arXiv subjects

Dane Taylor

Publications and source records attributed to Dane Taylor.

At least 19 recordsLinked to original sources

arXiv2026

Predictability of Human Movements across Industry Sectors using Multilayer Networks

Understanding the spatiotemporal patterns of human movement is important across diverse applications including urban design, disease control, social and cognitive science, and emergency response planning. Recently, multilayer mobility networks were used to study how movements between spatial units (e.g., census tracts) can significantly vary when they are stratified according to different industry sectors-e.g., movements to grocery stores, to schools, or to hospitals. Here, we study the predictability of movements across different industry sectors using statistical and machine learning models trained on demographic, socioeconomic, and infrastructure information. We compare ten predictive models and identify advantages for nonlinear models (with random forest regression being a consistent top performer). We identify the most important features enabling prediction (population size for outward movements from regions and industry-related infrastructure for movements into regions). Of the two, prediction for inward movements (i.e., in-degrees) is generally more difficult; however, the difference is small for movements associated with food services. We also compare the prediction of weekly and time-averaged movements, finding that with the addition of time-encoding input features, weekly movements are easier to predict than time-averaged values (at least for the nonlinear predictive models). These findings provide a practical step toward using machine learning for human movement modeling and the many downstream applications.

physics.soc-ph↗

arXiv2026

GradNet: A Gradient-Based Framework for Optimal Network Science

Network science has traditionally examined how structure determines dynamics. Here we invert this paradigm: we ask how functional dynamics and resource constraints shape network architecture. We introduce GradNet, an AI-enabled optimization framework that treats network topology as a continuously differentiable object. This allows designing networks that optimize arbitrary dynamical objectives, from synchronization to communication capacity, under realistic constraints. Applying this framework across diverse systems reveals that canonical network features emerge spontaneously from constrained optimization rather than requiring explicit imposition. Optimizing Kuramoto oscillator synchronization under fixed coupling budgets produces sparse, bipartite, frequency-disassortative architectures that eliminate classical synchronization thresholds. Minimizing social tension in opinion dynamics reproduces the empirically observed factional split in Zachary's karate club network. Maximizing entanglement distribution in spatial quantum networks under distance-dependent costs recovers minimum spanning tree architectures. These results demonstrate that optimization acts as both an engineering tool for network design, scalable to networks exceeding $10^5$ nodes, and a scientific probe revealing fundamental structure-function relationships. By recasting network architecture as the solution to constrained optimization problems, this variational perspective offers a unified framework connecting network analysis, design, and inference across physical, biological, and technological systems.

physics.soc-ph↗

arXiv2026

Hodge Decomposition Guides the Optimization of Synchronization over Simplicial Complexes

Despite growing interest in synchronization dynamics over "higher-order" network models, optimization theory for such systems is limited. Here, we study a family of Kuramoto models inspired by algebraic topology in which oscillators are coupled over simplicial complexes (SCs) using their associated Hodge Laplacian matrices. We optimize such systems by extending the synchrony alignment function -- an optimization framework for synchronizing graph-coupled heterogeneous oscillators. Computational experiments are given to illustrate how this approach can effectively solve a variety of combinatorial problems including the joint optimization of projected synchronization dynamics onto lower- and upper-dimensional simplices within SCs. We also investigate the role of SC homology and develop bifurcation theory to characterize the extent to which optimal solutions are contained within (or spread across) the three Hodge subspaces. Our work extends optimization theory to the setting of higher-order networks, provides practical algorithms for Hodge-Laplacian-related dynamics including (but not limited to) Kuramoto oscillators, and paves the way for an emerging field that interfaces algebraic topology, combinatorial optimization, and dynamical systems.

