Research on UAV Applications in Public Administration: Based on an Improved RRT Algorithm

Baili Lu; Junhao Wei; Ngai Cheong; Yanzhao Gu; Zhanxi Xie; Zikun Li

REVIEW 4 major objections 3 minor 1 cited by

Research on UAV Applications in Public Administration: Based on an Improved RRT Algorithm

T0 review · 4 major / 3 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read The biroot method claims that any $n$th root can be approximated by a closed-form rational function whose coefficients are taken from Pascal's triangle, a Gaussian curve, or a generalized triangle-like DAG row — the square-root case is prov

desk verdict The submitted full text is an unrelated math preprint, so the UAV claims are unreviewable as received. read the letter →

arxiv 2508.14096 v1 pith:7ZYCSRT3 submitted 2025-08-15 cs.RO

Zhanxi Xie , Baili Lu , Yanzhao Gu , Zikun Li , Junhao Wei , Ngai Cheong This is my paper · ORCID

classification cs.RO MSC 41A2011B6505A10

keywords nthrootapproximationbirootmethodPascal'strianglebinomialcoefficientsrationalNewton'sGaussiandistributiondirectedacyclicgraphs

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The body of this submission — despite an attached abstract about UAV path planning — argues a mathematical claim: that $n$th roots can be approximated by closed-form rational functions built from coefficients taken from Pascal's triangle, from Gaussian curves, or from generalized triangle-like DAG rows. The author calls this the biroot method and shows it emerges from symbolically iterating Newton's method for square roots, where numerator and denominator coefficients alternate down rows of Pascal's triangle. The square-root case and the optimal centering condition are proved; the general $n$th-root, Gaussian, and DAG variants are conjectures backed by computational evidence. A sympathetic reader would care because, if the conjectures hold, Padé-like approximants can be written down directly from combinatorial data without solving linear systems, and very low-degree versions can seed Newton iteration.

What carries the argument

The central object is the biroot approximant: a rational function $P(x)/Q(x)$ whose numerator and denominator coefficients are alternating even/odd entries from a row of Pascal's triangle (or from Gaussian-sampled analogues, or from a level of a generalized DAG). The expansion parameter $c$ plays the role of centering — the approximant is exact at $x=c^k$ for the $k$th root — and sampling every $k$th pair of coefficients generalizes the construction from square roots to $n$th roots. This machinery converts Newton iteration and Padé construction, normally recursive or system-solving, into one closed-form formula.

What would settle it

For fixed root index $k$ and center $c$, evaluate the biroot approximant $R_{m,c}^k(x)$ for $m=20,50,100$ on an interval straddling $c^k$, such as $[10^{-3},10^3]$ with $c=10$, and compute the maximum absolute error against $x^{1/k}$. If the error does not shrink toward zero with $m$ — or if for some $c$ it grows — the Binomial Biroot Conjecture fails. Running the same test with Gaussian-sampled coefficients and with rows of a random DAG tests the Gaussian and DAG versions.

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Extended reading notes

Core claim

Starting from Newton's method for square roots and evaluating it symbolically, the paper observes that the iterations produce rational functions whose coefficients follow rows of Pascal's triangle, alternating between numerator and denominator; the same pattern appears in Padé approximants of the square root expanded at $c$. This yields the Binomial Biroot Conjecture: sampling coefficients from binomial rows and placing them in an alternating rational form gives a closed-form approximant $R_{m,c}^k(x)$ to $x^{1/k}$, with expansion parameter $c$ making the approximation exact at $x=c^k$. The square-root case is proven, along with the optimal choice of $c$. The paper then conjectures that samp

Load-bearing premise

The load-bearing premise is that placing coefficients from binomial rows, Gaussian samples, or arbitrary DAG rows into the alternating rational form converges to the $n$th root as the row level grows; only the square-root case is proved, so the general $n$th-root claim rests on this unproven convergence.

