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Advancements in multimodal Large Language Models (LLMs), such as OpenAI's GPT-4o, offer significant potential for mediating human interactions across various contexts. However, their use in areas such as persuasion, influence, and recruitment raises ethical and security concerns. To evaluate these models ethically in public influence and persuasion scenarios, we developed a prompting strategy using "Where's Waldo?" images as proxies for complex, crowded gatherings. This approach provides a controlled, replicable environment to assess the model's ability to process intricate visual information, interpret social dynamics, and propose engagement strategies while avoiding privacy concerns. By positioning Waldo as a hypothetical agent tasked with face-to-face mobilization, we analyzed the model's performance in identifying key individuals and formulating mobilization tactics. Our results show that while the model generates vivid descriptions and creative strategies, it cannot accurately identify individuals or reliably assess social dynamics in these scenarios. Nevertheless, this methodology provides a valuable framework for testing and benchmarking the evolving capabilities of multimodal LLMs in social contexts., Comment: 11 pages, 2 figures, 2 tables

In this paper we showcase the strengths of polarized neutron imaging as a magnetic imaging technique through a case study on field-cooled multifilamentary YBCO tape carrying a transport current while containing a trapped magnetic field. The measurements were done at J-PARC's RADEN beamline, measuring a radiograph of a single polarization component, to showcase the analysis potential with minimal acquisition time. Regions of internal damage are easily and accurately identified as the technique probes the internal magnetic field of the sample, thereby avoiding surface-smearing effects. Quantitative measurements of the integrated field strength in various regions are acquired using time-of-flight information. Finally, we estimate the strength of the screening currents in the superconductor during the experiment by simulating an experiment with a model sample and comparing it to the experimental data. With this, we show that polarized neutron imaging is not only a useful tool for investigating magnetic structures but also for investigating samples carrying currents., Comment: 6 pages, 4 figures with total of 6 or 7 images (some bundles, some seperate)

Large language models (LLMs) are increasingly used to model human social behavior, with recent research exploring their ability to simulate social dynamics. Here, we test whether LLMs mirror human behavior in social dilemmas, where individual and collective interests conflict. Humans generally cooperate more than expected in laboratory settings, showing less cooperation in well-mixed populations but more in fixed networks. In contrast, LLMs tend to exhibit greater cooperation in well-mixed settings. This raises a key question: Are LLMs about to emulate human behavior in cooperative dilemmas on networks? In this study, we examine networked interactions where agents repeatedly engage in the Prisoner's Dilemma within both well-mixed and structured network configurations, aiming to identify parallels in cooperative behavior between LLMs and humans. Our findings indicate critical distinctions: while humans tend to cooperate more within structured networks, LLMs display increased cooperation mainly in well-mixed environments, with limited adjustment to networked contexts. Notably, LLM cooperation also varies across model types, illustrating the complexities of replicating human-like social adaptability in artificial agents. These results highlight a crucial gap: LLMs struggle to emulate the nuanced, adaptive social strategies humans deploy in fixed networks. Unlike human participants, LLMs do not alter their cooperative behavior in response to network structures or evolving social contexts, missing the reciprocity norms that humans adaptively employ. This limitation points to a fundamental need in future LLM design -- to integrate a deeper comprehension of social norms, enabling more authentic modeling of human-like cooperation and adaptability in networked environments.

Postdoctoral training is a career stage often described as a demanding and anxiety-laden time when many promising PhDs see their academic dreams slip away due to circumstances beyond their control. We use a unique data set of academic publishing and careers to chart the more or less successful postdoctoral paths. We build a measure of academic success on the citation patterns two to five years into a faculty career. Then, we monitor how students' postdoc positions -- in terms of relocation, change of topic, and early well-cited papers -- relate to their early-career success. One key finding is that the postdoc period seems more important than the doctoral training to achieve this form of success. This is especially interesting in light of the many studies of academic faculty hiring that link Ph.D. granting institutions and hires, omitting the postdoc stage. Another group of findings can be summarized as a Goldilocks principle: it seems beneficial to change one's direction, but not too much.

