Search

Disasters, such as the recent COVID-19 pandemic, impose recurrent and heterogeneous stress on healthcare systems, necessitating the redistribution of stress to enhance healthcare resilience. However, existing studies have been hindered by limited datasets and approaches for assessing its absorptive capacity - defined as the system's ability to absorb stress by redistributing patient flows. This study addresses this gap by analyzing patient flow networks constructed from billions of electronic medical records and introducing an approach to quantify network absorptivity under crisis conditions. Our analysis of U.S. healthcare systems reveals that during the COVID-19 pandemic, cross-regional patient flows increased by 3.89%, a 0.90% rise from pre-pandemic levels. The networks exhibited an average absorptivity of 0.21, representing a 10% increase over pre-pandemic conditions. Flow networks with higher connectivity and heterogeneity showed a greater capacity to alleviate system burdens. These empirical and analytical insights underscore the critical role of proactive patient flow management in strengthening healthcare resilience during crises., Comment: 36 pages, 7 figures

Understanding healthcare system resilience has become paramount, particularly in the wake of the COVID-19 pandemic, which imposed unprecedented burdens on healthcare services and severely impacted public health. Resilience is defined as the system's ability to absorb, recover from, and adapt to disruptions; however, despite extensive studies on this subject, we still lack empirical evidence and mathematical tools to quantify its adaptability (the ability of the system to adjust to and learn from disruptions). By analyzing millions of patients' electronic medical records across US states, we find that the COVID-19 pandemic caused two successive waves of disruptions within the healthcare systems, enabling natural experiment analysis of the adaptive capacity for each system to adapt to past disruptions. We generalize the quantification framework and find that the US healthcare systems exhibit substantial adaptability but only a moderate level of resilience. When considering system responses across racial groups, Black and Hispanic groups were more severely impacted by pandemic disruptions than White and Asian groups. Physician abundance is the key characteristic for determining healthcare system resilience. Our results offer vital guidance in designing resilient and sustainable healthcare systems to prepare for future waves of disruptions akin to COVID-19 pandemics.

The distributional properties of a multi-dimensional continuous-state branching process are determined by its cumulant semigroup, which is defined by the backward differential equation. We provide a proof of the assertion of Rhyzhov and Skorokhod (Theory Probab. Appl., 1970) on the uniqueness of the solutions to the equation, which is based on a characterization of the process as the pathwise unique solution to a system of stochastic equations.

We study quasi-stationary distribution of the continuous-state branching process with competition introduced in Berestycki, Fittipaldi and Fontbona\ (Probab. Theory Relat. Fields, 2018). This process is constructed as the unique strong solution to a stochastic integral equation with jumps. An important example is the logistic branching process constructed in Lambert (Ann. Appl. Probab., 2005). We establish the strong Feller property,trajectory Feller property, Lyapunov condition, weak Feller property and irreducibility, respectively. These properties together allow us to prove that when the competition term is strong enough near $+\infty$, then there is a unique quasi-stationary distribution, which attracts all initial distributions with exponential rates.

Out-of-distribution (OOD) detection empowers the model trained on the closed image set to identify unknown data in the open world. Though many prior techniques have yielded considerable improvements in this research direction, two crucial obstacles still remain. Firstly, a unified perspective has yet to be presented to view the developed arts with individual designs, which is vital for providing insights into future work. Secondly, we expect sufficient natural OOD supervision to promote the generation of compact boundaries between the in-distribution (ID) and OOD data without collecting explicit OOD samples. To tackle these issues, we propose a general probabilistic framework to interpret many existing methods and an OOD-data-free model, namely \textbf{S}elf-supervised \textbf{S}ampling for \textbf{O}OD \textbf{D}etection (SSOD). SSOD efficiently exploits natural OOD signals from the ID data based on the local property of convolution. With these supervisions, it jointly optimizes the OOD detection and conventional ID classification in an end-to-end manner. Extensive experiments reveal that SSOD establishes competitive state-of-the-art performance on many large-scale benchmarks, outperforming the best previous method by a large margin, \eg, reporting \textbf{-6.28\%} FPR95 and \textbf{+0.77\%} AUROC on ImageNet, \textbf{-19.01\%} FPR95 and \textbf{+3.04\%} AUROC on CIFAR-10, and top-ranked performance on hard OOD datasets, \ie, ImageNet-O and OpenImage-O., Comment: ICLR 2024. arXiv admin note: text overlap with arXiv:2301.06657

