ERRATUM

The online version of the original book can be found at http://dx.doi.org/10.1007/978-3-319-01321-3

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Realtime Data Mining

Self-Learning Techniques for Recommendation Engines

Corrections

Explanation

The errors are marked in the following form:

• P<page> (L<line> or reference): error → correction ([Author’s error])

FormalPara Remarks:

• 1. Line: line contains the line number, negative numbers are counted from the button of the page; the line number may slightly differ based on the counting method but are clear from the context

• 2. Error and correction are mostly in quotation marks, except for formulas

• 3. Sometimes after error → correction, “i.e.” followed by a description is included to make the error correction easier

• 4. [Author’s error] indicates errors in the original manuscript oft the authors

Summary of Notation

• Pxxii L14: ${s}^{\prime}\in S\overline{a}\to {s}^{\prime}\in {S}_{\overline{a}},$ i.e. lower subscript

Chapter 1

Chapter 2

Chapter 3

• P15 L3 of Abstract: “value factions” → “value functions”

• P26 L-7: add dot at the end of sentence

• P26 L-5: add dot at the end of sentence

• P32 L-10: “A node is” → “A node w is” [Author’s error]

• P33 L19: “p ₅₅ = 0, 5 > 0” → “p ₅₅ = 0.5 > 0” [in part Author’s error]

• P36 Proposition 3.1: shall be written cursive like other Propositions

• P36 L-5: “question of Sect. 3.4” → “question of Sect. 3.6” [Author’s error]

• P37 Algorithm 3.1: indent code block of lines 5.-7.

• P38 Algorithm 3.2: line 12: insert space before “arbitrarily”

• P38 Algorithm 3.3: line 1: insert space before “arbitrarily”

• P39, Theorem 3.2: in assumption 3 add dot after λ ∈ [0,1]

Chapter 4

• P43 L6: “(Fig. 4.2):” → “(Fig. 4.2).”

• P46 L-12: ${\overline{p}}_1={p}_1={p}_1\left(1-{p}_2\right)+{p}_1{p}_2\to {\overline{p}}_1={p}_1\left(1-{p}_2\right)+{p}_1{p}_2$ [Author’s error]

• P48 Equation (4.4): add dot after the equation

• P54 L5: “(Sect. 12.3.1)” → “(Sect. 12.3)” (already reported before)

• P54 L17: “386 AC17893” → “386AC17893”, i.e. remove space before “A”

Chapter 5

• P58 L7: “Approach 1” → “Approach I” [Author’s error]

• P66 L7: add dot at the end of sentence, i.e. after “same q ⁰ action value”.

• P67 Equation (5.9):

  $$\begin{array}{llllllll}{q}^{\pi}\left(s,a\right)={p}_{s{s}_a}^a\left[{p}_{s{s}_a}^a+\gamma {\displaystyle \sum_{a^{\prime }}\pi \left({s}_a,{a}^{\prime}\right){q}^{\pi}\left({s}_a,{a}^{\prime}\right)}\right]\cr\qquad \qquad+c\left(s,a\right){\displaystyle \sum_{s^{\prime}\ne {s}_a}{p}_{s{s}^{\prime}}^a}\left[{r}_{s{s}^{\prime}}^a+\gamma {\displaystyle \sum_{a^{\prime }}\pi \left({s}^{\prime },{a}^{\prime}\right){q}^{\pi}\left({s}^{\prime },{a}^{\prime}\right)}\right]\cr {}\to \cr {}{q}^{\pi}\left(s,a\right)={p}_{s{s}_a}^a\left[{r}_{s{s}_a}^a+\gamma {\displaystyle \sum_{a^{\prime }}\pi \left({s}_a,{a}^{\prime}\right){q}^{\pi}\left({s}_a,{a}^{\prime}\right)}\right]\cr\qquad\qquad+c\left(s,a\right){\displaystyle \sum_{s^{\prime}\ne {s}_a}{p}_{s{s}^{\prime}}^a}\left[{r}_{s{s}^{\prime}}^a+\gamma {\displaystyle \sum_{a^{\prime }}\pi \left({s}^{\prime },{a}^{\prime}\right){q}^{\pi}\left({s}^{\prime },{a}^{\prime}\right)}\right] \end{array}$$

  i.e. replace ${p}_{s{s}_a}^a$ by ${r}_{s{s}_a}^a$ in first term [Author’s error]

