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LaraPass v1 Installation Guide for cPanel powered Shared/VPS Hosting Servers.
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Open cPanel in your browser, usually available at the url address yourdomain.com:2082
.
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, Addon Domains
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The Widget component is the basis of all widgets (charts, etc). This example shows the available methods for this base component.


Create Reference out of Raw Image
Mirror Image:
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Degrees
Brightness:
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Resilient Estimation Against Sparse Integrity Attack
Zishuo Li 李子硕
Department of Automation, Tsinghua University
D-COS Zhizhen Academic Forum for Postgraduates， Dec 19, 2021
Background and introduction
BACKGROUND: Security Problem of Estimation
Safety Critical Industries
- High safety requirements.
- More vulnerable System
- Modern control systems are becoming more open to the cyber-world.
- More intelligent algorithms.
Threats:
Malicious Attack:
Malfunctioning components:
Diverse environment:
Requires safety-concerned estimators.
- System equation:
$$
x(k+1)=Ax(k)+w(k),
$$
where $x(k)\in{\color{var(--myred)}{\mathbb{R}^n}}$, $w(k)\sim\mathcal{N}(0,Q)$.
- Measurement equation of sensor $i$:
$$
y_i(k)=C_ix(k)+v_i(k)+a_i(k).
$$
- Full measurement equation:
$$
y(k)=Cx(k)+v(k)+a(k),
$$
where
$$
y(k)\triangleq \begin{bmatrix}
y_1(k)\\
\vdots\\
y_m(k)
\end{bmatrix}\in {\color{var(--myred)}\mathbb{R}^m}, C\triangleq \begin{bmatrix}
C_1\\
\vdots\\
C_m
\end{bmatrix}, v(k)\triangleq \begin{bmatrix}
v_1(k)\\
\vdots\\
v_m(k)
\end{bmatrix}\sim\mathcal{N}(0,R),
a(k)\triangleq \begin{bmatrix}
a_1(k)\\
\vdots\\
a_m(k)
\end{bmatrix}
$$
- $(A,C)$ is observable. Note that $(A, C_i)$ is not necessarily observable.
- Each sensor needs to estimate the state $x$.
Resilient Estimation vs Robust Estimation
Robust Estimation
(Uncertain) system model
Full state noise / disturbance
(Partly) Known noise / disturbance statistic property
Resilient Estimation
Known system model
Uncertain Sparse disturbance
Know nothing about disturbance (can be infinitely large)
Resilient:
1. 只有部分传感器有问题
2. 不知道是哪些传感器有问题
3. 有问题传感器观测可被任意篡改
Sparse Attack
The attack is called a $p$-sparse attack if the vector sequence $a(k)$ satisfy that,
there exists a time invariant index set $\mathcal{I}\subseteq \mathcal{R}\triangleq\{1,2,\cdots,m\} $ with $|\mathcal{I}| = p$ such that $\bigcup_{k=1}^{\infty} \text{supp}\left\{a(k)\right\} = \mathcal{I}$.
一共只有最多p个传感器受到攻击
Sparse Observability/Detectability
System $(A,C)$ is $s$-sparse observable (detectable) if system $(A,C_{\mathcal{I}\setminus\mathcal{C}})$ is observable
(detectable) for any set of sensors $\mathcal{C}$ with cardinality $|\mathcal{C}| = s$.
去掉任意$p$个传感器后系统仍然可观/可测
Estimator without attack
Kalman filter is the optimal estimator in an LTI Gaussian system.
$$
\begin{aligned}
\hat x(k|k-1)&=A\hat x(k-1),\\
P(k|k-1)&=AP(k-1)A^T+Q,\\
K(k)&=P(k|K-1)C^T[CP(k|k-1)C^T+R]^{-1},\\
\hat x(k)&=\hat x(k|k-1)+K(k)[y(k)-C\hat x(k|k-1)],\\
P(k)&=[I-K(k)C]P(k|k-1),
\end{aligned}
$$
where $\hat x(0)=0$ and $P(0)=\Sigma$.
Security of Linear Estimator
\(
\begin{align}
\hat{x}(k+1)&=(A-K C A) \hat{x}(k)+K y(k+1),\\
&=(A-K C A) \hat{x}(k)+\left[\begin{array}{c|c|c}K_1&\vdots&K_m \end{array}\right]\begin{bmatrix}y_1(k+1)\\ \vdots\\y_m(k+1)\end{bmatrix},\\
&=(A-K C A) \hat{x}(k)+\sum_{i=1}^m K_i y_i(k+1),
\end{align}
\)
Assumption 1
The matrix $A$ is nonsingular and in Jordan canonical form.
The matrix $A − KCA$ and matrix $A$ do not share any eigenvalue.
Remark
It does not lose generality, since we can perform invertible linear transformation $T$ on state $x$ and study the following system instead:
\begin{align*}
\bar{x}(k)&= \bar{A} \bar{x}(k) + TB\bar{x}(k)+Tw(k), \\
y(k)&=CT^{-1}\bar{x}(k)+v(k)+a(k) ,
\end{align*}
where $\bar{A}\triangleq TAT^{-1}$ is similar to $A$ and $\bar{x}=Tx$.
Since $(A,CA)$ is observable, we can freely assign the eigenvalues of $A-KCA$ by choosing $K$ to avoid the eigenvalues of $A$.
Local Estimator Design
$$
\hat{x}(k+1)=(A-KCA)\hat{x}(k)+\sum_{i=1}^m K_i y_i(k+1).
$$
$$
\zeta_i(k+1)=\Lambda \zeta_i(k) + \mathbf{1}_n y_i(k+1).
$$
(where $\Lambda$ is the Jordan canonical form of $A-KCA$.)
And $F_i$ is designed such that $\hat{x}$ can be recovered by a linear combination of $\zeta_i$:
$$
\hat{x}(k)=F_1 \zeta_1(k)+F_2 \zeta_2(k)+\cdots+F_m\zeta_m(k),\ \forall k.
$$
From Linear Combination to Resilient Fusion
The linear combination is not safe since one corrupted $\zeta_i$ may corrupt the $\tilde{x}$.
We replace the linear combination to a resilient fusion scheme.
What is $\zeta_i$ estimating ?
Lemma 1
The local estimation $\zeta_i(k)$ is a stable estimation of $G_ix(k)$ where $G_i$ is defined as following and the residue $\epsilon_i(k)\triangleq \zeta_i(k)-G_ix(k)$ satisfy:
$$
\epsilon_i(k+1)=\Lambda\epsilon_i(k) - (G_i-\mathbf{1}_n C-i) w_i(k)+ \mathbf{1}_n v_i(k)+\mathbf{1}_n a_i(k),
$$
and
$$
G_i=\begin{bmatrix}
G_{1,i}\\ \vdots \\ G_{p,i}
\end{bmatrix}\in\mathbb{C}^{n\times n},\;
G_{l, i}=\left[\begin{array}{c}
C_{i} A\left(A-\lambda_{l} I\right)^{-n_{l}}+\cdots+C_{i} A\left(A-\lambda_{l} I\right)^{-1} \\
\vdots \\
C_{i} A\left(A-\lambda_{l} I\right)^{-2}+C_{i} A\left(A-\lambda_{l} I\right)^{-1} \\
C_{i} A\left(A-\lambda_{l} I\right)^{-1}
\end{array}\right]\in\mathbb{C}^{n_{l} \times n} .
$$
Least Square Fusion Scheme
$$\epsilon_{i}(k+1)= \Lambda \epsilon_{i}(k)\underbrace{-\left(G_{i}-\mathbf{1}_{n} C_{i}\right) w(k)
+\mathbf{1}_{n} v_{i}(k+1)}_{\text{noise term}}
\underbrace{+\mathbf{1}_{n} a_{i}(k+1)}_{\text{attack term}} .$$
Define $\tilde{W}$ as the stable covariance of $\left[\epsilon_1'(k) \cdots \epsilon_m'(k)\right]'$ when $a(k)=0$, then $\tilde{W}$ satisfy
$$ \tilde{W}=\begin{bmatrix}\Lambda&&\\ &\ddots&\\ &&\Lambda \end{bmatrix} \tilde{W} \begin{bmatrix}\Lambda&&\\ &\ddots&\\ &&\Lambda \end{bmatrix} + \text{Cov}(\text{noise term}),$$
We have the following least square problem:
\begin{align}
&\underset{\check{x}(k), \mu(k)}{\operatorname{minimize}} \mu(k)' \tilde{W}^{-1} \mu(k)\\
&\text {subject to } \begin{bmatrix}
\hat{\zeta}_{1}(k) \\
\vdots \\
{\zeta}_{m}(k)
\end{bmatrix}=
\begin{bmatrix}
{G}_{1} \\
\vdots \\
{G}_{m}
\end{bmatrix} \check{x}(k)+\mu(k) .
\end{align}
Least Square Fusion Scheme
\begin{align}
&\underset{\check{x}(k), \mu(k)}{\operatorname{minimize}} \mu(k)' \tilde{W}^{-1} \mu(k)\\
&\text {subject to } \begin{bmatrix}
\zeta_{1}(k) \\
\vdots \\
{\zeta}_{m}(k)
\end{bmatrix}=
\begin{bmatrix}
{G}_{1} \\
\vdots \\
{G}_{m}
\end{bmatrix} \check{x}(k)+\mu(k) .
\end{align}
Theorem 1
