Simulating extended reproduction: Poverty reduction and class dynamics in Bolivia

An extended reproduction model is used to simulate the effects of alternative poverty reduction strategies. Three policy variables are introduced: (de)indebtedness policy, investment policy and income distribution policy, contributing respectively to the objectives of policy sovereignty, structural change and social justice. The Millennium Development Goal of halving extreme poverty by 2015 seems to be a difficult, but attainable goal for Bolivia. The model shows also the effects of poverty reduction strategies on the different social classes.industrial policy, income distribution, economic development, investment planning

Systematic Codes for Rank Modulation

The goal of this paper is to construct systematic error-correcting codes for permutations and multi-permutations in the Kendall's $\tau$-metric. These codes are important in new applications such as rank modulation for flash memories. The construction is based on error-correcting codes for multi-permutations and a partition of the set of permutations into error-correcting codes. For a given large enough number of information symbols $k$, and for any integer $t$, we present a construction for ${(k+r,k)}$ systematic $t$-error-correcting codes, for permutations from $S_{k+r}$, with less redundancy symbols than the number of redundancy symbols in the codes of the known constructions. In particular, for a given $t$ and for sufficiently large $k$ we can obtain $r=t+1$. The same construction is also applied to obtain related systematic error-correcting codes for multi-permutations.Comment: to be presented ISIT201

Derivations, extensions, and rigidity of subalgebras of the Witt algebra

Let $\Bbbk$ be an algebraically closed field of characteristic 0. We study some cohomological properties of Lie subalgebras of the Witt algebra $W = \operatorname{Der}(\Bbbk[t,t^{-1}])$ and the one-sided Witt algebra $W_{\geq -1} = \operatorname{Der}(\Bbbk[t])$. In the first part of the paper, we consider finite codimension subalgebras of $W_{\geq -1}$. We compute derivations and one-dimensional extensions of such subalgebras. These correspond to $\operatorname{Ext}_{U(L)}^1(M,L)$, where $L$ is a subalgebra of $W_{\geq -1}$ and $M$ is a one-dimensional representation of $L$. We find that these subalgebras exhibit a kind of rigidity: their derivations and extensions are controlled by the full one-sided Witt algebra. As an application of these computations, we prove that any isomorphism between finite codimension subalgebras of $W_{\geq -1}$ extends to an automorphism of $W_{\geq -1}$. The second part of the paper is devoted to explaining the observed rigidity. We define a notion of "completely non-split extension" and prove that $W_{\geq -1}$ is the universal completely non-split extension of any of its subalgebras of finite codimension. In some sense, this means that even when studying subalgebras of $W_{\geq -1}$ as abstract Lie algebras, they remember that they are contained in $W_{\geq -1}$. We also consider subalgebras of infinite codimension, explaining the similarities and differences between the finite and infinite codimension situations. Almost all of the results above are also true for subalgebras of the Witt algebra. We summarise results for $W$ at the end of the paper.Comment: 34 pages. Comments welcome

Tilings by (0.5,n)(0.5,n)-Crosses and Perfect Codes

The existence question for tiling of the $n$-dimensional Euclidian space by crosses is well known. A few existence and nonexistence results are known in the literature. Of special interest are tilings of the Euclidian space by crosses with arms of length one, known also as Lee spheres with radius one. Such a tiling forms a perfect code. In this paper crosses with arms of length half are considered. These crosses are scaled by two to form a discrete shape. We prove that an integer tiling for such a shape exists if and only if $n=2^t-1$ or $n=3^t-1$, $t>0$. A strong connection of these tilings to binary and ternary perfect codes in the Hamming scheme is shown

How to attract central and Northeneuropeans to a rural tourism establishment in the center of Portugal

A Work Project, presented as part of the requirements for the Award of a Masters Degree in Management from the NOVA – School of Business and EconomicsThe rural tourism market in Portugal has been growing, showing a positive trend of foreign people’s overnight stays. These individuals are motivated by factors like: rest and relax far from the cities, and interest in culture and traditions of the rural region. According to the study, the rural tourist can be segmented into two distinct groups, representing different primary motivations and behaviors. After having performed a set of researches, Monte do Areeiro - a Portuguese rural tourism establishment - is able to follow the best marketing strategies and the respective action plans to better satisfy its customers