Cross sections for geodesic flows and \alpha-continued fractions

We adjust Arnoux's coding, in terms of regular continued fractions, of the geodesic flow on the modular surface to give a cross section on which the return map is a double cover of the natural extension for the \alpha-continued fractions, for each $\alpha$ in (0,1]. The argument is sufficiently robust to apply to the Rosen continued fractions and their recently introduced \alpha-variants.Comment: 20 pages, 2 figure

The Lyapunov exponent in the Sinai billiard in the small scatterer limit

We show that Lyapunov exponent for the Sinai billiard is $\lambda = -2\log(R)+C+O(R\log^2 R)$ with $C=1-4\log 2+27/(2\pi^2)\cdot \zeta(3)$ where $R$ is the radius of the circular scatterer. We consider the disk-to-disk-map of the standard configuration where the disks is centered inside a unit square.Comment: 15 pages LaTeX, 3 (useful) figures available from the autho

Crystallization in Emulsions: A Thermo-Optical Method to Determine Single Crystallization Events in Droplet Clusters

Delivery systems with a solid dispersed phase can be produced in a melt emulsification process. For this, dispersed particles are melted, disrupted, and crystallized in a liquid continuous phase (melt emulsification). Different to bulk crystallization, droplets in oil-in-water emulsions show individual crystallization behavior, which differs from droplet to droplet. Therefore, emulsion droplets may form liquid, amorphous, and crystalline structures during the crystallization process. The resulting particle size, shape, and physical state influence the application properties of these colloidal systems and have to be known in formulation research. To characterize crystallization behavior of single droplets in micro emulsions (range 1 µm to several hundred µm), a direct thermo-optical method was developed. It allows simultaneous determination of size, size distribution, and morphology of single droplets within droplet clusters. As it is also possible to differentiate between liquid, amorphous, and crystalline structures, we introduce a crystallization index, CIi, in dispersions with a crystalline dispersed phase. Application of the thermo-optical approach on hexadecane-in-water model emulsion showed the ability of the method to detect single crystallization events of droplets within emulsion clusters, providing detailed information about crystallization processes in dispersions

Melatonin prevents cytosolic calcium overload, mitochondrial damage and cell death due to toxically high doses of dexamethasone-induced oxidative stress in human neuroblastoma SH-SY5Y cells

Stressor exposure activates the hypothalamic-pituitary-adrenal (HPA) axis and causes elevations in the levels of glucocorticoids (GC) from the adrenal glands. Increasing evidence has demonstrated that prolonged exposure to high GC levels can lead to oxidative stress, calcium deregulation, mitochondrial dysfunction and apoptosis in a number of cell types. However, melatonin, via its antioxidant activity, exhibits a neuroprotective effect against oxidative stress-induced cell death. Therefore, in the present study, we explored the protective effect of melatonin in GC-induced toxicity in human neuroblastoma SH-SY5Y cells. Cellular treatment with the toxically high doses of the synthetic GC receptor agonist, dexamethasone (DEX) elicited marked decreases in the levels of glutathione and increases in ROS production, lipid peroxidation and cell death. DEX toxicity also induced increases in the levels of cytosolic calcium and mitochondrial fusion proteins (Mfn1 and Opa1) but decreases in the levels of mitochondrial fission proteins (Fis1 and Drp1). Mitochondrial damage was observed in large proportions of the DEX-treated cells. Pretreatment of the cells with melatonin substantially prevented the DEX-induced toxicity. These results suggest that melatonin might exert protective effects against oxidative stress, cytosolic calcium overload and mitochondrial damage in DEX-induced neurotoxicity

Multi-level Dynamical Systems: Connecting the Ruelle Response Theory and the Mori-Zwanzig Approach

In this paper we consider the problem of deriving approximate autonomous dynamics for a number of variables of a dynamical system, which are weakly coupled to the remaining variables. In a previous paper we have used the Ruelle response theory on such a weakly coupled system to construct a surrogate dynamics, such that the expectation value of any observable agrees, up to second order in the coupling strength, to its expectation evaluated on the full dynamics. We show here that such surrogate dynamics agree up to second order to an expansion of the Mori-Zwanzig projected dynamics. This implies that the parametrizations of unresolved processes suited for prediction and for the representation of long term statistical properties are closely related, if one takes into account, in addition to the widely adopted stochastic forcing, the often neglected memory effects.Comment: 14 pages, 1 figur

Monomeric Alpha-Synuclein Exerts a Physiological Role on Brain ATP Synthase

Misfolded α-synuclein is a key factor in the pathogenesis of Parkinson's disease (PD). However, knowledge about a physiological role for the native, unfolded α-synuclein is limited. Using brains of mice lacking α-, β-, and γ-synuclein, we report that extracellular monomeric α-synuclein enters neurons and localizes to mitochondria, interacts with ATP synthase subunit α, and modulates ATP synthase function. Using a combination of biochemical, live-cell imaging and mitochondrial respiration analysis, we found that brain mitochondria of α-, β-, and γ-synuclein knock-out mice are uncoupled, as characterized by increased mitochondrial respiration and reduced mitochondrial membrane potential. Furthermore, synuclein deficiency results in reduced ATP synthase efficiency and lower ATP levels. Exogenous application of low unfolded α-synuclein concentrations is able to increase the ATP synthase activity that rescues the mitochondrial phenotypes observed in synuclein deficiency. Overall, the data suggest that α-synuclein is a previously unrecognized physiological regulator of mitochondrial bioenergetics through its ability to interact with ATP synthase and increase its efficiency. This may be of particular importance in times of stress or PD mutations leading to energy depletion and neuronal cell toxicity. SIGNIFICANCE STATEMENT: Misfolded α-synuclein aggregations in the form of Lewy bodies have been shown to be a pathological hallmark in histological staining of Parkinson's disease (PD) patient brains. It is known that misfolded α-synuclein is a key driver in PD pathogenesis, but the physiological role of unfolded monomeric α-synuclein remains unclear. Using neuronal cocultures and isolated brain mitochondria of α-, β-, and γ-synuclein knock-out mice and monomeric α-synuclein, this current study shows that α-synuclein in its unfolded monomeric form improves ATP synthase efficiency and mitochondrial function. The ability of monomeric α-synuclein to enhance ATP synthase efficiency under physiological conditions may be of importance when α-synuclein undergoes the misfolding and aggregation reported in PD