In the absence of attack, i.e. $a(k)=\mathbf{0}$, the solution $\check{x}(k)$ of the above optimization problem coincides with the Kalman estimation, i.e., $\check{x}(k)=\hat{x}(k)$.
LASSO Fusion Scheme
\begin{align}
&\underset{\tilde{x}(k), \mu(k)}{\operatorname{minimize}} \mu(k)' \tilde{W}^{-1} \mu(k) +\gamma \|\nu(k)\|_1\\
&\text {subject to } \begin{bmatrix}
\zeta_{1}(k) \\
\vdots \\
{\zeta}_{m}(k)
\end{bmatrix}=
\begin{bmatrix}
{G}_{1} \\
\vdots \\
{G}_{m}
\end{bmatrix} \tilde{x}(k)+\mu(k) +\nu(k).
\end{align}
We will prove in the following that:
In the absence of attack, our proposed estimation coincides with Kalman for centain probability, i.e. $$\mathbb{P}\left[\tilde{x}(k) = \hat{x}(k)\right]=f(\gamma).$$
And $f(\gamma)\rightarrow 1$ if $\gamma\rightarrow +\infty$.
In the presence of attack, our proposed estimation is resilient against $p$-sparse attack if one condition is satisfied.
Intuition of LASSO
$$\min_{x,\mu,\nu} \frac{1}{2}\mu'\mu+\gamma\|\nu\|_1$$
$$s.t. Y=Hx +\mu+\nu$$
$$\min_{x,\nu} \frac{1}{2}\|Y-Hx-\nu\|_2^2+\gamma\|\nu\|_1$$
If we define the following function:
$$
f(r) \triangleq \underset{\nu}{\operatorname{min}} \ \frac{1}{2}\|r-\nu\|_{2}^{2} +\gamma\|\nu\|_{1} .
$$
Then, one can easily prove that the optimization problem can be rewritten as follows:
$$
\underset{x}{\min } f\left(Y-H x\right) .
$$
Intuition of LASSO
$$\min_{x,\mu} \frac{1}{2}\mu'\mu$$
$$s.t. \begin{bmatrix}-1\\ 1 \\10\end{bmatrix}=\begin{bmatrix}1\\ 1 \\1\end{bmatrix}x +\mu$$
$$\min_{x} \frac{1}{2}\left[(x+1)^2+(x-1)^2+(x-10)^2\right]$$
$$\min_{x,\mu} \frac{1}{2}\mu'\mu+\|\nu\|_1$$
$$s.t. \begin{bmatrix}-1\\ 1 \\10\end{bmatrix}=\begin{bmatrix}1\\ 1 \\1\end{bmatrix}x +\mu+\nu$$
$$\min_{x} f(x+1)+f(x-1)+f(x-10)$$
$$f(r) \triangleq \underset{\nu}{\operatorname{min}} \ \frac{1}{2}\|r-\nu\|_{2}^{2} +\gamma\|\nu\|_{1}$$
LASSO Fusion Scheme
\begin{align}
&\underset{\tilde{x}(k), \mu(k)}{\operatorname{minimize}} \mu(k)' \tilde{W}^{-1} \mu(k) +\gamma \|\nu(k)\|_1\\
&\text {subject to } \begin{bmatrix}
\zeta_{1}(k) \\
\vdots \\
{\zeta}_{m}(k)
\end{bmatrix}=
\begin{bmatrix}
{G}_{1} \\
\vdots \\
{G}_{m}
\end{bmatrix} \tilde{x}(k)+\mu(k) +\nu(k).
\end{align}
We will prove in the following that:
In the absence of attack, our proposed estimation coincides with Kalman for centain probability, i.e. $$\mathbb{P}\left[\tilde{x}(k) = \hat{x}(k)\right]=f(\gamma).$$
And $f(\gamma)\rightarrow 1$ if $\gamma\rightarrow +\infty$.
In the presence of attack, our proposed estimation is resilient against $p$-sparse attack if one condition is satisfied.
Theorem 2 (Optimality without attack)
The solution $\tilde{x}(k)$ of the above optimization equals to Kalman estimation $\hat{x}(k)$ if the following condition is satisfied:
$$
\left\|\tilde{W}^{-1}\left(I-\left[\begin{array}{c}
{G}_{1} \\
\vdots \\
{G}_{m}
\end{array}\right]\left[\begin{array}{lll}
{F}_{1} & \ldots & {F}_{m}
\end{array}\right]\right) \left(\zeta(k)-Gx(k)\right)\right\| \leq \gamma
$$
Remark
The probability of this inequality holds can be explicity calculated given system parameters.
By tuning design parameter $\gamma$, the probability of recovering the Kalman estimation can be adjusted.
Theorem 3 (Security under attack)
The solution $\tilde{x}(k)$ of the above optimization problem is resilient against $p$-sparse attack if the following condition is satisfied:
$
\forall x\in\mathbb{R}^n , x\neq 0, \forall \mathcal{C}$ with $|\mathcal{C}|=p,$
$$
\sum_{i\in\mathcal{C}} \|G_i x \|_1 < \sum_{i\in\mathcal{I}\setminus\mathcal{C}} \|G_i x \|_1.
$$
Moreover, the estimation covariance upper bound is monotone increasing w.r.t $\gamma$.
Remark
$\gamma \rightarrow +\infty$ better performance without attack, poor performance under attack.
$\gamma \rightarrow 0\quad$ poor performance without attack, better performance under attack.
Problems of this result
$
\forall x\in\mathbb{R}^n , x\neq 0, \forall \mathcal{C}$ with $|\mathcal{C}|=p,$
$$
\sum_{i\in\mathcal{C}} \|G_i x \|_1 < \sum_{i\in\mathcal{I}\setminus\mathcal{C}} \|G_i x \|_1.
$$
Computational complexity: actually NP-hard.
Not necessary: do not achieve fundamental limit:
Define the observability matrix as
$$O_i\triangleq\left[\begin{array}{c}
C_{i} \\
C_{i} A \\
\vdots \\
C_{i} A^{n-1}
\end{array}\right].$$
The observable subspace with respect to sensor $i$ is $\text{Row}(O_i)=\text{Span} \left[C'_{i},(C_{i}A)',\cdots,\left(C_{i} A^{n-1}\right){'}\right]$.
We have proved the following theorem:
Theorem 4
When all the eigenvalues of $A$ have geometric multiplicity $1$, then
$$\text{Row}(O_i)=\text{Row}(G_i)=\text{Row}(H_i),$$
where $$H_i=\begin{bmatrix}\mathbb{I}\{O^{(1)}_i\neq 0\} && \\ &\ddots& \\ &&\mathbb{I}\{O^{(n)}_i\neq 0\}\end{bmatrix}.$$
Corollary 4.1
There exists an invertible $n\times n$ matrix $P_i$ such that $P_iG_i=H_i$.
Corollary 4.2
If the sparse observability index of system $(A,C)$ is $s$, then
\begin{equation}\label{eq:calc_index}
s=\min_{j=1,\cdots,n} \sum_{i\in\mathcal{I}}\mathbb{I}\{O^{(j)}_i\neq 0\} -1.
\end{equation}
Define $\tilde{P} \triangleq \text{diag}\left(P_1,\cdots,P_m\right),\ \tilde{M}\triangleq\tilde{P}\tilde{W}\tilde{P}{'}$, we have the following optimization problem:
\begin{align}
&\underset{\tilde{x}(k), \mu(k)}{\operatorname{minimize}} \mu(k)' \tilde{M}^{-1} \mu(k) +\gamma \|\nu(k)\|_1\\
&\text {subject to } \begin{bmatrix}
P_1\zeta_{1}(k) \\
\vdots \\
P_m{\zeta}_{m}(k)
\end{bmatrix}=
\begin{bmatrix}
{H}_{1} \\
\vdots \\
{H}_{m}
\end{bmatrix} \tilde{x}(k)+\mu(k) +\nu(k).
\end{align}
Theorem 5
When all the eigenvalues of $A$ have geometric multiplicity $1$, the solution $\tilde{x}(k)$ of the above optimization problem is resilient against $p$-sparse attack if the system sparse observability index $s$ satisfy $s\geq 2p$.
Step 1 done !
Computational complexity reduced to NP.
Improvement from observability to detectability
Since the stable states will finally converge to 0, the estimation of stable states can be trivially secure.
We can further relax our condition to $2p$-sparse detectable.
Separate matrix $A$ into two parts:
\begin{equation*}
A=\left[\begin{array}{c} A^\mathcal{U} \ | \ \ A^\mathcal{S}\end{array}\right] ,\ \ x= \left[\begin{array}{c} x^\mathcal{U} \\ x^\mathcal{S}\end{array}\right]
\end{equation*}
For example:
Corollary 4.3
When all the unstable eigenvalues of $A$ have geometric multiplicity $1$, then
$$\text{Row}(O^\mathcal{U}_i)=\text{Row}(G^\mathcal{U}_i)=\text{Row}(H^\mathcal{U}_i),$$
where $$H^\mathcal{U}_i=\begin{bmatrix}\mathbb{I}\{O^{(1)}_i\neq 0\} && \\ &\ddots& \\ &&\mathbb{I}\{O^{(n_u)}_i\neq 0\}\end{bmatrix}.$$
We proceed to deal with stable part.
Terminology:
All the unstable eigenvalues of $A$ have geometric multiplicity $1$ $\Leftrightarrow$ Regular linear system