Temporality, a crucial characteristic in the formation of social relationships, was used to quantify the long-term time effects of networks for link prediction models, ignoring the heterogeneity of time effects on different time scales. In this work, we propose a novel approach to link prediction in temporal networks, extending existing methods with a cognitive mechanism that captures the dynamics of the interactions. Our approach computes the weight of the edges and their change over time, similar to memory traces in the human brain, by simulating the process of forgetting and strengthening connections depending on the intensity of interactions. We utilized five ground-truth datasets, which were used to predict social ties, missing events, and potential links. We found: (a) the cognitive mechanism enables more accurate capture of the heterogeneity of the temporal effect, leading to an average precision improvement of 9\% compared to baselines with competitive AUC. (b) the local structure and synchronous agent behavior contribute differently to different types of datasets. (c) appropriately increasing the time intervals, which may reduce the negative impact from noise when dividing time windows to calculate the behavioral synchrony of agents, is effective for link prediction tasks., Comment: Equation 3 corrected, appendix added, acknowledgment extended

A stylized experiment, the public goods game, has taught us the peculiar reproducible fact that humans tend to contribute more to shared resources than expected from economically rational assumptions. There have been two competing explanations for this phenomenon: either contributing to the public good is an innate human trait (the prosocial preference hypothesis) or a transitory effect while learning the game (the confused learner hypothesis). We use large-scale experimental data from a novel experimental design to distinguish between these two hypotheses. By monitoring the effects of zealots (persistently cooperating bots) and varying the participants' awareness of them, we find a considerably more complex scenario than previously reported. People indeed have a prosocial bias, but not to the degree that they always forego taking action to increase their profit. While our findings end the simplistic theorizing of prosociality in the public goods game, an observed positive, cooperative response to zealots has actionable policy implications.

To realize a global quantum Internet, there is a need for communication between quantum subnetworks. To accomplish this task, there have been multiple design proposals for a quantum backbone network and quantum subnetworks. In this work, we elaborate on the design that uses entanglement and quantum teleportation to build the quantum backbone between packetized quantum networks. We design a network interface to interconnect packetized quantum networks with entanglement-based quantum backbone networks and, moreover, design a scheme to accomplish data transmission over this hybrid quantum network model. We analyze the use of various implementations of the backbone network, focusing our study on backbone networks that use satellite links to continuously distribute entanglement resources. For feasibility, we analyze various system parameters via simulation to benchmark the performance of the overall network., Comment: Accepted for publication in IEEE Communication Magazine

Purpose: To develop a generic radial sampling scheme that combines the advantages of golden ratio sampling with simplicity of equidistant angular patterns. The irrational angle between consecutive spokes in golden ratio based sampling schemes enables a flexible retrospective choice of temporal resolution, while preserving good coverage of k-space for each individual bin. Nevertheless, irrational increments prohibit precomputation of the point-spread function (PSF), can lead to numerical problems, and require more complex processing steps. To avoid these problems, a new sampling scheme based on a rational approximation of golden angles (RAGA) is developed. Methods: The theoretical properties of RAGA sampling are mathematically derived. Sidelobe-to-peak ratios (SPR) are numerically computed and compared to the corresponding golden ratio sampling schemes. The sampling scheme is implemented in the BART toolbox and in a radial gradient-echo sequence. Feasibility is shown for quantitative imaging in a phantom and a cardiac scan of a healthy volunteer. Results: RAGA sampling can accurately approximate golden ratio sampling and has almost identical PSF and SPR. In contrast to golden ratio sampling, each frame can be reconstructed with the same equidistant trajectory using different sampling masks, and the angle of each acquired spoke can be encoded as a small index, which simplifies processing of the acquired data. Conclusion: RAGA sampling provides the advantages of golden ratio sampling while simplifying data processing, rendering it a valuable tool for dynamic and quantitative MRI., Comment: 27 pages, 7 figures, 3 tables

A popular way to cluster a temporal network is to transform it into a sequence of networks, also called slices, where each slice corresponds to a time interval and contains the vertices and edges existing in that interval. A reason to perform this transformation is that after a network has been sliced, existing algorithms designed to find clusters in multilayer networks can be used. However, to use this approach, we need to know how many slices to generate. This chapter discusses how to select the number of slices when generalized modularity is used to identify the clusters.

