LaTeX vs MathPix image — penev_B

penev_B.pdf.drill/penev_B.lines.json · 62 expressions · providers: mathpix, tex
#refpscoreLaTeX (mathpix)KaTeX (mathpix)LaTeX (tex)KaTeX (tex)MathPix image
14.581agree 0.66
low_agreement
s^{r e c}=s_{\|}=\sum_{m=1}^{|M|} O_{m} p_{m}
\mathbf{s}_{||}=\sum_{r n=1}^{\mathcal{M} \mid} O_{m n} \mathbf{p}_{m}
conf 0.658
MathPix crop
24.591agree 0.97
O^{\text {rec }}(\mathbf{x})=\left(\hat{\mathbf{x}}, \mathbf{O}^{*} \sum_{m=1}^{|\mathcal{M}|} O_{m} \mathbf{p}_{m}\right)=\sum_{m=1}^{|\mathcal{M}|} O_{m}\left(\hat{\mathbf{x}}, \mathrm{O}^{*} \mathbf{p}_{m}\right)=\sum_{m=1}^{\mid \mathcal{M}} O_{m} a_{m}(\mathbf{x})
O^{\text {rec }}(\mathbf{x})=\left(\dot{\mathbf{x}}, \mathbf{O}^{*} \sum_{m=l}^{|\mathcal{M}|} O_{m} \mathbf{P} m\right)=\sum_{m=1}^{|\mathcal{M}|} O_{m}\left(\hat{\mathbf{x}}, \mathbf{O}^{*} \mathbf{p}_{m}\right)=\sum_{m=1}^{\mid \mathcal{M}} O_{m} a_{m}(\mathbf{x})
conf 0.966
MathPix crop
34.601agree 0.58
low_agreement
a_{m}(\mathbf{x}) \equiv\left(\hat{\mathbf{x}}, \mathbf{O}^{*} \mathbf{p}_{m}\right)
\mathbf{q}_{\mathbf{x}_{m}} \equiv \mathbf{O} \hat{\mathbf{x}}_{r n}
conf 0.583
MathPix crop
44.611agree 0.65
low_agreement
\delta_{m, l}=\left\langle\mathbf{q}_{m}, \sum_{n=1}^{|\mathcal{M}|} \mathbf{B}_{l n} \mathbf{q}_{n}\right\rangle=\sum_{n=1}^{\mathcal{M} \mid} \mathbf{B}_{l n}\left\langle\mathbf{q}_{m}, \mathbf{q}_{n}\right\rangle=\sum_{n=1}^{|\mathcal{M}|} \mathbf{B}_{l n} \mathbf{Q}_{m n}
\left\langle\mathbf{q}_{m}, \mathbf{s}_{\|}\right\rangle=\sum_{l=1}^{|\mathcal{M}|} O_{l}\left\langle\mathbf{q}_{m}, \mathbf{p}_{l}\right\rangle=\sum_{l=1}^{\mathcal{M} \mid} O_{l} \delta_{m l}=O_{m}=\left\langle\mathbf{q}_{m}, \mathbf{s}\right\rangle
conf 0.650
MathPix crop
54.621agree 0.88
\mathrm{p}_{l}=\sum_{\mathrm{n}=1}^{|\mathcal{M}|} \mathrm{Q}^{-1}{ }_{\mathrm{ln}} \mathrm{q}_{\mathrm{n}} .