The least square problem we intend to solve looks like:
\begin{align*}
&\underset{x, \mu}{\operatorname{minimize}}\quad \frac{1}{2} \mu{'} \tilde{M}^{-1} \mu &\underset{x}{\operatorname{minimize}}\quad \frac{1}{2} \left({Y}-{H}x\right){'} \tilde{M}^{-1} \left({Y}-{H}x\right) \\
& \text{subject to }\quad
{Y}=
{H}x+\mu.
\end{align*}
We show the processing of state entries by a example where $n=2,m=1$ and ${H}=I_{2}$. Suppose $x_1$ is unstable entry and $x_2$ is stable entry.
\begin{align*}
&\frac{1}{2}\begin{bmatrix}
Y_1-x_1\\Y_2-x_2
\end{bmatrix}'\tilde{M}^{-1}
\begin{bmatrix}
Y_1-x_1\\Y_2-x_2
\end{bmatrix}+\frac{1}{2}Y_2^2
=\frac{1}{2}\begin{bmatrix}Y_1-x_1\\Y_2-x_2\\Y_2
\end{bmatrix}'\begin{bmatrix}
\tilde{M}^{-1} & 0\\ 0& I
\end{bmatrix}
\begin{bmatrix}
Y_1-x_1\\Y_2-x_2\\Y_2
\end{bmatrix}\\
=&\frac{1}{2}\left(\begin{bmatrix}
1 & &\\&1&\\&1&1
\end{bmatrix}\begin{bmatrix}Y_1-x_1\\Y_2-x_2\\x_2
\end{bmatrix}\right)'\begin{bmatrix}
\tilde{M}^{-1} & 0\\ 0& I
\end{bmatrix}
\left(\begin{bmatrix}
1 & &\\&1&\\&1&1
\end{bmatrix}
\begin{bmatrix}
Y_1-x_1\\Y_2-x_2\\x_2
\end{bmatrix}\right)
\end{align*}
By the aforementioned operation, we have the following two equivalent least square problems:
\begin{align*}
\underset{x}{\operatorname{minimize}}\quad \frac{1}{2} \left({Y}-{H}x\right){'} \tilde{M}^{-1} \left({Y}-{H}x\right)
\end{align*}
\begin{align*}
\underset{x}{\operatorname{minimize}}\quad \frac{1}{2}\begin{bmatrix}{Y}-{H}x\\ x^\mathcal{S}\end{bmatrix}^{'} \widehat{M}^{-1} \begin{bmatrix}{Y}-{H}x\\ x^\mathcal{S}\end{bmatrix}
\end{align*}
and accordingly, two LASSO:
\begin{align*}
\underset{x,\nu}{\operatorname{minimize}}\quad \frac{1}{2} \left({Y}-{H}x-\nu\right){'} \tilde{M}^{-1} \left({Y}-{H}x-\nu\right) +\gamma\|\nu\|_1
\end{align*}
\begin{align*}
\underset{x,\nu}{\operatorname{minimize}}\quad \frac{1}{2}\begin{bmatrix}{Y}-{H}x-\nu\\ x^\mathcal{S}\end{bmatrix}^{'} \widehat{M}^{-1} \begin{bmatrix}{Y}-{H}x-\nu\\ x^\mathcal{S}\end{bmatrix}+\gamma\|\nu\|_1
\end{align*}
They are equivalent when $\nu=0$.
By placing $X^\mathcal{S}$ on the second order term, we can prove that estimation error covariance of $x^\mathcal{S}$ is always bounded.
Define
\begin{align*}
&{N}\triangleq
I_{m} \otimes
\begin{bmatrix}
\mathbf{0}_{n_s\times n_u} & I_{n_s}
\end{bmatrix}
\in \mathbb{R}^{mn_s\times mn },\
\mathcal{W}\triangleq \begin{bmatrix}
\tilde{P}'^{-1}\tilde{W}^{-1}\tilde{P}^{-1} + {N}{'}{N} & {N}{'} \\
{N} & I
\end{bmatrix}.
\end{align*}
Theorem 6
When the system is regular, in the presence of arbitrary $p$-sparse attack, if the system $(A,C)$ is $2p$-sparse detectable, the estimation $\tilde{x}(k)$ solved from the following problem is secure.
\begin{align}\label{pb:resilient_LASSO}
\underset{{\tilde{x}}(k), \mu(k),\nu(k)}{\text{minimize}}&\quad \frac{1}{2}
\begin{bmatrix}
\mu(k) \\
{N} {H} \tilde{x}(k)
\end{bmatrix}^{'} \mathcal{W}
\begin{bmatrix}
\mu(k) \\
{N} {H} \tilde{x}(k)
\end{bmatrix} + \gamma\left\|\nu(k)\right\|_1 \\
\text { subject to }&\quad
{Y} (k)= {H} \tilde{x}(k)+\mu(k)+\nu(k) .
\end{align}
Fundamental Limit
If the system is not $2p$-sparse detectable, there exists a $p$-sparse attack strategy that no estimator is secure.
Proof idea:
Find an attack that yields same $y(k)$ while with different $x(0)$.
When $x(0)=0$ attack sensors in set $\mathcal{C_1}$, when $x(0)=\xi$, attack sensors in set $\mathcal{C_2}$.
This $\xi$ can be found because $$ \bigcap_{i\in\mathcal{I}\setminus \mathcal{C_1}\cup\mathcal{C_2} }\operatorname{Ker}(O_i) \neq \varnothing.$$
Summary
We proposed an resilient estimator in the presence of $p$ sparse attack for regular linear system.
Theory:
No attack: Coincides with Kalman for certain probability.
With attack: Resilient when $2p$ detectable, achieve fundamental limit.
Application:
Accuracy
Can recover optimal Kalman without attack. Has bounded error covariance under attack. $\gamma$ balances them.
Efficiency
Off-line computation: easy to calculate sparse observability/detectability index.
On-line computation: solve a strongly convex optimization problem.
Simulation
$$A=\begin{bmatrix}
1 & 2.0\cdot 10^{-2} & -2.0\cdot 10^{-4} & 1.9\cdot 10^{-5}\\
0 & 1.0\cdot 10^{0} & -2.0\cdot 10^{-2} & 1.8\cdot 10^{-3}\\
0 & 1.0\cdot 10^{-5} & 1.0\cdot 10^{0} & 2.0\cdot 10^{-2}\\
0 & 1.0\cdot 10^{-3}& 2.1\cdot 10^{-1} & 9.8\cdot 10^{-1}
\end{bmatrix}, C=\begin{bmatrix}1&0&0&0\\ 1&0&0&0\\ 1&0&0&0\\ 0&0&1&0 \end{bmatrix}$$
The system dynamic matrix can be written as the following Jordan canonical form by an invertible linear transformation:
$$
\text{diag}(1.057,1,0.999,0.925),
$$
and we consider the system after transformation. System matrix $A$ have four Jordan blocks with size $1\times1$ and the upper left two blocks have unstable eigenvalues. Therefore, the set of unstable states and stable states are $\mathcal{U}=\{1,2\},\mathcal{S}=\{3,4\}.$
The canonical form of $G_i^\mathcal{U}$ are
\begin{align}
H_1^\mathcal{U}=H_2^\mathcal{U}=H_3^\mathcal{U}=\begin{bmatrix}
1 & 0 \\
0 & 1 \\
0 & 0 \\
0 & 0
\end{bmatrix},\ H_4^\mathcal{U}=\begin{bmatrix}
0 & 0 \\
0 & 1 \\
0 & 0 \\
0 & 0
\end{bmatrix}.
\end{align}
Only the first 3 sensors can observe unstable state 1, and all the four sensors can observe unstable state 2$.
Therefore, the system is 2-sparse detectable and our proposed estimator is secure in the presence of 1 corrupted sensor.
Random data injection attack
Random data injection attack
Resilient Estimation for Model Racecar Drifting Control
Sensors:
IMU
ZED Stereo Camera
2D LiDAR
Goal
On-board sensor State Estimation for aggressive Driving
Challenge
IMU: Violent vibration cause inaccurate
Stereo Camera: Image distortion
LiDAR: Slow matching speed
Sensor comparison
Camera+IMU coarse estimation:
High frequency (100Hz)
No out liers or interrupt
Drifting growing error
Camera+IMU coarse estimation:
Low frequency (30-60Hz)
Out liers and interrupt
No drifting growing error
Preliminary works
X. Liu, Y. Mo and E. Garone, Local Decomposition of Kalman Filters and its Application for Secure State Estimation, in IEEE Transactions on Automatic Control, vol. 66, no. 10, pp. 5037-5044, Oct. 2021, doi: 10.1109/TAC.2020.3044854.
Publishing paper
ZiShuo Li, Yilin Mo, Low Complexity Secure State Estimation Design for Linear System with Non-derogatory Dynamics, 2021 IEEE 60th Conference on Decision and Control (CDC), 2021, accepted.
ZiShuo Li, Yilin Mo, Efficient Secure State Estimation against Sparse Integrity Attack for System with Non-derogatory Dynamics, in International Journal of Robust and Nonlinear Control, 2nd round review.
Future Work
Asynchronous Non-uniform Sampled Measurements
Distributed Resilient Estimation
The slides can be seen at
https://zs-li.github.io/talk/resi_est/index.html
欢迎提问！


