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

Soluble Cytokine Receptors (sIL-2Rα, sIL-2Rβ) Induce Subunit-Specific Behavioral Responses and Accumulate in the Cerebral Cortex and Basal Forebrain

Soluble cytokine receptors are normal constituents of body fluids that regulate peripheral cytokine and lymphoid activity. Levels of soluble IL-2 receptors (sIL-2R) are elevated in psychiatric disorders linked with autoimmune processes, including ones in which repetitive stereotypic behaviors and motor disturbances are present. However, there is no evidence that sIL-2Rs (or any peripheral soluble receptor) induce such behavioral changes, or that they localize in relevant brain regions. Here, we determined in male Balb/c mice the effects of single peripheral injections of sIL-2Rα or sIL-2Rβ (0–2 µg/male Balb/c mouse; s.c.) on novelty-induced ambulatory activity and stereotypic motor behaviors. We discovered that sIL-2Rα increased the incidence of in-place stereotypic motor behaviors, including head up head bobbing, rearing/sniffing, turning, and grooming behavior. A wider spectrum of behavioral changes was evident in sIL-2Rβ-treated mice, including increases in vertical and horizontal ambulatory activity and stereotypic motor movements. To our knowledge, this is the first demonstration that soluble receptors induce such behavioral disturbances. In contrast, soluble IL-1 Type-1 receptors (0–4 µg, s.c.) didn't appreciably affect these behaviors. We further demonstrated that sIL-2Rα and sIL-2Rβ induced marked increases in c-Fos in caudate-putamen, nucleus accumbens and prefrontal cortex. Anatomical specificity was supported by the presence of increased activity in lateral caudate in sIL-2Rα treated mice, while sIL-2Rβ treated mice induced greater c-Fos activity in prepyriform cortex. Moreover, injected sIL-2Rs were widely distributed in regions that showed increased c-Fos expression. Thus, sIL-2Rα and sIL-2Rβ induce marked subunit- and soluble cytokine receptor-specific behavioral disturbances, which included increases in the expression of ambulatory activity and stereotypic motor behaviors, while inducing increased neuronal activity localized to cortex and striatum. These findings suggest that sIL-2Rs act as novel immune-to- brain messengers and raise the possibility that they contribute to the disease process in psychiatric disorders in which marked increases in these receptors have been reported

Laplacian Growth and Whitham Equations of Soliton Theory

The Laplacian growth (the Hele-Shaw problem) of multi-connected domains in the case of zero surface tension is proven to be equivalent to an integrable systems of Whitham equations known in soliton theory. The Whitham equations describe slowly modulated periodic solutions of integrable hierarchies of nonlinear differential equations. Through this connection the Laplacian growth is understood as a flow in the moduli space of Riemann surfaces.Comment: 33 pages, 7 figures, typos corrected, new references adde

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

Admission of advanced lung cancer patients to intensive care unit: A retrospective study of 76 patients

<p>Abstract</p> <p>Background</p> <p>Criteria for admitting patients with incurable diseases to the medical intensive care unit (MICU) remain unclear and have ethical implications.</p> <p>Methods</p> <p>We retrospectively evaluated MICU outcomes and identified risk factors for MICU mortality in consecutive patients with advanced lung cancer admitted to two university-hospital MICUs in France between 1996 and 2006.</p> <p>Results</p> <p>Of 76 included patients, 49 had non-small cell lung cancer (stage IIIB n = 20; stage IV n = 29). In 60 patients, MICU admission was directly related to the lung cancer (complication of cancer management, n = 30; cancer progression, n = 14; and lung-cancer-induced diseases, n = 17). Mechanical ventilation was required during the MICU stay in 57 patients. Thirty-six (47.4%) patients died in the MICU. Three factors were independently associated with MICU mortality: use of vasoactive agents (odds ratio [OR] 6.81 95% confidence interval [95%CI] [1.77-26.26], p = 0.005), mechanical ventilation (OR 6.61 95%CI [1.44-30.5], p = 0.015) and thrombocytopenia (OR 5.13; 95%CI [1.17-22.5], p = 0.030). In contrast, mortality was lower in patients admitted for a complication of cancer management (OR 0.206; 95%CI [0.058-0.738], p = 0.015). Of the 27 patients who returned home, four received specific lung cancer treatment after the MICU stay.</p> <p>Conclusions</p> <p>Patients with acute complications of treatment for advanced lung cancer may benefit from MCIU admission. Further studies are necessary to assess outcomes such as quality of life after MICU discharge.</p