Limiting distribution and error terms for the number of visits to balls in non-uniformly hyperbolic dynamical systems

We show that for systems that allow a Young tower construction with polynomially decaying correlations the return times to metric balls are in the limit Poisson distributed. We also provide error terms which are powers of logarithm of the radius. In order to get those uniform rates of convergence the balls centres have to avoid a set whose size is estimated to be of similar order. This result can be applied to non-uniformly hyperbolic maps and to any invariant measure that satisfies a weak regularity condition. In particular it shows that the return times to balls is Poissonian for SRB measures on attractors.Comment: 28 page

The neuronal structure of the preoptic area in the mole and the rabbit: Golgi and Nissl studies

The present studies were carried out on the brains of the adult mole and rabbit. The preparations were made by means of the Golgi technique and the Nissl method. Two types of neurons were distinguished in the preoptic area (POA) of both species: bipolar and multipolar. The bipolar neurons have oval, fusiform or round perikarya and two dendritic trunks arising from the opposite poles of the cell body. The dendrites bifurcate once or twice. The dendritic branches have swellings, single spine-like and filiform processes. The multipolar neurons usually have triangular and quadrangular perikarya and from 3 to 5 dendritic trunks. The dendrites of the mole neurons branch sparsely, whereas the dendrites of the rabbit neurons display 2 or 3 divisions. On the dendritic branches varicosities and different protuberances were observed. The general morphology of the bipolar and multipolar neurons is similar in the mammals studied, although the neurons of the rabbit POA display a more complicated structure. Their dendritic branches show more divisions and possess more swellings and different processes than the dendrites of the neurons of the mole POA. Furthermore, of the multipolar neurons only the dendrites in POA of the rabbit were observed to have a rosary-like beaded appearance

A morphometric comparative study of the lateral geniculate body in selected placental mammals: the common shrew, the bank vole, the rabbit, and the fox

The lateral geniculate body (LGN) was morphometrically examined and compared in representatives of four mammalian orders (Insectivora, Rodentia, Lagomorpha, and Carnivora). In each studied species, the lateral geniculate body was divided into two distinct parts: the dorsal nucleus (LGNd) and the ventral nucleus (LGNv). The lateral geniculate body of the common shrew and the bank vole are very similar in appearance and nuclear pattern. The dorsal and ventral nuclei of these two species also have the most similar statistical characteristics. The lateral geniculate body of the fox has the most complicated morphology and multilayered structure. A significant disproportion was observed between the sizes of both geniculate nuclei in the fox, where the dorsal nucleus definitely surpassed the ventral nucleus in terms of volume. With the exception of the fox, the neuronal density of the LGN nuclei was negatively correlated with the volumes of the LGN. The mean neuronal size of the LGNd and LGNv, which was the resultant of the length, width, area, and circumference of the soma, grew correlatively to the volumes of these nuclei. In all examined species, somas of the LGNd neurons are distinctly larger and have more similar shapes than the LGNv perikarya. In addition, the numerical density of neurons in the ventral nucleus is significantly higher than in the dorsal nucleus. All these morphometric parameters clearly differentiate the LGNd from the LGNv

The nerve cells of the neostriatum in the common shrew (Sorex araneus) and bank vole (Clethrionomys glareolus): a Golgi comparative study

The studies were carried out on 12 brains derived from adult representatives of two mammalian orders, Insectivora and Rodentia. The neostriatum was compared in the common shrew (Sorex araneus) and bank vole (Clethrionomys glareolus). Three main types of striatal neuron were distinguished in the common shrew and five types of neurons in the bank vole. The fifth type of bank vole neurons was additionally divided into two subtypes with respect to dendritic pattern

A morphometric study of the preoptic area of the guinea pig

The aim of the study was to provide the topography and morphometric characteristics of the preoptic area (POA) of the guinea pig. The study was carried out on the brains of sexually mature guinea pigs of both sexes. A uniform procedure was followed in the study of the paraffin-embedded brain tissue blocks of males and females. The blocks were cut in the coronal plane into 50 mm sections and stained according to the Nissl method. The guinea pig POA consists of four parts: the medial preoptic area (MPA), lateral preoptic area (LPA), periventricular preoptic nucleus (PPN), and median preoptic nucleus (MPN). The topography and general structure of POA parts are similar in males and females. However, the PPNa cells of females are more intensely stained and are more densely packed than the PPNa cells of males. For morphometric analysis, the MPA and LPA as well as PPN and MPN were considered respectively as uniform structures, namely MPA-LPA and PPN-MPN. The statistical analysis showed that the volume of the PPN-MPN was larger in males than in females, whereas the MPA-LPA volume did not differ between the sexes. Moreover, the numerical density and the total number of neurons were statistically larger in males than in females in both the MPA-LPA and PPN-MPN. The parameters describing POA neurons were larger for MPA-LPA neurons in comparison with the PPN-MPN neurons. However, in this respect no sex differences were observed in both studied complexes. Folia Morphol 2010; 69, 1: 15-2

The neuronal structure of the dorsal nucleus of the lateral geniculate body in the common shrew (Sorex araneus) and the bank vole (Clethrionomys glareolus): Golgi and Nissl studies

The topography and neuronal structure of the dorsal nucleus of the lateral geniculate body (GLd) of the common shrew and the bank vole are similar. The lateral geniculate body of both the species examined has a homogeneous structure and no observable cytoarchitectonic lamination. On the basis of the shape of the dendritic arbours as well as the pattern of dendritic arborisations the following two types of neurons were distinguished. Type I “bushy” neurons that have multipolar or round perikarya (common shrew perikarya 9–12 µm, bank vole perikarya 10–13 µm), with 4–6 short thick dendritic trunks that subdivide into many bush-like branches. The dendritic trunks are smooth, in contrast to the distal branches, which are covered with numerous spine-like protrusions of different lengths and forms. An axon emerges from the soma, sometimes very close to one of the primary dendrites. The type I neurons are typically projection cells that send their axons to the primary visual cortex. These neurons predominate in the GLd of both species. Type II neurons, which have an elongated soma with primary dendrites arising from opposite poles of the perikaryon (common shrew perikarya 8–10 µm, bank vole perikarya 9–11 µm). The dendritic arbours of these cells are less extensive and their dendrites have fewer spines than those of the type I neurons. Axons were seldom observed. The type II neurons are presumably interneurons and are definitely less numerous than the type I neurons