• P68 Equation (5.12): replace dot by comma

• P69 Algorithm 5.1: line 2: ${\bf F}^j{p}_{s{s}_a}\to {\bf F}_{j_{p_{s{s}_a}}},\ {\rm i.e.}{\ }^j{\bf p}^a:={\bf F}_{j_{p_{s{s}_a}}}\left({}^j{\bf p}^{\left[a\right]}\right)$

• P69 Algorithm 5.1: line 4: ${\bf F}^j{p}_{s{s}_a}-1\to {\bf F}_{j_{p_{s{s}_a}}}^{-1} \ {\rm an{d}} \ {\ ^{j+1}}{\bf p}\to {\;}^{j+1}{\bf p}^a,\ {\rm i.e.}{\ }^{j+1}{\bf p}^{\left[a\right]}:={\bf F}_{j_{p_{s{s}_a}}}^{-1}\left({}^{j+1}{\bf p}^a\right)$

• P72 L9: c(s, a) → c(s,a), i.e. remove space before a

• P73 L-2: “probability of the issued” → “probabilities of the issued” [Author’s error]

• P75 Algorithm 5.4: remove indent in line 8, i.e. ${}^{j+1}{\displaystyle {\prod}_{\overline{a}}:{=\ }^j}{\displaystyle {\prod}_{\overline{a}}}$ starts at same position as lines 7 and 9

• P76 L16: “Comparison of Linear and Nonlinear Approaches” shall be treated as a headline, i.e. add blank lines before and after

• P80 L2: add dot after “furniture shop”

• P80 L2: “off-line”→“offline”

• P85 L14: “but the complete ${p}_{s{s}^{\prime}}^a$ which”→“but the complete ${p}_{s{s}^{\prime}}^{\overline{a}}$ which”, i.e. replace ${p}_{s{s}^{\prime}}^a$ by ${p}_{s{s}^{\prime}}^{\overline{a}}$ [Author’s error]

• P88 L1-2: ${P}^c:=\left\{{p}_{s{s}^{\prime}}^{a_{s^{\prime }}}\right\}s\in S,s{^{\prime}}\in A(s)\to {P}^c:={\left\{{p}_{s{s}^{\prime}}^{a_{s^{\prime }}}\right\}}_{s\in S,s\rm{^{\prime}}\in A(\it s)},$ i.e. lower subscript

• P88 L-8: m-1 → m-1, i.e. “1” not cursive [Author’s error]

• P90 L8: “probabilities ${p}_{s{s}^{\prime}}^a$ was performed by Algorithm 5.3” → “probabilities ${p}_{s{s}^{\prime}}^{\overline{a}}$ was performed by Algorithm 5.3”, i.e. replace ${p}_{s{s}^{\prime}}^a\; {\rm by}\;{p}_{s{s}^{\prime}}^{\overline{a}}$ [Author’s error]

Chapter 6

• P95 L2: “multi-scales bases localize” → “multi-scale bases localize” [Author’s error]

• P96 L5: “Fedorenko [Fed64] and Bakhvalov [Bakh66]” → “Radii Fedorenko [Fed64] and Nikolai Bakhvalov [Bakh66]”, i.e. add first names [Author’s error]

• P97 Algorithm 6.1: in Output line: “von (6.3)” → “of (6.3)”

• P99 L-5: q(s, a) → q(s,a), i.e. remove space before a

• P100 L20: “real N×N matrix” →“real n×n matrix”

• P100 Equation (6.5): remove dot

• P101 L8: “entry in of a vector” → “entry of a vector” [Author’s error]

• P104 L-5: G _β , β = 1, …, m → G _β , β = 1,… , m, i.e. move space before “… ” behind [Author’s error]

• P107 Algorithm 6.2: line 7: “return”→“return”, i.e. boldface [Author’s error]

• P108 L6: “Proof”→“Proof”, i.e. cursive

• P112 Algorithm 6.3: lines 3–11 should start at same position as lines 2 and 12

• P113 L6: “an spd N × N-matrix”→“an spd N×N-matrix”, i.e. remove spaces around “×”

• P114 L1: “of Example 6.1”→“of Example 6.2” [Author’s error]

