Pith. sign in

REVIEW 3 major objections 6 minor 49 references

CWTHF: Identifying Dark Matter Halos with Continuous Wavelet Transform

T0 review · 3 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read The paper claims that dark matter halos in N-body simulations can be identified as cross-scale maxima of a continuous wavelet transform, producing catalogs comparable to friends-of-friends, with linear time complexity.

desk verdict A useful 3D wavelet halo finder with shipped code and a real FOF comparison, but the peak-correction calibration in Appendix B is hand-tuned and should be stress-tested before the method is trusted at face value. read the letter →

arxiv 2501.10622 v2 pith:XHQGTBX4 submitted 2025-01-18 astro-ph.CO

Minxing Li , Yun Wang , Ping He This is my paper · ORCID
classification astro-ph.CO
keywords darkmatterhaloshalofindercontinuouswavelettransformfriends-of-friendsN-bodysimulationscosmologicalMPIparallelizationmassfunction
topics Dark Matter
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 paper introduces CWTHF, a halo finder that identifies dark matter halos as peaks of a continuous wavelet transform computed on a cloud-in-cell density grid across multiple scales. The central claim is viability: CWTHF-produced halo catalogs agree with the conventional friends-of-friends (FOF) method at the catalog level, and the algorithm has linear time complexity O(N), promising gains for future exascale simulations. The paper shows that applying a self-boundness check to FOF groups removes most of the halo-mass-function discrepancy, implying that the remaining differences stem from physically unbound groups. The work also derives a calibration between wavelet scale and virial radius, rvir = 0.091/kw - 0.012, enabling physical interpretation of the wavelet scales. A sympathetic reader would care because the method offers a new, grid-based, parallelizable approach to halo finding with a well-defined boundary from the wavelet's positive region.

What carries the argument

The central object is the continuous wavelet transform computed from the cloud-in-cell (CIC) grid using the isotropic Mexican-hat wavelet, defined as Ψ(w,x) = $w^{{3/2}}$(6 - $w^{2}$ $r^{2}$) $e^{{-w^2 r^2/4}}$, where w is the scale parameter (kw = w Lbox/1000 in dimensionless form). Because the CIC grid turns particles into pseudo-particles on a regular lattice, the transform reduces to a weighted sum of wavelets over grid points, giving linear time O(N) and making MPI domain decomposition along one axis straightforward. The argument is carried by the criterion that real halos are local maxima in the 4D space of 3D position plus scale — the cross-scale maximum — together with the positive region of the wavelet as the halo boundary. Two correction steps are load-bearing: fitting a 3D isotropic quadratic to the peak grid point to remove grid-position bias, and rescaling peak values across different grid resolutions to remove the averaging bias.

What would settle it

Re-run CWTHF on the same dataset with the peak-bias correction replaced by a high-resolution direct evaluation of the wavelet transform at the true peak (bypassing the quadratic approximation), and compare the resulting halo sizes and HMF to the FOF catalog; if halo boundaries or the rvir–kw relation shift noticeably when the 3/5 factor is reintroduced, the central claim that CWT catalogs match FOF is not robust.

Watch

Extended reading notes

Core claim

CWTHF (Continuous Wavelet Transform Halo Finder) operates in 3D by binning particles onto a cloud-in-cell grid, computing the isotropic Mexican-hat wavelet transform at a sequence of scales, finding local maxima in each scale, and keeping only maxima that persist across adjacent scales. Around each cross-scale maximum the grid is segmented by the positive region of the wavelet, groups below a density threshold of 4ρ are discarded, and a self-boundness check removes unbound particles. Tested on a dark-matter-only sub-simulation with $512^{3}$ particles in a 50 h−1Mpc box, the CWT catalog contains 162,872 halos versus 253,112 FOF halos; when FOF groups are subjected to the same unbinding procedure the FOF count drops to 182,362 and the halo mass functions come into much closer agreement. The largest CWT halos match the largest FOF halos in position, mass, and particle content, and the halo power spectra agree once unbound FOF halos are removed. The paper also reports a fitted relation between the dimensionless wavelet scale and virial radius, rvir = 0.091/kw - 0.012 (equivalently rvir ≈ 1.8/w), giving the method a direct physical calibration.

Load-bearing premise

The load-bearing premise is that the continuous-wavelet field near a peak is well approximated by a 3D isotropic quadratic so that a grid-averaging bias can be corrected analytically — the paper itself concedes the real peak is sharper, and the 3/5 correction factor is removed by hand.

