# Laboratory for Cyber Physical Networks and Systems (CyPhyNets)

(Difference between revisions)
 Revision as of 06:52, 1 July 2009 (view source)← Previous diff Revision as of 06:58, 1 July 2009 (view source)Next diff → Line 66: Line 66: I repeat the formula above with a slight change and it does not show. I repeat the formula above with a slight change and it does not show. $x=\frac{+b\pm\sqrt{b^2-4acxv}}{2a}$ $x=\frac{+b\pm\sqrt{b^2-4acxv}}{2a}$ + + Some Sample Formulas for Testing By Nasir: + + $\int_a^x \!\!\!\int_a^s f(y)\,dy\,ds + = \int_a^x f(y)(x-y)\,dy$ + + $\sum_{m=1}^\infty\sum_{n=1}^\infty\frac{m^2\,n} + {3^m\left(m\,3^n+n\,3^m\right)}$ + + $u'' + p(x)u' + q(x)u=f(x),\quad x>a$ + + $\phi_n(\kappa) = + \frac{1}{4\pi^2\kappa^2} \int_0^\infty + \frac{\sin(\kappa R)}{\kappa R} + \frac{\partial}{\partial R} + \left[R^2\frac{\partial D_n(R)}{\partial R}\right]\,dR$ + + $\phi_n(\kappa) = + 0.033C_n^2\kappa^{-11/3},\quad + \frac{1}{L_0}\ll\kappa\ll\frac{1}{l_0}$ + + math> + f(x) = + \begin{cases} + 1 & -1 \le x < 0 \\ + \frac{1}{2} & x = 0 \\ + 1 - x^2 & \mbox{otherwise} + \end{cases} + [/itex] + + ${}_pF_q(a_1,\dots,a_p;c_1,\dots,c_q;z) + = \sum_{n=0}^\infty + \frac{(a_1)_n\cdots(a_p)_n}{(c_1)_n\cdots(c_q)_n} + \frac{z^n}{n!}$ + + $\frac {a}{b}\ \tfrac {a}{b}$

## Revision as of 06:58, 1 July 2009

CyPhyNets: Laboratory for Cyber Physical Networks and Systems.

School of Science & Engineering, SSE

Lahore University of Management Sciences LUMS

Lahore, Pakistan

# Group Members

Positions open.

### Affiliates

• Muhammad Ali, Consultant Engineer
• Zubair Khalid, Research Assistant

### Students

• Zahaib Akhtar, CmpE Senior
• Muhammad Ali Ahmed, CmpE Junior
• Muhammad Ammar Hassan, SSE freshman

### Former Members

• Shahzad Bhatti, Lecturer in Mathematics, COMSATS Institute of Technology, Islamabad

# Research

• Complex networked systems to enable the deployment of very-large scale uniquitous instances of sensor networks, robotic swarms and mobile networking
• Rapid information discovery in massive high-dimensional data sets in robotics, networks and other areas using geometrical and topological methods
• Quantum information theory and quantum control for understanding the physics of information

# Teaching

### Formal Courses

• COMP-208. Computers for engineers [McGill. Winter 2008]
• Phy-102. Electricity and magnetism [LUMS. Autumn 2009]
• CS-683. Information theory [LUMS. Winter 2009]
• BIO-103. Freshman biology (Module on systems biology) [LUMS. Winter 2009] $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

I repeat the formula above with a slight change and it does not show. $x=\frac{-b\pm\sqrt{b^2*4acxv}}{2a}$ I repeat the formula above with a slight change and it does not show. $x=\frac{-b\pm\sqrt{b^2+4acxv}}{2a}$ I repeat the formula above with a slight change and it does not show. $x=\frac{+b\pm\sqrt{b^2-4acxv}}{2a}$

Some Sample Formulas for Testing By Nasir: $\int_a^x \!\!\!\int_a^s f(y)\,dy\,ds = \int_a^x f(y)(x-y)\,dy$ $\sum_{m=1}^\infty\sum_{n=1}^\infty\frac{m^2\,n} {3^m\left(m\,3^n+n\,3^m\right)}$ $u'' + p(x)u' + q(x)u=f(x),\quad x>a$ $\phi_n(\kappa) = \frac{1}{4\pi^2\kappa^2} \int_0^\infty \frac{\sin(\kappa R)}{\kappa R} \frac{\partial}{\partial R} \left[R^2\frac{\partial D_n(R)}{\partial R}\right]\,dR$ $\phi_n(\kappa) = 0.033C_n^2\kappa^{-11/3},\quad \frac{1}{L_0}\ll\kappa\ll\frac{1}{l_0}$

math>

f(x) =
\begin{cases}
1 & -1 \le x < 0 \\
\frac{1}{2} & x = 0 \\
1 - x^2 & \mbox{otherwise}
\end{cases}
[/itex] ${}_pF_q(a_1,\dots,a_p;c_1,\dots,c_q;z) = \sum_{n=0}^\infty \frac{(a_1)_n\cdots(a_p)_n}{(c_1)_n\cdots(c_q)_n} \frac{z^n}{n!}$ $\frac {a}{b}\ \tfrac {a}{b}$