Page 5, right column, line 7: Change
$$ y_{\tau}^{l}=\left[ y_{\tau}^{l^{\prime}}\left({\bf 1}^{l}\right) \quad y_{\tau}^{l^{\prime}} \left( {\bf 2}^{l}\right) \quad \cdots \quad y_{\tau}^{l^{\prime}}\left( {\bf N}^{l}\right)\right]^{\prime} $$
to
$$ y_{\tau}^{l}=\left[y_{\tau}^{l\prime}\left({\bf 1}^{l}\right) \quad y_{\tau}^{l\prime }\left( {\bf 2}^{l}\right) \quad \cdots \quad y_{\tau}^{l\prime }\left( {\bf N}^{l}\right) \right]^{\prime} $$
Page 6, right column, line 32: Change “\(\breve{a}^{\prime}\breve{b}=1\)” to “\(\breve{a}^{\prime}\breve{b}=4\)”.
Page 7, left column, lines 8–10: A clear version of lines 8–10 follows
2. If a
k
b
k
= 0 for some k ∈ {1, … , m}, then
$$ \breve{a}^{\prime}\breve{b}=\prod\limits_{j=1,j\neq k}^{m}\left( 1+a_{j}b_{j}\right) $$
3. If \(\breve{a}^{\prime}\breve{b}\neq 0\), then \(\breve{a}^{\prime}\breve{b }=2^{a^{\prime}b}\).
Page 7, right column, lines 1–2: Change (3) and (4):
$$ \begin{aligned} D({\bf n}(u)) & = \Uplambda \sum_{t=1}^{T}\Uplambda^{T-t}r_{t}({\bf n}) \breve{x}_{t}^{\prime}({\bf n} (u))\\ C({\bf n}(u)) & = \Uplambda \sum_{t=1}^{T}\Uplambda^{T-t}\breve{x}_{t}^{\prime}({\bf n}(u)) \\ \end{aligned} $$
to
$$ \begin{aligned} D({\bf n}(u)) & =\Uplambda \sum_{t=1}^{T}\lambda^{T-t}r_{t}({\bf n}) \breve{x}_{t}^{\prime}({\bf n} (u)) \\ C({\bf n}(u)) & =\Uplambda \sum_{t=1}^{T}\lambda^{T-t}\breve{x}_{t}^{\prime}({\bf n}(u)) \\ \end{aligned} $$
Page 7, right column, lines 11–12: Change Eqs. (5) and (6):
$$ \begin{aligned} D({\bf n}(u)) & \leftarrow \Uplambda D({\bf n}(u)) +\Uplambda r_{t}({\bf n}) \breve{x}_{t}^{\prime}({\bf n}(u)) \\ C({\bf n}(u)) & \leftarrow \Uplambda C({\bf n}(u)) +\Uplambda \breve{x}_{t}^{\prime}({\bf n}(u)) \\ \end{aligned} $$
to
$$ \begin{aligned} D({\bf n}(u)) & \leftarrow \lambda D({\bf n}(u)) +\Uplambda r_{t}({\bf n}) \breve{x}_{t}^{\prime}({\bf n}(u)) \\ C({\bf n}(u)) & \leftarrow \lambda C({\bf n}(u)) +\Uplambda \breve{x}_{t}^{\prime}({\bf n}(u)) \\ \end{aligned} $$
Page 8, left column, lines 10: Change “the successive two-factor multiplication” to “the sequence of successive two-factor multiplications”.
Page 8, left column, lines 15: Change “p
τ(n)” to “y
τ(n) or p
τ(n)”.
Page 8, left column, lines 13 from the bottom: Change “\(\Uplambda =\Uplambda =1\)” to “\(\Uplambda = \lambda = 1\)”.
Page 8, right column, lines 9–10 from the bottom: Change
$$ \begin{aligned} a_{\tau j}({\bf n}(u)) & =\Uplambda \sum_{t\in G_{\tau j}\left( {\bf n}(u) ,+\right) }2^{\dim {\bf n} (u)} \Uplambda^{T-t}\\ c_{\tau}({\bf n}(u)) & =\Uplambda \sum_{t\in G_{\tau}({\bf n}(u)) }2^{\dim {\bf n}(u) }\Uplambda^{T-t} \\ \end{aligned} $$
to
$$ \begin{aligned} a_{\tau j}({\bf n}(u)) & =\Uplambda \sum_{t\in G_{\tau j}\left( {\bf n}(u) ,+\right) } 2^{\dim {\bf n} (u) }\lambda^{T-t} \\ c_{\tau}({\bf n}(u)) & =\Uplambda \sum_{t\in G_{\tau}({\bf n}(u)) }2^{\dim {\bf n}(u) }\lambda^{T-t} \\ \end{aligned} $$
Page 8, right column, line 3 from the bottom: Change
$$ \frac{a_{\tau j}({\bf n})}{c_{\tau}({\bf n})}=\frac{\sum_{u=1}^{U}\sum_{t\in G_{\tau j}({\bf n}(u),+)}\Uplambda^{T-t}}{\sum_{u=1}^{U}\sum_{t\in G_{\tau}({\bf n}(u))}\Uplambda^{T-t}} $$
to
$$ \frac{a_{\tau j}({\bf n})}{c_{\tau}({\bf n})}=\frac{\sum_{u=1}^{U}\sum_{t\in G_{\tau j}({\bf n}(u),+)}\lambda^{T-t}}{\sum_{u=1}^{U}\sum_{t\in G_{\tau}({\bf n}(u))}\lambda^{T-t}}$$
Page 9, left column, line 15: Change “C(n)” to “I
C(n)”.
