Continued-fraction expansion of eigenvalues of generalized evolution operators in terms of periodic orbits

A new expansion scheme to evaluate the eigenvalues of the generalized evolution operator (Frobenius-Perron operator) $H_{q}$ relevant to the fluctuation spectrum and poles of the order-$q$ power spectrum is proposed. The ``partition function'' is computed in terms of unstable periodic orbits and then used in a finite pole approximation of the continued fraction expansion for the evolution operator. A solvable example is presented and the approximate and exact results are compared; good agreement is found.Comment: CYCLER Paper 93mar00

Cutting the chorda tympani: not just a matter of taste

Abstract Introduction: Chorda tympani injury as a complication of middle-ear surgery has been extensively studied with regard to its effects upon taste. However, the chorda tympani also carries parasympathetic fibres to the salivary glands of the oral cavity. To date, little has been reported about the effect of chorda tympani section upon salivary function. Setting: Tertiary care centre. Material and methods: We report a case series of three patients with bilateral chorda tympani lesions. Chorda tympani function was assessed using ‘taste strips' and unstimulated sialometry. A careful history of oral symptoms was taken. Results: All patients showed transient or permanent bilateral ageusia of the anterior two-thirds of the tongue, and a decreased resting salivary flow rate. In addition, all patients suffered from transient or persistent, distressing xerostomia. Conclusion: Taste disorders may occur after middle-ear surgery but they are mostly transient, even when the chorda tympani nerves are sectioned bilaterally. In contrast, bilateral chorda tympani lesions may lead to severe, persistent and distressing xerostomia. Based on this neglected aspect of chorda tympani function, we emphasise the importance of preserving the chorda tympani whenever possibl

Bifurcations in Globally Coupled Map Lattices

The dynamics of globally coupled map lattices can be described in terms of a nonlinear Frobenius--Perron equation in the limit of large system size. This approach allows for an analytical computation of stationary states and their stability. The complete bifurcation behaviour of coupled tent maps near the chaotic band merging point is presented. Furthermore the time independent states of coupled logistic equations are analyzed. The bifurcation diagram of the uncoupled map carries over to the map lattice. The analytical results are supplemented with numerical simulations.Comment: 19 pages, .dvi and postscrip

Brownian motion with dry friction: Fokker-Planck approach

We solve a Langevin equation, first studied by de Gennes, in which there is a solid-solid or dry friction force acting on a Brownian particle in addition to the viscous friction usually considered in the study of Brownian motion. We obtain both the time-dependent propagator of this equation and the velocity correlation function by solving the associated time-dependent Fokker-Planck equation. Exact results are found for the case where only dry friction acts on the particle. For the case where both dry and viscous friction forces are present, series representations of the propagator and correlation function are obtained in terms of parabolic cylinder functions. Similar series representations are also obtained for the case where an external constant force is added to the Langevin equation.Comment: 18 pages, 13 figures (in color

Sedimentological processes and environmental variability at Lake Ohrid (Macedonia, Albania) between 640 ka and present day

Lake Ohrid (FYROM, Albania) is thought to be more than 1.2 million years old and hosts more than 200 endemic species. As a target of the International Continental Scientific Drilling Program (ICDP), a successful deep drilling campaign was carried out within the scope of the Scientific Collaboration on Past Speciation Conditions in Lake Ohrid (SCOPSCO) project in 2013. Here, we present lithological, sedimentological, and (bio-)geochemical data from the upper 247.8 m of the overall 569 m long DEEP site sediment succession from the central part of the lake. According to an age model, which is based on nine tephra layers (1st order tie points), and on tuning of biogeochemical proxy data to orbital parameters (2nd order tie points) and to the global benthic isotope stack LR04 (3rd order tie points), respectively, the analyzed sediment sequence covers the last 640 ka

