but weshould be cautious of the survivor bias and complement the research with carefully tuned models.

35

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Career duration

Career duration

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Figure 1: Distribution of agents career length and cosine similarity between first and last research
topic in an ABM where exploitation leads to risk free publication, while exploitation leads topublication with 50% chance. Population of agents has exploitation rate q = 0.5 (left) or uniformly
drawn q ∈ [0, 1] (middle and right). Agents leave academia with fixed rate (left and middle), orwith rate dependent on their productivity (right).
References[1] Aleta, A., Meloni, S., Perra, N. and Moreno, Y. Explore with caution: mapping the evolutionof scientific interest in physics. EPJ Data Sci. 8, 27 (2019).
57

Abnormal behavior of the Heider balance theory with heterogeneous triads
M. Bagherikalhor​1​, G. R. Jafari​1,2
1​Department of Physics, Shahid Beheshti University, G.C., Evin, Tehran 19839, Iran
2​
Institute for Cognitive and Brain Sciences, Shahid Beheshti University, G.C., Evin, Tehran,19839, Iran
Balance theory was first introduced by Heider as a concept in social psychology[1]. It has a vast
application and different comprehensive literature in different branches of science including
mathematical sociology[2], ecology[3], and studies of international networks[4]. This theory
deals with triplet interactions in which triads are equivalent, but in reality, we are a member ofvarious groups of relationships which are different in priority. Now the question is, does theimplementation of heterogeneity in triads confront us with astounding findings? To this purpose,
we have studied disordered triadic interactions in the framework of Heider balance theory[5]. In
Heider balance theory, the system experiences a first-order phase transition. Above a criticaltemperature, triads are randomly balanced and unbalanced and below it, all triads are balanced,
and the energy of the system reaches its minimum[6]. Here, we are dealing with heterogeneity as
a disorder where triads are assigned with different random weights that are quenched and comingfrom Gaussian probability distribution with mean, and the variance, . By setting the meanvalue of distribution equals one (), we study the network evolution in two regimes: i) weakdisorder (), ii) strong disorder (). For, the result is similar to the
Heider balance. The minimum energy of the network occurs in the mean value of the probability
distribution which is in agreement with our expectation since the network mostly consists oftriads with weights around. The network reaches the global minimum inand all triads are balanced. For, our results indicate the energy versus temperature
increases below a critical temperature due to the diversity of weights and the survival of
unbalanced triads (frustrated). Although we expect to see a reduction in the number of
unbalanced triads and the minimization of the energy, energy increases below a criticaltemperature (figure). This result can be more attractive compared to the Kondo effect [7]. The
Kondo effect is a phenomenon in superconductivity and states that adding magnetic impurities ina metal causes increasing resistivity while we expect zero resistivity below a critical temperature.
Here based on our modeling of a social network with heterogeneous triads, we see there is aschematic similarity in the behavior of these two phenomena.
[1] ​F. Heider, The Psychology of Interpersonal
Relations Wiley, New York, 1958.
[2]​Robert K. Leik, B. F. Meeker, Mathematicalsociology,Prentice-Hall Englewood Cliffs, N.J, 1975
[3]​H. Saiz, J. Gómez-Gardeñes, P. Nuche, A. Girón,
Y.Pueyo, and C. L. Alados, Ecography 40, 733, (2017).
[4]​J. Hart, J. Peace Res., 11, 229, (1974).
[5] ​M. Bagherikalhor, A. Kargaran, A.H. Shirazi, G.R.
Jafari, Phys. Rev. 103, 032305 (2021)[6] ​F. Rabbani, Amir H. Shirazi, and G. R. Jafari, Phys.
Rev. E, 99, 062302, (2019).
[7] ​J. Kondo, Progress of Theoretical Physics 32, 37,(1964)​.

58

Analyzing Eccentric Behavior of GAB Social Media Users
Sriniwas Pandey1,+ and Hiroki Sayama1,2
1Binghamton University, State University of New York
2
Waseda Innovation Lab, Waseda University, Tokyo, Japan+
spandey4@binghamton.edu
This work focuses on extremism in our day-to-day conversations and behavior, termed as ‘eccentricity’. In social media discussions, ‘normal’ is the center of conversations and distance fromthe center is degree of eccentricity. To analyze the dynamics of eccentricity, we collected posts andconnection information for a sample of GAB users. Our sample has approximately three thousand
users and a total of one hundred forty seven thousand gabs (posts) from August 2016 till January
2021. Using Doc2Vec and principal component analysis technique, each gab is converted into a
numerical vector. For each user, a knowledge base is maintained that contains gab-vectors posted
by the user and his neighbors in the past five days. The eccentricity indicates the degree of noncentrality of a post, relative to general discussion going on. We calculate f-score (the weighted(time decay term) average of absolute change in the eccentricity over time) and g-score (change
in eccentricity with direction of change). Users are classified into four categories: i) High f-scoreand g-score: ‘Marginalized’ ii) High f-score and low g-score: ‘Fickle minded’ iii) Low f-score andg-score: ‘Stable’ iv) High f-score and a very low g-score: ‘Mainstreamed’. We also classify users
based on degree of deviation from their own previous posts (self-eccentricity).

(b)

(a)

Figure 1: Eccentric behavior of GAB users a) Users represented in ‘f-score’-‘g-score’ space. Piechart shows proportion of each user class. b) Users in f-score and g-score space of self-eccentricity.
Figure 1a shows the distribution of user posts in f-score and g-score space for eccentricity.
21.7% users get marginalized in their neighborhood, 36.7% users’ behavior keeps fluctuating and19.6% users are stable. However, if we consider self eccentricity of a user, figure 1b, around 53%
users are fickle minded while only 6.8% users are marginalized. To analyze this further, we examined relation between user eccentricity and self eccentricity classes. An interesting observationis that a large proportion of fickle minded users in terms of self eccentricity are either becoming
marginalized or mainstream in their neighborhood. This also provides an interesting insight about
the eccentricity of overall environment. Many users, who become homogeneous with their own
previous ideas, get categorized as stable users in their neighborhood, this implies neighborhood’s
eccentricity is decreasing at a faster rate.
59

Bio-Inspired Water Distribution Network Design
Noha Abdel-Mottaleb1, Kashin Sugishita2, Naoki Masuda2,3, Qiong Zhang1
1. Department of Civil and Environmental Engineering, University of South Florida, Tampa, FL, USA
2. Department of Mathematics, State University of New York at Buffalo, USA
3. Computational and Data-Enabled Science and Engineering Program, State University of New York at Buffalo, USA

Water distribution networks are lifeline infrastructures of urban centers. Increased urbanism has
fueled the growth and morphogenesis of cities around the world. Yet it is not clear how to design
or reconfigure a water distribution network to accommodate the urban growth, while optimizing
for performance (i.e., how adequately a network provides water to users). Given that biologicalflow networks have been evolving for much longer than water distribution networks, this study
evaluates if the application of biological design principles to water distribution networks (i.e.,
bio-inspired) enhances their performance.
A growth model for Physarum mold is applied to a benchmark water distribution networkthat is based on a real system (Modena, Italy), where the water sources (i.e., root nodes) are
predefined. The Physarum growth model generates a new network, where the pipe diameters aredesigned based on the principles of Physarum growth. The distribution of the diameters from thegenerated network is compared with the pipe diameters of the original network. Then, theWaterGEMS criticality tool is used to quantify the system demand shortfall under eachindividual pipe isolation. For each network, the system demand shortfall is summed over all of
the pipe isolations, and the values are compared between the generated network and the original
network.
The results showed that the bio-inspired network had a more uniform distribution of pipe
diameters than the original network (see Figure below). This is not surprising because previous
research has shown that water distribution networks with more uniform diameter distributions
have higher redundancy of flow paths which enhances performance of the network under failure
scenarios. Additionally, the aggregate system demand shortfall was more than 50 percent lower
for the bio-inspired network. Future work will apply this methodology to more water distribution
networks and additional performance indicators will be used to more definitively determine theusefulness of applying the biological model to design water distribution networks.