• P117 L10: “resolution^N _j=1. ”→“resolution.”, i.e. remove formula part

Chapter 7

• P120 L13: “This may be user-centric” → “These may be user-centric” [Author’s error]

• P124 Equation (7.4): replace first ouccurence of “,” by “−”, i.e. $R\left({f}_N\right)=\frac{1}{M}{\displaystyle \sum_{i=1}^M\Big({f}_N\left({{\bf X}}_i\right)}-{y}_i\Big){}^2+\lambda {\left\Vert P{f}_N\right\Vert}_{L_2}^2$[Author’s error]

• P124 Equation (7.6):

  $$ \begin{array}{llll}{\displaystyle \sum_{j=1}^N{\alpha}_j\left[ M\lambda {\left(P{\varphi}_j,P{\varphi}_k\right)}_{L_2}+{\displaystyle \sum_{i=1}^M{y}_i{\varphi}_j\left({{\bf x}}_i\right)\cdot {\varphi}_k\left({{\bf x}}_i\right)}\right]}={\displaystyle \sum_{i=1}^M{y}_i{\varphi}_{k}\left({{\bf x}}_i\right)}\to\cr {\displaystyle \sum_{j=1}^N{\alpha}_j\left[ M\lambda {\left(P{\varphi}_j,P{\varphi}_k\right)}_{L_2}+{\displaystyle \sum_{i=1}^M{\varphi}_j\left({{\bf x}}_i\right)\cdot {\varphi}_k\left({{\bf x}}_i\right)}\right]}={\displaystyle \sum_{i=1}^M{y}_i{\varphi}_k\left({{\bf x}}_i\right)}\end{array} $$

  remove y _i from term ${\displaystyle \sum_{i=1}^M{y}_i{\varphi}_j\left({{\bf x}}_i\right)\cdot {\varphi}_k\left({{\bf x}}_i\right)}$[Author’s error]

• P125 L10: “where C corresponds to” → “where P corresponds to” [Author’s error]

• P125 L-15: x _i  = [0,1]^d → x _i  ∈ Ω = [0,1]^d [Author’s error]

• P126 L1: in equation “M. ” → “M · ”, i.e. dot not lowered

• P126 L2: in equation “ j ₁ ” → “ j _t ”, i.e. t instead of 1

• P126 L4: j _t  = 0,…,${2}^{l_t}\to {j}_t$ = 0,…,2ⁿ, i.e. replace ${2}^{l_t}$ by 2ⁿ [Author’s error]

• P126 L4: (α _n ) _j  → (α _n ) _j , i.e. bold index “j”

• P126 L6: in equation V _n  := span{ϕ _n,j , j _t  = 0, …, 2^d, t = 1, …, d}: “2^d” → “2ⁿ” [Author’s error]

• P127 L4: ${h}_1:=\left({j}_{l_1},\ldots, {j}_{l_d}\right):=\left({2}^{-{l}_1},\ldots, {2}^{-{l}_d}\right)\to {h}_1:=\left({h}_{l_1},\ldots, {h}_{l_d}\right):=\left({2}^{-{l}_1},\ldots, {2}^{-{l}_d}\right)$, i.e. replace ${j}_{l_1},\ldots, {j}_{l_d}$ by ${h}_{l_1},\ldots, {h}_{l_d}$ [Author’s error]

• P127 Equation (7.10): ${x}_{l,j}:=\left({x}_{\bf l_1,j},\ldots, {x}_{l_d}\right)\to {x}_{\bf l,j}:=\left({x}_{l_1,{j}_1},\ldots, {x}_{l_d,{j}_d}\right)$ [Author’s error]

• P127 L9: ${h}_{\bf 1}:=\left({h}_{l_1},\ldots, {h}_{l_d}\right):=\left({2}^{-{l}_1},\ldots, {2}^{-{l}_d}\right)\to {x}_{l_t,{j}_t}:={j}_t\cdot {h}_{l_t}={j}_t\cdot {2}^{-{l}_t},{j}_t=0,\ldots, {2}^{l_t}$ [Author’s error]

• P127 L9: V ₁  → V _l , i.e. replace bold “1” by bold “l”

• P127 Equation (7.11): in equation V _l  → V _l , i.e. replace “l” by bold “l” [Author’s error]

