Normal families and fixed points of iterates

Let F be a family of holomorphic functions and let K be a constant less than 4. Suppose that for all f in F the second iterate of f does not have fixed points for which the modulus of the multiplier is greater than K. We show that then F is normal. This is deduced from a result about the multipliers of iterated polynomials.Comment: 5 page

Spherical Spectral Synthesis and Two-Radius Theorems on Damek-Ricci Spaces

We prove that spherical spectral analysis and synthesis hold in Damek-Ricci spaces and derive two-radius theorems

Lyapunov exponents, bifurcation currents and laminations in bifurcation loci

Bifurcation loci in the moduli space of degree $d$ rational maps are shaped by the hypersurfaces defined by the existence of a cycle of period $n$ and multiplier 0 or $e^{i\theta}$. Using potential-theoretic arguments, we establish two equidistribution properties for these hypersurfaces with respect to the bifurcation current. To this purpose we first establish approximation formulas for the Lyapunov function. In degree $d=2$, this allows us to build holomorphic motions and show that the bifurcation locus has a lamination structure in the regions where an attracting basin of fixed period exists

derived neutrophil to lymphocyte ratio dnlr change between baseline and cycle 2 is correlated with benefit during immune checkpoint inhibitors ici in advanced non small cell lung cancer nsclc patients

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Characteristic functional equations of polynomials and the morera-carleman theorem

Several characteristic functional equations satisfied by classes of polynomials of bounded degree are examined in connection with certain generalizations of the Morera-Carleman Theorem. Certain functional equations which have nonanalytic polynomial solutions are also considered.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43923/1/10_2005_Article_BF02188016.pd

Random Matrices in 2D, Laplacian Growth and Operator Theory

Since it was first applied to the study of nuclear interactions by Wigner and Dyson, almost 60 years ago, Random Matrix Theory (RMT) has developed into a field of its own within applied mathematics, and is now essential to many parts of theoretical physics, from condensed matter to high energy. The fundamental results obtained so far rely mostly on the theory of random matrices in one dimension (the dimensionality of the spectrum, or equilibrium probability density). In the last few years, this theory has been extended to the case where the spectrum is two-dimensional, or even fractal, with dimensions between 1 and 2. In this article, we review these recent developments and indicate some physical problems where the theory can be applied.Comment: 88 pages, 8 figure

Deregulation of miRNAs in malignant pleural mesothelioma is associated with prognosis and suggests an alteration of cell metabolism

Malignant pleural mesothelioma (MPM) is an aggressive human cancer and miRNAs can play a key-role for this disease. In order to broaden the knowledge in this field, the miRNA expression was investigated in a large series of MPM to discover new pathways helpful in diagnosis, prognosis and therapy. We employed nanoString nCounter system for miRNA profiling on 105 MPM samples and 10 healthy pleura. The analysis was followed by the validation of the most significantly deregulated miRNAs by RT-qPCR in an independent sample set. We identified 63 miRNAs deregulated in a statistically significant way. MiR-185, miR-197, and miR-299 were confirmed differentially expressed, after validation study. In addition, the results of the microarray analysis corroborated previous findings concerning miR-15b-5p, miR-126-3p, and miR-145-5p. Kaplan-Meier curves were used to explore the association between miRNA expression and overall survival (OS) and identified a 2-miRNA prognostic signature (Let-7c-5p and miR-151a-5p) related to hypoxia and energy metabolism respectively. In silico analyses with DIANA-microT-CDS highlighted 5 putative targets in common between two miRNAs. With the present work we showed that the pattern of miRNAs expression is highly deregulated in MPM and that a 2-miRNA signature can be a new useful tool for prognosis in MPM

CYFRA 21-1 is a prognostic determinant in non-small-cell lung cancer: results of a meta-analysis in 2063 patients

SCOPUS: ar.jinfo:eu-repo/semantics/publishe

GBR 12909 administration as a mouse model of bipolar disorder mania: mimicking quantitative assessment of manic behavior

Mania is a core feature of bipolar disorder (BD) that traditionally is assessed using rating scales. Studies using a new human behavioral pattern monitor (BPM) recently demonstrated that manic BD patients exhibit a specific profile of behavior that differs from schizophrenia and is characterized by increased motor activity, increased specific exploration, and perseverative locomotor patterns as assessed by spatial d. It was hypothesized that disrupting dopaminergic homeostasis by inhibiting dopamine transporter (DAT) function would produce a BD mania-like phenotype in mice as assessed by the mouse BPM. We compared the spontaneous locomotor and exploratory behavior of C57BL/6J mice treated with the catecholamine transporter inhibitor amphetamine or the selective DAT inhibitor GBR 12909 in the mouse BPM. We also assessed the duration of the effect of GBR 12909 by testing mice in the BPM for 3 h and its potential strain dependency by testing 129/SvJ mice. Amphetamine produced hyperactivity and increased perseverative patterns of locomotion as reflected in reduced spatial d values but reduced exploratory activity in contrast to the increased exploration observed in BD patients. GBR 12909 increased activity and reduced spatial d in combination with increased exploratory behavior, irrespective of inbred strain. These effects persisted for at least 3 h. Thus, selectively inhibiting the DAT produced a long-lasting cross-strain behavioral profile in mice that was consistent with that observed in manic BD patients. These findings support the use of selective DAT inhibition in animal models of the impaired dopaminergic homeostasis putatively involved in the pathophysiology of BD mania