Figure: Histogram of the pipe diameters for the original and bio-inspired networks, where theaggregate system demand shortfall is 466 for the original network and 155 for the bio-inspired
network60

A Meta-Population Movement-Based Epidemic Model for COVID-19
Pandemic
Tayeb Jamali1, Olha Buchel2, Yaneer Bar-Yam2, Leila Hedayatifar2
1Department of Physics, Beheshti University, Tehran, Iran

2New England Complex Systems Institute, 277 Broadway St, Cambridge, MA, USA

We developed a meta-population movement-based epidemic model to investigate the role oflockdown strategies on slowing down the spread of the COVID-19 outbreak. Previously, wedemonstrated analytically that mobility preferences of the US population lead to the formation ofself-organized geographical fragmentation patterns, that reveal how areas are connected to eachother. We showed that lockdown policies in the US have substantially reduced the long-distancemovements, changed mobility patterns and reduced in size the mobility patches compared withthe ones before the COVID-19 pandemic (see Figure 1 below). Here, we introduce a generalized
Susceptible-Exposed-Infected-Recovered model on geographical networks of mobility patches
before/during/after lockdown strategies in the US. Our model has an extra term to account for themobility flows among the partitions. We study the effect of mobility patches’ sizes andconnection strengths among them on the disease dynamics. By comparing the results of themodel over time, we quantify the effectiveness of preventive mobility policies on slowing down
the geographical spread of the disease.

a)b)

Figure 1. Self-organized geographical fragmentation patterns and mobility flows in the US
before and during the pandemics: a.) mobility patterns and flows during February 23-29, 2020;b.) mobility patterns and flows during April 5-11, 2020, during the national lockdown. The colors
show different communities; similar color hues identify similar groups of closely interconnected
communities; line - connections between communities, and lines widths - strengths of theconnections.

61

NERCCS 2021: The Fourth Northeast Regional Conference on Complex Systems

COVID-19 and Financial Sustainability of Academic Institutions
Oleg Pavlov, Worcester Polytechnic Institute, opavlov@wpi.edu
Evangelos Katsamakas, Fordham University, katsamakas@fordham.edu
The COVID-19 pandemic has had a significant impact on higher education. Steering academic institutions
through the pandemic is a complex and multifaceted task that can be supported with model-based
scenario analysis. This article studies the short-term and long-term effects of the pandemic on thefinancial health of a college using scenario analyses and stress testing with a system dynamics model of arepresentative tuition-dependent college. The figure below shows six effects of COVID-19 (we refer tothem as stressors S1 through S6) that are studied in this article and their impact on a college. An upward
pointing red arrow indicates that this particular variable increases due to COVID-19 and a downward
pointing red arrow means that the value of the variable is likely to decrease due to COVID-19. A positive
link between two variables signifies a positive causality between them. Negative causalities are shownwith negative links. We find that different combinations of the pandemic mitigation protocols may havevarying effects on the financial sustainability of an academic institution. By simulating six individualcomponents of the COVID-19 shock, we learn that due to the causal complexity, nonlinear responses
and delays in the system, the negative shocks can propagate widely through the college, sometimes
with considerable delays and disproportionate effects. Simulations show that some pandemic mitigation
protocol choices may destabilize even financially healthy institutions. The article adds to the literatureon the economics of higher education, management of the pandemic-related risk on campus, college
stress-testing and model-informed decision making in higher education.

+

Tuition
and
fees

S6

+

Financial
aid

+

+

S5

Share ofstudents on
campus

S4

Typicalendowment
draw

Total
revenues+
Healthandsafetymeasures

S3

Liquidassets+-Netrevenue-

Total
operatingexpenses+
COVID
variable
cost

+

-

+

Additional
endowment draw+

Cashwithdrawals

Net room & board
revenue-

Endowment
+

+

+

+
S1

+

-

Students++

Net tuition
revenue+
S2

Revenuefromothersources+-Borrowing for
operations

+
+
COVID
preparedness

62

Debt
payments

Debt
+

+

Intermittent frequency chimeras in modular network of FitzHugh-Nagumo oscillators
Sangeeta Rani Ujjwal1 , Ulrike Feudel2 and Ramakrishna Ramaswamy3
1 Department of Physics, Institute of Science

Banaras Hindu University, Varanasi, Uttar Pradesh 221005, India
sujjwal@bhu.ac.in
2 Institute for Chemistry and Biology of the Marine Environment
University of Oldenburg, 26111 Oldenburg, Germany
ulrike.feudel@uni-oldenburg.de
3 Department of Chemistry, Indian Institute of Technology- Delhi
Hauz Khas, New Delhi 110016, India
ramakrishna.ramaswamy@gmail.com
We study the dynamics of FitzHugh-Nagumo oscillators in a modular network where the interactions
between the modules are nonlocal and include a phase lag. Depending upon the value of phase lag, in addition to global synchrony and modular synchronization we observe a novel type of chimera state which
we call as ‘intermittent frequency chimera’ where coherent domains consist of modules separately synchronized to different frequencies, coexist with modules within which the dynamics is desynchronized, and someof these modules show intermittency wherein they oscillate between synchronized and desynchrozed statewith time. We also observe multistability between these different dynamical states in a sizable region ofparameter space.

Figure 1: Average synchronization error (ζ a ) for four different modules is plotted with time showing theintermittent frequency chimera where oscillators in module-1 are synchronized (a), in module-2 and 3 (b)(c) are desynchronized while in module-4 (d) go in and out of synchrony with time.

63

Part XI

Poster Session 2

64

Network Symmetry Extraction
Y. Liu1. (1) Network Science Institute, Northeastern University, Boston MA, USA, lycrdfzpku@gmail.com.

Most literature on measuring the symmetry of networks uses graph automorphism algorithms
to find the automorphism group, and defines either the number of elements in the automorphismgroup or the number of nodes involved in the automorphism group as a measure of the level ofsymmetry of networks. However, this type of measure has two problems: first, it is a measurefor exact symmetry, meaning that it fails to capture a large group of approximate symmetriesof networks (for example, a lattice with one missing edge still has a high level of symmetry,
intuitively speaking, but according to the present symmetry measure it may have zero
symmetry); second, in real-world networks, most of the automorphism transformations foundare composed of local permutations, for example two degree-one nodes attached to the samenode are symmetric to each other. Therefore if a network has many automorphism
transformations it could mean that the network has a lot of local symmetries, instead of global
symmetries. For example, a lattice has translational and reflectional symmetries, both of which
are global. To overcome these problems, we introduce a new measure of the level of symmetryof a given network with adjacency matrix A:
S = min( ||A − QAQ+ || ),$where Q is a permutation operator with properties det(Q) = 1 and QQT = I, and ||·|| is order-1
norm. QAQT is the resulting adjacency matrix after a permutation of the node sequence. In
order to restrict the symmetries we find to global symmetries, we limit Q such that trace(Q) =0, meaning that all nodes are involved in the permutations. The difference between A and the0+ with permutation 𝑄. = argmin( ||A - QAQT|| ) is a measure
permuted adjacency matrix 𝑄. 𝐴𝑄
of how close 𝑄. is to exact symmetry.
Figure 1 shows S for networks with N = 100 nodes, generated from three different networkmodels: Erdös Rényi (ER), Random Geometric Graphs (RGG), and Stochastic Block Models(SBM), as a function of the number of edges M. For ER networks (blue) and RGGs (orange),when they are empty (M = 0) or complete (M = 5,000), they have complete symmetry, whichis reflected by S = 0. When half of the potential edge slots are filled (M = 2,500), thenetworks have the least level of symmetry, due to the high uncertainty of edge placements.