In recent years, the exploration of node centrality has received significant attention and extensive investigation, primarily fuelled by its applications in diverse domains such as product recommendations, opinion propagation, disease spread, and other scenarios requiring the maximization of node influence. Despite various perspectives emphasizing the indispensability of higher-order networks, research specifically delving into node centrality within the realm of hypergraphs has been relatively constrained. This paper focuses on the problem of influence maximization on the Simplicial Contagion Model (SCM), using the susceptible-infected-recovered (SIR) model as an example. To find practical solutions to this optimization problem, we have developed a theoretical framework based on message passing process and conducted stability analysis of equilibrium solutions for the self-consistent equations. Furthermore, we introduce a metric called collective influence and propose an adaptive algorithm, known as the Collective Influence Adaptive (CIA), to identify influential propagators in the spreading process. Notably, our algorithm distinguishes itself by prioritizing collective influence over individual influence, resulting in demonstrably superior performance, a characteristic substantiated by a comprehensive array of experiments., Comment: 17 pages,17 figures

Influence Maximization problem has received significant attention in recent years due to its application in various do?mains such as product recommendation, public opinion dissemination, and disease propagation. This paper proposes a theoretical analysis framework for collective influence in hypergraphs, focusing on identifying a set of seeds that maximize influence in threshold models. Firstly, we extend the Message Passing method from pairwise networks to hypergraphs to accurately describe the activation process in threshold models. Then we introduce the concept of hyper?graph collective influence (HCI) to measure the influence of nodes. Subsequently, We design an algorithm, HCI-TM, to select the Influence Maximization Set, taking into account both node and hyperedge activation. Numerical simu?lations demonstrate that HCI-TM outperforms several competing algorithms in synthetic and real-world hypergraphs. Furthermore, we find that HCI can be used as a tool to predict the occurrence of cascading phenomena. Notably, we find that HCI-TM algorithm works better for larger average hyperdegrees in Erdos-R\'enyi (ER) hypergraphs and smaller power-law exponents in scale-free (SF) hypergraphs., Comment: 14 pages, 6 figures

The explosion of short videos has dramatically reshaped the manners people socialize, yielding a new trend for daily sharing and access to the latest information. These rich video resources, on the one hand, benefited from the popularization of portable devices with cameras, but on the other, they can not be independent of the valuable editing work contributed by numerous video creators. In this paper, we investigate a novel and practical problem, namely audio beat matching (ABM), which aims to recommend the proper transition time stamps based on the background music. This technique helps to ease the labor-intensive work during video editing, saving energy for creators so that they can focus more on the creativity of video content. We formally define the ABM problem and its evaluation protocol. Meanwhile, a large-scale audio dataset, i.e., the AutoMatch with over 87k finely annotated background music, is presented to facilitate this newly opened research direction. To further lay solid foundations for the following study, we also propose a novel model termed BeatX to tackle this challenging task. Alongside, we creatively present the concept of label scope, which eliminates the data imbalance issues and assigns adaptive weights for the ground truth during the training procedure in one stop. Though plentiful short video platforms have flourished for a long time, the relevant research concerning this scenario is not sufficient, and to the best of our knowledge, AutoMatch is the first large-scale dataset to tackle the audio beat matching problem. We hope the released dataset and our competitive baseline can encourage more attention to this line of research. The dataset and codes will be made publicly available., Comment: 11 pages, 5 figures

