Computing median and antimedian sets in median graphs

The median (antimedian) set of a profile π = (u1, . . . , uk) of vertices of a graphG is the set of vertices x that minimize (maximize) the remoteness i d(x,ui ). Two algorithms for median graphs G of complexity O(nidim(G)) are designed, where n is the order and idim(G) the isometric dimension of G. The first algorithm computes median sets of profiles and will be in practice often faster than the other algorithm which in addition computes antimedian sets and remoteness functions and works in all partial cubes

Axiomatic Characterization of the Antimedian Function on Paths and Hypercubes

An antimedian of a pro le = (x1; x2; : : : ; xk) of vertices of a graph G is a vertex maximizing the sum of the distances to the elements of the pro le. The antimedian function is de ned on the set of all pro les on G and has as output the set of antimedians of a pro le. It is a typical location function for nding a location for an obnoxious facility. The `converse' of the antimedian function is the median function, where the distance sum is minimized. The median function is well studied. For instance it has been characterized axiomatically by three simple axioms on median graphs. The median function behaves nicely on many classes of graphs. In contrast the antimedian function does not have a nice behavior on most classes. So a nice axiomatic characterization may not be expected. In this paper such a characterization is obtained for the two classes of graphs on which the antimedian is well-behaved: paths and hypercubes.

Attribute reduction and missing value imputing with ANN: prediction of learning disabilities

Learning disability (LD) is a neurological condition that affects a child’s brain and impairs his ability to carry out one or many specific tasks. LD affects about 10% of children enrolled in schools. There is no cure for learning disabilities and they are lifelong. The problems of children with specific learning disabilities have been a cause of concern to parents and teachers for some time. Just as there are many different types of LDs, there are a variety of tests that may be done to pinpoint the problem The information gained from an evaluation is crucial for finding out how the parents and the school authorities can provide the best possible learning environment for child. This paper proposes a new approach in artificial neural network (ANN) for identifying LD in children at early stages so as to solve the problems faced by them and to get the benefits to the students, their parents and school authorities. In this study, we propose a closest fit algorithm data preprocessing with ANN classification to handle missing attribute values. This algorithm imputes the missing values in the preprocessing stage. Ignoring of missing attribute values is a common trend in all classifying algorithms. But, in this paper, we use an algorithm in a systematic approach for classification, which gives a satisfactory result in the prediction of LD. It acts as a tool for predicting the LD accurately, and good information of the child is made available to the concerned

Median Sets and Median Number of a Graph

A profile is a finite sequence of vertices of a graph. The set of all vertices of the graph which minimises the sum of the distances to the vertices of the profile is the median of the profile. Any subset of the vertex set such that it is the median of some profile is called a median set. The number of median sets of a graph is defined to be the median number of the graph. In this paper, we identify the median sets of various classes of graphs such as Kp − e, Kp,q forP > 2, and wheel graph and so forth. The median numbers of these graphs and hypercubes are found out, and an upper bound for the median number of even cycles is established.We also express the median number of a product graph in terms of the median number of their factors.

Equal opportunity networks, distance-balanced graphs, and Wiener game

Given a graph G and a set X ⊆ V(G), the relative Wiener index of X in G is defined as WX (G) = {u,v}∈X 2  dG(u, v) . The graphs G (of even order) in which for every partition V(G) = V1 +V2 of the vertex set V(G) such that |V1| = |V2| we haveWV1 (G) = WV2 (G) are called equal opportunity graphs. In this note we prove that a graph G of even order is an equal opportunity graph if and only if it is a distance-balanced graph. The latter graphs are known by several characteristic properties, for instance, they are precisely the graphs G in which all vertices u ∈ V(G) have the same total distance DG(u) = v∈V(G) dG(u, v). Some related problems are posed along the way, and the so-called Wiener game is introduced.

Median graphs, the remoteness function, periphery transversals, and geodetic number two

A periphery transversal of a median graph G is introduced as a set of vertices that meets all the peripheral subgraphs of G. Using this concept, median graphs with geodetic number 2 are characterized in two ways. They are precisely the median graphs that contain a periphery transversal of order 2 as well as the median graphs for which there exists a profile such that the remoteness function is constant on G. Moreover, an algorithm is presented that decides in O(mlog n) time whether a given graph G with n vertices and m edges is a median graph with geodetic number 2. Several additional structural properties of the remoteness function on hypercubes and median graphs are obtained and some problems listed

Multiple Antibiotic Resistances of Vibrio Isolates from Coastal and Brackish Water Areas