Figure 1: S for networks with N = 100 nodes, generated from three different network models.

65

Masculinity Contest Cultures and Inclusive Cultures:
Insights From a Network Model of Organizational Socialization and Promotion
John Meluso1, Laurent Hébert-Dufresne1,2, James Bagrow1,3, Rob Razzante4
1Vermont Complex Systems Center, University of Vermont
Department of Computer Science, University of Vermont
3
Department of Mathematics & Statistics, University of Vermont
4
Department of Communication Studies, The College of Wooster
2

Recent organizational scholarship finds that “work” becomes a masculinity contest when organizations valorize acts of dominance, acts which likely perpetuate barriers to the advancement ofmarginalized groups in organizations (as with the “glass ceiling”). But how such Masculinity Contest Cultures (MCCs) develop and sustain themselves remain open questions. This study juxtaposes MCCs with Inclusive Cultures (ICs) to examine how each culture spreads in organizations’social networks. Drawing upon systems theory, we simulated the processes of socialization andpromotion in organization networks via an agent-based model. Varying the hiring pools for different organizations from inclusive to contest-oriented revealed that inclusiveness emerged as selfreinforcing in all but organizations with the most contest-oriented hiring pools. In contrast, hiring
pools socialized into hegemonic masculinity made organizations more likely to resist ICs andshowed potential to evolve into MCCs in productivity-oriented, hierarchical organizations. Furthermore, organizations tended to see greater cultural change in higher ranks of the organizational
hierarchy than in lower ranks, regardless of the more-prevalent culture. Such cultural stratification
demonstrates the challenge in transforming the culture of every organizational level toward inclusiveness without further study of socialization processes.
Keywords: Agent-Based Modeling, Social Networks, Organizational Culture, Hierarchy, Inclusiveness, Socialization, Masculinity Contest Culture, Hegemonic Masculinity

Figure: (Left) Organization structure and relationships between employees. (Center/Right) Average change in contest-orientation (vertical axis) over 100 runs for different starting points forcontest-orientation (horizontal axis) in absolute and percentage terms, respectively. Insets show
the transition to contest culture reinforcement after an additional 500 runs for each starting contest-orientation ≥ 0.85.
66

Emergent hierarchy through conductance-based node constraints
Christopher Diggans, Jeremie Fish and Erik Bollt
See the full paper published in the Northeast Journal of Complex Systems:
https://orb.binghamton.edu/nejcs/vol3/iss1/4/

67

MULTICRITERIA SELECTION AND EVALUATION OF THE LIFESAVING UAVs FOR
A DETERMINED AREA (AEGEAN SEA COASTLINE) IN TURKEY BY COMPARING
TODIM&GOAL PROGRAMMING (GP) METHOD
Babek ERDEBİLLİ, İbrahim YILMAZ, Volkan SARIBAŞ
Abstract.
Unmanned Aerial Vehicles (UAVs) are taking part in our life day by day. UAVs are preferredalmost everywhere from the military, defense to surveillance, agriculture. Thus, the usage area
almost is expanding every day; however, there is a crucial topic to use UAVs in lifesaving for thevictims drowning. There are kinds of UAVs for lifesaving. It is aimed in this study to select thebest UAV. Seven UAV alternatives related to lifesaving for the victims drowning and ten criteria
proposed by the experts to evaluate the alternatives and select the best alternative. For this purpose,
AHP-TODIM (Analytic Hierarchy Process - Tomada de Decisão Iterativa Multicritério) and AHPGP (Analytic Hierarchy Process – Goal Programming) models are applied to solve this problem
with the same values. The calculations indicate that Alternative UAV-5 was chosen as the best ofthem by TODIM and Alternatives UAV-5 and UAV-7 were selected by Mixed Integer Goal
Programming. Finally, the results are compared and the solution sensitivity analysis is addressed.
Keywords: Unmanned Aerial Vehicles (UAVs), Rescue operations, drowning, floatation devices,
Multiple criteria analysis, method, Goal Programming, TODIM, weight consistency, decision
making.
Process Flow

PROBLEM SET UP

COLLECT DATAAND DEFINETHE PROBLEM

FORMULATE
THE
ALTERNATIVES

DETERMINE
THE CRITERIAFOR THEALTERNATIVESBY THEEXPERTSDERIVEWEIGHTS BY
AHP

APPLY TODIM WITH
THE WEIGHTS OF AHP

APPLY GP WITH THE
WEIGHTS OF AHPALTERNATIVE 5 WERE
CHOSENALTERANATIVE 5 AND 7
WERE CHOSENCOMPARE THE METHODS’ FINAL SELECTION OF ALTERNATIVESAND DECIDE68
THE BEST OPTIONALTERNATIVE 5 WERE DECIDED

Modeling epidemic spreading in Markovian temporal networks with different
degrees of concurrency
Ruodan Liu1 , Masaki Ogura2 , Elohim Fonseca dos Reis1 , and Naoki Masuda1,3
2

1
Department of Mathematics, University at Buffalo, SUNY
Graduate School of Information Science and Technology, Osaka University
3
Computational and Data-Enabled Sciences and Engineering Program,
University at Buffalo, SUNY

The concurrency of edges, quantified by the number of edges that share a node at a given time, isconsidered to influence epidemic processes, which has been a topic particularly debated for HIV/AIDS
infection in sub-Saharan Africa. More broadly, concurrency is likely to be a determinant of epidemic processes in temporal networks [1]. We study effects of concurrency on epidemic spreading in the stochastic
susceptible-infected-recovered (SIR) dynamics on three temporal network models, with which we cantune the amount of concurrency while keeping the probability that each edge is present and the structureof the aggregate (i.e., static) network the same across comparisons. In model 1, the appearance anddisappearance of edges are governed by independent continuous-time Markov processes [2], which lacks
surplus concurrency. In our model 2, each node independently obeys a two-state (i.e., active/inactive
states) continuous-time Markov process, and the edge between two nodes appears if and only if both
nodes are active. We also propose model 3, in which the edge between two nodes appears if and only ifeither node is active.
Using a concurrency measure, we analytically calculated the degree of concurrency of edges sharing
a node for the three models under the condition that each edge appears with the same stationary probability in the different models. We have found that models 2 and 3 are more concurrent than model 1.
Furthermore, model 2 is more concurrent than model 3 or vice versa depending on whether the stationary probability that an edge exists is larger than 0.5 (Figure 1(a)). We then numerically simulated thestochastic SIR dynamics on the three temporal network models on top of an underlying static network
generated by the Barabási-Albert model with N = 100 nodes and average degree hki = 7.68 (and othernetworks; results not shown). We started each simulation from an arbitrarily chosen single infected node,
while the other N − 1 nodes were initially susceptible. We set the parameters of the three models such29
9
= 0.36, 35 = 0.6, and 45≈ 0.64, respectively.
that the degree of concurrency for models 1, 2, and 3 are 25
Figure 1(b) suggests that the final epidemic size is large when the degree of concurrency is large acrossthe infection rate values. Our result affirmatively confirms the hypothesis that concurrency enhances
epidemic spreading on networks, and in a model of temporal networks for which one can strictly control
the probability of the edge being active and carry out some theoretical analysis.

