Global periodicity conditions for maps and recurrences via Normal Forms

We face the problem of characterizing the periodic cases in parametric families of (real or complex) rational diffeomorphisms having a fixed point. Our approach relies on the Normal Form Theory, to obtain necessary conditions for the existence of a formal linearization of the map, and on the introduction of a suitable rational parametrization of the parameters of the family. Using these tools we can find a finite set of values p for which the map can be p-periodic, reducing the problem of finding the parameters for which the periodic cases appear to simple computations. We apply our results to several two and three dimensional classes of polynomial or rational maps. In particular we find the global periodic cases for several Lyness type recurrences.Comment: 25 page

Electron-electron interaction corrections to the thermal conductivity in disordered conductors

We evaluate the electron-electron interaction corrections to the electronic thermal conductivity in a disordered conductor in the diffusive regime. We use a diagrammatic many-body method analogous to that of Altshuler and Aronov for the electrical conductivity. We derive results in one, two and three dimensions for both the singlet and triplet channels, and in all cases find that the Wiedemann-Franz law is violated.Comment: 8 pages, 2 figures Typos corrected in formulas (15) and (A.4) and Table 1; discussion of previous work in introduction extended; reference clarifying different definitions of parameter F adde

Thermal transport in granular metals

We study the electron thermal transport in granular metals at large tunnel conductance between the grains, $g_T \gg 1$ and not too low a temperature $T > g_T\delta$, where $\delta$ is the mean energy level spacing for a single grain. Taking into account the electron-electron interaction effects we calculate the thermal conductivity and show that the Wiedemann-Franz law is violated for granular metals. We find that interaction effects suppress the thermal conductivity less than the electrical conductivity.Comment: Replaced with published versio

Measurement of viscous sound absorption at 50-150 kHz in a model turbid environment

The visco-thermal absorption of sound by suspended particulate matter can be reliably measured using a reverberation technique. This absorption may have an adverse effect on the performance of sonars operating at 50–300 kHz in coastal waters where suspensions are often present in significant concentrations. A series of experiments has been performed to study the viscous absorption by suspensions in the frequency range of 50–150 kHz. In the test volumes employed, the effect is small. It is therefore measured by taking the difference in reverberation times of a volume of water with and without particles. This greatly reduces the effect on the measurement of the other sources of absorption. Even so, it is necessary to design the experiment to characterize and minimize acoustic losses which occur at the surfaces of the container, the hydrophones, and their cables, and losses associated with bubbles and turbulence. These effects are discussed and results for particulate absorption for suspensions of spherical glass beads are presented and compared to theoretical predictions. Measured absorption agrees well with that predicted by theory for concentrations above 0.5 kg/m3 and up to 2.0 kg/m

Random walk generated by random permutations of {1,2,3, ..., n+1}

We study properties of a non-Markovian random walk $X^{(n)}_l$, $l =0,1,2, >...,n$, evolving in discrete time $l$ on a one-dimensional lattice of integers, whose moves to the right or to the left are prescribed by the \text{rise-and-descent} sequences characterizing random permutations $\pi$ of $[n+1] = \{1,2,3, ...,n+1\}$. We determine exactly the probability of finding the end-point $X_n = X^{(n)}_n$ of the trajectory of such a permutation-generated random walk (PGRW) at site $X$, and show that in the limit $n \to \infty$ it converges to a normal distribution with a smaller, compared to the conventional P\'olya random walk, diffusion coefficient. We formulate, as well, an auxiliary stochastic process whose distribution is identic to the distribution of the intermediate points $X^{(n)}_l$, $l < n$, which enables us to obtain the probability measure of different excursions and to define the asymptotic distribution of the number of "turns" of the PGRW trajectories.Comment: text shortened, new results added, appearing in J. Phys.

