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1. Logarithmic notation is appropriate and shouldn't be modified.
2. Unbolding all bold greek characters was wrong. Here is the exhaustive list of mistakes you have introduced to the manuscript:
In equation (23) ω must be bold in its first appearance but not its second.
On line 273 ω must be bold.
In equation (24) ω must be bold in its first two appearances but not its third.
In equation (25) ω must be bold in its first two appearances but not its third.
On line 285 ω must be bold.
On line 287 ω must be bold.
In equation (26) all appearances of ω must be bold.
In equation (27) all appearances of ω must be bold.
In equation (28) all appearances of ω must be bold.
In equation (31) all appearances of ω must be bold.
In equation (34) all appearances of ω must be bold.
In equation (36) all appearances of ω must be bold.
In equation (37) all appearances of ω and η must be bold.
On line 356 all appearances of η must be bold.
In equation (40) all appearances of φ and η must be bold.
In equation (41) all appearances of φ and ω must be bold.
In equation (43) all appearances of φ and η must be bold.
In equation (44) ω must be bold in its first appearance only.
On line 409 φ must be bold.
In equation (48) all appearances of η must be bold.
In equation (49) all appearances of η must be bold.
In equation (61) ω must be bold in its first appearance only.
In equation (62) ω must be bold in its first appearance only.
In equation (76) all appearances of φ must be bold.
In equation (77) all appearances of φ must be bold.
In equation (78) all appearances of φ must be bold.
In equation (79) all appearances of φ must be bold.
In equation (80) all appearances of φ must be bold.
On line 768 all appearances of φ must be bold.
On line 769 φ must be bold.
In equation (A3) all appearances of φ and η must be bold.
On line 937 all appearances of η must be bold
On line 938 φ must be bold.
On line 940 φ must be bold.
In equation (A4) all appearances of φ and η must be bold.
In equation (A5) all appearances of φ and η must be bold.
In equation (A6) all appearances of φ and η must be bold.
On line 950 φ must be bold.
On line 951 all appearances of η must be bold.
In equation (A7) all appearances of φ must be bold.
On line 961 φ must be bold.
In equation (A8) all appearances of φ must be bold.
In equation (A10) all appearances of φ must be bold.
In equation (B1) ω must be bold.
On line 1010 all appearances of η must be bold.
In equation (B2) all appearances of η and ε must be bold.
On line 1012 all appearances of ε and η must be bold.
On line 1013 all appearances of ε and η must be bold.
On line 1015 ε must be bold.
In equation (B3) all appearances of ε and η must be bold.
In equation (B4) all appearances of η must be bold.
In equation (B5) all appearances of η must be bold.
In equation (B6) all appearances of η must be bold.
In equation (C1) ω must be bold in its first appearance only.
In equation (D1) all appearances of φ and η must be bold.
In equation (D2) all appearances of φ must be bold.
On line 1044 φ must be bold.
In equation (D3) all appearances of φ must be bold.
In equation (D4) all appearances of φ must be bold.
In equation (D5) all appearances of φ must be bold.
In equation (D6) all appearances of φ must be bold.
On line 1049 all appearances of φ must be bold.
In equation (D7) φ must be bold.
3. The definition is correct.
4. The use of the "multiplication sign" is correct and shouldn't be modified.
5. Ok.
6. The definition is correct.
7. For Ref [1], World Scientific lists the following cities: New Jersey; London; Singapore; Beijing; Shanghai; Hong Kong; Taipei; Chennai; Tokyo.
For Ref [9], North-Holland Publishing Company lists the following cities: Amsterdam; New York; Oxford.
For Ref [15], Elsevier lists the following cities: Amsterdam; Oxford; New York; Tokyo.
For Ref [54], IEEE list the following cities: Los Alamitos, California; Washington; Tokyo.
For Ref [57], Clarendon Press lists Oxford.
For Ref [58], Springer International Publishing lists Cham, Switzerland.
8. None of the cited eprints have since been published.
9. Ref [23] should be cited in the block of citations on line 131.
FQ. The information is correct.
Q. Ref [16] has DOI 10.1063/10.0034343
Ref [28] can be found at https://projecteuclid.org/journals/bulletin-of-the-american-mathematical-society-new-series/volume-49/issue-4/On-the-average-number-of-real-roots-of-a-random/bams/1183505112.full
Other corrections:
Changes of the text at line 70 affect its scientific meaning. A more appropriate text reads "is independent of the energy and the gradient."
In equation (39), Tr Hess H(x) should instead read Tr Hess H(x, ω) with a bold ω.
In equation (60), L(x) should instead read L(x, ω) with a bold ω.
In equation (D1), '\bar{θ}₁ θ₁ \hat{x}_a' should instead read 'i \hat{x}_a \bar{θ}₁ θ₁', similar to equation (40).
On line 1051, 'RSBorder' should be replaced by 'RSB order'.
References [21], [27], [39], [40], [50], and [51] have an empty set of parentheses that should be removed.
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