Link prediction -- to identify potential missing or spurious links in temporal network data -- has typically been based on local structures, ignoring long-term temporal effects. In this chapter, we propose link-prediction methods based on agents' behavioral synchrony. Since synchronous behavior signals similarity and similar agents are known to have a tendency to connect in the future, behavioral synchrony could function as a precursor of contacts and, thus, as a basis for link prediction. We use four data sets of different sizes to test the algorithm's accuracy. We compare the results with traditional link prediction models involving both static and temporal networks. Among our findings, we note that the proposed algorithm is superior to conventional methods, with the average accuracy improved by approximately 2% - 5%. We identify different evolution patterns of four network topologies -- a proximity network, a communication network, transportation data, and a collaboration network. We found that: (1) timescale similarity contributes more to the evolution of the human contact network and the human communication network; (2) such contribution is not observed through a transportation network whose evolution pattern is more dependent on network structure than on the behavior of regional agents; (3) both timescale similarity and local structural similarity contribute to the collaboration network.

Analytical studies of network epidemiology almost exclusively focus on the extreme situations where the time scales of network dynamics are well separated (longer or shorter) from that of epidemic propagation. In realistic scenarios, however, these time scales could be similar, which has profound implications for epidemic modeling (e.g., one can no longer reduce the dimensionality of epidemic models). We build a theory for the critical behavior of susceptible-infected-susceptible (SIS) epidemics in the vicinity of the critical threshold on the activity-driven model of temporal networks. We find that the persistence of links in the network leads to increasing recovery rates reducing the threshold. Dynamic correlations (coming from being close to infected nodes increases the likelihood of infection) drive the threshold in the opposite direction. These two counteracting effects make epidemic criticality in temporal networks a remarkably complex phenomenon.

Although the origin of the fat-tail characteristic of the degree distribution in complex networks has been extensively researched, the underlying cause of the degree distribution characteristic across the complete range of degrees remains obscure. Here, we propose an evolution model that incorporates only two factors: the node's weight, reflecting its innate attractiveness (nature), and the node's degree, reflecting the external influences (nurture). The proposed model provides a good fit for degree distributions and degree ratio distributions of numerous real-world networks and reproduces their evolution processes. Our results indicate that the nurture factor plays a dominant role in the evolution of social networks. In contrast, the nature factor plays a dominant role in the evolution of non-social networks, suggesting that whether nodes are people determines the dominant factor influencing the evolution of real-world networks., Comment: 8pages, 4 figures

Influence maximization (IM) is an important topic in network science where a small seed set is chosen to maximize the spread of influence on a network. Recently, this problem has attracted attention on temporal networks where the network structure changes with time. IM on such dynamically varying networks is the topic of this review. We first categorize methods into two main paradigms: single and multiple seeding. In single seeding, nodes activate at the beginning of the diffusion process, and most methods either efficiently estimate the influence spread and select nodes with a greedy algorithm, or use a node-ranking heuristic. Nodes activate at different time points in the multiple seeding problem, via either sequential seeding, maintenance seeding or node probing paradigms. Throughout this review, we give special attention to deploying these algorithms in practice while also discussing existing solutions for real-world applications. We conclude by sharing important future research directions and challenges.

This is a comment on a recent review article about reputation and reciprocity as mechanisms promoting cooperation. I also discuss the necessary changes for the currently game-theory-based cooperation studies to become a complete theory of cooperation in our contemporary society.

