An Analysis of Exports and Growth in Pakistan

The paper examines the export-led growth (ELG) paradigm for Pakistan, using data of the period from 1970-71 to 2003-04. The paper uses a number of analytical tools, including Unit Root Test, Phillips- Perron Tests, Co-integration Johansen Test, and the Granger Tests. The paper sets three hypotheses for testing the ELG paradigm for Pakistan; (a) whether GDP and exports are cointegrated, (b) whether exports Granger cause growth, and (c) whether exports Granger cause investment. The time series data on GDP growth, export growth and investment GDP ratio (proxy for capital formation), and the labour employed were used. The data were tested for stationarity using the Augmented Dickey-Fuller (ADF) test and Phillips-Perron test (1988), and then the relationship between GDP growth rate and the growth rate of other variables was determined using OLS with AR (1). The major finding of the present study is that growth rate of export, total investment, and labour employed have positively affected the GDP growth rate

Independent sets of some graphs associated to commutative rings

Let $G=(V,E)$ be a simple graph. A set $S\subseteq V$ is independent set of $G$, if no two vertices of $S$ are adjacent. The independence number $\alpha(G)$ is the size of a maximum independent set in the graph. %An independent set with cardinality Let $R$ be a commutative ring with nonzero identity and $I$ an ideal of $R$. The zero-divisor graph of $R$, denoted by $\Gamma(R)$, is an undirected graph whose vertices are the nonzero zero-divisors of $R$ and two distinct vertices $x$ and $y$ are adjacent if and only if $xy = 0$. Also the ideal-based zero-divisor graph of $R$, denoted by $\Gamma_I(R)$, is the graph which vertices are the set {x\in R\backslash I | xy\in I \quad for some \quad y\in R\backslash I\} and two distinct vertices $x$ and $y$ are adjacent if and only if $xy \in I$. In this paper we study the independent sets and the independence number of $\Gamma(R)$ and $\Gamma_I(R)$.Comment: 27 pages. 22 figure

Application of the χ2\chi^2 principle and unbiased predictive risk estimator for determining the regularization parameter in 3D focusing gravity inversion

The $\chi^2$ principle and the unbiased predictive risk estimator are used to determine optimal regularization parameters in the context of 3D focusing gravity inversion with the minimum support stabilizer. At each iteration of the focusing inversion the minimum support stabilizer is determined and then the fidelity term is updated using the standard form transformation. Solution of the resulting Tikhonov functional is found efficiently using the singular value decomposition of the transformed model matrix, which also provides for efficient determination of the updated regularization parameter each step. Experimental 3D simulations using synthetic data of a dipping dike and a cube anomaly demonstrate that both parameter estimation techniques outperform the Morozov discrepancy principle for determining the regularization parameter. Smaller relative errors of the reconstructed models are obtained with fewer iterations. Data acquired over the Gotvand dam site in the south-west of Iran are used to validate use of the methods for inversion of practical data and provide good estimates of anomalous structures within the subsurface

Intracranial Hemorrhage Due to Secondary Hypertension from Intracranial Large Vessel Occlusion

Simultaneous hemorrhagic and ischemic strokes have been previously reported in the literature. Typically, these occur in patients secondary to dialysis, cerebral amyloid angiopathy, or thrombotic thrombocytopenic purpura.1,2,3 However, this is the unique case of a 62-year-old Asian female who presented with a hemorrhagic stroke suspected to be secondary to refractory hypertension from intracranial large vessel atherosclerotic flow limiting stenosis, with rapid subsequent large vessel occlusion and ischemic stroke. Questions arise such as ideal blood pressure parameters for dual management, timeliness of computed tomography angiography imaging in the emergency department for detection of large vessel occlusion during intracranial hemorrhage, and subsequent selection of treatment plan in the dual-lesion patient population