2010.07071
Exact neural mass model for synaptic-based working memory
Halgurd Taher, Alessandro Torcini, Simona Olmi
correctmedium confidence
- Category
- math.DS
- Journal tier
- Strong Field
- Processed
- Sep 28, 2025, 12:55 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper derives Tb from the QIF neural-mass voltage ODE under quasi-constant inputs, simplifies C using r̄(e)=√(H(e)+IB)/π with r̄(i)≈r̄(e), and neglects the −(πτem r̄(e))^2 term to obtain Tb≈τemπ/√C, then combines this with Tc≈τd ln[(τf/τd)/(1−U0)] to estimate Nmax_c≈(τd/τem) ln[(τf/τd)/(1−U0)] √C/π (Eqs. (24)–(27)). The candidate reproduces exactly this line of argument and adds a small, correct error bound for the arctan approximation and an explicit timescale-separation justification. The steps and approximations match the paper’s derivation and assumptions, including the splay-state identity Tb=Tc/NI (paper: Tb=Tc/NI), hence both are correct and essentially the same proof .
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} strong field
\textbf{Justification:}
The derivation of Tb and Nmax\_c is consistent with the neural-mass framework and parameter regime explored. The approximations—quasi-constant couplings and rates on Tb, neglect of the quadratic rate term, similar E/I rates in the low-activity background, and large-threshold limits—are standard and justified by the model’s timescale separation and operating point. Explicitly stating C>0, quantifying the arctan approximation error, and reminding the reader which burst components are neglected in Tb would enhance rigor and clarity without altering the result.