G-biliaison of ladder Pfaffian varieties

The ideals generated by pfaffians of mixed size contained in a subladder of a skew-symmetric matrix of indeterminates define arithmetically Cohen-Macaulay, projectively normal, reduced and irreducible projective varieties. We show that these varieties belong to the G-biliaison class of a complete intersection. In particular, they are glicci.Comment: 15 page

Universal Gröbner Bases for Maximal Minors

Bernstein, Sturmfels, and Zelevinsky proved in 1993 that the maximal minors of a matrix of variables form a universal Gröbner basis. We present a very short proof of this result, along with broad generalization to matrices with multihomogeneous structures. Our main tool is a rigidity statement for radical Borel fixed ideals in multigraded polynomial ring

Radical Generic Initial Ideals

In this paper, we survey the theory of Cartwright\u2013Sturmfels ideals. These are \u2124n-graded ideals, whose multigraded generic initial ideal is radical. Cartwright\u2013Sturmfels ideals have surprising properties, mostly stemming from the fact that their Hilbert scheme only contains one Borel-fixed point. This has consequences, e.g., on their universal Gr\uf6bner bases and on the family of their initial ideals. In this paper, we discuss several known classes of Cartwright\u2013Sturmfels ideals and we find a new one. Among determinantal ideals of same-size minors of a matrix of variables and Schubert determinantal ideals, we are able to characterize those that are Cartwright\u2013Sturmfels

Úlcera bilateral por Acanthamoeba em usuária de lentes de contato gelatinosas descartáveis: um incidente trágico ou uma conseqüência da política agressiva de venda de lentes de contato gelatinosas?

This is the report of a case of bilateral Acanthamoeba keratitis in a 19-year-old woman who bought a pair of disposable soft contact lenses in a boutique. She wore this same pair of lenses for 3 months daily without the appropriate care. This led to bilateral corneal transplantation with cataract extraction and also trabeculectomy in the right eye. When last seen, both grafts were crystal clear but the visual acuities were far from satisfactory. She also had bilateral secondary glaucoma, barely controlled by topical medication. Actually, the physical features and the wearing time characteristics of the disposable soft contact lenses created unprecedented difficulties to the medical surveillance of their wearers. Without the right assistance they tend to become careless regarding routine cleaning. They also feel free to buy less expensive lenses, to use saline instead of lens solutions, to violate the limits of wearing time and to extend the use over the sleeping period. Additionally, the aggressive marketing and the wide distribution of these lenses increase the chances that economically or educationally unprepared people will acquire them. The question that remains is: Is the present case an accidental event or an example of what is likely to happen in the future if the indiscriminate selling of disposable soft contact lenses continues to evolve?Este é o relato de uma paciente do sexo feminino, de 19 anos, com ceratite bilateral por Acanthamoeba, devido ao uso de lentes de contato descartáveis, adquiridas em uma butique. Fez uso do mesmo par de lentes durante três meses, sem os cuidados adequados. Foi submetida a transplante penetrante de córnea e facectomia bilateral, além de trabeculectomia no olho direito. Quando vista pela última vez, os enxertos estavam transparentes, mas a visão de ambos os olhos não era satisfatória. Ela também apresentava glaucoma secundário bilateral, controlado precariamente com medicação tópica. Ocorre que, as características físicas e o regime de uso das lentes de contato gelatinosas descartáveis criam dificuldades adicionais para a vigilância médica dos seus usuários. Sem a assistência correta, eles relaxam com a rotina de limpeza, compram lentes mais baratas, usam soro fisiológico ao invés das soluções adequadas, violam os limites de uso e dormem com as mesmas. Além disso, o "marketing" agressivo e a ampla distribuição dessas lentes aumentam as chances de que pessoas, não preparadas econômica e educacionalmente, venham ter acesso às mesmas. A pergunta que fica é: Seria o presente caso um evento acidental ou um exemplo do que pode acontecer no futuro caso as lentes de contato descartáveis continuem sendo vendidas indiscriminadamente

La colonización alemana en General Roca (1884-1886)

Como en Alemania, también en Austria-Hungría fueron los aristócratas terratenientes, los que dejaron relegados a los trabajadores del campo y propagaron el hambre y la miseria en todas partes, mediante la introducción de un pesado sistema fiscal, creando aduanas protectoras a los productos agrícolas e industriales, y altos impuestos a los bienes de consumo.Departamento de Histori

Semi-regular sequences and other random systems of equations

The security of multivariate cryptosystems and digital signature schemes relies on the hardness of solving a system of polynomial equations over a finite field. Polynomial system solving is also currently a bottleneck of index-calculus algorithms to solve the elliptic and hyperelliptic curve discrete logarithm problem. The complexity of solving a system of polynomial equations is closely related to the cost of computing Groebner bases, since computing the solutions of a polynomial system can be reduced to finding a lexicographic Groebner basis for the ideal generated by the equations. Several algorithms for computing such bases exist: We consider those based on repeated Gaussian elimination of Macaulay matrices. In this paper, we analyze the case of random systems, where random systems means either semi-regular systems, or quadratic systems in n variables which contain a regular sequence of n polynomials. We provide explicit formulae for bounds on the solving degree of semi-regular systems with m > n equations in n variables, for equations of arbitrary degrees for m = n+1, and for any m for systems of quadratic or cubic polynomials. In the appendix, we provide a table of bounds for the solving degree of semi-regular systems of m = n + k quadratic equations in n variables for 2 <= k; n <= 100 and online we provide the values of the bounds for 2 <= k; n <= 500. For quadratic systems which contain a regular sequence of n polynomials, we argue that the Eisenbud-Green-Harris Conjecture, if true, provides a sharp bound for their solving degree, which we compute explicitly.Comment: 27 pages, 4 table