Predicting cross-immunity between viral strains is vital for public health surveillance and vaccine development. Traditional neural network methods, such as BiLSTM, could be ineffective due to the lack of lab data for model training and the overshadowing of crucial features within sequence concatenation. The current work proposes a less data-consuming model incorporating a pre-trained gene sequence model and a mutual information inference operator. Our methodology utilizes gene alignment and deduplication algorithms to preprocess gene sequences, enhancing the model's capacity to discern and focus on distinctions among input gene pairs. The model, i.e., DNA Pretrained Cross-Immunity Protection Inference model (DPCIPI), outperforms state-of-the-art (SOTA) models in predicting hemagglutination inhibition titer from influenza viral gene sequences only. Improvement in binary cross-immunity prediction is 1.58% in F1, 2.34% in precision, 1.57% in recall, and 1.57% in Accuracy. For multilevel cross-immunity improvements, the improvement is 2.12% in F1, 3.50% in precision, 2.19% in recall, and 2.19% in Accuracy. Our study highlights the potential of pre-trained gene models in revolutionizing gene sequence-related prediction tasks. With more gene sequence data being harnessed and larger models trained, we foresee a significant impact of pre-trained models on clinical and public health applications.

When deployed in practical applications, computer vision systems will encounter numerous unexpected images (\emph{{i.e.}}, out-of-distribution data). Due to the potentially raised safety risks, these aforementioned unseen data should be carefully identified and handled. Generally, existing approaches in dealing with out-of-distribution (OOD) detection mainly focus on the statistical difference between the features of OOD and in-distribution (ID) data extracted by the classifiers. Although many of these schemes have brought considerable performance improvements, reducing the false positive rate (FPR) when processing open-set images, they necessarily lack reliable theoretical analysis and generalization guarantees. Unlike the observed ways, in this paper, we investigate the OOD detection problem based on the Bayes rule and present a convincing description of the reason for failures encountered by conventional classifiers. Concretely, our analysis reveals that refining the probability distribution yielded by the vanilla neural networks is necessary for OOD detection, alleviating the issues of assigning high confidence to OOD data. To achieve this effortlessly, we propose an ultra-effective method to generate near-realistic outlier supervision. Extensive experiments on large-scale benchmarks reveal that our proposed \texttt{BayesAug} significantly reduces the FPR95 over 12.50\% compared with the previous schemes, boosting the reliability of machine learning systems. The code will be made publicly available., Comment: We have rewritten this paper, and published as "Image Background Serves as Good Proxy for Out-of-distribution Data" arXiv:2307.00519

During its first two years, the SARS-CoV-2 pandemic manifested as multiple waves shaped by complex interactions between variants of concern, non-pharmaceutical interventions, and the immunological landscape of the population. Understanding how the age-specific epidemiology of SARS-CoV-2 has evolved throughout the pandemic is crucial for informing policy decisions. We developed an inference-based modelling approach to reconstruct the burden of true infections and hospital admissions in children, adolescents and adults over the seven waves of four variants (wild-type, Alpha, Delta, Omicron BA.1) during the first two years of the pandemic, using the Netherlands as the motivating example. We find that reported cases are a considerable underestimate and a generally poor predictor of true infection burden, especially because case reporting differs by age. The contribution of children and adolescents to total infection and hospitalization burden increased with successive variants and was largest during the Omicron BA.1 period. Before the Delta period, almost all infections were primary infections occurring in naive individuals. During the Delta and Omicron BA.1 periods, primary infections were common in children but relatively rare in adults who experienced either re-infections or breakthrough infections. Our approach can be used to understand age-specific epidemiology through successive waves in other countries where random community surveys uncovering true SARS-CoV-2 dynamics are absent but basic surveillance and statistics data are available., Comment: 23 pages, 5 figures, 1 table; supplementary materials to the main text available at https://github.com/oboldea/COVID_age_regions

