{"id":"0277a62b-1f99-4358-8a64-232797da6255","arxiv_id":"2506.01997","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"NELM is an open-source impedance-spectra fitting package that combines CNLS, Monte Carlo multistart, adaptive filtering, and user-extensible equivalent-circuit models.","lead":"NELM is an open-source MatLab/GNU Octave package that fits electrical impedance spectra to equivalent circuit models, adding Monte Carlo stabilization, adaptive filtering for noisy data, and symbolic model generation. A generalist might read this to see how flexible open-source tooling is improving impedance analysis for biosensing, semiconductors, and electrochemistry.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Parameter identifiability in the RL-CPE model with delay exponent (Eq. 4) is the key unverified assumption; τ may trade off against α and L.","rationale":"The paper is a software manual with genuine validation efforts: the RLC circuit recovers factory ratings, the Lapicque test uses known component values, and the AF noise-immunity experiment has a clear ground truth. These are real supportive evidence. However, the universal use of Eq. (4) with a free delay exponent is the softest point. The delay factor e^(iωτ) can act as a phase-adjustment fudge factor, and without parameter uncertainties, correlation analysis, or a τ=0 baseline, the physical interpretation of the fitted elements (especially capacitance from W and α, and the cell-induced resistance change) is not uniquely grounded. The reader's weakest assumption (circuit adequacy) is related but not identical; my concern is more specific: even if the circuit is adequate, the parameters may not be identifiable. The reader's CONDITIONAL verdict remains appropriate, as the concern does not overturn the positive known-value benchmarks but adds a concrete condition for acceptance: demonstrate parameter identifiability or report full covariance information. I found no internal mathematical inconsistency that changes the verdict; the possible typographical issue in Eq. (2) is not central to the software's claims. Thus the verdict should remain CONDITIONAL, with the additional condition made explicit.","tokens_in":20587,"tokens_out":6517,"duration_ms":64304,"concrete_test":"Refit the photodiode spectra with τ fixed to zero (and optionally L fixed to zero) and compare the extracted C–V curve and barrier potential with the reported 0.7 V. Also compute the Jacobian-based parameter covariance at the optimum and report the correlation coefficients between τ and α, and between τ and L. If the barrier potential shifts by more than ~10% when τ is fixed, or if |corr(τ,α)| > 0.9, then the parameters of Eq. (4) are not independently identifiable, and the claim that NELM recovers reliable physical parameters requires an explicit identifiability analysis or constrained fitting.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that NELM reliably recovers physical equivalent-circuit parameters in real systems. All non-AF validation examples use the same model Z = (R + iωL + 1/(W(iω)^α)) × e^(iωτ) (Eq. 4), with τ a free 'delay exponent' attributed to ADC/cable time offsets. Because e^(iωτ) rotates the impedance phase linearly in frequency, it can partially mimic the CPE exponent α (which changes phase slope) and the inductance L (which rotates the high-frequency impedance). The paper never reports parameter uncertainties, correlations, or a comparison fit with τ fixed at zero. For the photodiode, only the derived barrier potential (0.7 V) is checked against the datasheet, not the individual parameters R, L, W, α, τ. If τ and α are strongly correlated over the measured band (10 Hz–40 kHz), the fitted capacitance C = W (α≈1) could be biased yet still produce a plausible C–V curve. The HeLa cell experiment is similarly affected: the resistance change attributed to cell blocking could be partially absorbed by adjustments in τ or α. Thus the load-bearing premise—that Eq. (4) yields physically meaningful, uniquely determined parameters—is not established by the presented evidence.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper introduces NELM, a free, open-source MatLab/GNU Octave package for complex nonlinear least-squares (CNLS) analysis of impedance spectra. It describes the package architecture, data-loading and model interfaces, built-in equivalent-circuit models, multiple minimization solvers, Monte-Carlo multistart stabilization, confidence-interval estimation, symbolic model construction via Make_Model, and an adaptive-filtering (AF) noise-reduction routine. Validation is demonstrated on factory-rated RLC circuits, a BPW 20 RF silicon photodiode (yielding a barrier potential of 0.7 V), HeLa cell detachment monitored on a multielectrode array, and a Lapicque-circuit noise-immunity test comparing AF with FFT. The central claim is that NELM provides a modern, flexible, open