Bushes of vibrational modes for Fermi-Pasta-Ulam chains

Some exact solutions and multi-mode invariant submanifolds were found for the Fermi-Pasta-Ulam (FPU) beta-model by Poggi and Ruffo in Phys. D 103 (1997) 251. In the present paper we demonstrate how results of such a type can be obtained for an arbitrary N-particle chain with periodic boundary conditions with the aid of our group-theoretical approach [Phys. D 117 (1998) 43] based on the concept of bushes of normal modes for mechanical systems with discrete symmetry. The integro-differential equation describing the FPU-alfa dynamics in the modal space is derived. The loss of stability of the bushes of modes for the FPU-alfa model, in particular, for the limiting case N >> 1 for the dynamical regime with displacement pattern having period twice the lattice spacing (Pi-mode) is studied. Our results for the FPU-alfa chain are compared with those by Poggi and Ruffo for the FPU-beta chain.Comment: To be published in Physica

TP53 codon 72 single nucleotide polymorphism in chronic lymphocytic leukemia

Defects in the tumor suppressor gene TP53 are known to be important in chronic lymphocytic leukemia (CLL) and TP53 inactivation is associated with a particularly aggressive form of the disease. The single nucleotide polymorphism in the TP53 gene at codon 72 (rs1042522), results in amino acid substitution influencing apoptotic potential of TP53 protein. The aim of the study was to evaluate the association of the TP53 codon 72 polymorphism and incidence of TP53 mutations in CLL patients. Methods: 261 CLL samples were analyzed by polymerase chain reaction and direct sequencing for TP53 mutations and single nucleotide polymorphism. Results: The 72Pro/Pro genotype was associated with an increased incidence of TP53 mutations in previously treated patients (OR = 2.503; 95% CI 1.142–5.487; р = 0.001). Conclusion: This study revealed that the TP53 codon 72 polymorphism may be used as a risk factor for incidence of TP53 mutations in CLL. Key Words: chronic lymphocytic leukemia, TP53 mutations, single nucleotide polymorphism

The distribution of TP53 gene polymorphisms in chronic lymphocytic leukemia patients, sufferers of chornobyl nuclear power plant accident

Previous analyses in a cohort of Chornobyl cleanup workers revealed significantly increased radiation-related risk for all leukemia types, including chronic lymphocytic leukemia (CLL). Numerous investigations emphasized the significance of genetic susceptibility to the radiation carcinogenesis. The aim of the work was to study the distribution of TP53 single nucleotide polymorphisms (SNPs) in CLL patients exposed to ionizing radiation (IR) due to Chornobyl nuclear power plant accident and estimate their impact on disease development. Materials and Methods: The TP53 exonic and intronic SNPs were analyzed in 236 CLL patients by polymerase chain reaction and direct sequencing. The main group included 106 IR exposed CLL patients and the control group was composed of 130 IR non-exposed CLL patients. Results: Nineteen TP53 SNPs were found in the observed CLL cohort. No significant differences were found between the main and the control groups, but increased frequencies of T/T rs12947788 + G/G rs12951053 homozygotes and rs146340390 C/T variants were found among IR-exposed CLL patients compared with healthy Europeans (data from the 1000 Genomes Project). Rare nucleotide substitution rs146340390 (c.665C>T) was found only in the main group. These features were primarily typical for the most affected group of IR-exposed patients, namely, cleanup workers engaged in emergency works in the 2nd quarter of 1986. Conclusion: These preliminary findings don’t contradict the assumption on possible influence of IR on CLL development via the p53-dependent pathway. This article is a part of a Special Issue entitled “The Chornobyl Nuclear Accident: Thirty Years After”

Analysis of the 3′UTR region of the NOTCH1 gene in chronic lymphocytic leukemia patients

