arXiv subjects

Alec Kirkley

Publications and source records attributed to Alec Kirkley.

At least 37 records · Page 2Linked to original sources

arXiv2024

Identifying hubs in directed networks

Nodes in networks that exhibit high connectivity, also called ``hubs'', play a critical role in determining the structural and functional properties of networked systems. However, there is no clear definition of what constitutes a hub node in a network, and the classification of network hubs in existing work has either been purely qualitative or relies on ad hoc criteria for thresholding continuous data that do not generalize well to networks with certain degree sequences. Here we develop a set of efficient nonparametric methods that classify hub nodes in directed networks using the Minimum Description Length principle, effectively providing a clear and principled definition for network hubs. We adapt our methods to both unweighted and weighted networks and demonstrate them in a range of example applications using real and synthetic network data.

cs.SI↗

arXiv2024

Inference of dynamic hypergraph representations in temporal interaction data

A range of systems across the social and natural sciences generate datasets consisting of interactions between two distinct categories of items at various instances in time. Online shopping, for example, generates purchasing events of the form (user, product, time of purchase), and mutualistic interactions in plant-pollinator systems generate pollination events of the form (insect, plant, time of pollination). These data sets can be meaningfully modeled as temporal hypergraph snapshots in which multiple items within one category (i.e. online shoppers) share a hyperedge if they interacted with a common item in the other category (i.e. purchased the same product) within a given time window, allowing for the application of hypergraph analysis techniques. However, it is often unclear how to choose the number and duration of these temporal snapshots, which have a strong influence on the final hypergraph representations. Here we propose a principled nonparametric solution to this problem by extracting temporal hypergraph snapshots that optimally capture structural regularities in temporal event data according to the minimum description length principle. We demonstrate our methods on real and synthetic datasets, finding that they can recover planted artificial hypergraph structure in the presence of considerable noise and reveal meaningful activity fluctuations in human mobility data.

cs.SI↗

arXiv2023

Implicit models, latent compression, intrinsic biases, and cheap lunches in community detection

The task of community detection, which aims to partition a network into clusters of nodes to summarize its large-scale structure, has spawned the development of many competing algorithms with varying objectives. Some community detection methods are inferential, explicitly deriving the clustering objective through a probabilistic generative model, while other methods are descriptive, dividing a network according to an objective motivated by a particular application, making it challenging to compare these methods on the same scale. Here we present a solution to this problem that associates any community detection objective, inferential or descriptive, with its corresponding implicit network generative model. This allows us to compute the description length of a network and its partition under arbitrary objectives, providing a principled measure to compare the performance of different algorithms without the need for "ground truth" labels. Our approach also gives access to instances of the community detection problem that are optimal to any given algorithm, and in this way reveals intrinsic biases in popular descriptive methods, explaining their tendency to overfit. Using our framework, we compare a number of community detection methods on artificial networks, and on a corpus of over 500 structurally diverse empirical networks. We find that more expressive community detection methods exhibit consistently superior compression performance on structured data instances, without having degraded performance on a minority of situations where more specialized algorithms perform optimally. Our results undermine the implications of the "no free lunch" theorem for community detection, both conceptually and in practice, since it is confined to unstructured data instances, unlike relevant community detection problems which are structured by requirement.

cs.SI↗

arXiv2023

Characterizing network circuity among heterogeneous urban amenities

The spatial configuration of urban amenities and the streets connecting them collectively provide the structural backbone of a city, influencing its accessibility, vitality, and ultimately the well-being of its residents. Most accessibility measures focus on the proximity of amenities in space or along transportation networks, resulting in metrics largely determined by urban density alone. These measures are unable to gauge how efficiently street networks can navigate between amenities, since they neglect the circuity component of accessibility. Existing measures also often require ad hoc modeling choices, making them less flexible for different applications and difficult to apply in cross-sectional analyses. Here we develop a simple, principled, and flexible measure to characterize the circuity of accessibility among heterogeneous amenities in a city, which we call the pairwise circuity (PC). The PC quantifies the excess travel distance incurred when using the street network to route between a pair of amenity types, summarizing both spatial and topological correlations among amenities. Measures developed using our framework exhibit significant statistical associations with a variety of urban prosperity and accessibility indicators when compared to an appropriate null model, and we find a clear separation in the PC values of cities according to development level and geographic region.