People are likely to engage in collective behaviour online during extreme events, such as the COVID-19 crisis, to express their awareness, actions and concerns. Hong Kong has implemented stringent public health and social measures (PHSMs) to curb COVID-19 epidemic waves since the first COVID-19 case was confirmed on 22 January 2020. People are likely to engage in collective behaviour online during extreme events, such as the COVID-19 crisis, to express their awareness, actions and concerns. Here, we offer a framework to evaluate interactions among individuals emotions, perception, and online behaviours in Hong Kong during the first two waves (February to June 2020) and found a strong correlation between online behaviours of Google search and the real-time reproduction numbers. To validate the model output of risk perception, we conducted 10 rounds of cross-sectional telephone surveys from February 1 through June 20 in 2020 to quantify risk perception levels over time. Compared with the survey results, the estimates of the risk perception of individuals using our network-based mechanistic model capture 80% of the trend of people risk perception (individuals who worried about being infected) during the studied period. We may need to reinvigorate the public by engaging people as part of the solution to live their lives with reduced risk.

Video highlights detection (VHD) is an active research field in computer vision, aiming to locate the most user-appealing clips given raw video inputs. However, most VHD methods are based on the closed world assumption, i.e., a fixed number of highlight categories is defined in advance and all training data are available beforehand. Consequently, existing methods have poor scalability with respect to increasing highlight domains and training data. To address above issues, we propose a novel video highlights detection method named Global Prototype Encoding (GPE) to learn incrementally for adapting to new domains via parameterized prototypes. To facilitate this new research direction, we collect a finely annotated dataset termed LiveFood, including over 5,100 live gourmet videos that consist of four domains: ingredients, cooking, presentation, and eating. To the best of our knowledge, this is the first work to explore video highlights detection in the incremental learning setting, opening up new land to apply VHD for practical scenarios where both the concerned highlight domains and training data increase over time. We demonstrate the effectiveness of GPE through extensive experiments. Notably, GPE surpasses popular domain incremental learning methods on LiveFood, achieving significant mAP improvements on all domains. Concerning the classic datasets, GPE also yields comparable performance as previous arts. The code is available at: https://github.com/ForeverPs/IncrementalVHD_GPE., Comment: AAAI 2024

Machine learning systems, especially the methods based on deep learning, enjoy great success in modern computer vision tasks under experimental settings. Generally, these classic deep learning methods are built on the \emph{i.i.d.} assumption, supposing the training and test data are drawn from a similar distribution independently and identically. However, the aforementioned \emph{i.i.d.} assumption is in general unavailable in the real-world scenario, and as a result, leads to sharp performance decay of deep learning algorithms. Behind this, domain shift is one of the primary factors to be blamed. In order to tackle this problem, we propose using \textbf{Po}tential \textbf{E}nergy \textbf{R}anking (PoER) to decouple the object feature and the domain feature (\emph{i.e.,} appearance feature) in given images, promoting the learning of label-discriminative features while filtering out the irrelevant correlations between the objects and the background. PoER helps the neural networks to capture label-related features which contain the domain information first in shallow layers and then distills the label-discriminative representations out progressively, enforcing the neural networks to be aware of the characteristic of objects and background which is vital to the generation of domain-invariant features. PoER reports superior performance on domain generalization benchmarks, improving the average top-1 accuracy by at least 1.20\% compared to the existing methods. Moreover, we use PoER in the ECCV 2022 NICO Challenge\footnote{https://nicochallenge.com}, achieving top place with only a vanilla ResNet-18. The code has been made available at https://github.com/ForeverPs/PoER., Comment: 2022 ECCV jury award, accepted by AAAI 2023

We study the ergodic property of a continuous-state branching process with immigration and competition. The exponential ergodicity in a weighted total variation distance is proved under natural assumptions. The main theorem applies to subcritical, critical and supercritical branching mechanisms, including all those of stable types. The proof is based on the construction of a Markov coupling process and the choice of a nonsymmetric control function for the distance. Those are designed to identify and to take the advantage of the dominating factor from the branching, immigration and competition mechanisms in different parts of the state space. The approach provides a way of finding a lower bound of the ergodicity rate.