Beginning at the top left in the toolbar, there are the three buttons , and . The button applies all changes and closes the window. The button applies all changes but does not close the window. The button closes the window without applying the changes to the data item. Note that changes you make to individual data points are applied immediately.
With the button at the right top you can select the drawing style of the
function.
With the button you open a
dialogbox where you can open a file that contains data.
In the textbox at the top you can enter a name for the data. This name will appear in the legend.
Below the toolbar you can choose how many dimensions your data points will have, either 1, 2 or 3, and you can choose if your data points have error estimates.
Below you can edit the data in a table.
In the first data-row of the table (denoted with a "=" at the left) you can enter a formula for the
corresponding data-column. The formula must be an ordinary C# expression. You can refer to the varaibles n
, Length
,
x[n]
, y[n]
, dx[n]
and dy[n]
in this expression.
n
denotes the current row index and Length
denotes the number of data points.
Alternatively you can enter the columns data into the data fields of the table. If you enter some data in the last row, the table is extended by one row.


A custom framework for working with Type 1 Fuzzy Logic, produced by the University of Nottingham IMA Group.
| Version: | 1.0 |
| Depends: | R (≥ 2.15.1), splines |
| Published: | 2013-04-26 |
| Author: | Craig Knott, Luke Hovell, Nathan Karimian with supervision from Dr. Jon Garibaldi |
| Maintainer: | Jon Garibaldi <jon.garibaldi at ima.ac.uk> |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| URL: | http://ima.ac.uk |
| NeedsCompilation: | No |
| CRAN checks: | FuzzyToolkitUoN results |
| Reference manual: | FuzzyToolkitUoN.pdf |
| Package source: | FuzzyToolkitUoN_1.0.tar.gz |
| Windows binaries: | r-devel: FuzzyToolkitUoN_1.0.zip, r-release: FuzzyToolkitUoN_1.0.zip, r-oldrel: FuzzyToolkitUoN_1.0.zip |
| OS X binaries: | r-release: FuzzyToolkitUoN_1.0.tgz, r-oldrel: FuzzyToolkitUoN_1.0.tgz |
Please use the canonical form https://CRAN.R-project.org/package=FuzzyToolkitUoN to link to this page.


Fulton Reunion 1946
(See the picture below for the identification of
individuals. If you can add
Names to any of the individuals, please contact the
webmaster at R.E. Harrington.
On back of picture
Photo taken: August 14, 1946
|
# |
Name |
# |
Name |
# |
Name |
|
|
|
|
|
|
|
|
1 |
|
11 |
|
21 |
Ida Fulton Montgomery |
|
2 |
|
12 |
Marjorie Alberta Parks |
22 |
Howard Fulton Parks |
|
3 |
|
13 |
|
23 |
Mary Jane Fulton Parks |
|
4 |
|
14 |
|
24 |
Dr. Everett Fulton |
|
5 |
Mary Jane Feldner |
15 |
Luella Elizabeth Huddle Parks |
25 |
Alice Fulton Kasserman |
|
6 |
|
16 |
|
26 |
Everett Parks |
|
7 |
|
17 |
Rolande Cardinal Parks |
27 |
Katherine Fulton Holden |
|
8 |
|
18 |
|
28 |
Robert Charles Parks |
|
9 |
Mary Jane Feldner
Kamp |
19 |
Charles Parks |
|
|
|
10 |
|
20 |
Ribert Charles Parks |
|
|
The following note is from Kym
Kittell. I
will leave it here temporarily so the rest of you can know where it comes from
and decide if you agree. Any of these
names can be changed. Please let me know
what you think and add any names you can.
Let s try to put names on everyone in the picture. Use the number on the person s body (or near
their head if there is no body showing).
In photo 14, my mother, Marjorie Alberta Parks, is standing just behind the tallest of the little girls. Her head is turned to her right and she is talking with Julie's mom, Mary Jane Feldner. I believe the woman in the middle, back against the building in the polka dot dress is my aunt, Luella Elizabeth Huddle Parks, first wife of Howard Fulton Parks. I'm not sure, but that might be Howard's head further right in the very back peeking through the older ladies in front. The blurry man on the right edge of the photo looks a bit like my uncle, Robert Charles Parks, but that is a guess. The woman to my mother's left, might be Rolande Cardinal Parks, Robert's wife. Or that might be Robert standing to Rolande's right, barely visible. Comparing with #11, I think the elderly woman with her hand touching the littlest girl might be my grandmother, Mary Jane Fulton Parks. She is in #13 too. What do the rest of you think?
The following note is from Julia Kamp
1-8 Unsure or unknown
9. Mary Jane feldner Kamp - my mother
10-11 unsure or
unknown
12 Aunt Marjorie
Parks Kittell -kym's mother
13-14 unknown or
unsure
15 Aunt Luella
Parks
16 unsure
17 Rolande Parks
18 unsure
19 Charles
Parks
20 Ribert Charles Parks
21 Ida Fulton
Montgomery
22 Howard Parks
23 Mary Jane
Fulton Parks
24 Dr. Everett
Fulton
25 Alice FUlton Kasserman
26 Everett Parks
27 Katherine
Fulton Holden
No 13 - 14
-18 Could be Elizabeth Parks Rubrake, Sally
Parks, KItty Jo Parks, if these are the girls I
wonder where their parents are in the Picture, Clyde and Mary Parks, Helen
Parks, Everett Parks wife.
I also wonder
where my grandmother Dorothy Parks Feldner is in the
picture since my mom is in the photo. I have sent the
picture on to Patsy Parks Lawrence, and have not heard back on if she knows if
that the little girls in the front are her sisters Sally and Kitty Jo. Julie, did
you ever hear back from Patsy Parks Lawrence on this??? Dick
Julie, also notice that Kym thought that
# 21 might be Mary Jane Fulton Parks, but she was uncertain. I have renamed # 21 to Ida Fulton Montgomery
as you had called her. Are you comfortable
with the current names? Do you know of
anyone else we might ask who might be able to fill in some of the blanks?
Photo # 12-2
Provided by Julia Kamp
Click here for the Short-Cut Table of Contents


Select skills to see projects
code, coding, programming, software engineer, software developer, mean stack, web development, development, engineering, node.js, angular.js, express.js, mongoDB, javascript, open source, frontend development, frontend, CSS, SVG, angular, restAPI, rest, freelancer, freelance, SEO, coding4lifeblog, freecodecamp, IOG-Austria, engineers without borders,
HTL Pinkafeld, developer's rising, FCC Vienna, webclerks, sector5, metalab


Hi <%= buyer.name %>,
Congratulations! The purchase of <%= itemSold.name %> is completed successfully! 🎉
Contact the seller for the delivery. The details are given below.
Be sure to be on the lookout for more such steals at https://rishabhrawat.tech/item/sell.
Happy flipping! 🎉🎉🎉
- Flipit Support.


Common Foot Problems
Dr. Langford treats foot and ankle problems for people of all ages, from infants to the elderly. Anyone experiencing warning signs such as pain, redness, swelling, cramping, numbness, itching, burning or abnormal shoe wear should be examined by a podiatrist. Chronic conditions that once meant years of pain, inconvenience and expense, can now be corrected or controlled.
For more information on these common foot problems please refer to the Family Foot Health Specialists' Resource Page
Common Foot Problems Treated By Dr. Langford
Reconstructive Foot Surgery
- Bunions
- Hammertoes
- Heel Pain
- Flat Feet
- Cavus Feet (high arch)
- Club Feet
- Birth Defects
- Tumor/Masses
- Fractures (broken bones)
Children's Deformities
- Gait Problems (walking)
- Intoe/Outtoe
- Flat Feet
- Birth Defects
Sports Medicine
- Foot/Ankle Sprains
- Foot/Ankle Fractures
- Jogger's/Runner's Syndromes
Dermatology
- Ingrown Nails
- Fungus/Bacterial Nail Infections
- Athlete's Feet
- Skin Problems
- Soft Tissue Infections
Vascular Problems
- Swelling
- Cramping
- Discoloration


