Analysis of urban human mobility behavior based on random matrix theory

Kernel methods are an extremely popular set of techniques used for many important machine learning and data analysis applications. In addition to having good practical performance, these methods are supported by a well-developed theory. Kernel methods use an implicit mapping of the input data into a high dimensional feature space defined by a kernel function, i.e., a function returning the inner product between the images of two data points in the feature space. Central to any kernel method is the kernel matrix, which is built by evaluating the kernel function on a given sample dataset. In this paper, we initiate the study of non-asymptotic spectral properties of random kernel matrices. These are n x n random matrices whose (i,j)th entry is obtained by evaluating the kernel function on x_i and x_j, where x_1,..,x_n are a set of n independent random high-dimensional vectors. Our main contribution is to obtain tight upper bounds on the spectral norm (largest eigenvalue) of random kernel matrices constructed by using common kernel functions such as polynomials and Gaussian radial basis. As an application of these results, we provide lower bounds on the distortion needed for releasing the coefficients of kernel ridge regression under attribute privacy, a general privacy notion which captures a large class of privacy definitions. Kernel ridge regression is standard method for performing non-parametric regression that regularly outperforms traditional regression approaches in various domains. Our privacy distortion lower bounds are the first for any kernel technique, and our analysis assumes realistic scenarios for the input, unlike all previous lower bounds for other release problems which only hold under very restrictive input settings.

The quality of life for people in urban regions can be improved by predicting urban human mobility and adjusting urban planning accordingly. In this study, we compared several possible variables to verify whether a gravity model (a human mobility prediction model borrowed from Newtonian mechanics) worked as well in inner-city regions as it did in intra-city regions. We reviewed the resident population, the number of employees, and the number of SNS posts as variables for generating mass values for an urban traffic gravity model. We also compared the straight-line distance, travel distance, and the impact of time as possible distance values. We defined the functions of urban regions on the basis of public records and SNS data to reflect the diverse social factors in urban regions. In this process, we conducted a dimension reduction method for the public record data and used a machine learning-based clustering algorithm for the SNS data. In doing so, we found that functional distance could be defined as the Euclidean distance between social function vectors in urban regions. Finally, we examined whether the functional distance was a variable that had a significant impact on urban human mobility.

Location-based check-in services enable individuals to share their activity-related choices and providing a new source of human activity data for researchers. In this paper urban human mobility and activity patterns are analyzed using location-based data collected from social media applications (e.g. Foursquare and Twitter). We first characterize aggregate activity patterns by finding the distributions of different activity categories over a city geography and thus determine the purpose-specific activity centers. We then characterize individual activity patterns by finding the timing distribution of visiting different places depending on activity category. We also explore the frequency of visiting a place with respect to the rank of the place in individual's visitation records and show interesting match with other results based on mobile phone mobility data. We finally propose a physics-based model of human mobility patterns that can explain the scaling laws observed in the data.

Urban human mobility prediction is forecasting how people move in cities. It is crucial for many smart city applications including route optimization, preparing for dramatic shifts in modes of transportation, or mitigating the epidemic spread of viruses such as COVID-19. Previous research propose the maximum predictability to derive the theoretical limits of accuracy that any predictive algorithm could achieve on predicting urban human mobility. However, existing maximum predictability only considers the sequential patterns of human movements and neglects the contextual information such as the time or the types of places that people visit, which plays an important role in predicting one's next location. In this paper, we propose new theoretical limits of predictability, namely Context-Transition Predictability, which not only captures the sequential patterns of human mobility, but also considers the contextual information of human behavior. We compare our Context-Transition Predictability with other kinds of predictability and find that it is larger than these existing ones. We also show that our proposed Context-Transition Predictability provides us a better guidance on which predictive algorithm to be used for forecasting the next location when considering the contextual information. Source code is at https://github.com/zcfinal/ContextTransitionPredictability.

We survey the connections between the six-vertex (square ice) model of 2D statistical mechanics and random matrix theory. We highlight the same universal probability distributions appearing on both sides, and also indicate related open questions and conjectures. We present full proofs of two asymptotic theorems for the six-vertex model: in the first one the Gaussian Unitary Ensemble (GUE) and GUE–corners process appear; the second one leads to the Tracy–Widom distribution F 2 F_2 . While both results are not new, we found shorter transparent proofs for this text. On our way we introduce the key tools in the study of the six-vertex model, including the Yang–Baxter equation and the Izergin–Korepin formula.