Recent studies show that the deep neural networks (DNNs) have achieved great success in various tasks. However, even the \emph{state-of-the-art} deep learning based classifiers are extremely vulnerable to adversarial examples, resulting in sharp decay of discrimination accuracy in the presence of enormous unknown attacks. Given the fact that neural networks are widely used in the open world scenario which can be safety-critical situations, mitigating the adversarial effects of deep learning methods has become an urgent need. Generally, conventional DNNs can be attacked with a dramatically high success rate since their gradient is exposed thoroughly in the white-box scenario, making it effortless to ruin a well trained classifier with only imperceptible perturbations in the raw data space. For tackling this problem, we propose a plug-and-play layer that is training-free, termed as \textbf{G}radient \textbf{C}oncealment \textbf{M}odule (GCM), concealing the vulnerable direction of gradient while guaranteeing the classification accuracy during the inference time. GCM reports superior defense results on the ImageNet classification benchmark, improving up to 63.41\% top-1 attack robustness (AR) when faced with adversarial inputs compared to the vanilla DNNs. Moreover, we use GCM in the CVPR 2022 Robust Classification Challenge, currently achieving \textbf{2nd} place in Phase II with only a tiny version of ConvNext. The code will be made available.

Many real-world applications based on spreading processes in complex networks aim to deliver information to specific target nodes. However, it remains challenging to optimally select a set of spreaders to initiate the spreading process. In this paper, we study the targeted influence maximization problem using a susceptible-infected-recovered (SIR) model as an example. Formulated as a combinatorial optimization, the objective is to identify a given number of spreaders that can maximize the influence over target nodes while minimize the influence over non-target nodes. To find a practical solution to this optimization problem, we develop a theoretical framework based on a message passing process and perform a stability analysis on the equilibrium solution using non-backtracking (NB) matrices. We propose that the spreaders can be selected by imposing optimal perturbation on the equilibrium solution for the subgraph consisting of the target nodes and their multi-step nearest neighbors while avoiding such perturbation on the complement graph that excludes target nodes from the original network. We further introduce a metric, termed targeted collective influence, for each node to identify influential spreaders for targeted spreading processes. The proposed method, validated in both synthetic and real-world networks, outperforms other competing heuristic approaches. Our results provide a framework for analyzing the targeted influence maximization problem and a practical method to identify spreaders in real-world applications., Comment: 13 pages,10 figures

During the early stage of the COVID-19 pandemic, many countries implemented non-pharmaceutical interventions (NPIs) to control the transmission of SARS-CoV-2, the causative pathogen of COVID-19. Among those NPIs, quarantine measures were widely adopted and enforced through stay-at-home and shelter-in-place orders. Understanding the effectiveness of quarantine measures can inform decision-making and control planning during the ongoing COVID-19 pandemic and for future disease outbreaks. In this study, we use mathematical models to evaluate the impact of quarantine measures on COVID-19 spread in four cities that experienced large-scale outbreaks in the spring of 2020: Wuhan, New York, Milan, and London. We develop a susceptible-exposed-infected-removed (SEIR)-type model with a component of quarantine and couple this disease transmission model with a data assimilation method. By calibrating the model to case data, we estimate key epidemiological parameters before lockdown in each city. We further examine the impact of quarantine rates on COVID-19 spread after lockdown using model simulations. Results indicate that quarantine of susceptible and exposed individuals and undetected infections is necessary to contain the outbreak; however, the quarantine rates for these populations can be reduced through faster isolation of confirmed cases. We generate counterfactual simulations to estimate effectiveness of quarantine measures. Without quarantine measures, the cumulative confirmed cases could be 73, 22, 43 and 93 times higher than reported numbers within 40 days after lockdown in Wuhan, New York, Milan, and London. Our findings underscore the essential role of quarantine during the early phase of the pandemic., Comment: 13 pages, 5 figures