\mathbf{p}_{l}=\sum_{n=1}^{|\mathcal{M}|} \mathbf{B}_{l n} \mathbf{q}_{n}
conf 0.883
MathPix crop
64.631agree 0.55
low_agreement
\mathbf{Q}_{n m}=\left\langle\mathbf{q}_{n}, \mathbf{q}_{m}\right\rangle=\left\langle\mathbf{O} \hat{\mathbf{x}}_{n}, \mathbf{q}_{m}\right\rangle=P_{m}\left(\mathbf{x}_{n}\right)
\mathbf{Q}_{\mathbf{x}_{m}}=\frac{\mathbf{q}_{\mathbf{x}_{m}}\left\langle\mathbf{q}_{\mathbf{x}_{m}},\right\rangle}{\left\langle\mathbf{q}_{\mathbf{x}_{m},}, \mathbf{q}_{\mathbf{x}_{m}}\right\rangle}=\mathbf{p}_{\boldsymbol{x}_{m}}\left\langle\mathbf{q}_{\boldsymbol{x}_{m}},\right\rangle
conf 0.551
MathPix crop
74.641agree 0.60
low_agreement
P_{m}(\mathrm{x}) \equiv P_{\mathrm{x}_{\mathrm{m}}}(\mathrm{x}) .
\mathbf{q}_{m} \equiv \mathbf{q}_{x_{m}}=\mathbf{O} \hat{\mathbf{x}}_{m}
conf 0.605
MathPix crop
84.651
no_competing_reading
\mathbf{Q}=\left.\mathbf{P}\right|_{\mathcal{M}} .
——MathPix crop
94.661agree 0.74
low_agreement
a_{m}(\mathbf{x})=\left\langle\hat{\mathbf{x}}, \mathbf{O}^{*} \mathbf{p}_{m}\right\rangle=\sum_{n=1}^{|\mathcal{M}|} \mathbf{Q}_{m n}^{-1}\left(\hat{\mathbf{x}}, \mathbf{O}^{*} \mathbf{q}_{n}\right)=\sum_{n=1}^{|\mathcal{M}|} \mathbf{Q}_{m n}^{-1} P_{n}(\mathbf{x}) .
\begin{aligned} & a_{m}(\mathbf{x})=\left\langle\hat{\mathbf{x}}, \mathbf{O}^{*} \mathbf{p}_{m}\right\rangle=\sum_{n=1}^{|\mathcal{M}|} \mathbf{Q}^{-1}{ }_{m n}\left\langle\hat{\mathbf{x}}, \mathbf{O}^{*} \mathbf{q}_{n}\right\rangle=\sum_{n=1}^{|\mathcal{M}|} \mathbf{Q}^{-1}{ }_{m n} P_{n}(\mathbf{x}) . \\ & \text { Finally, } \\ & O^{79}(\mathbf{x})=\sum_{m=1}^{|\mathcal{M}|} O_{m} a_{m}(\mathbf{x}) \end{aligned}
conf 0.741
MathPix crop
104.671agree 0.95
O^{r e n}(\mathbf{x})=\sum_{m=1}^{|\mathcal{M}|} O_{m} a_{m}(\mathbf{x})
O(x)=\sum_{m=1}^{|\mathcal{M}|} O_{m} a_{m}(x)
conf 0.950
MathPix crop
114.681agree 0.61
low_agreement
a_{m}(\mathbf{x})=\sum_{n=1}^{|\mathcal{M}|} \mathbf{Q}^{-1}{ }_{m n} P_{n}(\mathbf{x}) .
s^{r e c}=s_{\|}=\sum_{m=1}^{|\mathcal{M}|} O_{m} p_{m}
conf 0.615
MathPix crop
124.691agree 0.95
a_{m}\left(\mathbf{x}_{l}\right)=\sum_{n=1}^{|\mathcal{M}|} \mathbf{Q}^{-1}{ }_{m n} P_{n}\left(\mathbf{x}_{l}\right)=\sum_{n=1}^{|\mathcal{M}|} \mathbf{Q}^{-1}{ }_{m n} \mathbf{Q}_{n l}=\delta_{m l} .