Figure 1: (a) Normalized concurrency index as a function of the stationary probability that an edge is active.
(b) The relationship between the infection rate and the final epidemic size. We used the Barabási-Albert network
generated with N = 100 and hki = 7.68. The final size shown is the average over 1000 simulations.

References[1] N. Masuda, J. C. Miller, P. Holme (2020), arXiv: 2012.13317.
[2] X. Zhang, C. Moore, and M. E. J. Newman (2017), Eur. Phys. J. B, 90: 200.

69

Complexity and Curriculum:
Examining the Role of Connectivity in a Precalculus CourseJohn O’Meara, Ashwin Vaidya, Stephen Essien
Department of Mathematical Sciences, Montclair State University, Montclair, NJ 07042

This project aims to utilize the mathematical theory of networks and statistical analysis to understandthe significance of connectivity in mathematics education. We collectively hypothesize that education
is a complex system, at various scales, composed of different ideas and concepts which areconnected. Therefore, the task of a good teacher lies in elucidating these connections and helping
students make their own connections. Such a pedagogy allows students and educators alike topersonalize learning and strive to be ‘creative’, which essentially amounts to ‘meaning making’ orassigning new meaning from the foundation of old ideas.
In this project, we test our hypothesis by examining the network structure of a precalculus course. We
identify the curricular network of different, well known precalculus textbooks by identifying various
topics covered in this course and their connectivity, i.e. relationships between different topics. The
topics covered in each respective text are nodes, and explicit relationships between topics are edges.
Connections are made using a uniform procedural rubric which essentially allows us to link concepts
if they are related sufficiently strongly. Figure 1 below exemplifies such a graph based on a standard
textbook on precalculus.

(a)

(b)

Through examination of network indices such as connectivity index, average path length and degree
distribution of these networks, we may gather a measure of qualitative efficacy through a highly
quantitative investigation to objectively analyze the effectiveness of a given textbook and thepedagogy in a course that emphasizes a similar approach. We also investigate statistical correlations
between the computed network indices and ratings of these texts which give us some indication of
their effectiveness. Effective textbooks, as recognized by publicly available user ratings, are indicatednot only by expected magnitude of relevant metrics, but also by the consideration of the synthesis ofglobal and local connectivity, within and between topics. Fitting degree distributions to a probability
model allows insight into concentration of the presentation of curriculum, and the family of
distributions to which precalculus curricula belong.

70

Exploring the connectivity of a hospital: A network analysis of patient movement
community structures
EE. Boncea1, P. Expert1, CE. Costelloe1
1
Global Digital Health Unit, Imperial College London, UK.
A hospital patient’s movement trajectory, which encompasses intrahospital transfers throughvarious locations, involves many interactions between heterogenous, autonomous yet
interdependent healthcare staff. Diffusion of control is characteristic of a complex system,
meaning that the coordination of patient transfers can be a ‘problem of many hands’, with no single
actor held responsible [1]. Without an overarching view of the connected whole, system-level
improvements are difficult to achieve. We present a network based exploration of patient
movement structures within a London hospital. Ward-transfer data from electronic health records
pertaining to patients from 2015-2018 were used to create a weighted patient movement network.
The communities found using Newman-Girvan modularity were clearly interpretable, comprisingof maternity, paediatric, surgical and medical specialities (Fig 1 left). As patient specialities are a
determinant of movement [2], the primary speciality of patients on wards informed an alternative
null model adapted from [3], based on similarity of ward specialities, aiming to identify speciality
independent communities. The speciality null model yielded more granular communities
correlating with patient illness severity (Fig 1 right): e.g., low severity general medical wards(yellow), medium severity wards equipped to treat deteriorating patients (orange) and high severity
wards, including the adult intensive care unit and a major trauma ward (dark blue). These results
demonstrate that meaningful ward communities can be found within a hospital and give insights
into the system’s complex topology, highlighting patient severity and speciality as mechanisms
shaping movement patterns. Examining their interconnectedness and understanding theiremergence is the first step in building a data-driven, shared perception of ward functionality andlinking these to micro-level inefficiencies, as well as new interventions to optimise patient
movement.
Well Babies
Gynaecology
Trauma & Orthopaedics

Obstetrics
Obstetrics

Vascular Surgery
Hepatology

Midwife EpisodeAccident & Emergency

GynaecologyHepatology
Respiratory Medicine
General Medicine
Vascular Surgery

Midwife Episode
Gynaecology

Obstetrics

Obstetrics
General Medicine
General Medicine
General Surgery
Obstetrics
General Medicine
General Medicine
General Surgery
General Medicine
General Medicine
Obstetrics
Vascular Surgery
Gastroenterology
Gastroenterology
General Surgery Accident & Emergency
Gastroenterology
Obstetrics
General Surgery
Hepatology
General Medicine General Medicine
General Surgery
General Medicine
General Surgery
General Surgery
General Medicine
Vascular Surgery

Obstetrics
Neonatology

Obstetrics

Vascular Surgery

Obstetrics
General Medicine
Obstetrics
Obstetrics
General Medicine
General Medicine
Neonatology
General Surgery
Obstetrics
General Medicine
General Medicine
General Surgery
General Medicine
Geriatric Medicine
General Medicine
Obstetrics
Obstetrics
Gynaecology Vascular Surgery
Gastroenterology
Vascular Surgery

Accident & Emergency

General Surgery

Paediatrics

Gynaecology
Paediatrics

General Surgery

General Surgery

Endocrinology
Gynaecology

Paediatric Clinical Haematology
Paediatrics

Obstetrics

Trauma & Orthopaedics
Trauma & Orthopaedics
General Surgery

Paediatric Ear Nose And Throat

Gastroenterology

Hepatology

Trauma & Orthopaedics
General Surgery

Paediatric Intensive Care

Endocrinology

Midwife Episode
Midwife Episode
Gynaecology

General Medicine General Medicine
General Medicine
Respiratory Medicine
General Surgery
General Medicine
Gastroenterology
General Surgery Trauma & OrthopaedicsGeneral Medicine

General Surgery
Gynaecology

Hepatology

Accident & Emergency
Vascular Surgery
Geriatric Medicine
Respiratory Medicine

Trauma & Orthopaedics

General Medicine
General Surgery Trauma & Orthopaedics
Geriatric Medicine Respiratory Medicine
Trauma & Orthopaedics
Trauma & Orthopaedics Geriatric Medicine
Trauma & Orthopaedics

Hepatology

General Surgery

General Surgery

General Surgery

Obstetrics

Obstetrics

Well Babies

Paediatric Intensive Care

Paediatric Ear Nose And Throat Paediatric Clinical Haematology
General Surgery
Paediatrics
Paediatrics
Paediatrics
Paediatric Clinical Immunology And Allergy

