Spatial patterning in modified Turing systems: Application to pigmentation patterns on marine fish

In this paper we extend the study of Turing models to investigate the rôle of boundary conditions, parameter modulation, domain growth, and coupling of models. Our numerical simulations show that such modifications lead to patterns that cannot be reproduced by the standard model. By comparing our results with pigmentation patterning on marine fish we conclude that such models may have wider application than originally imagined

Correction to the Moliere's formula for multiple scattering

The quasiclassical correction to the Moliere's formula for multiple scattering is derived. The consideration is based on the scattering amplitude, obtained with the first quasiclassical correction taken into account for arbitrary localized but not spherically symmetric potential. Unlike the leading term, the correction to the Moliere's formula contains the target density $n$ and thickness $L$ not only in the combination $nL$ (areal density). Therefore, this correction can be reffered to as the bulk density correction. It turns out that the bulk density correction is small even for high density. This result explains the wide region of applicability of the Moliere's formula.Comment: 6 pages, RevTe

Polysialic Acid Is Required for Dopamine D2 Receptor-Mediated Plasticity Involving Inhibitory Circuits of the Rat Medial Prefrontal Cortex

Decreased expression of dopamine D2 receptors (D2R), dysfunction of inhibitory neurotransmission and impairments in the structure and connectivity of neurons in the medial prefrontal cortex (mPFC) are involved in the pathogenesis of schizophrenia and major depression, but the relationship between these changes remains unclear. The polysialylated form of the neural cell adhesion molecule (PSA-NCAM), a plasticity-related molecule, may serve as a link. This molecule is expressed in cortical interneurons and dopamine, via D2R, modulates its expression in parallel to that of proteins related to synapses and inhibitory neurotransmission, suggesting that D2R-targeted antipsychotics/antidepressants may act by affecting the plasticity of mPFC inhibitory circuits. To understand the role of PSA-NCAM in this plasticity, rats were chronically treated with a D2R agonist (PPHT) after cortical PSA depletion. PPHT-induced increases in GAD67 and synaptophysin (SYN) neuropil expression were blocked when PSA was previously removed, indicating a role for PSA-NCAM in this plasticity. The number of PSA-NCAM expressing interneuron somata also increased after PPHT treatment, but the percentages of these cells belonging to different interneuronal subpopulations did not change. Cortical pyramidal neurons did not express PSA-NCAM, but puncta co-expressing this molecule and parvalbumin could be found surrounding their somata. PPHT treatment increased the number of PSA-NCAM and parvalbumin expressing perisomatic puncta, but decreased the percentage of parvalbumin puncta that co-expressed SYN. PSA depletion did not block these effects on the perisomatic region, but increased further the number of parvalbumin expressing puncta and increased the percentage of puncta co-expressing SYN and parvalbumin, suggesting that the polysialylation of NCAM may regulate perisomatic inhibition of mPFC principal neurons. Summarizing, the present results indicate that dopamine acting on D2R influences structural plasticity of mPFC interneurons and point to PSA-NCAM as a key player in this remodeling

Oxygen vacancy related distortions in rutile TiO_2 nanoparticles: a combined experimental and theoretical study

The effects of doubly ionized oxygen vacancies [(V_O)ˆ(2+)]on the electronic structure and charge distribution in rutile TiO_2 are studied by combining first-principles calculations based on density functional theory and experimental results from x-ray photoelectron and x-ray absorption measurements carried out in synchrotron facilities on rutile TiO_2 nanoparticles. The generalized gradient approximation of the Perdew-Burke-Ernzerhof functional has demonstrated its suitability for the analysis of the [(V_O)ˆ(2+)]defects in rutile TiO_2. It has been found that the presence of empty electronic states at the conduction band shifted ̴1 eV from t_(2g) and e_(g) states can be associated with local distortions induced by [(V_O)ˆ(2+)]defects, in good agreement with Gauss-Lorentzian band deconvolution of experimental O K-edge spectra. The asymmetry of t(2g) and e(g) bands at the O-K edge has been associated with [(V_O)ˆ(2+)], which can enrich the understanding of studies where the presence of these defects plays a key role, as in the case of doped TiO_2

Development of a GPU-based Monte Carlo dose calculation code for coupled electron-photon transport

Monte Carlo simulation is the most accurate method for absorbed dose calculations in radiotherapy. Its efficiency still requires improvement for routine clinical applications, especially for online adaptive radiotherapy. In this paper, we report our recent development on a GPU-based Monte Carlo dose calculation code for coupled electron-photon transport. We have implemented the Dose Planning Method (DPM) Monte Carlo dose calculation package (Sempau et al, Phys. Med. Biol., 45(2000)2263-2291) on GPU architecture under CUDA platform. The implementation has been tested with respect to the original sequential DPM code on CPU in phantoms with water-lung-water or water-bone-water slab geometry. A 20 MeV mono-energetic electron point source or a 6 MV photon point source is used in our validation. The results demonstrate adequate accuracy of our GPU implementation for both electron and photon beams in radiotherapy energy range. Speed up factors of about 5.0 ~ 6.6 times have been observed, using an NVIDIA Tesla C1060 GPU card against a 2.27GHz Intel Xeon CPU processor.Comment: 13 pages, 3 figures, and 1 table. Paper revised. Figures update