a_{m}\left(\mathbf{x}_{l}\right)=\sum_{n=1}^{|\mathcal{M}|} \mathbf{Q}^{-1}{ }_{m n} P_{n}\left(\mathbf{x}_{l}\right)=\sum_{n=1}^{|\mathcal{M}|} \mathbf{Q}_{m n}^{-1} \mathbf{Q}_{n l}=\delta_{m, l}
conf 0.946
MathPix crop
134.701agree 0.63
low_agreement
\phi^{r e c}(\mathrm{x})=\sum_{m=1}^{|\mathcal{M}|} O_{m} \sum_{n=1}^{|\mathcal{M}|} \mathrm{Q}_{m n}^{-1} K^{(-1)}{ }_{n}(\mathrm{x})
a_{m}(\mathbf{x})=\sum_{n=1}^{|\mathcal{M}|} \mathbf{Q}_{m n}^{-1} P_{n}(\mathbf{x})
conf 0.632
MathPix crop
144.711agree 1.00
O^{\text {err }}(\mathbf{x})=O(\mathbf{x})-O^{\text {rec }}(\mathbf{x}) .
O^{e r r}(\mathbf{x})=O(\mathbf{x})-O^{r e c}(\mathbf{x})
conf 1.000
MathPix crop
154.723agree 0.69
low_agreement
\mathcal{O}_{l} \equiv \mathbf{Q}^{-1}{ }_{l m} O_{m} .
O_{l} \equiv \mathbf{Q}_{l m}^{-1} O_{m}
conf 0.692
MathPix crop
164.733agree 0.98
\begin{aligned} & O^{r e x}(\mathbf{x})=\sum_{i=1}^{|\mathcal{M}|} \mathcal{O}_{l} P_{l}(\mathbf{x}) \\ & \phi^{r e c}(\mathbf{x})=\sum_{l=1}^{|\mathcal{M}|} \mathcal{O}_{l} K_{l}^{-1}(\mathbf{x}) \end{aligned}
\begin{aligned} O^{r e c}(\mathbf{x}) & =\sum_{l=1}^{|\mathcal{M}|} \mathcal{O}_{l} P_{l}(\mathbf{x}) \\ \phi^{r e c}(\mathbf{x}) & =\sum_{l=1}^{|\mathcal{M}|} \mathcal{O}_{l} K_{l}^{-1}(\mathbf{x}) . \end{aligned}
conf 0.977
MathPix crop
174.743agree 0.64
low_agreement
\sum_{l=1}^{|\mathcal{M}|} \mathrm{Q}_{m l} \mathcal{O}_{l}=O_{m}
\mathbf{p}_{l}=\sum_{n=1}^{|\mathcal{M}|} \mathbf{Q}^{-1}{ }_{l n} q_{n}
conf 0.635
MathPix crop
184.754agree 1.00
-\tau \frac{d}{d t} \mathcal{O}(\mathbf{x})=\mathrm{K} \phi-\mathbf{P} G(\mathcal{O})
-\tau \frac{d}{d t} \mathcal{O}(\mathbf{x})=\mathbf{K} \phi-\mathbf{P} G(\mathcal{O})
conf 1.000
MathPix crop
194.764agree 1.00
\mathbf{P O}=\mathbf{K} \phi .
\mathbf{P O}=\mathbf{K} \phi
conf 1.000
MathPix crop
205.15agree 1.00
\alpha^{t}=\left(\theta^{t}, S^{t}, X^{t}, Y^{t}\right) .
\alpha^{t}=\left(\theta^{t}, S^{t}, X^{t}, Y^{t}\right)
conf 1.000
MathPix crop
215.25agree 1.00
\phi^{t}=H\left(I^{t} ; \alpha^{t}\right)
\phi^{t}=H\left(I^{t} ; \alpha^{t}\right)
conf 1.000
MathPix crop
225.46agree 1.00
N\langle S\rangle(N, \alpha)=\left\|\Phi_{N}^{*+} \phi(\alpha)\right\|_{S}^{2} .
