We consider a family of probability distributions depending on a real parameter and including the binomial, Poisson and negative binomial distributions. The corresponding index of coincidence satisfies a Heun differential equation and is a logarithmically convex function. Combining these facts we get bounds for the index of coincidence, and consequently for Renyi and Tsallis entropies of order 2.
The mean square displacement and instantaneous diffusion coefficient for different configurations of charged particles in stochastic motion are calculated by numerically solving the associated equations of motion. The method is suitable for obtaining accurate descriptions of diffusion in both intermediate and long time regimes. It is also appropriate for studying a variety of astrophysical configurations since it may incorporate microscopic physics that analytical methods cannot cope with. The results show that, in the intermediary time regime, the diffusion coefficient has an irregular behavior, which can be described in terms of the complex interplay appearing between the physical parameters describing the configuration. The main conclusion is that such an approach may serve at differential diagnosis of different astrophysical configurations.
We consider the indices of coincidence for the binomial, Poisson, and negative binomial distributions. They are related in a simple manner to the R\'{e}nyi entropy and Tsallis entropy. We investigate some families of Heun functions containing these indices of coincidence. For the involved Heun functions we obtain closed forms, explicit expressions, or representations in terms of hypergeometric functions.
Somatic frameshift mutations in exon 9 of calreticulin (CALR) gene are recognized as disease drivers in primary myelofibrosis (PMF), one of the three classical Philadelphia-negative myeloproliferative neoplasms (MPNs). Type 1/type 1-like CALR mutations particularly confer a favorable prognostic and survival advantage in PMF patients. We report an unusual case of PMF incidentally diagnosed in a 68-year-old woman known with hepatitis C virus (HCV) cirrhosis who developed a progressive painful splenomegaly, without anomalies in blood cell counts. While harboring a type 1 CALR mutation, the patient underwent a leukemic transformation in less than 1 year from diagnosis, with a lethal outcome. Analysis of paired DNA samples from chronic and leukemic phases by a targeted next-generation sequencing (NGS) panel and single-nucleotide polymorphism (SNP) microarray revealed that the leukemic clone developed from the CALR-mutated clone through the acquisition of genetic events in the RAS signaling pathway: an increased variant allele frequency of the germline NRAS Y64D mutation present in the chronic phase (via an acquired uniparental disomy of chromosome 1) and gaining NRAS G12D in the blast phase. SNP microarray analysis showed five clinically significant copy number losses at regions 7q22.1, 8q11.1-q11.21, 10p12.1-p11.22, 11p14.1-p11.2, and Xp11.4, revealing a complex karyotype already in the chronic phase. We discuss how additional mutations, detected by NGS, as well as HCV infection and antiviral therapy, might have negatively impacted this type 1 CALR-mutated PMF. We suggest that larger studies are required to determine if more careful monitoring would be needed in MPN patients also carrying HCV and receiving anti-HCV treatment.
The mean square displacement and instantaneous diffusion coefficient for different configurations of charged particles in stochastic motion are calculated by numerically solving the associated equations of motion. The method is suitable for obtaining accurate descriptions of diffusion in both intermediate and long time regimes. It is also appropriate for studying a variety of astrophysical configurations since it may incorporate microscopic physics that analytical methods cannot cope with. The results show that, in the intermediary time regime, the diffusion coefficient has an irregular behavior, which can be described in terms of the complex interplay appearing between the physical parameters describing the configuration. The main conclusion is that such an approach may serve at differential diagnosis of different astrophysical configurations.
We consider the indices of coincidence for the binomial, Poisson, and negative binomial distributions. They are related in a simple manner to the R\'{e}nyi entropy and Tsallis entropy. We investigate some families of Heun functions containing these indices of coincidence. For the involved Heun functions we obtain closed forms, explicit expressions, or representations in terms of hypergeometric functions.
We investigate the propagation of both sausage and kink modes channelled by expanding coronal loops, with time-dependent, inhomogeneous density. The aim of this paper is to extend the study of the effects of loop cooling and expansion on standing sausage modes. We follow a linearized magnetohydrodynamical (MHD) approach in deriving the laws of motion for the coronal loops, and due to the complexity of the obtained equations, the solutions are found numerically. It was found that the cooling phenomenon leads to the damping of both kink and sausage type oscillations. On the other hand, the expansion of the loop alters mainly the period of the oscillations. This study may found possible application in the field of Coronal Seismology.
This paper reports on the statistical behavior of the optical Intraday Variability of BL Lac S5 0716+714. Available Intraday Variability data in the optical are tested to see whether or not the magnitude is lognormally distributed. Our results consistently indicate that this is not the case. This is in agreement with a previous discussion about data for the same object but in a different observational period. Simultaneously, the spectral slope of the light curves is calculated. The implications of these findings on models that describe both the location and source of Intraday Variability are presented.
