Pith. sign in

REVIEW 4 major objections 5 minor 45 references

Weighted Levenberg-Marquardt methods for fitting multichannel nuclear cross section data

T0 review · 4 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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

Pith's one-line read Replacing the Fisher information metric with a dataset-weighted version keeps Levenberg-Marquardt fits of multichannel nuclear cross sections inside physically plausible parameter regions and improves convergence, and a geometric…

desk verdict A genuinely useful empirical idea, but the wLM update as printed does not minimize the stated marginalized likelihood; the paper needs major revision before the central claim can be trusted. read the letter →

arxiv 2508.19468 v2 pith:XPU5BS5C submitted 2025-08-26 nucl-th stat.ML

M. Imbrišak , A. E. Lovell , M. R. Mumpower This is my paper · ORCID
classification nucl-thstat.ML
keywords weightedLevenberg-MarquardtFisherinformationmetricmultichannelnuclearcrosssectionfittingHauser-Feshbachstatisticalmodelopticalparameterssloppymodelsdatasetweightinguncertaintyquantification
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

This paper introduces a weighted Levenberg-Marquardt (wLM) algorithm for fitting nuclear reaction models to heterogeneous experimental cross-section data, targeting a known weakness of the classical method when models have many weakly constrained, 'sloppy' parameters. The algorithm builds a weighted Fisher information metric by marginalizing over per-dataset weight hyperparameters, so that a channel with many data points or very small reported errors does not silently dominate the fit. Applied to neutron cross sections on 148Sm, the paper shows that weighted fits keep optical-model tweaks near physically expected values, while the unweighted fit drives them outside that band. It also shows that a geometric scaling of the update step, based on the angle between successive steps measured with the weighted metric, speeds convergence without moving the final parameters. The paper argues this is a practical alternative to trust-region methods for nuclear data evaluation.

What carries the argument

The central object is the weighted Fisher information metric (wFIM), constructed by treating each dataset's reported uncertainties as scaled by a per-dataset inverse-variance weight $\alpha_k$ and marginalizing the likelihood over $\alpha_k$ under a chosen prior (exponential, bounded uniform, or cropped exponential). This yields an effective per-dataset weight $w_k(\theta)$, for example $w_k = (n_k+2)\chi_k^2/(\chi_k^2+2)^2$ for the exponential prior, multiplying each group's unweighted FIM contribution $g^{(0,k)}_{\mu\nu}$. The wLM update replaces the FIM in the classical LM step with this weighted metric, $\delta\theta^\mu = -(g^{(W,\lambda)})^{\mu\nu} \sum_k \sum_{i_k} w_k(\theta)\,\partial_\nu r_{k i_k}\, r_{k i_k}$, so that datasets with extreme chi-squared values are automatically rebalanced. A geometric scaling factor $s = g^{(W,\lambda)}_{\mu\nu}\,\delta\theta^\mu_{n-1}\,\delta\theta^\nu_n$ rescales each update by the wFIM-angle between successive steps, lengthening aligned steps and shortening abrupt directional changes.

What would settle it

Repeat the same CoH3 fitting pipeline on another nucleus with similarly heterogeneous total and capture data, and check whether the unweighted fit again leaves the 0.8–1.2 multiplier band while the weighted fit stays inside; a case where both stay inside would weaken the claimed advantage, and an independent microscopic optical-model calculation of the out-of-band parameters would settle whether they are truly unphysical.

Watch

Extended reading notes

Core claim

The paper claims that classical Levenberg-Marquardt on a multichannel, sloppy model such as the coupled-channels reaction code CoH3 tends to concentrate on the best-populated or most precise channel, producing fits whose parameters leave a physically reasonable band around the standard optical-model baseline. By contrast, the weighted Levenberg-Marquardt algorithm, which incorporates a dataset-specific weight obtained by marginalizing an inverse-variance hyperparameter under a chosen prior, balances the channels and keeps the fitted multiplicative tweaks within that band for both raw and FBET-smoothed data. On the 148Sm benchmark, the exponential weighting prior gives the lowest overall chi-squared but the broadest posterior uncertainties, while the cropped-exponential prior performs best after FBET smoothing; the choice of optimal weighting is data-dependent. The paper also demonstrates that geometric scaling of the update steps consistently reduces the number of iterations to convergence without altering the converged parameter estimates.