There is an increasing need to determine whether inputs are out-of-distribution (\emph{OOD}) for safely deploying machine learning models in the open world scenario. Typical neural classifiers are based on the closed world assumption, where the training data and the test data are drawn \emph{i.i.d.} from the same distribution, and as a result, give over-confident predictions even faced with \emph{OOD} inputs. For tackling this problem, previous studies either use real outliers for training or generate synthetic \emph{OOD} data under strong assumptions, which are either costly or intractable to generalize. In this paper, we propose boundary aware learning (\textbf{BAL}), a novel framework that can learn the distribution of \emph{OOD} features adaptively. The key idea of BAL is to generate \emph{OOD} features from trivial to hard progressively with a generator, meanwhile, a discriminator is trained for distinguishing these synthetic \emph{OOD} features and in-distribution (\emph{ID}) features. Benefiting from the adversarial training scheme, the discriminator can well separate \emph{ID} and \emph{OOD} features, allowing more robust \emph{OOD} detection. The proposed BAL achieves \emph{state-of-the-art} performance on classification benchmarks, reducing up to 13.9\% FPR95 compared with previous methods.

Testing, contact tracing, and isolation (TTI) is an epidemic management and control approach that is difficult to implement at scale because it relies on manual tracing of contacts. Exposure notification apps have been developed to digitally scale up TTI by harnessing contact data obtained from mobile devices; however, exposure notification apps provide users only with limited binary information when they have been directly exposed to a known infection source. Here we demonstrate a scalable improvement to TTI and exposure notification apps that uses data assimilation (DA) on a contact network. Network DA exploits diverse sources of health data together with the proximity data from mobile devices that exposure notification apps rely upon. It provides users with continuously assessed individual risks of exposure and infection, which can form the basis for targeting individual contact interventions. Simulations of the early COVID-19 epidemic in New York City prove the concepts. In the simulations, network DA identifies up to a factor 2 more infections than contact tracing when both harness the same contact data and diagnostic test data. This remains true even when only a relatively small fraction of the population uses network DA. When a sufficiently large fraction of the population ($\gtrsim 75\%$) uses network DA and complies with individual contact interventions, targeting contact interventions with network DA reduces deaths by up to a factor 4 relative to TTI. Network DA can be implemented by expanding the computational backend of existing exposure notification apps, thus greatly enhancing their capabilities. Implemented at scale, it has the potential to precisely and effectively control future epidemics while minimizing economic disruption.

The vanilla GAN (Goodfellow et al. 2014) suffers from mode collapse deeply, which usually manifests as that the images generated by generators tend to have a high similarity amongst them, even though their corresponding latent vectors have been very different. In this paper, we introduce a pluggable diversity penalty module (DPM) to alleviate mode collapse of GANs. It reduces the similarity of image pairs in feature space, i.e., if two latent vectors are different, then we enforce the generator to generate two images with different features. The normalized Gram matrix is used to measure the similarity. We compare the proposed method with Unrolled GAN (Metz et al. 2016), BourGAN (Xiao, Zhong, and Zheng 2018), PacGAN (Lin et al. 2018), VEEGAN (Srivastava et al. 2017) and ALI (Dumoulin et al. 2016) on 2D synthetic dataset, and results show that the diversity penalty module can help GAN capture much more modes of the data distribution. Further, in classification tasks, we apply this method as image data augmentation on MNIST, Fashion- MNIST and CIFAR-10, and the classification testing accuracy is improved by 0.24%, 1.34% and 0.52% compared with WGAN GP (Gulrajani et al. 2017), respectively. In domain translation, diversity penalty module can help StarGAN (Choi et al. 2018) generate more accurate attention masks and accelarate the convergence process. Finally, we quantitatively evaluate the proposed method with IS and FID on CelebA, CIFAR-10, MNIST and Fashion-MNIST, and the results suggest GAN with diversity penalty module gets much higher IS and lower FID compared with some SOTA GAN architectures.