Influence maximization (IM) is the task of finding the most important nodes in order to maximize the spread of influence or information on a network. This task is typically studied on static or temporal networks where the complete topology of the graph is known. In practice, however, the seed nodes must be selected before observing the future evolution of the network. In this work, we consider this realistic ex ante setting where $p$ time steps of the network have been observed before selecting the seed nodes. Then the influence is calculated after the network continues to evolve for a total of $T>p$ time steps. We address this problem by using statistical, non-negative matrix factorization and graph neural networks link prediction algorithms to predict the future evolution of the network and then apply existing influence maximization algorithms on the predicted networks. Additionally, the output of the link prediction methods can be used to construct novel IM algorithms. We apply the proposed methods to eight real-world and synthetic networks to compare their performance using the Susceptible-Infected (SI) diffusion model. We demonstrate that it is possible to construct quality seed sets in the ex ante setting as we achieve influence spread within 87\% of the optimal spread on seven of eight network. In many settings, choosing seed nodes based only historical edges provides results comparable to the results treating the future graph snapshots as known. The proposed heuristics based on the link prediction model are also some of the best-performing methods. These findings indicate that, for these eight networks under the SI model, the latent process which determines the most influential nodes may not have large temporal variation. Thus, knowing the future status of the network is not necessary to obtain good results for ex ante IM.

Let $k$ be an algebraically closed field of characteristic $p > 3$ and $S$ be a smooth projective surface over $k$ with $k$-rational point $x$. For $n \geq 2$, let $S^{[n]}$ denote the Hilbert scheme of $n$ points on $S$. In this note, we compute the fundamental group scheme $\pi^{\textrm{alg}}(S^{[n]}, \tilde{nx})$ defined by the Tannakian category of stratified bundles on $S^{[n]}$., Comment: 13 pages

Academic publishing is the principal medium of documenting and disseminating scientific discoveries. At the heart of its daily operations are the editorial boards. Despite their activities and recruitment often being opaque to outside observers, they play a crucial role in promoting fair evaluations and gender parity. Literature on gender inequality lacks the connection between women as editors and as research-active scientists, thereby missing the comparison between the gender balances in these two academic roles. Literature on editorial fairness similarly lacks longitudinal studies on the conflicts of interest arising from editors being research active, which motivates them to expedite the publication of their papers. We fill these gaps using a dataset of 103,000 editors, 240 million authors, and 220 million publications spanning five decades and 15 disciplines. This unique dataset allows us to compare the proportion of female editors to that of female scientists in any given year or discipline. Although women are already underrepresented in science (26%), they are even more so among editors (14%) and editors-in-chief (8%); the lack of women with long-enough publishing careers explains the gender gap among editors, but not editors-in-chief, suggesting that other factors may be at play. Our dataset also allows us to study the self-publication patterns of editors, revealing that 8% of them double the rate at which they publish in their own journal soon after the editorship starts, and this behavior is accentuated in journals where the editors-in-chief self-publish excessively. Finally, men are more likely to engage in this behaviour than women.

Spin--orbit interaction (SOI) plays a fundamental role in many low-dimensional semiconductor and hybrid quantum devices. In the rapidly evolving field of semiconductor spin qubits, SOI is an essential ingredient that can allow for ultrafast qubit control. The exact manifestation of SOI in a given device is, however, often both hard to predict theoretically and probe experimentally. Here, we develop a detailed theoretical connection between the leakage current through a double quantum dot in Pauli spin blockade and the underlying SOI in the system. We present a general analytic expression for the leakage current, which allows to connect experimentally observable features to both the magnitude and orientation of the effective spin--orbit field acting on the moving carriers. Motivated by the large recent interest in hole-based quantum devices, we further zoom in on the case of Pauli blockade of hole spins, assuming a strong transverse confinement potential. In this limit we also find an analytic expression for the current at low external magnetic field, that includes the effect of hyperfine coupling of the hole spins to randomly fluctuating nuclear spin baths. This result can be used to extract detailed information about both hyperfine and spin--orbit coupling parameters for hole spins in devices with a significant fraction of non-zero nuclear spins., Comment: 9 pages, 5 figures