Understanding the effects of Cr doping in rutile TiO₂ by DFT calculations and X-ray spectroscopy

The effects of Cr on local environment and electronic structure of rutile TiO₂ are studied combining theoretical and experimental approaches. Neutral and negatively charged substitutional Cr impurities Cr_(Ti)(0)* and Cr_(Ti)(-1)* as well as Cr-oxygen vacancy complex 2Cr_(Ti) + V₀ are studied by the density functional theory (DFT) within the generalized gradient approximation (GGA) of Perdew-Burke-Ernzerhof (PBE) functional. Experimental results based on X-Ray absorption spectroscopy (XAS) and X-Ray photoelectron spectroscopy (XPS) performed on Cr doped TiO₂ at the Synchrotron facility were compared to the theoretical results. It is shown that the electrons of the oxygen vacancy tend to be localized at the t_(2g) states of the Cr ions in order to reach the stable oxidation state of Cr(3+)*. Effects of Cr on crystal field (CF) and structural distortions in the rutile TiO₂ cell were analyzed by the DFT calculations and XAS spectra revealing that the CF and tetragonal distortions in TiO₂ are very sensitive to the concentration of Cr

Stability analysis of non-autonomous reaction-diffusion systems: the effects of growing domains

By using asymptotic theory, we generalise the Turing diffusively-driven instability conditions for reaction-diffusion systems with slow, isotropic domain growth. There are two fundamental biological differences between the Turing conditions on fixed and growing domains, namely: (i) we need not enforce cross nor pure kinetic conditions and (ii) the restriction to activator-inhibitor kinetics to induce pattern formation on a growing biological system is no longer a requirement. Our theoretical findings are confirmed and reinforced by numerical simulations for the special cases of isotropic linear, exponential and logistic growth profiles. In particular we illustrate an example of a reaction-diffusion system which cannot exhibit a diffusively-driven instability on a fixed domain but is unstable in the presence of slow growth

The Saffman-Taylor problem on a sphere

The Saffman-Taylor problem addresses the morphological instability of an interface separating two immiscible, viscous fluids when they move in a narrow gap between two flat parallel plates (Hele-Shaw cell). In this work, we extend the classic Saffman-Taylor situation, by considering the flow between two curved, closely spaced, concentric spheres (spherical Hele-Shaw cell). We derive the mode-coupling differential equation for the interface perturbation amplitudes and study both linear and nonlinear flow regimes. The effect of the spherical cell (positive) spatial curvature on the shape of the interfacial patterns is investigated. We show that stability properties of the fluid-fluid interface are sensitive to the curvature of the surface. In particular, it is found that positive spatial curvature inhibits finger tip-splitting. Hele-Shaw flow on weakly negative, curved surfaces is briefly discussed.Comment: 26 pages, 4 figures, RevTex, accepted for publication in Phys. Rev.

Characterization of Turing diffusion-driven instability on evolving domains

In this paper we establish a general theoretical framework for Turing diffusion-driven instability for reaction-diffusion systems on time-dependent evolving domains. The main result is that Turing diffusion-driven instability for reaction-diffusion systems on evolving domains is characterised by Lyapunov exponents of the evolution family associated with the linearised system (obtained by linearising the original system along a spatially independent solution). This framework allows for the inclusion of the analysis of the long-time behavior of the solutions of reaction-diffusion systems. Applications to two special types of evolving domains are considered: (i) time-dependent domains which evolve to a final limiting fixed domain and (ii) time-dependent domains which are eventually time periodic. Reaction-diffusion systems have been widely proposed as plausible mechanisms for pattern formation in morphogenesis

Astrocytic glycogen accumulation drives the pathophysiology of neurodegeneration in Lafora disease

The hallmark of Lafora disease, a fatal neurodegenerative disorder, is the accumulation of intracellular glycogen aggregates, called Lafora bodies. Until recently, it was widely believed that brain Lafora bodies were present exclusively in neurons and thus that Lafora disease pathology derived from their accumulation in this cell population. However, recent evidence indicates that Lafora bodies are also present in astrocytes. To define the role of astrocytic Lafora bodies in Lafora disease pathology, we deleted glycogen synthase specifically from astrocytes in a mouse model of the disease (malinKO). Strikingly, blocking glycogen synthesis in astrocytes-thus impeding Lafora bodies accumulation in this cell type-prevented the increase in neurodegeneration markers, autophagy impairment, and metabolic changes characteristic of the malinKO model. Conversely, mice that overaccumulate glycogen in astrocytes showed an increase in these markers. These results unveil the deleterious consequences of the deregulation of glycogen metabolism in astrocytes and change the perspective that Lafora disease is caused solely by alterations in neuron