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

Economic assessment of biomass gasification technology in providing sustainable electricity in Nigerian rural areas.

Renewable Energy Technologies (RET) in general, and biomass source in particular, remains one of the means of providing sustainable electricity to rural areas in developing countries. This is because of its strategic value in identifying when and where electricity is really required thus, reducing/eliminating the high cost of grid network. The majority of Nigeria's rural dwellers are farmers and use little or none of their residues at the end of the farming season. Nigeria has also been experiencing dwindling power supply at both national and rural level with accessibility representing only 35% and 10% respectively. The rural areas are the most affected causing significant disruption of their socio-economic settings. Considering the enormous biomass resources in these communities, and they constitute approximately 65% of the country's total population, it is feasible to provide sustainable electricity to these communities through Biomass Gasification Technology (BGT). Cost has been found to be the major constraint in adopting RETs. Hence, this paper aims to evaluate and optimise the unit cost of generating electricity through BGT in Nigerian rural areas. Whole Life Costing approach has been used to evaluate various capacities of BGT. The findings reflect that cost/kW of BGT ranges between US{dollar}594(NGN118, 800)-US{dollar}3,604(NGN720,800) for capacities between 125kW-10kW. The Net Present Value(NPV)/kWh of generating electricity has been calculated for several scenarios including 125kW, 100kW, 50kW, 32kW, 24kW and 10kW system capacities under 3 different operational hours (8, 12 and 16), with and without feed-in tariff(FIT) incentive is from US{dollar}0.015-US{dollar}0.11(NGN3.08-N21.79). The only scenario that exceeds the current unit price of generating electricity from fossil fuel source in Nigeria which is averagely US{dollar}0.083(NGN16.50) is 8 hour operation without FIT at 10kW capacity. More so, in the event fuel wood price increases by 50%, 75% and 100%, the average increase in NPV/kWh will be 13%, 20% and 27% respectively

Renewable energy technology means of providing sustainable electricity in Nigerian rural areas: a review.

Following the failure of the Power Holding Company of Nigeria (PHCN) and fossil fuel source applications for the provision of electricity in Nigeria, the country has been experiencing power energy shortages for over three decades now. More than 65% of the population lack commercial electricity, particularly in the rural areas. This has caused socio-economic problems involving relocation of manufacturing companies to neighbouring countries, unemployment, and endemic rural-urban migration. The research that underpins this paper aims to investigate the potential of Renewable Energy Technologies (RETs) in the provision of sustainable electricity in Nigeria's rural areas. This has been motivated by the strategic value of RETs in identifying when and where electricity is actually required thereby eliminating/reducing the high cost of gridline network and offering a more sustainable alternative to fossil fuels. A systematic review method has been used to examine various RETs regarding their viability and applicability in Nigeria. The sustainability of various RETs is then evaluated using SWOT analysis to screen the technologies to be used in an energy supply mix in Nigeria's rural areas. Biomass, hydro and solar sources are appropriate for use in Nigeria rural areas. The utilisation level of RETs in Nigeria is extremely low except for hydropower source. The major problems of RETs implementation are lack of implementable energy policy, government apathy towards development of RETs and the low purchasing power of majority of citizens. Further work includes the application of whole life costing (WLC) to assess and optimise the economic performance of the identified RETs

Association of Researchers in Construction Management

Following the failure of the Power Holding Company of Nigeria (PHCN) and fossil fuel source applications for the provision of electricity in Nigeria, the country has been experiencing power energy shortages for over three decades now. More than 65% of the population lack commercial electricity, particularly in the rural areas. This has caused socio-economic problems involving relocation of manufacturing companies to neighbouring countries, unemployment, and endemic rural-urban migration. The research that underpins this paper aims to investigate the potential of Renewable Energy Technologies (RETs) in the provision of sustainable electricity in Nigeria's rural areas. This has been motivated by the strategic value of RETs in identifying when and where electricity is actually required thereby eliminating/reducing the high cost of gridline network and offering a more sustainable alternative to fossil fuels. A systematic review method has been used to examine various RETs regarding their viability and applicability in Nigeria. The sustainability of various RETs is then evaluated using SWOT analysis to screen the technologies to be used in an energy supply mix in Nigeria's rural areas. Biomass, hydro and solar sources are appropriate for use in Nigeria rural areas. The utilisation level of RETs in Nigeria is extremely low except for hydropower source. The major problems of RETs implementation are lack of implementable energy policy, government apathy towards development of RETs and the low purchasing power of majority of citizens. Further work includes the application of whole life costing (WLC) to assess and optimise the economic performance of the identified RETs

AN EMPIRICAL COMPARISON OF NEO4J AND TIGERGRAPH DATABASES FOR NETWORK CENTRALITY

Graph databases have recently gained a lot of attention in areas where the relationships between data and the data itself are equally important, like the semantic web, social networks, and biological networks. A graph database is simply a database designed to store, query, and modify graphs. Recently, several graph database models have been developed. The goal of this research is to evaluate the performance of the two most popular graph databases, Neo4j and TigerGraph, for network centrality metrics including degree centrality, betweenness centrality, closeness centrality, eigenvector centrality, and PageRank. We applied those metrics to a set of real-world networks in both graph databases to see their performance. Experimental results show Neo4j outperforms TigerGraph for computing the centrality metrics used in this study, but TigerGraph performs better during the data loading phase

