Novel Retinal Imaging Technologies

Newly-developed imaging techniques show extensive promise and potential to improve early detection, accurate diagnosis, and management of retinal diseases. Optical coherernce tomography angiography (OCTA), photoacoustic imaging (PAI), and molecular imaging (MI) are all new and promising imaging modalities. As these imaging instruments have advanced, they have enabled visualization of the retina at an unprecedented resolution. Published studies have established the efficacy of these modalities in the assessment of common retinal diseases, such as age-related macular degeneration, diabetic retinopathy, and retinal vascular occlusions. Each of these systems is built upon different principles and all have different limitations. In addition, the three imaging modalities have complementary features and thus can be integrated in to a multimodal imaging system, which will be more powerful in future

Proof of a Conjecture of Hirschhorn and Sellers on Overpartitions

Let $\bar{p}(n)$ denote the number of overpartitions of $n$. It was conjectured by Hirschhorn and Sellers that \bar{p}(40n+35)\equiv 0\ ({\rm mod\} 40) for $n\geq 0$. Employing 2-dissection formulas of quotients of theta functions due to Ramanujan, and Hirschhorn and Sellers, we obtain a generating function for $\bar{p}(40n+35)$ modulo 5. Using the $(p, k)$-parametrization of theta functions given by Alaca, Alaca and Williams, we give a proof of the congruence \bar{p}(40n+35)\equiv 0\ ({\rm mod\} 5). Combining this congruence and the congruence \bar{p}(4n+3)\equiv 0\ ({\rm mod\} 8) obtained by Hirschhorn and Sellers, and Fortin, Jacob and Mathieu, we give a proof of the conjecture of Hirschhorn and Sellers.Comment: 11 page

Interlacing Log-concavity of the Boros-Moll Polynomials

We introduce the notion of interlacing log-concavity of a polynomial sequence $\{P_m(x)\}_{m\geq 0}$, where $P_m(x)$ is a polynomial of degree m with positive coefficients $a_{i}(m)$. This sequence of polynomials is said to be interlacing log-concave if the ratios of consecutive coefficients of $P_m(x)$ interlace the ratios of consecutive coefficients of $P_{m+1}(x)$ for any $m\geq 0$. Interlacing log-concavity is stronger than the log-concavity. We show that the Boros-Moll polynomials are interlacing log-concave. Furthermore we give a sufficient condition for interlacing log-concavity which implies that some classical combinatorial polynomials are interlacing log-concave.Comment: 10 page

KDM2B/FBXL10 targets c-Fos for ubiquitylation and degradation in response to mitogenic stimulation.

KDM2B (also known as FBXL10) controls stem cell self-renewal, somatic cell reprogramming and senescence, and tumorigenesis. KDM2B contains multiple functional domains, including a JmjC domain that catalyzes H3K36 demethylation and a CxxC zinc-finger that recognizes CpG islands and recruits the polycomb repressive complex 1. Here, we report that KDM2B, via its F-box domain, functions as a subunit of the CUL1-RING ubiquitin ligase (CRL1/SCF(KDM2B)) complex. KDM2B targets c-Fos for polyubiquitylation and regulates c-Fos protein levels. Unlike the phosphorylation of other SCF (SKP1-CUL1-F-box)/CRL1 substrates that promotes substrates binding to F-box, epidermal growth factor (EGF)-induced c-Fos S374 phosphorylation dissociates c-Fos from KDM2B and stabilizes c-Fos protein. Non-phosphorylatable and phosphomimetic mutations at S374 result in c-Fos protein which cannot be induced by EGF or accumulates constitutively and lead to decreased or increased cell proliferation, respectively. Multiple tumor-derived KDM2B mutations impaired the function of KDM2B to target c-Fos degradation and to suppress cell proliferation. These results reveal a novel function of KDM2B in the negative regulation of cell proliferation by assembling an E3 ligase to targeting c-Fos protein degradation that is antagonized by mitogenic stimulations