Revisiting Complex Moments For 2D Shape Representation and Image Normalization

When comparing 2D shapes, a key issue is their normalization. Translation and scale are easily taken care of by removing the mean and normalizing the energy. However, defining and computing the orientation of a 2D shape is not so simple. In fact, although for elongated shapes the principal axis can be used to define one of two possible orientations, there is no such tool for general shapes. As we show in the paper, previous approaches fail to compute the orientation of even noiseless observations of simple shapes. We address this problem. In the paper, we show how to uniquely define the orientation of an arbitrary 2D shape, in terms of what we call its Principal Moments. We show that a small subset of these moments suffice to represent the underlying 2D shape and propose a new method to efficiently compute the shape orientation: Principal Moment Analysis. Finally, we discuss how this method can further be applied to normalize grey-level images. Besides the theoretical proof of correctness, we describe experiments demonstrating robustness to noise and illustrating the method with real images.Comment: 69 pages, 20 figure

Quantum Analogy of Poisson Geometry, Related Dendriform Algebras and Rota-Baxter Operators

We will introduce an associative (or quantum) version of Poisson structure tensors. This object is defined as an operator satisfying a "generalized" Rota-Baxter identity of weight zero. Such operators are called generalized Rota-Baxter operators. We will show that generalized Rota-Baxter operators are characterized by a cocycle condition so that Poisson structures are so. By analogy with twisted Poisson structures, we propose a new operator "twisted Rota-Baxter operators" which is a natural generalization of generalized Rota-Baxter operators. It is known that classical Rota-Baxter operators are closely related with dendriform algebras. We will show that twisted Rota-Baxter operators induce NS-algebras which is a twisted version of dendriform algebra. The twisted Poisson condition is considered as a Maurer-Cartan equation up to homotopy. We will show the twisted Rota-Baxter condition also is so. And we will study a Poisson-geometric reason, how the twisted Rota-Baxter condition arises.Comment: 18 pages. Final versio

Axon diversity of lamina I local-circuit neurons in the lumbar spinal cord

Spinal lamina I is a key area for relaying and integrating information from nociceptive primary afferents with various other sources of inputs. Although lamina I projection neurons have been intensively studied, much less attention has been given to local-circuit neurons (LCNs), which form the majority of the lamina I neuronal population. In this work the infrared light-emitting diode oblique illumination technique was used to visualize and label LCNs, allowing reconstruction and analysis of their dendritic and extensive axonal trees. We show that the majority of lamina I neurons with locally branching axons fall into the multipolar (with ventrally protruding dendrites) and flattened (dendrites limited to lamina I) somatodendritic categories. Analysis of their axons revealed that the initial myelinated part gives rise to several unmyelinated small-diameter branches that have a high number of densely packed, large varicosities and an extensive rostrocaudal (two or three segments), mediolateral, and dorsoventral (reaching laminae III–IV) distribution. The extent of the axon and the occasional presence of long, solitary branches suggest that LCNs may also form short and long propriospinal connections. We also found that the distribution of axon varicosities and terminal field locations show substantial heterogeneity and that a substantial portion of LCNs is inhibitory. Our observations indicate that LCNs of lamina I form intersegmental as well as interlaminar connections and may govern large numbers of neurons, providing anatomical substrate for rostrocaudal “processing units” in the dorsal horn

Pseudoscorpiones (Arachnida) in phoretic association with Passalidae (Insecta, Coleoptera) in the Amazon State, Brazil

Pseudoscorpions were collected nocturnally at the upper Urubu River, Amazonas, Brazil, using artificial light, at monthly intervals between January 1982 and December 1983. 312 specimens of phoretic species, in three families, were collected from twelve species of passalid beetles. The pseudoscorpions collected were Tridenchthonius mexicanus CHAMB. & CHAMB., 1945 (Tridenchthoniidae) , Lustrochernes intermedius (BALZAN, 1891), Lustrochernes aff. reimoseri BEIER, 1932, and Americhernes aff. incertus MAHNERT, 1979 (Chernetidae), and Parawithius (Victorwithius) gracilimanus MAHNERT, 1979 (Withiidae). Observations on the phoretic behavior of each pseudoscorpion species, the frequency of individuals per carrier, their monthly occurrences, and the relative abundance of males, females and tritonymphs, the occurrence of females with brood sacs, and the frequency of each passalid beetle species with or without pseudoscorpions, are reported and discussed

Combinatorial Hopf algebra of superclass functions of type DD

We provide a Hopf algebra structure on the space of superclass functions on the unipotent upper triangular group of type D over a finite field based on a supercharacter theory constructed by Andr\'e and Neto. Also, we make further comments with respect to types B and C. Type A was explores by M. Aguiar et. al (2010), thus this paper is a contribution to understand combinatorially the supercharacter theory of the other classical Lie types.Comment: Last section modified. Recent development added and correction with respect to previous version state

Atrazine (a short review of literature).

The triazines constitute a large family of herbicides. Various substitutions on the triazine basic structure yield compounds of widely different chemical and biological properties

Relatório de viagem aos Estados Unidos e ao México.

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