Load-bearing premise

The paper's case that weighted fits are more physically consistent rests on the unstated assumption that each fitted multiplier should stay between roughly 0.8 and 1.2 of the baseline optical-model value; if the unweighted fit's out-of-band parameters are actually admissible, the central comparison loses its force.

Editorial extensions

If this is right

  • On the 148Sm benchmark, the weighted schemes fit both total and capture channels in a single run without letting one channel dominate, whereas the unweighted LM fit visibly sacrifices one channel for the other.
  • The exponential weighting prior gives the lowest overall chi-squared but the broadest posterior parameter uncertainties, so comparing fits by chi-squared alone is misleading for sloppy models.
  • Geometric scaling reduces the number of iterations needed to reach convergence for every weighting scheme tested, while leaving the final parameter estimates essentially unchanged.
  • When the capture data are smoothed with FBET, the cropped-exponential prior performs best, and the optimum parameters remain consistent with the raw-data fits.
  • The unweighted LM Fisher information for this CoH3 problem is nearly degenerate, with only three nonzero eigenvalues, explaining its failure to converge unless initialized at a good point; the weighted variants produce a broader eigenvalue spectrum.

Reading between the lines

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

  • Editorial inference: the weighting construction naturally acts as a data-balancing regularizer, so it could also be tested as a general robustness device for fitting any multichannel dataset where one experimental group is overrepresented or assigned overconfident uncertainties.
  • Editorial inference: a direct way to separate the paper's physical-consistency claim from its choice of the 0.8–1.2 multiplier band would be a synthetic-data test with known true parameters and deliberately imbalanced channels, checking whether weighted estimates stay closer to the truth than unweighted ones.
  • Editorial inference: the geometric scaling factor uses the wFIM inner product of successive steps, so it should behave like a local preconditioner; comparing it directly with standard adaptive step-size or momentum schedules on the same CoH3 problem would clarify whether the acceleration comes from the angle alignment or from the damping schedule.
  • Editorial inference: because the paper finds that the best weighting prior shifts between raw and smoothed data and across nuclei, a practical extension would be to choose the prior width and shape by cross-validation or predictive holdout rather than by prior guesswork.
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

4 major / 5 minor

Summary. The paper proposes a weighted extension of the Levenberg-Marquardt algorithm (wLM) for fitting multichannel nuclear cross-section data. The weights are derived by marginalizing over per-dataset inverse-variance hyperparameters with several priors (exponential, uniform, cropped exponential), leading to a weighted Fisher information metric. The authors test the method on neutron total and capture cross sections for 148Sm using the CoH3 Hauser-Feshbach code, fitting multiplicative tweaks to the Koning-Delaroche optical potential. They report that weighted schemes balance the total and capture channels better than unweighted LM, keep fitted optical-model tweaks inside an asserted physical band, and remain stable when the capture data are first smoothed with FBET. A geometric scaling of the update step is added to accelerate convergence.

Significance. If the derivation and numerics were consistent, the paper would offer a practically useful recipe for heterogeneous nuclear-data evaluation: a transparent way to down-weight overrepresented or overly precise datasets, a natural-gradient-type update, and a cheap acceleration heuristic for sloppy models. The empirical comparison across four weighting schemes on a real CoH3 problem, with z-score and eigenvalue diagnostics, is a useful contribution to the nuclear-data fitting literature. However, the central theoretical derivation currently contains load-bearing inconsistencies, and the main qualitative conclusion ('physical consistency') rests on an unstated band. The strengths are the clear problem formulation, the explicit acceptance/rejection protocol for the LM step, and the comparative diagnostics in Figs. 8-10; these give the paper a solid empirical core that could support a revised version.