Differential scaling within an insect compound eye

Environmental and genetic influences cause individuals of a species to differ in size. As they do so, organ size and shape are scaled to available resources whilst maintaining function. The scaling of entire organs has been investigated extensively but scaling within organs remains poorly understood. By making use of the structure of the insect compound eye, we show that different regions of an organ can respond differentially to changes in body size. Wood ant (Formica rufa) compound eyes contain facets of different diameters in different regions. When the animal body size changes, lens diameters from different regions can increase or decrease in size either at the same rate (a ‘grade’ shift) or at different rates (a ‘slope’ shift). These options are not mutually exclusive, and we demonstrate that both types of scaling apply to different regions of the same eye. This demonstrates that different regions within a single organ can use different rules to govern their scaling, responding differently to their developmental environment. Thus, the control of scaling is more nuanced than previously appreciated, diverse responses occurring even among homologous cells within a single organ. Such fine control provides a rich substrate for the diversification of organ morphology

Barriers to positive mental health in a young offenders institution: A qualitative study

Objective: To explore the barriers to positive mental health in a group of young offenders. Design A qualitative approach was used to provide insight into the ways in which mental health for young offenders is experienced and managed. Setting A Young Offenders Institute (YOI) accommodating males aged between 18 and 21 years. Method: Participants were recruited voluntarily using posters. Twelve offenders participated in focus groups and an additional three interviews were carried out with individuals who felt uncomfortable in the focus group situation. Results: Participants stressed that feelings in a YOI could not be shared due to the masculine ethos that had been created on the wings. Listener services were reported to be ineffective for support because using them would show weakness and vulnerability to other prisoners. Visiting time was the main highlight in the routine for most young offenders; however, leaving family and friends was difficult. In dealing with these emotions young offenders would use coping mechanisms, including acts of aggression to vent built-up frustrations. The issue of prison staff and their effect on mental health was raised by all offenders involved in the research. Unanimously, it was suggested that there are both excellent prison officers who engage with the prisoners, and staff who abuse their power and treat prisoners disrespectfully. Conclusion: Promoting mental health is not the principle business of a YOI. However, this research has generated some issues for consideration for governors and those working within this setting

Consequences of converting graded to action potentials upon neural information coding and energy efficiency

Information is encoded in neural circuits using both graded and action potentials, converting between them within single neurons and successive processing layers. This conversion is accompanied by information loss and a drop in energy efficiency. We investigate the biophysical causes of this loss of information and efficiency by comparing spiking neuron models, containing stochastic voltage-gated Na+ and K+ channels, with generator potential and graded potential models lacking voltage-gated Na+ channels. We identify three causes of information loss in the generator potential that are the by-product of action potential generation: (1) the voltage-gated Na+ channels necessary for action potential generation increase intrinsic noise and (2) introduce non-linearities, and (3) the finite duration of the action potential creates a ‘footprint’ in the generator potential that obscures incoming signals. These three processes reduce information rates by ~50% in generator potentials, to ~3 times that of spike trains. Both generator potentials and graded potentials consume almost an order of magnitude less energy per second than spike trains. Because of the lower information rates of generator potentials they are substantially less energy efficient than graded potentials. However, both are an order of magnitude more efficient than spike trains due to the higher energy costs and low information content of spikes, emphasizing that there is a two-fold cost of converting analogue to digital; information loss and cost inflation

Factorizations and Physical Representations

A Hilbert space in M dimensions is shown explicitly to accommodate representations that reflect the prime numbers decomposition of M. Representations that exhibit the factorization of M into two relatively prime numbers: the kq representation (J. Zak, Phys. Today, {\bf 23} (2), 51 (1970)), and related representations termed $q_{1}q_{2}$ representations (together with their conjugates) are analysed, as well as a representation that exhibits the complete factorization of M. In this latter representation each quantum number varies in a subspace that is associated with one of the prime numbers that make up M

A CDCL-style calculus for solving non-linear constraints

In this paper we propose a novel approach for checking satisfiability of non-linear constraints over the reals, called ksmt. The procedure is based on conflict resolution in CDCL style calculus, using a composition of symbolical and numerical methods. To deal with the non-linear components in case of conflicts we use numerically constructed restricted linearisations. This approach covers a large number of computable non-linear real functions such as polynomials, rational or trigonometrical functions and beyond. A prototypical implementation has been evaluated on several non-linear SMT-LIB examples and the results have been compared with state-of-the-art SMT solvers.Comment: 17 pages, 3 figures; accepted at FroCoS 2019; software available at <http://informatik.uni-trier.de/~brausse/ksmt/