Editorial extensions

If this is right

  • If the central claim holds, CWTHF provides a halo finder with linear time complexity whose memory use can be traded against the maximum scale kw high, letting users inspect large halos quickly with low memory.
  • The comparison implies that roughly 30% of FOF halos are unbound, and that an unbinding post-processing step reconciles FOF and wavelet catalogs; this supports the community practice of unbinding FOF outputs.
  • The CWT boundary combined with self-boundness check effectively turns CWTHF into a phase-space halo finder, addressing the 'linking bridge' problem of FOF.
  • The fitted scale–radius relation rvir ≈ 1.8/w gives a direct way to translate wavelet scales into physical halo sizes, useful for designing multiscale searches.
  • Because the algorithm's complexity is independent of grid resolution, larger simulations with fixed box length can be processed in roughly linear time.

Reading between the lines

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

  • The quadratic peak-shape assumption in Appendix B is the main technical risk; an obvious extension is to replace it with the exact wavelet peak profile or an empirically calibrated correction, which would remove the hand-tuned 3/5 factor and likely stabilize halo sizes further.
  • The rvir–kw calibration is derived from one simulation at one resolution; testing it on simulations with different box sizes, resolutions, and cosmologies would show whether the relation is universal or needs re-fitting.
  • Because the algorithm segments the grid by the positive wavelet region, the method implicitly defines halo boundaries by the scale of the wavelet; comparing CWT boundaries against other boundary definitions (e.g., splashback radii) could reveal whether the wavelet boundary carries physical meaning.
  • If linear-time complexity is realized in a compiled implementation, CWT-based halo finding could become competitive with FOF for trillions of particles, where FOF's linked-list overhead grows.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. The paper introduces CWTHF, a halo finder that identifies dark matter halos in cosmological simulations by computing the continuous wavelet transform (CWT) of a cloud-in-cell density grid and locating local maxima in the resulting 4D (3D plus scale) space. The algorithm segments the grid around these maxima, applies a density threshold and a self-boundness check, and assigns particles to halos. The method is MPI-parallelized and claimed to have O(N) time complexity. The authors test CWTHF on the SIMBA m50n512 dark-matter sub-simulation, compare the resulting catalog with a friends-of-friends (FOF) catalog built with yt, and report catalog counts, halo mass functions, halo power spectra, and a fitted relation between wavelet scale and virial radius. The central claim is that the agreement with FOF demonstrates the viability of CWT for halo finding, with the linear time complexity cited as the route to future gains.

Significance. If the central claim holds, CWTHF represents a novel and potentially scalable approach to halo identification, and the paper's release of the source code on Zenodo is a useful contribution to the community. The validation against an external FOF catalog on public SIMBA data, the parameter study in Section 4, and the actual performance measurements in Appendix A are all strengths. However, the paper's central comparison depends on a peak-correction calibration (Appendix B) that is explicitly conceded to be an analytic model with a manually adjusted factor, and this calibration affects which maxima survive cross-scale verification, the segmented halo boundaries, and the fitted wavelet-scale-to-virial-radius relation. The grid-resolution dependence noted in Section 4 further suggests that the halo sizes and statistics may not be converged at the default settings. These issues are fixable but must be addressed before the viability claim is fully established.

