9,342 research outputs found
Polar Varieties and Efficient Real Elimination
Let be a smooth and compact real variety given by a reduced regular
sequence of polynomials . This paper is devoted to the
algorithmic problem of finding {\em efficiently} a representative point for
each connected component of . For this purpose we exhibit explicit
polynomial equations that describe the generic polar varieties of . This
leads to a procedure which solves our algorithmic problem in time that is
polynomial in the (extrinsic) description length of the input equations and in a suitably introduced, intrinsic geometric parameter, called
the {\em degree} of the real interpretation of the given equation system .Comment: 32 page
Polar Varieties, Real Equation Solving and Data-Structures: The hypersurface case
In this paper we apply for the first time a new method for multivariate
equation solving which was developed in \cite{gh1}, \cite{gh2}, \cite{gh3} for
complex root determination to the {\em real} case. Our main result concerns the
problem of finding at least one representative point for each connected
component of a real compact and smooth hypersurface. The basic algorithm of
\cite{gh1}, \cite{gh2}, \cite{gh3} yields a new method for symbolically solving
zero-dimensional polynomial equation systems over the complex numbers. One
feature of central importance of this algorithm is the use of a
problem--adapted data type represented by the data structures arithmetic
network and straight-line program (arithmetic circuit). The algorithm finds the
complex solutions of any affine zero-dimensional equation system in non-uniform
sequential time that is {\em polynomial} in the length of the input (given in
straight--line program representation) and an adequately defined {\em geometric
degree of the equation system}. Replacing the notion of geometric degree of the
given polynomial equation system by a suitably defined {\em real (or complex)
degree} of certain polar varieties associated to the input equation of the real
hypersurface under consideration, we are able to find for each connected
component of the hypersurface a representative point (this point will be given
in a suitable encoding). The input equation is supposed to be given by a
straight-line program and the (sequential time) complexity of the algorithm is
polynomial in the input length and the degree of the polar varieties mentioned
above.Comment: Late
Polar Varieties and Efficient Real Equation Solving: The Hypersurface Case
The objective of this paper is to show how the recently proposed method by
Giusti, Heintz, Morais, Morgenstern, Pardo \cite{gihemorpar} can be applied to
a case of real polynomial equation solving. Our main result concerns the
problem of finding one representative point for each connected component of a
real bounded smooth hypersurface. The algorithm in \cite{gihemorpar} yields a
method for symbolically solving a zero-dimensional polynomial equation system
in the affine (and toric) case. Its main feature is the use of adapted data
structure: Arithmetical networks and straight-line programs. The algorithm
solves any affine zero-dimensional equation system in non-uniform sequential
time that is polynomial in the length of the input description and an
adequately defined {\em affine degree} of the equation system. Replacing the
affine degree of the equation system by a suitably defined {\em real degree} of
certain polar varieties associated to the input equation, which describes the
hypersurface under consideration, and using straight-line program codification
of the input and intermediate results, we obtain a method for the problem
introduced above that is polynomial in the input length and the real degree.Comment: Late
Real root finding for equivariant semi-algebraic systems
Let be a real closed field. We consider basic semi-algebraic sets defined
by -variate equations/inequalities of symmetric polynomials and an
equivariant family of polynomials, all of them of degree bounded by .
Such a semi-algebraic set is invariant by the action of the symmetric group. We
show that such a set is either empty or it contains a point with at most
distinct coordinates. Combining this geometric result with efficient algorithms
for real root finding (based on the critical point method), one can decide the
emptiness of basic semi-algebraic sets defined by polynomials of degree
in time . This improves the state-of-the-art which is exponential
in . When the variables are quantified and the
coefficients of the input system depend on parameters , one
also demonstrates that the corresponding one-block quantifier elimination
problem can be solved in time
The new resilience of emerging and developing countries: systemic interlocking, currency swaps and geoeconomics
The vulnerability/resilience nexus that defined the interaction between advanced and developing economies in the post-WWII era is undergoing a fundamental transformation. Yet, most of the debate in the current literature is focusing on the structural constraints faced by the Emerging and Developing Countries (EDCs) and the lack of changes in the formal structures of global economic governance. This paper challenges this literature and its conclusions by focusing on the new conditions of systemic interlocking between advanced and emerging economies, and by analysing how large EDCs have built and are strengthening their economic resilience. We find that a significant redistribution of ‘policy space’ between advanced and emerging economies have taken place in the global economy. We also find that a number of seemingly technical currency swap agreements among EDCs have set in motion changes in the very structure of global trade and finance. These developments do not signify the end of EDCs’ vulnerability towards advanced economies. They signify however that the economic and geoeconomic implications of this vulnerability have changed in ways that constrain the options available to advanced economies and pose new challenges for the post-WWII economic order