alternative to EC-Lab, ZView, and LEVM that reliably recovers physical equivalent-circuit parameters from experimental impedance spectra.","tokens_in":20954,"tokens_out":5618,"duration_ms":55899,"significance":"If the parameter-recovery claim holds, NELM is a valuable open-source contribution: it supports bridge circuits, arbitrary user-defined equivalent circuits, symbolic Jacobian generation, parallel Monte-Carlo initialization, and AF noise reduction, and it is demonstrated on four distinct application classes against external reference values (factory-rated components, a manufacturer's C-V plot, and nominal Lapicque element ratings). The GitHub distribution and example data support reproducibility, and the software addresses genuine limitations of existing packages. However, the validation is at proof-of-concept level, and the central identifiability question for the delay-exponent model used in most demonstrations is not addressed; the quantitative reliability claims therefore need additional support before they can be accepted.","major_comments":[{"comment":"The silicon-photodiode validation checks only the derived barrier potential (0.7 V) and the observation that the CPE exponent is close to unity; the individual fitted parameters R, L, W, alpha, tau and their uncertainties are not reported. Because e^{i omega tau} rotates the impedance phase linearly in frequency, tau can trade off against both alpha (which changes phase slope) and L (which rotates the high-frequency impedance) over the 10 Hz to 40 kHz band. A biased W with a compensating tau could still produce a plausible linear C-V curve. Please report the fitted parameters with confidence intervals and correlations, and include a comparison with tau fixed at zero; without this, the claim that NELM recovers the physical junction capacitance is not established.","section":"Sec. 6.1, Eq. (4)"},{"comment":"The HeLa cell conclusion, that the electrode resistance rises while pseudo-capacitance remains stable during cell detachment, rests on the same RL-CPE-with-delay model of Eq. (4). No confidence intervals, time-resolved parameter trajectories, or alternative fits with tau fixed are shown, so one cannot exclude the possibility that adjustments in tau or alpha absorb part of the cell-induced impedance change. The authors should quantify the stability of the CPE parameters, show the resistance trace with error bars, and demonstrate that the observed response is not an artefact of parameter trade-off before attributing it specifically to cell resistance.","section":"Sec. 6.2"},{"comment":"NELM already includes both Monte-Carlo-based and Jacobian-based confidence-interval machinery, and the AF test in Sec. 6.3 reports 99.9% intervals over 10 experiments. Yet the RLC, photodiode, and HeLa validations report no parameter uncertainties or correlations at all. To substantiate the reliability claim for Eq. (4), at least one of these validation studies should include a full parameter report (best values, MC scatter or Jacobian confidence intervals, and a correlation matrix), ideally accompanied by a synthetic-data recovery test with known parameters. Without this, the absence of uncertainty reporting is a load-bearing gap, not merely a presentation issue.","section":"Secs. 4.2, 6.1, 6.2"}],"minor_comments":[{"comment":"The Hermitian-conjugation symbol is missing in the typeset normal equations: the expression 'J +J' should read J^dagger J and J^dagger F; as printed the equation is not mathematically valid.","section":"Eq. (2)"},{"comment":"The lower panels (c)-(e) are described only as 'Lower panels'; the text should state explicitly which panel shows which element rating to make the figure self-contained.","section":"Sec. 6.3, Fig. 7"},{"comment":"The program name is spelled inconsistently as 'EC-lab' and 'EC-Lab'; please standardize.","section":"Throughout"},{"comment":"The sentence 'we does not use build into MatLab method MultiStart' should read 'we do not use the built-in MatLab MultiStart method'.","section":"Sec. 4.2"},{"comment":"The text refers to 'asimplde_DRT.m' and 's implde_DRT.m' while Table 2 lists 'Simple_DRT.m'; please verify the actual file name in the distribution.","section":"Sec. 5.2, Table 2"},{"comment":"The abstract claims 'artificial intelligence' and the text calls AF 'AI-based adaptive filtering,' but the implemented AF method is a Wiener least-squares filter; this wording overstates the AI content.","section":"Abstract, Sec. 4.3"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is essentially a software manual with proof-of-concept validations; for a journal article the decisive weakness is the lack of identifiability and uncertainty analysis for the delay-exponent model of Eq. (4), which is fixable within the paper's scope. The heavy reliance on the authors' prior work, Refs. [12] and [30], for the AF and Monte-Carlo stabilization methods is not circular because the validation targets are external, but those sections should clearly state that the methods are presented in the cited papers and are reused here. A software DOI for the GitHub release would strengthen the archival value. The paper is within scope for applied physics, though its contribution is primarily methodological and software-oriented."