Graded Betti numbers of a hyperedge ideal associated to join of graphs

Let $G$ be a finite simple graph on the vertex set $V(G)$ and let $r$ be a positive integer. We consider the hypergraph $\mathrm{Con}_r(G)$ whose vertices are the vertices of $G$ and the (hyper)edges are all $A\subseteq V(G)$ such that $|A|=r+1$ and the induced subgraph $G[A]$ is connected. The (hyper)edge ideal $I_r(G)$ of $\mathrm{Con}_r(G)$ is also the Stanley-Reisner ideal of a generalisation of the independence complex of $G$, called the $r$-independence complex $\mathrm{Ind}_r(G)$. In this article we make extensive use of the Mayer-Vietoris sequence to find the graded Betti numbers of $I_r(G_1*G_2)$ in terms of the graded Betti numbers of $I_r(G_1)$ and $I_r(G_2)$, where $G_1*G_2$ is the join of $G_1$ and $G_2$. Moreover, we find formulas for all the graded Betti numbers of $I_r(G)$, when $G$ is a complete graph, complete multipartite graph, cycle graph and the wheel graph.Comment: Comments are welcome

Mixing global and local competition in genetic optimization based design space exploration of analog circuits

The knowledge of optimal design space boundaries of component circuits can be extremely useful in making good subsystem-level design decisions which are aware of the parasitics and other second-order circuit-level details. However, direct application of popular Multi-objective genetic optimization algorithms were found to produce Pareto fronts with poor diversity for analog circuits problems. This work proposes a novel approach to control the diversity of solutions by paritioning the solution space, using Local Competition to promote diversity and Global competition for convergence, and by controlling the proportion of these two mechanisms by a Simulated Annealing based formulation. The algorithm was applied to extract numerical results on analog switched capacitor integrator circuits with a wide range of tight specifications. The results were found to be significantly better than traditional GA based uncontrolled optimization methods

Production of genuine multimode entanglement in circular waveguides with long-range interactions

Starting with a product initial state, squeezed (coherent squeezed) state in one of the modes, and vacuum in the rest, we report that a circular waveguide comprising modes coupled with varying interaction strength is capable of producing genuine multimode entanglement (GME), quantified via the generalized geometric measure (GGM). We demonstrate that for a fixed interaction and squeezing strength, the GME content of the resulting state increases as the range of interactions between the waveguides increases, although the GGM collapses and revives with the variation of interaction strength and time. To illustrate the advantage of long-range interactions, we propose a quantity, called accumulated GGM, measuring the area under the GGM curve, which clearly illustrates the growing trends with the increasing range of interactions. We analytically determine the exact expression of GGM for systems involving an arbitrary number of modes, when all the modes interact with each other equally. The entire analysis is performed in phase-space formalism. We manifest the constructive effect of disorder in the coupling parameter, which promises a steady production of GME, independent of the interaction strength.Comment: 13 pages, 6 figure

Simple Point of Care microfluidic device for detection of Tuberculosis

Nano/microfluidic technologies are emerging as powerful enabling tools for diagnosis and monitoring of infectious diseases in both developed and developing countries. Miniaturized nano/ microfluidic platforms that precisely manipulate small fluid volumes can be used to enable medical diagnosis in a more rapid and accurate manner. In particular, these nano/microfluidic diagnostic technologies are potentially applicable to global health applications, because they are disposable, inexpensive, portable, and easy-to-use for detection of infectious diseases

Characterizations of GEM detector prototype

At NISER-IoP detector laboratory an initiative is taken to build and test Gas Electron Multiplier (GEM) detectors for ALICE experiment. The optimisation of the gas flow rate and the long-term stability test of the GEM detector are performed. The method and test results are presented.Comment: 3 Pages, 4 figure

Active emulsions in living cell membranes driven by contractile stresses and transbilayer coupling

The spatiotemporal organisation of proteins and lipids on the cell surface has direct functional consequences for signaling, sorting and endocytosis. Earlier studies have shown that multiple types of membrane proteins including transmembrane proteins that have cytoplasmic actin binding capacity and lipid-tethered GPI-anchored proteins (GPI-APs) form nanoscale clusters driven by active contractile flows generated by the actin cortex. To gain insight into the role of lipids in organizing membrane domains in living cells, we study the molecular interactions that promote the actively generated nanoclusters of GPI-APs and transmembrane proteins. This motivates a theoretical description, wherein a combination of active contractile stresses and transbilayer coupling drive the creation of active emulsions, mesoscale liquid ordered (lo) domains of the GPI-APs and lipids, at temperatures greater than equilibrium lipid-phase segregation. To test these ideas we use spatial imaging of homo-FRET combined with local membrane order and demonstrate that mesoscopic domains enriched in nanoclusters of GPI-APs are maintained by cortical actin activity and transbilayer interactions, and exhibit significant lipid order, consistent with predictions of the active composite model

Hydrogen bonded molecular rectangle of N,N-bis(3-quinolyl- methylene)diphenylethanedionedihydrazone

416-419The title compound, N,N-bis (3-quinolylmethylene) diphenylethanedionedihydrazone (I) (molecular formula, C34H24N6) has been synthesized by the reaction of quinoline 3-carboxaldehyde and diphenylethanedionedihydrazone in 2:1 molar ratio. The molecular structure has been characterized by room-temperature single-crystal X-ray diffraction which reveals that two quinoline moieties are disposed nearly perpendicularly around the central C-C bond giving an ‘L’ shape to the molecule. This particular geometry gives rise to the hydrogen bonded supramolecular rectangle of two self-complementary molecules. These supramolecular units are further assembled by - interaction