Deregulation of NOTCH1-signalling pathway is common in chronic lymphocytic leukemia (CLL). The most of studies are focused on detection of the hotspot c.7541_7542delCT NOTCH1 mutations in exon 34, while studies of mutations in the 3′UTR region are rare. The aims of work were to evaluate the frequencies of mutations in the 3′UTR region of the NOTCH1 gene (9:136,495553-136,495994) in Ukrainian CLL patients, the distribution of rs3124591 genotypes located in that area, and association of NOTCH1 mutations with structure of B-cell receptor. Materials and Methods: Detection of mutations in the 3′UTR region of the NOTCH1 was performed by direct sequencing in 87 previously untreated CLL patients (from the total group of 237 CLL patients) with unmutated immunoglobulin heavy-chain variable (UM IGHV) genes and without mutations in hotspot regions of TP53, SF3B1, and exon 34 of NOTCH1 genes. Results: Mutations in the 3′UTR region of the NOTCH1 were revealed in three of 87 CLL patients (3.4%). Two cases with non-coding mutations were related to subset #1 of stereotyped B-cell receptors, and one case belonged to stereotyped subset #28a. Analysis with inclusion of 30 UM IGHV cases with previously detected c.7544_7545delCT mutations revealed that the frequency of UM IGHV genes of I phylogenetic clan (except IGHV1-69) was significantly increased, and the frequency of UM IGHV3 and IGHV4 genes, on the contrary, was reduced in NOTCH1-mutated cases comparing with NOTCH1-unmutated cases (p = 0.002) and the general group (p = 0.013). SNP rs3124591 did not affect the risk of CLL and survival parameters of the patients. At the same time, differences were found in the frequency of IGHV gene usage and in the structure of HCDR3 in carriers of individual genotypes. Conclusion: The frequency of NOTCH1 mutations in 3′UTR region was low. Our findings confirmed current data on the association between the structure of the B-cell receptor and the appearance of NOTCH1 mutations. Some features of HCDR3 structure were identified in carriers of TT and CC genotypes of rs3124591. Key Words: NOTCH1 mutations, 3′UTR region of the NOTCH1, rs3124591, IGHV genes

Detection of notch1 c.7544_7545deICT mutation in chronic lymphocytic leukemia using conventional and real-time polymerase chain reaction

Aim: To evaluate real-time polymerase chain reaction (PCR) assay system for detection of NOTCH1 c.7541_754delCT mutation in chronic lymphocytic leukemia (CLL) patients. Material and Methods: A total of 325 CLL patients were included in the study. Screening for NOTCH1 c.7544_7545delCT was performed using conventional PCR-based amplification refractory mutation system (ARMS) method. All 33 samples harboring c.7544_7545delCT allele and 5 negative cases as control were submitted to real-time PCR. Results: Specificity and sensitivity of two PCR techniques were comparable. NOTCH1 c.7544_7545delCT mutation was found by ARMS in 10.1% of CLL patients, which is consistent with the data of other studies. However, the results of ARMS PCR in a minority of cases (2.15%) were doubtful and required reinvestigation. Real-time PCR, being less time-consuming, showed advantage in the assessment of the amplification’s specificity (using the melting curve analysis). It also allows the quantitative assessment of NOTCH1-mutated clone. Conclusion: NOTCH1 c.7544_7545delCT mutation resulting in removal of the C-terminal PEST domain, deregulation of NOTCH1-dependent signaling pathways, has negative influence on prognosis of CLL and efficiency of therapy with anti-CD20 monoclonal antibodies. Real-time PCR allows the fast and reliable detection of c.7544_7545delCT mutation and can be used for the screening of this molecular lesion in CLL patients

Current Helicity and Twist as Two Indicators of The Mirror Asymmetry of solar Magnetic Fields

A comparison between the two tracers of magnetic field mirror asymmetry in solar active regions, twist and current helicity, is presented. It is shown that for individual active regions these tracers do not possess visible similarity while averaging by time over the solar cycle, or by latitude, reveals similarities in their behaviour. The main property of the dataset is anti-symmetry over the solar equator. Considering the evolution of helical properties over the solar cycle we find signatures of a possible sign change at the beginning of the cycle, though more systematic observational data are required for a definite confirmation. We discuss the role of both tracers in the context of the solar dynamo theory.Comment: 14 pages, 6 figure

Are Solar Active Regions with Major Flares More Fractal, Multifractal, or Turbulent than Others?

Multiple recent investigations of solar magnetic field measurements have raised claims that the scale-free (fractal) or multiscale (multifractal) parameters inferred from the studied magnetograms may help assess the eruptive potential of solar active regions, or may even help predict major flaring activity stemming from these regions. We investigate these claims here, by testing three widely used scale-free and multiscale parameters, namely, the fractal dimension, the multifractal structure function and its inertial-range exponent, and the turbulent power spectrum and its power-law index, on a comprehensive data set of 370 timeseries of active-region magnetograms (17,733 magnetograms in total) observed by SOHO's Michelson Doppler Imager (MDI) over the entire Solar Cycle 23. We find that both flaring and non-flaring active regions exhibit significant fractality, multifractality, and non-Kolmogorov turbulence but none of the three tested parameters manages to distinguish active regions with major flares from flare-quiet ones. We also find that the multiscale parameters, but not the scale-free fractal dimension, depend sensitively on the spatial resolution and perhaps the observational characteristics of the studied magnetograms. Extending previous works, we attribute the flare-forecasting inability of fractal and multifractal parameters to i) a widespread multiscale complexity caused by a possible underlying self-organization in turbulent solar magnetic structures, flaring and non-flaring alike, and ii) a lack of correlation between the fractal properties of the photosphere and overlying layers, where solar eruptions occur. However useful for understanding solar magnetism, therefore, scale-free and multiscale measures may not be optimal tools for active-region characterization in terms of eruptive ability or, ultimately,for major solar-flare prediction.Comment: 25 pages, 7 figures, 2 tables, Solar Phys., in pres

