Minimal cut-generating functions are nearly extreme

We study continuous (strongly) minimal cut generating functions for the model where all variables are integer. We consider both the original Gomory–Johnson setting as well as a recent extension by Y?ld?z and Cornuéjols (Math Oper Res 41:1381–1403, 2016). We show that for any continuous minimal or strongly minimal cut generating function, there exists an extreme cut generating function that approximates the (strongly) minimal function as closely as desired. In other words, the extreme functions are “dense” in the set of continuous (strongly) minimal functions.     

Testing statistical hypotheses based on the density power divergence

The family of density power divergences is an useful class which generates robust parameter estimates with high efficiency. None of these divergences require any non-parametric density estimate to carry out the inference procedure. However, these divergences have so far not been used effectively in robust testing of hypotheses. In this paper, we develop tests of hypotheses based on this family of divergences. The asymptotic variances of the estimators are generally different from the inverse of the Fisher information matrix, so that the usual drop-in-divergence type statistics do not lead to standard Chi-square limits. It is shown that the alternative test statistics proposed herein have asymptotic limits which are described by linear combinations of Chi-square statistics. Extensive simulation results are presented to substantiate the theory developed.     

Absorbing phase transition in energy exchange models

We study energy exchange models with dissipation (λ) and noise (of amplitude σ) and show that in presence of a threshold these models undergo an absorbing phase transition when either dissipation or noise strength or both are varied. Using Monte Carlo simulations we find that the behaviour along the critical line, which separates the active phase from the absorbing one, belongs to directed percolation (DP) universality class. We claim that the conserved version with λ = 1 and σ = 0 also shows a DP transition; the apparent non-DP behaviour observed earlier is an artifact of undershooting in the decay of activity density starting from a random initial condition.     

Comparison of the effect of anti-hyperlipidemic drugs from different groups on the phase profile of liposomal membrane–a fluorescence anisotropy study

The study compares the effect of incorporation of three different groups of anti-hyperlipidemic drugs, namely niacin, simvastatin, and fenofibrate on the phase profile of liposomal membranes of dipalmitoylphosphatidylcholine (DPPC). The fluorescence anisotropy studies, using 1,6-diphenyl-1,3,5-hexatriene as fluorescent probe, have shown that the lipophilic molecule fenofibrate changes phase behavior of DPPC liposomal membrane to a greater extent compared to the changes produced by amphiphilic simvastatin and hydrophilic niacin. This variation in effect can be attributed to the nature of the drug molecules and hence their location in different parts of the liposomal membrane. We have also calculated the changes in van’t Hoff enthalpy values in all these three cases and observed that these values decreased with increase in drug concentrations in the case of simvastatin but for fenofibrate and niacin the effect is completely the reverse. In order to get a better insight, the fraction of motionally restricted lipid molecules has been calculated.     

Role of non-lamellar-forming lipid in promotion of liposomal fusion

Membrane fusion is an important process in a wide range of cellular and sub-cellular activities. It is evident that during the intermediate stages of fusion some transitory non-bilayer configurations must appear within the lipid moiety. Using fluorescence techniques, we have studied here the process of aggregation and fusion of liposomes made of lipids, namely 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) and 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC). When mixed together, the complete fusion between these two liposomes took around 44 h as both DPPC and DMPC favour lamellar configuration. When the mixture was incubated at 42°C the fusion process was completed after 23 h. But, when 1,2-dipalmitoyl-sn-glycero-3-phosphoethanolamine (DPPE) was added in the liposomal matrix the time for fusion was reduced to 21 h for mixture without incubation and 17 h when the mixture was incubated. This indicates that DPPE having a tendency to assume non-lamellar conformation, promoted destabilisation of the lamellar conformation within the liposome which facilitated the fusion between two apposing bilayers.     