major comments (3)
  1. [Section 2.2 and Appendix B, Eqs. (B2)-(B6)] The cross-scale peak comparison, which decides which maxima are real halos and how large they are, rests on the assumption that the CWT near a peak is a 3D isotropic quadratic function. The paper itself concedes, in the last paragraph of Appendix B, that 'the precise form of the CWT peak is sharper than that of a quadratic function' and that 'removing the factor 3/5 will improve consistency across different resolutions.' This is a one-parameter ad hoc adjustment, not a derived result. Because this correction feeds directly into the cross-scale verification and the segmented halo boundary, and through Eq. (5) into the conversion from wavelet scale to virial radius, the catalog-level agreement with FOF reported in Section 3 could be partly a product of this calibration. I ask the authors to add a synthetic recovery test: insert halos with known density profiles, sizes, and masses into a particle distribution, run CWTHF, and show that the recovered sizes and masses, the cross-scale maxima, and the rvir-kw relation are unbiased and converge as n_ref and w_resolution increase. This test would also address the residual grid-resolution bias noted in Section 4.
  2. [Section 4 and Figure 12] The paper states that 'increasing n_ref consistently results in a reduction in halo size' and that the HMF changes significantly for n_ref < 300. This means the default n_ref=400 may not be at numerical convergence, and the HMF/HPS comparisons in Section 3 are made at a resolution where halo sizes are still resolution-dependent. This is load-bearing because the abstract's viability claim relies on these comparisons. Please provide a convergence test in n_ref and w_resolution for the m50n512 catalog, showing that the HMF, the HPS, and the rvir-kw fit (Eq. 5) stabilize at the default settings within the quoted uncertainties. If convergence cannot be reached at practical grid sizes, the paper should state the systematic uncertainty on the halo-catalog statistics.
  3. [Section 3, Figures 9 and 10] The comparison FOF catalog is post-processed by a self-boundness check that, as the paper notes, 'does not retain any particles' and discards entire FOF groups when a large fraction of particles are unbound. This crude unbinding is not the standard way to produce a bound FOF catalog, and it is different from the iterative unbinding used inside CWTHF. The resulting 182,362-halo FOF catalog is therefore not a standard reference, and the claim that the HMF discrepancy at the low-mass end is 'primarily due to the unbound halos identified by the FOF method' is not fully supported. Please either compare against a properly unbound FOF catalog (e.g., from AHF or ROCKSTAR on the same data) or clearly frame the comparison as being against FOF-plus-crude-unbinding, and adjust the conclusions accordingly.
minor comments (6)
  1. [Section 3, first paragraph] The catalog name 'd4 r400 w20' is used without defining the meaning of the 'd4' component; footnote 3 gives the naming pattern only implicitly. Please define the notation explicitly.
  2. [Section 3, Figure 11 and Eq. (5)] The fit of rvir versus 1/kw excludes 'halos from the three largest scales' with the justification that very large virial radii are not feasible in CDM. Please quantify this cutoff (e.g., by comparing with the maximum expected halo radius in the m50n512 box) and test the sensitivity of Eq. (6) to the exclusion.
  3. [Section 2.1, Eq. (4)] The normalization of the Mexican hat wavelet is not explained; please state the normalization convention and cite the source (Wang & He 2021) more explicitly.
  4. [Section 4, Figures 12 and 13] The text states that 'increasing n_ref consistently results in a reduction in halo size, as questionable boundary regions are excluded.' Please specify which boundary regions are 'questionable' and how they are identified.
  5. [Section 1] The claim of being 'the first wavelet-based, MPI-parallelized halo finder' should be supported by a more thorough literature search or weakened to 'to our knowledge'.
  6. [Appendix A] The performance statement 'A dataset that is eight times larger results in only approximately 0.6 times more computation time' is ambiguous; please clarify whether this is total time or time per particle and specify the exact numbers.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: CWTHF's viability claim is benchmarked against an external FOF catalog; self-citations are lineage, and the 3/5 correction is an acknowledged calibration, not an input that forces the comparison.

full rationale

The paper's load-bearing claim is that CWT halo catalogs agree with an FOF catalog for the SIMBA m50n512 dark-matter sub-simulation, as measured by spatial distribution, halo mass function, and power spectrum. That FOF reference catalog is built independently with the yt-project on public SIMBA data, and the unbinding procedure applied to the FOF catalog is the standard AHF-style self-boundness check, applied symmetrically rather than derived from the CWT algorithm. The CWTHF code does not take the FOF catalog as input, so the reported agreement is external and falsifiable, not forced by construction. The methodological elements borrowed from the authors' own prior series (Wang & He 2021, 2022, 2023, 2024; Li et al. 2024) are explicit definitions and conventions: the Mexican-hat wavelet is given in Eq. 4, the halo boundary is defined by CWT > 0, and cross-scale maxima define halo centers and sizes. These are assumptions of the method, not uniqueness theorems or hidden fits to the benchmark. The closest candidate for a circularity concern is Appendix B: the paper assumes a 3D isotropic quadratic peak, derives a grid-bias correction, then concedes that 'the precise form of the CWT peak is sharper than that of a quadratic function' and hand-removes the factor 3/5 to 'improve consistency across different resolutions.' This is an acknowledged calibration or correctness risk: if the quadratic model and the hand-removed factor are wrong, halo sizes, the fitted scale-radius relation in Eq. 5, and the HMF comparison shift. But it is not circularity, because the factor is not fitted to the FOF benchmark in the text, and the central viability comparison remains an independent external test. No specific reduction of a prediction to an input, by equation or by self-citation chain, was found.

