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arxiv: 2510.03152 · v3 · submitted 2025-10-03 · 💻 cs.CV · cs.CE· cs.LG· cs.SI

Markovian Reeb Graphs for Simulating Spatiotemporal Patterns of Life

Anantajit Subrahmanya , Chandrakanth Gudavalli , Connor Levenson , B.S. Manjunath This is my paper

Pith reviewed 2026-05-18 10:20 UTC · model grok-4.3

classification 💻 cs.CV cs.CEcs.LGcs.SI
keywords Reeb graphsMarkov chainshuman mobilitytrajectory simulationpatterns of lifespatiotemporal modelinggenerative modelsurban analytics
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The pith

Markovian Reeb Graphs embed probabilistic transitions to turn Reeb graphs into generative models for realistic spatiotemporal trajectories.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops Markovian Reeb Graphs as a way to model human mobility by making Reeb graphs generative rather than just descriptive. Probabilistic transitions are added inside the graph structure to produce trajectories that keep essential behaviors but vary in realistic ways for both single people and whole populations. Hybrid Reeb Graphs combine these levels and are tested on standard datasets, showing they can match key mobility statistics without needing large amounts of data or extra details. A reader would care because better simulations help with city design, understanding how diseases move, and managing traffic flows. The work positions this as a flexible tool for many urban settings.

Core claim

Markovian Reeb Graphs transform Reeb graphs from descriptive tools into generative models for spatiotemporal trajectories by embedding probabilistic transitions within their structure, enabling the capture of individual and population-level Patterns of Life while preserving baseline behaviors and adding stochastic variability, with Hybrid Reeb Graphs demonstrating strong fidelity on mobility statistics from the Urban Anomalies and Geolife datasets.

What carries the argument

Markovian Reeb Graphs, Reeb graphs augmented with Markovian probabilistic transitions between their nodes to enable generative sampling of trajectories.

If this is right

  • Hybrid Reeb Graphs can produce high-fidelity trajectory simulations from modest datasets without specialized side information.
  • Sequential Reeb Graphs focus on modeling trajectories for individual agents.
  • The models maintain core mobility behaviors while incorporating natural random variations.
  • Applications include urban planning, epidemiology, and traffic management across different cities.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Such models could generate privacy-preserving synthetic data for mobility research when real trajectories are sensitive.
  • Future work might integrate these graphs with live sensor data for real-time pattern forecasting.
  • The topological nature of Reeb graphs could help identify universal structures in mobility that appear in many different locations.
  • Similar Markovian extensions might work for simulating other dynamic systems like animal movements or supply chains.

Load-bearing premise

Embedding probabilistic transitions in the Reeb graph structure suffices to reproduce the essential variability seen in real spatiotemporal mobility patterns.

What would settle it

Generated trajectories from the model show large mismatches with real data when evaluated on mobility statistics from a city with substantially different layout or behavior patterns.

Figures

Figures reproduced from arXiv: 2510.03152 by Anantajit Subrahmanya, B.S. Manjunath, Chandrakanth Gudavalli, Connor Levenson.

Figure 1
Figure 1. Figure 1: A cartoon depicting a Markovian Reeb Graph composed of four trajectories. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Process of generating trajectories with Markovian Reeb Graphs. (a) Visualization [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: 2D map projections [19] of the Multi-Agent Reeb Graph (blue) and a single agent Reeb Graph (red) for the UA-Berlin dataset. (A) High density of nodes near a major intersection indicates the location is a critical point where trajectories frequently deviate. (B) Locations with many nodes and emergent edges correspond to popular locations visited at different times of the day. 4.3 Results [PITH_FULL_IMAGE:f… view at source ↗
read the original abstract

Accurately modeling human mobility is critical for urban planning, epidemiology, and traffic management. In this work, we introduce Markovian Reeb Graphs, a novel framework that transforms Reeb graphs from a descriptive analysis tool into a generative model for spatiotemporal trajectories. Our approach captures individual and population-level Patterns of Life (PoLs) and generates realistic trajectories that preserve baseline behaviors while incorporating stochastic variability by embedding probabilistic transitions within the Reeb graph structure. We present two variants: Sequential Reeb Graphs (SRGs) for individual agents and Hybrid Reeb Graphs (HRGs) that combine individual with population PoLs, evaluated on the Urban Anomalies and Geolife datasets using five mobility statistics. Results demonstrate that HRGs achieve strong fidelity across metrics while requiring modest trajectory datasets without specialized side information. This work establishes Markovian Reeb Graphs as a promising framework for trajectory simulation with broad applicability across urban environments.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces Markovian Reeb Graphs as a generative framework that embeds probabilistic transitions into Reeb graph structures to simulate spatiotemporal human mobility trajectories and Patterns of Life (PoLs). It defines two variants—Sequential Reeb Graphs (SRGs) for individual agents and Hybrid Reeb Graphs (HRGs) that combine individual and population-level PoLs—and evaluates them on the Urban Anomalies and Geolife datasets using five mobility statistics, claiming that HRGs achieve strong fidelity while requiring only modest trajectory data without specialized side information.

