Arithmetic Branching Programs with Memory

We extend the well known characterization of VPws as the class of polynomials computed by polynomial size arithmetic branching programs to other complexity classes. In order to do so we add additional memory to the computation of branching programs to make them more expressive. We show that allowing different types of memory in branching programs increases the computational power even for constant width programs. In particular, this leads to very natural and robust characterizations of VP and VNP by branching programs with memory. 1

Knotty-Centrality: Finding the Connective Core of a Complex Network

A network measure called knotty-centrality is defined that quantifies the extent to which a given subset of a graph’s nodes constitutes a densely intra-connected topologically central connective core. Using this measure, the knotty centre of a network is defined as a sub-graph with maximal knotty-centrality. A heuristic algorithm for finding subsets of a network with high knotty-centrality is presented, and this is applied to previously published brain structural connectivity data for the cat and the human, as well as to a number of other networks. The cognitive implications of possessing a connective core with high knotty-centrality are briefly discussed

Effect of Bilayer Partitioning of Curcumin on the Adsorption and Transport of a Cationic Dye Across POPG Liposomes Probed by Second-Harmonic Spectroscopy

The effect of Curcumin partitioning into the bilayer during the adsorption and transport of a cationic dye, LDS, across a negatively charged POPG bilayer was investigated by the interface-selective second-harmonic (SH) spectroscopic technique. The intensity of SH electric field (<i>E</i>_2ω) arising due to LDS adsorbed on the outer bilayer of the POPG liposome was observed to increase instantaneously (<1 s) following the addition of Curcumin. The fractional increase in the SH electric field (<i>E</i>^f_2ω) and the bilayer transport rates (<i>k</i>_T) of LDS were studied with respect to the pH of the solution and also with the Curcumin content in the lipid bilayer. Results obtained indicate that compared with the anionic form of the drug, its neutral form is more conducive of increasing the <i>E</i>^f_2ω of LDS. With increasing Curcumin content in the lipid bilayer, two distinct regimes could be observed in terms of <i>E</i>^f_2ω and <i>k</i>_T values of LDS. For Curcumin:Lipid (C/L) ratio ≤0.02, the <i>E</i>^f_2ω of LDS increases rapidly, while <i>k</i>_T remains unchanged; and for C/L ratio ≥0.02, the <i>E</i>^f_2ω values remains more or less constant, while there is a significant (∼40 times) increase followed by a modest increase in the <i>k</i>_T values of LDS. The observed results support an earlier two-state binding model of Curcumin with the POPG bilayer. In addition, it is further proposed that at low C/L ratio Curcumin binds to the surface of the bilayer replacing the counterions (Na⁺) bound to the lipid head groups, which changes the bilayer surface charge density, thereby causing more LDS cations to adsorb on the bilayer surface. At high C/L ratio, Curcumin intercalates within the hydrophobic domain of the bilayer, altering its hydrophobicity and inducing enhanced transport of the LDS cation. Results presented in this work provide further insights into how Curcumin alters bilayer properties when it partitions from the aqueous to the bilayer phase

Network Decontamination

The Network Decontamination problem consists in coordinating a team of mobile agents in order to clean a contaminated network. The problem is actually equivalent to tracking and capturing an invisible and arbitrarily fast fugitive. This problem has natural applications in network security in computer science or in robotics for search or pursuit-evasion missions. In this Chapter, we focus on networks modeled by graphs. Many different objectives have been studied in this context, the main one being the minimization of the number of mobile agents necessary to clean a contaminated network. Another important aspect is that this optimization problem has a deep graph-theoretical interpretation. Network decontamination and, more precisely, graph searching models, provide nice algorithmic interpretations of fundamental concepts in the Graph Minors theory by Robertson and Seymour. For all these reasons, graph searching variants have been widely studied since their introduction by Breish (1967) and mathematical formaliza-tions by Parsons (1978) and Petrov (1982). This chapter consists of an overview of algorithmic results on graph de-contamination and graph searching