Baker's conjecture for functions with real zeros

Baker's conjecture states that a transcendental entire functions of order less than 1/2 has no unbounded Fatou components. It is known that, for such functions, there are no unbounded periodic Fatou components and so it remains to show that they can also have no unbounded wandering domains. Here we introduce completely new techniques to show that the conjecture holds in the case that the transcendental entire function is real with only real zeros, and we prove the much stronger result that such a function has no orbits consisting of unbounded wandering domains whenever the order is less than 1. This raises the question as to whether such wandering domains can exist for any transcendental entire function with order less than 1. Key ingredients of our proofs are new results in classical complex analysis with wider applications. These new results concern: the winding properties of the images of certain curves proved using extremal length arguments, growth estimates for entire functions, and the distribution of the zeros of entire functions of order less than 1

Integrative Transcriptomics Reveals Activation of Innate Immune Responses and Inhibition of Inflammation During Oral Immunotherapy for Egg Allergy in Children

We previously reported the results of a randomized, open-label trial of egg oral immunotherapy (OIT) in 50 children where 44% were desensitized and 46% were partially desensitized after 8 months of treatment. Here we focus on cell-mediated molecular mechanisms driving desensitization during egg OIT. We sought to determine whether changes in genome-wide gene expression in blood cells during egg OIT correlate with humoral responses and the clinical outcome. The blood cell transcriptome of 50 children receiving egg OIT was profiled using peripheral blood mononuclear cell (PBMC) samples obtained at baseline and after 3 and 8 months of OIT. We identified 467 differentially expressed genes (DEGs) after 3 or 8 months of egg OIT. At 8 months, 86% of the DEGs were downregulated and played a role in the signaling of TREM1, IL-6, and IL-17. In correlation analyses, Gal d 1-4-specific IgG4 antibodies associated positively with DEGs playing a role in pathogen recognition and antigen presentation and negatively with DEGs playing a role in the signaling of IL-10, IL-6, and IL-17. Desensitized and partially desensitized patients had differences in their antibody responses, and although most of the transcriptomic changes were shared, both groups had also specific patterns, which suggest slower changes in partially desensitized and activation of NK cells in the desensitized group. OIT for egg allergy in children inhibits inflammation and activates innate immune responses regardless of the clinical outcome at 8 months. Changes in gene expression patterns first appear as posttranslational protein modifications, followed by more sustained epigenetic gene regulatory functions related to successful desensitization.Peer reviewe

Properties of the series solution for Painlevé I

We present some observations on the asymptotic behaviour of the coefficients in the Laurent series expansion of solutions of the first Painlevé equation. For the general solution, explicit recursive formulae for the Taylor expansion of the tau-function around a zero are given, which are natural extensions of analogous formulae for the elliptic sigma function, as given by Weierstrass. Numerical and exact results on the symmetric solution which is singular at the origin are also presented

Attenuated Semliki Forest virus for cancer treatment in dogs : safety assessment in two laboratory Beagles

Background: Dogs suffer from spontaneous tumors which may be amenable to therapies developed for human cancer patients, and dogs may serve as large-animal cancer models. A non-pathogenic Semliki Forest virus vector VA7-EGFP previously showed promise in targeting human tumor xenografts in mice, but the oncolytic capacity of the virus in canine cancer cells and the safety of the virus in higher mammals such as dogs, are not known. We therefore assessed the oncolytic potency of VA7-EGFP against canine cancer cells by infectivity and viability assays in two dog solid tumor cell lines. Furthermore we performed a 3-week safety study in two adult Beagles which received a single intravenous injection of similar to 2 x 10(5) plaque forming units of parental A7(74) strain. Results: VA7-EGFP was able to replicate in and kill both canine cancer cell lines tested. No adverse events were observed in either of the two virus-injected adult Beagles and no infective virus could be recovered from any of the biological samples collected over the course of the study. Neutralizing antibodies to Semliki Forest virus became detectable in the dogs at 5 days post infection and remained elevated until study termination. Conclusions: Based on these results, testing of the oncolytic potential of attenuated Semliki Forest virus in canine cancer patients appears feasible.Peer reviewe