We study the phenomenon of "crowding" near the largest eigenvalue $\lambda_{\max}$ of random $N \times N$ matrices belonging to the Gaussian Unitary Ensemble (GUE) of random matrix theory. We focus on two distinct quantities: (i) the density of states (DOS) near $\lambda_{\max}$, $\rho_{\rm DOS}(r,N)$, which is the average density of eigenvalues located at a distance $r$ from $\lambda_{\max}$ and (ii) the probability density function of the gap between the first two largest eigenvalues, $p_{\rm GAP}(r,N)$. In the edge scaling limit where $r = {\cal O}(N^{-1/6})$, which is described by a double scaling limit of a system of unconventional orthogonal polynomials, we show that $\rho_{\rm DOS}(r,N)$ and $p_{\rm GAP}(r,N)$ are characterized by scaling functions which can be expressed in terms of the solution of a Lax pair associated to the Painlev\'e XXXIV equation. This provides an alternative and simpler expression for the gap distribution, which was recently studied by Witte, Bornemann and Forrester in Nonlinearity 26, 1799 (2013). Our expressions allow to obtain precise asymptotic behaviors of these scaling functions both for small and large arguments.

Maladaptive Mobile Phone Use (MMPU) (also known as Smartphone Addiction, Nomophobia, Fear of Missing Out, or Problematic Mobile Phone Use) is a growing mental health problem. However, the health and safety consequences of MMPU remain unexplored in many real-life contexts. A potential setting where MMPU may have some negative repercussions is on the road. It is well established that road users (e.g., drivers, motorcyclists, pedestrians, and cyclists) increasingly injure themselves or others due to distractions such as phone use while on the road. Emerging research suggests that MMPU is a possible determinant of this risky behaviour. Therefore, it is essential to investigate the relationship between MMPU and mobile phone use behaviour on the road, as it could help guide and improve interventions aimed at increasing road safety. This systematic review investigated the relationship between maladaptive mobile phone use and mobile phone use behaviour on the road in terms of attitudes and risk perception, intention, phone use engagement, performance changes, and safety outcomes. A total of 44 studies were identified with 47 unique samples of road users, of which 68.1% (32/47) were comprised of drivers, 19.1% (9/47) were pedestrians, 8.5% (4/47) were unspecified road users, and there was one group of motorcyclists and cyclists. Our findings confirmed that MMPU is related to risky behaviour on the roads. In the 29 studies considering observed or self-reported behaviour, 90.9% (30/33) found that road users who scored higher in MMPU are more likely to use their phones on the road as cyclists, drivers, motorcyclists, and pedestrians. Of the nine studies that analysed performance changes, 55.6% (5/9) showed evidence that MMPU changes the performance of road users engaging in mobile phone use, meaning that there is evidence suggesting that MMPU determines the level of impairment. Of the nine studies that analysed the safety-related-outcomes, 66.7% (6/9) found that the higher the MMPU score, the more likely road users are to experience safety–critical traffic events. This review contributes to the literature by showing a pathway between the negative health consequences of MMPU and road trauma. We also identified that the quality of the studies was generally low due to study design and blinding aspects. This field of research also lacks standard practices as researchers avoid using established and well-validated questionnaires, often creating new ones to measure MMPU. This hinders the generalisability of the findings and raises questions about the construct validity and external validity of MMPU. The usefulness of future research would be enhanced by a consistent methodological approach using the same scales based on standard behavioural definitions. The cross-disciplinary nature of MMPU effects means that transport and road safety professionals need to work with healthcare professionals and technology organisations to understand and address MMPU as a contributing factor to road crashes.

The most representative form of cyber-physical systems (CPSs) involves wireless sensor networks (WSNs) as the main means to interact with physical entities. This chapter reviews a number of such WSN-CPS applications and reveals how these applications bridge the gap between sensing information in the cyber world and diverse entities in the physical world. We divide these applications into five categories: smart space systems, healthcare systems, emergency response systems, human activity inference, and smart city systems. Smart space systems monitor energy usage, temperature, and various other attributes of appliances in an indoor space. Healthcare systems assist people to improve physical and emotional well-being through automatic sensing and sense-making technologies. Emergency response systems search for and rescue people as soon as possible in emergency situations such as fire outbreaks. Human activity inference systems interpret human intention behind sensing information to facilitate human daily activities related to social events, road safety, mood detection, interactive games, etc. Smart city systems concentrate on city dynamics such as urban environmental monitoring, human mobility, and transport information. Our discussion in this chapter is steered from simple to complex systems in terms of networking technologies, service ranges, system integration, and human engagement. We conclude by discussing important technical components, future trends, and open issues in WSN-CPS applications in order to provide readers with technical pointers for designing next-generation WSN-CPS applications.

