Species are embedded in an intricate web of interactions known as a food web. A food web is the most fundamental network representation of an ecosystem. It is therefore nature to assess species importance from a network perspective. Past literatures emphasize the use of centrality measurements to quantify species importance. Recent advances of species importance research have proposed the concept of species uniqueness as an complementary measure to species importance. In this presentation, we discuss what uniqueness is and review its recent developments. We start with the concept of species trophic field, which is the set of species a focal species can strongly affect, and how this can be applied to measure species uniqueness. This trophic field-overlap approach can be extend to consider both strong and weak interactors of a focal species, providing a more complete view on species uniqueness. We then show how this extended approach can be simplified by using a matrix that represents the interaction structure of a food web. All the above approaches consider how species can affect all others, but we argue that information such as how a species is affected by all others can also be utilized for species uniqueness measurements. This new concept spurs us to develop yet another specie uniqueness measure that considers simultaneously information on effects exerted and received by a species. We analyze 92 food webs to show the relationship between past approaches and our new approach.

To understand how the interconnected and interdependent world of the twenty-first century operates and make model-based predictions, joint probability models for networks and interdependent outcomes are needed. We propose a comprehensive regression framework for networks and interdependent outcomes with multiple advantages, including interpretability, scalability, and provable theoretical guarantees. The regression framework can be used for studying relationships among attributes of connected units and captures complex dependencies among connections and attributes, while retaining the virtues of linear regression, logistic regression, and other regression models by being interpretable and widely applicable. On the computational side, we show that the regression framework is amenable to scalable statistical computing based on convex optimization of pseudo-likelihoods using minorization-maximization methods. On the theoretical side, we establish convergence rates for pseudo-likelihood estimators based on a single observation of dependent connections and attributes. We demonstrate the regression framework using simulations and an application to hate speech on the social media platform X in the six months preceding the insurrection at the U.S. Capitol on January 6, 2021.

The abstract is a crucial frontmatter element that provides readers with key insights into a manuscript's core ideas and subject categories. Identifying the most important words in abstracts can offer valuable clues about the central themes and evolving trends within a particular subject area. This work introduces a novel analysis method to determine the importance of words within a subject category over time, based on various centrality measures in a word co-occurrence network. The network is constructed from words extracted from the abstracts of manuscripts within a specific scientific subject. We demonstrate the effectiveness of this method using a subset of the Semantic Scholar database, focusing on the field of Statistics from 2019 to 2023.

This study estimates the size of personal networks (number of friends and acquaintances) using the event subpopulation model (Bernard, Johnsen, Killworth, and Robinson, 1989), including individuals infected with COVID-19 and those who died in the Great East Japan Earthquake. Initial estimates varied significantly depending on population definitions, such as (a) whole Japan, (b) urban / (c) rural prefectures for COVID-19, and (b) inside / (c) outside tsunami-affected prefectures for GEJE. To improve accuracy, we refined the estimation model by incorporating inbreeding bias within a biased network framework (Fararo, 1981).

The estimation method is based on the proportion of respondents who know an affected individual. The basic formula is:

c = t p / e ...(1)

where e is the number of event participants, p is the proportion of respondents who know a participant, and t is the total population. Adjusting for inbreeding bias:

c = t p / (e (1 - tau)) ...(2)

where 0 <= tau <= 1. Further incorporating binomial variance correction leads to:

c = (t p / (e (1 - tau))) * (1 + (p (1 - p) / e)) ... (3)

which is always larger than the uncorrected estimate.

When we applied these models to Japan, we still observed significant regional variations. Although the refined models improve plausibility, the exact value of tau remains uncertain. Results suggest that estimates from natural disasters, where information spreads widely, may be more reliable than those from infectious disease events, where social stigma limits disclosure.

Clustering is a fundamental task in network analysis, essential for uncovering hidden structures within complex systems. Edge clustering, which focuses on relationships between nodes rather than the nodes themselves, has gained increased attention in recent years. This provides benefits in terms of (1) understanding the network in terms of the environments or events leading to edge formation, and (2) computational feasibility, as the computational cost of edge clustering is, for sparse networks, linear in the number of network nodes. However, existing edge clustering algorithms often overlook the significance of edge weights, which can represent the strength or capacity of connections, and fail to account for noisy edges—connections that obscure the true structure of the network. To address these challenges, the Weighted Edge Clustering Adjusting for Noise (WECAN) model is introduced. This novel algorithm integrates edge weights into the clustering process and includes a noise component that filters out spurious edges. WECAN offers a data-driven approach to distinguishing between meaningful and noisy edges, avoiding the arbitrary thresholding commonly used in network analysis. Its effectiveness is demonstrated through simulation studies and applications to real-world datasets, showing significant improvements over traditional clustering methods. Additionally, the R package "WECAN" (https://github.com/HaominLi7/WECAN) has been developed to facilitate its practical implementation.