Assumptions & free parameters 6 free parameters · 6 assumptions · 0 invented entities

No new physical entities are introduced. The '4D wavelet space' (3D physical space plus a scale axis) is a standard wavelet-analysis construction, not a physical dimension or a new conserved quantity, so it is not an invented entity in the graviton sense. The free parameters listed are the constants the paper tunes or fits; several are explicitly calibrated to the m50n512 box.

free parameters (6)
  • dens_th, grid density threshold = 4 rho (any value 1 to 7 'produces acceptable results')
    Chosen so that each candidate maximum 'should correspond to a structure with a density greater than 4 rho' (Section 2.4), calibrated against the method's own halo density function in Figure 6.
  • Peak-correction compensation factor = 3/5 removed by hand
    The quadratic model underestimates the grid-size bias; the paper states 'Removing the factor 3/5 will improve consistency across different resolutions in our program' (Appendix B). This is a tuned constant, not a derived one.
  • rvir-kw fit coefficients = 0.091 and -0.012 (Eq. 5)
    Fit to the wavelet-scale versus virial-radius relation in Figure 11, with the three largest scales excluded because the 1/r relation 'is no longer applicable'; used to state rvir ~ 1.8/w (Eq. 6).
  • kw high, upper scale limit = 2.5
    Determines the smallest structures searched for; the paper states the defaults 'are suitable only for simulations with a box length of 50 h^-1 Mpc and 512^3 particles' (Table 1) and must be re-tuned for other boxes.
  • n ref and w resolution = 400 and 20
    Spatial and scale resolution parameters; the parameter study (Figures 12 and 13) shows they materially shift the halo power spectrum.
  • particle th, minimum particle number = 15
    Minimum particle count for a halo; the low-mass end of the HMF comparison is defined relative to this threshold (Table 1, Section 3).
assumptions (6)
  • domain assumption The isotropic Mexican hat wavelet (Eq. 4, with its positive core and negative ring) is the right probe at each scale, so the CWT > 0 region marks the halo boundary (Section 2.3).
    The kernel is taken from the authors' prior work (Wang and He 2021; Wang et al. 2022); the boundary rule follows from this specific kernel shape.
  • domain assumption The CIC grid faithfully approximates the particle distribution, with grid resolution Ng = Int(400 kw + 150) tying physical resolution to scale (Section 2.1).
    Standard interpolation practice, but the dynamic resolution couples the grid to the wavelet scale and drives the bias the paper must correct.
  • ad hoc to paper The CWT field near a peak is a 3D isotropic quadratic, and the grid-averaging bias between scales can be corrected analytically (Appendix B).
    The paper admits the true peak is sharper than quadratic and compensates by removing the 3/5 factor.
  • domain assumption A candidate is a real halo only if its maximum persists to an adjacent smaller scale (cross-scale maximum, Section 2.4).
    This criterion, plus the density threshold, filters Poisson noise maxima; it is a definitional choice, not an independently verified physical criterion.
  • domain assumption Self-boundness can be judged with a spherical escape-velocity estimate and a 40% unbinding threshold (Section 2.3, citing Knollmann and Knebe 2009).
    Borrowed from AHF; for irregular halos the spherical approximation is rough, and this check removes 30% of FOF halos in the comparison.
  • domain assumption LCDM cannot produce halos with very large virial radii, justifying exclusion of the three largest wavelet scales from the fit (Section 3, Figure 11).
    Standard CDM reasoning, but a post-hoc exclusion that changes the fitted rvir-kw relation.

how reviews work

0 comments
Cite this review

Pith. "Pith review of CWTHF: Identifying Dark Matter Halos with Continuous Wavelet Transform." pith.science (2026). https://pith.science/paper/XHQGTBX4

@misc{pith2026250110622,
  author       = {Pith},
  title        = {Pith review of: CWTHF: Identifying Dark Matter Halos with Continuous Wavelet Transform},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XHQGTBX4}},
  note         = {Machine review of arXiv:2501.10622}
}
abstract