• P127 Equation (7.11): in equation ϕ _1,j  → ϕ _l,j , i.e. replace bold “1” by bold “l” (as in “leverage”)

• P127 Equation (7.12): in equation ϕ _1,j  → ϕ _l,j , i.e. replace bold “1” by bold “l”

• P127 L14: ${\phi}_{l_t,{j}_t}\left({x}_i\right)\to {\phi}_{l_t,{j}_t}\left({x}_j\right)$, i.e. replace x _i by x _j

• P127 L-5: ϕ _1,j(x) → ϕ _l,j (x), i.e. replace bold “1” by bold “l”

• P127 Equation (7.15): replace bold “1” by bold “l” in all of three subscripts

• P127 L-2: e ₁  → e _l , i.e. replace bold “1” by bold “l”

• P127 L-1: V ₁  = 0 → V _l  = 0, i.e. replace bold “1” by bold “l”

• P127 L-1: W ₁  → W _l , i.e. replace bold “1” by bold “l”

• P128 L1: V ₁  → V _l , i.e. replace bold “1” by bold “l”

• P128 L1: ${V}_{{\bf 1}-{e}_t}\to {V}_{{\bf l}-{e}_t}$, i.e. replace bold “1” by bold “l”

• P128 Equation (7.16): in equation |1| _∞  → |l| _∞ , i.e. replace “1” by bold “l”

• P128 Equation (7.16): in equation W ₁ → W _l , i.e. replace “1” by bold “l”

• P128 L8: I ₁ → I _l , i.e. replace “1” by bold “l”

• P128 Equation (7.17): in equation I ₁ → I _l , i.e. replace “1” by bold “l”

• P128 Equation (7.18): in equation ϕ _1,j  → ϕ _l,j , i.e. replace bold “1” by bold “l”

• P128 Equation (7.18): in equation I ₁ → I _l , i.e. replace “1” by bold “l”

• P128 Equation (7.19): in equation ϕ _1,j  → ϕ _l,j , i.e. replace bold “1” by bold “l”

• P128 Equation (7.19): in equation I ₁ → I _l , i.e. replace “1” by bold “l”

• P128 L-10: ϕ _1,j (x) → ϕ _l,j (x), i.e. replace bold “1” by bold “l”

• P128 L-10: W ₁  → W _l , i.e. replace bold “1” by bold “l”

• P128 Equation (7.20): replace all bold “1” by bold “l” (9 times)

• P128 L-6: α _1,j  ∈ ℜ → α _l,j  ∈ ℜ, i.e. replace bold “1” by bold “l”

• P128 Equation (7.21): in equation W ₁  → W _l , i.e. replace bold “1” by bold “l”

• P129 Equation (7.22): in equation I ₁ → I _l , i.e. replace “1” by bold “l”

• P129 Equation (7.22): in equation add “ = ”, i.e. ${f}_n^{(s)}({\bf x})=\sum\limits_{\left|{\bf l}\right|{}_1\le n+d-1}\sum\limits_{{\bf j}\in {{\bf I}}_{\bf l}}{\alpha}_{\bf l,j}{\phi}_{\bf l,j}(\bf x)$

• P130 L4: in equation I ₁ → I _l , i.e. replace “1” by bold “l”

• P130 L9: in both equations replace all bold “1” by bold “l” (4 times)

• P130 L10: j ∈ I ₁ → j ∈ I _l , i.e. replace “1” by bold “l”

• P130 L10: before k ∈ I _r: “.” → “,”

• P131 L2: Ω₁ → Ω _l , i.e. replace “1” by bold “l”

• P131 L4: Ω₁ → Ω _l , i.e. replace “1” by bold “l”

• P132 Equation (7.27): f ₁ → f _l , i.e. replace “1” by bold “l”

• P132 L-5: Ω₁ → Ω _l , i.e. replace “1” by bold “l”

• P133 Algorithm 7.1 L10: B ^T_l  → B ^T _l , i.e. replace normal-“l” by bold-“l”

• P134 L-12: α _I  → α _l , i.e., replace bold-"I" (capital-"eye") by bold-“l” (lower-case-“l” as in “leverage”)

• P134 L-3: C ^′_I  → C ^′ _l , i.e., replace bold-"I" (capital-"eye") by bold-“l” (lower-case-“l” as in “leverage”) and remove spacing before subscript

