mm-cluster categories and mm-replicated algebras

Let A be a hereditary algebra over an algebraically closed field. We prove that an exact fundamental domain for the m-cluster category of A is the m-left part of the m-replicated algebra $A^{(m)}$ of A. Moreover, we obtain a one-to-one correspondence between the tilting objects in the m-cluster category (that is, the m-clusters) and those tilting $A^{(m)}$-modules for which all non projective-injective direct summands lie in the m-left part of $A^{(m)}$.Comment: 28 pages, 2 figure

Snake graph calculus and cluster algebras from surfaces III: Band graphs and snake rings

We introduce several commutative rings, the snake rings, that have strong connections to cluster algebras and that are interesting on their own right as combinatorially defined rings. The elements of these rings are residue classes of unions of certain labeled graphs that were instrumental to construct canonical bases in the theory of cluster algebras. We obtain several rings by varying the conditions on the structure as well as the labeling of the graphs. A general form of this ring contains all cluster algebras of unpunctured surface type. The definition of the rings requires the snake graph calculus which we also complete in this article building on two earlier articles on the subject. Identities in the snake ring correspond to bijections between the posets of perfect matchings of the graphs. One of the main results of this article is the completion of the explicit construction of these bijections

Structural and thermodynamic characterization of the adrenodoxin-like domain of the electron-transfer protein Etp1 from Schizosaccharomyces pombe

The protein Etp1 of Schizosaccharomyces pombe consists of an amino-terminal COX15-like domain and a carboxy-terminal ferredoxin-like domain, Etp1(fd), which is cleaved off after mitochondrial import. The physiological function of Etp1(fd) is supposed to lie in the participation in the assembly of iron-sulfur clusters and the synthesis of heme A. In addition, the protein was shown to be the first microbial ferredoxin being able to support electron transfer in mitochondrial steroid hydroxylating cytochrome P450 systems in vivo and in vitro, replacing thereby the native redox partner, adrenodoxin. Despite a sequence similarity of 39% and the fact that fission yeast is a mesophilic organism, thermodynamic studies revealed that Etp1(fd) has a melting temperature more than 20°C higher than adrenodoxin. The three-dimensional structure of Etp1(fd) has been determined by crystallography. To the best of our knowledge it represents the first three-dimensional structure of a yeast ferredoxin. The structure-based sequence alignment of Etp1(fd) with adrenodoxin yields a rational explanation for their observed mutual exchangeability in the cytochrome P450 system. Analysis of the electron exchange with the S. pombe redox partner Arh1 revealed differences between Etp1(fd) and adrenodoxin, which might be linked to their different physiological functions in the mitochondria of mammals and yeast

Metodologia para controle e análise de custo da produção de leite.

Por que interessa conhecer o custo de produção do litro de leite em nível de produtor ou de cada sistema de produção que a pesquisa desenvolve? Num regime de concorrência perfeita, se o preço do produto estiver acima do custo médio mínimo os produtores estarão auferindo lucro maior do que o esperado por eles. Como conseqüência novos produtores entrarão na atividade ou ocorrerão importações de leite. Como resultado o preço do litro de leite começará a cair até que finalmente se atinja o nível equivalente ao custo médio mínimo. Quando se obtém a igualdade entre o preço do produto e o custo médio mínimo, o sistema tende ao equilíbrio, não havendo incentivos para entrada de novos produtores ou para velhos produtores deixarem a atividade. O equilíbrio pode ser quebrado pela importação de leite. Se não houver tecnologia disponível, alguns produtores deixarão atividade e o preço voltará a subir, forçando o gorverno a importar mais leite. Este processo de eliminação e de importações adicionais continuará até que as importações convirjam para seu equilíbrio e o mesmo ocorrerá com o número de produtores. O equilíbrio também pode ser quebrado quando se introduz tecnologias que reduzem o custo de produção ou quando os preços dos insumos sobem ou descem, estabelecendo novo equilíbrio.Resumo Expandid

Elastic-Net Regularization: Error estimates and Active Set Methods

This paper investigates theoretical properties and efficient numerical algorithms for the so-called elastic-net regularization originating from statistics, which enforces simultaneously l^1 and l^2 regularization. The stability of the minimizer and its consistency are studied, and convergence rates for both a priori and a posteriori parameter choice rules are established. Two iterative numerical algorithms of active set type are proposed, and their convergence properties are discussed. Numerical results are presented to illustrate the features of the functional and algorithms

Beyond convergence rates: Exact recovery with Tikhonov regularization with sparsity constraints

The Tikhonov regularization of linear ill-posed problems with an $\ell^1$ penalty is considered. We recall results for linear convergence rates and results on exact recovery of the support. Moreover, we derive conditions for exact support recovery which are especially applicable in the case of ill-posed problems, where other conditions, e.g. based on the so-called coherence or the restricted isometry property are usually not applicable. The obtained results also show that the regularized solutions do not only converge in the $\ell^1$-norm but also in the vector space $\ell^0$ (when considered as the strict inductive limit of the spaces $\R^n$ as $n$ tends to infinity). Additionally, the relations between different conditions for exact support recovery and linear convergence rates are investigated. With an imaging example from digital holography the applicability of the obtained results is illustrated, i.e. that one may check a priori if the experimental setup guarantees exact recovery with Tikhonov regularization with sparsity constraints

Cluster algebras of type A2(1)A_2^{(1)}

In this paper we study cluster algebras \myAA of type $A_2^{(1)}$. We solve the recurrence relations among the cluster variables (which form a T--system of type $A_2^{(1)}$). We solve the recurrence relations among the coefficients of \myAA (which form a Y--system of type $A_2^{(1)}$). In \myAA there is a natural notion of positivity. We find linear bases \BB of \myAA such that positive linear combinations of elements of \BB coincide with the cone of positive elements. We call these bases \emph{atomic bases} of \myAA. These are the analogue of the "canonical bases" found by Sherman and Zelevinsky in type $A_{1}^{(1)}$. Every atomic basis consists of cluster monomials together with extra elements. We provide explicit expressions for the elements of such bases in every cluster. We prove that the elements of \BB are parameterized by \ZZ^3 via their $\mathbf{g}$--vectors in every cluster. We prove that the denominator vector map in every acyclic seed of \myAA restricts to a bijection between \BB and \ZZ^3. In particular this gives an explicit algorithm to determine the "virtual" canonical decomposition of every element of the root lattice of type $A_2^{(1)}$. We find explicit recurrence relations to express every element of \myAA as linear combinations of elements of \BB.Comment: Latex, 40 pages; Published online in Algebras and Representation Theory, springer, 201

Avaliação sistemática do grau de satisfação dos clientes da Embrapa.

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