N\langle S\rangle(N, \alpha)=\left\|\Phi_{N}^{*+} \phi(\alpha)\right\|_{S}^{2}
conf 1.000
MathPix crop
235.57agree 1.00
\alpha_{h}^{t}=\left(\theta^{t},(1+h) S^{t}, X^{t}, Y^{t}\right)
\alpha_{h}^{t}=\left(\theta^{t},(1+h) S^{t}, X^{t}, Y^{t}\right)
conf 1.000
MathPix crop
245.69agree 0.56
low_agreement
\mathbf{K}_{j}^{(n)}=\sum_{\mathbf{f} \in \Delta_{j}} \Psi_{\mathbf{f}}\left(\frac{1}{\sigma_{\mathbf{f}}}\right)^{n}\left(\Psi_{\mathbf{f}},\right) .
\mathrm{O}^{+} \mathrm{O}=\sum_{\boldsymbol{f}} \Psi_{\boldsymbol{f}}\left(\Psi_{\boldsymbol{f}},\right)
conf 0.556
MathPix crop
255.79agree 1.00
O_{j}=\mathbf{K}_{j} \phi_{j}=\mathbf{K}_{j} \mathbf{P}_{j} \phi=\mathbf{K}_{j} \phi
O_{j}=\mathbf{K}_{j} \phi_{j}=\mathbf{K}_{j} \mathbf{P}_{j} \phi=\mathbf{K}_{j} \phi
conf 1.000
MathPix crop
265.89agree 0.48
low_agreement
\mathbf{O}_{j}^{*} \mathbf{O}_{j}=\mathbf{P}_{j} \neq \mathbf{1} .
\mathrm{O}^{*} \mathrm{O}=\mathbf{1}_{U}
conf 0.552
MathPix crop
275.910agree 1.00
W=\left[\begin{array}{cc} w & x \\ y & z \end{array}\right]=\left[\begin{array}{cc} 1_{n^{\prime}} & 0 \\ y w^{-1} & 1_{n^{\prime \prime}} \end{array}\right]\left[\begin{array}{cc} w & x \\ 0 & \tilde{z}^{-1} \end{array}\right]
W=\left[\begin{array}{cc} w & x \\ y & z \end{array}\right]=\left[\begin{array}{cc} 1_{n^{\prime}} & \mathbf{0} \\ y w^{-1} & \mathbf{1}_{n^{\prime \prime}} \end{array}\right]\left[\begin{array}{cc} w & x \\ \mathbf{0} & \tilde{z}^{-1} \end{array}\right]
conf 1.000
MathPix crop
285.1010agree 0.95
\tilde{z}^{1}=z \quad y w{ }^{1} x
\tilde{z}^{1}=z \quad y w^{1} x
conf 0.955
MathPix crop
295.1110agree 0.97
\begin{aligned} W^{1} & =\left[\begin{array}{cc} w^{1} & -w^{1} x \tilde{z} \\ 0 & \tilde{z} \end{array}\right]\left[\begin{array}{cc} 1 & 0 \\ -y w^{-1} & 1 \end{array}\right]= \\ & =\left[\begin{array}{cc} w^{-1}+w^{-1} x \bar{z} y w^{-1} & -w^{-1} x \bar{z} \\ -\tilde{z} y w^{-1} & \bar{z} \end{array}\right]= \\ & =\left[\begin{array}{cc} w^{-1} & 0 \\ 0 & 0 \end{array}\right]+\left[\begin{array}{cc} w^{-1} x \tilde{z} y w^{-1} & -w^{-1} x \tilde{z} \\ -\tilde{z} y w^{-1} & \tilde{z} \end{array}\right] . \end{aligned}
\begin{aligned} W^{1} & =\left[\begin{array}{cc} w^{1} & -w^{1} x \bar{z} \\ 0 & \tilde{z} \end{array}\right]\left[\begin{array}{cc} 1 & 0 \\ -y w^{-1} & \mathbf{1} \end{array}\right]= \\ & =\left[\begin{array}{cc} w^{-1}+w^{-1} x \bar{z} y w^{-1} & -w^{-1} x \bar{z} \\ -\tilde{z} y w^{-1} & \bar{z} \end{array}\right]= \\ & =\left[\begin{array}{cc} w^{-1} & 0 \\ 0 & 0 \end{array}\right]+\left[\begin{array}{cc} w^{-1} x \bar{z} y w^{-1} & -w^{-1} x \tilde{z} \\ -\tilde{z} y w^{-1} & \tilde{z} \end{array}\right] . \end{aligned}
conf 0.972
MathPix crop
305.1210agree 1.00
Q_{m l}=\left.P_{m}\left(\mathbf{x}_{l}\right)\right|_{l, m=1} ^{M} .