nlin.AO↗

arXiv2025

Emergent Topology of Optimal Networks for Synchrony

Designing high-performing networks requires optimizing for functionality while respecting physical, geometric, or budget constraints. Yet, mathematical and computational tools to design such systems remain limited, particularly for collective dynamics arising from heterogeneous dynamical units. Here, we develop a gradient-based optimization framework to identify synchrony-optimal weighted networks under a constrained coupling budget. The resulting networks exhibit counterintuitive properties: they are sparse, bipartite, elongated, and extremely monophilic (i.e., the neighbors of any node are similar to one another while differing from the node itself). These structural patterns persist across dynamical models ranging from the power-grid swing equations to chaotic R\"ossler systems, suggesting broad applicability to coupled oscillator technologies. To gain insight, we develop a "constructive" theory for coupled Kuramoto oscillators: a nonlinear differential equation identifies which pairs of nodes are coupled, while a variational principle prescribes the budget allocated to each node. Dynamics unfolding over optimal networks provably lack a synchronization threshold; instead, as the budget exceeds a calculable critical value, the system globally phase-locks, exhibiting critical scaling at the transition. Together, our findings offer design principles for synchrony-dependent technologies with potential applications ranging from microgrids to laser arrays and quantum oscillators.

nlin.AO↗

arXiv2025

Multilayer networks characterize human-mobility patterns by industry sector for the 2021 Texas winter storm

Understanding human mobility during disastrous events is crucial for emergency planning and disaster management. We develop a methodology to construct time-varying, multilayer networks where edges encode observed movements between spatial regions (census tracts) and network layers encode movement categories by industry sectors (e.g., schools, hospitals). Using the 2021 Texas winter storm as a case study, we find that people markedly reduced movements to ambulatory healthcare services, restaurants, and schools, but prioritized movements to grocery stores and gas stations. Additionally, we study the predictability of nodes' in- and out-degrees in the multilayer networks, which encode movements into and out of census tracts. Inward movements prove harder to predict than outward movements, especially during the storm. Our findings on the reduction, prioritization, and predictability of sector-specific movements aim to support mobility-related decisions during future extreme weather events.

physics.soc-ph↗

arXiv2024

A Parrondo paradox in susceptible-infectious-susceptible dynamics over periodic temporal networks

Many social and biological networks periodically change over time with daily, weekly, and other cycles. Thus motivated, we formulate and analyze susceptible-infectious-susceptible (SIS) epidemic models over temporal networks with periodic schedules. More specifically, we assume that the temporal network consists of a cycle of alternately used static networks, each with a given duration. We observe a phenomenon in which two static networks are individually above the epidemic threshold but the alternating network composed of them renders the dynamics below the epidemic threshold, which we refer to as a Parrondo paradox for epidemics. We find that network structure plays an important role in shaping this phenomenon, and we study its dependence on the connectivity between and number of subpopulations in the network. We associate such paradoxical behavior with anti-phase oscillatory dynamics of the number of infectious individuals in different subpopulations.

physics.soc-ph↗

arXiv2022

Ranking Edges by their Impact on the Spectral Complexity of Information Diffusion over Networks

Despite the numerous ways now available to quantify which parts or subsystems of a network are most important, there remains a lack of centrality measures that are related to the complexity of information flows and are derived directly from entropy measures. Here, we introduce a ranking of edges based on how each edge's removal would change a system's von Neumann entropy (VNE), which is a spectral-entropy measure that has been adapted from quantum information theory to quantify the complexity of information dynamics over networks. We show that a direct calculation of such rankings is computationally inefficient (or unfeasible) for large networks: e.g.\ the scaling is $\mathcal{O}(N^3)$ per edge for networks with $N$ nodes. To overcome this limitation, we employ spectral perturbation theory to estimate VNE perturbations and derive an approximate edge-ranking algorithm that is accurate and fast to compute, scaling as $\mathcal{O}(N)$ per edge. Focusing on a form of VNE that is associated with a transport operator $e^{-\beta{ L}}$, where ${ L}$ is a graph Laplacian matrix and $\beta>0$ is a diffusion timescale parameter, we apply this approach to diverse applications including a network encoding polarized voting patterns of the 117th U.S. Senate, a multimodal transportation system including roads and metro lines in London, and a multiplex brain network encoding correlated human brain activity. Our experiments highlight situations where the edges that are considered to be most important for information diffusion complexity can dramatically change as one considers short, intermediate and long timescales $\beta$ for diffusion.

physics.soc-ph↗

arXiv2022

Persistent Homology with k-nearest-neighbor Filtrations reveals Topological Convergence of PageRank