major comments (4)
  1. [II.B, Eq. (40)] The wLM update is not the natural-gradient or Gauss-Newton step for the marginalized likelihood in Eq. (8). From Eq. (8), the negative log-likelihood has gradient -∂_μ ln L = Σ_k (n_k+2)/(χ_k^2+2) Σ_i r_i ∂_μ r_i, whereas Eq. (40) uses Σ_k w_k(θ) Σ_i r_i ∂_μ r_i with w_k = (n_k+2)χ_k^2/(χ_k^2+2)^2. These coefficients coincide only in the limit χ_k^2 ≫ 2, which is not the regime of the reported fits. Consequently, the printed wLM step does not minimize the likelihood the paper claims to optimize; it corresponds to a different, unstated objective, and if one tries to interpret it as a weighted least-squares step the derivative-of-weight terms are also omitted. The central algorithmic claim therefore needs either a corrected gradient in Eq. (40) or an explicit statement of the objective that Eq. (40) actually minimizes, together with a re-run of the numerical demonstration under that objective.
  2. [II.A, Eq. (15)] The general weight formula in Eq. (15) has the wrong sign on the variance term. For a dataset with marginal likelihood L_k(s) = L_s[α^{n_k/2} f(α)], the Fisher-information coefficient is ℓ'(s)+ℓ''(s) with ℓ = -ln L_k, i.e. L_1/L_0 + (L_1/L_0)^2 - L_2/L_0, not L_1/L_0 + L_2/L_0 - (L_1/L_0)^2 as printed. For the exponential prior this makes Eq. (15) reduce to (n_k+2)(χ_k^2+4)/(χ_k^2+2)^2 rather than the correct Eq. (21), (n_k+2)χ_k^2/(χ_k^2+2)^2. Because Eq. (15) is the basis for the uniform and cropped-exponential weights, all weights derived through it inherit the error; the numerical results for those schemes in Section IV should be re-examined.
  3. [II.A, Eqs. (25), (34)-(37)] The incomplete-gamma functions appear with an off-by-one index. With the definition γ(s,x)=∫_0^x t^{s-1}e^{-t}dt in Eq. (26), the Laplace transform of α^{n_k/2}f(α) requires γ(n_k/2+1, ·), not γ(n_k/2, ·). Equation (25) and the Δ functions in Eqs. (34)-(37) use n_k/2, which corresponds to the transform of α^{n_k/2-1}. This changes the numerical weights for the uniform and cropped-exponential priors and must be corrected before the corresponding fits can be trusted.
  4. [IV, Figs. 5 and 7] The central qualitative claim that unweighted fits are 'physically inconsistent' while weighted fits are not rests entirely on the dashed horizontal lines at approximately 0.8-1.2 times the Koning-Delaroche values. No derivation, citation, or quantitative criterion is given for this band. If the unweighted tOW value is in fact physically admissible, the main conclusion of the paper is not established. Please justify the band from the adopted optical-model uncertainties or templates, or replace the physical-consistency argument with an explicit quantitative metric.
minor comments (5)
  1. [II.A, Eq. (8)] The normalization in Eq. (8) appears incorrect: marginalizing the likelihood in Eq. (4) over α_k with prior e^{-α_k} gives a coefficient 2Γ(n_k/2+1)/π^{n_k/2}, not 2Γ(n_k/2+2)/π^{n_k/2}. The constant does not affect the minimization, but the formula as printed is misleading.
  2. [II.A, Eq. (31)] The expression for E[α] for the cropped exponential distribution mixes α with the integration limits and is hard to parse; please write it explicitly in terms of α_L and α_U and verify the η = 1, symmetric-support convention used in the fits.
  3. [II.C, Eq. (46)] The quantity s in Eq. (46) is called an 'angle', but it is an unnormalized metric inner product and is not bounded in [-1,1]. Scaling δθ by this quantity therefore changes the step magnitude as well as its direction; please clarify the intended geometric meaning and state whether normalization by the relevant norms is required.
  4. [II.B, Eqs. (40)-(43)] The notation g^{(W,λ)}_{μν} is used both for the damped matrix and for its inverse; using upper and lower indices consistently, or a different symbol for the inverse, would remove ambiguity.
  5. [II.B, Eqs. (44)-(45)] The indices in the acceptance criterion appear shifted (θ_n vs θ_{n-1}); please make the iteration index consistent throughout the recursion.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the wLM weights and updates are derived from the marginalized likelihood, and the 148Sm comparison is an external demonstration.

