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arxiv: 2606.22025 · v1 · pith:AY3J5GAL · submitted 2026-06-20 · physics.soc-ph · cond-mat.dis-nn

Distance from home matters: Investigation of a basic movement strategy

Mohsen Ghasemi Nezhadhaghighi , Yahya Khalili , Behafarid Hemmatpour , Abolfazl Ramezanpour This is my paper

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classification physics.soc-ph cond-mat.dis-nn
keywords human mobilitypower-law distributiondistance ratioagent-based modeltraveled distancesspatial latticepreferential return
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The pith

A movement rule based on distance ratios from home reproduces power-law travel distances even for a single agent.

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

The paper explores a basic movement process where each trip destination is selected with probability depending on the ratio of the starting and ending distances from the agent's home. This rule is applied to a sequence of trips satisfying demands from suppliers placed on a two-dimensional lattice. The authors show that the resulting trajectories match key empirical patterns, including the power-law distribution of traveled distances, using only uniform random placements and a single agent. The outcomes persist when agent interactions are added through queues and when demand or supplier placements become more realistic.

Core claim

We consider a movement process in which each user performs a sequence of trips to satisfy a set of demands, given a spatial distribution of suppliers on a two-dimensional lattice. In each trip, destinations are chosen with a probability that depends on the ratio of the initial and final distances from the user's origin (home). We show that even a single agent with uniformly distributed demands and suppliers qualitatively reproduces key empirical statistics, such as the power-law distribution of traveled distances. The results are also robust to introducing interactions between agents via queues and incorporating more realistic demand and supplier distributions.

What carries the argument

The probability of choosing a destination that depends on the ratio of initial and final distances from home, which creates the observed correlation between endpoint distances of each trip.

If this is right

  • The power-law distribution of traveled distances emerges directly from the ratio-based destination choice.
  • A single agent without interactions is sufficient to match the main empirical statistics.
  • The same statistics remain when agents interact through queues at suppliers.
  • The results hold under more realistic, non-uniform placements of demands and suppliers.

Where Pith is reading between the lines

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

  • Home location acts as an anchor that shapes the entire distribution of trip lengths.
  • The model could be tested by checking whether real trajectories show the same initial-to-final distance ratio dependence.
  • Similar ratio rules might appear in other spatial processes that involve repeated returns to a fixed origin.

Load-bearing premise

The probability of choosing a destination depends on the ratio of the initial and final distances from the user's origin (home).

What would settle it

Measure the distribution of traveled distances in simulations where agents follow the ratio-based choice rule on a lattice and check whether it deviates from a power law.

Figures

Figures reproduced from arXiv: 2606.22025 by Abolfazl Ramezanpour, Behafarid Hemmatpour, Mohsen Ghasemi Nezhadhaghighi, Yahya Khalili.

Figure 1
Figure 1. Figure 1: FIG. 1. Empirical data for (Euclidean) distances [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Illustration of the movement strategy. The probability of going from [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Main quantities of the effective model for [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Efficiencies of the effective model for [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. The mean consumed energy [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Exploration probability [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Cumulative distribution functions for travel distance ∆ [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
read the original abstract

Discovering the fundamental dynamical rules that generate the main statistical features of human mobility is essential for understanding the mechanisms underlying such processes. A prominent example is the exploration and preferential return model and its generalizations, which successfully reproduce several empirical findings. Here, we exploit another observation: the endpoint distances of a trip from the trajectory's starting point are strongly correlated. We consider a movement process in which each user performs a sequence of trips to satisfy a set of demands, given a spatial distribution of suppliers on a two-dimensional lattice. In each trip, destinations are chosen with a probability that depends on the ratio of the initial and final distances from the user's origin (home). We show that even a single agent with uniformly distributed demands and suppliers qualitatively reproduces key empirical statistics, such as the power-law distribution of traveled distances. The results are also robust to introducing interactions between agents via queues and incorporating more realistic demand and supplier distributions.

