Solve Non-Linear Parabolic Partial Differential Equation by Spline Collocation Method

This paper provides an overview of the formulation, analysis and implementation of Spline collocation method for the numerical solution of partial differential equation with two space variable which is of parabolic type. The method includes the solution of non-linear equation which can be expressed as in matrix form. The use of spline collocation methods in the solution of initial-boundary value problems for parabolic-type system id described, with emphasis on alternating direction implicit methods. Problem of vertical groundwater recharge solve by spline collocation method. Finally, recent applications of spline collocation method are outlined

Froth-like minimizers of a non local free energy functional with competing interactions

We investigate the ground and low energy states of a one dimensional non local free energy functional describing at a mean field level a spin system with both ferromagnetic and antiferromagnetic interactions. In particular, the antiferromagnetic interaction is assumed to have a range much larger than the ferromagnetic one. The competition between these two effects is expected to lead to the spontaneous emergence of a regular alternation of long intervals on which the spin profile is magnetized either up or down, with an oscillation scale intermediate between the range of the ferromagnetic and that of the antiferromagnetic interaction. In this sense, the optimal or quasi-optimal profiles are "froth-like": if seen on the scale of the antiferromagnetic potential they look neutral, but if seen at the microscope they actually consist of big bubbles of two different phases alternating among each other. In this paper we prove the validity of this picture, we compute the oscillation scale of the quasi-optimal profiles and we quantify their distance in norm from a reference periodic profile. The proof consists of two main steps: we first coarse grain the system on a scale intermediate between the range of the ferromagnetic potential and the expected optimal oscillation scale; in this way we reduce the original functional to an effective "sharp interface" one. Next, we study the latter by reflection positivity methods, which require as a key ingredient the exact locality of the short range term. Our proof has the conceptual interest of combining coarse graining with reflection positivity methods, an idea that is presumably useful in much more general contexts than the one studied here.Comment: 38 pages, 2 figure

Exponential martingales and changes of measure for counting processes

We give sufficient criteria for the Dol\'eans-Dade exponential of a stochastic integral with respect to a counting process local martingale to be a true martingale. The criteria are adapted particularly to the case of counting processes and are sufficiently weak to be useful and verifiable, as we illustrate by several examples. In particular, the criteria allow for the construction of for example nonexplosive Hawkes processes as well as counting processes with stochastic intensities depending on diffusion processes

The Glial Regenerative Response to Central Nervous System Injury Is Enabled by Pros-Notch and Pros-NFκB Feedback

Organisms are structurally robust, as cells accommodate changes preserving structural integrity and function. The molecular mechanisms underlying structural robustness and plasticity are poorly understood, but can be investigated by probing how cells respond to injury. Injury to the CNS induces proliferation of enwrapping glia, leading to axonal re-enwrapment and partial functional recovery. This glial regenerative response is found across species, and may reflect a common underlying genetic mechanism. Here, we show that injury to the Drosophila larval CNS induces glial proliferation, and we uncover a gene network controlling this response. It consists of the mutual maintenance between the cell cycle inhibitor Prospero (Pros) and the cell cycle activators Notch and NFκB. Together they maintain glia in the brink of dividing, they enable glial proliferation following injury, and subsequently they exert negative feedback on cell division restoring cell cycle arrest. Pros also promotes glial differentiation, resolving vacuolization, enabling debris clearance and axonal enwrapment. Disruption of this gene network prevents repair and induces tumourigenesis. Using wound area measurements across genotypes and time-lapse recordings we show that when glial proliferation and glial differentiation are abolished, both the size of the glial wound and neuropile vacuolization increase. When glial proliferation and differentiation are enabled, glial wound size decreases and injury-induced apoptosis and vacuolization are prevented. The uncovered gene network promotes regeneration of the glial lesion and neuropile repair. In the unharmed animal, it is most likely a homeostatic mechanism for structural robustness. This gene network may be of relevance to mammalian glia to promote repair upon CNS injury or disease

MTG16 regulates colonic epithelial differentiation, colitis, and tumorigenesis by repressing E protein transcription factors

Aberrant epithelial differentiation and regeneration contribute to colon pathologies, including inflammatory bowel disease (iBD) and colitis-associated cancer (CAC). Myeloid translocation gene 16 (MTG16, also known as CBFA2T3) is a transcriptional corepressor expressed in the colonic epithelium. MTG16 deficiency in mice exacerbates colitis and increases tumor burden in CAC, though the underlying mechanisms remain unclear. Here, we identified MTG16 as a central mediator of epithelial differentiation, promoting goblet and restraining enteroendocrine cell development in homeostasis and enabling regeneration following dextran sulfate sodium-induced (DSS-induced) colitis. Transcriptomic analyses implicated increased Ephrussi box-binding transcription factor (E protein) activity in MTG16-deficient colon crypts. Using a mouse model with a point mutation that attenuates MTG16:E protein interactions (Mtg16(P20ST)), we showed that MTG16 exerts control over colonic epithelial differentiation and regeneration by repressing E protein-mediated transcription. Mimicking murine colitis, MTG16 expression was increased in biopsies from patients with active IBD compared with unaffected controls. Finally, uncoupling MTG16:E protein interactions partially phenocopied the enhanced tumorigenicity of Mtg16(-/)(-) colon in the azoxymethane/DSS-induced model of CAC, indicating that MTG16 protects from tumorigenesis through additional mechanisms. Collectively, our results demonstrate that MTG16, via its repression of E protein targets. is a key regulator of cell fate decisions during colon homeostasis, colitis, and cancer.Peer reviewe