Cosmological simulations are an important method for investigating the evolution of the Universe. In order to gain further insight into the processes of structure formation, it is necessary to identify isolated bound objects within the simulations, namely, the dark matter halos. The continuous wavelet transform (CWT) is an effective tool used as a halo finder due to its ability to extract clustering information from the input data. In this study, we introduce CWTHF (Continuous Wavelet Transform Halo Finder), the first wavelet-based, MPI-parallelized halo finder, marking a novel approach in the field of cosmology. We calculate the CWT from the cloud-in-cell (CIC) grid and segment the grid based on the local CWT maxima. We then investigate the effects of the parameters that influence our program and identify the default settings. A comparison with the conventional friends-of-friends (FOF) method demonstrates the viability of CWT for halo finding. Although the actual performance is not faster than FOF, the linear time complexity of $\mathcal{O}(N)$ of our identification scheme indicates its significant potential for future optimization and application.

Figures

Figures reproduced from arXiv: 2501.10622 by the authors.

Figure 1
Figure 1. The flowchart of the logical methodology of our CWTHF program. In this flowchart, we use the default values of the param￾eters as detailed in Section 4. (CWTHF). Unlike traditional methods that directly identify structures in the density field, the CWTHF employs a multi￾scale analysis to identify halos in the 4D (3D physical plus 1D scale) wavelet space. This methodology allows for the se￾lection of specific scales … view at source ↗
Figure 3
Figure 3. The rank (top) and the mass (bottom) of the six largest halos in the FOF catalog, as observed in other uncorrected catalogs. For the meaning of the catalog names see Section 3. compute the wavelet Ψ(w, x) on a regular grid, where the grid spacing is set to match the CIC grid mentioned earlier. Then, for each grid point g with mg > 0, weight the wavelet by mg and add the weighted wavelet to the grid points cen￾tered … view at source ↗
Figure 5
Figure 5. The scatter plot of a medium-sized CWT halo and its cor￾responding virial radius r200 (gray circle). The color of the particles indicates their local density, with yellow representing low density and black representing high density. It is evident that the size of this halo is 2-3 times larger than r200, resulting in a grid density that is 10-30 times smaller than 200ρ. putational efficiency. Reallocating the grid in… view at source ↗
Figures from the paper (8 more)
Figure 6
Figure 6. Figure 6: The halo density function of non-threshold CWT halos with two vertical lines denoting ρ and 100ρ, respectively. There is a significant number of low-density halos with densities even less than ρ. sources, and the threshold obtained through this method does not have a c…
Figure 7
Figure 7. Figure 7: Left: The distribution of FOF halos in two slices located at z = 20.0 h −1Mpc and 43.2 h −1Mpc, each with a thickness of ∆z = 0.3 h −1Mpc. Right: The distribution of CWT halos in the same two slices. parameters (Planck Collaboration et al. 2016). To assess the reliabil…
Figure 8
Figure 8. Figure 8: Left: The largest and the second largest FOF halos that survive the self-boundness check. Right: The corresponding CWT halos of the above two FOF halos. Both two halos exhibit an elliptical central structure. from each other, and as a result, these FOF groups may cease…
Figure 10
Figure 10. Figure 10: The power spectrum of FOF and CWT halos. The solid red and blue lines represent the power spectrum of CWT and FOF halos, respectively. The dashed blue line represents the power spec￾trum of FOF halos after an unbinding procedure. With the unbind￾ing procedure, the shi…
Figure 9
Figure 9. Figure 9: The HMFs of FOF and CWT halos (top) and the relative differences between the FOF and CWT catalogs (bottom). The solid red and blue lines represent the HMFs of CWT and FOF halos, re￾spectively. The dashed blue line represents the HMF of FOF halos after an unbinding proc…
Figure 11
Figure 11. Figure 11: The relationship between the wavelet scales (dimension￾less scale parameter) and the physical scales (virial radius) is illus￾trated by a solid blue line, with a 1-σ uncertainty limit indicated by a dashed red line. The solid green line represents an inverse propor￾ti…
Figure 12
Figure 12. Figure 12: Effects of different parameters on the HMFs of CWT Catalogs. From the top left to the bottom right, we examine the effects of w resolution, kw high, dens th, and n ref, respectively. The solid blue line represents the HMF of the FOF catalog for comparison. It should b…
Figure 13
Figure 13. Figure 13: Similar to [PITH_FULL_IMAGE:figures/full_fig_p013_13.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

49 extracted references · 14 canonical work pages

  1. [1]

