Moduli stacks of Serre stable representations in tilting theory

We introduce a new moduli stack, called the Serre stable moduli stack, which corresponds to studying families of point objects in an abelian category with a Serre functor. This allows us in particular, to re-interpret the classical derived equivalence between most concealed-canonical algebras and weighted projective lines by showing they are induced by the universal sheaf on the Serre stable moduli stack. We explain why the method works by showing that the Serre stable moduli stack is the tautological moduli problem that allows one to recover certain nice stacks such as weighted projective lines from their moduli of sheaves. As a result, this new stack should be of interest in both representation theory and algebraic geometry

Numerical Analysis of Sparse Initial Data Identification for Parabolic Problems

In this paper we consider a problem of initial data identification from the final time observation for homogeneous parabolic problems. It is well-known that such problems are exponentially ill-posed due to the strong smoothing property of parabolic equations. We are interested in a situation when the initial data we intend to recover is known to be sparse, i.e. its support has Lebesgue measure zero. We formulate the problem as an optimal control problem and incorporate the information on the sparsity of the unknown initial data into the structure of the objective functional. In particular, we are looking for the control variable in the space of regular Borel measures and use the corresponding norm as a regularization term in the objective functional. This leads to a convex but non-smooth optimization problem. For the discretization we use continuous piecewise linear finite elements in space and discontinuous Galerkin finite elements of arbitrary degree in time. For the general case we establish error estimates for the state variable. Under a certain structural assumption, we show that the control variable consists of a finite linear combination of Dirac measures. For this case we obtain error estimates for the locations of Dirac measures as well as for the corresponding coefficients. The key to the numerical analysis are the sharp smoothing type pointwise finite element error estimates for homogeneous parabolic problems, which are of independent interest. Moreover, we discuss an efficient algorithmic approach to the problem and show several numerical experiments illustrating our theoretical results.Comment: 43 pages, 10 figure

Measuring Regional Disparities in Small Countries

Though individual studies of regional disparity may deal with separate development measures - population growth, wages, welfare, regional productivity, etc. - the use of an integrated indicator is often essential, particularly if a comparative (cross-country) analysis is required. In order to measure the extent of disparities, various indices of inequality are commonly used. The goal of present study was to determine whether commonly used inequality measures (Gini, coefficient of variation, etc.) produce meaningful estimates when applied to small countries, thus making it possible to compare the results of analysis obtained for such countries with those obtained elsewhere. As we argue, a small country may differ from a country of larger size in three fundamental features. First, it is likely to have a relatively small number of regional divisions. Second, its regional divisions are likely to vary considerably in their population sizes. Lastly, regions of a small country may rapidly change their rank-order positions in the country-wide hierarchy, by changing their attributes (e.g., population and incomes). In contrast, in a large country such rank-order changes may be both less pronounced and slower-acting. In order to formalize these distinctions, we designed simple empirical tests, in which income and population distributions, presumably characteristic for small countries, were compared with a “reference” distribution, assumed to represent more accurately a country of a larger size. In the latter (reference) distribution, the population was distributed evenly across regional divisions and assumed to be static. In the first test, we checked whether the overall number of regions matters. In the second, we tested whether different inequality indices respond to differences in the regional distribution of population, viz., evenly spread population in the reference distribution vs. unevenly spread population in the test distribution. Finally, in the third test, we verified whether different inequality indices were sensitive to the sequence in which regions are introduced into the calculation. Somewhat surprisingly, none of the indices we tested appeared to pass all the tests, meaning that they may produce (at least in theory) misleading estimates if used for small countries. However, two population weighted indices – Williamson and Gini - appeared to exhibit only minor flaws and may thus be considered as more or less reliable regional inequality measures. Although further studies on the performance of different inequality indices may be needed to verify the generality of our observations, the present analysis clearly cautions against indiscriminate use of inequality indices for regional analysis and comparison.

Quantum hypermultiplet moduli spaces in N=2 string vacua: a review

The hypermultiplet moduli space M_H in type II string theories compactified on a Calabi-Yau threefold X is largely constrained by supersymmetry (which demands quaternion-K\"ahlerity), S-duality (which requires an isometric action of SL(2, Z)) and regularity. Mathematically, M_H ought to encode all generalized Donaldson-Thomas invariants on X consistently with wall-crossing, modularity and homological mirror symmetry. We review recent progress towards computing the exact metric on M_H, or rather the exact complex contact structure on its twistor space.Comment: 31 pages; Contribution to the Proceedings of String Math 2012; v2: references added, misprints corrected, published versio

RATES OF RETURN TO PRIVATE AGRICULTURAL EXTENSION: EVIDENCE FROM TWO FARM MANAGEMENT CENTERS IN EL SALVADOR

This paper evaluates the economic and the financial viability of implementing private farm management centers (FMC) in El Salvador. In doing so, an ex ante cost-benefit analysis is performed. The results of this analysis suggest that a combination of better farm prices (paid and received), reallocation of resources, and crop diversification that would be promoted by a FMC can lead to an increase in farm level profits that is sufficient to cover the operation of the center and to still generate net gains in household income.Farm Management,

Hierarchical Bayesian inference of galaxy redshift distributions from photometric surveys

Accurately characterizing the redshift distributions of galaxies is essential for analysing deep photometric surveys and testing cosmological models. We present a technique to simultaneously infer redshift distributions and individual redshifts from photometric galaxy catalogues. Our model constructs a piecewise constant representation (effectively a histogram) of the distribution of galaxy types and redshifts, the parameters of which are efficiently inferred from noisy photometric flux measurements. This approach can be seen as a generalization of template-fitting photometric redshift methods and relies on a library of spectral templates to relate the photometric fluxes of individual galaxies to their redshifts. We illustrate this technique on simulated galaxy survey data, and demonstrate that it delivers correct posterior distributions on the underlying type and redshift distributions, as well as on the individual types and redshifts of galaxies. We show that even with uninformative priors, large photometric errors and parameter degeneracies, the redshift and type distributions can be recovered robustly thanks to the hierarchical nature of the model, which is not possible with common photometric redshift estimation techniques. As a result, redshift uncertainties can be fully propagated in cosmological analyses for the first time, fulfilling an essential requirement for the current and future generations of surveys.Comment: 10 pages, matches version accepted in MNRAS, including new appendix describing the effect of Bayesian shrinkage in a simplified settin