Semi-equivelar toroidal maps and their vertex covers

If the face\mbox{-}cycles at all the vertices in a map are of same type then the map is called semi\mbox{-}equivelar. A map is called minimal if the number of vertices is minimal. We know the bounds of number of vertex orbits of semi-equivelar toroidal maps. These bounds are sharp. Datta \cite{BD2020} has proved that every semi-equivelar toroidal map has a vertex-transitive cover. In this article, we prove that if a semi-equivelar map is $k$ orbital then it has a finite index $m$-orbital minimal cover for $m \le k$. We also show the existence and classification of $n$-sheeted covers of semi-equivelar toroidal maps for each $n \in \mathbb{N}$

Photophysical Detection of Singlet Oxygen

The chemical reactivity of singlet oxygen (1O2) (SO) derives from its electronically excited state. Being a unique reactive oxygen species SO takes part in many important atmospheric, biological physical, chemical, and therapeutic process and attracted current research interest. To understand the mechanistic pathways in various process the detection and quantification of SO is very important. The direct method of detection is very challenging due to its highly reactive nature. Only direct method of determination of phosphorescence of SO at 1270 nm has been utilised but that also puts some limitation due to very low luminescence quantum yield. Indirect method using UV–Vis spectrophotometric, fluorescent and chemiluminescent probes has been extensively studied for this purpose. Elucidation of various mechanistic processes improvised the use of sophisticated spectroscopic detection probe for SO have been discussed in a simple and lucid manner in this article through citation of literature examples. Four major spectroscopic methods i.e. spectrophotometry, fluorescence, emission and chemiluminescence are elaborately discussed with special emphasis to chemical probes having high selectivity and sensitivity for SO

Efficient inference in general semiparametric regression models

Semiparametric regression has become very popular in the field of Statistics over the years. While on one hand more and more sophisticated models are being developed, on the other hand the resulting theory and estimation process has become more and more involved. The main problems that are addressed in this work are related to efficient inferential procedures in general semiparametric regression problems. We first discuss efficient estimation of population-level summaries in general semiparametric regression models. Here our focus is on estimating general population-level quantities that combine the parametric and nonparametric parts of the model (e.g., population mean, probabilities, etc.). We place this problem in a general context, provide a general kernel-based methodology, and derive the asymptotic distributions of estimates of these population-level quantities, showing that in many cases the estimates are semiparametric efficient. Next, motivated from the problem of testing for genetic effects on complex traits in the presence of gene-environment interaction, we consider developing score test in general semiparametric regression problems that involves Tukey style 1 d.f form of interaction between parametrically and non-parametrically modeled covariates. We develop adjusted score statistics which are unbiased and asymptotically efficient and can be performed using standard bandwidth selection methods. In addition, to over come the difficulty of solving functional equations, we give easy interpretations of the target functions, which in turn allow us to develop estimation procedures that can be easily implemented using standard computational methods. Finally, we take up the important problem of estimation in a general semiparametric regression model when covariates are measured with an additive measurement error structure having normally distributed measurement errors. In contrast to methods that require solving integral equation of dimension the size of the covariate measured with error, we propose methodology based on Monte Carlo corrected scores to estimate the model components and investigate the asymptotic behavior of the estimates. For each of the problems, we present simulation studies to observe the performance of the proposed inferential procedures. In addition, we apply our proposed methodology to analyze nontrivial real life data sets and present the results

A Simple Flood Forecasting Scheme Using Wireless Sensor Networks

This paper presents a forecasting model designed using WSNs (Wireless Sensor Networks) to predict flood in rivers using simple and fast calculations to provide real-time results and save the lives of people who may be affected by the flood. Our prediction model uses multiple variable robust linear regression which is easy to understand and simple and cost effective in implementation, is speed efficient, but has low resource utilization and yet provides real time predictions with reliable accuracy, thus having features which are desirable in any real world algorithm. Our prediction model is independent of the number of parameters, i.e. any number of parameters may be added or removed based on the on-site requirements. When the water level rises, we represent it using a polynomial whose nature is used to determine if the water level may exceed the flood line in the near future. We compare our work with a contemporary algorithm to demonstrate our improvements over it. Then we present our simulation results for the predicted water level compared to the actual water level.Comment: 16 pages, 4 figures, published in International Journal Of Ad-Hoc, Sensor And Ubiquitous Computing, February 2012; V. seal et al, 'A Simple Flood Forecasting Scheme Using Wireless Sensor Networks', IJASUC, Feb.201