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The one thing to know: this paper is an honest software manual with a real artifact behind it. NELM is a free, open-source MatLab/GNU Octave package for CNLS fitting of impedance spectra, and it actually ships on GitHub. It combines features that existing tools lack: bridge circuits, arbitrary immittance types, symbolic Jacobian generation, Monte Carlo multistart, and adaptive filtering. The validation examples are concrete and mostly external: RLC circuits with factory-rated components, a photodiode whose 0.7 V barrier potential is checked against the datasheet, HeLa cell time series, and an adaptive-filtering noise test against known Lapicque element values. That is reproducible evidence, and it earns real credit.\n\nWhere the paper is soft: all the non-AF validation examples use the same model, Eq. (4), which includes a free delay exponent τ multiplying the whole impedance by e^{iωτ}. This term rotates the phase linearly in frequency, so it can partially mimic both the CPE exponent α and the inductance L. The paper never reports parameter uncertainties, correlations, or a comparison fit with τ fixed at zero. For the photodiode, only the derived 0.7 V barrier potential is checked against the datasheet, not the individual parameters B, L, W, α, τ. If τ and α are correlated over the measured band, the fitted capacitance could be biased while still producing a plausible C-V curve. The HeLa experiment has the same issue: the resistance change attributed to cell blocking could be partly absorbed by adjustments in τ or α. This does not sink the paper; the software clearly fits the data well. But it does mean the physical interpretation of the fitted parameters is less secure than the text suggests.\n\nMinor points: the abstract sells the package as using 'artificial intelligence'; the adaptive filtering method is a standard Wiener filter, not AI. And the repository was not independently inspected, so availability of all raw datasets is unverified. Both are minor.\n\nBottom line: this is a genuinely useful open-source tool for impedance spectroscopy, and the paper is a solid introduction to it. The identifiability gap is addressable: add confidence intervals, correlation matrices, and a τ=0 comparison for the photodiode and cell data. I would send this to a serious referee with EIS fitting expertise and ask for exactly that analysis. The artifact deserves peer review, and a revision that addresses identifiability would strengthen it considerably.","headline":"Open-source impedance fitting package with real features and honest validation examples, but the universal RL-CPE+delay model needs identifiability checks before the physics claims carry weight.","tokens_in":21370,"tokens_out":2633,"would_cite":true,"duration_ms":23999,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"NELM is a free, open-source MatLab/GNU Octave package for CNLS fitting of impedance spectra to arbitrary equivalent circuits, with Monte Carlo multistart stabilization and adaptive filtering, validated on RLC circuits, a silicon…","keywords":["impedance spectroscopy","CNLS","equivalent circuits","constant phase element","adaptive filtering","Monte Carlo multistart","biosensing","open-source software"],"falsifier":"Generate a synthetic impedance spectrum from a known equivalent circuit that contains an element the fitting model omits, such as a second RC time constant, and run NELM's CNLS with Monte Carlo stabilization on it. If the fit produces low residuals but recovered parameters that deviate from the known values, or if the Monte Carlo confidence intervals exclude the true values, then the claim that NELM reliably recovers physical parameters from real spectra would be weakened.","tokens_in":20394,"feed_emoji":"🧪","tokens_out":12496,"duration_ms":120707,"temperature":0.7,"pith_summary":"The paper introduces NELM, a free and open-source MatLab/GNU Octave package for electrical impedance spectroscopy analysis. Its central claim is that NELM can fit measured immittance spectra to essentially arbitrary equivalent circuits by complex nonlinear least squares, with user-chosen solvers, weights, immittance representations, Monte Carlo multistart stabilization, and an adaptive filtering mode for noisy time-domain data. The authors argue this matters because existing impedance analysis software is largely closed-source, dated, or limited to series/parallel circuits, and cannot handle delay exponents or high-resolution noisy spectra. They