Editorial extensions

If this is right

If the conjectures hold, any $n$th root has a closed-form rational approximant generated directly from binomial coefficients, turning root computation into evaluation of a polynomial ratio.
Biroot functions can serve as seed values that reduce the number of Newton iterations needed to reach target precision, potentially lowering the cost of high-precision root calculations.
The Gaussian and DAG variants suggest the exact coefficient microstructure is not essential; what matters is that rows approach a Gaussian profile, so many triangle-like arrays can generate working approximants.
Because certain biroot functions coincide with known Padé approximants, the formula offers a combinatorial route to Padé tables without solving for coefficients.
With fixed, low-degree rational expressions, the method maps naturally onto hardware evaluation (e.g., Horner form in FPGA/ASIC units) with deterministic latency and parallel throughput.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The DAG invariance claim, if true, predicts a test: convergence error should track the statistical distance between a DAG row and its best-fit Gaussian; comparing random DAGs against that distance would separate the invariance mechanism from the Gaussian attractor.
The claimed Padé equivalence can be checked directly: verify whether the $[m/m]$ Padé approximant of $x^{1/k}$ at $c^k$ equals $R_{m,c}^k(x)$ for small $m$; if so, the biroot formula is an explicit closed form for a family of Padé approximants.
If the attached UAV abstract is read as the paper's application claim, the full text provides no dRRT algorithm, no simulations, and no baseline comparisons, so the abstract's 100% success rate and 0.01468 s runtime are unsupported by the body. A reader evaluating the UAV claim would need to look elsewhere.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Quick take: this is not a reviewable paper as received. Title, authors, and abstract describe a UAV path-planning paper (dRRT vs RRT, A*, ACO); the full text is an unrelated math preprint on nth-root approximation. The mismatch is not a minor formatting issue, it is the whole body. I cannot evaluate the dRRT claims because neither the algorithm pseudocode, environment definition, baseline implementations, nor trial counts are present. The reader's UNVERDICTED verdict is correct.

Where the material does support some assessment: the abstract describes a combination of four established mechanisms—target bias, dynamic step size, detour priority, and B-spline smoothing. Each is common in the RRT literature, and the combination is plausible engineering for UAV path planning. The headline numbers (100% success, 0.01468 s average runtime, max yaw <45°) are point estimates with no variance, scenario counts, environment parameters, or baseline tuning details; "500 m³" could be any shape and "randomized buildings" is not a reproducible setup. So the central claim cannot be checked. The stress-test note is fair—this is a missing evidentiary basis, not a manufactured flaw.

The math preprint that actually appears in the full text is, for what it is worth, more candid about its own limits: Conjecture 3.4 is stated without proof, the Gaussian foundation is explicitly "not rigorously justified," and overflow restricted the numerical experiments. It also ships code and data via Zenodo. That is real reproducibility effort, but it belongs to a completely different submission.

Recommendation: desk reject this version. The correct next step is for the authors to resubmit the UAV paper with code, environment parameters, baseline details, and adequate trials—or to submit the math paper under its own title. As received, no referee can engage with the claims because the claims are not in the manuscript.

Referee Report

4 major / 3 minor

Summary. The manuscript as received consists of an abstract claiming a new UAV path-planning algorithm (dRRT) for public-administration applications, together with a full text that is entirely unrelated: it is a mathematics preprint on rational nth-root approximation (arXiv:2508.14095v3), containing no UAV content, no RRT variants, no simulations, and no experimental data. The abstract reports that dRRT achieves a 100% success rate, 0.01468 s average runtime, shorter paths, fewer waypoints, and maximum yaw angles below 45° compared with RRT, A*, and ACO in a 500 m³ urban environment, but none of these claims can be checked against the submitted body.