Graph-based representations of point-cloud data are widely used in data science and machine learning, including epsilon-graphs that contain edges between pairs of data points that are nearer than epsilon and kNN-graphs that connect each point to its k-nearest neighbors. Recently, topological data analysis has emerged as a family of mathematical and computational techniques to investigate topological features of data using simplicial complexes. These are a higher-order generalization of graphs and many techniques such as Vietoris-Rips (VR) filtrations are also parameterized by a distance epsilon. Here, we develop kNN complexes as a generalization of kNN graphs, leading to kNN-based persistent homology techniques for which we develop stability and convergence results. We apply this technique to characterize the convergence properties PageRank, highlighting how the perspective of discrete topology complements traditional geometrical-based analyses of convergence. Specifically, we show that convergence of relative positions (i.e., ranks) is captured by kNN persistent homology, whereas persistent homology with VR filtrations coincides with vector-norm convergence. Beyond PageRank, kNN-based persistent homology is expected to be useful to other data-science applications in which the relative positioning of data points is more important than their precise locations.

math.AT↗

arXiv2022

A tensor factorization model of multilayer network interdependence

Multilayer networks describe the rich ways in which nodes are related by accounting for different relationships in separate layers. These multiple relationships are naturally represented by an adjacency tensor. In this work we study the use of the nonnegative Tucker decomposition (NNTuck) of such tensors under a KL loss as an expressive factor model that naturally generalizes existing stochastic block models of multilayer networks. Quantifying interdependencies between layers can identify redundancies in the structure of a network, indicate relationships between disparate layers, and potentially inform survey instruments for collecting social network data. We propose definitions of layer independence, dependence, and redundancy based on likelihood ratio tests between nested nonnegative Tucker decompositions. Using both synthetic and real-world data, we evaluate the use and interpretation of the NNTuck as a model of multilayer networks. Algorithmically, we show that using expectation maximization (EM) to maximize the log-likelihood under the NNTuck is step-by-step equivalent to tensorial multiplicative updates for the NNTuck under a KL loss, extending a previously known equivalence from nonnegative matrices to nonnegative tensors.

cs.SI↗

arXiv2022

The role of alcohol outlet visits derived from mobile phone location data in enhancing domestic violence prediction at the neighborhood level

Domestic violence (DV) is a serious public health issue, with 1 in 3 women and 1 in 4 men experiencing some form of partner-related violence every year. Existing research has shown a strong association between alcohol use and DV at the individual level. Accordingly, alcohol use could also be a predictor for DV at the neighborhood level, helping identify the neighborhoods where DV is more likely to happen. However, it is difficult and costly to collect data that can represent neighborhood-level alcohol use especially for a large geographic area. In this study, we propose to derive information about the alcohol outlet visits of the residents of different neighborhoods from anonymized mobile phone location data, and investigate whether the derived visits can help better predict DV at the neighborhood level. We use mobile phone data from the company SafeGraph, which is freely available to researchers and which contains information about how people visit various points-of-interest including alcohol outlets. In such data, a visit to an alcohol outlet is identified based on the GPS point location of the mobile phone and the building footprint (a polygon) of the alcohol outlet. We present our method for deriving neighborhood-level alcohol outlet visits, and experiment with four different statistical and machine learning models to investigate the role of the derived visits in enhancing DV prediction based on an empirical dataset about DV in Chicago. Our results reveal the effectiveness of the derived alcohol outlets visits in helping identify neighborhoods that are more likely to suffer from DV, and can inform policies related to DV intervention and alcohol outlet licensing.

cs.CY↗

arXiv2022

Simplicial cascades are orchestrated by the multidimensional geometry of neuronal complexes

Cascades arise in many contexts (e.g., neuronal avalanches, social contagions, and system failures). Despite evidence that propagations often involve higher-order dependencies, cascade theory has largely focused on models with pairwise/dyadic interactions. Here, we develop a simplicial threshold model (STM) for nonlinear cascades over simplicial complexes that encode dyadic, triadic and higher-order interactions. We study STM cascades over ``small-world'' models that contain both short- and long-range $k$-simplices, exploring how spatio-temporal patterns manifest as a frustration between local and nonlocal propagations. We show that higher-order coupling and nonlinear thresholding can coordinate to robustly guide cascades along a simplicial-generalization of paths that we call $k$-dimensional ``geometrical channels''. We also find this coordination to enhance the diversity and efficiency of cascades over a ``neuronal complex'', i.e., a simplicial-complex-based model for a neuronal network. We support these findings with bifurcation theory and a data-driven approach based on latent geometry. Our findings and mathematical techniques provide fruitful directions for uncovering the multiscale, multidimensional mechanisms that orchestrate the spatio-temporal patterns of nonlinear cascades.