Q_{m l}=\left.P_{m}\left(\mathbf{x}_{l}\right)\right|_{l, m=1} ^{M}
conf 1.000
MathPix crop
315.1310agree 0.86
p^{T}{ }_{l} \equiv y^{T}{ }_{l}=x_{l}=Q_{M l}=\left.P_{M}\left(\mathbf{x}_{l}\right)\right|_{l=1} ^{M-1} .
p_{l}^{T} \equiv y_{l}^{T}=x_{l}=Q_{M l}=P_{M}\left(\mathbf{x}_{l}\right)_{l=1}^{M-1}
conf 0.857
MathPix crop
325.1410agree 1.00
z=P_{M}\left(\mathbf{x}_{M}\right) .
z=P_{M}\left(\mathbf{x}_{M}\right)
conf 1.000
MathPix crop
335.1510agree 0.98
\left[\begin{array}{cc} -u & 1 \end{array}\right] \equiv\left[\begin{array}{ll} -y w^{-1} & 1 \end{array}\right]=\left[\begin{array}{ll} -p q^{-1} & 1 \end{array}\right]
\left[\begin{array}{ll} -u & 1 \end{array}\right] \equiv\left[\begin{array}{ll} -y w^{-1} & 1 \end{array}\right]=\left[\begin{array}{ll} -p q^{-1} & 1 \end{array}\right]
conf 0.980
MathPix crop
345.1610agree 0.98
\mathrm{Q}^{-1}=\left[\begin{array}{cc} q^{-1} & 0 \\ 0 & 0 \end{array}\right]+\bar{z}\left[\begin{array}{c} -u^{T} \\ 1 \end{array}\right]\left[\begin{array}{ll} -u & 1 \end{array}\right] .
\mathrm{Q}^{-1}=\left[\begin{array}{cc} q^{-1} & 0 \\ 0 & 0 \end{array}\right]+\bar{z}\left[\begin{array}{c} -u^{T} \\ 1 \end{array}\right]\left[\begin{array}{cc} -u & 1 \end{array}\right]
conf 0.980
MathPix crop
355.1710agree 1.00
O^{r e c}(\mathbf{x})=A^{m}(\mathbf{x}) O\left(\mathbf{x}_{m}\right)
O^{r e c}(\mathbf{x})=A^{m}(\mathbf{x}) O\left(\mathbf{x}_{\mathbf{m}}\right)
conf 1.000
MathPix crop
365.1810agree 0.96
A^{m}(\mathbf{x})=P^{l}(\mathbf{x})\left(\mathbf{Q}^{-1}\right)_{l}^{m}
A^{m}(\mathbf{x})=P^{l}(\mathbf{x})\left(\mathbf{Q}^{-1}\right)_{3}^{m}
conf 0.960
MathPix crop
375.1910agree 1.00
\begin{aligned} A^{m}(\mathbf{x})= & {\left[\begin{array}{ll} p^{l}(\mathbf{x}) & P^{M}(\mathbf{x}) \end{array}\right]\left[\begin{array}{cc} \left(q^{-1}\right) r^{m} & \mathbf{0} \\ 0 & 0 \end{array}\right]+} \\ & +\bar{z}\left[\begin{array}{ll} p^{l}(\mathbf{x}) & P^{M}(\mathbf{x}) \end{array}\right]\left(\left[\begin{array}{c} -u^{T} \\ 1 \end{array}\right]\left[\begin{array}{ll} -u & 1 \end{array}\right]\right)_{1}^{m}= \\ = & {\left[\begin{array}{ll} p^{l}(\mathbf{x})\left(q^{-1}\right) I^{m} & 0 \end{array}\right]+\tilde{z}\left(P^{M}(\mathbf{x})-p^{l}(\mathbf{x}) u^{T}\right)\left[\begin{array}{ll} -u^{m} & 1 \end{array}\right]=} \\ = & {\left[\begin{array}{ll} a^{m}(\mathbf{x}) & \mathbf{0} \end{array}\right]+\bar{z} A(\mathbf{x})\left[\begin{array}{ll} -u^{m} & 1 \end{array}\right] } \end{aligned}
