We show that every locally sparse graph contains a linearly sized expanding subgraph. For constants c1 > c2 > 1, 0 < α < 1, a graph G on n vertices is called a (c1, c2, α)-graph if it has at least c1n edges, but every vertex subset W ⊂ V (G) of size |W | ≤ αn spans less than c2|W | edges. We prove that every (c1, c2, α)-graph with bounded degrees contains an induced expander on linearly many ve...

Introduction: The upper cervical spine includes the atlas (C1) and Axis (C2). anatomy of twovertebrae is unique from each other. Atlanto-axial articulation most unique, mobile segment spine,which largely depends on ligamentous supports based integrity odontoid for its stability. Historically,atlanto-axial subluxation was treated by reduction fusion C1-C2 joint. However, High riding vertebralart...

Particle swarm optimization (PSO) is one of the most successful optimization techniques of swarm intelligence and has been fast developed in recent years. However, the performance of PSO is significantly depended on the acceleration coefficients c1 and c2 which control the exploration and convergence abilities. Parameters c1 and c2 are the “self-cognitive” coefficient and “social-influence” coe...