Christopher Monterola

The simplified self-consistent probabilities method for percolation and its application to interdependent networks

Interdependent networks in areas ranging from infrastructure to economics are ubiquitous in our society, and the study of their cascading behaviors using percolation theory has attracted much attention in recent years. To analyze the percolation phenomena of these systems, different mathematical frameworks have been proposed, including generating functions and eigenvalues, and others. These different frameworks approach phase transition behaviors from different angles and have been very successful in shaping the different quantities of interest, including critical threshold, size of the giant component, order of phase transition, and the dynamics of cascading. These methods also vary in their mathematical complexity in dealing with interdependent networks that have additional complexity in terms of the correlation among different layers of networks or links. In this work, we review a particular approach of simple, self-consistent probability equations, and we illustrate that this approach can greatly simplify the mathematical analysis for systems ranging from single-layer network to various different interdependent networks. We give an overview of the detailed framework to study the nature of the critical phase transition, the value of the critical threshold, and the size of the giant component for these different systems.

Self-organized critical branching in systems that violate conservation laws

A non-conservative critical branching model is proposed to demonstrate that self-organized criticality (SOC) can occur in mean-field sandpiles that violate a conservation law. The critical state is characterized by avalanche sizes and lifetimes that obey an inverse power-law distribution with exponents τS = 3/2 and τT = 2, respectively. Criticality is achieved when the branching process is coupled to a background activity characterized by the spontaneous switching between refractoriness and quiescence among system components. The stationary state of the system is analysed mathematically and numerically, and is shown to exhibit a transition from a subcritical phase to a critical phase. SOC in sandpile models has been widely believed to occur only when grains are conserved during avalanches. However, such a conservation law is likely to be violated by open, non-equilibrium systems such as biological networks and socially interacting systems like animal groups. The model explores the role of dynamic synapses and synaptic plasticity in maintaining criticality of cortical networks. These brain networks have been found to display neuronal avalanches that obey a power-law distribution. The non-conservative model also emulates the main features of the size distributions of free-swimming tuna schools and red deer herds. Demonstrating criticality in self-organizing systems that violate conservation laws enhances the predictive ability of the theory of SOC in the arena of biocomplexity.

The Emergence of Urban Land Use Patterns Driven by Dispersion and Aggregation Mechanisms

We employ a cellular-automata to reconstruct the land use patterns of cities that we characterize by two measures of spatial heterogeneity: (a) a variant of spatial entropy, which measures the spread of residential, business, and industrial activity sectors, and (b) an index of dissimilarity, which quantifies the degree of spatial mixing of these land use activity parcels. A minimalist and bottom-up approach is adopted that utilizes a limited set of three parameters which represent the forces which determine the extent to which each of these sectors spatially aggregate into clusters. The dispersion degrees of the land uses are governed by a fixed pre-specified power-law distribution based on empirical observations in other cities. Our method is then used to reconstruct land use patterns for the city state of Singapore and a selection of North American cities. We demonstrate the emergence of land use patterns that exhibit comparable visual features to the actual city maps defining our case studies whilst sharing similar spatial characteristics. Our work provides a complementary approach to other measures of urban spatial structure that differentiate cities by their land use patterns resulting from bottom-up dispersion and aggregation processes.

Automated Identification of Core Regulatory Genes in Human Gene Regulatory Networks.

Human gene regulatory networks (GRN) can be difficult to interpret due to a tangle of edges interconnecting thousands of genes. We constructed a general human GRN from extensive transcription factor and microRNA target data obtained from public databases. In a subnetwork of this GRN that is active during estrogen stimulation of MCF-7 breast cancer cells, we benchmarked automated algorithms for identifying core regulatory genes (transcription factors and microRNAs). Among these algorithms, we identified K-core decomposition, pagerank and betweenness centrality algorithms as the most effective for discovering core regulatory genes in the network evaluated based on previously known roles of these genes in MCF-7 biology as well as in their ability to explain the up or down expression status of up to 70% of the remaining genes. Finally, we validated the use of K-core algorithm for organizing the GRN in an easier to interpret layered hierarchy where more influential regulatory genes percolate towards the inner layers. The integrated human gene and miRNA network and software used in this study are provided as supplementary materials (S1 Data) accompanying this manuscript.

Classification and unification of the microscopic deterministic traffic models.

We identify a universal mathematical structure in microscopic deterministic traffic models (with identical drivers), and thus we show that all such existing models in the literature, including both the two-phase and three-phase models, can be understood as special cases of a master model by expansion around a set of well-defined ground states. This allows any two traffic models to be properly compared and identified. The three-phase models are characterized by the vanishing of leading orders of expansion within a certain density range, and as an example the popular intelligent driver model is shown to be equivalent to a generalized optimal velocity (OV) model. We also explore the diverse solutions of the generalized OV model that can be important both for understanding human driving behaviors and algorithms for autonomous driverless vehicles.