A Statistical Study on Photospheric Magnetic Nonpotentiality of Active Regions and Its Relationship with Flares during Solar Cycles 22-23

A statistical study is carried out on the photospheric magnetic nonpotentiality in solar active regions and its relationship with associated flares. We select 2173 photospheric vector magnetograms from 1106 active regions observed by the Solar Magnetic Field Telescope at Huairou Solar Observing Station, National Astronomical Observatories of China, in the period of 1988-2008, which covers most of the 22nd and 23rd solar cycles. We have computed the mean planar magnetic shear angle (\bar{\Delta\phi}), mean shear angle of the vector magnetic field (\bar{\Delta\psi}), mean absolute vertical current density (\bar{|J_{z}|}), mean absolute current helicity density (\bar{|h_{c}|}), absolute twist parameter (|\alpha_{av}|), mean free magnetic energy density (\bar{\rho_{free}}), effective distance of the longitudinal magnetic field (d_{E}), and modified effective distance (d_{Em}) of each photospheric vector magnetogram. Parameters \bar{|h_{c}|}, \bar{\rho_{free}}, and d_{Em} show higher correlation with the evolution of the solar cycle. The Pearson linear correlation coefficients between these three parameters and the yearly mean sunspot number are all larger than 0.59. Parameters \bar{\Delta\phi}, \bar{\Delta\psi}, \bar{|J_{z}|}, |\alpha_{av}|, and d_{E} show only weak correlations with the solar cycle, though the nonpotentiality and the complexity of active regions are greater in the activity maximum periods than in the minimum periods. All of the eight parameters show positive correlations with the flare productivity of active regions, and the combination of different nonpotentiality parameters may be effective in predicting the flaring probability of active regions.Comment: 20 pages, 5 figures, 4 tables, accepted for publication in Solar Physic

Enhanced Group Analysis and Exact Solutions of Variable Coefficient Semilinear Diffusion Equations with a Power Source

A new approach to group classification problems and more general investigations on transformational properties of classes of differential equations is proposed. It is based on mappings between classes of differential equations, generated by families of point transformations. A class of variable coefficient (1+1)-dimensional semilinear reaction-diffusion equations of the general form $f(x)u_t=(g(x)u_x)_x+h(x)u^m$ ($m\ne0,1$) is studied from the symmetry point of view in the framework of the approach proposed. The singular subclass of the equations with $m=2$ is singled out. The group classifications of the entire class, the singular subclass and their images are performed with respect to both the corresponding (generalized extended) equivalence groups and all point transformations. The set of admissible transformations of the imaged class is exhaustively described in the general case $m\ne2$. The procedure of classification of nonclassical symmetries, which involves mappings between classes of differential equations, is discussed. Wide families of new exact solutions are also constructed for equations from the classes under consideration by the classical method of Lie reductions and by generation of new solutions from known ones for other equations with point transformations of different kinds (such as additional equivalence transformations and mappings between classes of equations).Comment: 40 pages, this is version published in Acta Applicanda Mathematica

Evolution and Flare Activity of Delta-Sunspots in Cycle 23

The emergence and magnetic evolution of solar active regions (ARs) of beta-gamma-delta type, which are known to be highly flare-productive, were studied with the SOHO/MDI data in Cycle 23. We selected 31 ARs that can be observed from their birth phase, as unbiased samples for our study. From the analysis of the magnetic topology (twist and writhe), we obtained the following results. i) Emerging beta-gamma-delta ARs can be classified into three topological types as "quasi-beta", "writhed" and "top-to-top". ii) Among them, the "writhed" and "top-to-top" types tend to show high flare activity. iii) As the signs of twist and writhe agree with each other in most cases of the "writhed" type (12 cases out of 13), we propose a magnetic model in which the emerging flux regions in a beta-gamma-delta AR are not separated but united as a single structure below the solar surface. iv) Almost all the "writhed"-type ARs have downward knotted structures in the mid portion of the magnetic flux tube. This, we believe, is the essential property of beta-gamma-delta ARs. v) The flare activity of beta-gamma-delta ARs is highly correlated not only with the sunspot area but also with the magnetic complexity. vi) We suggest that there is a possible scaling-law between the flare index and the maximum umbral area