full rationale

I walked the derivation chain from Eq. (4) through Eq. (40). The group likelihood with per-dataset weight α_k is marginalized over the entropy-maximizing prior e^{-α_k} to obtain the effective likelihood in Eq. (8); the wFIM in Eqs. (19)-(21) is obtained by differentiating that likelihood and using E[r_i r_j]=δ_ij. The wLM update in Eq. (40) is then a Gauss-Newton-type step built from those weights and the unweighted FIM blocks. Nothing here is fitted to a subset and then 'predicted' back: the weights w_k(θ) are deterministic functions of the current residuals (via χ²_k(θ)) that follow from the stated statistical model, not free parameters tuned to force the reported conclusions. The demonstration on 148Sm uses external EXFOR data and diagnoses the fits with z-scores and FIM spectra, so the central claims are not true by construction. Two caveats are correctness issues rather than circularity: (i) the printed step Eq. (40) uses w_k=(n_k+2)χ²_k/(χ²_k+2)^2 multiplying the gradient term, while the gradient of −ln L from Eq. (8) has coefficient (n_k+2)/(χ²_k+2), so the update does not exactly coincide with the LM/natural-gradient step for the printed likelihood; and (ii) the 'reasonable/physical range' dashed lines in Figs. 5 and 7 are asserted without derivation, which is an unsupported evaluation criterion, not an input-output reduction. Self-citations ([4], [44]) play no load-bearing role in the derivation, which is self-contained.

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

The method's load-bearing components are the likelihood model, the chosen priors over weights, and the implicit physical range used for evaluation. No new physical entities are introduced.

free parameters (4)
  • weighting prior family = exponential for raw data; cropped exponential for smoothed data
    The choice of prior over dataset weights is made after inspecting fit quality on the same 148Sm data; the paper states the most effective weighting choice is inherently data-dependent (Section IV).
  • prior width h for uniform and cropped exponential priors = 0.4 (h = 0.2, 0.4, 1.0 explored in Fig. 1)
    Controls the support [1-h/2, 1+h/2] around unit mean. The paper reports convergence with h = 0.4 for a wider set of nuclei and instability for larger h.
  • cropped exponential shape parameter eta = 1
    Set to 1 by hand; the paper says 'we find satisfactory results by setting eta = 1' (Section II A).
  • FBET smoothing hyperparameters eps0, eps1, s0, s1, rho = not reported; found by grid search minimizing generalized chi-square (Eq. 56)
    These define the smoothed capture dataset used as input to the fit; the wLM results depend on them.
assumptions (4)
  • domain assumption Residuals are independently and normally distributed with known covariance up to a per-dataset scale factor alpha_k (Eqs. 1-4).
    Underlies the likelihood in Eq. 4 and the entire marginalization; EXFOR data often have unreported correlations.
  • domain assumption The prior over each dataset weight alpha_k has unit mean, E[alpha_k] = 1 (Section II A).
    Used to set alpha_L, alpha_U symmetric around 1; invalid if reported uncertainties are systematically biased.
  • ad hoc to paper Multiplicative tweaks to the Koning-Delaroche optical potential are the varied parameters, with physically admissible values near 1 (Figs. 5, 7).
    The dashed 'physical range' band is not derived; it is the yardstick for judging fits.
  • standard math The weighted FIM inverse estimates parameter covariance via the Cramer-Rao bound (Section II B).
    Assumes unbiased estimators and regular likelihood; approximate for nonlinear models with data-dependent weights.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Weighted Levenberg-Marquardt methods for fitting multichannel nuclear cross section data." pith.science (2026). https://pith.science/paper/XPU5BS5C

