Slimness of graphs

Slimness of a graph measures the local deviation of its metric from a tree metric. In a graph $G=(V,E)$, a geodesic triangle $\bigtriangleup(x,y,z)$ with $x, y, z\in V$ is the union $P(x,y) \cup P(x,z) \cup P(y,z)$ of three shortest paths connecting these vertices. A geodesic triangle $\bigtriangleup(x,y,z)$ is called $\delta$-slim if for any vertex $u\in V$ on any side $P(x,y)$ the distance from $u$ to $P(x,z) \cup P(y,z)$ is at most $\delta$, i.e. each path is contained in the union of the $\delta$-neighborhoods of two others. A graph $G$ is called $\delta$-slim, if all geodesic triangles in $G$ are $\delta$-slim. The smallest value $\delta$ for which $G$ is $\delta$-slim is called the slimness of $G$. In this paper, using the layering partition technique, we obtain sharp bounds on slimness of such families of graphs as (1) graphs with cluster-diameter $\Delta(G)$ of a layering partition of $G$, (2) graphs with tree-length $\lambda$, (3) graphs with tree-breadth $\rho$, (4) $k$-chordal graphs, AT-free graphs and HHD-free graphs. Additionally, we show that the slimness of every 4-chordal graph is at most 2 and characterize those 4-chordal graphs for which the slimness of every of its induced subgraph is at most 1

Parametric prediction of finite population total under Informative sampling and nonignorable nonresponse

In this paper, we combine two methodologies used in the model-based survey sampling, namely the prediction of the finite population total, named T, under informative sampling and full response, see Sverchkov and Pfeffermann (2004), and the prediction of T with a noninformative sampling design and the nonignorable nonresponse mechanism, see Eideh (2012). The former approach involves the dependence of the first order inclusion probabilities on the study variable, while the latter involves the dependence of the probability of nonresponse on unobserved or missing observations. The main aim of the paper is to consider how to account for the joint effects of informative sampling designs and notmissing- at-random response mechanism in statistical models for complex survey data. For this purpose, theoretically, we use the response distribution and relationships between the moments of the superpopoulation, the sample, sample-complement, response, and nonresponse distributions for the prediction of finite population totals, see Eideh (2016). The derived parametric predictors of T use the observation for the response set of the study variable or variable of interest, values of auxiliary variables and their population totals, sampling weights, and propensity scores. An interesting outcome of the T study is that most predictors known from model-based survey sampling can be derived as a special case from this general theory, see Chambers and Clark (2012).The research was partially supported by a grant from DAAD (Deutscher Akademischer Austauschdienst German Academic Exchange Service) - Research Stays for University Academics and Scientists, 2018. Also, the author would like to thank Professor Timo Schmid for hosting the author during his visit to Free University Berlin

Renewable energy technologies assessment in providing sustainable electricity to Nigerian rural areas.

The research work that underpins this thesis aims to investigate the viability of renewable energy technologies (RETs) and to develop a RETs implementation framework for providing sustainable electricity to Nigerias rural areas. As a result of electricity supply deficiency in Nigeria, rural communities have been negatively affected in their socio-economic activities. A strength, weakness, opportunity and threat (SWOT) analysis in combination with an assessment of sustainability indicators of RETs, identified the most appropriate technology for providing sustainable electricity in Nigeria's rural areas. Biomass energy technologies (BETs) are the most appropriate RET given significant resource availability. However, cost has been identified as the major barrier in adopting BETs. Both BETs and grid extension (GE) systems have been assessed. Whole Life Costing (WLC) and interview methods have been used to evaluate the economics of various capacities of BETs and GE systems, and assessed suitability of BETs respectively. Typical findings revealed that all the BETs capacities evaluated other than a 50kW direct combustion system are currently cost-competitive with existing fossil fuel (FF) sources used in generating electricity in Nigeria (US$0.13/kWh without incentives). BETs are identified as the preferable option than GE system for electricity provision to communities of demand capacity less than 50kW and distance less than five kilometre from load centres. Similarly, the interview method confirmed that BETs utilisation in the countrys rural areas are suitable and desirable. For implementation, all the identified drivers and enablers of BETs should be considered, along with the identified constraints to the adoption and development of BETs, some of which should be addressed before implementation. Further, a BETs implementation framework for sustainable electricity provision in rural areas has been developed through the selection of appropriate biomass feedstock and conversion technologies, and support through suitable incentive strategies. The framework was then evaluated and validated using six villages as case study. The benefit of the framework is ensuring successful electricity provision in rural areas. Thus, this study recommends that the existing rural areas energy policies be reviewed to include incentive strategies like economic subsidies in order to encourage investors participation given lack of energy infrastructures in rural areas

Estimation of Finite Population Mean and Superpopulation Parameters when the Sampling Design is Informative and Nonresponse Mechanism is Nonignorable

In this paper we study the joint treatment of not missing at random response mechanism and informative sampling for survey data. This is the most general situation in surveys and other combinations of sampling informativeness and response mechanisms can be considered as special cases. The proposed method combines two methodologies used in the analysis of sample surveys for the treatment of informative sampling and the nonignorable nonresponse mechanism. One incorporates the dependence of the first order inclusion probabilities on the study variable, while the other incorporates the dependence of the probability of nonresponse on unobserved or missing observations. The main purpose here is the estimation of finite population mean and superpopulation parameters when the sampling design is informative and nonresponse mechanism is nonignorable. Under four scenarios of sampling design and nonresponse mechanism, we obtained the method of moment estimators of finite population mean, with their biases and mean square errors. Furthermore, a four-step estimation method is introduced for the estimation of superpopulation parameters under informative sampling and nonignorable nonresponse mechanism. New relationships between moments of response, nonresponse, sample, sample-complement and population distributions were derived. Most estimators for finite population mean known from sampling surveys can be derived as a special case of the results derived in this paper