Inertial spin Hall effect in non-commutative space

In the present Letter the study of inertial spin current (that appears in an accelerated frame of reference) is extended to Non-Commutative (NC) space. In the Hamiltonian framework, the Dirac Hamiltonian in an accelerating frame is computed in the low energy regime by exploiting the Foldy–Wouthuysen scheme. The NC θ-effect appears from the replacement of normal products and commutators by Moyal ?-products and ?-commutators. In particular, the commutator between the external magnetic vector potential and the potential induced by acceleration becomes non-trivial. Expressions for θ-corrected inertial spin current and conductivity are derived explicitly. We have provided yet another way of experimentally measuring θ. The θ bound is obtained from the out of plane spin polarization, which is experimentally observable.     

Interactions of Nile Blue with Micelles, Reverse Micelles and a Genomic DNA

In this contribution we report studies on the nature of binding of a small ligand/drug Nile blue (NB) with sodium dodecyl sulfate (SDS) micelles, bis-(2-ethylehexyl) sulfosuccinate (AOT)/isooctane reverse micelles (RM) and a genomic DNA extracted from Salmon sperm. With detailed steady state and picosecond resolved optical spectroscopic techniques, we examined the fluorescence quenching of the ligand upon complexation with the SDS monomers and DNA. Polarization analyzed picosecond-resolved fluorescence measurements reveal geometrical restriction on the probe in SDS micelles, AOT-RM and DNA. Steady state and time resolved studies on the probe in nanocages of AOT RM with various degrees of hydration (w₀) reveal the existence of NB as two distinct species namely, neutral and cationic. This study confirms that the emission of NB in aqueous micelles and DNA solution is due to the cationic form of the drug. Our experiments clearly identified non-specific electrostatic and intercalative modes of interaction of the probe with the DNA at lower and higher DNA concentrations respectively. The nature of binding of NB in presence of the DNA and SDS micelles reveals that the binding affinity of the probe is higher with the micelles than with the DNA. The complex rigidity of NB with DNA and its fluorescence quenching with DNA elucidate a strong recognition mechanism between NB and DNA.     

Thermal and non-thermal fluctuations in active polar gels

We discuss general features of noise and fluctuations in active polar gels close to and away from equilibrium. We use the single-component hydrodynamic theory of active polar gels built by Kruse and coworkers to describe the cytoskeleton in cells. Close to equilibrium, we calculate the response function of the gel to external fields and introduce Langevin forces in the constitutive equations with correlation functions respecting the fluctuation-dissipation theorem. We then discuss the breakage of the fluctuation-dissipation theorem due to an external field such as the activity of the motors. Active gels away from equilibrium are considered at the scaling level. As an example of application of the theory, we calculate the density correlation function (the dynamic structure factor) of a compressible active polar gel and discuss possible instabilities.     

Synthesis of a series of ethylene glycol modified water-soluble tetrameric TPE-amphiphiles with pyridinium polar heads: Towards applications as light-up bioprobes in protein and DNA assay,and wash-free imaging of bacteria

Available online Development of water soluble AIE-active “light-up” bioprobes for the detection of biomacromolecules has drawn huge research interests in recent past. In this study, a series of ethylene glycol modified water soluble tetrameric tetraphenylethylene amphiphiles with pyridinium polar heads (TPE-xEG-Py, x = 3, 4, 6 or 1a-c) have been synthesized by varying the ethylene glycol spacer. Their unique structure allows them to form vesicles and other nanoaggregates in aqueous solutions. These amphiphiles were successfully utilized for fluorimetric detection and quantitation of BSA and DNA based on the electrostatic interactions to trigger AIE-emission from the TPE moiety. The electrostatic interaction was also proved very effective in wash-free imaging of both Gram-negative (E. coli) and Gram-positive (S. aureus) bacteria with up to 92 folds increase in fluorescence response within bacterial concentration 0–12 × 10⁸ CFU mL^?1. The strategy is advantageous due to cost-effective and easy synthesis, high water solubility, and fast response.