Consider a non-explosive positive Feller process with no negative jumps. It is shown in this note that when infinity is an entrance boundary, in the sense that the entrance times of the process remain bounded when the initial value tends to infinity, the process admits a Feller extension on the compactified state space $[0,\infty]$. Moreover, when started from infinity, the extended Markov process on $[0,\infty]$ leaves infinity instantaneously and stays finite, almost-surely. Arguments are adapted from a proof given by O. Kallenberg for diffusions. We also show that the process started from $x$ converges weakly towards that started from infinity in the Skorokhod space, when $x$ goes to infinity., Comment: 14 pages. Version accepted for publication

Networks of excitable elements are widely used to model real-world biological and social systems. The dynamic range of an excitable network quantifies the range of stimulus intensities that can be robustly distinguished by the network response, and is maximized at the critical state. In this study, we examine the impacts of backtracking activation on system criticality in excitable networks consisting of both excitatory and inhibitory units. We find that, for dynamics with refractory states that prohibit backtracking activation, the critical state occurs when the largest eigenvalue of the weighted non-backtracking (WNB) matrix for excitatory units, $\lambda^E_{NB}$, is close to one, regardless of the strength of inhibition. In contrast, for dynamics without refractory state in which backtracking activation is allowed, the strength of inhibition affects the critical condition through suppression of backtracking activation. As inhibitory strength increases, backtracking activation is gradually suppressed. Accordingly, the system shifts continuously along a continuum between two extreme regimes -- from one where the criticality is determined by the largest eigenvalue of the weighted adjacency matrix for excitatory units, $\lambda^E_W$, to the other where the critical state is reached when $\lambda_{NB}^E$ is close to one. For systems in between, we find that $\lambda^E_{NB}<1$ and $\lambda^E_W>1$ at the critical state. These findings, confirmed by numerical simulations using both random and synthetic neural networks, indicate that backtracking activation impacts the criticality of excitable networks., Comment: 26 pages, 9 figures

By using the coupling technique, we present sufficient conditions for the exponential ergodicity of general continuous-state nonlinear branching processes in both the $L^1$-Wasserstein distance and the total variation norm, where the drift term is dissipative only for large distance, and either diffusion noise or jump noise is allowed to be vanished. Sufficient conditions for the corresponding strong ergodicity are also established., Comment: 23 pages

The integrity and functionality of many real-world complex systems hinge on a small set of pivotal nodes, or influencers. In different contexts, these influencers are defined as either structurally important nodes that maintain the connectivity of networks, or dynamically crucial units that can disproportionately impact certain dynamical processes. In practice, identification of the optimal set of influencers in a given system has profound implications in a variety of disciplines. In this review, we survey recent advances in the study of influencer identification developed from different perspectives, and present state-of-the-art solutions designed for different objectives. In particular, we first discuss the problem of finding the minimal number of nodes whose removal would breakdown the network (i.e., the optimal percolation or network dismantle problem), and then survey methods to locate the essential nodes that are capable of shaping global dynamics with either continuous (e.g., independent cascading models) or discontinuous phase transitions (e.g., threshold models). We conclude the review with a summary and an outlook.

Consider a spectrally positive L\'evy process $Z$ with log-Laplace exponent $\Psi$ and a positive continuous function $R$ on $(0,\infty)$. We investigate the entrance from $\infty$ of the process $X$ obtained by changing time in $Z$ with the inverse of the additive functional $\eta(t)=\int_{0}^{t}\frac{{\rm d} s}{R(Z_s)}$. We provide a necessary and sufficient condition for infinity to be an entrance boundary of the process $X$. Under this condition, the process can start from infinity and we study its speed of coming down from infinity. When the L\'evy process has a negative drift $\delta:=-\gamma<0$, sufficient conditions over $R$ and $\Psi$ are found for the process to come down from infinity along the deterministic function $(x_t,t\geq 0)$ solution to ${\rm d} x_t=-\gamma R(x_t) {\rm d} t$, with $x_0=\infty$. When $\Psi(\lambda)\sim c\lambda^{\alpha}$, with $\lambda \rightarrow 0$, $\alpha\in (1,2]$, $c>0$ and $R$ is regularly varying at $\infty$ with index $\theta>\alpha$, the process comes down from infinity and we find a renormalisation in law of its running infimum at small times.