physics.soc-ph↗

arXiv2023

Heterogeneous message passing for heterogeneous networks

Message passing (MP) is a computational technique used to find approximate solutions to a variety of problems defined on networks. MP approximations are generally accurate in locally tree-like networks but require corrections to maintain their accuracy level in networks rich with short cycles. However, MP may already be computationally challenging on very large networks and additional costs incurred by correcting for cycles could be prohibitive. We show how the issue can be addressed. By allowing each node in the network to have its own level of approximation, one can focus on improving the accuracy of MP approaches in a targeted manner. We perform a systematic analysis of 109 real-world networks and show that our node-based MP approximation is able to increase both the accuracy and speed of traditional MP approaches. We find that, compared to conventional MP, a heterogeneous approach based on a simple heuristic is more accurate in 81% of tested networks, faster in 64% of cases, and both more accurate and faster in 49% of cases.

physics.soc-ph↗

arXiv2023

Compressing network populations with modal networks reveals structural diversity

Analyzing relational data consisting of multiple samples or layers involves critical challenges: How many networks are required to capture the variety of structures in the data? And what are the structures of these representative networks? We describe efficient nonparametric methods derived from the minimum description length principle to construct the network representations automatically. The methods input a population of networks or a multilayer network measured on a fixed set of nodes and output a small set of representative networks together with an assignment of each network sample or layer to one of the representative networks. We identify the representative networks and assign network samples to them with an efficient Monte Carlo scheme that minimizes our description length objective. For temporally ordered networks, we use a polynomial time dynamic programming approach that restricts the clusters of network layers to be temporally contiguous. These methods recover planted heterogeneity in synthetic network populations and identify essential structural heterogeneities in global trade and fossil record networks. Our methods are principled, scalable, parameter-free, and accommodate a wide range of data, providing a unified lens for exploratory analyses and preprocessing large sets of network samples.

physics.soc-ph↗

arXiv2022

Spatial regionalization based on optimal information compression

Regionalization, spatially contiguous clustering, provides a means to reduce the effect of noise in sampled data and identify homogeneous areas for policy development among many other applications. Existing regionalization methods require user input such as the number of regions or a similarity measure between regions, which does not allow for the extraction of the natural regions defined solely by the data itself. Here we view the problem of regionalization as one of data compression and develop an efficient, parameter-free regionalization algorithm based on the minimum description length principle. We demonstrate that our method is capable of recovering planted spatial clusters in noisy synthetic data, and that it can meaningfully coarse-grain real demographic data. Using our description length formulation, we find that spatial ethnoracial data in U.S. metropolitan areas has become less compressible over the period from 1980 to 2010, reflecting the rising complexity of urban segregation patterns in these metros.

physics.soc-ph↗

arXiv2022

Improved estimates for the number of non-negative integer matrices with given row and column sums

The number of non-negative integer matrices with given row and column sums appears in a variety of problems in mathematics and statistics but no closed-form expression for it is known, so we rely on approximations of various kinds. Here we describe a new such approximation, motivated by consideration of the statistics of matrices with non-integer numbers of columns. This estimate can be evaluated in time linear in the size of the matrix and returns results of accuracy as good as or better than existing linear-time approximations across a wide range of settings. We also use this new estimate as the starting point for an improved numerical method for either counting or sampling matrices using sequential importance sampling. Code implementing our methods is provided.

stat.CO↗

arXiv2022

Impact of urban structure on infectious disease spreading

The ongoing SARS-CoV-2 pandemic has been holding the world hostage for more than a year now. Mobility is key to viral spreading and its restriction is the main non-pharmaceutical interventions to fight the virus expansion. Previous works have shown a connection between the structural organization of cities and the movement patterns of their residents. This puts urban centers in the focus of epidemic surveillance and interventions. Here we show that the organization of urban flows has a tremendous impact on disease spreading and on the amenability of different mitigation strategies. By studying anonymous and aggregated intra-urban flows in a variety of cities in the United States and other countries, and a combination of empirical analysis and analytical methods, we demonstrate that the response of cities to epidemic spreading can be roughly classified in two major types according to the overall organization of those flows. Hierarchical cities, where flows are concentrated primarily between mobility hotspots, are particularly vulnerable to the rapid spread of epidemics. Nevertheless, mobility restrictions in such types of cities are very effective in mitigating the spread of a virus. Conversely, in sprawled cities which present many centers of activity, the spread of an epidemic is much slower, but the response to mobility restrictions is much weaker and less effective. Investing resources on early monitoring and prompt ad-hoc interventions in more vulnerable cities may prove helpful in containing and reducing the impact of future pandemics.