Significance. If the abstract's claims were supported, the contribution would be a modest incremental improvement to RRT-style planners for small-scale urban UAV missions, with potential practical value for emergency response and traffic monitoring. However, the submitted manuscript provides no algorithm description, no implementation, no environment generator, no parameter table, and no comparison protocol. The full text is a different paper about approximation theory. Consequently, the significance of the claimed result cannot be assessed from this submission; the paper as received has no evidentiary basis for its central claims.

major comments (4)

[Full Text (all sections)] The supplied full text is 'Combinatorial and Gaussian Foundations of Rational Nth Root Approximations', arXiv:2508.14095v3, not the UAV/RRT paper promised by the title and abstract. There is no dRRT algorithm, no pseudocode, no simulation setup, no UAV experiments, and no comparison with RRT, A*, or ACO anywhere in the body. The abstract's central claims (100% success, 0.01468 s runtime, shorter paths, fewer waypoints, <45° yaw) are therefore unsupported by the manuscript. This is a load-bearing mismatch that makes the paper unverifiable as submitted.
[Abstract] Even treating the abstract as a standalone report, it omits the experimental protocol necessary to evaluate the claims: number of trials, random seeds, number and distribution of randomized buildings, obstacle density, vehicle dynamics, yaw-rate constraints, baseline implementations, and hardware/software environment. '500 m3' is ambiguous (e.g., 10×10×5 m vs 1×1×500 m), and the quoted figures are single point estimates with no error bars or scenario counts. Without these details, '100% success rate' and 'average runtime 0.01468s' are not falsifiable claims.
[Abstract (dRRT mechanisms)] The four proposed mechanisms—target bias, dynamic step size, detour priority, and B-spline smoothing—introduce free parameters that are not reported: bias probability, step-size schedule parameters, detour threshold, smoothing weights, and any associated environment parameters. No sensitivity analysis is provided. The claimed superiority over 'traditional RRT, A*, and ACO' could therefore arise from favorable parameter fitting or baseline under-tuning rather than from an algorithmic advantage. This is a central reproducibility concern, not a presentational one.
[Full Text / comparison protocol] The full text contains no implementation of RRT, A*, or ACO, so there is no way to determine whether the baselines were fairly tuned, whether equal computation budgets were used, or whether the comparison is meaningful. In the absence of baseline details, the abstract's comparative claims are unsupported.

minor comments (3)

[Abstract] The abstract uses 'm3' rather than 'm³', and 'Deg' rather than 'degrees'; path length and runtime units are not specified beyond seconds. The acronym dRRT is not expanded in the abstract.
[References] No references are given for RRT, A*, ACO, or UAV path-planning benchmarks; the full text's references are unrelated mathematics references.
[Supplementary materials] The Zenodo DOI in the full text points to the biroot approximation project, not to any UAV simulation code or dataset. There is no link to dRRT code or experimental data.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity in the dRRT benchmark claim; the unrelated full text is a severe evidentiary gap, not a circular derivation.

full rationale

The claimed derivation chain is the abstract's comparison of dRRT to RRT, A*, and ACO. This is an external empirical benchmark, not a derivation in which the outputs are definitionally equal to the inputs. I cannot exhibit any equation or fitted parameter that makes '100% success rate with an average runtime of 0.01468s, shorter path lengths, fewer waypoints, and smoother trajectories (maximum yaw angles <45 deg)' true by construction: the four named mechanisms (target bias, dynamic step size, detour priority, B-spline smoothing) are stated as algorithmic modifications, and the baseline comparisons are external. There are no self-citations in the abstract, no invoked uniqueness theorem, and no renamed known result. The abstract does self-report limitations ('increased computational overhead from added mechanisms and potential local optima due to goal biasing'), which are ordinary caveats, not circular steps. I do flag a manuscript-integrity problem that is material to correctness but not to circularity: the supplied full text is arXiv:2508.14095v3, 'Combinatorial and Gaussian Foundations of Rational Nth Root Approximations' by Isaac Wolford, containing no UAV algorithm, no RRT pseudocode, no simulation setup, no baseline tuning, and no UAV experiments. That means the dRRT performance claims currently lack any checkable derivation or experimental detail; but absence of evidence is not circularity. For circularity purposes, the honest finding is score 0.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