Page 12, left column, line 12: Change
$$ a_{\tau}({\bf n}) :=\frac{1}{2} (c_{\tau}({\bf n}) +d_{\tau}({\bf n})) $$
to
$$ a_{\tau}({\bf n}) :=\frac{1}{2} ({\bf I}c_{\tau}({\bf n}) + d_{\tau}({\bf n}) ) $$
Page 12, left column, line 19: Change “c
τ(n(u))” to “I
c
τ(n(u))”.
Page 12, left column, line 20: Change “c
τ(n)” to “I
c
τ(n)”.
Page 12, left column, line 26: Change
$$ \left[ d_{\tau 1}({\bf n})/c_{\tau 1}({\bf n}) \quad d_{\tau 2}({\bf n}) /c_{\tau 2}({\bf n}) \quad \cdots \quad d_{\tau R}({\bf n}) /c_{\tau R}({\bf n}) \right]^{\prime} $$
to
$$ \left[ d_{\tau 1}({\bf n}) /c_{\tau}({\bf n}) \quad d_{\tau 2}({\bf n}) /c_{\tau}({\bf n}) \quad \cdots \quad d_{\tau R}({\bf n}) /c_{\tau}({\bf n}) \right]^{\prime} $$
Page 15, right column, line 16: Change “\(\Upomega (i)\)” to “ω(i)”.
Page 15, right column, line 7 from the bottom: Change “\(\Upomega (i)\)” to “ω(i)”.
Page 15, right column, line 3 from the bottom: Change “\(\Upomega (i)\)” to “ω(i)”.
Page 15, right column, line 2 from the bottom: Change “\(\{ x_{t}({\bf n}(u,\Upomega)), \Upomega \in \Upomega ({\bf n})\}\)” to “\(\{ x_{t} ({\bf n}(u,\omega)), \omega \in \Upomega ({\bf n})\}\)”.
Page 16, left column, line 4: Change “\(\Upomega (i)\)” to “ω(i)”.
Page 16, left column, line 5: Change “\(\sum_{\Upomega \in \Upomega ({\bf n})}\breve{x}_{t}({\bf n}(u,\Upomega))\)” to “\(\sum_{\omega \in \Upomega ({\bf n}) }\breve{x }_{t}\left({\bf n}\left(u,\omega \right) \right)\)”.
Page 16, left column, lines 12–13: Change
$$ \begin{aligned} C({\bf n}(u)) & =\Uplambda \sum_{t=1}^{T}\Uplambda^{T-t}\sum_{\Upomega \in \Upomega ({\bf n}) }\breve{x} _{t}^{\prime}({\bf n}(u,\Upomega))\\ D({\bf n}(u)) & =\Uplambda \sum_{t=1}^{T}\Uplambda^{T-t}r_{t}({\bf n}) \sum_{\Upomega \in \Upomega ({\bf n})} \breve{x}_{t}^{\prime}({\bf n}(u,\Upomega))\\ \end{aligned} $$
to
$$ \begin{aligned} C({\bf n}(u)) & =\Uplambda \sum_{t=1}^{T}\lambda^{T-t}\sum_{\omega \in \Upomega ({\bf n}) }\breve{x} _{t}^{\prime}({\bf n}(u,\omega))\\ D({\bf n}(u)) & =\Uplambda \sum_{t=1}^{T}\lambda^{T-t}r_{t}({\bf n}) \sum_{\omega \in \Upomega ({\bf n}) }\breve{x}_{t}^{\prime}({\bf n}(u,\omega))\\ \end{aligned} $$
Page 16, left column, line 17: Change
$$ \Uplambda D({\bf n}(u)) +\Uplambda r_{\tau}({\bf n}) \sum_{\Upomega \in \Upomega ({\bf n}) }\breve{x} _{t}^{\prime}({\bf n}(u,\Upomega)) $$
to
$$ \lambda D({\bf n}(u)) +\Uplambda r_{\tau}({\bf n}) \sum_{\omega \in \Upomega ({\bf n}) }\breve{x} _{t}^{\prime}({\bf n}(u,\omega)) $$
Page 16, left column, line 18: Change
$$ \Uplambda C({\bf n}(u)) +\Uplambda \sum_{\Upomega \in \Upomega ({\bf n}) }\breve{x}_{t}^{\prime}({\bf n} (u,\Upomega)) $$
to
$$ \lambda C({\bf n}(u)) +\Uplambda \sum_{\omega \in \Upomega ({\bf n})}\breve{x}_{t}^{\prime}({\bf n}(u,\omega )) $$
Page 16, left column, line 20: Change “\(\sum_{\Upomega \in \Upomega ({\bf n})}\breve{x}_{t}({\bf n}(u,\Upomega))\)” to “\(\sum_{\omega \in \Upomega ({\bf n}) }\breve{x}_{t}({\bf n}(u,\omega))\)”.
Page 16, left column, line 26: Change
$$ \breve{x}_{t}^{\prime}\left( {\bf n},\Upomega \right) =\left[\sum_{\Upomega \in \Upomega ({\bf n})} \breve{x}_{t}^{\prime}({\bf n}(1,\Upomega)) \quad \cdots \quad \sum_{\Upomega \in \Upomega ({\bf n})} \breve{x}_{t}^{\prime} ({\bf n} (2,\Upomega))\right] $$
to
$$ \breve{x}_{t}^{\prime}({\bf n},\Upomega) =\left[ \sum_{\omega \in \Upomega ({\bf n})}\breve{x}_{t}^{\prime}({\bf n}(1,\omega)) \quad \cdots \quad \sum_{\omega \in \Upomega ({\bf n})} \breve{x}_{t}^{\prime}({\bf n}(2,\omega))\right] $$
