Equal Sum Sequences and Imbalance Sets of Tournaments

Reid conjectured that any finite set of non-negative integers is the score set of some tournament and Yao gave a non-constructive proof of Reid's conjecture using arithmetic arguments. No constructive proof has been found since. In this paper, we investigate a related problem, namely, which sets of integers are imbalance sets of tournaments. We completely solve the tournament imbalance set problem (TIS) and also estimate the minimal order of a tournament realizing an imbalance set. Our proofs are constructive and provide a pseudo-polynomial time algorithm to realize any imbalance set. Along the way, we generalize the well-known equal sum subsets problem (ESS) to define the equal sum sequences problem (ESSeq) and show it to be NP-complete. We then prove that ESSeq reduces to TIS and so, due to the pseudo-polynomial time complexity, TIS is weakly NP-complete.Comment: Presented at the Retrospective Workshop on Discrete Geometry, Optimization and Symmetry, 25-29 Nov 2013, The Fields Institute, Toronto, Canad

In vitro Evolution and Engineering for Improved Ribozyme Polymerase Production

According to the "RNA World Hypothesis" the first self replicating molecule formed from the prebiotic chemicals is the ribozyme. A model compartmentalized self replicating system for ribozyme polymerases is designed and used to improve activity, fidelity and generality of the enzyme

The small and medium enterprises Act as catalyst for economic growth and development in Pakistan: Economic growth and development perspective

This paper explores the value of small and medium enterprises for the economic growth and development especially in Pakistan. Moreover, it assesses the usage of information technology in SMEs sector of Pakistan. According to the recent Census of Establishments conducted by the Federal Bureau of Statistics (FBS) there are about 3.2 million economic establishments in Pakistan. Out of these Small & Medium sized enterprises (SMEs) (with employment base up to 99) constitute 90% of all private enterprises employing approximately 78% of non-agriculture labor force1. SMEs contributed over 30% to GDP, 25% in export earnings besides sharing 35% in manufacturing value addition2. The paper suggests that SMEs act as a catalyst to economical growth and development where IT embedded in their operations, planning and decisions like Hong Kong, Denmark and USA. Many other societies also place great value on the small and medium enterprises and encourage their activity. In fact, wealth and a high majority of jobs are created by small & medium businesses in the world. As a result, many experienced business people, political leaders, economists, and educators believe that fostering a robust small and medium business culture will maximize individual and collective economic and social success on a local, national, and global scale. It is recommended that SMEs may be offered access to inexpensive capital, tax exemptions and management advice & experiences and IT infrastructure which further leads toward the economical growth & development. The economical growth and development in a country can brings happiness and prosperity to its nation

Export potential of cottage industry: a case study of Sialkot (Pakistan)

Sialkot, the export city of Pakistan is earning $900 million per annum by exports. The major exports are the sports goods, surgical instruments, leather products, martial art instruments, musical instruments and sports wear. All these products are value-added by cottage industry. How the export potential of cottage industry in Sialkot may be increased,that is the question. The current paper estimated the export potential of the cottage industry by measuring it through Cobb-Douglas production function. The data has been collected from 354 cottage industrial units selected by random sampling. The results explain that labor, capital, experience and education of entrepreneur, and working conditions enhance the export potential of the units. The labor is more used in cottage industrial units as compared to capital so the elasticity of export production with respect to labor is higher as compared to capital. The football making units and other sports goods producing units use a minor ratio of capital and largely depend upon labor for production. Although leather and surgical producing units use higher ratio of capital in production. The education and experience of the entrepreneur also lead to increased export production. The better working condition increases the export production by raising the productivity of labor. The study proposes the education and training of the individuals involved in cottage industry and provision of good working conditions by the Export Promotion Bureau, Sialkot Chamber of Commerce and Industry and vocational training institutes in their respective areas. The surprising results of the study are that credit availed by the units decrease the export production while distance to market from the unit raises the export production. The relationship between credit and export production explains the misutilization of credit while positive association between distance to market and export production explains the involvement of more number of household members in production in the units away from city as compared to the units situated near to market or city. The misutilization of loaning is needed to be checked.Cottage industry, Pakistan, Exports, Cobb-Douglas production function, Sialkot