Thermo-Diffusion Effects of a Stagnation Point Flow in a Nanofluid with Convection using the Adomian Decomposition Method

The Thermo-diffusion solution effects a stagnation point flow of a nanofluid with convection using. Adomian Decomposition Method (ADM) is presented. The Partial differential equation representing the problem was reduced to an ordinary differential equation by introducing some similarity transformation variables. The transformed equations were solved using the ADM and the results were compared with existing results in the literatures. There is a good agreement between the method and the existing one, which indicate reliability of the method. The physical parameters that occurred in the solutions such as magnetic parameter, thermal Grashof numbers, concentration Grashof numbers, nano Lewis number, velocity ratio, Prandtl number were varied to determine their respective effects. It was observed that when the wall velocity is higher than the free stream velocity, the fluid velocity drop and rises when velocity at free stream is higher than the wall velocity .&nbsp

Random weather phenomena in free-space optical - FTTx communication system

In the last few decades, optical wireless communication became an essential technology in various applications. Researchers have paid more attention to achieving high bandwidth and low loss. However, the random weather phenomena cause attenuation of optical signals, thus will decrease the bandwidth in optical wireless communication. In this article, we investigate a hybrid free-space optical (FSO) and fiber-to-the-x (FTTx) communications link based on wavelength-division multiple access (WDMA) over different random weather phenomena that operate over different wavelengths. The performance of the hybrid FSO-FTTx system is evaluated under clear sky weather phenomena, heavy rain weather phenomena, and heavy haze weather phenomena based on BER and Q-Factor measurements. The results show that we can transmit 140 Gbit/s data over 9650 meters a hybrid link under the clear sky and heavy rain weather phenomena, 3950 meters over. Additionally, the transmission of 140 Gbit/s data can be achieved for 1450 meters under the heavy haze weather phenomenon

On N-Dimensional Achr-Algebras

We prove that a homomorphismfrom complete normed algebra A into an n-dimensional normed algebra B is automatically continuous. As a consequence, B is ACHR-algebra

Fast Approximation and Exact Computation of Negative Curvature Parameters of Graphs

In this paper, we study Gromov hyperbolicity and related parameters, that represent how close (locally) a metric space is to a tree from a metric point of view. The study of Gromov hyperbolicity for geodesic metric spaces can be reduced to the study of graph hyperbolicity. Our main contribution in this note is a new characterization of hyperbolicity for graphs (and for complete geodesic metric spaces). This characterization has algorithmic implications in the field of large-scale network analysis, which was one of our initial motivations. A sharp estimate of graph hyperbolicity is useful, {e.g.}, in embedding an undirected graph into hyperbolic space with minimum distortion [Verbeek and Suri, SoCG\u2714]. The hyperbolicity of a graph can be computed in polynomial-time, however it is unlikely that it can be done in subcubic time. This makes this parameter difficult to compute or to approximate on large graphs. Using our new characterization of graph hyperbolicity, we provide a simple factor 8 approximation algorithm for computing the hyperbolicity of an n-vertex graph G=(V,E) in optimal time O(n^2) (assuming that the input is the distance matrix of the graph). This algorithm leads to constant factor approximations of other graph-parameters related to hyperbolicity (thinness, slimness, and insize). We also present the first efficient algorithms for exact computation of these parameters. All of our algorithms can be used to approximate the hyperbolicity of a geodesic metric space

Fast approximation and exact computation of negative curvature parameters of graphs

In this paper, we study Gromov hyperbolicity and related parameters, that represent how close (locally) a metric space is to a tree from a metric point of view. The study of Gromov hyperbolicity for geodesic metric spaces can be reduced to the study of graph hyperbolicity. The main contribution of this paper is a new characterization of the hyperbolicity of graphs. This characterization has algorithmic implications in the field of large-scale network analysis. A sharp estimate of graph hyperbolicity is useful, e.g., in embedding an undirected graph into hyperbolic space with minimum distortion [Verbeek and Suri, SoCG'14]. The hyperbolicity of a graph can be computed in polynomial-time, however it is unlikely that it can be done in subcubic time. This makes this parameter difficult to compute or to approximate on large graphs. Using our new characterization of graph hyperbolicity, we provide a simple factor 8 approximation algorithm for computing the hyperbolicity of an $n$-vertex graph $G=(V,E)$ in optimal time $O(n^2)$ (assuming that the input is the distance matrix of the graph). This algorithm leads to constant factor approximations of other graph-parameters related to hyperbolicity (thinness, slimness, and insize). We also present the first efficient algorithms for exact computation of these parameters. All of our algorithms can be used to approximate the hyperbolicity of a geodesic metric space. We also show that a similar characterization of hyperbolicity holds for all geodesic metric spaces endowed with a geodesic spanning tree. Along the way, we prove that any complete geodesic metric space $(X,d)$ has such a geodesic spanning tree. We hope that this fundamental result can be useful in other contexts