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

A Random Matrix Approach to VARMA Processes

We apply random matrix theory to derive spectral density of large sample covariance matrices generated by multivariate VMA(q), VAR(q) and VARMA(q1,q2) processes. In particular, we consider a limit where the number of random variables N and the number of consecutive time measurements T are large but the ratio N/T is fixed. In this regime the underlying random matrices are asymptotically equivalent to Free Random Variables (FRV). We apply the FRV calculus to calculate the eigenvalue density of the sample covariance for several VARMA-type processes. We explicitly solve the VARMA(1,1) case and demonstrate a perfect agreement between the analytical result and the spectra obtained by Monte Carlo simulations. The proposed method is purely algebraic and can be easily generalized to q1>1 and q2>1.Comment: 16 pages, 6 figures, submitted to New Journal of Physic

Wilson Fermions on a Randomly Triangulated Manifold

A general method of constructing the Dirac operator for a randomly triangulated manifold is proposed. The fermion field and the spin connection live, respectively, on the nodes and on the links of the corresponding dual graph. The construction is carried out explicitly in 2-d, on an arbitrary orientable manifold without boundary. It can be easily converted into a computer code. The equivalence, on a sphere, of Majorana fermions and Ising spins in 2-d is rederived. The method can, in principle, be extended to higher dimensions.Comment: 18 pages, latex, 6 eps figures, fig2 corrected, Comment added in the conclusion sectio

Maximal entropy random walk in community finding

The aim of this paper is to check feasibility of using the maximal-entropy random walk in algorithms finding communities in complex networks. A number of such algorithms exploit an ordinary or a biased random walk for this purpose. Their key part is a (dis)similarity matrix, according to which nodes are grouped. This study encompasses the use of the stochastic matrix of a random walk, its mean first-passage time matrix, and a matrix of weighted paths count. We briefly indicate the connection between those quantities and propose substituting the maximal-entropy random walk for the previously chosen models. This unique random walk maximises the entropy of ensembles of paths of given length and endpoints, which results in equiprobability of those paths. We compare performance of the selected algorithms on LFR benchmark graphs. The results show that the change in performance depends very strongly on the particular algorithm, and can lead to slight improvements as well as significant deterioration.Comment: 7 pages, 4 figures, submitted to European Physical Journal Special Topics following the 4-th Conference on Statistical Physics: Modern Trends and Applications, July 3-6, 2012 Lviv, Ukrain

18O isotope effect in the photosynthetic water splitting process

AbstractIn mass spectroscopic experiments of oxygen evolution in Photosystem II at 50% enrichment of H218O, one expects equal signals of 18O2 and 16O2 unless one of the isotopes is favored by the oxygen evolving complex (OEC). We have observed a deviation from this expectation, being a clear indication of an isotope effect. We have measured the effect to be 1.14–1.30, which is higher than the theoretically predicted value of 1.014–1.06. This together with the strong temperature variation of the measured effect with a discontinuity at 11 °C observed for wild-type tobacco and at 9 °C for a yellow-green tobacco mutant suggest that an additional mechanism is responsible for the observed high isotope effect. The entry of a finite size of water clusters to the cleavage site of the OEC can explain the observation

Portfolio Optimization and the Random Magnet Problem

Diversification of an investment into independently fluctuating assets reduces its risk. In reality, movement of assets are are mutually correlated and therefore knowledge of cross--correlations among asset price movements are of great importance. Our results support the possibility that the problem of finding an investment in stocks which exposes invested funds to a minimum level of risk is analogous to the problem of finding the magnetization of a random magnet. The interactions for this ``random magnet problem'' are given by the cross-correlation matrix {\bf \sf C} of stock returns. We find that random matrix theory allows us to make an estimate for {\bf \sf C} which outperforms the standard estimate in terms of constructing an investment which carries a minimum level of risk.Comment: 12 pages, 4 figures, revte

Emergence of a 4D World from Causal Quantum Gravity

Causal Dynamical Triangulations in four dimensions provide a background-independent definition of the sum over geometries in nonperturbative quantum gravity, with a positive cosmological constant. We present evidence that a macroscopic four-dimensional world emerges from this theory dynamically.Comment: 11 pages, 3 figures; some short clarifying comments added; final version to appear in Phys. Rev. Let

On the top eigenvalue of heavy-tailed random matrices

We study the statistics of the largest eigenvalue lambda_max of N x N random matrices with unit variance, but power-law distributed entries, P(M_{ij})~ |M_{ij}|^{-1-mu}. When mu > 4, lambda_max converges to 2 with Tracy-Widom fluctuations of order N^{-2/3}. When mu < 4, lambda_max is of order N^{2/mu-1/2} and is governed by Fr\'echet statistics. The marginal case mu=4 provides a new class of limiting distribution that we compute explicitely. We extend these results to sample covariance matrices, and show that extreme events may cause the largest eigenvalue to significantly exceed the Marcenko-Pastur edge. Connections with Directed Polymers are briefly discussed.Comment: 4 pages, 2 figure

Ordered assembly of the asymmetrically branched lipid-linked oligosaccharide in the endoplasmic reticulum is ensured by the substrate specificity of the individual glycosyltransferases

The assembly of the lipid-linked core oligosaccharide Glc3Man9GlcNAc2, the substrate for N-linked glycosylation of proteins in the endoplasmic reticulum (ER), is catalyzed by different glycosyltransferases located at the membrane of the ER. We report on the identification and characterization of the ALG12 locus encoding a novel mannosyltransferase responsible for the addition of the α-1,6 mannose to dolichollinked Man7GlcNAc2. The biosynthesis of the highly branched oligosaccharide follows an ordered pathway which ensures that only completely assembled oligosaccharide is transferred from the lipid anchor to proteins. Using the combination of mutant strains affected in the assembly pathway of lipid-linked oligosaccharides and overexpression of distinct glycosyltransferases, we were able to define the substrate specificities of the transferases that are critical for branching. Our results demonstrate that branched oligosaccharide structures can be specifically recognized by the ER glycosyltransferases. This substrate specificity of the different transferases explains the ordered assembly of the complex structure of lipid-linked Glc3Man9GlcNAc2 in the endoplasmic reticulu

Levy targeting and the principle of detailed balance

We investigate confined L\'{e}vy flights under premises of the principle of detailed balance. The master equation admits a transformation to L\'{e}vy - Schr\"{o}dinger semigroup dynamics (akin to a mapping of the Fokker-Planck equation into the generalized diffusion equation). We solve a stochastic targeting problem for arbitrary stability index $0<\mu <2$ of L\'{e}vy drivers: given an invariant probability density function (pdf), specify the jump - type dynamics for which this pdf is a long-time asymptotic target. Our ("$\mu$-targeting") method is exemplified by Cauchy family and Gaussian target pdfs. We solve the reverse engineering problem for so-called L\'{e}vy oscillators: given a quadratic semigroup potential, find an asymptotic pdf for the associated master equation for arbitrary $\mu$