This chapter highlights the critical value of analyzing urban human mobility during natural disasters, focusing on how emerging data sources and advanced analytical techniques inform disaster response, preparedness, and resilience planning. As urbanization intensifies and climate-related hazards become more frequent, understanding evacuation patterns, transportation disruptions, and compliance with evacuation orders is increasingly vital. The chapter first reviews traditional survey methods and introduces newer data types—including mobile phone global positioning system (GPS) traces, social media posts, and remote sensing imagery—that provide near real-time, high-resolution insights into population movements. It then discusses cutting-edge geospatial artificial intelligence (GeoAI) approaches for integrating these diverse datasets to detect complex mobility patterns. A case study of Hurricane Ian in Florida demonstrates how mobility data can uncover spatial variations in evacuation behaviors and highlight the impacts of evacuation orders. This example illustrates how data-driven methods reveal routes, destinations, and population segments most affected, guiding more equitable and effective interventions. Despite these advances, challenges remain concerning privacy, data representativeness, and integrating multisource information. The chapter concludes that as data and technologies evolve, harnessing human mobility insights will enhance disaster preparedness, promote targeted resource allocation, and ultimately support the development of more resilient urban communities.

In this paper we study, Prob (n, a, b), the probability that all the eigenvalues of finite n unitary ensembles lie in the interval (a, b). This is identical to the probability that the largest eigenvalue is less than b and the smallest eigenvalue is greater than a. It is shown that a quantity allied to Prob (n, a, b), namely, [Formula: see text] in the Gaussian Unitary Ensemble (GUE) and [Formula: see text], in the Laguerre Unitary Ensemble (LUE) satisfy certain nonlinear partial differential equations for fixed n, interpreting Hn(a, b) as a function of a and b. These partial differential equations may be considered as two variable generalizations of a Painlevé IV and a Painlevé V system, respectively. As an application of our result, we give an analytic proof that the extreme eigenvalues of the GUE and the LUE, when suitably centered and scaled, are asymptotically independent.

BackgroundHuman mobility behaviour modelling plays an essential role in the understanding and control of the spread of contagious diseases by limiting the contact among individuals, predicting the spatio-temporal evolution of an epidemic and inferring migration patterns. It informs programmatic and policy decisions for effective and efficient intervention. The objective of this research is to assess the human mobility pattern and analyse its implication for malaria disease epidemiology.MethodsIn this study, human mobility patterns in Benishangul-Gumuz and Gambella regions in Western Ethiopia were explored based on a cellular network mobility parameter (e.g., handover rate) via real world data. Anonymized data were retrieved for mobile active users with mobility related information. The data came from anonymous traffic records collected from all the study areas. For each cell, the necessary mobility parameter data per hour, week and month were collected. A scale factor was computed to change the mobility parameter value to the human mobility pattern. Finally, the relative human mobility probability for each scenario was estimated. MapInfo and Matlab softwares were used for visualization and analysis purposes. Hourly travel patterns in the study settings were compared with hourly malaria mosquito vector feeding behaviour.ResultsHeterogeneous human movement patterns were observed in the two regions with some areas showing typically high human mobility. Furthermore, the number of people entering into the two study regions was high during the highest malaria transmission season. Two peaks of hourly human movement, 8:00 to 9:00 and 16:00 to 18:00, emerged in Benishangul-Gumuz region while 8:00 to 10:00 and 16:00 to 18:00 were the peak hourly human mobility time periods in Gambella region. The high human movement in the night especially before midnight in the two regions may increase the risk of getting mosquito bite particularly by early biters depending on malaria linked human behaviour of the population.ConclusionsHigh human mobility was observed both within and outside the two regions. The population influx and efflux in these two regions is considerably high. This may specifically challenge the transition from malaria control to elimination. The daily mobility pattern is worth considering in the context of malaria transmission. In line with this malaria related behavioural patterns of humans need to be properly addressed.

