Finding Rumor Sources on Random Trees

We consider the problem of detecting the source of a rumor which has spread in a network using only observations about which set of nodes are infected with the rumor and with no information as to \emph{when} these nodes became infected. In a recent work \citep{ref:rc} this rumor source detection problem was introduced and studied. The authors proposed the graph score function {\em rumor centrality} as an estimator for detecting the source. They establish it to be the maximum likelihood estimator with respect to the popular Susceptible Infected (SI) model with exponential spreading times for regular trees. They showed that as the size of the infected graph increases, for a path graph (2-regular tree), the probability of source detection goes to $0$ while for $d$-regular trees with $d \geq 3$ the probability of detection, say $\alpha_d$, remains bounded away from $0$ and is less than $1/2$. However, their results stop short of providing insights for the performance of the rumor centrality estimator in more general settings such as irregular trees or the SI model with non-exponential spreading times. This paper overcomes this limitation and establishes the effectiveness of rumor centrality for source detection for generic random trees and the SI model with a generic spreading time distribution. The key result is an interesting connection between a continuous time branching process and the effectiveness of rumor centrality. Through this, it is possible to quantify the detection probability precisely. As a consequence, we recover all previous results as a special case and obtain a variety of novel results including the {\em universality} of rumor centrality in the context of tree-like graphs and the SI model with a generic spreading time distribution.Comment: 38 pages, 6 figure

Rumors in a Network: Who's the Culprit?

We provide a systematic study of the problem of finding the source of a rumor in a network. We model rumor spreading in a network with a variant of the popular SIR model and then construct an estimator for the rumor source. This estimator is based upon a novel topological quantity which we term \textbf{rumor centrality}. We establish that this is an ML estimator for a class of graphs. We find the following surprising threshold phenomenon: on trees which grow faster than a line, the estimator always has non-trivial detection probability, whereas on trees that grow like a line, the detection probability will go to 0 as the network grows. Simulations performed on synthetic networks such as the popular small-world and scale-free networks, and on real networks such as an internet AS network and the U.S. electric power grid network, show that the estimator either finds the source exactly or within a few hops of the true source across different network topologies. We compare rumor centrality to another common network centrality notion known as distance centrality. We prove that on trees, the rumor center and distance center are equivalent, but on general networks, they may differ. Indeed, simulations show that rumor centrality outperforms distance centrality in finding rumor sources in networks which are not tree-like.Comment: 43 pages, 13 figure

Measuring Push, Pull And Personal Factors Affecting Turnover Intention: A Case Of University Teachers In Pakistan

It has been observed that professional and qualified teacher’s retention become a challenge for Higher Education Institutions (HEIs) in Pakistan as the turnover rate has been significantly increased in recent years. The main objective of this paper is to access personal, push and pull factors and to find out that which factors contribute more to turnover intention. Primary data were collected from 100 teachers of 5 HEIs using questionnaire methods. The results indicate that all factors (personal, pull and push) have contributed in the employees’ turnover intentions. However, some facets of personal factor have significantly contributed in turnover intentions.Turnover, Higher Education Institution, Job Quit, Personal Factors, Push Factors, Pull Factors

Trade Openness and FDI Inflows: A Comparative Study of Asian Countries

This study presents the new regression estimates of relationship among openness of trade and Foreign Direct Investment inflows for India, Iran and Pakistan over the period 1982-2012. Fixed effect and Pooled OLS techniques are used to analyze the panel data for measuring individual country effects, group effects and time effects while exploring the relationship among openness of trade and FDI inflows. Results showed that higher openness of trade have significant positive impact on FDI inflows. The results also investigated that FDI inflows seem to be affected significantly by conventional determinants like as Exchange rate, Inflation (consumer price index) and GDP per capita etc. Based on results the author has concluded that increase in trade openness would be a better option for more and sustained FDI inflows for the long run and also improving the welfare of the people