physics.soc-ph↗

arXiv2022

Representative community divisions of networks

Methods for detecting community structure in networks typically aim to identify a single best partition of network nodes into communities, often by optimizing some objective function, but in real-world applications there may be many competitive partitions with objective scores close to the global optimum and one can obtain a more informative picture of the community structure by examining a representative set of such high-scoring partitions than by looking at just the single optimum. However, such a set can be difficult to interpret since its size can easily run to hundreds or thousands of partitions. In this paper we present a method for analyzing large partition sets by dividing them into groups of similar partitions and then identifying an archetypal partition as a representative of each group. The resulting set of archetypal partitions provides a succinct, interpretable summary of the form and variety of community structure in any network. We demonstrate the method on a range of example networks.

cs.SI↗

arXiv2022

Clustering of heterogeneous populations of networks

Statistical methods for reconstructing networks from repeated measurements typically assume that all measurements are generated from the same underlying network structure. This need not be the case, however. People's social networks might be different on weekdays and weekends, for instance. Brain networks may differ between healthy patients and those with dementia or other conditions. Here we describe a Bayesian analysis framework for such data that allows for the fact that network measurements may be reflective of multiple possible structures. We define a finite mixture model of the measurement process and derive a fast Gibbs sampling procedure that samples exactly from the full posterior distribution of model parameters. The end result is a clustering of the measured networks into groups with similar structure. We demonstrate the method on both real and synthetic network populations.

cs.SI↗

arXiv2021

The impact of inter-city mobility on urban welfare

While much effort has been devoted to understand the role of intra-urban characteristics on sustainability and growth, much remains to be understood about the effect of inter-urban interactions and the role cities have in determining each other's urban welfare. Here we consider a global mobility network of population flows between cities as a proxy for the communication between these regions, and analyze how these flows impact socioeconomic indicators that measure economic success. We use several measures of centrality to rank cities according to their importance in the mobility network, finding PageRank to be the most effective measure for reflecting these prosperity indicators. Our analysis reveals that the characterization of the welfare of cities based on mobility information hinges on their corresponding development stage. Namely, while network-based predictions of welfare correlate well with economic indicators in mature cities, for developing urban areas additional information about the prosperity of their mobility neighborhood is needed. For these developing cities, those that are connected to sets of mature cities show markedly better socio-economic indicators than those connected to less mature cities. We develop a simple generative model for the allocation of population flows out of a city that balances the costs and benefits of interaction with other cities that are successful, finding that it provides a strong fit to the flows observed in the global mobility network and highlights the differences in flow patterns between developed and developing urban regions. Our results hint towards the importance of leveraging inter-urban connections in service of urban development and welfare.

physics.soc-ph↗

arXiv2021

Belief propagation for networks with loops

Belief propagation is a widely used message passing method for the solution of probabilistic models on networks such as epidemic models, spin models, and Bayesian graphical models, but it suffers from the serious shortcoming that it works poorly in the common case of networks that contain short loops. Here we provide a solution to this long-standing problem, deriving a belief propagation method that allows for fast calculation of probability distributions in systems with short loops, potentially with high density, as well as giving expressions for the entropy and partition function, which are notoriously difficult quantities to compute. Using the Ising model as an example, we show that our approach gives excellent results on both real and synthetic networks, improving significantly on standard message passing methods. We also discuss potential applications of our method to a variety of other problems.

cond-mat.stat-mech↗

arXiv2020

The friendship paradox in real and model networks

The friendship paradox is the observation that the degrees of the neighbors of a node in any network will, on average, be greater than the degree of the node itself. In common parlance, your friends have more friends than you do. In this paper we develop the mathematical theory of the friendship paradox, both in general as well as for specific model networks, focusing not only on average behavior but also on variation about the average and using generating function methods to calculate full distributions of quantities of interest. We compare the predictions of our theory with measurements on a large number of real-world network data sets and find remarkably good agreement. We also develop equivalent theory for the generalized friendship paradox, which compares characteristics of nodes other than degree to those of their neighbors.