Spark Connect Overview
Building client-side Spark applications
In Apache Spark 3.4, Spark Connect introduced a decoupled client-server architecture that allows remote connectivity to Spark clusters using the DataFrame API and unresolved logical plans as the protocol. The separation between client and server allows Spark and its open ecosystem to be leveraged from everywhere. It can be embedded in modern data applications, in IDEs, Notebooks and programming languages.
To get started, see Quickstart: Spark Connect.
How Spark Connect works
The Spark Connect client library is designed to simplify Spark application development. It is a thin API that can be embedded everywhere: in application servers, IDEs, notebooks, and programming languages. The Spark Connect API builds on Spark’s DataFrame API using unresolved logical plans as a language-agnostic protocol between the client and the Spark driver.
The Spark Connect client translates DataFrame operations into unresolved logical query plans which are encoded using protocol buffers. These are sent to the server using the gRPC framework.
The Spark Connect endpoint embedded on the Spark Server receives and translates unresolved logical plans into Spark’s logical plan operators. This is similar to parsing a SQL query, where attributes and relations are parsed and an initial parse plan is built. From there, the standard Spark execution process kicks in, ensuring that Spark Connect leverages all of Spark’s optimizations and enhancements. Results are streamed back to the client through gRPC as Apache Arrow-encoded row batches.
Operational benefits of Spark Connect
With this new architecture, Spark Connect mitigates several multi-tenant operational issues:
Stability: Applications that use too much memory will now only impact their own environment as they can run in their own processes. Users can define their own dependencies on the client and don’t need to worry about potential conflicts with the Spark driver.
Upgradability: The Spark driver can now seamlessly be upgraded independently of applications, for example to benefit from performance improvements and security fixes. This means applications can be forward-compatible, as long as the server-side RPC definitions are designed to be backwards compatible.
Debuggability and observability: Spark Connect enables interactive debugging during development directly from your favorite IDE. Similarly, applications can be monitored using the application’s framework native metrics and logging libraries.
How to use Spark Connect
Starting with Spark 3.4, Spark Connect is available and supports PySpark and Scala applications. We will walk through how to run an Apache Spark server with Spark Connect and connect to it from a client application using the Spark Connect client library.
Download and start Spark server with Spark Connect
First, download Spark from the Download Apache Spark page. Spark Connect was introduced in Apache Spark version 3.4 so make sure you choose 3.4.0 or newer in the release drop down at the top of the page. Then choose your package type, typically “Pre-built for Apache Hadoop 3.3 and later”, and click the link to download.
Now extract the Spark package you just downloaded on your computer, for example:
In a terminal window, go to the spark
folder in the location where you extracted
Spark before and run the start-connect-server.sh
script to start Spark server with
Spark Connect, like in this example:
Note that we include a Spark Connect package (spark-connect_2.12:3.4.0
), when starting
Spark server. This is required to use Spark Connect. Make sure to use the same version
of the package as the Spark version you downloaded previously. In this example,
Spark 3.4.0 with Scala 2.12.
Now Spark server is running and ready to accept Spark Connect sessions from client applications. In the next section we will walk through how to use Spark Connect when writing client applications.
Use Spark Connect in client applications
When creating a Spark session, you can specify that you want to use Spark Connect and there are a few ways to do that outlined as follows.
If you do not use one of the mechanisms outlined here, your Spark session will work just like before, without leveraging Spark Connect, and your application code will run on the Spark driver node.
Set SPARK_REMOTE environment variable
If you set the SPARK_REMOTE
environment variable on the client machine where your
Spark client application is running and create a new Spark Session as in the following
example, the session will be a Spark Connect session. With this approach, there is no
code change needed to start using Spark Connect.
In a terminal window, set the SPARK_REMOTE
environment variable to point to the
local Spark server you started previously on your computer:
And start the Spark shell as usual:
The PySpark shell is now connected to Spark using Spark Connect as indicated in the welcome message:
And if you write your own program, create a Spark session as shown in this example:
This will create a Spark Connect session from your application by reading the
SPARK_REMOTE
environment variable we set previously.
Specify Spark Connect when creating Spark session
You can also specify that you want to use Spark Connect explicitly when you create a Spark session.
For example, you can launch the PySpark shell with Spark Connect as illustrated here.
To launch the PySpark shell with Spark Connect, simply include the remote
parameter and specify the location of your Spark server. We are using localhost
in this example to connect to the local Spark server we started previously:
And you will notice that the PySpark shell welcome message tells you that you have connected to Spark using Spark Connect:
You can also check the Spark session type. If it includes .connect.
you
are using Spark Connect as shown in this example:
Now you can run PySpark code in the shell to see Spark Connect in action:
Or, when writing your own code, include the remote
function with a reference to
your Spark server when you create a Spark session, as in this example:
Client application authentication
While Spark Connect does not have built-in authentication, it is designed to work seamlessly with your existing authentication infrastructure. Its gRPC HTTP/2 interface allows for the use of authenticating proxies, which makes it possible to secure Spark Connect without having to implement authentication logic in Spark directly.
What is supported in Spark 3.4
PySpark: In Spark 3.4, Spark Connect supports most PySpark APIs, including DataFrame, Functions, and Column. However, some APIs such as SparkContext and RDD are not supported. You can check which APIs are currently supported in the API reference documentation. Supported APIs are labeled “Supports Spark Connect” so you can check whether the APIs you are using are available before migrating existing code to Spark Connect.
Scala: In Spark 3.4, Spark Connect supports most Scala APIs, including Dataset, functions, and Column.
Support for more APIs is planned for upcoming Spark releases.


MY GIRL A film review by Randy Parker Copyright 1996 Randy Parker
RATING: **1/2 (out of ****)
(Review written in 1991)
MY GIRL ultimately takes you on a road to nowhere, but at least the ride there is reasonably pleasant.  Chlumsky spends her time hanging out with best pal Macaulay Culkin (HOME ALONE), while her inattentive father (Dan Aykroyd) embarks on an unlikely romance with beautician Jamie Lee Curtis. Over the course of the movie, Chlumsky comes to terms with death and learns to accept Curtis as a mother figure.
Unfortunately, this paper-thin premise doesn't lead to anything meaningful. For starters, the performances are perfunctory. It's hard to blame the actors, however, when their characters are so underwritten. The movie fails to harvest the talents of Curtis and Culkin, though Griffin Dunne is appealing as Chlumsky's English teacher. A bigger problem: the dramatic scenes, which should have been sensitive and heartfelt, are heavy-handed and cliched.
--- Randy Parker<EMAIL_ADDRESS>http://www.shoestring.org
The review above was posted to the
rec.arts.movies.reviews newsgroup (de.rec.film.kritiken for German reviews).
The Internet Movie Database accepts no responsibility for the contents of the
review and has no editorial control. Unless stated otherwise, the copyright
belongs to the author.
Please direct comments/criticisms of the review to relevant newsgroups.
Broken URLs inthe reviews are the responsibility of the author.
The formatting of the review is likely to differ from the original due
to ASCII to HTML conversion.
Related links: index of all rec.arts.movies.reviews reviews


General
Buttons
block
- input[type=button].btn
- button.btn
-
- span.btn
- span
modifiers
- aria-pressed=true
-
span
- disabled
-
span
- hover or focused
- try it out on the above
Anchors
block
- with href attribute
- 404.html
- with empty href attribute
- where am I going?
- without href attribute
- what kind of anchor is this?
modifiers
- same-page
- #target
- current-page
- not accessible vs aria-describedby =
current
- same-domain
- 404.html
- cross-domain or target _blank
- my portfolio
- skiplink
- refresh and press tab


You have asked to reset your login to {{project.title}}.
Please click here to choose another password
{{config.email.signoff}}


To start splitting your bills you have to first create a session. To do this go to create and fill the form. The page will respond with a pin, save this somewhere safe. By creating a session you allow all your friends to add what they paid from their own device.
To add a payment go to edit. Use your pin (the one you saved somewhere safe!) to access your session and add your payment.
Note: the cost should be a numeric value. Inputs like $15.05 or 3.95 dollars won't get processed by the app.
 By splitting you get your session's whole history (payments by each person with date, description and cost) and who owns who.


Drider Project
Online
Lobbies
New Lobby
An icon-only button
Online Users
Welcome,
Send
Do you want to create a new lobby?


Toggle theme
Documentation
Manifest
Provide HTML and CSS for custom components
Only layout – No design (well, almost no design)
No pre-processors
No JavaScript (We made some for demo-purposes)
Modular down to atom. Pick only what you need.
Components : Actions and Input
Button
Normal
Disabled
Checkbox
I'm ticky small
I'm ticky medium
I'm ticky big
Switch
I make a small switch
I make a medium switch
I make a large switch
I make a medium switch
Components : Content
Modal
Open modal
My fresh modal
Close
Some text goes here…
Components : Navigation
Bar
Item 1
Item 2
Item 3
Item A
Item B


-
Generators
The
geddy-gen
utility is your friend. Creating an app is a snap withgeddy-gen app
. Create resources and models for your app withgeddy-gen resource
andgeddy-gen model
. -
Flexible DSL for routes
Intuitive syntax for creating routes — just
match
paths and paramsto
controllers and actions. Set up resource-based routes with the uber-simpleresource
, or letgeddy-gen
do it for you. -
Content negotiation
Serve out your RESTful resources in whatever format you want — HTML, JSON, even XML (if you're into that type of thing). Geddy looks at the file extension and the accept-header, and does the right thing.
-
Templates and partials
Geddy does EJS templating, with recursive partials support. Templates and sub-templates load and render asynchronously. Yes, pluggable templates are on the way for you fans of 'stache, Haml, et al.
-
Models and validations
Should look familiar to users of DataMapper or SQLAlchemy. A simple, intuitive syntax for defining properties and validations — but the code is pure JS, which allows sweet, sweet code-reuse in the browser.
-
JavaScripty goodness
Geddy is built on Node.js, a JavaScript I/O system that uses Google's V8 engine. Node.js is very fast — but you get to use the JavaScript we all know and love (okay, maybe that's stretching it) from the browser.
Get started
Geddy is a web framework for Node.js. Geddy requires version 0.1.94 of Node.js.
Get Geddy from GitHub and install it:
$ ~/work$ git clone git://github.com/mde/geddy.git $ ~/work$ cd geddy $ ~/work$ make && sudo make install
Create a Geddy app
Geddy comes with a utility called geddy-gen
you can use to create an app. Run geddy
to start the server.
$ ~/work$ geddy-gen app bytor Created app bytor. $ ~/work$ cd bytor $ ~/work/bytor$ geddy Server running at http://<IP_ADDRESS>:4000/
Community
Geddy is very new, so now is a great time to get involved in the community. You can find Geddy peeps in a variety of places online:


Page heading
Has role and should be highlighted
No role. Shouldn't be highlighted
This is just a paragraph. It should not have an Accessible name
Heading has empty accessible name
Files
This is not from author, so won't be highlighted
Some text
60%
A meter
A section
This is the term element
Article element
Some blockquote text
The premiere show starts at today.
Contest Entrants
This table shows the total number of entrants (500) the contest accepted over
the past four weeks.
Let x = 10
New Tests
An unordered list. Highlight
An unordered second list. No highlight
An ordered list. Highlight
An ordered second list. No highlight
- orange
-
mango