\begin{aligned} A^{m}(\mathbf{x})= & {\left[\begin{array}{ll} p^{l}(\mathbf{x}) & P^{M}(\mathbf{x}) \end{array}\right]\left[\begin{array}{cc} \left(q^{-1}\right)^{m} & 0 \\ 0 & 0 \end{array}\right]+} \\ & +\bar{z}\left[\begin{array}{ll} p^{l}(\mathbf{x}) & P^{M}(\mathbf{x}) \end{array}\right]\left(\left[\begin{array}{c} -u^{T} \\ 1 \end{array}\right]\left[\begin{array}{ll} -u & 1 \end{array}\right]\right)_{1}^{m}= \\ = & {\left[\begin{array}{ll} p^{l}(\mathbf{x})\left(q^{-1}\right)^{m} & \mathbf{0} \end{array}\right]+\tilde{z}\left(P^{M}(\mathbf{x})-p^{l}(\mathbf{x}) u^{T}\right)\left[\begin{array}{ll} -u^{m} & 1 \end{array}\right]=} \\ = & {\left[\begin{array}{ll} a^{m}(\mathbf{x}) & \mathbf{0} \end{array}\right]+\bar{z} A(\mathbf{x})\left[\begin{array}{ll} -u^{m} & 1 \end{array}\right] } \end{aligned}
conf 0.997
MathPix crop
385.2010agree 0.90
A(\mathbf{x}) \equiv P^{M}(\mathbf{x})-p^{l}(\mathbf{x}) u^{T}{ }_{l}
A(\mathbf{x}) \equiv P^{M}(\mathbf{x})-p^{l}(\mathbf{x}) u_{l}^{T}
conf 0.897
MathPix crop
395.2110agree 1.00
\Delta A^{m}(\mathbf{x})=\bar{z} A(\mathbf{x})\left[\begin{array}{ll} -u^{m} & 1 \end{array}\right]
\Delta A^{m}(\mathbf{x})=\bar{z} A(\mathbf{x})\left[\begin{array}{ll} -u^{m} & 1 \end{array}\right]
conf 1.000
MathPix crop
405.2210agree 1.00
A^{M}(\mathbf{x})=\bar{z} A(\mathbf{x})
A^{M}(\mathbf{x})=\bar{z} A(\mathbf{x})
conf 1.000
MathPix crop
415.2310agree 0.95
\Delta A^{m}(\mathbf{x})=A^{M}(\mathbf{x})\left[\begin{array}{ll} -u^{m} & 1 \end{array}\right] .
\Delta A^{m}(\mathbf{x})=A^{M}(\mathbf{x})\left[\begin{array}{ll} -u^{\pi n} & 1 \end{array}\right]
conf 0.949
MathPix crop
425.2410
no_competing_reading
u^{m}=p^{l}\left(\mathbf{x}_{M}\right)\left(q^{-1}\right)_{l}^{m}=a^{m}\left(\mathbf{x}_{M}\right) .
——MathPix crop
435.2510agree 0.57
low_agreement
A(\mathbf{x})=P^{M}(\mathbf{x})-a^{\mathbf{m}}(\mathbf{x}) P^{M}\left(\mathbf{x}_{\boldsymbol{m}}\right) .