Purpose: To develop a deep-learning-based image reconstruction framework for reproducible research in MRI. Methods: The BART toolbox offers a rich set of implementations of calibration and reconstruction algorithms for parallel imaging and compressed sensing. In this work, BART was extended by a non-linear operator framework that provides automatic differentiation to allow computation of gradients. Existing MRI-specific operators of BART, such as the non-uniform fast Fourier transform, are directly integrated into this framework and are complemented by common building blocks used in neural networks. To evaluate the use of the framework for advanced deep-learning-based reconstruction, two state-of-the-art unrolled reconstruction networks, namely the Variational Network [1] and MoDL [2], were implemented. Results: State-of-the-art deep image-reconstruction networks can be constructed and trained using BART's gradient based optimization algorithms. The BART implementation achieves a similar performance in terms of training time and reconstruction quality compared to the original implementations based on TensorFlow. Conclusion: By integrating non-linear operators and neural networks into BART, we provide a general framework for deep-learning-based reconstruction in MRI., Comment: Submitted to Magnetic Resonance in Medicine

This is an essay about understanding complexity science, via some peculiarities of the field, as a meeting place for a special kind of scientist. It comes out of my hobby of reading popular-science complex systems books, and builds on notes that have been collecting dust for almost a decade.

Purpose: To develop a free-breathing myocardial T1 mapping technique using inversion-recovery (IR) radial fast low-angle shot (FLASH) and calibrationless motion-resolved model-based reconstruction. Methods: Free-running (free-breathing, retrospective cardiac gating) IR radial FLASH is used for data acquisition at 3T. First, to reduce the waiting time between inversions, an analytical formula is derived that takes the incomplete T1 recovery into account for an accurate T1 calculation. Second, the respiratory motion signal is estimated from the k-space center of the contrast varying acquisition using an adapted singular spectrum analysis (SSA-FARY) technique. Third, a motion-resolved model-based reconstruction is used to estimate both parameter and coil sensitivity maps directly from the sorted k-space data. Thus, spatiotemporal total variation, in addition to the spatial sparsity constraints, can be directly applied to the parameter maps. Validations are performed on an experimental phantom, eleven human subjects, and a young landrace pig with myocardial infarction. Results: In comparison to an IR spin-echo reference, phantom results confirm good T1 accuracy when reducing the waiting time from five seconds to one second using the new correction. The motion-resolved model-based reconstruction further improves precision compared to the spatial regularization-only reconstruction. Aside from showing that a reliable respiratory motion signal can be estimated using modified SSA-FARY, in vivo studies demonstrate that dynamic myocardial T1 maps can be obtained within two minutes with good precision and repeatability. Conclusion: Motion-resolved myocardial T1 mapping during free-breathing with good accuracy, precision and repeatability can be achieved by combining inversion-recovery radial FLASH, self-gating and a calibrationless motion-resolved model-based reconstruction., Comment: Part of this work has been presented at the ISMRM Annual Conference 2021 (Virtual), accepted by Magnetic Resonance in Medicine

Qubits encoded in the spin state of heavy holes confined in Si- and Ge-based semiconductor quantum dots are currently leading the efforts toward spin-based quantum information processing. The virtual absence of spinful nuclei in purified samples yields long qubit coherence times and the intricate coupling between spin and momentum in the valence band can provide very fast spin-orbit-based qubit control, e.g., via electrically induced modulations of the heavy-hole $g$-tensor. A thorough understanding of all aspects of the interplay between spin-orbit coupling, the confining potentials, and applied magnetic fields is thus quintessential for the development of the optimal hole-spin-based qubit platform. Here we theoretically investigate the manifestation of the effective $g$-tensor and effective mass of heavy holes in two-dimensional hole gases as well as in lateral quantum dots. We include the effects of the anisotropy of the effective Luttinger Hamiltonian (particularly relevant for Si-based systems) and we focus on the detailed role of the orientation of the transverse confining potential. We derive most general analytic expressions for the anisotropic $g$-tensor and we present a general and straightforward way to calculate corrections to this $g$-tensor for localized holes due to various types of spin-orbit interaction, exemplifying the approach by including a simple linear Rashba-like term. Our results thus contribute to the understanding needed to find optimal points in parameter space for hole-spin qubits, where confinement is effective and spin-orbit-mediated electric control over the spin states is efficient., Comment: 12 pages, 5 figures

