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In the late 70’s A. Kouchnirenko posed the problem of bounding from above the number of positive real roots (that is, with positive coordinates) of a system of k polynomial equations in k variables not in function of the degrees of the polynomials (like in Bezout Theorem), but in function of the number of terms involved, and he conjectured an upper bound.(More)
M. Mosconi,1 K. Fujii,2 A. Mengoni,3,18 C. Domingo-Pardo,1,4 F. Käppeler,1 U. Abbondanno,2 G. Aerts,5 H. Álvarez-Pol,6 F. Alvarez-Velarde,7 S. Andriamonje,5 J. Andrzejewski,8 P. Assimakopoulos,9 L. Audouin,1 G. Badurek,10 P. Baumann,11 F. Bečvář,12 F. Belloni,2 E. Berthoumieux,5 S. Bisterzo,1,13 M. Calviani,14 F. Calviño,15 D. Cano-Ott,7 R. Capote,3,16 A.(More)
We consider linear ill-posed inverse problems y = Ax, in which we want to infer many count parameters x from few count observations y, where the matrix A is binary and has some unimodularity property. Such problems are typical in applications such as contingency table analysis and network tomog-raphy (on which we present testing results). These properties(More)
We consider here an election ballot as a document, a document that works as the carrier of a voter's choice in an election's accounting system for determining a winning candidate. And we consider a voting system as a way to manage both the document and its flow in compliance with the requirements of the election. Trustworthy elections are the core of a(More)
G. Tagliente,1,* K. Fujii,2 P. M. Milazzo,2 C. Moreau,2 G. Aerts,3 U. Abbondanno,2 H. Álvarez,4 F. Alvarez-Velarde,5 S. Andriamonje,3 J. Andrzejewski,6 P. Assimakopoulos,7 L. Audouin,8 G. Badurek,9 P. Baumann,10 F. Bečvář,11 E. Berthoumieux,3 S. Bisterzo,12 F. Calviño,13 M. Calviani,14 D. Cano-Ott,5 R. Capote,15,16 C. Carrapiço,17 P. Cennini,18 V. Chepel,19(More)
INTRODUCTION There was a growing need for practical guidelines for the most common OIs in Germany and Austria under consideration of the local epidemiological conditions. MATERIALS AND METHODS The German and Austrian AIDS societies developed these guidelines between March 2010 and November 2011. A structured Medline research was performed for 12 diseases,(More)
G. Tagliente,1,2,* P. M. Milazzo,3 K. Fujii,3 U. Abbondanno,3 G. Aerts,4 H. Álvarez,5 F. Alvarez-Velarde,6 S. Andriamonje,4 J. Andrzejewski,7 L. Audouin,8 G. Badurek,9 P. Baumann,10 F. Bečvář,11 F. Belloni,3 E. Berthoumieux,4 S. Bisterzo,12 F. Calviño,13 M. Calviani,14 D. Cano-Ott,6 R. Capote,15,16 C. Carrapiço,17 P. Cennini,18 V. Chepel,19 E. Chiaveri,18(More)
Foot-and-mouth disease (FMD) is a highly contagious viral disease of cloven-hoofed animals, which leads to the formation of vesicles, erosions und ulcerations in the mouth and hairless parts of the skin, in particular on the feet. Due to its dramatic economic consequences, FMD is considered to be one of the most important diseases of animals. There is a(More)
T-curves are piecewise linear curves which have been used with success since the beginning of the 1990's to construct new real algebraic curves with prescribed topol-ogy mainly on the real projective plane (see [11,7,3]). In fact T-curves can be used on any real projective toric surface. We generalize here the construction of the latter by departing from(More)
1 Introduccion These expository notes present several examples of how combinatorial methods can be used in Algebraic Geometry. The rst part describes the state and secondary polytopes and how they are useful to understand the structure of Grr obner bases of a toric variety. A central point is an interesting bijection between triangulations and initial(More)