Secret Sharing Schemes with a large number of players from Toric Varieties

A general theory for constructing linear secret sharing schemes over a finite field \Fq from toric varieties is introduced. The number of players can be as large as $(q-1)^r-1$ for $r\geq 1$. We present general methods for obtaining the reconstruction and privacy thresholds as well as conditions for multiplication on the associated secret sharing schemes. In particular we apply the method on certain toric surfaces. The main results are ideal linear secret sharing schemes where the number of players can be as large as $(q-1)^2-1$. We determine bounds for the reconstruction and privacy thresholds and conditions for strong multiplication using the cohomology and the intersection theory on toric surfaces.Comment: 15 pages, 4 figures. arXiv admin note: text overlap with arXiv:1203.454

Quantum Codes from Toric Surfaces

A theory for constructing quantum error correcting codes from Toric surfaces by the Calderbank-Shor-Steane method is presented. In particular we study the method on toric Hirzebruch surfaces. The results are obtained by constructing a dualizing differential form for the toric surface and by using the cohomology and the intersection theory of toric varieties. In earlier work the author developed methods to construct linear error correcting codes from toric varieties and derive the code parameters using the cohomology and the intersection theory on toric varieties. This method is generalized in section to construct linear codes suitable for constructing quantum codes by the Calderbank-Shor-Steane method. Essential for the theory is the existence and the application of a dualizing differential form on the toric surface. A.R. Calderbank, P.W. Shor and A.M. Steane produced stabilizer codes from linear codes containing their dual codes. These two constructions are merged to obtain results for toric surfaces. Similar merging has been done for algebraic curves with different methods by A. Ashikhmin, S. Litsyn and M.A. Tsfasman.Comment: IEEE copyrigh

The Return to Foreign Aid

This paper investigates the marginal productivity of investment in the world’s poorest economies. The aim is to estimate the return on investments financed by foreign aid as well as by domestic resource mobilization, using crosscountry aggregate data. In practice the return on both investment categories can be expected to vary considerably across countries and time. As a consequence we develop a correlated random coefficients approach to the issue at hand, which allows us to estimate the average aggregate rate of return on “aid investments” and “domestic investments”. Across a wide array of estimators our principal finding is remarkably robust; the average aggregate gross return on “aid investments” falls in a 20-30 percent range, roughly the same as the return on investments funded by other sources than aid. This finding is well in accord with micro estimates of the economic return to aid.productivity, foreign aid, random coefficients, panel data

Evaluating Aid Effectiveness in the Aggregate: A critical assessment of the evidence

The purpose of the present evaluation study is to discuss the empirical studies that attempt to estimate the impact of foreign aid on economic growth. The study draws on a previous evaluation study (Dalgaard and Hansen, 2009), which introduces the general econometric methodology involved in making assessments about the aggregate impact of aid. In order to fully benefit from the discussion below it is therefore advisable for readers without prior knowledge of econometrics to review the material discussed in Dalgaard and Hansen (2009). The present study provides insights into the following questions 1. What are the central mechanisms linking aid to growth? 2. How much should one expect from aid a priori? 3. What are the best available estimates of the impact from total aid on economic growth in income per capita? 4. Does aid modality matter?Economic growth; foreign aid

Evaluating Aid Effectiveness in the Aggregate: Methodological Issues

The purpose of the present Evaluation Study is to discuss the methodological problems researchers are facing in gauging the impact of aid on economic growth. The discussion is nontechnical and aimed at an audience without much prior knowledge in the fields of macroeconomics and econometrics. The paper provides insights into the following questions: 1. Why do economists view “aid effectiveness” as synonymous to asking whether aid increases growth in income per capita? 2. Why is it difficult to determine the macroeconomic impact of foreign aid on economic growth? 3. How is it, in principle, possible to solve the difficulties present in evaluating aggregate aid effectiveness?Economic growth; foreign aid; instrumental variable regression

Measuring the 3D shape of X-ray clusters

Observations and numerical simulations of galaxy clusters strongly indicate that the hot intracluster x-ray emitting gas is not spherically symmetric. In many earlier studies spherical symmetry has been assumed partly because of limited data quality, however new deep observations and instrumental designs will make it possible to go beyond that assumption. Measuring the temperature and density profiles are of interest when observing the x-ray gas, however the spatial shape of the gas itself also carries very useful information. For example, it is believed that the x-ray gas shape in the inner parts of galaxy clusters is greatly affected by feedback mechanisms, cooling and rotation, and measuring this shape can therefore indirectly provide information on these mechanisms. In this paper we present a novel method to measure the three-dimensional shape of the intracluster x-ray emitting gas. We can measure the shape from the x-ray observations only, i.e. the method does not require combination with independent measurements of e.g. the cluster mass or density profile. This is possible when one uses the full spectral information contained in the observed spectra. We demonstrate the method by measuring radial dependent shapes along the line of sight for CHANDRA mock data. We find that at least 10^6 photons are required to get a 5-{\sigma} detection of shape for an x-ray gas having realistic features such as a cool core and a double powerlaw for the density profile. We illustrate how Bayes' theorem is used to find the best fitting model of the x-ray gas, an analysis that is very important in a real observational scenario where the true spatial shape is unknown. Not including a shape in the fit may propagate to a mass bias if the x-ray is used to estimate the total cluster mass. We discuss this mass bias for a class of spacial shapes.Comment: 29 pages, 16 figure

On the Empirics of Foreign Aid and Growth.

This paper takes a fresh look at two issues in the aid effectiveness debate. We begin by providing theoretical foundations for the various claims made with regard to the effectiveness of aid in stimulating long-run productivity. When foreign aid is modelled as an exogenous transfer of income or capital in a standard OLG model, aid wil in general impact on productivity. Moreover in this setting, the “returns to aid” may depend on both policy and structural characteristics. Next we reexamine the case for policy-based conditionality. Our empirical analysis suggests that aid is generally effective, even in “bad” environments. However, the degree to which aid enhances growth depends on climate-related circumstances. In light of this finding we argue that the Collier-Dollar allocation rule should be seriously reconsidered by donor agencies.

Income Skewness, Redistribution and Growth: A Reconciliation.

The so-called “fiscal policy approach" predicts that increases in income skewness should be associated with an intensification of redistributive efforts, at least in democracies. If redistribution is detrimental to growth, then this implies that a poor middle class is bad for long-run productivity; a prediction which has found empirical support. However, cross-country studies tend to find a negative association between income skewness and the amount of redistribution taking place, and, a positive relationship between redistributive taxation and growth. This paper offers a reconciliation of the existing theory and these puzzling findings. Specifically, the model predicts that the traditionally stipulated chains of causality holds within countries, whereas the puzzling correlations mentioned above may arise across countries. We provide a test of our explanation and find support for our approach using data on income taxes, taxes on property and expenditures on education.income distribution; political economy; endogenous growth