11,446 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
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
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 effect of a boots preparation and pure natural secretin and pancreozymin on pancreatic and gastric function in man
Secretin was found to be a powerful inhibitor of basal gastric acid secretion in man. Pure natural secretin was more effective and more rapid in its action on gastric secretion than Boots secretin.Boots pancreozymin and Swedish CCK (cholecystoktnin) had a variable effect on basal gastric acid secretion and all the changes were modest and unimpressive
The effect of a boots preparation and pure natural secretin and pancreozymin on pancreatic and 'gastric function in man
Secretin was found to be a powerful inhibitor of basal gastric acid secretion in man. Pure natural secretin was more effective and more rapid in its action on gastric secretion than Boots secretin. Boots pancreozymin and Swedish CCK (cholecystoktnin) had a variable effect on basal gastric acid secretion and all the changes were modest and unimpressive
Progress in small-bowel physiology and disease
There have been many interesting and exciting developments in the field of gastro-enterology in the past few years. Many of these advances have been due to technical skills in physiology, biochemistry and radiology, but newer diagnostic and therapeutic measures have also been introduced. The complex functions of the small bowel and especially the mucosal lining of the intestine, provide particular scope for detailed multidisciplinary research, clinical, paraclinical and scientific. The present communication reflects our own brief selection of recent advances in the field of small-bowel physiology and disease and does not represent a comprehensive coverage of all the advances in the past decade
Progress in small-bowel physiology and disease
There have been many interesting and exciting developments in the field of gastro-enterology in the past few years. Many of these advances have been due to technical skills in physiology, biochemistry and radiology, but newer diagnostic and therapeutic measures have also been introduced. The complex functions of the small bowel andespecially the mucosal lining of the intestine, provide particular scope for detailed multidisciplinary research, clinical, paraclinical and scientific.The present communication reflects our own brief selection of recent advances in the field of small-bowel physiology and disease and does not represent a comprehensive coverage of all the advances in the past decade
- …