    A., Jones, B

    Arag´on-Calvo, M. A., Jones, B. J. T., van de Weygaert, R., & van der Hulst, J. M. 2007, A&A, 474, 315, doi: 10.1051/0004-6361:20077880

    doi:10.1051/0004-6361:20077880 2007

  2. [2]

    2024, JCAP, 2024, 001, doi: 10.1088/1475-7516/2024/02/001

    Balaudo, A., Calore, F., De Romeri, V ., & Donato, F. 2024, JCAP, 2024, 001, doi: 10.1088/1475-7516/2024/02/001

    work page doi:10.1088/1475-7516/2024/02/001 2024

  3. [3]

    V ., & Rodionov, E

    Baluev, R. V ., & Rodionov, E. I. 2020, Celestial Mechanics and Dynamical Astronomy, 132, 34, doi: 10.1007/s10569-020-09976-2

    doi:10.1007/s10569-020-09976-2 2020

  4. [4]

    S., Wechsler, R

    Behroozi, P. S., Wechsler, R. H., & Wu, H.-Y . 2013, ApJ, 762, 109, doi: 10.1088/0004-637X/762/2/109

    doi:10.1088/0004-637x/762/2/109 2013

  5. [5]

    1991, A&A, 251, 312

    Bendjoya, P., Slezak, E., & Froeschle, C. 1991, A&A, 251, 312

    work page 1991

  6. [6]

    Bertschinger, E., & Gelb, J. M. 1991, Computers in Physics, 5, 164, doi: 10.1063/1.4822978

    doi:10.1063/1.4822978 1991

  7. [7]

    1992, in Distribution of Matter in the Universe, ed

    Bijaoui, A., Slezak, E., & Mars, G. 1992, in Distribution of Matter in the Universe, ed. G. A. Mamon & D. Gerbal, 323–332 Cay´on, L., Sanz, J. L., Barreiro, R. B., et al. 2000, MNRAS, 315, 757, doi: 10.1046/j.1365-8711.2000.03462.x

    arXiv 1992

  8. [8]

    2007, in American Institute of Physics Conference Series, V ol

    Ciprini, S., Tosti, G., Marcucci, F., et al. 2007, in American Institute of Physics Conference Series, V ol. 921, The First GLAST Symposium, ed. S. Ritz, P. Michelson, & C. A. Meegan, 546–547 Dav´e, R., Angl´es-Alc´azar, D., Narayanan, D., et al. 2019, MNRAS, 486, 2827, doi: 10.1093/mnras/stz937

    doi:10.1093/mnras/stz937 2007

Show all 49 references
  1. [9]

    S., & White, S

    Davis, M., Efstathiou, G., Frenk, C. S., & White, S. D. M. 1985, ApJ, 292, 371, doi: 10.1086/163168

    1985 doi

  2. [10]

    2012, SoPh, 281, 863, doi: 10.1007/s11207-012-0109-3

    Djafer, D., Irbah, A., & Meftah, M. 2012, SoPh, 281, 863, doi: 10.1007/s11207-012-0109-3

    2012 doi

  3. [11]

    J., & Hut, P

    Eisenstein, D. J., & Hut, P. 1998, ApJ, 498, 137, doi: 10.1086/305535

    1998 doi

  4. [12]

    2006, A&A, 450, 9, doi: 10.1051/0004-6361:20041635

    Flin, P., & Krywult, J. 2006, A&A, 450, 9, doi: 10.1051/0004-6361:20041635

    2006 doi

  5. [13]

    E., Kashyap, V ., Rosner, R., & Lamb, D

    Freeman, P. E., Kashyap, V ., Rosner, R., & Lamb, D. Q. 2002, ApJS, 138, 185, doi: 10.1086/324017

    2002 doi

  6. [14]

    S., & White, S

    Frenk, C. S., & White, S. D. M. 2012, Annalen der Physik, 524, 507, doi: 10.1002/andp.201200212

    2012 doi

  7. [15]

    M., & Bertschinger, E

    Gelb, J. M., & Bertschinger, E. 1994, ApJ, 436, 467, doi: 10.1086/174922

    1994 doi

  8. [16]

    P., & Brandenberger, R

    Goetz, M., Huchra, J. P., & Brandenberger, R. H. 1998, arXiv e-prints, astro, doi: 10.48550/arXiv.astro-ph/9811393 Gonz´alez-G´omez, D. I., Blanco-Cano, X., & Raga, A. C. 2010, Advances in Space Research, 46, 22, doi: 10.1016/j.asr.2010.02.022