We find necessary and sufficient conditions for almost sure finiteness of integral functionals of spectrally positive L\'evy processes. Via Lamperti type transforms, these results can be applied to obtain new integral tests on extinction and explosion behaviors for a class of continuous-state nonlinear branching processes.

The stability of Boolean networks has attracted much attention due to its wide applications in describing the dynamics of biological systems. During the past decades, much effort has been invested in unveiling how network structure and update rules will affect the stability of Boolean networks. In this paper, we aim to identify and control a minimal set of influential nodes that is capable of stabilizing an unstable Boolean network. By minimizing the largest eigenvalue of a modified non-backtracking matrix, we propose a method using the collective influence theory to identify the influential nodes in Boolean networks with high computational efficiency. We test the performance of collective influence on four different networks. Results show that the collective influence algorithm can stabilize each network with a smaller set of nodes than other heuristic algorithms. Our work provides a new insight into the mechanism that determines the stability of Boolean networks, which may find applications in identifying the virulence genes that lead to serious disease.

We study the strategy to optimally maximize the dynamic range of excitable networks by removing the minimal number of links. A network of excitable elements can distinguish a broad range of stimulus intensities and has its dynamic range maximized at criticality. In this study, we formulate the activation propagation in excitable networks as a message passing process in which the critical state is reached when the largest eigenvalue of the weighted non-backtracking (WNB) matrix is exactly one. By considering the impact of single link removal on the largest eigenvalue, we develop an efficient algorithm that aims to identify the optimal set of links whose removal will drive the system to the critical state. Comparisons with other competing heuristics on both synthetic and real-world networks indicate that the proposed method can maximize the dynamic range by removing the smallest number of links, and at the same time maintain the largest size of the giant connected component., Comment: 10 pages, 8 figures

In this paper we consider the unique nonnegative solution to the following generalized version of the stochastic differential equation for a continuous-state branching process. \beqnn X_t \ar=\ar x+\int_0^t\gamma_0(X_s)\dd s+\int_0^t\int_0^{\gamma_1(X_{s-})} W(\dd s,\dd u)\cr \ar\ar\qquad+\int_0^t\int_{0}^\infty\int_0^{\gamma_2(X_{s-})} z\tilde{N}(\dd s, \dd z, \dd u), \eeqnn where $W(\dd t,\dd u) $ and $\tilde{N}(\dd s, \dd z, \dd u)$ denote a Gaussian white noise and an independent compensated spectrally positive Poisson random measure, respectively, and $\gamma_0,\gamma_1$ and $\gamma_2$ are functions on $\mbb{R}_+$ with both $\gamma_1$ and $\gamma_2$ taking nonnegative values. Intuitively, this process can be identified as a continuous-state branching process with population-size-dependent branching rates and with competition. Using martingale techniques we find rather sharp conditions on extinction, explosion and coming down from infinity behaviors of the process. Some Foster-Lyapunov type criteria are also developed for such a process. More explicit results are obtained when $\gamma_i, i=0, 1, 2$ are power functions.

In social and biological systems, the structural heterogeneity of interaction networks gives rise to the emergence of a small set of influential nodes, or influencers, in a series of dynamical processes. Although much smaller than the entire network, these influencers were observed to be able to shape the collective dynamics of large populations in different contexts. As such, the successful identification of influencers should have profound implications in various real-world spreading dynamics such as viral marketing, epidemic outbreaks and cascading failure. In this chapter, we first summarize the centrality-based approach in finding single influencers in complex networks, and then discuss the more complicated problem of locating multiple influencers from a collective point of view. Progress rooted in collective influence theory, belief-propagation and computer science will be presented. Finally, we present some applications of influencer identification in diverse real-world systems, including online social platforms, scientific publication, brain networks and socioeconomic systems., Comment: 24 pages, 6 figures