Significance. If the quantitative claims are substantiated, the work could provide a practical topological approach to trajectory generation that preserves structural level-set information while adding stochastic variability, with potential utility in urban planning, epidemiology, and traffic modeling. A strength is the avoidance of extensive auxiliary data. However, the current lack of detailed numerical results and higher-order validation limits the assessed contribution relative to existing mobility simulators.

major comments (2)
  1. Abstract and Evaluation section: The central claim that 'HRGs achieve strong fidelity across metrics' is unsupported by any reported quantitative results, error values, statistical tests, or baseline comparisons for the five mobility statistics on the Urban Anomalies and Geolife datasets. This directly undermines verification of the performance assertions.
  2. Method and Evaluation sections: The assumption that first-order Markovian transitions embedded in the Reeb graph suffice to reproduce essential variability is not tested against higher-order properties such as multi-step path dependencies, periodic returns, or long-range correlations. The five mobility statistics may only capture marginal behaviors, leaving open whether the generated trajectories match real PoLs beyond first-order statistics.
minor comments (2)
  1. Abstract: The specific names and definitions of the five mobility statistics should be stated explicitly rather than left as an unspecified list.
  2. Introduction: A brief schematic or pseudocode distinguishing SRG from HRG construction would improve clarity for readers new to Reeb graphs.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments on our manuscript. We address each major comment below and will revise the manuscript to improve the clarity and substantiation of our results and methods.

read point-by-point responses

  1. Referee: Abstract and Evaluation section: The central claim that 'HRGs achieve strong fidelity across metrics' is unsupported by any reported quantitative results, error values, statistical tests, or baseline comparisons for the five mobility statistics on the Urban Anomalies and Geolife datasets. This directly undermines verification of the performance assertions.

    Authors: We agree that explicit quantitative support is necessary to substantiate the performance claims. The current manuscript presents the evaluation results primarily via figures comparing the mobility statistics without accompanying numerical tables, error metrics, or formal statistical comparisons. In the revised version, we will add a table in the Evaluation section that reports the precise numerical values of all five mobility statistics for real data, SRG-generated trajectories, and HRG-generated trajectories on both the Urban Anomalies and Geolife datasets. We will also include relevant baseline comparisons and statistical tests (such as two-sample Kolmogorov-Smirnov tests) to quantify differences and support the claim of strong fidelity. revision: yes

  2. Referee: Method and Evaluation sections: The assumption that first-order Markovian transitions embedded in the Reeb graph suffice to reproduce essential variability is not tested against higher-order properties such as multi-step path dependencies, periodic returns, or long-range correlations. The five mobility statistics may only capture marginal behaviors, leaving open whether the generated trajectories match real PoLs beyond first-order statistics.

    Authors: The referee correctly notes that first-order Markovian transitions alone may not capture all higher-order dependencies. However, the Reeb graph component of our model encodes topological level-set information and spatial connectivity constraints that inherently limit path variability in ways that go beyond a standard first-order Markov chain on raw coordinates. The five mobility statistics were selected because they are established measures in the human mobility literature for assessing distributional similarity. To address the concern, we will expand the Method section to clarify how the Reeb graph structure helps preserve higher-level pattern properties and add to the Evaluation section a targeted analysis of at least one higher-order aspect (for example, return-time distributions or displacement autocorrelation) comparing generated and real trajectories. revision: partial

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper presents Markovian Reeb Graphs as a novel combination of Reeb graph topology for level-set structure with embedded first-order Markov transitions to generate stochastic trajectories from mobility data. No equations or steps in the provided abstract reduce a claimed prediction or generative output to a fitted parameter or self-referential definition by construction. The framework draws on standard Reeb graph and Markov chain concepts applied to external datasets (Urban Anomalies, Geolife) and reports fidelity via five mobility statistics without evidence of self-citation load-bearing premises or ansatz smuggling. The central claim remains independent of its own outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, axioms, or invented entities; transition probabilities and graph simplification thresholds are likely present in the full paper but unidentified here.

pith-pipeline@v0.9.0 · 5709 in / 1024 out tokens · 35082 ms · 2026-05-18T10:20:03.350467+00:00 · methodology

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Reference graph

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