Self-Similar Solutions to a Density-Dependent Reaction-Diffusion Model

In this paper, we investigated a density-dependent reaction-diffusion equation, $u_t = (u^{m})_{xx} + u - u^{m}$. This equation is known as the extension of the Fisher or Kolmogoroff-Petrovsky-Piscounoff equation which is widely used in the population dynamics, combustion theory and plasma physics. By employing the suitable transformation, this equation was mapped to the anomalous diffusion equation where the nonlinear reaction term was eliminated. Due to its simpler form, some exact self-similar solutions with the compact support have been obtained. The solutions, evolving from an initial state, converge to the usual traveling wave at a certain transition time. Hence, it is quite clear the connection between the self-similar solution and the traveling wave solution from these results. Moreover, the solutions were found in the manner that either propagates to the right or propagates to the left. Furthermore, the two solutions form a symmetric solution, expanding in both directions. The application on the spatiotemporal pattern formation in biological population has been mainly focused.Comment: 5 pages, 2 figures, accepted by Phys. Rev.

Ultrastructural anatomy of nodes of Ranvier in the peripheral nervous system as revealed by STED microscopy.

We used stimulated emission depletion (STED) superresolution microscopy to analyze the nanoscale organization of 12 glial and axonal proteins at the nodes of Ranvier of teased sciatic nerve fibers. Cytoskeletal proteins of the axon (betaIV spectrin, ankyrin G) exhibit a high degree of one-dimensional longitudinal order at nodal gaps. In contrast, axonal and glial nodal adhesion molecules [neurofascin-186, neuron glial-related cell adhesion molecule (NrCAM)] can arrange in a more complex, 2D hexagonal-like lattice but still feature a ∼190-nm periodicity. Such a lattice-like organization is also found for glial actin. Sodium and potassium channels exhibit a one-dimensional periodicity, with the Nav channels appearing to have a lower degree of organization. At paranodes, both axonal proteins (betaII spectrin, Caspr) and glial proteins (neurofascin-155, ankyrin B) form periodic quasi–one-dimensional arrangements, with a high degree of interdependence between the position of the axonal and the glial proteins. The results indicate the presence of mechanisms that finely align the cytoskeleton of the axon with the one of the Schwann cells, both at paranodal junctions (with myelin loops) and at nodal gaps (with microvilli). Taken together, our observations reveal the importance of the lateral organization of proteins at the nodes of Ranvier and pave the way for deeper investigations of the molecular ultrastructural mechanisms involved in action potential propagation, the formation of the nodes, axon–glia interactions, and demyelination diseases

RC Coupling Beams with High-Strength Steel Bars: Summary of Test Results

The use of high-strength steel bars in reinforced concrete coupling beams is expected to reduce reinforcement congestion. A series of tests was conducted to investigate the effects of high-strength reinforcement on coupling beam behavior. This report summarizes the test program and test results. Eleven large-scale coupling beam specimens were tested under fully reversed cyclic displacements of increasing magnitude. The main variables of the test program included: yield stress of the primary longitudinal reinforcement (Grade 80, Grade 100, and Grade 120 [550, 690, and 830]), span-to-depth (aspect) ratio (1.5, 2.5, and 3.5), and layout of the primary longitudinal reinforcement (diagonal [D] and parallel [P]). All beams had the same nominal concrete compressive strength (8,000 psi [55 MPa]) and cross-sectional dimensions (12 by 18 in. [305 by 457 mm]). Beams were designed for a target shear strength based on the upper limits specified in ACI 318-14. All transverse reinforcement was Grade 80 (550), except one specimen that had Grade 120 (830) transverse reinforcement. The test program is documented by presenting the details of specimen construction, test setup, instrumentation, and loading protocol. Documentation of test results include material properties and cyclic force-deformation response.Charles Pankow FoundationConcrete Research CouncilConcrete Reinforcing Steel Institut