Finding an optimal subset of nodes or links to disintegrate harmful networks is a fundamental problem in network science, with potential applications to anti-terrorism, epidemic control, and many other fields of study. The challenge of the network disintegration problem is to balance the effectiveness and efficiency of strategies. In this paper, we propose a cost-effective targeted enumeration method for network disintegration. The proposed approach includes two stages: searching for candidate objects and identifying an optimal solution. In the first stage, we use rank aggregation to generate a comprehensive ranking of node importance, upon which we identify a small-scale candidate set of nodes to remove. In the second stage, we use an enumeration method to find an optimal combination among the candidate nodes. Extensive experimental results on synthetic and real-world networks demonstrate that the proposed method achieves a satisfying trade-off between effectiveness and efficiency. The introduced two-stage targeted enumeration framework can also be applied to other computationally intractable combinational optimization problems, from team assembly via portfolio investment to drug design., Comment: 9 pages, 5 figures

Quantifying the structural and functional differences of temporal networks is a fundamental and challenging problem in the era of big data. This work proposes a temporal dissimilarity measure for temporal network comparison based on the fastest arrival distance distribution and spectral entropy based Jensen-Shannon divergence. Experimental results on both synthetic and empirical temporal networks show that the proposed measure could discriminate diverse temporal networks with different structures by capturing various topological and temporal properties. Moreover, the proposed measure can discern the functional distinctions and is found effective applications in temporal network classification and spreadability discrimination.

Recent decades have seen a rise in the use of physics methods to study different societal phenomena. This development has been due to physicists venturing outside of their traditional domains of interest, but also due to scientists from other disciplines taking from physics the methods that have proven so successful throughout the 19th and the 20th century. Here we dub this field 'social physics' and pay our respect to intellectual mavericks who nurtured it to maturity. We do so by reviewing the current state of the art. Starting with a set of topics that are at the heart of modern human societies, we review research dedicated to urban development and traffic, the functioning of financial markets, cooperation as the basis for our evolutionary success, the structure of social networks, and the integration of intelligent machines into these networks. We then shift our attention to a set of topics that explore potential threats to society. These include criminal behaviour, large-scale migrations, epidemics, environmental challenges, and climate change. We end the coverage of each topic with promising directions for future research. Based on this, we conclude that the future for social physics is bright. Physicists studying societal phenomena are no longer a curiosity, but rather a force to be reckoned with. Notwithstanding, it remains of the utmost importance that we continue to foster constructive dialogue and mutual respect at the interfaces of different scientific disciplines., Comment: 359 pages, 78 figures; published in Physics Reports

Social network analysis tools can infer various attributes just by scrutinizing one's connections. Several researchers have studied the problem faced by an evader whose goal is to strategically rewire their social connections in order to mislead such tools, thereby concealing their private attributes. However, to date, this literature has only considered static networks, while neglecting the more general case of temporal networks, where the structure evolves over time. Driven by this observation, we study how the evader can conceal their importance from an adversary armed with temporal centrality measures. We consider computational and structural aspects of this problem: Is it computationally feasible to calculate optimal ways of hiding? If it is, what network characteristics facilitate hiding? This topic has been studied in static networks, but in this work, we add realism to the problem by considering temporal networks of edges changing in time. We find that it is usually computationally infeasible to find the optimal way of hiding. On the other hand, by manipulating one's contacts, one could add a surprising amount of privacy. Compared to static networks, temporal networks offer more strategies for this type of manipulation and are thus, to some extent, easier to hide in., Comment: 27 pages, 9 figures, 3 tables. arXiv admin note: text overlap with arXiv:2102.10539