\bar{z}^{1}=P^{M}\left(\mathbf{x}_{M}\right)-a^{m}\left(\mathbf{x}_{M}\right) P^{M}\left(\mathbf{x}_{m}\right)=\mathcal{D}_{P M}\left(\mathbf{x}_{M}\right) .
conf 0.571
MathPix crop
445.2610agree 1.00
\mathcal{R}_{V}^{|\mathcal{M}|}(\mathbf{x})=A^{m}(\mathbf{x}) V\left(\mathbf{x}_{\boldsymbol{m}}\right) .
\mathcal{R}_{V}^{|\mathcal{M}|}(\mathbf{x})=A^{m}(\mathbf{x}) V\left(\mathbf{x}_{m}\right)
conf 1.000
MathPix crop
455.2711agree 0.65
low_agreement
O^{r e c}(\mathbf{x})=\mathcal{R}_{O}^{M}(\mathbf{x})
O^{r e c}(\mathbf{x})=O_{m} a_{x_{\mathrm{ra}}}(\mathbf{x})
conf 0.652
MathPix crop
465.2811agree 0.92
A(\mathbf{x})=P^{M}(\mathbf{x})-\mathcal{R}_{P^{M}}^{M-1}(\mathbf{x}) .
A(\mathbf{x})=P^{M}(\mathbf{x})-\mathcal{R}_{P^{M-1}}^{M}(\mathbf{x})
conf 0.917
MathPix crop
475.2911agree 1.00
\mathcal{D}_{V}(\mathbf{x})=V(\mathbf{x})-\mathcal{R}_{V}^{|\mathcal{M}|-1}(\mathbf{x})
\mathcal{D}_{V}(\mathbf{x})=V(\mathbf{x})-\mathcal{R}_{V}^{|\mathcal{M}|-1}(\mathbf{x})
conf 1.000
MathPix crop
485.3011agree 0.75
A(\mathbf{x})=\mathcal{D}_{P^{M}}(\mathbf{x})
O^{r e c}(\mathbf{x})=\mathcal{R}_{O}^{M}(\mathbf{x})
conf 0.750
MathPix crop
495.3111agree 1.00
A\left(\mathbf{x}_{m}\right)=\left.0\right|_{m=1} ^{M-1} .
A\left(\mathbf{x}_{m}\right)=\left.0\right|_{m=1} ^{M-1}
conf 1.000
MathPix crop
505.3211agree 0.57
low_agreement
\bar{z}^{1}=P^{M}\left(\mathbf{x}_{M}\right)-a^{m}\left(\mathbf{x}_{M}\right) P^{M}\left(\mathbf{x}_{m}\right)=\mathcal{D}_{P^{M}}\left(\mathbf{x}_{M}\right) .
A(\mathbf{x})=\mathcal{D}_{P^{M}}(\mathbf{x})
conf 0.571
MathPix crop
515.3311agree 0.94
A^{M}(\mathbf{x})=\frac{\mathcal{D}_{P M}(\mathbf{x})}{\mathcal{D}_{P M}\left(\mathbf{x}_{M}\right)}
A^{M}(\mathbf{x})=\frac{\mathcal{D}_{P^{M}}(\mathbf{x})}{\mathcal{D}_{P^{M}}\left(\mathbf{x}_{M}\right)}
conf 0.941
MathPix crop
525.3411agree 0.70
low_agreement
\Delta A^{m}(\mathbf{x})=A^{M}(\mathbf{x})\left[\begin{array}{ll} -a^{m}\left(\mathbf{x}_{M}\right) & 1 \end{array}\right] .