Fitting general linear model for longitudinal survey data under informative sampling

The purpose of this article is to account for informative sampling in fitting superpopulation model for multivariate observations, and in particular multivariate normal distribution, for longitudinal survey data. The idea behind the proposed approach is to extract the model holding for the sample data as a function of the model in the population and the first order inclusion probabilities, and then fit the sample model using maximum likelihood, pseudo maximum likelihood and estimating equations methods. As an application of the results, we fit the general linear model for longitudinal survey data under informative sampling using different covariance structures: the exponential correlation model, the uniform correlation model, and the random effect model, and using different conditional expectations of first order inclusion probabilities given the study variable. The main feature of the present estimators is their behaviours in terms of the informativeness parameters

Informative Sampling on Two Occasions: Estimation and Prediction

The sample distribution is defined as the distribution of the sample measurements given the selected sample. Under informative sampling, this distribution may be different from the corresponding population distribution. Sampling on two occasions under informative sampling design, utilizing the sample and sample-complement distributions for occasion one, the matched sample and unmatched sample distributions, and matched sample-complement and unmatched sample-complement for occasion two, is proposed for predicting finite population total of a variable under study for the current (second) occasion, viewing information collected on the first (previous) occasion as auxiliary information. An interesting result of the present analysis is that known predictors in common use are shown to be special cases of the present predictors obtained under informative sampling, thus providing them a new justification.The author is grateful to the Associate Editor, to the referees, and to Gad Nathan, and Danny Pfeffermann for their valuable comments

Detecting the License Plate and Segmentation by Using Digital Photos

Large number of traffic accidents and the difficulty of identifying whom are doing those irregularities such as skip the legal speed or skip the traffic signals and other irregularities and the difficulty of controlling the traffic, all these complex reasons make this research more important. In this research (digital image processing) concepts and pattern recognition concepts applied to building a system increase the efficiency of the traffic process and reduce the mistakes in the manual systems that are managed by human. It is possible to determine the system area from image acquisition stage by cameras until identifying the content of the plate. Where it pass from every initial operation for processing images to enhancement them then locate the plate then make image segmentation and extract basic symbols to identify them in the last stage. The result will be the vehicle plate. This research aims to identify the offending or stolen vehicles by security cameras. Provides help, saving in time and in effort for traffic police. Keywords: Digital image processing, Pattern recognition, License plate, Plate Segmentation

Methods to induce earlier onset of cyclicity in transitional mares

The purpose of this study was to investigate methods to induce earlier onset of cyclicity in transitional mares. Two experiments were conducted evaluating the effect of follicular aspiration to advance the onset of cyclicity, more succinctly define criteria for selection of mares for follicular aspiration and to compare aspiration to deslorelin treatment for initiating cyclicity in transitional mares. In Experiment 1, anestrous mares were assigned to control (n=6) or follicular aspiration (n=11). The control mares were monitored twice weekly, until ovulation was detected. The aspiration mares were similarly monitored until a follicle \u3e35 mm was identified, then transvaginal ultrasound guided follicular aspiration was performed. After aspiration, the mares were monitored for luteal tissue formation. In Experiment 2, anestrous mares were assigned to control (n=14), follicular aspiration (n=10), or deslorelin (n=12). The control mares were treated as in Experiment 1. The aspiration mares were monitored in the same manner as Experiment 1 but were treated only if uterine edema was present. The deslorelin treated mares were monitored similarly to the aspiration mares, but instead of aspiration the mares were administered deslorelin. In both experiments, plasma was obtained at each examination from all mares to verify a rise in progesterone. In Experiment 1, the time from January 1 to the first rise in serum progesterone was 23.8 days earlier for aspiration treated mares than for control mares (80.5±7.3 and 104.3±8.8 days, mean±SE, for aspiration and control groups, respectively; P=0.024). In Experiment 2, there was no significant difference in time from January 1 to the first rise in serum progesterone between groups (100.4±5.8, 113.0±3.0 and 110±6.7 days, for the aspiration, control and deslorelin groups, respectively, P=0.328). However, if mares that did not receive a repeat aspiration treatment due to lack of uterine edema are excluded, there was a significant difference between the aspiration and control groups (93.9±6.7 and 113.0±3.0 days, for the aspiration and control groups, respectively, P=0.045). Results of this study indicate that follicular aspiration of a follicle \u3e 35 mm during late transition may be a means to advance the onset of cyclicity in mares

INFORMATIVE SAMPLING ON TWO OCCASIONS: ESTIMATION AND PREDICTION

The sample distribution is defined as the distribution of the sample measurements given the selected sample. Under informative sampling, this distribution may be different from the corresponding population distribution. Sampling on two occasions under informative sampling design, utilizing the sample distribution is proposed for predicting the population total of a variable under study for the current (second) occasion, viewing information collected on the first (previous) occasion as auxiliary information