Paediatric Clinical Immunology And Allergy

Paediatric Clinical Haematology

Paediatric Clinical Haematology
Paediatric Respiratory Medicine

Paediatric Respiratory Medicine

Paediatric Clinical Immunology And Allergy

Paediatric Clinical Immunology And Allergy

Figure 1: Communities found in the patient movement network with the Newman-Girvan
modularity (left) and the speciality modularity (right). Node labels pertain to specialities.
References:[1] M.Dixon-Woods, PJ Pronovost., “Patient safety and the problem of many hands”. BMJ Qual.
Saf. 2016;25(7): 485–488. [2] H. Xu, W. Wu, S. Nemati et al., "Patient Flow Prediction via
Discriminative Learning of Mutually-Correcting Processes. IEEE TKDE. 2017; 29(1):157-17 [3]P. Expert, et al., PNAS. 2011;108(19):7663-8
71

On the relation between transversal and longitudinal scaling in cities
Fabiano L. Ribeiro1
Department of Physics (DFI)
Universidade Federal de Lavra (UFLA), Lavras, MG, Brazil
fribeiro@ufla.br1

Abstract

Empirical evidence has been shown that some urban variables scale non-linearlywith the city population size. More specifically, some socio-economic variables, suchas the number of patents, wages and GDP, show a super-linear behaviour with thecity’s population. On the other hand, infrastructure variables, such as the number ofgas stations and streets’ length, scale sub-linearly with the city population, generating a scale economy. However, do these scaling properties observed in a system ofcities (transversal scaling) also work for individual cities in their growth process (longitudinal scaling)? The answer to this question has important policy implications, but
the lack of relevant data has hindered rigorous empirical tests. The work that will bepresented was developed looking at the evolution of two urban variables, GDP (seeFig. (1)) and water network length, for over 5500 cities in Brazil. It will be shown that
longitudinal scaling exponents are city-specific; however, they are distributed aroundan average value that approaches the transversal scaling exponent provided that thedata is decomposed to eliminate external factors, and only for cities with a sufficiently
high growth rate. This result adds complexity to the idea that longitudinal dynamics isa micro-scaling version of the transversal dynamics of the entire urban system.

Figure 1: Log-log plot of the time evolution (longitudinal scaling) of the GDP (Y ) as a function of
population size (N ), for all Brazilian metropolitan areas greater than 500.000 inhabitants. The redstraight line is the power-law equation representing the transversal scaling.

72Perfect synchronization in networks of Sakaguchi-Kuramoto oscillators
Prosenjit Kundu1, Chittaranjan Hens2, Baruch Barzel3, and Pinaki Pal4
1
Department of Mathematics, State University of New York at Buffalo, Buffalo, New York, USA
2
Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata, India
3
Departmrnt of Mathematics, Bar-Ilan University, Ramat-Gan, Israel
4
Department of Mathematics, National Institute of Technology, Durgapur, India
From the power grid to neuronal networks, synchronization phenomena have found diverse and pertinent
applications capturing the emergence of collective behavior in complex systems. However, the common scenario
where the coupling between the system’s components induces phase-lags avoid global synchronization evenunder extremely strong coupling or with a homogeneous frequency.
Here we show that such systems𝑑𝜃!
= 𝜔! + 𝐾 ) A"# sin (𝜃$ − 𝜃! − 𝛼!$ )𝑑𝑡$

can still exhibit perfect synchronization with the appropriate choice of the nodes’ frequencies ω𝜔! = − ) 𝐴!$ 𝑠𝑖𝑛6− 𝛼!$ 7 +$1) 𝐴!$ 𝑠𝑖𝑛(− 𝛼!$ )𝑁!,$

Where, A is the connectivity matrix. 𝜃, 𝛼 & 𝐾 are phase, lag and coupling strength respectively.
We find that high levels of synchronization are sustained in the vicinity of the optimal set, allowing for somelevel of deviation in the frequencies without significant degradation of synchronization. Demonstrating our
results on first and second-order phase-frustrated Kuramoto dynamics, we implement them on both synthetic andreal power grid networks, showing how to achieve synchronization in a phase-frustrated environment.

Figure 1: (a) Synchronization order parameter r of a phase-frustrated scale-free oscillator network of SK
oscillators with different selections of ω by numrically solving the SK model. (b) Increasing thecoupling strengths K we find that the system persistently avoids synchronization even for large K, under
the general frequency distributions. Synchronization is only obtained using our optimal ω.
[1] Pikovsky A., Rosenblum M. and Kurths J., Synchronization: A Universal Concept in Nonlinear Sciences(Cambridge University Press, Cambridge, England) 2003.
[2] Kundu P., Hens C., Barzel B. and Pal P., Europhys. Lett. 120 (2017) 40001.

73

Optimal control problem of variable order fractional systems with Riemann–Liouville
derivative
Touria Karite1 , Adil Khazari2 and Delfim F. M. Torres3
LISA Laboratory, Electrical Engineering and Informatics Department,
National School of Applied Sciences, Sidi Mohamed Ben Abdellah University, Fez, Morocco
touria.karite@usmba.ac.ma
2
LAMA Laboratory, National School of Commerce and Managment,
Sidi Mohamed Ben Abdellah University, Fez, Moroccoadil.khazari@usmba.ac.ma
3
CIDMA center, Department of Mathematics, University of Aveiro,
3810-193 Aveiro, Portugaldelfim@ua.pt
1

Abstract

System analysis consists of studying a set of concepts allowing a better knowledge of its properties. Among these notions, there are controllability, observability,
stability, stabilization, detectability, spreadability, and so forth. The ability to formulate evolutionary governing equations has led to the successful application of variable
order fractional operators to the modeling of complex real-world problems ranging
from mechanics, to transport processes, to control theory, to biology. Variable-order
fractional computation is a relatively less known branch of computation that offers
remarkable opportunities to simulate interdisciplinary processes. They are a powerfulmathematical tool that are acknowledged as an alternative and precise approach in effectively describing real-world phenomena. In this paper we are interested in studying
the problem of optimal control of fractional system with variable order operator. The
fractional time derivative is considered in Riemann–Liouville sense. We first study the
problem by using the Lax-Milgram Theorem, the existence and the uniqueness of thesolution of the variable order fractional differential system in a Hilbert space. Then
we show that the considered optimal control problem has a unique solution.
References[1] C.F. Lorenzo and T.T. Hartley, Variable order and distributed order fractional operators, Nonlinear Dynam. Vol. 29, No. 1 (2002) 57-98.
[2] H.G. Sun, W. Chen, H. Wei and Y. Chen, A comparative study of constant-order and variableorder fractional models in characterizing memory property of systems. Eur. Phys. J. Spec.
Top. Vol. 193, No. 1 (2011) 185-192.
[3] R. Almeida, D. Tavares and D.F.M. Torres, The Variable-Order Fractional Calculus of Variations, Springer International Publishing, 201974

Detecting Fraudulent Users in Online Marketplaces Using Temporal Motifs
Rupam Acharyya1 , Penghang Liu2 , Ahmet Erdem Sariyüce2 , Naoki Masuda1,3
Department of Mathematics, University at Buffalo, Buffalo, NY, USA
Department of Computer Science and Engineering, University at Buffalo, Buffalo, NY, USA
3
Computational and Data-Enabled Science and Engineering Program, University at Buffalo, Buffalo, NY, USA
1

