Statistical Analysis of Bus Networks in India

Through the past decade the field of network science has established itself as a common ground for the cross-fertilization of exciting inter-disciplinary studies which has motivated researchers to model almost every physical system as an interacting network consisting of nodes and links. Although public transport networks such as airline and railway networks have been extensively studied, the status of bus networks still remains in obscurity. In developing countries like India, where bus networks play an important role in day-to-day commutation, it is of significant interest to analyze its topological structure and answer some of the basic questions on its evolution, growth, robustness and resiliency. In this paper, we model the bus networks of major Indian cities as graphs in \textit{L}-space, and evaluate their various statistical properties using concepts from network science. Our analysis reveals a wide spectrum of network topology with the common underlying feature of small-world property. We observe that the networks although, robust and resilient to random attacks are particularly degree-sensitive. Unlike real-world networks, like Internet, WWW and airline, which are virtual, bus networks are physically constrained. The presence of various geographical and economic constraints allow these networks to evolve over time. Our findings therefore, throw light on the evolution of such geographically and socio-economically constrained networks which will help us in designing more efficient networks in the future.Comment: Submitted to PLOS ON

Higher Weights of Codes from Projective Planes and Biplanes

We study the higher weights of codes formed from planes and biplanes. We relate the higher weights of the Hull and the code of a plane and biplane. We determine all higher weight enumerators of planes and biplanes of order less or equal to 4.</p

Microcavity supported lipid membranes: versatile platforms for building asymmetric lipid bilayers and for protein recognition

Microcavity supported lipid bilayers (MSLB) are contact-free membranes suspended across aqueousfilled pores that maintain the lipid bilayer in a highly fluidic state and free from frictional interactions with substrate. Such platforms offer the prospect of liposome-like fluidity with the compositional versatility and addressability of supported lipid bilayers and thus offer significant opportunity for modelling membrane asymmetry, protein-membrane interactions and aggregation at the membrane interface. Herein, we evaluate their performance by studying the effect of transmembrane lipid asymmetry on lipid diffusivity, membrane viscosity and cholera toxin- ganglioside recognition across six symmetric and asymmetric membranes including binary compositions containing both fluid and gel phase, and ternary phase separated membrane compositions. Fluorescence lifetime correlation spectroscopy (FLCS) was used to determine the lateral mobility of lipid and protein, and electrochemical impedance spectroscopy (EIS) enabled detection of protein-membrane assembly over the nanomolar range. Transmembrane leaflet asymmetry was observed to have profound impact on membrane electrochemical resistance where the resistance of a ternary symmetric phase separated bilayer was found to be at least 2.6 times higher than the asymmetric bilayer with analogous composition at the distal leaflet but where the lower leaflet comprised only 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC). Similarly, the diffusion coefficient for MSLBs was observed to be 2.5 fold faster for asymmetric MSLBs where the lower leaflet is DOPC alone. Our results demonstrate that interplay of lipid packing across both membrane leaflets and concentration of GM1 both affect the extent of cholera toxin aggregation and consequent diffusion of the cholera-GM1 aggregates. Given that true biomembranes are both fluidic and asymmetric, MSLBs offer the opportunity for building greater biomimicry into biophysical models and the approach described demonstrates the value of MSLBs in studying aggregation and membrane associated multivalent interactions prevalent in many carbohydrates mediated processes

AC - conductivity studies on Y1-xBixCrO3 solid solution

YCrO3 and the substitution of Bi+3(6s2) in the Y-site were synthesized by the sol gel process. The conductivity measurements using dielectric spectroscopy reveals that conductivity increases with increase of composition. Dielectric loss were used to understand the nature of conducting species and it reveals that chromates exhibits the usual reciprocal behaviour of charge carriers to motion of oxygen vacancies as we increase the Bi composition and temperature. Impedance and microstructural studies revealed that conductivity of the chromates was dominated by the grain contribution