• P135 L12: B ^T₁  → B ^T _l , i.e. replace “1” by bold “l”

• P135 L13: B ^T₁  → B ^T _l , i.e. replace “1” by bold “l”

• P135 L17: h ₁ → h _l , i.e. replace bold-“1” by bold “l”

• P135 L17: B ₁ → B _l , i.e. replace bold-“1” by bold “l”

• P135 L17: ${\overline{h}}_1\to {h}_{\bf l}$, i.e. replace bold-“1” by bold “l”

Chapter 8

• P176 L11 (isolated unnumbered formula): replace first occurrence of lower-case-“x” by capital-“X”, i.e., $a := x^{T}y = (x_{i}^{T}y)_{i\in\{1,\ldots,m\}} \rightarrow a := X^{T}y = (x_{i}^{T}y)_{i\in\{1,\ldots,m\}}$

• P177 L11 (eq. 8.38): mind case differences in the subscript below “min”

  $$\min_{{C}_1,\ldots, {C_k,C},\ldots, {C}_k}{\displaystyle \sum_{l=1}^k{\displaystyle \sum_{i\in {C}_l}{\left|\left|{x}_i-{c}_l\right|\right|}_2^2}}\\ {}\to \\ \min_{{C}_1,\ldots, {C_k,{c}_1},\ldots, {c}_k}{\displaystyle \sum_{l=1}^k{\displaystyle \sum_{i\in {C}_l}{\left|\left|{x}_i-{c}_l\right|\right|}_2^2}}$$

• P177, eq. 8.39:

  $$ \begin{array}{llllll}{\min\limits_{{C\in {\mathbb R}}^{r\times k},B\in {\mathbb R}^{m\times k}}}{\left\Vert X-C{B}^T\right\Vert}_F^2\ s\cdot t\cdot {b}_{ij}\in \left\{0,1\right\},\cr{\displaystyle \sum_{s=1}^k{b}_{is}=1\forall i\in \forall \left\{1,\ldots, m\right\},j\in \left\{1,\ldots, k\right\}.} \cr \to\cr{ {\min\limits_{{C\in {\mathbb R}}^{r\times k},B\in {\mathbb R}^{m\times k}}}{\left\Vert X-C{B}^T\right\Vert}_F^2\ s.t.\ {b}_{ij}\in \left\{0,1\right\},}\cr {\displaystyle \sum_{s=1}^k{b}_{is}=1\forall i\in \forall \left\{1,\ldots, m\right\},j\in \left\{1,\ldots, k\right\}.}\end{array}$$

Chapter 9

• P183, §1 L2, last but one word: thought → though [Author’s error]

• P188, Algorithm 9.1, line with label 4:

  $$ C:=A \times_{\ \ 1}{U}_1 \times_{\ \ 2\cdots} \times_{\ \ d}{U}_d^T\to C:=A\;{\times}_1\;{U}_1^T\;{\times}_{2\cdots }{\times}_d\;{U}_d^t $$

• P191, isolated formula in the first paragraph below section title:

  $$\begin{array}{llll} {\tilde{a}}_{\bf i}= \Big\{ {\begin{array}{lll} {a}_{\bf i}, \quad{\bf i}\le {\bf n}-{e}_d \\ {b}_{{\bf i}^{(d)}}, \ {\bf i}_d={n}_d\ \end{array}} \to {\tilde{a}}_{\bf i}=\Big\{ \begin{array}{lll}{a}_{\bf i}, {\bf i}\le {\bf n}-{\bf e}_d \\ {b}_{{\bf i}^{(d)}}, {\bf i}_d={n}_d \end{array}\end{array}$$

• P199:

  $$ {a}_{i_{1,\ldots }{i}_d}={\displaystyle \sum_{j=1}^t{u_{i_{1,}}^1}_j\cdots {u_{i_{d,}}^d}_j.}\to {a}_{i_{1,\ldots, }{i}_d}={\displaystyle \sum_{j=1}^t{u_{i_{1,}}^1}_j\cdots {u_{i_{d,}}^d}_j.} $$

• P204, isolated, unnumbered formula starting with ${a}_{i_1,\ldots, {i}_d}$: replace all subscripts “i” of “c” with “j”, i.e.