2

Over the years online marketplaces have become a fast moving and popular part of the e-commerce industry. Unfortunately, such rapid growth often results in increases in fraudulent transactions. Detecting fraudulent transactions
has since been a challenge in the field of AI when designing applications for the e-commerce industry. Researchers
have borrowed techniques and algorithms from, for example, natural language processing or computer vision in determining fraudulent behavior. One prime drawback of these techniques is that fraudsters can easily outwit them with thehelp of encrypted communication. Another complementary approach towards detecting fraudulent users is to explore
the local (i.e., egocentric) transaction network of individual users. (By convention, each transaction is a directed edge
from seller to buyer.) In Ref. [1], the authors analyzed egocentric networks of users in an online marketplace, Mercari
Inc. They showed that indices derived from static local network fed to standard machine learning algorithms werecapable of distinguishing fraudulent users from normal users with a high accuracy. In the current work, we extend
their work by analyzing the temporal transaction network of Mercari.
We start with a user which is manually labeled as normal or fraudulent (known as seed user) and create the egocentric network for them by adding its neighbors and the connections among the neighbors. Crucially, each transaction
between users is time-stamped. Then, we examine the abundance of consecutive transactions in this network that
occur within a small time span (i.e., 6 days for this work), which are known as temporal network motifs. We consider
motifs with two nodes and two edges that contain a seed user. Note that these seed users may also be involved in otherselling and buying transactions. First, we show that the abundance of static counterpart of such motifs (in particular,
the one to the left in Fig. 1A) is considerably different between the normal and fraudulent users. Then, we observethat the number of each type of temporal motifs in the local network of fraudulent users is considerably higher thanthat of normal users except for the most frequent type of temporal motif (see Fig. 1B). Finally, we use these countsof each type of static and temporal motifs in the local network as features to a random forest classifier. We find thatthe classification performance improves by adding the temporal motif features (see Fig. 1C). We are currently further
exploring temporal motifs of larger size to obtain more insight and better classification accuracy.
References[1] S. Kodate, R. Chiba, S. Kimura, and N. Masuda. Applied Network Science, 5:90, 2020.

Average motif countA

NormalFraudulent

B

C

t1

Static motif types

t2

t1
t2

t1

t1

t2

t2

Temporal motif types

Feature type
Degree features (sameas [1])
Degree features+ Static motifs
Degree features 

+ Static motifs 

+ Temporal motifs

AUC
ROC
0.62
0.64
0.65

Figure 1: Average count of static (A) and temporal (B) network motifs with two nodes and two edges. The green circle denotes theseed user, and t1 and t2 are the timestamps of the first and second events in the temporal motif, respectively. The error bar indicatesthe standard error. (C) Area under the curve receiver operating characteristics (AUC-ROC) curve as a measure of classification
performance. It improves when temporal and static motif counts are added to the degree features from [1].

75Extreme financial losses and gains: mutually-exciting arrivals or conditional volatility?
Matthew F. Tomlinson1∗ , David Greenwood2 , and Marcin Mucha-Kruczyński1
Department of Physics, University of Bath, Bath BA2 7AY, United Kingdom
CheckRisk LLP, 4 Miles’s Buildings, George Street, Bath BA1 2QS, United Kingdom∗
mft28@bath.ac.uk
1

2

Self-exciting bursts of extreme activity are observed in many disparate complex systems, including seismic shocks, neural networks, and financial returns. Statistical models that describe thisclustering offer potential insight into the mechanisms behind such extreme events. We construct a
two-tailed peaks-over-threshold Hawkes model that captures asymmetric self- and cross-excitationin and between left- and right-tail extreme values within a time series and apply it to extreme gains
and losses within the daily log-returns of developed market equity indices [1]. We find that thearrivals of extreme losses and gains are described by a common conditional intensity to which
losses contribute twice as much as gains. However, the contribution of the former decays almost
five times more quickly than that of the latter. We attribute these asymmetries to the different
reactions of market traders to extreme upward and downward price movements: an example ofnegativity bias, wherein trauma is more salient than euphoria. When compared against standard
conditional volatility description of returns, our model of mutually-exciting extremes is found to
more accurately forecast out-of-sample extreme values. This suggests a fundamental distinctionin the data-generating process for extreme versus bulk returns – a signature that could potentiallyconstrain different classes of systems or characterise different regimes within the same system.
′′t / td−1

8005

8075

λ ← = μ ← + 0.61 0.20 χ ←μ→0.66 0.25 χ →
λ→

SPX

0.0

4

0.00

α ← = 0.5
α → = 322.4

0.05

μt

κ⇋⇋m⇋)
00.25

λ⇋ [χ⇋] / td−1

t / td−150−1β ← = 0.064 td
β → = 0.015 td−10ϕ⇋⇋t )

0.1

0F⇋⇋m⇋)

1t / td−1

8005

8075

−0.05

Figure 1: Bivariate 2T-POT Hawkes model fitted to historic S&P 500 daily log-returns [1]. Left:endogenous excitement time kernels φ and excess magnitude impact functions κ. Right: response(top, equation shows fitted values of the branching matrix Γ) of the conditional intensities λ andendogenous excitements χ to a cluster of extreme S&P 500 log-returns (bottom, excesses in bold).
References[1] M. F. Tomlinson et al., arXiv:2011.12291 [q-n.ST] (2020).
76

Defining extremism in opinion models
André C. R. Martins1
1

Universidade de São Paulo, São Paulo, Brazil
amartins@usp.br

Extremism, how it appears and spreads, is one of the main questions studied by opinion dynamics models. And yet, there is no consensus on how to define it mathematically. Even more worrying, theconcept of what being an extremist means can be very different when
we look at distinct classes of models. When opinions are represented
by a continuous number, extremists are often associated with views
that lie on the edges of the range of possible values. On the other
hand, discrete models, where there is no range, identify extremism
as an inability to change opinions. Those definitions are inspired by
the mathematical details and limitations of each class. To better understand how those concepts relate to each other, or how they do not,we need more general models where the more traditional and simpler
versions can be seen as special cases.
An extension of the Continuous Opinions and Discrete Actions(CODA) model has been suggested as a generalization of both discrete and continuous opinion models. Those extensions explore theBayesian-inspired ideas of the initial model to create new models
from assumptions about the agents’ view of the world. In this talk,I will show how to generalize the CODA model so that the generalcase where there is any number of discrete choices can be treated. The
model parameters allow us to describe situations where those choices
are all equivalent and the case where they can be better described as
positions over a political decision space. Since there is a strength ofopinion associated with those choices, this model allows us to distinguish what it means to be at the edge of the spectrum versus an inability to learn due to strong positions. As extremism is a problem related
to tragic actions, I will discuss why it might be more related, from amathematical point of view, to a inability to change one’s mind, represented in the model by the strength of the agent opinion, then by the
position over a range of possible opinions.

Figure 1: Opinion landscapes showing final preferences for M = 5 choices
model after T = 50 average interactions per agent.
Each color corresponds
to a specific choice, andopinion strength is shownby a lighter (weaker opinion) to darker (stronger)hue.