@misc{pith2026250819468,
  author       = {Pith},
  title        = {Pith review of: Weighted Levenberg-Marquardt methods for fitting multichannel nuclear cross section data},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XPU5BS5C}},
  note         = {Machine review of arXiv:2508.19468}
}
abstract

We present an extension of the Levenberg-Marquardt algorithm for fitting multichannel nuclear cross section data. Our approach offers a practical and robust alternative to conventional trust-region methods for analyzing experimental data. The CoH$_3$ code, based on the Hauser-Feshbach statistical model, involves a large number of interdependent parameters, making optimization challenging due to the presence of "sloppy" directions in parameter space. To address the uneven distribution of experimental data across reaction channels, we construct a weighted Fisher Information Metric by integrating prior distributions over dataset weights. This framework enables a more balanced treatment of heterogeneous data, improving both parameter estimation and convergence robustness. We show that the resulting weighted Levenberg-Marquardt method yields more physically consistent fits for both raw and smoothed datasets, using experimental data for ${}^{148}$Sm as a representative example. Additionally, we introduce a geometric scaling strategy to accelerate convergence -- a method based on the local geometry of the manifold.

Figures

Figures reproduced from arXiv: 2508.19468 by the authors.

Figure 1
Figure 1. FIG. 1: Negative log-likelihoods (top row) and corresponding wFIM weights (bottom row) for the weighting schemes [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Schematic overview of the weighted Levenberg–Marquardt (wLM) procedure. Blue callouts indicate steps [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Experimental data for (a) total and (b) capture cross section data for neutrons on [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: FIG. 4: Best-fitting CoH [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: Best-fit CoH [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6: Same as Fig. 4 where FBET smoothing was used for the capture data. Black curves show the unsmoothed [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7: Best-fit CoH [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8: Log-likelihood ratio evolution over the number of optimization steps, [PITH_FULL_IMAGE:figures/full_fig_p008_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9: Absolute z-scores for various fitting schemes, evaluated against [PITH_FULL_IMAGE:figures/full_fig_p009_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10: (w)FIM eigenvalue spectra for various [PITH_FULL_IMAGE:figures/full_fig_p009_10.png]
Figure 10
Figure 10. Figure 10: All schemes reveal the inherent sloppiness of the [PITH_FULL_IMAGE:figures/full_fig_p012_10.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

45 extracted references · 21 canonical work pages

  1. [1]

    D. W. Marquardt, Journal of the society for Industrial and Applied Mathematics 11, 431 (1963)

    1963

  2. [2]

    (54) We modelA0 to be proportional to a matrix described by a correlation factor ρ

    Consequently, this procedure provides linearized esti- mates for y1 and Σ: y1 = y0 +A0ST (SA0ST +B)−1(ym−Sy0), (53) Σ =A0−A0ST (SA0ST +B)−1SA0. (54) We modelA0 to be proportional to a matrix described by a correlation factor ρ. A0 = ssT (1 +ρ(11T− 1)). (55) We take factors ϵ and s to be functions of the measure- ments’ energies and gridpoint energies,ϵi =...

    work page

  3. [3]

    M. K. Transtrum, B. B. Machta, and J. P. Sethna, Phys. Rev. Lett. 104, 060201 (2010), arXiv:0909.3884 [cond- mat.stat-mech]

    arXiv 2010

  4. [4]

    M. K. Transtrum and J. P. Sethna, arXiv e-prints , arXiv:1201.5885 (2012), arXiv:1201.5885 [physics.data- an]

    arXiv 2012

  5. [5]

    C. D. Pruitt, A. E. Lovell, C. Hebborn, and F. M. Nunes, arXiv e-prints , arXiv:2403.00753 (2024), arXiv:2403.00753 [nucl-th]. 14

    arXiv 2024

  6. [6]

    Cram´ er,Mathematical methods of statistics , Vol

    H. Cram´ er,Mathematical methods of statistics , Vol. 26 (Princeton university press, 1999)

    1999

  7. [7]