Long-term changes in milk component immunoglobulins reflect milk oral immunotherapy outcomes in Finnish children

Background Milk oral immunotherapy (OIT) may increase the amount of milk protein that can be ingested without triggering an allergic reaction. It is important to understand why some patients benefit from the treatment while others do not. Objective The aim was to define the differences in the milk allergen component-specific (casein, alpha-lactalbumin, ss-lactoglobulin) immunoglobulin (sIg [sIgE, sIgG4, and sIgA]) levels relative to the long-term outcomes of milk OIT. Methods In this long-term, open-label follow-up study, 286 children started milk OIT between 2005 and 2015. Follow-up data were collected at two points: the post-buildup phase and long term (range 1-11 years, median 6 years). Comparisons of sIg levels were made among three outcome groups of self-reported long-term milk consumption (high-milk dose, low-milk dose, and avoidance). Results A total of 168 (59%) of the 286 patients on OIT participated. Most patients (57%) were in the high-dose group; here, 80% of these patients had a baseline casein sIgE value less than 28 kUA/L, they had the lowest casein sIgE levels at all time (p < .001), their casein sIgG4/IgE levels increased, and long-term casein sIgA was highest compared with the low-dose and avoidance groups (p = .02). Low-milk dose group had the highest casein sIgG4/IgE levels in long term (p = .002). Conclusion The baseline Ig profiles and responses to milk OIT differed depending on long-term milk consumption. Lower casein sIgE levels were associated with better outcome. Milk casein sIgA differed in the long term among high-milk consumers.Peer reviewe

The iterated minimum modulus and conjectures of Baker and Eremenko

In transcendental dynamics significant progress has been made by studying points whose iterates escape to infinity at least as fast as iterates of the maximum modulus. Here we take the novel approach of studying points whose iterates escape at least as fast as iterates of the minimum modulus, and obtain new results related to Eremenko's conjecture and Baker's conjecture, and the rate of escape in Baker domains. To do this we prove a result of wider interest concerning the existence of points that escape to infinity under the iteration of a positive continuous function

Non-real zeros of derivatives of meromorphic functions

A number of results are proved concerning non-real zeros of derivatives of real and strictly non-real meromorphic functions in the plane

Slow escaping points of quasiregular mappings

This article concerns the iteration of quasiregular mappings on Rd and entire functions on C. It is shown that there are always points at which the iterates of a quasiregular map tend to infinity at a controlled rate. Moreover, an asymptotic rate of escape result is proved that is new even for transcendental entire functions. Let f:Rd→Rd be quasiregular of transcendental type. Using novel methods of proof, we generalise results of Rippon and Stallard in complex dynamics to show that the Julia set of f contains points at which the iterates fn tend to infinity arbitrarily slowly. We also prove that, for any large R, there is a point x with modulus approximately R such that the growth of |fn(x)| is asymptotic to the iterated maximum modulus Mn(R,f)

The impact of changes in stakeholder salience on CSR activities in Russian energy firms: a contribution to the divergence / convergence debate

This empirical paper examines the drivers underpinning changes to socially-responsible behaviours in the Russian energy sector. Responding to recent requests to contextualise CSR research, we focus on the changing set of stakeholders and developments in their saliency as reflected in corporations’ CSR activities. Based on interviews with more than thirty industry professionals, our findings suggest that Russian energy companies’ CSR is strongly stakeholder driven, and organisations adapt their activities according to their dependence on the resources that these salient stakeholders possess. We challenge the proposition that CSR in Russia arises from purely endogenous, historical, paternalism or neo-paternalism. We identify stakeholders that now shape CSR in the Russian energy sector, both endogenous (institutional and contextual forces relevant to the national business system) and exogenous (relating to the organisational field of the energy industry - international by nature). We thereby contribute to the convergence / divergence debate within CSR theory by demonstrating that both national business systems and the organisational field must be taken into account when analysing the forces that shape CSR strategies in any one country

On theorems of Jackson and Bernstein type in the complex plane

We consider best polynomial approximation to functions analytic in a Jordan domain D and continuous on . We relate theorems of Jackson and Bernstein type to the Hölder continuity of the exterior conformal mapping functions for D .Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41343/1/365_2005_Article_BF02075464.pd