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 / 1 minor

Summary. The manuscript introduces a mobility model where a single agent on a 2D lattice fulfills uniformly distributed demands by choosing suppliers with a destination probability that depends on the ratio of initial to final distances from the agent's home. It claims this setup qualitatively reproduces the empirical power-law distribution of traveled distances, and remains robust under multi-agent queue interactions or heterogeneous demand/supplier distributions.

Significance. If the power-law is not imposed by the specific ratio-based functional form, the work would provide a minimal, single-agent mechanism grounded in an observed distance correlation, offering a simple baseline that contrasts with multi-agent models like exploration and preferential return. The uniform lattice setup and claimed lack of free parameters would strengthen its value as a falsifiable starting point for mobility statistics.

major comments (2)
  1. [Model definition] Model definition (abstract and main text): The destination choice probability is defined to depend on the ratio of initial and final distances from home, but no derivation is provided showing this functional form follows necessarily from the empirical correlation; without this, it remains possible that the power-law reproduction is enforced by the postulated ratio rule rather than emerging from the uniform single-agent dynamics on the lattice.
  2. [Results] Results section: The claim of qualitative reproduction of the power-law is central, yet the abstract provides no equations, fitted exponents, or statistical comparisons (e.g., to a null model using pure distance decay); this makes it impossible to assess whether the result is distinctive or load-bearing for the mechanism.
minor comments (1)
  1. The abstract refers to 'qualitatively reproduces' without defining the exact probability function or any validation metrics; the full text should include these explicitly for reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments on our manuscript. We address each major comment below with point-by-point responses. Revisions will be incorporated where they strengthen the presentation without altering the core claims.

read point-by-point responses

  1. Referee: Model definition (abstract and main text): The destination choice probability is defined to depend on the ratio of initial and final distances from home, but no derivation is provided showing this functional form follows necessarily from the empirical correlation; without this, it remains possible that the power-law reproduction is enforced by the postulated ratio rule rather than emerging from the uniform single-agent dynamics on the lattice.

    Authors: We agree that the ratio-based functional form is a modeling choice motivated by the observed empirical correlation between initial and final trip distances from home, rather than a first-principles derivation. The manuscript frames this as a basic strategy that exploits the correlation to test whether it can generate power-law statistics under uniform lattice conditions. To address the concern, we will revise the model definition section to explicitly describe the form as phenomenological, clarify its grounding in the correlation, and add a brief discussion of why alternatives (such as pure distance decay) were not used as the baseline. This will make clearer that the power-law arises from the combination of the rule with the single-agent uniform dynamics, as supported by the robustness results already in the paper. revision: yes

  2. Referee: Results section: The claim of qualitative reproduction of the power-law is central, yet the abstract provides no equations, fitted exponents, or statistical comparisons (e.g., to a null model using pure distance decay); this makes it impossible to assess whether the result is distinctive or load-bearing for the mechanism.

    Authors: We acknowledge that the abstract is concise and omits the destination probability equation, specific fitted exponents, and direct null-model comparisons. The full text reports the qualitative match to empirical power-laws and includes robustness tests, but we agree these details would aid assessment. In revision we will expand the abstract to include the key probability equation and the simulated exponent range, and add a short comparison in the results section to a pure distance-decay null model to demonstrate that the ratio rule produces a distinct outcome from simple decay. These additions will be limited to clarification and will not change the reported findings. revision: yes

Circularity Check

0 steps flagged

No significant circularity; model input (ratio-based choice) is independent of reproduced output (power-law distances)

full rationale

The paper postulates a destination probability depending on the ratio of initial/final distances from home, motivated by an external empirical correlation observation. It then shows this rule, applied to uniform demands/suppliers on a lattice, yields power-law traveled distances. No equations or text indicate the probability form is defined using the power-law, fitted to output statistics, or reduced to self-citation. The central result is a forward simulation from the stated rule, not a definitional equivalence or fitted-input prediction. This is the common case of an independent mechanistic model.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, axioms, or invented entities beyond the core modeling choice of ratio-dependent probability; full manuscript would be needed to audit fitted constants or background assumptions.

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discussion (0)

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Reference graph

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