    M. P. Hobson, S. L. Bridle, and O. Lahav, MNRAS 335, 377 (2002), arXiv:astro-ph/0203259 [astro-ph]

    work page Pith review arXiv 2002

  8. [8]

    F. V. Berghen, These de doctorat, Universit´ e Libre de Bruxelles, Belgium (2004)

    work page 2004

Show all 45 references
  1. [9]

    James and M

    F. James and M. Roos, Comput. Phys. Commun. 10, 343 (1975)

    1975

  2. [10]

    MINUIT2 — The C++ Minimization Package in ROOT , CERN, section 2.3.1: parameter transformation using arcsin mapping

  3. [11]

    Otuka, E

    N. Otuka, E. Dupont, V. Semkova, B. Pritychenko, A. I. Blokhin, M. Aikawa, S. Babykina, M. Bossant, G. Chen, S. Dunaeva, R. A. Forrest, T. Fukahori, N. Fu- rutachi, S. Ganesan, Z. Ge, O. O. Gritzay, M. Herman, S. Hlavaˇ c, K. Kat¯ o, B. Lalremruata, Y. O. Lee, A. Mak- inaga, K...

    2014 arXiv

  4. [12]

    H. Leeb, D. Neudecker, and T. Srdinko, Nuclear Data Sheets 109, 2762 (2008)

    2008

  5. [13]

    H. Leeb, S. Gundacker, D. Neudecker, T. Srdinko, and V. Wildpaner, Journal of Korean Physical Society 59, 959 (2011)

    2011

  6. [14]

    Neudecker, P

    D. Neudecker, P. Talou, T. Kawano, and F. Tovesson, Nuclear Data Sheets 118, 353 (2014)

    2014

  7. [15]

    Neudecker, R

    D. Neudecker, R. Capote, and H. Leeb, Nuclear Instru- ments and Methods in Physics Research A 723, 163 (2013)

    2013

  8. [16]

    Neudecker, B

    D. Neudecker, B. Hejnal, F. Tovesson, M. C. White, D. L. Smith, D. Vaughan, and R. Capote, EPJ Nuclear Sci- ences & Technologies 4, 21 (2018)

    2018

  9. [17]

    Neudecker, A

    D. Neudecker, A. M. Lewis, E. F. Matthews, J. Vanhoy, R. C. Haight, D. L. Smith, P. Talou, S. Croft, A. D. Carl- son, B. Pierson, A. Wallner, A. Al-Adili, L. Bernstein, R. Capote, M. Devlin, M. Drosg, D. L. Duke, S. Finch, M. W. Herman, K. J. Kelly, A. Koning, A. E. Lovell, P....

    2023

  10. [18]

    Herman, R

    M. Herman, R. Capote, M. Sin, A. Trkov, B. Carl- son, P. Obloˇ zinsk´ y, C. Mattoon, H. Wienke, S. Hoblit, Y. Cho, G. Nobre, V. Plujko, and V. Zerkin, Indc(nds)- 0603, International Atomic Energy Agency (2013)

    2013

  11. [19]

    A. J. Koning and D. Rochman, Nuclear Data Sheets 113, 2841 (2012)

    2012

  12. [20]

    Iwamoto, Journal of Nuclear Science and Technology 44, 687 (2007)

    O. Iwamoto, Journal of Nuclear Science and Technology 44, 687 (2007)

    2007

  13. [21]

    Kawano, P

    T. Kawano, P. Talou, M. B. Chadwick, and T. Watan- abe, Journal of Nuclear Science and Technology 47, 462 (2010)

    2010

  14. [22]

    Kawano, arXiv e-prints , arXiv:1901.05641 (2019), arXiv:1901.05641 [nucl-th]

    T. Kawano, arXiv e-prints , arXiv:1901.05641 (2019), arXiv:1901.05641 [nucl-th]

    2019 arXiv

  15. [23]

    A. J. Koning and J. P. Delaroche, Nuclear Physics A713, 231 (2003)

    2003

  16. [24]