  $$ \eqalign{{a}_{i_1,\ldots, {i}_d}={\displaystyle \sum_{j_1=1}^t\cdots {\displaystyle \sum_{j_d=1}^t{\displaystyle \sum_{s=1}^t{c}_{i_1,\ldots, {i}_k,s}{c}_{i_{k+1},\ldots, {i}_d,s}{u}_{i_1,{j}_i}^1\cdots {u}_{i_d,{j}_d}^d}}}\cr {}\to \cr {}{a}_{i_1,\ldots, {i}_d}={\displaystyle \sum_{j_1=1}^t\cdots {\displaystyle \sum_{j_d=1}^t{\displaystyle \sum_{s=1}^t{c}_{j_1,\ldots, {j}_k,s}{c}_{j_{k+1},\ldots, {j}_d,s}{u}_{i_1,{j}_i}^1\cdots {u}_{i_d,{j}_d}^d}}}} $$

Chapter 10

• P210, isolated unnumbered formula: replace occurrence of “s” by “S”

  $$ \tilde{S}:=\displaystyle {\cup_{ j=1}^{k}}{{s}^{j}}.\to \tilde{S}:={\displaystyle{\bigcup _{j=1}^{k}}}\; {S}^{j}. $$

• P211, unnumbered formula in line 3: replace first occurrence of s′ by s′, i.e.,

  $$\begin{array}{lll}{\tilde{p}}_{s\left(s^{\prime},s^{\prime}\right)}^a:= \Big\{ {\begin{array}{lll} {p}_{{\bf s},s^{\prime}}^a, \quad {\bf s}^{\prime}={\bf s}_{*,}\\ 0, \;\qquad {\rm otherwise,}\end{array}} a\in A.\to \\{\tilde{p}}_{s\left({\bf s}^{\prime},s^{\prime}\right)}^a:= \Big\{ {\begin{array}{lll} {p}_{{\bf s},s^{\prime}}^a, \quad {\bf s}^{\prime}= {\bf s}_{*,} \\ 0, \;\qquad {\rm otherwise,}\end{array}}a\in A.\end{array} $$

• P212, paragraph below eq. 10.4, fist line: replace both occurrences of “s” in the superscript of C by “S”, i..e.,

  $$ C\in {\Re}^{m\times s\times s}\to C\in {\Re}^{m\times S\times S} $$

• P213, isolated unnumbered formula after eq. 10.6, subscript below “min”:

  • replace “C” by “$\bar{C}$”

  • replace all occurrences of “s” by “S”

    $$ { \min }_{{C\in {\Re}^{m\times s\times s}}}{\left\Vert \widehat{P}-U{\otimes}_1\overline{C}\right\Vert}_F\to { \min }_{\overline{C}\in {\Re}^{m\times S\times S}}{\left\Vert \widehat{P}-U{\otimes}_1\overline{C}\right\Vert}_F. $$

• P214, unnumbered isolated formula in the middle of the page:

  • replace $" {\widehat{p}}_{(1)}","{\widehat{p}}_{(2)}","{\widehat{p}}_{(3)}" \ {\rm by}\ "{\widehat{P}}_{(1)}","{\widehat{P}}_{(2)}","{\widehat{P}}_{(3)}"$

• P214: paragraph below unnumbered isolated formula in the middle of the page

  • L1: replace first occurrence of $"{\widehat{p}}_{(i)}" \ {\rm by}\ "{\widehat{P}}_{(i)}"$

  • L2: replace only occurrence of $"{\widehat{p}}_{(2)}" \ {\rm by}\ "{\widehat{P}}_{(2)}"$

• P215, top (first formula):

  • replace occurrence of $"{\widehat{p}}^{(1)}" \ {\rm by}\ "{\widehat{P}}^{(1)}"$

• P216, first unnumbered isolated formula after section title:

  • replace all occurrences of $"\overline{P}" \;{\rm by}\;"\overline{p}"$, i.e.,

    $$ {\overline{P}}_{{\bf s}ss^{\prime}}:=\left(1-{t}^{-1}\right){\overline{P}}_{{\bf s}ss^{\prime}}+{t}^{-1}.\to {\overline{p}}_{{\bf s}ss^{\prime}}:=\left(1-{t}^{-1}\right){\overline{p}}_{{\bf s}ss^{\prime}}+{t}^{-1} $$

