On the Conjectures Regarding the 4-Point Atiyah Determinant

For the case of 4 points in Euclidean space, we present a computer aided proof of Conjectures II and III made by Atiyah and Sutcliffe regarding Atiyah's determinant along with an elegant factorization of the square of the imaginary part of Atiyah's determinant

Uniform Asymptotics of Orthogonal Polynomials Arising from Coherent States

In this paper, we study a family of orthogonal polynomials $\{\phi_n(z)\}$ arising from nonlinear coherent states in quantum optics. Based on the three-term recurrence relation only, we obtain a uniform asymptotic expansion of $\phi_n(z)$ as the polynomial degree $n$ tends to infinity. Our asymptotic results suggest that the weight function associated with the polynomials has an unusual singularity, which has never appeared for orthogonal polynomials in the Askey scheme. Our main technique is the Wang and Wong's difference equation method. In addition, the limiting zero distribution of the polynomials $\phi_n(z)$ is provided

GX15-070 (obatoclax) overcomes glucocorticoid resistance in acute lymphoblastic leukemia through induction of apoptosis and autophagy

Glucocorticoids (GCs) are common components of many chemotherapeutic regimens for lymphoid malignancies including acute lymphoblastic leukemia (ALL). The BCL-2 family has an essential role in regulating GC-induced cell death. Here we show that downregulation of antiapoptotic BCL-2 family proteins, especially MCL-1, enhances GC-induced cell death. Thus we target MCL-1 by using GX15-070 (obatoclax) in ALL cells. Treatment with GX15-070 in both dexamethasone (Dex)-sensitive and -resistant ALL cells shows effective growth inhibition and cell death. GX15-070 induces caspase-3 cleavage and increases the Annexin V-positive population, which is indicative of apoptosis. Before the onset of apoptosis, GX15-070 induces LC3 conversion as well as p62 degradation, both of which are autophagic cell death markers. A pro-apoptotic molecule BAK is released from the BAK/MCL-1 complex following GX15-070 treatment. Consistently, downregulation of BAK reduces caspase-3 cleavage and cell death, but does not alter LC3 conversion. In contrast, downregulation of ATG5, an autophagy regulator, decreases LC3 conversion and cell death, but does not alter caspase-3 cleavage, suggesting that apoptosis and autophagy induced by GX15-070 are independently regulated. Downregulation of Beclin-1, which is capable of crosstalk between apoptosis and autophagy, affects GX15-070-induced cell death through apoptosis but not autophagy. Taken together, GX15-070 treatment in ALL could be an alternative regimen to overcome glucocorticoid resistance by inducing BAK-dependent apoptosis and ATG5-dependent autophagy

The bright outburst of a new black hole candidate: Optical observations of MAXI J1820+070 from the Montsec observatory

The motivation of this thesis is to monitor the data of the 2018 outburst of the black hole candidate MAXI J1820+070. This project combines theoretical background about X-ray binaries with the experimental work done in the process of achieving optical magnitudes using a CCD camera: Telescopi Joan Oró ground based telescope. We present the optical light curves and colours of MAXI J1820+070 during the March-November 2018 outburst. After obtaining the magnitudes, using MAXI and Swift-UVOT as space observatories we extend our range to the X-ray band and study the different states and physical processes that occur in them. Finally, we give physical interpretation of all obtained data and characterize the spectral shape of the infrared, optical, UV and X-ray emission in the different components of MAXI J1820+070 outburst. We conclude that MAXI J1820+070 show the typical properties of a BHT: our results show the canonical BHT states, the disk irradiation changing in the soft state and the linear increase of the R-I colour indicating a cooling of the disk. We also give evidence that the optical emission in the soft state is bluer than in the hard

Combined inhibition of Bcl-2/Bcl-xL and Usp9X/Bag3 overcomes apoptotic resistance in glioblastoma in vitro and in vivo

Despite great efforts taken to advance therapeutic measures for patients with glioblastoma, the clinical prognosis remains grim. The antiapoptotic Bcl-2 family protein Mcl-1 is overexpressed in glioblastoma and represents an important resistance factor to the BH-3 mimetic ABT263. In this study, we show that combined treatment with ABT263 and GX15-070 overcomes apoptotic resistance in established glioblastoma cell lines, glioma stem-like cells and primary cultures. Moreover, this treatment regimen also proves to be advantageous in vivo. On the molecular level, GX15-070 enhanced apoptosis by posttranslational down-regulation of the deubiquitinase, Usp9X, and the chaperone Bag3, leading to a sustained depletion of Mcl-1 protein levels. Moreover, knock-down of Usp9X or Bag3 depleted endogenous Mcl-1 protein levels and in turn enhanced apoptosis induced through Bcl-2/Bcl-xL inhibition. In conclusion, combined treatment with ABT263 and GX15-070 results in a significantly enhanced anti-cancer activity in vitro as well as in vivo in the setting of glioblastoma. Both drugs, ABT263 and GX15-070 have been evaluated in clinical studies which facilitates the translational aspect of taking this combinatorial approach to the clinical setting. Furthermore we present a novel mechanism by which GX15-070 counteracts Mcl-1 expression which may lay a foundation for a novel target in cancer therapy