New Set of Codes for the Maximum-Likelihood Decoding Problem

The maximum-likelihood decoding problem is known to be NP-hard for general linear and Reed-Solomon codes. In this paper, we introduce the notion of A-covered codes, that is, codes that can be decoded through a polynomial time algorithm A whose decoding bound is beyond the covering radius. For these codes, we show that the maximum-likelihood decoding problem is reachable in polynomial time in the code parameters. Focusing on bi- nary BCH codes, we were able to find several examples of A-covered codes, including two codes for which the maximum-likelihood decoding problem can be solved in quasi-quadratic time.Comment: in Yet Another Conference on Cryptography, Porquerolle : France (2010

Re-encoding reformulation and application to Welch-Berlekamp algorithm

The main decoding algorithms for Reed-Solomon codes are based on a bivariate interpolation step, which is expensive in time complexity. Lot of interpolation methods were proposed in order to decrease the complexity of this procedure, but they stay still expensive. Then Koetter, Ma and Vardy proposed in 2010 a technique, called re-encoding, which allows to reduce the practical running time. However, this trick is only devoted for the Koetter interpolation algorithm. We propose a reformulation of the re-encoding for any interpolation methods. The assumption for this reformulation permits only to apply it to the Welch-Berlekamp algorithm

Application of a Two-Parameter Quantum Algebra to Rotational Spectroscopy of Nuclei

A two-parameter quantum algebra $U_{qp}({\rm u}_2)$ is briefly investigated in this paper. The basic ingredients of a model based on the $U_{qp}({\rm u}_2)$ symmetry, the $qp$-rotator model, are presented in detail. Some general tendencies arising from the application of this model to the description of rotational bands of various atomic nuclei are summarized.Comment: 8 pages, Latex File, to be published in Reports on Mathematical Physic

Water and Economic Growth

Several hydrological studies forecast a global problem of water scarcity. This raises the question as to whether increasing water scarcity may impose constraints on the growth of countries. The influence of water utilization on economic growth is depicted through a growth model that includes this congestible public good as a productive input for private producers. Growth is negatively affected by the government's appropriation of output to supply water but positively influenced by the contribution of increased water use to capital productivity, leading to an inverted-U relationship between economic growth and the rate of water utilization. Crosscountry estimations confirm this relationship and suggest that for most economies current rates of freshwater utilization are not yet constraining growth. However, for a handful of countries, moderate or extreme water scarcity may affect economic growth adversely. Nevertheless, even for water-scarce countries, there appears to be little evidence that there are severe diminishing returns to allocating more output to provide water, thus resulting in falling income per capita. These results suggest caution over the claims of some hydrological-based studies of a widespread global "water crisis".Congestible public goods, cross-country regressions, economic growth, freshwater, water scarcity.

The variety of reductions for a reductive symmetric pair

We define and study the variety of reductions for a reductive symmetric pair (G,theta), which is the natural compactification of the set of the Cartan subspaces of the symmetric pair. These varieties generalize the varieties of reductions for the Severi varieties studied by Iliev and Manivel, which are Fano varieties. We develop a theoretical basis to the study these varieties of reductions, and relate the geometry of these variety to some problems in representation theory. A very useful result is the rigidity of semi-simple elements in deformations of algebraic subalgebras of Lie algebras. We apply this theory to the study of other varieties of reductions in a companion paper, which yields two new Fano varieties.Comment: 23 page

The Role of Natural Resources in Economic Development

In recent years economists have recognized that, along with physical and human capital, environmental resources should be viewed as important economic assets, which can be called natural capital. However, the services provided by natural capital are unique. They include the use of resources for material and energy inputs, the "assimilative capacity" to absorb waste, and the provision of ecological services. The latter services are particularly not well understood, and lie at the heart of the debate over the role of natural capital in sustainable development. That is, does the environment have a unique or "essential" role in sustaining human welfare, and if so, are special "compensation rules" required to ensure that future generations are not made worse off by natural capital depletion today? A further debate has emerged over whether environmental degradation in an economy may initially increase, but eventually declines, as per capita income increases. This hypothesis, called the environmental Kuznets curve (EKC) has led to a number of attempts to estimate empirically an "inverted U" shaped relationship between a variety of indicators of environmental pollution or resource depletion and the level of per capita income. Finally, recent economic theories and empirical evidence have questioned whether poorer economies that are endowed with abundant natural resources develop more rapidly than economies that are relatively resource poor. It is possible that resource abundant economies are not reinvesting the rents generated from natural resource exploitation into productive assets, or that resource booms actually divert economic resources from more productive and innovative sectors. The result is a "boom and bust" pattern of economic development. There is evidence of this phenomenon particularly with regard to economic development and land expansion, especially in Latin America. Overall, although our understanding of the role of natural resources in economic development has improved markedly in recent decades, there is still much to learn. How natural resource depletion is affecting the ecological services provided by the environment is one concern. In the case of the poor economies, there is increasing evidence that their prospects for economic "take off" are being adversely affected by the lack of efficient and sustainable management of their natural resource base. Yet the "underpricing" and "undervaluing" of natural capital makes it difficult to design appropriate policies for ensuring that natural resource rents are reinvested in other productive assets of the economy.Economic development, Environmental Kuznets curve, Natural capital, Natural resources, Resource-abundant economies, Sustainable development

The Joseph ideal for sl(m∣n)\mathfrak{sl}(m|n)

Using deformation theory, Braverman and Joseph obtained an alternative characterisation of the Joseph ideal for simple Lie algebras, which included even type A. In this note we extend that characterisation to define a remarkable quadratic ideal for sl(m|n). When m-n>2 we prove the ideal is primitive and can also be characterised similarly to the construction of the Joseph ideal by Garfinkle

Improving success probability and embedding efficiency in code based steganography

For stegoschemes arising from error correcting codes, embedding depends on a decoding map for the corresponding code. As decoding maps are usually not complete, embedding can fail. We propose a method to ensure or increase the probability of embedding success for these stegoschemes. This method is based on puncturing codes. We show how the use of punctured codes may also increase the embedding efficiency of the obtained stegoschemes

Steps and terraces at quasicrystal surfaces. Application of the 6d-polyhedral model to the analysis of STM images of i-AlPdMn

6-d polyhedral models give a periodic description of aperiodic quasicrystals. There are powerful tools to describe their structural surface properties. Basis of the model for icosahedral quasicrystals are given. This description is further used to interpret high resolution STM images of the surface of i-AlPdMn which surface preparation was followed by He diffraction. It is found that both terrace structure and step-terrace height profiles in STM images can be consistently interpreted by the described model