support the claim with demonstrations on RLC circuits, a silicon photodiode whose 0.7 V barrier potential is recovered, cultured-cell biosensing where cell-induced resistance changes are tracked, and a noise-immunity test at -6 dB signal-to-noise ratio.","feed_headline":"Open-source NELM fits impedance spectra that commercial tools miss","feed_subtitle":"Free MatLab/GNU Octave package: bridge circuits, delay exponents, Monte Carlo stabilization, adaptive filtering.","key_machinery":"The engine is the CNLS working function $$$E^{2}$ = \\frac{1}{L}\\sum_{\\ell=1}^{L} |Y_m(\\omega_\\ell)-$Y^{{ex}}$(\\omega_\\ell)|^2 W(\\omega_\\ell),$$ minimized by a switchable set of solvers, including simplex search, damped Newton-type refinement, coordinate and gradient descent, trust region, and homotopy methods. The workhorse model in most validations is the generalized RL-CPE circuit with delay exponent, $$Z = \\left(R+i\\omega L + \\frac{1}{W(i\\omega)^\\$\\alpha$}\\right)$e^{{i\\omega\\tau}}$,$$ in which $1/(W(i\\omega)^\\alpha)$ is the constant-phase element modelling non-ideal capacitive behaviour and $e^{i\\omega\\tau}$ accounts for the time offset between voltage and current sampling; fixing the CPE exponent at unity reduces it to an RLC circuit, which is how the same model spans resonant circuits, photodiodes, and cell-covered electrodes. The adaptive filtering mode uses a separately implemented optimal linear filter, trained on the measured voltage and current sequences, to produce clean spectra before CNLS fitting. Making the model an anonymous function and generating Jacobians symbolically is what lets users define bridge circuits and custom models without touching the core solver.","core_discovery":"The paper's central claim is that NELM supplies a complete and flexible CNLS fitting pipeline: the user selects the immittance type, the weighting, the minimization solver, and the equivalent circuit, either from built-in models, by fixing parameters in the style of the classic CNLS construction method, or by generating a new model symbolically with automatic Jacobian computation. Around this core, NELM layers a Monte Carlo multistart that seeds parallel fits from the previous spectrum, a warming-up mode for the first spectrum, confidence intervals from both Monte Carlo statistics and linearized error analysis, and an adaptive filtering method that estimates spectra from noisy time-domain recordings. The validation results reported are that NELM recovers the ratings of RLC circuits, identifies the photodiode pn-junction as near-ideal and abrupt with a 0.7 V diffusion barrier matching the datasheet, detects a single cultured cell floating over a microelectrode as a synchronous rise and fall in fitted resistance while pseudo-capacitance stays stable, and, in the adaptive filtering test, recovers the parameters of a cell-like R-CPE circuit at -6 dB SNR where the FFT-based approach fails. The paper's position is that these demonstrations establish NELM as a general-purpose tool for semiconductor, electrochemical, and biosensing applications.","pith_inferences":["If NELM is adopted, impedance analyses become more reproducible: the settings files, model definitions, and fixed parameters together form an explicit record of the analysis, which the paper does not highlight as a sharing feature.","The warm-start plus Monte Carlo multistart recipe is a general remedy for drift-prone time-series fitting and could transfer to other spectroscopies that suffer the same local-minimum and noise problems.","The adaptive-filtering result implies that visual fit quality is not a reliable success criterion: spectra can look well approximated while parameter estimates are wrong, so future EIS studies should report parameter uncertainties and the noise-handling method used.","The symbolic model generator suggests a broader reach than electrochemistry: any system whose response can be written as an immittance-like transfer function could in principle be fitted with the same core, making NELM a general immittance-fitting platform rather than an EIS-only tool."],"forward_implications":["Users of impedance spectroscopy gain a free alternative to closed packages for fitting arbitrary equivalent circuits, including bridge topologies and delay-exponent terms that series/parallel-only tools cannot represent.","Batch time-series data, such as long cell-culture or corrosion experiments, can be fitted with warm starts from the previous spectrum and Monte Carlo multistart, reducing the impact of local minima on long runs.","The adaptive filtering mode makes CNLS fitting practical on spectra recorded at negative signal-to-noise ratios, which matters for implantable and wearable bioimpedance sensors.","Because models and solvers are user-extensible and the code is open, the package can be adapted to new equivalent circuits or new minimization protocols by