Functional anatomy of the middle and inner ears of the red fox, in comparison to domestic dogs and cats

Anatomical middle and inner ear parameters are often used to predict hearing sensitivities of mammalian species. Given that ear morphology is substantially affected both by phylogeny and body size, it is interesting to consider whether the relatively small anatomical differences expected in related species of similar size have a noticeable impact on hearing. We present a detailed anatomical description of the middle and inner ears of the red fox Vulpes vulpes, a widespread, wild carnivore for which a behavioural audiogram is available. We compare fox ears to those of the well‐studied and similarly sized domestic dog and cat, taking data for dogs and cats from the literature as well as providing new measurements of basilar membrane (BM) length and hair cell numbers and densities in these animals. Our results show that the middle ear of the red fox is very similar to that of dogs. The most obvious difference from that of the cat is the lack of a fully formed bony septum in the bulla tympanica of the fox. The cochlear structures of the fox, however, are very like those of the cat, whereas dogs have a broader BM in the basal cochlea. We further report that the mass of the middle ear ossicles and the bulla volume increase with age in foxes. Overall, the ear structures of foxes, dogs and cats are anatomically very similar, and their behavioural audiograms overlap. However, the results of several published models and correlations that use middle and inner ear measurements to predict aspects of hearing were not always found to match well with audiogram data, especially when it came to the sharper tuning in the fox audiogram. This highlights that, although there is evidently a broad correspondence between structure and function, it is not always possible to draw direct links when considering more subtle differences between related species

New spectral relations between products and powers of isotropic random matrices

We show that the limiting eigenvalue density of the product of n identically distributed random matrices from an isotropic unitary ensemble (IUE) is equal to the eigenvalue density of n-th power of a single matrix from this ensemble, in the limit when the size of the matrix tends to infinity. Using this observation one can derive the limiting density of the product of n independent identically distributed non-hermitian matrices with unitary invariant measures. In this paper we discuss two examples: the product of n Girko-Ginibre matrices and the product of n truncated unitary matrices. We also provide an evidence that the result holds also for isotropic orthogonal ensembles (IOE).Comment: 8 pages, 3 figures (in version 2 we added a figure and discussion on finite size effects for isotropic orthogonal ensemble

Network Transitivity and Matrix Models

This paper is a step towards a systematic theory of the transitivity (clustering) phenomenon in random networks. A static framework is used, with adjacency matrix playing the role of the dynamical variable. Hence, our model is a matrix model, where matrices are random, but their elements take values 0 and 1 only. Confusion present in some papers where earlier attempts to incorporate transitivity in a similar framework have been made is hopefully dissipated. Inspired by more conventional matrix models, new analytic techniques to develop a static model with non-trivial clustering are introduced. Computer simulations complete the analytic discussion.Comment: 11 pages, 7 eps figures, 2-column revtex format, print bug correcte

Wounded Healers in Practice: A Phenomenological Study of Jungian Analysts\u27 Countertransference Experiences

This study explored Jungian analysts\u27 experiences of countertransference (CT) using the qualitative method interpretive phenomenological analysis (IPA). The purpose of this study was to better understand how Jungian analysts experience, understand, make use of, and manage CT in daily practice. Six certified Jungian analysts were interviewed about their CT experiences from their analytic work with a past client. The study\u27s main findings were that CT originated primarily from analysts\u27 personal wounds and tended to manifest as analysts\u27 disengagement or withdrawal from the client. Furthermore, analysts often used awareness and understanding of their CT to better manage CT. The nature of the therapeutic relationship was often influenced by CT and also emerged as an important factor in analytic process and outcome. Finally, this study found that contextual factors such as time, culture, and spiritual elements were key influences in the transference-countertransference dynamic. Overall, this study represents a step towards developing an empirical understanding of CT in Jungian models and hopefully facilitates a long-overdue dialogue between Jungians and mainstream practitioners, particularly those adhering to relational or interpersonal approaches

Employment Duration and Resistance to Wage Reductions: Experimental Evidence

One of the long-standing puzzles in economics is why wages do not fall sufficiently in recessions so as to avoid increases in unemployment. Put differently, if the competitive market wage declines, why don't employers simply force their employees to accept lower wages as well? As an alternative to reviewing statistical data we have performed an experiment with a lower competitive wage in the second phase of an employment relationship that is known to both parties. Our hypothesis is that employers will not lower wages correspondingly and that employees will resist such wage cuts. Our experiment casts two subjects in the highly stylized roles of employer and employee. We find at most mild evidence for resistance to wage declines. Instead, the experimental results can be more fruitfully interpreted in terms of an "ultimatum game", in which some surplus between employers and employees is split. In this view, wages and their lack of decline are simply the mechanical tool for accomplishing this split.wage flexibility;ratchet effect (of wages);(wage) bargaining;labour market;ultimatum game;fair wages

Asymmetric correlation matrices: an analysis of financial data

We analyze the spectral properties of correlation matrices between distinct statistical systems. Such matrices are intrinsically non symmetric, and lend themselves to extend the spectral analyses usually performed on standard Pearson correlation matrices to the realm of complex eigenvalues. We employ some recent random matrix theory results on the average eigenvalue density of this type of matrices to distinguish between noise and non trivial correlation structures, and we focus on financial data as a case study. Namely, we employ daily prices of stocks belonging to the American and British stock exchanges, and look for the emergence of correlations between two such markets in the eigenvalue spectrum of their non symmetric correlation matrix. We find several non trivial results, also when considering time-lagged correlations over short lags, and we corroborate our findings by additionally studying the asymmetric correlation matrix of the principal components of our datasets.Comment: Revised version; 11 pages, 13 figure

Eigenvalues and Singular Values of Products of Rectangular Gaussian Random Matrices (The Extended Version)

We consider a product of an arbitrary number of independent rectangular Gaussian random matrices. We derive the mean densities of its eigenvalues and singular values in the thermodynamic limit, eventually verified numerically. These densities are encoded in the form of the so called M-transforms, for which polynomial equations are found. We exploit the methods of planar diagrammatics, enhanced to the non-Hermitian case, and free random variables, respectively; both are described in the appendices. As particular results of these two main equations, we find the singular behavior of the spectral densities near zero. Moreover, we propose a finite-size form of the spectral density of the product close to the border of its eigenvalues' domain. Also, led by the striking similarity between the two main equations, we put forward a conjecture about a simple relationship between the eigenvalues and singular values of any non-Hermitian random matrix whose spectrum exhibits rotational symmetry around zero.Comment: 50 pages, 8 figures, to appear in the Proceedings of the 23rd Marian Smoluchowski Symposium on Statistical Physics: "Random Matrices, Statistical Physics and Information Theory," September 26-30, 2010, Krakow, Polan