    F. D. Becchetti and G. W. Greenlees, Phys. Rev. 182, 1190 (1969)

    1969

  17. [25]

    Varner, W

    R. Varner, W. Thompson, T. McAbee, E. Ludwig, and T. Clegg, Physics Reports 201, 57 (1991)

    1991

  18. [26]

    Feller, An Introduction to Probability Theory and Its Applications

    W. Feller, An Introduction to Probability Theory and Its Applications. Volume I, 3rd ed. (Wiley, New York, 1968)

    1968

  19. [27]

    Lahav, S

    O. Lahav, S. L. Bridle, M. P. Hobson, A. N. Lasenby, and L. Sodr´ e, MNRAS 315, L45 (2000), arXiv:astro- ph/9912105 [astro-ph]

    2000

  20. [28]

    C. E. Shannon, The Bell System Technical Journal 27, 379 (1948)

    1948

  21. [29]

    E. T. Jaynes, Phys. Rev. 106, 620 (1957)

    1957

  22. [30]

    Qian, Neural Networks 12, 145 (1999)

    N. Qian, Neural Networks 12, 145 (1999)

    1999

  23. [31]

    Neal, in Handbook of Markov Chain Monte Carlo (2011) pp

    R. Neal, in Handbook of Markov Chain Monte Carlo (2011) pp. 113–162

    2011

  24. [32]

    Feng and Y

    Y. Feng and Y. Tu, Proceedings of the National Academy of Science 118, e2015617118 (2021)

    2021

  25. [33]

    Loshchilov and F

    I. Loshchilov and F. Hutter, arXiv e-prints , arXiv:1711.05101 (2017), arXiv:1711.05101 [cs.LG]

    2017 arXiv

  26. [34]

    Schnabel, arXiv e-prints , arXiv:1803.00960 (2018), arXiv:1803.00960 [nucl-th]

    G. Schnabel, arXiv e-prints , arXiv:1803.00960 (2018), arXiv:1803.00960 [nucl-th]

    2018 arXiv

  27. [35]

    Wisshak, K

    K. Wisshak, K. Guber, F. Voss, F. K¨ appeler, and G. Reffo, Phys. Rev. C 48, 1401 (1993)

    1993

  28. [36]

    R. E. Shamu, E. M. Bernstein, J. J. Ramirez, and C. La- grange, Phys. Rev. C 22, 1857 (1980)

    1980

  29. [37]

    A. N. Dyumin, A. I. Egorov, G. N. Popova, and V. A. Smolin, Bulletin of the Russian Academy of Sciences: Physics 37, 91 (1973)

    1973

  30. [38]

    R. R. Winters, F. Kaeppeler, K. Wisshak, A. Mengoni, and G. Reffo, ApJ 300, 41 (1986)

    1986

  31. [39]

    DUAMET, M

    B. DUAMET, M. IGASHIRA, M. MIZU- MACHI, S. MIZUNO, J. ichi HORI, K. MA- SUDA, and T. OHSAKI, Journal of Nu- clear Science and Technology 36, 865 (1999), https://doi.org/10.1080/18811248.1999.9726277

    1999

  32. [40]

    R. L. Macklin, J. H. Gibbons, and T. Inada, Nature 197, 369 (1963)

    1963

  33. [41]

    R. L. Macklin and J. H. Gibbons, ApJ 149, 577 (1967)

    1967

  34. [42]

    Z. BAO, H. BEER, F. K ¨APPELER, F. VOSS, K. WIS- SHAK, and T. RAUSCHER, Atomic Data and Nuclear Data Tables 76, 70 (2000)

    2000

  35. [43]

    S. F. Mughabghab, Atlas of Neutron Resonances (Else- vier Science, 2006) reference code: C,NEUT.RES

    2006

  36. [44]

    V. V. Zerkin and B. Pritychenko, Nuclear Instruments and Methods in Physics Research A 888, 31 (2018), arXiv:1802.05714 [physics.comp-ph]

    2018 arXiv

  37. [45]

    Imbriˇ sak, in prep

    M. Imbriˇ sak, in prep

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.