Trade Openness and FDI Inflows: A Comparative Study of Asian Countries

This study presents the new regression estimates of relationship among openness of trade and Foreign Direct Investment inflows for India, Iran and Pakistan over the period 1982-2012. Fixed effect and Pooled OLS techniques are used to analyze the panel data for measuring individual country effects, group effects and time effects while exploring the relationship among openness of trade and FDI inflows. Results showed that higher openness of trade have significant positive impact on FDI inflows. The results also investigated that FDI inflows seem to be affected significantly by conventional determinants like as Exchange rate, Inflation (consumer price index) and GDP per capita etc. Based on results the author has concluded that increase in trade openness would be a better option for more and sustained FDI inflows for the long run and also improving the welfare of the people

Situational Analysis of Public Sector Schools in Rural Areas of Southern Punjab, Pakistan

Training assumes an imperative part in the improvement of the nation and people. Pakistan is among the most thickly populated countries of the world. Pakistan has a standout amongst the most insignificant capability rates on the planet and as showed by the United Nations Educational, Scientific and Cultural Organization (UNESCO), it is 55 for each penny and stays at 160th in total countries of the world. The target of this examination is to distinguish the reason of low proficiency rate in rustic territories and to recognize physical structure we likewise checkout essential security courses of action in government schools and break down effect of missing offices on youngsters. We likewise discover the reason of dropout youngsters from school and recognize Staff nearness at school. A Situational logical examination was led in region Punjab and in multi arranges testing system was utilized in local Muzaffargarh. Two tehsils from locale were chosen purposively for information accumulation. Tehsil jatoi and Alipur were chosen from locale Muzaffargarh. 150 respondents were selected as a specimen size of the examination. Rate, chi square, gamma, examinations were utilized to investigate the connection between various factors. The outcomes with respect to sexual orientation, age, territory, instruction level, wage level, among various factors are tried by utilizing SPSS for discoveries of the examination. Government should actualize the instructive arrangements from the gross root level. Guys and females ought to incorporate equivalent level for instructive basic leadership process. Conventional esteems, financial obstructions and some other social imperatives ought to be debilitated at all levels in instruction segment particularly in provincial southern Punjab

SUBSTANCE ABUSE AMONG EDUCATED YOUTH: CHALLENGES AND PROBLEMS FACED BY THE FAMILIES IN KARACHI, PAKISTAN

This paper intended to determine the impact of the contributory factor of substance use and its collision on the family of the educated user in Pakistan. This study used a quantitative research methodology for data collection. The target population for this study is based on higher education students at Karachi, Pakistan. The sample size was 316 responses which were analyzed using regression analysis via PLS-SEM. The results have shown that the availability of substances is positive and important with respect to substance use. Peer influence has a positive and significant effect on substance use. Substance use has a positive and significant impact on family avoidance and family conflict. Finally, addictions have a positive and significant impact on the plight of families

Reflection on learning about forces

Force is a basic concept in the physical sciences. It is included in Pakistan’s national curriculum from the primary level through the higher levels. Because of the abstract nature of the concept of force, both students and teachers have alternative frameworks in this area. This was revealed in our classroom discussions on force during the Lower Secondary Science Module of the M.Ed. program at the Aga Khan University Institute for Educational Development (AKU-IED) in Karachi, Pakistan. In-depth discussions and a variety of activities we carried out while teaching about forces challenged our previous concepts and allowed us to think critically about the teaching and learning of forces. In this article, we reflect on our teaching and learning experiences and possible ways, in light of our new learning, to make the concept of force understandable to students

BRAND ANALYSIS OF LG ELECTRONICS: A CASE STUDY

LG Electronics is a Korean based global brand in the field of consumer electronics, home appliances and mobile communications. The critical analysis in identifying the steps taken by the LG Electronics in the light of the existing literature review helps us to correlate these steps with the enhanced brand image, brand value and brand positioning. Information is collected from various reports i.e., LG Annual reports; International Magazines from the world of Business and Tech-nology; research literatures and other reputable sources. Innovation & design and constant obsolescence of ICT and IT Products (i.e., mobiles in particular), LG have to stick on R&D, design strategies and innovation and creativity for competing in the global market