88 research outputs found
The averaged characteristic polynomial for the Gaussian and chiral Gaussian ensembles with a source
In classical random matrix theory the Gaussian and chiral Gaussian random
matrix models with a source are realized as shifted mean Gaussian, and chiral
Gaussian, random matrices with real , complex ( and
real quaternion ) elements. We use the Dyson Brownian motion model
to give a meaning for general . In the Gaussian case a further
construction valid for is given, as the eigenvalue PDF of a
recursively defined random matrix ensemble. In the case of real or complex
elements, a combinatorial argument is used to compute the averaged
characteristic polynomial. The resulting functional forms are shown to be a
special cases of duality formulas due to Desrosiers. New derivations of the
general case of Desrosiers' dualities are given. A soft edge scaling limit of
the averaged characteristic polynomial is identified, and an explicit
evaluation in terms of so-called incomplete Airy functions is obtained.Comment: 21 page
Asymptotics for products of characteristic polynomials in classical -Ensembles
We study the local properties of eigenvalues for the Hermite (Gaussian),
Laguerre (Chiral) and Jacobi -ensembles of random matrices.
More specifically, we calculate scaling limits of the expectation value of
products of characteristic polynomials as . In the bulk of the
spectrum of each -ensemble, the same scaling limit is found to be
whose exact expansion in terms of Jack polynomials is well
known. The scaling limit at the soft edge of the spectrum for the Hermite and
Laguerre -ensembles is shown to be a multivariate Airy function, which
is defined as a generalized Kontsevich integral. As corollaries, when
is even, scaling limits of the -point correlation functions for the three
ensembles are obtained. The asymptotics of the multivariate Airy function for
large and small arguments is also given. All the asymptotic results rely on a
generalization of Watson's lemma and the steepest descent method for integrals
of Selberg type.Comment: [v3] 35 pages; this is a revised and enlarged version of the article
with new references, simplified demonstations, and improved presentation. To
be published in Constructive Approximation 37 (2013
Optimisation of Biochemical Condition and Substrates In Vitro for Tissue Engineering of Ligament
In this work, we analysed the effect of growth factors on in vitro cell proliferation and collagens synthesis by fibroblasts cultured for 72 h on different substrates (silicon sheet with or without 1% gelatin, and glass as control surface) for ligament tissue engineering. A human fibroblast cell line (CRL-2703) was used. The synthesis of type I and type III collagens were evaluated qualitatively and quantitatively by RT-PCR and confocal microscopy, respectively. Cell proliferation was evaluated by two methods: (1) MTT assay (2) cell cycle analysis. It was found that PDGF-AB stimulate the proliferation of fibroblast cultured on gelatin coated silicon sheet in dose dependant manner with a maximum effect at 10 ng ml(â1). The exogenous TGF-ÎČ1 induced the expression of type I and type III collagens in a dose and substrate-dependant manner. We deduce from this work that biochemical conditions and substrates have an important impact for optimisation of the tissue neo synthesis
Cancer Biomarker Discovery: The Entropic Hallmark
Background: It is a commonly accepted belief that cancer cells modify their transcriptional state during the progression of the disease. We propose that the progression of cancer cells towards malignant phenotypes can be efficiently tracked using high-throughput technologies that follow the gradual changes observed in the gene expression profiles by employing Shannon's mathematical theory of communication. Methods based on Information Theory can then quantify the divergence of cancer cells' transcriptional profiles from those of normally appearing cells of the originating tissues. The relevance of the proposed methods can be evaluated using microarray datasets available in the public domain but the method is in principle applicable to other high-throughput methods. Methodology/Principal Findings: Using melanoma and prostate cancer datasets we illustrate how it is possible to employ Shannon Entropy and the Jensen-Shannon divergence to trace the transcriptional changes progression of the disease. We establish how the variations of these two measures correlate with established biomarkers of cancer progression. The Information Theory measures allow us to identify novel biomarkers for both progressive and relatively more sudden transcriptional changes leading to malignant phenotypes. At the same time, the methodology was able to validate a large number of genes and processes that seem to be implicated in the progression of melanoma and prostate cancer. Conclusions/Significance: We thus present a quantitative guiding rule, a new unifying hallmark of cancer: the cancer cell's transcriptome changes lead to measurable observed transitions of Normalized Shannon Entropy values (as measured by high-throughput technologies). At the same time, tumor cells increment their divergence from the normal tissue profile increasing their disorder via creation of states that we might not directly measure. This unifying hallmark allows, via the the Jensen-Shannon divergence, to identify the arrow of time of the processes from the gene expression profiles, and helps to map the phenotypical and molecular hallmarks of specific cancer subtypes. The deep mathematical basis of the approach allows us to suggest that this principle is, hopefully, of general applicability for other diseases
Purinergic signalling and immune cells
This review article provides a historical perspective on the role of purinergic signalling in the regulation of various subsets of immune cells from early discoveries to current understanding. It is now recognised that adenosine 5'-triphosphate (ATP) and other nucleotides are released from cells following stress or injury. They can act on virtually all subsets of immune cells through a spectrum of P2X ligand-gated ion channels and G protein-coupled P2Y receptors. Furthermore, ATP is rapidly degraded into adenosine by ectonucleotidases such as CD39 and CD73, and adenosine exerts additional regulatory effects through its own receptors. The resulting effect ranges from stimulation to tolerance depending on the amount and time courses of nucleotides released, and the balance between ATP and adenosine. This review identifies the various receptors involved in the different subsets of immune cells and their effects on the function of these cells
International Consensus Statement on Rhinology and Allergy: Rhinosinusitis
Background: The 5 years since the publication of the first International Consensus Statement on Allergy and Rhinology: Rhinosinusitis (ICARâRS) has witnessed foundational progress in our understanding and treatment of rhinologic disease. These advances are reflected within the more than 40 new topics covered within the ICARâRSâ2021 as well as updates to the original 140 topics. This executive summary consolidates the evidenceâbased findings of the document. Methods: ICARâRS presents over 180 topics in the forms of evidenceâbased reviews with recommendations (EBRRs), evidenceâbased reviews, and literature reviews. The highest grade structured recommendations of the EBRR sections are summarized in this executive summary. Results: ICARâRSâ2021 covers 22 topics regarding the medical management of RS, which are grade A/B and are presented in the executive summary. Additionally, 4 topics regarding the surgical management of RS are grade A/B and are presented in the executive summary. Finally, a comprehensive evidenceâbased management algorithm is provided. Conclusion: This ICARâRSâ2021 executive summary provides a compilation of the evidenceâbased recommendations for medical and surgical treatment of the most common forms of RS
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10.1016/j.jaci.2009.10.016Journal of Allergy and Clinical Immunology1252507-508JACI
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