Reinforced Concrete Coupling Beams with High-Strength Steel Bars

The use of high-strength steel bars in reinforced concrete coupling beams has the potential to reduce reinforcement congestion and support more efficient design and construction methods. A series of tests was conducted to investigate the effects of high-strength reinforcement on coupling beam behavior. Eleven large-scale coupling beam specimens were tested under fully reversed cyclic displacements of increasing magnitude. The main variables of the test program included: yield stress of the primary longitudinal reinforcement (Grades 80, 100, and 120 [550, 690, and 830]), span-to-depth (aspect) ratio (1.5, 2.5, and 3.5), and layout of the primary longitudinal reinforcement (diagonal [D] and parallel [P]). All beams had the same nominal concrete compressive strength (8,000 psi [55 MPa]) and cross-sectional dimensions (12 by 18 in. [310 by 460 mm]). Beams were designed for target shear stresses of 8√f’c psi (0.67√f’c) for D-type beams and 6√f’c psi (0.5√f’c) for P- type beams. Transverse reinforcement was Grade 80 (550) in all but one beam, which had Grade 120 (830) reinforcement. The test program is documented by presenting the details of specimen construction, test setup, instrumentation, and loading protocol. Documentation of test data includes material properties, cyclic force-deformation response, progression of damage, calculated and measured strengths, initial stiffness, and measured reinforcement strains. Analysis of test data includes hysteretic energy, changes in beam length and depth, components of chord rotation, and the development of an equation for estimating chord rotation capacity.Charles Pankow FoundationACI Foundation’s Concrete Research CouncilConcrete Reinforcing Steel Institut

MAD2L2 promotes open chromatin in embryonic stem cells and derepresses the Dppa3 locus.

The chromatin of naive embryonic stem cells (ESCs) has a largely open configuration, as evident by the lack of condensed heterochromatin and the hypomethylation of DNA. Several molecular mechanisms promoting this constellation were previously identified. Here we present evidence for an important epigenetic function of MAD2L2, a protein originally known for its role in DNA damage repair, and for its requirement in germ cell development. We demonstrate using super-resolution microscopy that numerous MAD2L2 microfoci are exclusively associated with euchromatin, similar to other factors of the DNA damage response. In the absence of MAD2L2 the amount of heterochromatin demarcated by H3K9me2 was significantly increased. Among the most strongly suppressed genes was Dppa3, an ESC- and germ-cell-specific gene regulating DNA methylation. In Mad2l2-deficient ESCs 5-methylcytosine levels were globally increased, while several imprinted genes became hypomethylated and transcriptionally activated. Our results emphasize the important function of MAD2L2 for the open chromatin configuration of ESCs

Subcortical cytoskeleton periodicity throughout the nervous system

Superresolution fluorescence microscopy recently revealed a ~190 nm periodic cytoskeleton lattice consisting of actin, spectrin, and other proteins underneath the membrane of cultured hippocampal neurons. Whether the periodic cytoskeleton lattice is a structural feature of all neurons and how it is modified when axons are ensheathed by myelin forming glial cells is not known. Here, STED nanoscopy is used to demonstrate that this structure is a commonplace of virtually all neuron types in vitro. To check how the subcortical meshwork is modified during myelination, we studied sciatic nerve fibers from adult mice. Periodicity of both actin and spectrin was uncovered at the internodes, indicating no substantial differences between unmyelinated and myelinated axons. Remarkably, the actin/spectrin pattern was also detected in glial cells such as cultured oligodendrocyte precursor cells. Altogether our work shows that the periodic subcortical cytoskeletal meshwork is a fundamental characteristic of cells in the nervous system and is not a distinctive feature of neurons, as previously thought

Charlie Chaplin's Red Letter Days: At Work with the Comic Genius

A British actor who joined Chaplin’s stock company in early 1915, Fred Goodwins began writing short accounts of life at the studio and submitted them to publications. In February 1916 the British magazine Red Letter published the first of what became a series of more than thirty-five of Goodwins’s articles. Reproduced here for the first time, the articles have been edited by film historian David James and annotated by Chaplin expert Dan Kamin to highlight their revelations

On the asymptotic behaviour of solutions to the fractional porous medium equation with variable density

We are concerned with the long time behaviour of solutions to the fractional porous medium equation with a variable spatial density. We prove that if the density decays slowly at infinity, then the solution approaches the Barenblatt-type solution of a proper singular fractional problem. If, on the contrary, the density decays rapidly at infinity, we show that the minimal solution multiplied by a suitable power of the time variable converges to the minimal solution of a certain fractional sublinear elliptic equation.Comment: To appear in DCDS-