Differences in the social and economic environment across countries encourage humans to migrate in search of better living conditions, including job opportunities, higher salaries, security and welfare. Quantifying global migration is, however, challenging because of poor recording, privacy issues and residence status. This is particularly critical for some classes of migrants involved in stigmatised, unregulated or illegal activities. Escorting services or high-end prostitution are well-paid activities that attract workers all around the world. In this paper, we study international migration patterns of sex-workers by using network methods. Using an extensive international online advertisement directory of escorting services and information about individual escorts, we reconstruct a migrant flow network where nodes represent either origin or destination countries. The links represent the direct routes between two countries. The migration network of sex-workers shows different structural patterns than the migration of the general population. The network contains a strong core where mutual migration is often observed between a group of high-income European countries, yet Europe is split into different network communities with specific ties to non-European countries. We find non-reciprocal relations between countries, with some of them mostly offering while others attract workers. The GDP per capita is a good indicator of country attractiveness for incoming workers and service rates but is unrelated to the probability of emigration. The median financial gain of migrating, in comparison to working at the home country, is 15.9%. Only sex-workers coming from 77% of the countries have financial gains with migration and average gains decrease with the GDPc of the country of origin. Our results shows that high-end sex-worker migration is regulated by economic, geographic and cultural aspects., Comment: Comments and feedback welcomed. Two tables and 6 figures including SI

Understanding the causes and consequences of, and devising countermeasures to, global warming is a profoundly complex problem. Network representations are sometimes the only way forward, and sometimes able to reduce the complexity of the original problem. Networks are both necessary and natural elements of climate science. Furthermore, networks form a mathematical foundation for a multitude of computational and analytical techniques. We are only beginning to see the benefits of this connection between the sciences of climate change and network science. In this review, we cover the wide spectrum of network applications in the climate-change literature -- what they represent, how they are analyzed, and what insights they bring. We also discuss network data, tools, and problems yet to be explored.

The study of temporal networks is motivated by the simple and important observation that just as network structure can affect dynamics, so can structure in time. Just as network topology can teach us about the system in question, so can its temporal characteristics. In many cases, leaving out either one of these components would lead to an incomplete understanding of the system or poor predictions. We argue that including time into network modeling inevitably leads researchers away from the trodden paths of network science. Temporal network theory requires something different -- new methods, new concepts, new questions -- compared to static networks. In this introductory chapter, we overview the ideas that the field of temporal networks has brought forward in the last decade. We also place the contributions to the current volume on this map of temporal-network approaches., Comment: Introductory chapter to the book: Holme, Saram\"aki, Temporal Network Theory (Springer, Cham, 2019)

Threshold models of cascades in the social sciences and economics explain the spread of opinion and innovation due to social influence. In threshold cascade models, fads or innovations spread between agents as determined by their interactions with other agents and their personal threshold of resistance. Typically, these models do not account for structure in the timing of interaction between the units. In this work, we extend a model of social cascades by Duncan Watts to temporal interaction networks. In our model, we assume friends and acquaintances influence agents for a certain time into the future. That is the influence of the past ages and becomes unimportant. Thus, our modified cascade model has an effective time window of influence. We explore two types of thresholds -- thresholds to fractions of the neighbors or absolute numbers. We try our model on six empirical datasets and compare them with null models., Comment: Chapter in Holme, Saram\"aki, eds., Temporal Networks (Springer, Berlin, 2013)

To understand large, connected systems, we cannot only zoom into the details. We also need to see the large-scale features from afar. One way to take a step back and get the whole picture is to model the systems as a network. However, many systems are not static, but consisting of contacts that are off and on as time progresses. This Chapter introduces the mathematical and computational modeling of such systems and thus an introduction to the rest of the book. We will cover some of the earlier developments that form the foundation for the more specialized topics of the other Chapters., Comment: Introductory chapter to Holme, Saram\"aki, eds., Temporal Networks (Springer, Berlin, 2013)

We develop a theory for the susceptible-infected-susceptible (SIS) epidemic model on networks that incorporate both network structure and dynamic correlations. This theory can account for the multistage onset of the epidemic phase in scale-free networks. This phenomenon is characterized by multiple peaks in the susceptibility as a function of the infection rate. It can be explained by that, even under the global epidemic threshold, a hub can sustain the epidemics for an extended period. Moreover, our approach improves theoretical calculations of prevalence close to the threshold in heterogeneous networks and also can predict the average risk of infection for neighbors of nodes with different degree and state on uncorrelated static networks.