Geo-additive models of Childhood Undernutrition in three Sub-Saharan African Countries
We investigate the geographical and socioeconomic determinants of childhood undernutrition in Malawi, Tanzania and Zambia, three neighboring countries in Southern Africa using the 1992 Demographic and Health Surveys. We estimate models of undernutrition jointly for the three countries to explore regional patterns of undernutrition that transcend boundaries, while allowing for country-specific interactions. We use semiparametric models to flexibly model the effects of selected so-cioeconomic covariates and spatial effects. Our spatial analysis is based on a flexible geo-additive model using the district as the geographic unit of anal-ysis, which allows to separate smooth structured spatial effects from random effect. Inference is fully Bayesian and uses recent Markov chain Monte Carlo techniques. While the socioeconomic determinants generally confirm what is known in the literature, we find distinct residual spatial patterns that are not explained by the socioeconomic determinants. In particular, there appears to be a belt run-ning from Southern Tanzania to Northeastern Zambia which exhibits much worse undernutrition, even after controlling for socioeconomic effects. These effects do transcend borders between the countries, but to a varying degree. These findings have important implications for targeting policy as well as the search for left-out variables that might account for these residual spatial patterns
Risk attitudes and informal employment in a developing economy
© 2012 Bennett et al.; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons
Attribution License(http://creativecommons.org/licenses/by/2.0),which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.We model an urban labour market in a developing economy, incorporating workers’ risk attitudes. Trade-offs between risk aversion and ability determine worker allocation across formal and informal wage employment, and voluntary and involuntary self employment. Greater risk of informal wage non-payment can raise or lower informal wage employment, depending on the source of risk. Informal wage employment can be reduced by increasing detection efforts or by strengthening contract enforcement for informal wage payment. As the average ability of workers rises, informal wage employment first rises, then falls. Greater demand for formal production may lead to more involuntary self employment
Constraints to the sustainability of a ‘systematised’ approach to livestock marketing amongst smallholder cattle producers in South Africa
Commercialization of smallholder agriculture in South Africa is underpinned by reforms to improve livestock off-take in communal areas and engage smallholder farmers with formal markets. To achieve this, Custom Feeding Programmes (CFPs) were established to improve the condition of communal cattle prior to their sale into formal markets and to ‘systematise’ the informal marketing of cattle in communal areas by enabling participants to achieve higher informal market prices. We evaluate the sustainability of eight CFPs located in Eastern Cape Province in terms of their ability to add value to smallholder cattle production and encourage market participation. Communities with CFPs achieved a 16.6% mean cattle off-take rate, substantially higher than in most communal systems. Furthermore, cattle sold through CFPs attained a 17% higher mean selling price than those sold through other marketing channels. However, these benefits were mainly realized by better-off farmers with larger cattle herds and greater ability to transport animals to and from CFPs. More marginalized farmers, particularly women, had low participation. CFPs also face challenges to their sustainability, including inconsistent feed and water supplies, poor infrastructure and high staff turnover. Key to enhancing participation in CFPs, will be improving the way they are supported and embedded within communities
Life below excellence: exploring the links between top-ranked universities and regional competitiveness
[EN] This paper examines interactions between the presence of top-ranked universities and other conditions that encourage regional competitiveness. Fuzzy-set qualitative comparative analysis (fsQCA) was conducted to assess the combined effect of the conditions. The analysis yields several noteworthy conclusions. First, no single condition is necessary for a region to be competitive. Second, R&D expenditure is important for regional competitiveness. Third, different configurations of conditions are sufficient for high competitiveness in different regional clusters. Furthermore, some of these configurations do not include the presence of top-ranked universities. A 'magic recipe' consists of the combination of a private research system, an inter-firm collaboration network and high levels of human capital. The analysis shows that university excellence is valuable. However, in terms of its contribution to regional development, it is not crucial and must always be contextualised. This conclusion is important for smart strategic planning of local knowledge systems.Jose-Maria Garcia-Alvarez-Coque and Francisco Mas-Verdu wish to thank Project RTI2018-093791-B-C22, funded by the Ministry of Science, Innovation and Universities (Spain), for supporting this research.García Alvarez-Coque, JM.; Mas Verdú, F.; Roig Tierno, H. (2021). Life below excellence: exploring the links between top-ranked universities and regional competitiveness. Studies in Higher Education. 46(2):369-384. https://doi.org/10.1080/03075079.2019.1637843S369384462Alamá-Sabater, L., Budí, V., García-Álvarez-Coque, J. M., & Roig-Tierno, N. (2019). Using mixed research approaches to understand rural depopulation. Economía Agraria y Recursos Naturales, 19(1), 99. doi:10.7201/earn.2019.01.06Baldacci, E., Clements, B., Gupta, S., & Cui, Q. (2008). Social Spending, Human Capital, and Growth in Developing Countries. 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