nlin.AO↗

arXiv2021

Balanced Hodge Laplacians Optimize Consensus Dynamics over Simplicial Complexes

Despite the vast literature on network dynamics, we still lack basic insights into dynamics on higher-order structures (e.g., edges, triangles, and more generally, $k$-dimensional "simplices") and how they are influenced through higher-order interactions. A prime example lies in neuroscience where groups of neurons (not individual ones) may provide the building blocks for neurocomputation. Here, we study consensus dynamics on edges in simplicial complexes using a type of Laplacian matrix called a Hodge Laplacian, which we generalize to allow higher- and lower-order interactions to have different strengths. Using techniques from algebraic topology, we study how collective dynamics converge to a low-dimensional subspace that corresponds to the homology space of the simplicial complex. We use the Hodge decomposition to show that higher- and lower-order interactions can be optimally balanced to maximally accelerate convergence, and that this optimum coincides with a balancing of dynamics on the curl and gradient subspaces. We additionally explore the effects of network topology, finding that consensus over edges is accelerated when 2-simplices are well dispersed, as opposed to clustered together.

physics.soc-ph↗

arXiv2021

Persistent homology of convection cycles in network flows

Convection is a well-studied topic in fluid dynamics, yet it is less understood in the context of networks flows. Here, we incorporate techniques from topological data analysis (namely, persistent homology) to automate the detection and characterization of convective/cyclic/chiral flows over networks, particularly those that arise for irreversible Markov chains (MCs). As two applications, we study convection cycles arising under the PageRank algorithm, and we investigate chiral edges flows for a stochastic model of a bi-monomer's configuration dynamics. Our experiments highlight how system parameters -- e.g., the teleportation rate for PageRank and the transition rates of external and internal state changes for a monomer -- can act as homology regularizers of convection, which we summarize with persistence barcodes and homological bifurcation diagrams. Our approach establishes a new connection between the study of convection cycles and homology, the branch of mathematics that formally studies cycles, which has diverse potential applications throughout the sciences and engineering.

math.DS↗

arXiv2021

Grass-roots optimization of coupled oscillator networks

Despite the prevalence of biological and physical systems for which synchronization is critical, existing theory for optimizing synchrony depends on global information and does not sufficiently explore local mechanisms that enhance synchronization. Thus, there is a lack of understanding for the self-organized, collective processes that aim to optimize/repair synchronous systems, e.g., the dynamics of paracrine signaling within cardiac cells. Here we present ``grass-roots'' optimization of synchronization, which is a multiscale mechanism in which local optimizations of smaller subsystems cooperate to collectively optimize an entire system. Considering models of cardiac tissue and a power grid, we show that grass-roots-optimized systems are comparable to globally optimized systems, but they also have the added benefit of being robust to targeted attacks or subsystem islanding. Our findings motivate and support further investigation into the physics of local mechanisms that can support self-optimization for complex systems.

nlin.AO↗

arXiv2021

Higher-order interactions improve optimal collective dynamics on networks

Collective behavior plays a key role in the function of a wide range of physical, biological, and neurological systems where empirical evidence has recently uncovered the prevalence of higher-order interactions, i.e., structures that represent interactions between more than just two individual units, in complex network structures. Here, we study the optimization of collective behavior in networks with higher-order interactions encoded in clique complexes. Our approach involves adapting the Synchrony Alignment Function framework to a new composite Laplacian matrix that encodes multi-order interactions including, e.g., both dyadic and triadic couplings. We show that as higher-order coupling interactions are equitably strengthened, so that overall coupling is conserved, the optimal collective behavior improves. We find that this phenomenon stems from the broadening of a composite Laplacian's eigenvalue spectrum, which improves the optimal collective behavior and widens the range of possible behaviors. Moreover, we find in constrained optimization scenarios that a nontrivial, ideal balance between the relative strengths of pair-wise and higher-order interactions leads to the strongest collective behavior supported by a network. This work provides insight into how systems balance interactions of different types to optimize or broaden their dynamical range of behavior, especially for self-regulating systems like the brain.