Relation between coupled map lattices and kinetic Ising models

A spatially one dimensional coupled map lattice possessing the same symmetries as the Miller Huse model is introduced. Our model is studied analytically by means of a formal perturbation expansion which uses weak coupling and the vicinity to a symmetry breaking bifurcation point. In parameter space four phases with different ergodic behaviour are observed. Although the coupling in the map lattice is diffusive, antiferromagnetic ordering is predominant. Via coarse graining the deterministic model is mapped to a master equation which establishes an equivalence between our system and a kinetic Ising model. Such an approach sheds some light on the dependence of the transient behaviour on the system size and the nature of the phase transitions.Comment: 15 pages, figures included, Phys. Rev. E in pres

Dopamine D_2-receptor activation elicits akinesia, rigidity, catalepsy, and tremor in mice expressing hypersensitive 4 nicotinic receptors via a cholinergic-dependent mechanism

Recent studies suggest that high-affinity neuronal nicotinic acetylcholine receptors (nAChRs) containing α4 and β2 subunits (α4β2*) functionally interact with G-protein-coupled dopamine (DA) D_2 receptors in basal ganglia. We hypothesized that if a functional interaction between these receptors exists, then mice expressing an M2 point mutation (Leu9'Ala) rendering 4 nAChRs hypersensitive to ACh may exhibit altered sensitivity to a D_2-receptor agonist. When challenged with the D_(2)R agonist, quinpirole (0.5–10 mg/kg), Leu9'Ala mice, but not wild-type (WT) littermates, developed severe, reversible motor impairment characterized by rigidity, catalepsy, akinesia, and tremor. While striatal DA tissue content, baseline release, and quinpirole-induced DA depletion did not differ between Leu9'Ala and WT mice, quinpirole dramatically increased activity of cholinergic striatal interneurons only in mutant animals, as measured by increased c-Fos expression in choline acetyltransferase (ChAT)-positive interneurons. Highlighting the importance of the cholinergic system in this mouse model, inhibiting the effects of ACh by blocking muscarinic receptors, or by selectively activating hypersensitive nAChRs with nicotine, rescued motor symptoms. This novel mouse model mimics the imbalance between striatal DA/ACh function associated with severe motor impairment in disorders such as Parkinson’s disease, and the data suggest that a D_(2)R–α4*-nAChR functional interaction regulates cholinergic interneuron activity.—Zhao-Shea, R., Cohen, B. N., Just, H., McClure-Begley, T., Whiteaker, P., Grady, S. R., Salminen, O., Gardner, P. D., Lester, H. A., Tapper, A. R. Dopamine D2-receptor activation elicits akinesia, rigidity, catalepsy, and tremor in mice expressing hypersensitive α4 nicotinic receptors via a cholinergic-dependent mechanism

The combinatorics of the Baer-Specker group

Denote the integers by Z and the positive integers by N. The groups Z^k (k a natural number) are discrete, and the classification up to isomorphism of their (topological) subgroups is trivial. But already for the countably infinite power Z^N of Z, the situation is different. Here the product topology is nontrivial, and the subgroups of Z^N make a rich source of examples of non-isomorphic topological groups. Z^N is the Baer-Specker group. We study subgroups of the Baer-Specker group which possess group theoretic properties analogous to properties introduced by Menger (1924), Hurewicz (1925), Rothberger (1938), and Scheepers (1996). The studied properties were introduced independently by Ko\v{c}inac and Okunev. We obtain purely combinatorial characterizations of these properties, and combine them with other techniques to solve several questions of Babinkostova, Ko\v{c}inac, and Scheepers.Comment: To appear in IJ

Cryogenic Design of a PrFeB Based Undulator

A PrFeB based cryogenic undulator has been built at Helmholtz Zentrum Berlin HZB in collaboration with the Ludwig Maximilian University München LMU . LMU will operate the undulator at a laser plasma accelerator at the Max Planck Institut für Quantenoptik in Garching. The 20 period device has a period length of 9mm and a fixed gap of 2.5mm. The operation of a small gap device at a high emittance electron beam requires stable magnetic material. A high coercivity is achieved with PrFeB material cooled down to 20 30K. In this paper we present the mechanic, magnetic and cryogenic design and compare predictions with measured dat