Phase field modeling of nonlinear material behavior

Materials that undergo internal transformations are usually described in solid mechanics by multi-well energy functions that account for both elastic and transformational behavior. In order to separate the two effects, physicists use instead phase-field-type theories where conventional linear elastic strain is quadratically coupled to an additional field that describes the evolution of the reference state and solely accounts for nonlinearity. In this paper we propose a systematic method allowing one to split the non-convex energy into harmonic and nonharmonic parts and to convert a nonconvex mechanical problem into a partially linearized phase-field problem. The main ideas are illustrated using the simplest framework of the Peierls-Nabarro dislocation model.Comment: 12 pages, 4 figures. v1: as submitted. v2: as published (conclusion added, unessential part of appendix removed, minor typesetting revisions). To appear in: K. Hackl (ed.), Proceedings of the IUTAM Symposium on Variational Concepts with Applications to the Mechanics of Materials, September 22-26, 2008, Bochum. (Springer-Verlag, 2010 presumably

Notch and Prospero Repress Proliferation following Cyclin E Overexpression in the Drosophila Bristle Lineage

Understanding the mechanisms that coordinate cell proliferation, cell cycle arrest, and cell differentiation is essential to address the problem of how “normal” versus pathological developmental processes take place. In the bristle lineage of the adult fly, we have tested the capacity of post-mitotic cells to re-enter the cell cycle in response to the overexpression of cyclin E. We show that only terminal cells in which the identity is independent of Notch pathway undergo extra divisions after CycE overexpression. Our analysis shows that the responsiveness of cells to forced proliferation depends on both Prospero, a fate determinant, and on the level of Notch pathway activity. Our results demonstrate that the terminal quiescent state and differentiation are regulated by two parallel mechanisms acting simultaneously on fate acquisition and cell cycle progression

Identification of 14-3-3γ as a Mieap-interacting protein and its role in mitochondrial quality control

Mieap, a p53-inducible protein, controls mitochondrial integrity by inducing the accumulation of lysosomal proteins within mitochondria. This phenomenon is designated MALM, for Mieap-induced accumulation of lysosome-like organelles within mitochondria. To identify this novel Mieap-interacting protein(s), we performed a two-dimensional image-converted analysis of liquid chromatography and mass spectrometry (2DICAL) on the proteins immunoprecipitated by an anti-Mieap antibody. We indentified 14-3-3γ as one of the proteins that was included in the Mieap-binding protein complex when MALM was induced. The interaction between Mieap and 14-3-3γ was confirmed on the exogenous and endogenous proteins. Interestingly, 14-3-3γ was localized within mitochondria when MALM occurred. A 14-3-3γ deficiency did not affect the accumulation of Mieap and lysosomal proteins within mitochondria, but dramatically inhibited the elimination of oxidized mitochondrial proteins. These results suggest that 14-3-3γ plays a critical role in eliminating oxidized mitochondrial proteins during the MALM process by interacting with Mieap within mitochondria

Human Centric Facial Expression Recognition

Facial expression recognition (FER) is an area of active research, both in computer science and in behavioural science. Across these domains there is evidence to suggest that humans and machines find it easier to recognise certain emotions, for example happiness, in comparison to others. Recent behavioural studies have explored human perceptions of emotion further, by evaluating the relative contribution of features in the face when evaluating human sensitivity to emotion. It has been identified that certain facial regions have more salient features for certain expressions of emotion, especially when emotions are subtle in nature. For example, it is easier to detect fearful expressions when the eyes are expressive. Using this observation as a starting point for analysis, we similarly examine the effectiveness with which knowledge of facial feature saliency may be integrated into current approaches to automated FER. Specifically, we compare and evaluate the accuracy of ‘full-face’ versus upper and lower facial area convolutional neural network (CNN) modelling for emotion recognition in static images, and propose a human centric CNN hierarchy which uses regional image inputs to leverage current understanding of how humans recognise emotions across the face. Evaluations using the CK+ dataset demonstrate that our hierarchy can enhance classification accuracy in comparison to individual CNN architectures, achieving overall true positive classification in 93.3% of cases

Prox1 Regulates the Notch1-Mediated Inhibition of Neurogenesis

During development of the spinal cord, Prox1 controls the balance between proliferation and differentiation of neural progenitor cells via suppression of Notch1 gene expression