An experiment was designed to assess the occurrence of multiple antibiotic resistances in Vibrio sp from different (brackish and marine) environments. Water samples from nine marine landing sites and two coastal inland aquaculture farms were screened for the Vibrio spp and assessed their resistance to twenty-two different antibiotics, which are commonly encountered in the aquatic ecosystem. Tissue samples (shrimp, mussel and sepia) were tested from the sampling site with highest antibiotic resistance. Of the total 119 Vibrio isolates, 16. 8% were susceptible to all antibiotics. Of the resistant (83.19%) Vibrio strains, 30.3% were resistant against three antibiotics, 55.5% were resistant against 4-10 antibiotics, 14.14% were resistant against more than 10 antibiotics and 54% have shown multiple antibiotics resistance (MAR). Antibiotic resistance index was higher in Coastal 3, 6, Aqua farm 2 in isolates from water samples and all the tissues tested. Interestingly, incidence of antibiotic resistance in isolates from water samples was comparatively lower in aquaculture farms than that observed in coastal areas. Highest incidence of antibiotic resistance was evident against Amoxycillin, Ampicillin, Carbencillin and Cefuroxime followed by Rifampicin and Streptomycin and lowest against Chloramphenicol, Tetracycline, Chlortetracycline, Furazolidone, Nalidixic acid, Gentamycin Sulphafurazole, Trimethoprirn, Neomycin and Amikacin irrespective of the sampling sites. Results from various tissue samples collected from the sites of highest antibiotic resistance indicated that antibiotic resistance Vibrio spp collected from fish and tissue samples were higher than that of water samples. Overall results indicated that persistent use of antibiotics against diseases in human beings and other life forms may pollute the aquatic system and their impact on developing antibiotic resistant Vibrio sp may be a serious threat in addition to the use of antibiotics in aquaculture farms.

A Literature Review on the Benefits of Ethnic and Minority Entrepreneurship

Ethnic/Minority entrepreneur is a business owner who does not represent the majority population of a country. Ethnic/Minority entrepreneurship can bring benefits to individual, society, region, economy, and globe too. So, understanding the importance of ethnic/minority entrepreneurship will really be useful to all the stakeholders. The unique culture and value system of ethnic minorities are the most wanted characteristics for any successful entrepreneur in general. Many industrial nations like U.S, U.K., Germany, etc. have utilised the ethnic minorities to build their economy. The future of the minority businesses looks bright as the world economy is booming, availability of experienced and already successful minority entrepreneurs as role models, and institutional support services. In this paper, literature relating to the benefits of ethnic and minority entrepreneurship is reviewed to understand its magnitude of benefits.

Higher Education Sector in India: Issues and Imperatives

The 21st century is marked by a paradigm shift in education that has resulted both in threats and opportunities. It has brought new challenges and an opportunity for higher education. Higher education in India is undergoing rapid changes. The challenges ahead are multifaceted and multidimensional. Though the data show a massive growth in the number of students' enrollment in colleges/universities, holistic view reveals that still only a meager of the total population has access to higher education. Globalization and privatization are imposing new challenges but the nations are still entangled in solving the basic problems of accessibility to higher education for all. In the wake of the transition from elitist to mass education, universities worldwide are under pressure to enhance access and equity, on the one hand, and to maintain high standards of quality and excellence, on the other. Today the notion of equity not only implies greater access to higher education, but also opportunities for progress. In recent debates on higher education, the notions of equity and access go beyond minority to diversity. Affirmative action, too, has become raceexclusive and gender-neutral.1

Finite size effects on the structural and magnetic properties of sol–gel synthesized NiFe2O4 powders

Nanoparticles of nickel ferrite have been synthesized by the sol–gel method and the effect of grain size on its structural and magnetic properties have been studied in detail. X-ray diffraction (XRD) studies revealed that all the samples are single phasic possessing the inverse spinel structure. Grain size of the sol–gel synthesized powders has been determined from the XRD data and the strain graph. A grain size of 9 nm was observed for the as prepared powders of NiFe2O4 obtained through the sol–gel method. It was also observed that strain was induced during the firing process. Magnetization measurements have been carried out on all the samples prepared in the present series. It was found that the specific magnetization of the nanosized NiFe2O4 powders was lower than that of the corresponding coarse-grained counterparts and decreased with a decrease in grain size. The coercivity of the sol–gel synthesized NiFe2O4 nanoparticles attained a maximum value when the grain size was 15nm and then decreased as the grain size was increased further.

Structural, magnetic and electrical properties of the sol-gel prepared Li0.5Fe2.5O4 fine particles

Fine particles of lithium ferrite were synthesized by the sol-gel method. By subsequent heat treatment at different temperatures, lithium ferrites of different grain sizes were prepared. A structural characterization of all the samples was conducted by the x-ray diffraction technique. A grain size of around 12 nm was observed for Li0.5Fe2.5O4 obtained through the sol-gel method. Magnetic properties of lithium ferrite nanoparticles with grain size ranging from 12 to 32 nm were studied. Magnetization measurements showed that Li0.5Fe2.5O4 fine particles exhibit a deviation from the predicted magnetic behaviour. The as-prepared sample of lithium ferrite showed a maximum saturation magnetization of 75 emu g−1. Variation of coercivity is attributed to the transition from multi-domain to single domain nature. Dielectric permittivity and ac conductivity of all the samples were evaluated as a function of frequency, temperature and grain size. Variation of permittivity and ac conductivity with frequency reveals that the dispersion is due to the Maxwell–Wagner type interfacial polarization