Digital technologies have recently become more advanced, allowing for the development of social networking sites and applications. Despite these advancements, phone calls and text messages still make up the largest proportion of mobile data usage. It is possible to study human communication behaviors and mobility patterns using the useful information that mobile phone data provide. Specifically, the digital traces left by the large number of mobile devices provide important information that facilitates a deeper understanding of human behavior and mobility configurations for researchers in various fields, such as criminology, urban sensing, transportation planning, and healthcare. Mobile phone data record significant spatiotemporal (i.e., geospatial and time-related data) and communication (i.e., call) information. These can be used to achieve different research objectives and form the basis of various practical applications, including human mobility models based on spatiotemporal interactions, real-time identification of criminal activities, inference of friendship interactions, and density distribution estimation. The present research primarily reviews studies that have employed mobile phone data to investigate, assess, and predict human communication and mobility patterns in the context of crime prevention. These investigations have sought, for example, to detect suspicious activities, identify criminal networks, and predict crime, as well as understand human communication and mobility patterns in urban sensing applications. To achieve this, a systematic literature review was conducted on crime research studies that were published between 2014 and 2022 and listed in eight electronic databases. In this review, we evaluated the most advanced methods and techniques used in recent criminology applications based on mobile phone data and the benefits of using this information to predict crime and detect suspected criminals. The results of this literature review contribute to improving the existing understanding of where and how populations live and socialize and how to classify individuals based on their mobility patterns. The results show extraordinary growth in studies that utilized mobile phone data to study human mobility and movement patterns compared to studies that used the data to infer communication behaviors. This observation can be attributed to privacy concerns related to acquiring call detail records (CDRs). Additionally, most of the studies used census and survey data for data validation. The results show that social network analysis tools and techniques have been widely employed to detect criminal networks and urban communities. In addition, correlation analysis has been used to investigate spatial–temporal patterns of crime, and ambient population measures have a significant impact on crime rates.

The aim of this work is to build a class of financial crisis indicators based on the spectral properties of the dynamics of market data. After choosing an appropriate size for a rolling window, the historical market data inside this rolling window are seen every trading day as a random matrix from which a correlation matrix is obtained. Our goal is to study the correlations between the assets that constitute this market and look for reproducible patterns that are indicative of an impending financial crisis. A weighting of the assets in the market is then introduced and is proportional to the daily traded volumes. This manipulation is realized in order to give more importance to the most liquid assets. Our financial crisis indicators are based on the spectral radius of this weighted correlation matrix. The idea behind this type of financial crisis indicators is that large eigenvalues are a sign of dynamic instability. The out-of-sample predictive power of the financial crisis indicators in this framework is then demonstrated, in particular by using them as decision-making tools in a protective put strategy.

Rapidly developing location acquisition technologies provide a powerful tool for understanding and predicting human mobility in cities, which is very significant for urban planning, traffic regulation, and emergency management. However, with the existing methodologies, it is still difficult to accurately predict millions of peoples’ mobility in a large urban area such as Tokyo, Shanghai, and Hong Kong, especially when collected data used for model training are often limited to a small portion of the total population. Obviously, human activities in city are closely linked with point-of-interest (POI) information, which can reflect the semantic meaning of human mobility. This motivates us to fuse human mobility data and city POI data to improve the prediction performance with limited training data, but current fusion technologies can hardly handle these two heterogeneous data. Therefore, we propose a unique POI-embedding mechanism, that aggregates the regional POIs by categories to generate an artificial POI-image for each urban grid and enriches each trajectory snippet to a four-dimensional tensor in an analogous manner to a short video. Then, we design a deep learning architecture combining CNN with LSTM to simultaneously capture both the spatiotemporal and geographical information from the enriched trajectories. Furthermore, transfer learning is employed to transfer mobility knowledge from one city to another, so that we can fully utilize other cities’ data to train a stronger model for the target city with only limited data available. Finally, we achieve satisfactory performance of human mobility prediction at the citywide level using a limited amount of trajectories as training data, which has been validated over five urban areas of different types and scales.

The prediction of human and vehicle mobility in a city is becoming an attracting field. This topic attracts researchers from broad fields including behavioral sciences, where understanding the complexity of the human mobility behavior is one of the hot topic, and also to the industrial partners, who apply such results to many beneficial applications. Recent progress to sensing human mobility via smartphones is boosting this trend. However, due to the complexity and context-dependence of human behavior and the incompleteness and noise of geospatial data collecting from various sensors, the prediction of human and vehicle mobility is still far from solved. This workshop aimed at collecting contributions on the cutting-edge studies in human mobility description, modeling, intelligent computational method which can advance the human and vehicle prediction research. Potential topics included, but were not limited to 1) The next location prediction of individual mobility, 2) The crowd or population mobility prediction, 3) Dynamics of pedestrians, 4) commute flow and migration flow, 5) Traffic congestion, road usage forecast and optimal vehicle routing, 6) Social event forecast using geospatial data, 7) Novel agent mobility simulators, and 8) Case studies of mobility estimation in academia as well as in industrial field.