Inferring Passenger Type from Commuter Eigentravel Matrices

ABSTRACT A sufficient knowledge of the demographics of a commuting public is essential in formulating and implementing more targeted transportation policies. Here, a procedure is demonstrated that classifies passengers (Adult, Child/Student, and Senior Citizen) based on their three-month travel patterns. The method proceeds by constructing distinct commuter matrices, we refer to as eigentravel matrices, that capture a commuters characteristic travel routine. Comparing various classification models, we show that the gradient boosting method gives the best prediction with 76% accuracy, 81% better than the minimum model accuracy (42%) computed using proportional chance criterion. The models are verified and validated; consequently, the procedure demonstrated should serve as a benchmark for problems of this type. The generally intuitive pattern of the demographic classification also points to a possible universal ‘travelprint’ of commuters, and can inspire development of unsupervised machine learning methods for automated fare collection systems that do not provide additional demographic detail.

A Method to Ascertain Rapid Transit Systems’ throughput Distribution Using Network Analysis

Abstract We present a method of predicting the distribution of passenger throughput across stations and lines of a city rapid transit system by calculating the normalized betweenness centrality of the nodes (stations) and edges of the rail network. The method is evaluated by correlating the distribution of betweenness centrality against throughput distribution which is calculated using actual passenger ridership data. Our ticketing data is from the rail transport system of Singapore that comprises more than 14 million journeys over a span of one week. We demonstrate that removal of outliers representing about 10% of the stations produces a statistically significant correlation above 0.7. Interestingly, these outliers coincide with stations that opened six months before the time the ridership data was collected, hinting that travel routines along these stations have not yet settled to its equilibrium. The correlation is improved significantly when the data points are split according to their separate lines, illustrating differences in the intrinsic characteristics of each line. The simple procedure established here shows that static network analysis of the structure of a transport network can allow transport planners to predict with sufficient accuracy the passenger ridership, without requiring dynamic and complex simulation methods.

A QUANTITATIVE PROCEDURE FOR THE SPATIAL CHARACTERIZATION OF URBAN LAND USE

We have developed a procedure that characterizes the land use pattern of an urban system using: (a) Spatial entropy that measures the extent of spread of residential, business and industrial sectors; and (b) Index of dissimilarity that quantifies the degree of mixing in space of different sectors. The approach is illustrated by using the land use zoning maps of the city state of Singapore and a selection of North American cities. We show that a common feature of most cities is for the industrial areas to be highly clustered while at the same time segregated from the residential or business districts. We also demonstrate that the combination of entropy of residential and dissimilarity index between residential and business areas provides a quantitative and potentially useful means of differentiating the land use pattern of different cities.

Efficiency and robustness of different bus network designs

We compare the efficiencies and robustness of four transport networks that can be possibly formed as a result of deliberate city planning. The networks are constructed based on their spatial resemblance to the cities of Manhattan (lattice), Sudan (random), Beijing (single-blob) and Greater Cairo (dual-blob). For a given type, a genetic algorithm is employed to obtain an optimized set of the bus routes. We then simulate how commuter travels using Yens algorithms for k shortest paths on an adjacency matrix. The cost of traveling such as walking between stations is captured by varying the weighted sums of matrices. We also consider the number of transfers a posteriori by looking at the computed shortest paths. With consideration to distances via radius of gyration, redundancies of travel and number of bus transfers, our simulations indicate that random and dual-blob are more efficient than single-blob and lattice networks. Moreover, dual-blob type is least robust when node removals are targeted but is most resilient when node failures are random. The work hopes to guide and provide technical perspectives on how geospatial distribution of a city limits the optimality of transport designs.

Simulating Congestion Dynamics of Train Rapid Transit Using Smart Card Data

Investigating congestion in train rapid transit systems (RTS) in todays urban cities is a challenge compounded by limited data availability and difficulties in model validation. Here, we integrate information from travel smart card data, a mathematical model of route choice, and a full-scale agent-based model of the Singapore RTS to provide a more comprehensive understanding of the congestion dynamics than can be obtained through analytical modelling alone. Our model is empirically validated, and allows for close inspection of the dynamics including station crowdedness, average travel duration, and frequency of missed trains---all highly pertinent factors in service quality. Using current data, the crowdedness in all 121 stations appears to be distributed log-normally. In our preliminary scenarios, we investigate the effect of population growth on service quality. We find that the current population (2 million) lies below a critical point; and increasing it beyond a factor of