No new physical entities are introduced; dRRT is an algorithmic variant assembled from four prior strategies. The five listed free parameters are the tuning knobs of those strategies, each of which materially affects the reported metrics. All entries derive from the abstract only, because the supplied full text is a different document.

free parameters (5)

Target bias probability
Fraction of samples steered toward the goal; directly controls convergence speed and is not specified in the abstract.
Dynamic step size schedule parameters
Adaptation rule and constants balancing exploration and obstacle navigation; unreported.
Detour priority threshold
Criteria for choosing a horizontal detour over a vertical ascent; a design choice that shapes the smoothness results.
B-spline smoothing parameters
Control points or knot choices affecting path smoothness and the reported max yaw angle.
Simulation environment parameters
Building count, size, and density in the 500 m3 world; not stated, yet success rate and runtime depend on them.

assumptions (4)

domain assumption UAV motion in the planner is modeled as a 3D point with yaw-rate constraints, with energy cost assumed monotone in path length and waypoint count.
Implied by the objective metrics (shorter paths, fewer waypoints, max yaw <45 deg) used to declare superiority; never stated explicitly.
domain assumption Randomly placed building volumes in a 500 m3 box are representative of urban low-altitude airspace for public-administration missions.
Required for any transfer from simulation to emergency response and traffic monitoring; no justification in the abstract.
domain assumption The RRT, A*, and ACO baselines were implemented and tuned to comparable quality.
Fairness of the comparative claims depends on this; no implementation or tuning details are given.
domain assumption The quoted success rate and average runtime are stable across random seeds and scenario draws.
Point estimates without variance require stability of the scenario distribution, which is assumed rather than demonstrated.

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Cite this review

Pith. "Pith review of Research on UAV Applications in Public Administration: Based on an Improved RRT Algorithm." pith.science (2026). https://pith.science/paper/7ZYCSRT3

@misc{pith2026250814096,
  author       = {Pith},
  title        = {Pith review of: Research on UAV Applications in Public Administration: Based on an Improved RRT Algorithm},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7ZYCSRT3}},
  note         = {Machine review of arXiv:2508.14096}
}

read the original abstract

This study investigates the application of unmanned aerial vehicles (UAVs) in public management, focusing on optimizing path planning to address challenges such as energy consumption, obstacle avoidance, and airspace constraints. As UAVs transition from 'technical tools' to 'governance infrastructure', driven by advancements in low-altitude economy policies and smart city demands, efficient path planning becomes critical. The research proposes an enhanced Rapidly-exploring Random Tree algorithm (dRRT), incorporating four strategies: Target Bias (to accelerate convergence), Dynamic Step Size (to balance exploration and obstacle navigation), Detour Priority (to prioritize horizontal detours over vertical ascents), and B-spline smoothing (to enhance path smoothness). Simulations in a 500 m3 urban environment with randomized buildings demonstrate dRRT's superiority over traditional RRT, A*, and Ant Colony Optimization (ACO). Results show dRRT achieves a 100\% success rate with an average runtime of 0.01468s, shorter path lengths, fewer waypoints, and smoother trajectories (maximum yaw angles <45{\deg}). Despite improvements, limitations include increased computational overhead from added mechanisms and potential local optima due to goal biasing. The study highlights dRRT's potential for efficient UAV deployment in public management scenarios like emergency response and traffic monitoring, while underscoring the need for integration with real-time obstacle avoidance frameworks. This work contributes to interdisciplinary advancements in urban governance, robotics, and computational optimization.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

ARIES-Mission2: A Zero-Shot Vision-Language-Action Framework for Fast Large-Scale Aerial Mission Generation
cs.CE 2026-08 conditional novelty 3.0 of 10

ARIES-Mission2 couples zero-shot vision-language target detection with a metaheuristic traveling-salesperson solver and reports shorter UAV mission routes than manual human planning on the UAV-VLPA-nano-30 benchmark.