Impact evaluation of structural adjustment program: a case of Pakistan

We analyzed the effect of Structural Adjustment Program (SAP) on macroeconomic variables of Pakistan using annual time series data for the years 1981-2001. The impact of four policy instruments of SAP, i.e. reduction in budget deficit, increase in indirect taxes,adjusting the exchange rate and sliding down of subsidies, on employment, income distribution, per-capita income and inflation has been analyzed. It is found that the first policy instrument, i.e. decrease in budget deficit has affected employment, income distribution and inflation adversely. The second policy instrument of imposition of indirect tax negatively affected the employment, income distribution, per capita income and positively affected the inflation. The third policy instrument of SAP was adjustment of exchange rate. It is estimated that adjusting exchange rate has resulted into increased unemployment and inflation. The fourth policy instrument of shrink in subsidies augmented the unemployment, unequal distribution of income and inflation and dwindled the percapita income. It appears that SAP has adversely affected the major socioeconomic variables of the economy. Currently the government is considering for loan from IMF, so it is proposed to avoid such type of policy directives from IMF.Structural Adjustment Program, Budget deficit, Indirect taxes, Exchange rate, Subsidies, Employment, Income distribution, Per-capita income, Inflation,Pakistan

Procyclical Monetary Policy and Governance

Weak governance adversely affects firm’s net worth and consequently the value of its collateral. This negative impact on the collateral reduces the external credit available for importing inputs constraining potential output. As a result, a stronger procyclical monetary policy stance is adopted for protecting the exchange rate and hence arresting the degradation in the collateral constraint.Collateral Constraints; Governance; Monetary Policy

Financial Liberalization And Demand For Money: A Case of Pakistan

Literature in economics has identified many channels through which the financial liberalization may affect demand for money. There are evidences of stability as well as instability of demand for money due to financial development for developing economies. The objective of the current study is to examine the effect of financial liberalization on demand for money in Pakistan, i.e. whether financial liberalization has affected the demand for money or not. The issue is important as stable demand for money function is a prerequisite for formulating and operating monetary policy. To achieve the objective JJ cointegration and auto regressive distributed lag (ARDL) to the cointegration is employed to estimate the long-run equilibrium relationship between broad money M2 and composite financial liberalization index along with other determinants of demand for money like gross domestic product, real deposit rate and exchange rate. In order to assess the stability of the model, the parameter constancy tests, i.e. recursive residuals, CUSUM and CUSUMSQ tests have been applied. The empirical results indicated that for broad money, there exists long-run money demand function. The financial liberalization, gross domestic product and real deposit rate positively affect the demand for money in the long as well as short-run.Demand for money, Financial liberalization, Real deposit rate, Financial reforms, Pakistan, ARDL

Industrial Sector Input Demand Responsiveness and Policy Interventions

In Pakistan, government intervention in the input market of the industrial sector is considerable. It regulates prices of virtually all energy and certain other non-labour inputs. To stimulate industrial production and output growth, it also encourages the provision of extended credit facilities to the industrial producers. Further, it has also often announced adjustments/reductions in duties and tariffs on products used in industrial production. Conversely, government also imposes taxes on outputs. It may desire to levy new taxes on the industrial inputs. All interventions have profound implications for producers, consumers and the government alike. Therefore, it is important to know how they may affect the industrial input demand. Further, it is equally important to know how effective they may be for the government in the realisation of its objectives. The most pertinent approach to ascertain the industrial input demand responsiveness to government interventions is to obtain valid estimates of price elasticities. In fact, competent elasticity estimates of the producer input demand derived with a sound methodology can serve as a solid basis to predict producer responsiveness to market changes and thereby the effectiveness and desirability of government interventions. While the price elasticities of products over the years have been estimated for Pakistan, renewed interest on estimating responsiveness of producer input demand with modern estimation procedures has recently surged. Idrees (1997) and Khan (1998) have determined elasticities for the domestic large-scale manufacturing sector from a demand system. Although these research studies make a good addition to the literature, their scope is extremely limited because they have combined industrial inputs into large aggregates. At present, there is no study that has investigated the input demand elasticities of the domestic industrial sector at the dis-aggregated level.