Acknowledgments
This work was supported by the Fundação de Amparo a Pesquisa do Estado de São Paulo (FAPESP)
under grant 2019/26987-2.
77

Longitudinal Subject Fluency Networks of Psychology and Biology Students
Cynthia S. Q. Siew1,* & Anutra Guru1
1
Department of Psychology, National University of Singapore*
corresponding author; email: cynthia@nus.edu.sg
Within the cognitive sciences, the category fluency task (i.e., list as many items from thesemantic category of animals) is commonly used to investigate the representation of concepts
within semantic memory [1]. Fluency responses can be represented as networks ofinterconnected concepts [2]. We attempted to use this task to investigate how knowledge
representation of an academic domain (e.g., biology and psychology) might change over thecourse of a semester. 200 students enrolled in introductory psychology and 200 students enrolled
in introductory biology participated. Students were asked to complete a subject fluency task
where they listed as many concepts as they could (in 2 minutes) for their respective course (i.e.,
psychology students provided fluency responses for the domain of psychology). The same groupof students completed the task at the beginning (pre-network) and at the end of the semester(post-network). Subject fluency networks were estimated using various network estimation
methods (e.g., [3]) and bootstrapping analyses were conducted to statistically compare networks
on global network measures (ASPL, CC) and community structure (using the Louvain method[4]). Although post-networks tended to have lower ASPL and higher CC than pre-networks,
possibly reflecting increased network connectivity that we had hypothesized to reflect increasing
domain expertise, bootstrapping analyses indicated that these differences were not stable acrossdifferent network estimation methods. This work illustrates both the potential and challenges
associated with investigating knowledge representations using the category fluency task.
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ratFigure 1. Biology (left) and psychology (right) fluency networks at the beginning and the end of
the semester as generated by the community network estimation method.
[1] Bousfield, W. A., & Sedgewick, C. H. W. (1944). An analysis of sequences of restricted associative
responses. The Journal of General Psychology, 30, 149–165.
[2] Kenett, Y. N., Anaki, D., & Faust, M. (2014). Investigating the structure of semantic networks in low
and high creative persons. Frontiers in Human Neuroscience, 8, 407.
[3] Goñi, J., Arrondo, G., Sepulcre, J., Martincorena, I., de Mendizábal, N. V., Corominas-Murtra, B., . . .
Villoslada, P. (2011). The semantic organization of the animal category: Evidence from semantic verbal
fluency and network theory. Cognitive Processing, 12, 183–196.
[4] Blondel, V. D., Guillaume, J.-L., Lambiotte, R., & Lefebvre, E. (2008). Fast unfolding ofcommunities in large networks. Journal of Statistical Mechanics: Theory and Experiment, P10008.

78

Emergence of Risk Sensitivity in a First-principles Agent-based model
F. Bertolotti1, A. Locoro1, L. Mari1.(1)Università Cattaneo - LIUC, Castellanza (VA), Italy,{fbertolotti, alocoro, lmari}@liuc.it

Risk aversion and risk-seeking are acknowledged features of human and non-human behaviour. Biology
identifies risk-sensible behaviours in various species like non-human animals, plants and bacteria. Risk
preferences also appear at a super-human level, such as in organizations. The risk sensitivity of different
entities seems to be shaped by the same underlying principles. Thus, there could be a regularity concerningwherewith living entities originate risk-sensible behaviour. Some existent works examine this occurrence
through computer simulations. They show that risk preferences can arise under evolutive forces when
individuals interact in unsafe conditions. Other works propose a perspective that includes the role ofcultural processes.
The goal of this work is to identify risk sensitivity emergence from both cultural and genetic adaptation.
Moreover, it aims at finding relationships between this emergence, the adaptation styles and theenvironmental variables. It presents an agent-based model in which a single variety of agents exists on a
two-dimensional toroidal surface divided into squared cells. Each cell can either contain an energy sourceor be empty. Energy sources have an initial level of energy, progressively drained by agents. Once anenergy source is consumed, it disappears and another one appears in a different cell. Agents use a given
amount of energy at each time step. When an agent terminates energy, it dies. It implies that agentsnecessitate recharging to survive. There are two alternatives to do it. An agent can head towards an energy
source and supply from it. Otherwise, it can move towards a different agent and attack it with a given
probability of success. Therefore, both attacking and defending agents can win. We analysed scenarioswith various chances of victory. A winning agent subtracts a share of energy from the disputant. So, themodel forces agents to decide between a risky and safe opportunity. For each possibility, agents computea payoff, which is the distance from the option times the desirability of that specific event. Risk sensitivity
is the difference between risk proneness and risk aversion of agents. Each agent has two risk sensitivities.
One is genetic, and it is inherited from parents. The other comes from individual learning and thetransmission (partial or complete) of the experience to offsprings. Distinct simulations consider
populations that give different importance to knowledge and genotype (i.e. the adaptation style).

Figure 1: Risk sensitivity of population plotted on the dangerousness of the system with respect to different style of adaptation,from evolution (left) to learning (right)

The simulation of the model confirms both risk aversion and risk-seeking behaviours emerge from theinteraction of agents. A relationship between environmental variables and the emergence of risk
sensitivity is found. This link seems to be affected by the adaptation style. Besides, it seems to exist a
non-monotonic non-linear relationship between environmental dangerousness and the emergence of risk
sensitivity (Figure 1). We propose this is due to the combination of two elements: the existence of
incentives to develop risk preferences, which varies with the dangerousness of the surroundings; the direct
relationship between the harshness of the environment and how beneficial is the development of risk
preferences. The simplicity of this model indicates that these findings could apply to different application
fields. Future studies include the generalization of the results and the identification of connections
between the pace of life and the emergence of risk preferences.

79

A Modular Common Pool Resource Model with Social Planning
Andreas Pape and Peter DiCola
Ostrom’s famous Principles of Polycentric Governance (Ostrom, 1990) are characteristics of institutions that manage common pool resources (CPRs) that she found, from case studies, tend todescribe those that successfully administer those CPRs. This prompts the observation: If theseprinciples tend to improve management of CPRs by a community, and successful management
would increase the long-term viability of the community, then in an appropriately specified evolutionary, agent-based model, we should see the emergence of these principles. This project attempts
to validate this observation.
In this aspect of this larger project, we share a general, modular Common Pool Resource modelwith GA-driven agents who can seek to maximize their own or social benefit. We also provide a”Policy” framework and introduce a GA-driven social planner who selects among policies. We
show that in some CPRs, the social planner is able to find a policy to persuade ”selfish” agentsto behave like ”altruistic” ones; one aspect of the emergent policies is that they feature graduatedsanctions, which is one of Ostrom’s principles.

80Modeling behavioral experiments on uncertainty and cooperation with population-based
reinforcement learning – Extended Abstract
Elias Fernández Domingos1,2,*, Jelena Grujić1, Juan C. Burguillo3, Francisco C. Santos4, Tom
Lenaerts1,2
1
AI-Lab, Computer Science Department, Vrije Universiteit Brussel, Brussels, 1050, Belgium
2MLG, Département d'Informatique, Université Libre de Bruxelles, Brussels, 1050, Belgium
3
atlanTTic Research Center, Universidade de Vigo, 36310 Vigo, Spain
4
INESC-ID & IST, Universidade de Lisboa, 2744-016 Porto Salvo, Portugal*
elias.fernandez.domingos@vub.be
From climate action to public health measures,
defection dominanttransientcoordination
human collective endeavors are often shaped bydifferent uncertainties. In a manuscript recently
published in the Journal of Simulation Practice andTheory [1] we introduce a novel population-basedlearning model wherein a group of individuals
facing a collective risk dilemma [2] acquire theirstrategies over time through reinforcement
learning, while handling different sources of
uncertainty. In such an N-person collective risk
dilemma players make step-wise contributions to
Figure 1. Effect of risk on group avoid a catastrophe that would result in a loss ofachievement and average normalized payoff. wealth for all players. Success is attained if theycollectively reach a certain contribution level over time. The dilemma lies in the trade-off between
the proportion of personal contributions that players wish to give to collectively reach the goal andthe remainder of the wealth they can keep at the end of the game. This tradeoff is affected by therisk that a cataclysm will occur when the collective target is not reached, and all participants lose
their remaining wealth. Figure 1 shows that groups only start to successfully achieve the target
when the risk is higher than 0.5. We also show that the strategies learned with the model
correspond to those observed experimentally, even when there is uncertainty about either the riskof failing when the goal is not reached, the target that should be attained or the time available toreach it. Furthermore, we confirm that being unsure about the time-window favors more extreme
reactions and polarization, diminishing the number of agents that contribute fairly. The populationbased on-line learning framework we propose is general enough to be applicable in a wide rangeof collective action problems and arbitrarily large sets of available policies.
risk < costrisk > cost

