In general, network alignment identifies a bijection between the full (or partial) vertex sets of two networks such that the size of corresponding common subgraph is maximized. This problem is closely related to the quadratic assignment problem and is known to be NP-hard not only to solve, but also to approximate. Because of its applications in different areas like systems biology or social sciences, finding efficient algorithm to approximate the optimal alignment is essential problem. In this talk I will first mention applications of this problem in biology then review some known algorithms which are mainly based on spectral techniques and state some of our new results at the end.
Joint work with: Mohammad Hadi Foroughmand, Zeinab Maleki and Sina Mansour
IITRoorkee, India, Email: firstname.lastname@example.org
We present a mathematical model of non-spherical nano particulate suspension and deposition underneath periodic breathing in pulmonary region for different stages of lungs. The pulsatile flow behavior inside airways with sinusoidal wall oscillation through a non-Darcian porous medium is studied. Possible effects of non-spherical nan particulate is modeled through aerodynamic diameter concept and considering the drag force term in the translational momentum equation.
The transport equations are formulated in a two dimensional coordinate system using boundary layer theory and solved numerically. General solution of governed unsteady non-linear Navier-Stokes equations is obtained for inlet Reynolds number $0.01 \le Re \le 1.2$, Womersley number ($\alpha $) is of $O(4)$ or less, Forchsheimer number and particle shape factor $ \le 1000$. Results for velocity of fluid and dust particles and wall shear stress distribution are discussed to understand the critical condition of interstitial lung diseases.