cs.SI↗

arXiv2020

Information theoretic network approach to socioeconomic correlations

Due to its wide reaching implications for everything from identifying hotspots of income inequality to political redistricting, there is a rich body of literature across the sciences quantifying spatial patterns in socioeconomic data. In particular, the variability of indicators relevant to social and economic well-being between localized populations is of great interest, as it pertains to the spatial manifestations of inequality and segregation. However, heterogeneity in population density, sensitivity of statistical analyses to spatial aggregation, and the importance of pre-drawn political boundaries for policy intervention may decrease the efficacy and relevance of existing methods for analyzing spatial socioeconomic data. Additionally, these measures commonly lack either a framework for comparing results for qualitative and quantitative data on the same scale, or a mechanism for generalization to multi-region correlations. To mitigate these issues associated with traditional spatial measures, here we view local deviations in socioeconomic variables from a topological lens rather than a spatial one, and use a novel information theoretic network approach based on the Generalized Jensen Shannon Divergence to distinguish distributional quantities across adjacent regions. We apply our methodology in a series of experiments to study the network of neighboring census tracts in the continental US, quantifying the decay in two-point distributional correlations across the network, examining the county-level socioeconomic disparities induced from the aggregation of tracts, and constructing an algorithm for the division of a city into homogeneous clusters. These results provide a new framework for analyzing the variation of attributes across regional populations, and shed light on new, universal patterns in socioeconomic attributes.

physics.soc-ph↗

arXiv2020

Robust Design from Systems Physics

A crucial challenge in engineering modern, integrated systems is to produce robust designs. Ensuring robust design is difficult because subsystem couplings produce unpredictable response to changes in whole system specifications. Here, we show that the response of design elements to whole-system specification changes can be characterized, as materials are, using strong/weak and brittle/ductile dichotomies. We find these dichotomies emerge from a mesoscale treatment of early stage design problems that we cast in terms of stress-strain relationships. Compared with other state-of-the-art techniques, we propose a two-factor robustness metric that is computable for sets of design solutions. We illustrate the use of this approach with examples of arrangement problems drawn from naval engineering, however our approach is immediately applicable to a broad range of problems in integrated systems design.

physics.soc-ph↗

arXiv2020

Online geolocalized emotion across US cities during the COVID crisis: Universality, policy response, and connection with local mobility

As the COVID-19 pandemic began to sweep across the US it elicited a wide spectrum of responses, both online and offline, across the population. To aid the development of effective spatially targeted interventions in the midst of this turmoil, it is important to understand the geolocalization of these online emotional responses, as well as their association with offline behavioral responses. Here, we analyze around 13 million geotagged tweets in 49 cities across the US from the first few months of the pandemic to assess regional dependence in online sentiments with respect to a few major topics, and how these sentiments correlate with policy development and human mobility. Surprisingly, we observe universal trends in overall and topic-based sentiments across cities over the time period studied, with variability primarily seen only in the immediate impact of federal guidelines and local lockdown policies. We also find that these local sentiments are highly correlated with and predictive of city-level mobility, while the correlations between sentiments and local cases and deaths are relatively weak. Our findings point to widespread commonalities in the online public emotional responses to COVID across the US, both temporally and relative to offline indicators, in contrast with the high variability seen in early local containment policies. This study also provides new insights into the use of social media data in crisis management by integrating offline data to gain an in-depth understanding of public emotional responses, policy development, and local mobility.

physics.soc-ph↗

arXiv2020

Mixing Patterns in Interdisciplinary Collaboration Networks: Assessing Interdisciplinarity Through Multiple Lenses

There are inherent challenges to interdisciplinary research collaboration, such as bridging cognitive gaps and balancing transaction costs with collaborative benefits. This raises the question: Does interdisciplinary research necessarily result in interdisciplinary collaborations? This study aims to explore this question and assess collaboration preferences in interdisciplinary research at the individual, dyadic, and team level by examining mixing patterns in a collaboration network. Using a network of over 2,000 researchers from the field of artificial intelligence in education, we find that "interdisciplinarity" is demonstrated by diverse research experiences of individual researchers rather than diversity among researchers within collaborations. We also examine intergroup mixing by applying a novel approach to classify the active and non-active researchers in the collaboration network based on participation in multiple teams. We find a significant difference in indicators of academic performance and experience between the clusters of active and non-active researchers, suggesting intergroup mixing as a key factor in academic success. Our results shed light on the nature of team formation in interdisciplinary research, as well as highlight the importance of interdisciplinary programs.

cs.SI↗