• P216, eq. 10.7:

  • replace occurrence of $"{C}^{-1}\;"\; {\rm by}\;"\overline{C}"$, i.e.,

    $$ \eqalign{\overline{C}:=\left(1-{t}^{-1}\right){C}^{-1}+{t}^{-1}\frac{e_{\beta (\bf s)}}{G_{\beta (\bf s)}}\otimes {e}_s\otimes {e}_{s^{\prime }},\cr {}\to \cr {}\overline{C}:=\left(1-{t}^{-1}\right)\overline{C}+{t}^{-1}\frac{e_{\beta (\bf s)}}{\left|{G}_{\beta (\bf s)}\right|}\otimes {e}_s\otimes {e}_{s^{\prime }},} $$

• P216, eq. 10.8:

  • replace all occurrences of “C” by “c”, i.e.,

    $$ {C}_{s{s}^{\prime}\beta (\bf s)}:=\left(1-{t}^{-1}\right){C}_{s{s}^{\prime}\beta (\bf s)}+{t}^{-1}.\to {c}_{s{s}^{\prime}\beta (\bf s)}:=\left(1-{t}^{-1}\right){c}_{s{s}^{\prime}\beta (\bf s)}+{t}^{-1}. $$

• P219, last formula in the proof of Proposition 10.1:

  • replace all occurrences of “U” by “u” and remove spaces before subscripts, i.e.,

    $$ \hfill{U}_{\beta }={U}_{\ \beta_1^{\prime}}^{\prime }+\cdots +{U}_{\ \beta_1^{\prime}}^{\prime }.\to {u}_{\beta }={u}_{\beta_1^{\prime}}^{\prime }+\cdots +{u}_{\beta_1^{\prime}}^{\prime }.$$

• P219, formula before last line:

  • replace first occurrence of “s” by “s” (bold!), i.e.,

    $$ z:=\gamma \lambda z+{e}_{\left(s,s\right) ,}\theta :=\theta +\alpha {\varPhi}^T zd\left(\varPhi \theta \right) ,\to z:=\gamma \lambda z+{e}_{\left({ s},s\right),}\theta :=\theta +\alpha {\varPhi}^T zd\left(\varPhi \theta \right), $$

• P223, formula after “Moreover, we obtain”:

  • replace last occurrence of “β” by “$\tilde{\beta}$”, i.e.,

    $$ {U}^TU={\left(\left|{G}_{\beta}\cap \tilde{G}_{\tilde\beta }\right|{\delta}_{\alpha \beta}\right)}_{\beta, \beta \in \underline{m}}\to {U}^TU={\left(\left|{G}_{\beta}\cap {\tilde{G}}_{\tilde{\beta}}\right|{\delta}_{\alpha \beta}\right)}_{\beta, \tilde{\beta}\in \underline{m}}. $$

• P224, eq. 10.13:

  • Replace occurrences of “s” in the superscript of “ℜ” by “S”, i.e.,

    $$ P\in {\Re}^{\hat{s}\times s\times s\times \overline{A}}\to P\in {\Re}^{\hat{S}\times S\times S\times \overline{A}} $$

• P223, paragraph after eq. 10.13, L2:

  • Replace occurrences of “s” in the superscript of “ℜ” by “S”, i.e.,

    $$ R\in {\Re}^{\hat{s}\times s\times s\times \overline{A}}\to R\in {\Re}^{\hat{S}\times S\times S\times \overline{A}} $$

• P223, paragraph after eq. 10.13, L3:

  • 5th word: replace occurrences of “s” in the superscript of “ℜ” by “S”, i.e.,

    $$ R\in {\Re}^{\hat{s}\times s\times s}\to R\in {\Re}^{\hat{S}\times S\times S\times \overline{A}} $$

  • last-but-one-word: replace occurrences of “s” in the superscript of “ℜ” by “S”, i.e.,

    $$ {\Re}^{\hat{s}\times s\times s}{\to}{\Re^{\hat{S}\times S\times S}} $$

• P223, paragraph after eq. 10.13, L4, last word:

  • replace occurrence of “s” in the superscript of “ℜ” by “S”, i.e.,

    $$ {\Re}^{\hat{s}\times s}\to {\Re}^{\hat{S}\times S} $$