Closed symmetric 2-differentials of the 1st kind

A closed symmetric differential of the 1st kind is a differential that locally is the product of closed holomorphic 1-forms. We show that closed symmetric 2-differentials of the 1st kind on a projective manifold $X$ come from maps of $X$ to cyclic or dihedral quotients of Abelian varieties and that their presence implies that the fundamental group of $X$ (case of rank 2) or of the complement $X\setminus E$ of a divisor $E$ with negative properties (case of rank 1) contains subgroup of finite index with infinite abelianization. Other results include: i) the identification of the differential operator characterizing closed symmetric 2-differentials on surfaces (which provides in this case a connection to flat Riemannian metrics) and ii) projective manifolds $X$ having symmetric 2-differentials $w$ that are the product of two closed meromorphic 1-forms are irregular, in fact if $w$ is not of the 1st kind (which can happen), then $X$ has a fibration $f:X \to C$ over a curve of genus $\ge 1$

NP-hardness of circuit minimization for multi-output functions

Can we design efficient algorithms for finding fast algorithms? This question is captured by various circuit minimization problems, and algorithms for the corresponding tasks have significant practical applications. Following the work of Cook and Levin in the early 1970s, a central question is whether minimizing the circuit size of an explicitly given function is NP-complete. While this is known to hold in restricted models such as DNFs, making progress with respect to more expressive classes of circuits has been elusive. In this work, we establish the first NP-hardness result for circuit minimization of total functions in the setting of general (unrestricted) Boolean circuits. More precisely, we show that computing the minimum circuit size of a given multi-output Boolean function f : {0,1}^n ? {0,1}^m is NP-hard under many-one polynomial-time randomized reductions. Our argument builds on a simpler NP-hardness proof for the circuit minimization problem for (single-output) Boolean functions under an extended set of generators. Complementing these results, we investigate the computational hardness of minimizing communication. We establish that several variants of this problem are NP-hard under deterministic reductions. In particular, unless ? = ??, no polynomial-time computable function can approximate the deterministic two-party communication complexity of a partial Boolean function up to a polynomial. This has consequences for the class of structural results that one might hope to show about the communication complexity of partial functions

Resposta da macieira e fluxo de nitrogênio em um solo submetido à aplicação de fontes de nutrientes e manejo de plantas de cobertura

TCC (graduação) - Universidade Federal de Santa Catarina, Centro de Ciências Agrárias, Curso de Agronomia.O estado de Santa Catarina (SC) possui a maior área cultivada com a macieira do Brasil. Em geral, a macieira é cultivada em solos com médios a altos teores de matéria orgânica, que conferem boa disponibilidade de nitrogênio (N). Porém, aplicações de diferentes fontes do nutriente são necessárias para repor ao solo a quantidade de N exportada via fruto. Assim, pode-se causar impacto no estado nutricional e na produção das plantas. Mas parte do N aplicado pode ser lixiviado no perfil do solo. Além disso, espécies de plantas espontâneas são cultivadas e manejadas nos pomares e podem minimizar as perdas de N por lixiviação. No entanto, podem competir por nutrientes e água com a macieira, interferindo no seu estado nutricional e na sua produção. O presente trabalho objetivou avaliar a resposta da macieira e o fluxo de N no solo e na solução em pomares submetidos à aplicação de fontes de nutrientes e com manejos de plantas espontâneas. Foram conduzidos 2 experimentos no município de Urubici (SC). O experimento 1 foi realizado para avaliar a resposta da macieira e o fluxo de N no solo e na solução, em um pomar submetido à aplicação de diferentes fontes de N. O experimento 2 foi realizado para avaliar a resposta da macieira e fluxo de N no solo e na solução, em um pomar submetido aos diferentes manejos de plantas espontâneas. Nos dois experimentos foram avaliados a produção, o teor de N nas folhas e parâmetros de crecimento, bem como o teor de N no solo e na solução. A aplicação de diferentes fontes de N na cultura da macieira não afetou os parâmetros de crescimento, tampouco a produção. Porém, alteram as formas de N-mineral no perfil do solo, podendo aumentar o sincronismo entre a liberação e a absorção de N pelas plantas. Mas, pode potencializar as perdas de N-mineral por lixiviação. Os manejos de plantas espontâneas como o dessecamento na linha de plantio pode alterar os parâmetros de crescimento da macieira, e a concentração do N-mineral no solo e na solução do solo aumentando os riscos de perdas por lixiviação

The Physical Structure of Protoplanetary Disks: the Serpens Cluster Compared with Other Regions

Spectral energy distributions are presented for 94 young stars surrounded by disks in the Serpens Molecular Cloud, based on photometry and Spitzer IRS spectra. Taking a distance to the cloud of 415 pc rather than 259 pc, the distribution of ages is shifted to lower values, in the 1-3 Myr range, with a tail up to 10 Myr. The mass distribution spans 0.2-1.2 Msun, with median mass of 0.7 Msun. The distribution of fractional disk luminosities in Serpens resembles that of the young Taurus Molecular Cloud, with most disks consistent with optically thick, passively irradiated disks in a variety of disk geometries (Ldisk/Lstar ~ 0.1). In contrast, the distributions for the older Upper Scorpius and Eta Chamaeleontis clusters are dominated by optically thin lower luminosity disks (Ldisk/Lstar ~ 0.02). This evolution in fractional disk luminosities is concurrent with that of disk fractions. The actively accreting and non-accreting stars (based on Ha data) in Serpens show very similar distributions in fractional disk luminosities, differing only in the brighter tail dominated by strongly accreting stars. In contrast with a sample of Herbig Ae/Be stars, the T Tauri stars in Serpens do not have a clear separation in fractional disk luminosities for different disk geometries: both flared and flat disks present wider, overlapping distributions. This result is consistent with previous suggestions of a faster evolution for disks around Herbig Ae/Be stars. Furthermore, the results for the mineralogy of the dust in the disk surface do not show any correlation to either stellar and disk characteristics or mean cluster age in the 1-10 Myr range probed here. A possible explanation for the lack of correlation is that the processes affecting the dust within disks have short timescales, happening repeatedly, making it difficult to distinguish long lasting evolutionary effects. [abridged]Comment: ApJ in pres