nlin.AO↗

arXiv2021

Coupling Asymmetry Optimizes Collective Dynamics over Multiplex Networks

Networks are often interconnected, with one system wielding greater influence over another. However, the effects of such asymmetry on self-organized phenomena (e.g., consensus and synchronization) are not well understood. Here, we study collective dynamics using a generalized graph Laplacian for multiplex networks containing layers that are asymmetrically coupled. We explore the nonlinear effects of coupling asymmetry on the convergence rate toward a collective state, finding that asymmetry induces one or more optima that maximally accelerate convergence. When a faster and a slower system are coupled, depending on their relative timescales, their optimal coupling is either cooperative (network layers mutually depend on one another) or non-cooperative (one network directs another without a reciprocated influence). It is often optimal for the faster system to more-strongly influence the slower one, yet counter-intuitively, the opposite can also be true. As an application, we model collective decision-making for a human-AI system in which a social network is supported by an AI-agent network, finding that a cooperative optimum requires that these two networks operate on a sufficiently similar timescale. More broadly, our work highlights the optimization of coupling asymmetry and timescale balancing as fundamental concepts for the design of collective behavior over interconnected systems.

physics.soc-ph↗

arXiv2021

Rigidity percolation in random 3D rod systems

In composite materials composed of soft polymer matrix and stiff, high-aspect-ratio particles, the composite undergoes a transition in mechanical strength when the inclusion phase surpasses a critical density. This phenomenon (rheological or mechanical percolation) is well-known to occur in many composites at a critical density that exceeds the conductivity percolation threshold. Conductivity percolation occurs as a consequence of contact percolation, which refers to the conducting particles' formation of a connected component that spans the composite. Rheological percolation, however, has evaded a complete theoretical explanation and predictive description. A natural hypothesis is that rheological percolation arises due to rigidity percolation, whereby a rigid component of inclusions spans the composite. We model composites as random isotropic dispersions of soft-core rods, and study rigidity percolation in such systems. Building on previous results for two-dimensional systems, we develop an approximate algorithm that identifies spanning rigid components through iteratively identifying and compressing provably rigid motifs -- equivalently, decomposing giant rigid components into rigid assemblies of successively smaller rigid components. We apply this algorithm to random rod systems to estimate a rigidity percolation threshold and explore its dependence on rod aspect ratio. We show that this transition point, like the contact percolation transition point, scales inversely with the average (aspect ratio-dependent) rod excluded volume. However, the scaling of the rigidity percolation threshold, unlike the contact percolation scaling, is valid for relatively low aspect ratio. Moreover, the critical rod contact number is constant for aspect ratio above some relatively low value; and lies below the prediction from Maxwell's isostatic condition.

cond-mat.soft↗

arXiv2020

Impact of Community Structure on Consensus Machine Learning

Consensus dynamics support decentralized machine learning for data that is distributed across a cloud compute cluster or across the internet of things. In these and other settings, one seeks to minimize the time $\tau_\epsilon$ required to obtain consensus within some $\epsilon>0$ margin of error. $\tau_\epsilon$ typically depends on the topology of the underlying communication network, and for many algorithms $\tau_\epsilon$ depends on the second-smallest eigenvalue $\lambda_2\in[0,1]$ of the network's normalized Laplacian matrix: $\tau_\epsilon\sim\mathcal{O}(\lambda_2^{-1})$. Here, we analyze the effect on $\tau_\epsilon$ of network community structure, which can arise when compute nodes/sensors are spatially clustered, for example. We study consensus machine learning over networks drawn from stochastic block models, which yield random networks that can contain heterogeneous communities with different sizes and densities. Using random matrix theory, we analyze the effects of communities on $\lambda_2$ and consensus, finding that $\lambda_2$ generally increases (i.e., $\tau_\epsilon$ decreases) as one decreases the extent of community structure. We further observe that there exists a critical level of community structure at which $\tau_\epsilon$ reaches a lower bound and is no longer limited by the presence of communities. We support our findings with empirical experiments for decentralized support vector machines.

cs.LG↗