modifying settings files rather than rewriting the analysis core."],"supporting_citations":[{"why":"supplies the bioimpedance measurement setup and ECIS context used for the cell validation.","marker":"[1]"},{"why":"supplies the adaptive-filtering impedance spectroscopy theory and the earlier version of NELM that this work extends.","marker":"[12]"},{"why":"defines the complex nonlinear least squares method that the whole package is built around.","marker":"[22]"},{"why":"documents the classic CNLS program whose limitations NELM is designed to overcome.","marker":"[26]"},{"why":"documents a commercial package that lacks bridge-circuit and delay-exponent support, establishing the baseline NELM improves on.","marker":"[27]"},{"why":"documents another commercial package with limited batch processing and spectral resolution, used as a comparison baseline.","marker":"[29]"},{"why":"provides the proof of concept for Monte Carlo randomization that NELM turns into batch stabilization.","marker":"[30]"},{"why":"supplies the multistart global optimization concept behind the Monte Carlo searches.","marker":"[56]"},{"why":"supplies the optimal linear filter equations used to train the adaptive filter.","marker":"[82]"}],"fun_headline_variants":["NELM: open-source impedance fitting with Monte Carlo and adaptive filtering","Impedance analysis gets a free, modern tool: NELM for MatLab/Octave","NELM: free tool fits noisy impedance data with adaptive filtering","NELM: open-source MatLab/Octave package for CNLS impedance fitting"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the simple model circuits chosen for the test systems actually represent the physics of those systems, so the fitted values, such as the 0.7 V photodiode barrier or the cell-induced resistance change, are real properties and not artifacts absorbed by the model.","fun_headline_variants_meta":{"raw":{"variants":["NELM: open-source impedance fitting with Monte Carlo and adaptive filtering","Impedance analysis gets a free, modern tool: NELM for MatLab/Octave","NELM: free tool fits noisy impedance data with adaptive filtering","NELM: open-source MatLab/Octave package for CNLS impedance fitting"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001403,"raw_usage":{"total_tokens":5735,"prompt_tokens":1072,"completion_tokens":4663,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":688,"completion_tokens_details":{"reasoning_tokens":4576}},"tokens_in":688,"tokens_out":4663,"duration_ms":34388,"temperature":1.0,"reasoning_tokens":4576,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T20:17:50.470928+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Generate a synthetic impedance spectrum from a known equivalent circuit that contains an element the fitting model omits, such as a second RC time constant, and run NELM's CNLS with Monte Carlo stabilization on it. If the fit produces low residuals but recovered parameters that deviate from the known values, or if the Monte Carlo confidence intervals exclude the true values, then the claim that NELM reliably recovers physical parameters from real spectra would be weakened.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"supplies the adaptive-filtering impedance spectroscopy theory and the earlier version of NELM that this work extends."},{"cited_title":"Macdonald, CNLS (complex nonlinear least squares): Immittance, inversion, and simulation fitting programs–LEVM manual","cited_arxiv_id":null,"evidence_quote":"defines the complex nonlinear least squares method that the whole package is built around."},{"cited_title":"URLhttps://jrossmacdonald.com/jrm/wp-content/uploads/LEVMMANUAL.pdf","cited_arxiv_id":null,"evidence_quote":"documents the classic CNLS program whose limitations NELM is designed to overcome."},{"cited_title":"URLhttps://mmrc.caltech.edu/BioLogic%20Echem/ECLab%20Manuals/EC-Lab%20software%20user%27s%20manual.pdf","cited_arxiv_id":null,"evidence_quote":"documents a commercial package that lacks bridge-circuit and delay-exponent support, establishing the baseline NELM improves on."},{"cited_title":", ZView 4.0 Operating ManualImpedance/Gain-Phase Graphing & Analysis Software (Rev","cited_arxiv_id":null,"evidence_quote":"documents another commercial package with limited batch processing and spectral resolution, used as a comparison baseline."},{"cited_title":"Petersburg State Polytechnical University Jour- nal","cited_arxiv_id":null,"evidence_quote":"provides the proof of concept for Monte Carlo randomization that NELM turns into batch stabilization."},{"cited_title":"Hiriart-Urruty (auth.), Reiner Horst, Panos M","cited_arxiv_id":null,"evidence_quote":"supplies the multistart global optimization concept behind the Monte Carlo searches."},{"cited_title":"Widrow, P","cited_arxiv_id":null,"evidence_quote":"supplies the optimal linear filter equations used to train the adaptive filter."}],"review_version":1}