References[1] Fernández Domingos, E., Grujić, J., Burguillo, J. C., Santos, F. C., & Lenaerts, T. (2021).
Modeling behavioral experiments on uncertainty and cooperation with population-based
reinforcement learning. Simulation Modelling Practice and Theory, 109, 102299.
[2] Milinski, M., Sommerfeld, R. D., Krambeck, H. J., Reed, F. A., & Marotzke, J. (2008). The
collective-risk social dilemma and the prevention of simulated dangerous climate change.
Proceedings of the National Academy of Sciences, 105(7), 2291-2294.

81

Evolution of brain networks after traumatic brain injury
Tong Wu1 , Matthew McGuire2,3 , David Poulsen2,3 , and Sarah F. Muldoon1,2,4
CDSE Program
Neuroscience Program3
Department of Neurosurgery
4
Department of Mathematics
University at Buffalo, State University of New York
1

2

The brain can be described as a complex network that evolves over time in both health and diseasestates. However, how to track meaningful or predictable changes in brain networks remains an unsolved
problem. In particular, brain dynamics are significantly altered in many brain diseases (e.g. in epilepsy or
Parkinson’s disease) which suggests that for early prevention and treatment, it is crucial to study changes inunderlying brain network structure that can give rise to these observed changes in brain network dynamics.
Changes in brain network structure associated with epileptogenesis are particularly pertinent in regards tothe development of post-traumatic epilepsy (PTE) resulting from traumatic brain injury (TBI). Diffusion
tensor imaging (DTI) can be used to measure such changes in white matter integrity measured through theFractional Anisotropy (FA) index and/or tractography analysis. In our study, we acquired in vivo DTI datafrom both TBI and uninjured control (sham) groups of rats in hopes of linking specific changes in brain
network structure to the process of epileptogenesis and the development of PTE. We find both increases anddecreases in FA values or certain regions, indicated network induced changes in brain structure resulting
from injury. Specifically, we see a reduction of the FA value in the right corpus callosum and primary
auditory cortex of TBI animals, likely representing the initial injury. However, also observe an increase in
the FA value for the left side parietal cortex, indicating that the injury results in more widespread changes
in brain network structure.

Figure 1: A) 3D reconstructed models of the corpus callosum from FA values. Red circle represents site of injury. B)(i) Mean FA values for the Corpus Callosum, (ii) Primary Auditory Cortex, and (iii) Parietal Cortex in Control (blue)
and TBI (red) groups for left and right hemispheres.

82

Optimizing Wind Farm Efficiency with Self-Adaptivity Mechanism in Evolutionary
Algorithm
Xinglong Ju1 and Feng Liu2
12

School of Civil and Environmental Engineering, Cornell University
School of Systems and Enterprises, Stevens Institute of Technology

1 Introduction
In the past decades, a significant amount of wind farms across the world have been constructed
to reduce greenhouse gas emission across the world. Numerous algorithms have been proposedto optimize layout of wind farms and reducing the impact of wake effect. Wake effect refers to
the input wind speed reduction after wind passing through the turbines in the upwind direction.
Genetic algorithm has been widely used to find the optimal solution of wind farm layout.
2 Methods
In this study, we devised an insightful bi-criteria identification and relocation (BCIR) mechanism ingenetic algorithm to alleviate the solutions trapping into suboptimal conditions. We introduce theInfluence Matrix (Fig.1(a)) to guide the bi-criteria wind turbine selection without adding additional
computational cost.
3 Results
The cost of energy comparison between existing algorithms [1] CGA, AGA, IGA, SIGA, IAGA,
and our proposed method (ISIGA) are illustrated in Fig.1(b), and ISIGA achieved the lowest energy
cost than other comparison algorithms.
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(a) Influence matrix(b) Performance comparison
Figure 1: Illustration of Influence Matrix (IM) (a) and cost of energy convergence curves (b).

4 Conclusions
Our algorithm demonstrated superior performance than the benchmark algorithms, which demonstrates the effectiveness of self-adaptivity (BCIR mechanism) in genetic algorithm.
References[1] Liu, F., Ju, X., etc. (2020). Wind farm macro-siting optimization with insightful bi-criteria
identification and relocation mechanism in genetic algorithm. ECM, 217, 112964.
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Resiliency of Global Medical Equipment Supply Chains
Zachary M. Boyd (Mathematics, UNC—Chapel Hill)and Kayvan Lavassani (Business, NC Central Univ.)
Several contemporary events, including cyber-attacks, terrorism, and COVID-19, havehighlighted the fragility of global supply chains (Sherkarian et al. 2020). One significant
challenge in studying the global supply chains is that companies are highly protective of theirtrade information, including the identity of suppliers and customers (Okeagu et al. 2021). Using
U.S. Security and Exchange Commission filings of all publicly-traded firms, we determined theglobal network of notable suppliers and customers involved in medical equipment firm (MEF)
supply across ten tiers. That is, starting at MEFs (tier 0), we found their suppliers (tier 1), thenthese suppliers’ suppliers (tier 2), and so on, capturing the complex set of relationships required
to go from raw materials to usable medical equipment. This is the most extensive medical supply
chain network in existence and is the largest possible data set of this kind.
We investigated network resiliency
under random disruptions, as well as
centrality-based and firm-size-based failures.
This included individual firm disruptions anddisruptions at the level of industries, countries,
and country-industries. In order to understandlong-range supply dependencies, we focusedon reachability of MEFs’ end suppliers. A
firm’s end suppliers are the highest-tier (i.e.
most distant in the network) suppliers on
which they rely. These end suppliers may be
producing raw materials that must go throughseveral intermediate parties before being usedin medical devices, and disruption in those
Ability of medical supply firms to reach end
intermediate links interferes with MEF
suppliers when other firms fail in random or
operations. We say that an end supplier B istargeted ways.
reachable by a particular firm A if there is achain of supply relationships from A to B.
We find that the MEF supply chain is vulnerable to both random and targeted disruptions.
For example, random disruption of 10% of firms causes MEFs to be able to reach only 60% of
their end suppliers, with 20% of MEFs unable to reach any end suppliers. For targeted attacks or
random failures correlated with firm size, the situation is much worse: with 10% firm disruption,
MEFs can only reach 20% of their end suppliers on average. We also consider more specificscenarios. For example, if US-China trade relationships broke down, China’s MEFs could reachon average 57% of their end suppliers, while the US MEFs are essentially unaffected.
References
Shekarian M., Nooraie S.V.R., Parast M.M. (2020). An examination of the impact of flexibility
and agility on mitigating supply. Intr. J. Production Econ., 220, pp 1-16.
Okeagu C.N., et al. (2021). Principles of supply chain management in the time of crisis. Best
Practice & Research Clinical Anaesthesiology, in press.
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