    1998 doi arXiv

  9. [17]

    A., Forman, W., Jones, C., & Murray, S

    Grebenev, S. A., Forman, W., Jones, C., & Murray, S. 1995, ApJ, 445, 607, doi: 10.1086/175725

    1995 doi

  10. [18]

    2022, MNRAS, 509, 501, doi: 10.1093/mnras/stab2980

    Maksimova, N. 2022, MNRAS, 509, 501, doi: 10.1093/mnras/stab2980

    2022 doi

  11. [19]

    R., Millman, K

    Harris, C. R., Millman, K. J., van der Walt, S. J., et al. 2020, Nature, 585, 357, doi: 10.1038/s41586-020-2649-2

    2020 doi

  12. [20]

    2012, Geophysical Journal International, 189, 1430, doi: 10.1111/j.1365-246X.2012.05455.x

    Hayn, M., Panet, I., Diament, M., et al. 2012, Geophysical Journal International, 189, 1430, doi: 10.1111/j.1365-246X.2012.05455.x

    2012 arXiv

  13. [21]

    Hopkins, P. F. 2015, MNRAS, 450, 53, doi: 10.1093/mnras/stv195 18 L I, WANG & H E

    2015 doi

  14. [22]

    Hunter, J. D. 2007, Computing in Science and Engineering, 9, 90, doi: 10.1109/MCSE.2007.55

    2007 doi

  15. [23]

    R., Muldrew, S

    Knebe, A., Knollmann, S. R., Muldrew, S. I., et al. 2011, MNRAS, 415, 2293, doi: 10.1111/j.1365-2966.2011.18858.x

    2011

  16. [24]

    R., Lux, H., et al

    Knebe, A., Pearce, F. R., Lux, H., et al. 2013, MNRAS, 435, 1618, doi: 10.1093/mnras/stt1403

    2013 doi

  17. [25]

    R., & Knebe, A

    Knollmann, S. R., & Knebe, A. 2009, ApJS, 182, 608, doi: 10.1088/0067-0049/182/2/608

    2009 doi

  18. [26]

    2012, Physics of the Dark Universe, 1, 50, doi: 10.1016/j.dark.2012.10.002

    Kuhlen, M., V ogelsberger, M., & Angulo, R. 2012, Physics of the Dark Universe, 1, 50, doi: 10.1016/j.dark.2012.10.002

    2012 doi

  19. [27]

    1994, MNRAS, 271, 676, doi: 10.1093/mnras/271.3.676

    Lacey, C., & Cole, S. 1994, MNRAS, 271, 676, doi: 10.1093/mnras/271.3.676

    1994 doi

  20. [28]

    R., & Tagliaferri, G

    Lazzati, D., Campana, S., Rosati, P., Panzera, M. R., & Tagliaferri, G. 1999, ApJ, 524, 414, doi: 10.1086/307788

    1999 doi

  21. [29]

    2025, CWTHF (Continuous Wavelet Transform Halo Finder), Zenodo, doi: 10.5281/zenodo.15015510

    Li, M. 2025, CWTHF (Continuous Wavelet Transform Halo Finder), Zenodo, doi: 10.5281/zenodo.15015510. https://doi.org/10.5281/zenodo.15015510

    2025 doi

  22. [30]

    2024, ApJ, 973, 39, doi: 10.3847/1538-4357/ad65d1

    Li, M., Wang, Y ., & He, P. 2024, ApJ, 973, 39, doi: 10.3847/1538-4357/ad65d1

    2024 doi

  23. [31]

    2018, Communications in Theoretical Physics, 70, 728, doi: 10.1088/0253-6102/70/6/728

    Li, Z.-W., & He, P. 2018, Communications in Theoretical Physics, 70, 728, doi: 10.1088/0253-6102/70/6/728

    2018 doi

  24. [32]

    2015, A&A, 574, A67, doi: 10.1051/0004-6361/201424566

    Mertens, F., & Lobanov, A. 2015, A&A, 574, A67, doi: 10.1051/0004-6361/201424566

    2015 doi

  25. [33]

    2019, Computational Astrophysics and Cosmology, 6, 2, doi: 10.1186/s40668-019-0028-x

    Nelson, D., Springel, V ., Pillepich, A., et al. 2019, Computational Astrophysics and Cosmology, 6, 2, doi: 10.1186/s40668-019-0028-x