%UseLnInsteadOfLog
TurnOffApproximations(0);
aCoeff=RandomInteger{}( (1,2));
bCoeff=RandomInteger{}( -5,5);
cCoeff=RandomInteger{}( (-3,3));
leftPoint=RandomInteger{}(-4,4);
rightPoint=leftPoint+RandomInteger{}( (1,5));
curve1= x^2+bCoeff x +cCoeff;
curve2= aCoeff (x-leftPoint)(x-rightPoint) + curve1;
theDifference=curve1-curve2;
theInt=\int theDifference dx;
TurnOffRules
("IntegratePowerRule",
"ConvertShortDenominatorToNegativePower", "IntegrateBlockIb",
"IntegratePartialFractions", "CommonDenominator", "CommonDenominatorOneNonFraction");
PlotFill(
Plot2D(curve1, leftPoint,rightPoint)
+Plot2D(curve2, rightPoint, leftPoint)
, cyan)
+Plot2D(curve1, leftPoint-1,rightPoint+1)
+Plot2D(curve2, leftPoint-1,rightPoint+1)
+PlotWindow(300,300)
Find the area locked between the curve \(y=
\displaystyle curve1
\) and the curve \(y=
\displaystyle curve2
\). Do not include units in your answer.
Answer:
AlgebraAnswer==(x=rightPoint; theInt)_2-(x=leftPoint; theInt)_2
TurnOnRules
("DistributeMultiplication", "IntegratePowerRule",
"ConvertShortDenominatorToNegativePower", "IntegrateBlockIb",
"IntegratePartialFractions");
EnsureExpressionDependsOnlyOn(AlgebraAnswer,none)
(x=rightPoint; theInt)_2-(x=leftPoint; theInt)_2
finalAnswer=(x=rightPoint; theInt)_2-(x=leftPoint; theInt)_2;
TurnOffRules("PowerIntegerByInteger", "PowerRationalByRational",
"CombineExponents", "AddRationals", "AddTerms", "MultiplyRationals", "ConstantExtraction");
leftSub=(x=leftPoint; theInt)_2;
rightSub=(x=rightPoint; theInt)_2;
We start by finding the intersection of the two curves.
\(
EvaluateSymbols{}(
"\begin{array}{rcll|l}
curve1&=&curve2 &&\text{Transfer~all~terms~to~one~side}\\\\
theDifference&=&0&& \displaystyle \text{Solve~using~}x_1,x_2=\frac{-b\pm \sqrt{b^2-4 a c}}{2a}\\\\
x_1&=&leftPoint\\\\
x_2&=&rightPoint
\end{array}
")
\)
Since both parabolas open upwards, the ``steeper'' (higher leading coefficient)
parabola must be the lower one (as seen on the computer generated plot).
Therefore, between the two intersection points, we have that
curve1>curve2,
and so the area \(A\) between the two curves becomes:
\(
EvaluateSymbols{}(
"\begin{array}{rcll|l}
A&=&\displaystyle \int_{leftPoint}^{rightPoint} \left|curve1-\left(curve2\right) \right|{\text d} x && curve1>curve2,
\text{so~we~can~drop~the~absolute~values}\\\\
&=&\displaystyle \int_{leftPoint}^{rightPoint} \left(curve1-\left(curve2\right) \right){\text d} x\\\\
&=&\displaystyle \int_{leftPoint}^{rightPoint} \left(theDifference \right){\text d} x\\\\
&=&\displaystyle \left[theInt\right]_{leftPoint}^{rightPoint} \\\\
&=&\displaystyle \left(rightSub\right)-\left(leftSub\right)\\\\
&=&\displaystyle finalAnswer
\end{array}
")
\)


--- layout: post date: 2009-08-24 time: "11:00:00" authors: ["Greg Wilson"] title: Science and JoVE tags: ["Noticed"] ---
Science and JoVE, the Journal of Visualized Experiments, have partnered to produce and publish scientific videos online. The aim is to enhance scientific articles published in Science through video demonstrations of experimental techniques. See the announcement for a link to the first joint work.


Circle Center (Lat,Long)
Linestring Coordinates (Eg: [[-77.03, 38.89], [-77.05, 38.88]])
[[-77.03, 38.89], [-77.05, 38.88]]
[[-77.03, 38.89], [-77.05, 38.88],...,[-77.03, 38.89]]


{% comment %} Display episode's timings and learning objectives. Regarding the `if page.*** == nil` below: all-in-one page combines all episodes into one. It, therefore, does not define its own objectives, exercises, and questions, which 'normal' episodes define in the front matter. To display episodes' teaching and exercise times, as well as episode questions and objectives, we pass them as parameters to the Liquid's `include` statement when we generate the page: include episode_overview.html teaching_time=e.teaching ... Here we obtain the information we need either from the episode itself or from the parameters passed in. {% endcomment %} {% if page.teaching == nil %} {% assign teaching_time = include.teaching_time %} {% else %} {% assign teaching_time = page.teaching %} {% endif %} {% if page.exercises == nil %} {% assign exercise_time = include.exercise_time %} {% else %} {% assign exercise_time = page.exercises %} {% endif %} {% if page.questions == nil %} {% assign episode_questions = include.episode_questions %} {% else %} {% assign episode_questions = page.questions %} {% endif %} {% if page.objectives == nil %} {% assign episode_objectives = include.episode_objectives %} {% else %} {% assign episode_objectives = page.objectives %} {% endif %}
Overview
Teaching: {{ teaching_time }} min
Exercises: {{ exercise_time }} minQuestions{% for question in episode_questions %}
- {{ question|markdownify }}
{% endfor %}Objectives{% for objective in episode_objectives %}
- {{ objective|markdownify }}
{% endfor %}


Calcite Bootstrap
Calcite Bootstrap is an Esri custom theme and a custom build system for Bootstrap 3. The theme is based on Calcite Web - a web adaptation of Calcite, the desktop framework for ArcGIS Pro. Calcite Bootstrap was built for developers who have experience working with Bootstrap and would like to use the Calcite theme in their web pages and apps.
To find out more about how to setup this theme or about the changes between v0.3.2 and the latest version, visit Get Started.
There are four types of alerts: .alert-info
,.alert-success
,.alert-warning
,.alert-danger
.
Writing an alert looks like:

Well done! You successfully read this important alert message.

Panels may also be given alert states; however, a panel alert state only affects the .panel-heading
and border-color, so stick with alerts in error handling and form validation.
Panel title

Panel title

Panel content

Badges can be added to stand-alone links or used within Navs.
Inbox 42
To achieve breadcrumb styling, use an ordered list with the .breadcrumb
class. This will inject the forward slash in between link items as well as bold the active item.

Home

Library

Data

Example using the

tags.
This is simply a

with the .lead
class on it.
There are 7 types of buttons.
| Button Class | Style |
.btn-default |
white button, blue text/border |
.btn-primary |
blue button, white text |
.btn-info |
white button, gray text |
.btn-success |
green button, white text |
.btn-warning |
yellow button, gray text |
.btn-danger |
white button, red text/border |
.btn-link |
transparent button, blue text |
Button size can be changed by including .btn-xs
, .btn-sm
, and .btn-lg
. By default all buttons and inputs use the equivalent of .btn-md/.input-md
, although this is not explicitly set.
<button type="button" class="btn btn-default">Default</button>
<button type="button" class="btn btn-primary">Primary</button>
<button type="button" class="btn btn-success">Success</button>
<button type="button" class="btn btn-info">Info</button>
<button type="button" class="btn btn-warning">Warning</button>
<button type="button" class="btn btn-danger">Danger</button>
<button type="button" class="btn btn-link">Link</button>
Anything using button classes can be disabled. Both <button>
and
will require the .disabled
class in order to inherit disabled styling. However, only actual <button>
can be disabled from selection with the disabled
property. Rather than attempting to disable a link with button classes, one should use the .btn-link
class to make their <button>
appear to be a text link instead.
Link Link Link Link Link Link Link Link Link Link Link Link
For implementation of carousel, refer to Bootstrap Documentation.
Carousels require inclusion of Bootstrap 3.3 Javascript: https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/js/bootstrap.min.js
For implementation of dropdown menu, refer to Bootstrap Documentation.
Dropdown menus require inclusion of Bootstrap 3.3 Javascript: https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/js/bootstrap.min.js
All related form elements belong inside a .form-group
. This may include a
,<input>
, and a
containing errors or help text. By appending .has-error
,.has-warning
, or .has-success
on the .form-group
, this will change the input border color to the corresponding warning and any
tags containing the .help-block
class to the matching text-color of that input border. (When using .help-block
, it must be used on
tags to inherit error colors.

will not work.)
It is important to also use a for
attribute on the label with a matching id
on the input to associate the
with the <input>
for assistive technologies. In addition, using aria-describedby
with a matching id
on any error messages will make sure assistive technologies relate the error to the correct input.

Input with error
<input type="text" class="form-control" id="inputError1" aria-describedby="helpBlock2">
The best way to write accessible errors. If not doing it this way, errors should be sandwiched between associated label and input.

Form - Validation States (Labels Hidden)
Labels can be hidden from sighted users, but stay present for assistive technologies by using the .sr-only
class on the
.

Home Address
<input type="text" class="form-control" placeholder="Home Address" id="thing1">

Alert Symbology
To display alert style icons, the .with-addon-alert
class must be added to the <input>
and the
displaying the glyphicon must use the corresponding .input-group-addon
and as above there should be an aria-describedby
on the <input>
that associates it with an id
on the
.