\Delta A^{m}(\mathbf{x})=A^{M}(\mathbf{x})\left[-a^{m}\left(\mathbf{x}_{M}\right) \quad 1\right]
conf 0.719
MathPix crop
535.3511agree 0.90
\begin{aligned} \Delta O^{r e c}(\mathbf{x}) & =\Delta A^{m}(\mathbf{x}) O\left(\mathbf{x}_{m}\right)= \\ & =A^{M}(\mathbf{x})\left[-a^{m}\left(\mathbf{x}_{M}\right) \quad 1\right]\left[\begin{array}{l} O\left(\mathbf{x}_{m}\right) \\ O\left(\mathbf{x}_{M}\right) \end{array}\right]= \\ & =A^{M}(\mathbf{x}) \mathcal{D}_{O}\left(\mathbf{x}_{M}\right) \end{aligned}
\begin{aligned} & \Delta O^{\text {rec }}(\mathbf{x})=\Delta A^{m}(\mathbf{x}) O\left(\mathbf{x}_{m}\right)= \\ & =A^{M}(\mathbf{x})\left[\begin{array}{ll} -a^{m}\left(\mathbf{x}_{M}\right) & 1 \end{array}\right]\left[\begin{array}{l} O\left(\mathbf{x}_{m}\right) \\ O\left(\mathbf{x}_{M}\right) \end{array}\right]= \\ & =A^{M}(\mathbf{x}) \mathcal{D}_{O}\left(\mathbf{x}_{M}\right) \text {. } \end{aligned}
conf 0.889
MathPix crop
545.3611agree 1.00
\Delta O^{r e c}(\mathbf{x})=\frac{\mathcal{D}_{P^{M}}(\mathbf{x})}{\mathcal{D}_{P^{M}}\left(\mathbf{x}_{M}\right)} \mathcal{D}_{O}\left(\mathbf{x}_{M}\right)
\Delta O^{\text {rec }}(\mathbf{x})=\frac{\mathcal{D}_{P^{M}}(\mathbf{x})}{\mathcal{D}_{P^{M}}\left(\mathbf{x}_{M}\right)} \mathcal{D}_{O}\left(\mathbf{x}_{M}\right)
conf 1.000
MathPix crop
5511
no_competing_reading
120
——MathPix crop
565.3711agree 1.00
\hat{f}_{n}=\sum_{m=1}^{M-1} \alpha_{m} f_{n-m}
\hat{f}_{n}=\sum_{m=1}^{M-1} \alpha_{m} f_{n-m}
conf 1.000
MathPix crop
575.3811agree 0.92
\alpha^{m}=\left(q^{-1}\right)_{l}^{m} Q_{0}^{l}
\alpha^{m}=\left(q^{-1}\right)_{i}^{m} Q_{0}^{1}
conf 0.923
MathPix crop
585.3911agree 1.00
q_{m l}=\left.Q_{m l}\right|_{m, l=1} ^{M-1}
q_{m l}=\left.Q_{m l}\right|_{m, l=1} ^{M-1}
conf 1.000
MathPix crop
595.4011agree 1.00
Q_{m l}=\left.E\left\{f_{n-l} f_{n-m}\right\}\right|_{m, l=0} ^{M-1}
Q_{m l}=\left.E\left\{f_{n-l} f_{n-m}\right\}\right|_{m, l=0} ^{M-1}
conf 1.000
MathPix crop
605.4111agree 1.00
e_{n}=f_{n}-\hat{f}_{n}=\mathcal{D}_{f}\left(\mathbf{x}_{M}\right)
e_{n}=f_{n}-\hat{f}_{n}=\mathcal{D}_{f}\left(\mathbf{x}_{M}\right)
conf 1.000
MathPix crop
615.4211agree 1.00
\Delta f^{r e c}\left(\mathbf{x}_{M}\right)=e_{\mathbf{n}}=1 \times \mathcal{D}_{f}\left(\mathbf{x}_{M}\right) .
\Delta f^{\text {rec }}\left(\mathbf{x}_{M}\right)=e_{n}=1 \times \mathcal{D}_{f}\left(\mathbf{x}_{M}\right) .
conf 1.000
MathPix crop
625.4312agree 1.00
\Delta v^{r e c}(t)=A^{M}(t) \times 1
\Delta v^{\text {rec }}(t)=A^{M}(t) \times 1
conf 1.000
MathPix crop