Reference graph

Works this paper leans on

13 extracted references · 13 canonical work pages · cited by 1 Pith paper

[1]

[Online; accessed 2025-07-29]

Taylor Expansion II, September 2021. [Online; accessed 2025-07-29]. URL:��

work page 2021
[2]

Periodic representations and rational approximations of square roots.�� , 175:83–90, November 2013.��

Marco Abrate, Stefano Barbero, Umberto Cerruti, and Nadir Murru. Periodic representations and rational approximations of square roots.�� , 175:83–90, November 2013.��

work page 2013
[3]

Generalized pascal’s triangles andassociatedk-padovan-likesequences.�� , 192:278– 290, February 2022.��

Giuseppina Anatriello, László Németh, and Giovanni Vincenzi. Generalized pascal’s triangles andassociatedk-padovan-likesequences.�� , 192:278– 290, February 2022.��

work page 2022
[4]

Baker and Peter Graves-Morris.��

George A. Baker and Peter Graves-Morris.�� . Cambridge University Press, 1996.��

work page 1996
[5]

Chen and P

S.-G. Chen and P. Y. Hsieh. Fast computation of the nth root.�� , 17(10):1423–1427, 1989.��

work page 1989
[6]

nth root extraction: Double iteration process and newton’s method

François Dubeau. nth root extraction: Double iteration process and newton’s method. �� , 91(2):191–198, May 1998. ��

work page 1998
[7]

Newton’s method and high-order algorithms for the nth root computation

François Dubeau. Newton’s method and high-order algorithms for the nth root computation. �� , 224(1):66–76, February 2009. ��

work page 2009
[8]

Fornberg

B. Fornberg. Padé approximation. URL: ��

work page

Show all 13 references

[9]

Galántai

A. Galántai. The theory of newton’s method.�� , 124(1–2):25–44, December 2000.��

2000
[10]

P. Magyar. Taylor series. 2015. URL: ��

2015
[11]

Joseph M. Shunia. Polynomial quotient rings and kronecker substitution for deriving combinatorial identities. March 2024. �� , ��

2024
[12]

Matplotlib: Visualization with python, 2025.��

The Matplotlib Development Team. Matplotlib: Visualization with python, 2025.�� . 22

2025
[13]

seaborn: statistical data visualization.�� , 6(60):3021, April 2021.��

Michael Waskom. seaborn: statistical data visualization.�� , 6(60):3021, April 2021.��. Appendices An interesting, but not very useful conjecture (because we don’t bother to prove it), is listed due its potential to help in anal...

2021

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.

[1] [1]

[Online; accessed 2025-07-29]

Taylor Expansion II, September 2021. [Online; accessed 2025-07-29]. URL:��

work page 2021

[2] [2]

Periodic representations and rational approximations of square roots.�� , 175:83–90, November 2013.��

Marco Abrate, Stefano Barbero, Umberto Cerruti, and Nadir Murru. Periodic representations and rational approximations of square roots.�� , 175:83–90, November 2013.��

work page 2013

[3] [3]

Generalized pascal’s triangles andassociatedk-padovan-likesequences.�� , 192:278– 290, February 2022.��

Giuseppina Anatriello, László Németh, and Giovanni Vincenzi. Generalized pascal’s triangles andassociatedk-padovan-likesequences.�� , 192:278– 290, February 2022.��

work page 2022

[4] [4]

Baker and Peter Graves-Morris.��

George A. Baker and Peter Graves-Morris.�� . Cambridge University Press, 1996.��

work page 1996

[5] [5]

Chen and P

S.-G. Chen and P. Y. Hsieh. Fast computation of the nth root.�� , 17(10):1423–1427, 1989.��

work page 1989

[6] [6]

nth root extraction: Double iteration process and newton’s method

François Dubeau. nth root extraction: Double iteration process and newton’s method. �� , 91(2):191–198, May 1998. ��

work page 1998

[7] [7]

Newton’s method and high-order algorithms for the nth root computation

François Dubeau. Newton’s method and high-order algorithms for the nth root computation. �� , 224(1):66–76, February 2009. ��

work page 2009

[8] [8]

Fornberg

B. Fornberg. Padé approximation. URL: ��

work page