Input with error
<input type="text" class="form-control with-addon-alert" placeholder="Email Address" id="inputError2" aria-describedby="error-state-addon">

Input with warning
<input type="text" class="form-control with-addon-alert" placeholder="Service Start Date" id="inputWarning2" aria-describedby="warning-state-addon">

Input with success
<input type="text" placeholder="Pet's Name" class="form-control with-addon-alert" id="inputSuccess2" aria-describedby="success-state-addon">

Labels look very similar to badges, but use a less exaggerated border-radius and use the same colors for default, primary, success, info, warning, and danger as seen on buttons.
 This style can be achieved with a .list-group
containing .list-group-items
made into links.
Supplemental classes that may be used within a .list-group-item
are .list-group-item-heading
and .list-group-item-text
.
- Cras justo odio
- Dapibus ac facilisis in
- Morbi leo risus
- Porta ac consectetur ac
- Vestibulum at eros
List group item heading
Donec id elit non mi porta gravida at eget metus. Maecenas sed diam eget risus varius blandit.
List group item heading
Donec id elit non mi porta gravida at eget metus. Maecenas sed diam eget risus varius blandit.
List group item heading
Donec id elit non mi porta gravida at eget metus. Maecenas sed diam eget risus varius blandit.
Modal structure is very important to achieving a Calcite look. Within .modal-content
there must be a .modal-header
that contains the .close
button and modal titles must use the

element. In addition, the modal needs to use .modal-body
for the main content and .modal-footer
for any action buttons. If these three inner modal regions are not used, then the padding for entire modal will not be consistent.
Cancel or Close buttons should use .btn-default
and be positioned to the left of the dominant action button, which should use .btn-primary
.
For implementation of modals, refer to Bootstrap Documentation.
Note: Modal styling has been hacked to show example.
Modals require inclusion of Bootstrap 3.3 Javascript: https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/js/bootstrap.min.js

<button aria-label="Close" class="close" data-dismiss="modal" type="button">x</button>

Modal title

One fine body…

<button class="btn btn-default" data-dismiss="modal" type="button">Close</button> <button class="btn btn-primary" type="button">Save changes</button>

To achieve the classic Calcite top navigation style, use Bootstrap's .navbar-default
in conjunction with .navbar-fixed
or .navbar-static
to set whether it should remain affixed to the top of the page or scroll with the page. Using .navbar-inverse
rather than .navbar-default
will produce a dark gray navbar with white text. Use of the .container
class within the navbar will keep navigation from going beyond a fixed width. Use of .container-fluid
will produce a fluid-width navbar.
The collapsing functionality of navbars requires inclusion of Bootstrap 3.3 Javascript: https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/js/bootstrap.min.js

<button aria-controls="navbar" aria-expanded="false" class="navbar-toggle collapsed" data-target="#navbar" data-toggle="collapse" type="button">Toggle navigation   </button> Bootstrap theme

Home

About

Contact

Dropdown

Action

Another action

Something else here

Nav header

Separated link

One more separated link

.nav-pills
is recommended for inline tertiary navigation in full-page layouts and can be used in conjunction with .nav-stacked
to get a style very similar to the mobile view of .navbar-default
.

Home

Profile

Messages

For secondary navigation, .nav-tabs[role="navigation"]
should be used for subnav within the navbar experience and .nav-tabs[role="tablist"]
for standard tab interfaces. Wrapping .nav-tabs
in .secondary-nav
will remove the nav-tab bottom border for a cleaner line.

Home

Profile

Messages

Tab panes require inclusion of Bootstrap 3.3 Javascript: https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/js/bootstrap.min.js

Home

Profile

Messages

Settings

Tab pane content

Tab pane content

Tab pane content

Tab pane content

For implementation of pagination, refer to Bootstrap Documentation.
For implementation the pager, refer to Bootstrap Documentation.
Panels are composed of three parts: .panel-heading
,.panel-body
, and .panel-footer
; however, unlike modals, a given panel may include only one or all of these parts.
Panel title
Panel title
Panel title
Panel title
Panel title
Panel title

Panel title

Panel content

Panel footer

For implementation of popovers, refer to Boostrap Documentation.
Popovers require inclusion of Bootstrap 3.3 Javascript: https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/js/bootstrap.min.js
Note: Popover styling has been hacked to show example, do not use the code of this popover.
Popover top
Sed posuere consectetur est at lobortis. Aenean eu leo quam. Pellentesque ornare sem lacinia quam venenatis vestibulum.
For implementation of progress bars, refer to Bootstrap Documentation.
All table styling should be handled automatically, except for .blue-table
which is an additional class within the calcite-bootstrap-expansion.scss file that will achieve the blue table seen in Calcite Web.
Table customizations may occur by overwriting the table variables set by Calcite Bootstrap. For those using SASS, $table-bg-accent
controls the alternating background row color. To get a mobile-friendly table, adding a

around a

will allow horizontal scrolling of the table on small devices.
Alert background colors can also be added to table rows or cells by using .active
,.success
,.info
,.warning
,.danger
.
For implementation of tables, refer to Bootstrap Documentation.
| # | First Name | Last Name | Username |
|---|---|---|---|
| 1 | Mark | Otto | @mdo |
| 2 | Jacob | Thornton | @fat |
| 3 | Larry | the Bird |
| # | First Name | Last Name | Username |
|---|---|---|---|
| 1 | Mark | Otto | @mdo |
| 2 | Jacob | Thornton | @fat |
| 3 | Larry | the Bird |
| # | First Name | Last Name | Username |
|---|---|---|---|
| 1 | Mark | Otto | @mdo |
| Mark | Otto | @TwBootstrap | |
| 2 | Jacob | Thornton | @fat |
| 3 | Larry the Bird |
| # | First Name | Last Name | Username |
|---|---|---|---|
| 1 | Mark | Otto | @mdo |
| 2 | Jacob | Thornton | @fat |
| 3 | Larry the Bird |
For implementation of progress bars, refer to Bootstrap Documentation.
Tooltips require inclusion of Bootstrap 3.3 Javascript: https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/js/bootstrap.min.js
Note: Tooltip styling has been hacked to show example, do not use the code of this tooltip.
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EZ Notes is simply the fastest most flexible organizer for Android Smartphones. Simplification of common tasks combined with single tap auto saving features dramatically boost mobility and time savings. For example, our One-of-a-Kind (award winning) Voice Notes pop-up and save instantly, without any Additional Steps or hindrances found in other Apps. Editing can be done at any time of user convenience, but not when the person is rushed and wants to instantly take advantage of our "Hands-Free" voice note features !
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| System.Int32 | num_filter | Input filter. Only used by bilinear sample_type.Since bilinear upsampling uses deconvolution, num_filters is set to the number of channels. |
| UpsamplingMultiInputMode | multi_input_mode | How to handle multiple input. concat means concatenate upsampled images along the channel dimension. sum means add all images together, only available for nearest neighbor upsampling. |
| System.UInt64 | workspace | Tmp workspace for deconvolution (MB) |
Returns
| Type | Description |
|---|---|
| NDArray | returns new NDArray |
Where(NDArray, NDArray, NDArray)
Return the elements, either from x or y, depending on the condition.
Given three ndarrays, condition, x, and y, return an ndarray with the elements from x or y,
depending on the elements from condition are true or false. x and y must have the same shape.
If condition has the same shape as x, each element in the output array is from x if the
corresponding element in the condition is true, and from y if false.
If condition does not have the same shape as x, it must be a 1D array whose size is
the same as x's first dimension size. Each row of the output array is from x's row
if the corresponding element from condition is true, and from y's row if false.
Note that all non-zero values are interpreted as ``True`` in condition.
Examples::
x = [[1, 2], [3, 4]]
y = [[5, 6], [7, 8]]
cond = [[0, 1], [-1, 0]]
where(cond, x, y) = [[5, 2], [3, 8]]
csr_cond = cast_storage(cond, 'csr')
where(csr_cond, x, y) = [[5, 2], [3, 8]]
Defined in C:\Jenkins\workspace\mxnet\mxnet\src\operator\tensor\control_flow_op.cc:L57
Declaration
public static NDArray Where(NDArray condition, NDArray x = null, NDArray y = null)
Parameters
| Type | Name | Description |
|---|---|---|
| NDArray | condition | condition array |
| NDArray | x | |
| NDArray | y |
Returns
| Type | Description |
|---|---|
| NDArray | returns new NDArray |
WhileLoop(NDArray, NDArray, NDArrayList, Int32, Int32, Int32, Int32, Tuple<Double>, Tuple<Double>, Tuple<Double>)
Run a while loop over with user-defined condition and computation
From:C:\Jenkins\workspace\mxnet\mxnet\src\operator\control_flow.cc:1317
Declaration
public static NDArray WhileLoop(NDArray cond, NDArray func, NDArrayList data, int num_args, int num_outputs, int num_out_data, int max_iterations, Tuple<double> cond_input_locs, Tuple<double> func_input_locs, Tuple<double> func_var_locs)
Parameters
| Type | Name | Description |
|---|---|---|
| NDArray | cond | Input graph for the loop condition. |
| NDArray | func | Input graph for the loop body. |
| NDArrayList | data | The input arrays that include data arrays and states. |
| System.Int32 | num_args | Number of input arguments, including cond and func as two NDArray inputs. |
| System.Int32 | num_outputs | The number of outputs of the subgraph. |
| System.Int32 | num_out_data | The number of outputs from the function body. |
| System.Int32 | max_iterations | Maximum number of iterations. |
| Tuple<System.Double> | cond_input_locs | The locations of cond's inputs in the given inputs. |
| Tuple<System.Double> | func_input_locs | The locations of func's inputs in the given inputs. |
| Tuple<System.Double> | func_var_locs | The locations of loop_vars among func's inputs. |
Returns
| Type | Description |
|---|---|
| NDArray | returns new NDArray |
Zeros(Shape, Context, DType)
fill target with zeros
Declaration
public static NDArray Zeros(Shape shape = null, Context ctx = null, DType dtype = null)
Parameters
| Type | Name | Description |
|---|---|---|
| Shape | shape | The shape of the output |
| Context | ctx | Context of output, in format cpu|gpu|cpu_pinned.Only used for imperative calls. |
| DType | dtype | Target data type. |
Returns
| Type | Description |
|---|---|
| NDArray | returns new NDArray |
ZerosLike(NDArray)
Return an array of zeros with the same shape, type and storage type
as the input array.
The storage type of ``zeros_like`` output depends on the storage type of the input
- zeros_like(row_sparse) = row_sparse
- zeros_like(csr) = csr
- zeros_like(default) = default
Examples::
x = [[ 1., 1., 1.],
[ 1., 1., 1.]]
zeros_like(x) = [[ 0., 0., 0.],
[ 0., 0., 0.]]
Declaration
public static NDArray ZerosLike(NDArray data)
Parameters
| Type | Name | Description |
|---|---|---|
| NDArray | data | The input |
Returns
| Type | Description |
|---|---|
| NDArray | returns new NDArray |
ZerosWithoutDtype(Shape, Context, DType)
fill target with zeros without default dtype
Declaration
public static NDArray ZerosWithoutDtype(Shape shape = null, Context ctx = null, DType dtype = null)
Parameters
| Type | Name | Description |
|---|---|---|
| Shape | shape | The shape of the output |
| Context | ctx | Context of output, in format cpu|gpu|cpu_pinned.Only used for imperative calls. |
| DType | dtype | Target data type. |
Returns
| Type | Description |
|---|---|
| NDArray | returns new NDArray |


