First proofs and response.HEADmaster

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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.