A note on q-Euler numbers and polynomials

The purpose of this paper is to construct q-Euler numbers and polynomials by using p-adic q-integral equations on Zp. Finally, we will give some interesting formulae related to these q-Euler numbers and polynomials.Comment: 6 page

Synthesis of tacrine analogues derived from n-aryl-5-amino-4-cyanopyrazoles

Synthesis of eleven tacrine analogues derived from N-aryl-5-amino-4-cyanopyrazoles, by a Friedländer type reaction, is described. Their structures were confirmed by 1H and 13C NMR spectroscopy, elemental analysis and/or mass spectrometry.Fundação para a Ciência e Tecnologia and FEDER (POCTI-SFA-3-686

A Selberg integral for the Lie algebra A_n

A new q-binomial theorem for Macdonald polynomials is employed to prove an A_n analogue of the celebrated Selberg integral. This confirms the g=A_n case of a conjecture by Mukhin and Varchenko concerning the existence of a Selberg integral for every simple Lie algebra g.Comment: 32 page

Deep learning-assisted radiomics facilitates multimodal prognostication for personalized treatment strategies in low-grade glioma

Determining the optimal course of treatment for low grade glioma (LGG) patients is challenging and frequently reliant on subjective judgment and limited scientific evidence. Our objective was to develop a comprehensive deep learning assisted radiomics model for assessing not only overall survival in LGG, but also the likelihood of future malignancy and glioma growth velocity. Thus, we retrospectively included 349 LGG patients to develop a prediction model using clinical, anatomical, and preoperative MRI data. Before performing radiomics analysis, a U2-model for glioma segmentation was utilized to prevent bias, yielding a mean whole tumor Dice score of 0.837. Overall survival and time to malignancy were estimated using Cox proportional hazard models. In a postoperative model, we derived a C-index of 0.82 (CI 0.79-0.86) for the training cohort over 10 years and 0.74 (Cl 0.64-0.84) for the test cohort. Preoperative models showed a C-index of 0.77 (Cl 0.73-0.82) for training and 0.67 (Cl 0.57-0.80) test sets. Our findings suggest that we can reliably predict the survival of a heterogeneous population of glioma patients in both preoperative and postoperative scenarios. Further, we demonstrate the utility of radiomics in predicting biological tumor activity, such as the time to malignancy and the LGG growth rate

Block-Anti-Circulant Unbalanced Oil and Vinegar

We introduce a new technique for compressing the public keys of the UOV signature scheme that makes use of block-anti-circulant matrices. These matrices admit a compact representation as for every block, the remaining elements can be inferred from the first row. This space saving translates to the public key, which as a result of this technique can be shrunk by a small integer factor. We propose parameters sets that take into account several important attacks

Simple deterministic dynamical systems with fractal diffusion coefficients

We analyze a simple model of deterministic diffusion. The model consists of a one-dimensional periodic array of scatterers in which point particles move from cell to cell as defined by a piecewise linear map. The microscopic chaotic scattering process of the map can be changed by a control parameter. This induces a parameter dependence for the macroscopic diffusion coefficient. We calculate the diffusion coefficent and the largest eigenmodes of the system by using Markov partitions and by solving the eigenvalue problems of respective topological transition matrices. For different boundary conditions we find that the largest eigenmodes of the map match to the ones of the simple phenomenological diffusion equation. Our main result is that the difffusion coefficient exhibits a fractal structure by varying the system parameter. To understand the origin of this fractal structure, we give qualitative and quantitative arguments. These arguments relate the sequence of oscillations in the strength of the parameter-dependent diffusion coefficient to the microscopic coupling of the single scatterers which changes by varying the control parameter.Comment: 28 pages (revtex), 12 figures (postscript), submitted to Phys. Rev.

Restricted Expression of Epstein-Barr Virus Latent Genes in Murine B Cells Derived from Embryonic Stem Cells

Background: Several human malignancies are associated with Epstein-Barr virus (EBV) and more than 95 % of the adult human population carries this virus lifelong. EBV efficiently infects human B cells and persists in this cellular compartment latently. EBV-infected B cells become activated and growth transformed, express a characteristic set of viral latent genes, and acquire the status of proliferating lymphoblastoid cell lines in vitro. Because EBV infects only primate cells, it has not been possible to establish a model of infection in immunocompetent rodents. Such a model would be most desirable in order to study EBV’s pathogenesis and latency in a suitable and amenable host. Methodology/Principal Findings: We stably introduced recombinant EBV genomes into mouse embryonic stem cells and induced their differentiation to B cells in vitro to develop the desired model. In vitro differentiated murine B cells maintained the EBV genomes but expression of viral genes was restricted to the latent membrane proteins (LMPs). In contrast to human B cells, EBV’s nuclear antigens (EBNAs) were not expressed detectably and growth transformed murine B cells did not arise in vitro. Aberrant splicing and premature termination of EBNA mRNAs most likely prevented the expression of EBNA genes required for B-cell transformation. Conclusions/Significance: Our findings indicate that fundamental differences in gene regulation between mouse and ma