Slug_Forecasting¶
Slug_Forecasting¶
Part of slugdetection package
@author: Deirdree A Polak github: dapolak
-
class
slugdetection.Slug_Forecasting.
Slug_Forecasting
(slug_flow_whp)¶ Trains an ARIMA model to forecast slug flow in offshore oil wells. :param slug_flow_whp: well data frame, including a WHP and ts column. Must be presenting slug flow characteristics :type slug_flow_whp: Pandas DataFrame
-
slug_df
¶ well data frame, with DateTimeIndex and single WHP column.
Type: Pandas DataFrame
-
ARIMA_model
(p, d, q, show=True)¶ Instantiate, fits and plots best fit of an ARIMA model with the parameters p, d and q. :param p: ARIMA Auto Regressive Property. As approximated from the PACF plot. :type p: int :param d: ARIMA Integrated Property. As approximated by the difference value required to reach stationarity :type d: int :param q: ARIMA Moving Average Property. As approximated from the ACF plot. :type q: int
Returns: ARIMA fit figure Return type: Figure
-
ARIMA_pred
(pred_time, y_true=True, show=True)¶ Forecasts and plots the expected values Instantiate, fits and plots best fit of an ARIMA model with the parameters p, d and q. :param pred_time: Number of minutes to forecast until :type pred_time: int :param y_true: Whether true data for the forecasting interval is known (default is True) :type y_true: bool (optional)
Returns: ARIMA forecast figure Return type: Figure
-
autocorrelation_plot
(lags=25)¶ Plots Auto Correlation figure :param lags: Number of lags to plot ACF for :type lags: int
Returns: ACF figure Return type: Figure
-
error_metrics
(error, verbose=True)¶ Computes error metrics for the error of the regression as compared to the true data
Parameters: error (str) – Keyword to compute error metrics for the ARIMA model regression for the training data, or the forecast for the testing data. Takes “fit” ot “pred”. Returns: - mape (float) – Mean Absolute Percentage Error for the regression. The smaller the value, the better the fit
- mse (float) – Mean Squared Error for the regression. The smaller error, the better the fit
- rmse (float) – Root Mean Squared Error for the regression. The smaller the error the better the fit
- r2 (float) – Coefficient of Determination for the regression. The closer to 1, the better the fit.
-
error_metrics_plot
(error)¶ Plots infographics on the error of the ARIMA model regression
Parameters: error (str) – Keyword to compute error metrics for the ARIMA model regression for the training data, or the forecast for the testing data. Takes “fit” ot “pred”. Returns: Error infographics figure Return type: Figure
-
partial_autocorrelation_plot
(lags=25)¶ Plots Partial Auto Correlation figure :param lags: Number of lags to plot PACF for :type lags: int
Returns: PACF figure Return type: Figure
-
split_data
(train_size=180, predict_size=60)¶ Splits data into a training set and a testing set. Split is performed chronologically. :param train_size: Number of minutes to train the data on :type train_size: int :param predict_size: Number of minutes to calculate prediction error on :type predict_size: int
-
stationarity_check
(diff=0)¶ Checks whether slug_df attribute is stationary by applying the Augmented Dickey-Fuller test.
Parameters: diff (int (optional)) – If data is not stationary, can be used to stationarise it. Value should be used as the d parameter in the ARIMA model training (default is 0)
-


MED Majestic Education Digital
CloudBooks
Menu
Go back
Crossword 2
Daily routines
•
Solve the crossword puzzle by writing the correct answers. Remember that a letter is written in each cell.
Across
1.
I
to work by car.
2.
I
work at 9:00 a. m.
4.
After dinner I
the dishes.
6.
My brothers
bed at 10:00 p. m.
8.
Before go running I
a shower.
10.
I
dressed before to have a breakfast.
12.
After breakfast I
home.
14.
I
up at 7:05 in the morning.
15.
When I arrive at home I
to the radio.
16.
Before cook the lunch I
shopping.
17.
My typical day I
up at 7:00 in the morning.
18.
I always
a book before to sleep.
Down
1.
My brother and sister
school every day.
3.
On Friday I
work at 8:00 p. m.
5.
My mom and I
the housework at the weekend.
7.
On Sunday I
TV all day.
8.
I
a breakfast with my son.
9.
I often
a taxi to go home.
10.
My family and I
home at about 9:00 p. m.
Answers
Restart


First Name
Last Name
Adress
City
State
Zip/Postal Code
Country
Bulgaria
United Sates
United Kingdom
Phone, (country code, area code, number)
(+
)
-
Email
Birth date
Month
Day
Year (4 digit)
Gender
Male
Female
Starting date
Spring 2009
Summer 2010
Comments/Questions


| betabinomial {pomp} | R Documentation |
Density and random generation for the Beta-binomial distribution with parameters size
, mu
, and theta
.
rbetabinom(n = 1, size, prob, theta)
dbetabinom(x, size, prob, theta, log = FALSE)
n |
integer; number of random variates to generate. |
size |
|
prob |
mean of the Beta distribution |
theta |
Beta distribution dispersion parameter |
x |
vector of non-negative integer quantiles |
log |
logical; if TRUE, return logarithm(s) of probabilities. |
A variable X
is Beta-binomially distributed if
X\sim{\mathrm{Binomial}(n,P)}
where P\sim{\mathrm{Beta}(\mu,\theta)}
.
Using the standard (a,b)
parameterization, a=\mu\,\theta
and b=(1-\mu)\,\theta
.
rbetabinom |
Returns a vector of length |
dbetabinom |
Returns a vector (of length equal to the number of columns of |
An interface for C codes using these functions is provided by the package. Visit the package homepage to view the pomp C API document.
More on implementing POMP models:
Csnippet
,
accumvars
,
basic_components
,
covariates
,
dinit_spec
,
dmeasure_spec
,
dprocess_spec
,
emeasure_spec
,
eulermultinom
,
parameter_trans()
,
pomp-package
,
pomp_constructor
,
prior_spec
,
rinit_spec
,
rmeasure_spec
,
rprocess_spec
,
skeleton_spec
,
transformations
,
userdata
,
vmeasure_spec


Dissertation: Scalable Data Visualization Methods for Academic Careers
Thesis: Interfacing Information in User Studies with Mixed Methods
Major GPA: 3.9/4.0
Data Visualization, Web Developement, Fullstack, AWS
React, Vue, Python, Flask, JavaScript, PostgreSQL, D3.js


[1]
Fun and useful; Unreliable
[2]
Brilliant concept, flawless execution, fast.; ...don't know, really. No camera I suppose, but...


In Rwanda, girls are often seen to have only two roles during their lives: daughter and then wife. Ni Nyampinga showcases a different reality: that girls are Rwanda's greatest untapped source of economic and social growth. One way of doing this is to expose girls to positive role models who have broken through the invisible barriers holding them back. These Ni Nyampinga heroes are not only changing the way Rwanda views girls, but the way girls view themselves.


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PINTU is one of the largest cryptocurrency exchanges worldwide by market volume and has offices in Indonesia.
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PINTU is one of the largest cryptocurrency exchanges worldwide by market volume and has offices in Indonesia.
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PINTU is one of the largest cryptocurrency exchanges worldwide by market volume and has offices in Indonesia.
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PINTU is one of the largest cryptocurrency exchanges worldwide by market volume and has offices in Indonesia.
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PINTU is one of the largest cryptocurrency exchanges worldwide by market volume and has offices in Indonesia.
Terdaftar
PINTU is one of the largest cryptocurrency exchanges worldwide by market volume and has offices in Indonesia.
-
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Excellent
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PINTU is one of the largest cryptocurrency exchanges worldwide by market volume and has offices in Indonesia.
Terdaftar
PINTU is one of the largest cryptocurrency exchanges worldwide by market volume and has offices in Indonesia.
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Excellent
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< 24 Hours
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Disclaimer
Perdagangan Digital Asset (Bitcoin, Ethereum, dll) merupakan aktivitas beresiko tinggi, ketahui dan kelola risiko Anda dalam melakukan perdagangan Digital Asset. Perdagangan Digital Asset sebaiknya dilakukan pada platform
Kami tidak memaksa pengguna untuk membeli atau menjual Digital Asset, sebagai investasi, atau aksi mencari keuntungan. Semua keputusan perdagangan Digital Asset merupakan keputusan independen oleh pengguna.