    2019 doi

  26. [34]

    2006, A&A, 458, 441, doi: 10.1051/0004-6361:20065225

    Patrikeev, I., Fletcher, A., Stepanov, R., et al. 2006, A&A, 458, 441, doi: 10.1051/0004-6361:20065225

    2006 doi

  27. [35]

    Peebles, P. J. E. 1974, ApJL, 189, L51, doi: 10.1086/181462 Planck Collaboration, Ade, P. A. R., Aghanim, N., et al. 2016, A&A, 594, A13, doi: 10.1051/0004-6361/201525830

    1974 doi

  28. [36]

    2010, A&A, 519, A94, doi: 10.1051/0004-6361/201014214

    Planelles, S., & Quilis, V . 2010, A&A, 519, A94, doi: 10.1051/0004-6361/201014214

    2010 doi

  29. [37]

    H., & Schechter, P

    Press, W. H., & Schechter, P. 1974, ApJ, 187, 425, doi: 10.1086/152650

    1974 doi

  30. [38]

    B., Agertz, O., Moore, B., & Stadel, J

    Romeo, A. B., Agertz, O., Moore, B., & Stadel, J. 2008, ApJ, 686, 1, doi: 10.1086/591236

    2008 doi

  31. [39]

    1993, ApJ, 409, 517, doi: 10.1086/172683

    Slezak, E., de Lapparent, V ., & Bijaoui, A. 1993, ApJ, 409, 517, doi: 10.1086/172683

    1993 doi

  32. [40]

    Springel, V ., White, S. D. M., Tormen, G., & Kauffmann, G. 2001, MNRAS, 328, 726, doi: 10.1046/j.1365-8711.2001.04912.x

    2001

  33. [41]

    Stadel, J. G. 2001, PhD thesis, University of Washington, Seattle

    2001

  34. [42]

    J., Smith, B

    Turk, M. J., Smith, B. D., Oishi, J. S., et al. 2011, ApJS, 192, 9, doi: 10.1088/0067-0049/192/1/9 Vall´es-P´erez, D., Planelles, S., & Quilis, V . 2022, A&A, 664, A42, doi: 10.1051/0004-6361/202243712 van der Walt, S., Colbert, S. C., & Varoquaux, G. 2011, Computing in Scienc...

    2011 doi

  35. [43]

    B., & Babyk, I

    Vavilova, I. B., & Babyk, I. V . 2018, Odessa Astronomical Publications, 30, 239, doi: 10.18524/1810-4215.2018.31.146678

    2018

  36. [44]

    2020, ApJS, 250, 2, doi: 10.3847/1538-4365/ab9d82

    Villaescusa-Navarro, F., Hahn, C., Massara, E., et al. 2020, ApJS, 250, 2, doi: 10.3847/1538-4365/ab9d82

    2020 doi

  37. [45]

    E., et al

    Virtanen, P., Gommers, R., Oliphant, T. E., et al. 2020, Nature Methods, 17, 261, doi: 10.1038/s41592-019-0686-2

    2020 doi

  38. [46]

    2008, MNRAS, 387, 601, doi: 10.1111/j.1365-2966.2008.13292.x

    Wang, L., Rowan-Robinson, M., Yamamura, I., et al. 2008, MNRAS, 387, 601, doi: 10.1111/j.1365-2966.2008.13292.x

    2008

  39. [47]

    2021, Communications in Theoretical Physics, 73, 095402, doi: 10.1088/1572-9494/ac10be —

    Wang, Y ., & He, P. 2021, Communications in Theoretical Physics, 73, 095402, doi: 10.1088/1572-9494/ac10be —. 2022, ApJ, 934, 112, doi: 10.3847/1538-4357/ac7a3d —. 2023, RAS Techniques and Instruments, 2, 307, doi: 10.1093/rasti/rzad020 —. 2024a, MNRAS, 528, 3797, doi: 10.1093...

    2021 doi arXiv

  40. [48]

    2022, ApJ, 934, 77, doi: 10.3847/1538-4357/ac752c

    Wang, Y ., Yang, H.-Y ., & He, P. 2022, ApJ, 934, 77, doi: 10.3847/1538-4357/ac752c

    2022 doi

  41. [49]

    H., Hernquist, L., & Katz, N

    Weinberg, D. H., Hernquist, L., & Katz, N. 1997, ApJ, 477, 8, doi: 10.1086/303683

    1997 doi

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.