Universal transforms of the geometric series under generalized Riesz methods

In this paper generalized Riesz methods (R, p, M) of summability are considered. We prove that, to each open set O ⊂ C with adequate topological properties and each sequence {Pn} ⊂ C tending to infinity, we can associate a corresponding P-regular (R, p, M)-method so that the geometric series and a certain trigonometric series become universal in the sense that its (R, p, M)-transforms approximate any member of certain spaces of holomorphic functions or measurable functions.Plan Andaluz de Investigación (Junta de Andalucía

Large linear manifolds of non-continuable boundary-regular holomorphic functions

We prove in this paper that if G is a domain in the complex plane satisfying adequate topological or geometrical conditions then there exists a large (dense or closed infinite-dimensional) linear submanifold of boundary-regular holomorphic functions on G all of whose nonzero members are not continuable across any boundary point of G.Ministerio de Ciencia y Tecnología (MCYT). EspañaPlan Andaluz de Investigación (Junta de Andalucía

Dense-lineability of sets of Birkhoff-universal functions with rapid decay

Let A be an unbounded Arakelian set in the complex plane whose complement has infinite inscribed radius, and ψ be an increasing positive function on the positive real numbers. We prove the existence of a dense linear manifold M of entire functions all of whose nonzero members are Birkhoff-universal, such that each function in M has overall growth faster than ψ and, in addition, exp(|z|α)f(z) → 0 (z → ∞, z ∈ A) for all α < 1/2 and f ∈ M. With slightly more restrictive conditions on A, we get that the last property also holds for the action T f of certain holomorphic operators T. Our results unify, extend and complete recent work by several authors.Plan Andaluz de Investigación (Junta de Andalucía)Ministerio de Educación y Ciencia (MEC). Españ

Universal entire functions with gap power series

AbstractLet M be the family of all compact sets in C which have connected complement. For K ϵ M we denote by A(K) the set of all functions which are continuous on K and holomorphic in its interior.Suppose that {zn} is any unbounded sequence of complex numbers and let Q be a given sub-sequence of N0.If Q has density Δ(Q) = 1 then there exists a universal entire function ϑ with lacunary power series 1.(1) ϑ(z) = ϵ∞v = 0 ϑvZv, ϑv = 0 for v ∉ Q, which has for all K ϵ M the following properties simultaneously2.(2) the sequence {ϑ(Z + Zn)} is dense in A(K)3.(3) the sequence {ϑ (ZZn)} is dense in A(K) if 0 ∉ K.Also a converse result is proved: If ϑ is an entire function of the form (1) which satisfies (3), then Q must have maximal density Δmax(Q) = 1

Lacunary non-continuable boundary-regular holomorphic functions with universal properties

A holomorphic function in a Jordan domain G in the complex plane is constructed with all its derivatives extending continuously up to the boundary G that happens to be a natural boundary of In addition the action of a certain class of operators on presents some universal properties related to the overconvergence phenomenon.Plan Andaluz de Investigación (Junta de Andalucía)Ministerio de Ciencia y Tecnologí

Universal matrix transforms of holomorphic functions

The phenomenon of overconvergence is related with the convergence of subsequences of the sequence of partial sums of Taylor series at points outside their disk of convergence. During the seventies Chui and Parnes and the third author provided a holomorphic function in the unit disk which is universal with respect to overconvergence. The generic nature of this kind of universality has been recently shown by Nestoridis. In this paper, we connect the overconvergence with the summability theory. We show that there are “many” holomorphic functions in the unit disk such that their sequences of A-transforms have the overconvergence property, A being an infinite matrix. This strengthens Nestoridis’ result.Plan Andaluz de Investigación (Junta de Andalucía)Dirección General de Enseñanza Superio

Ruxolitinib for Glucocorticoid-Refractory Acute Graft-versus-Host Disease

BACKGROUND: Acute graft-versus-host disease (GVHD) remains a major limitation of allogeneic stem-cell transplantation; not all patients have a response to standard glucocorticoid treatment. In a phase 2 trial, ruxolitinib, a selective Janus kinase (JAK1 and JAK2) inhibitor, showed potential efficacy in patients with glucocorticoid-refractory acute GVHD. METHODS: We conducted a multicenter, randomized, open-label, phase 3 trial comparing the efficacy and safety of oral ruxolitinib (10 mg twice daily) with the investigator's choice of therapy from a list of nine commonly used options (control) in patients 12 years of age or older who had glucocorticoid-refractory acute GVHD after allogeneic stem-cell transplantation. The primary end point was overall response (complete response or partial response) at day 28. The key secondary end point was durable overall response at day 56. RESULTS: A total of 309 patients underwent randomization; 154 patients were assigned to the ruxolitinib group and 155 to the control group. Overall response at day 28 was higher in the ruxolitinib group than in the control group (62% [96 patients] vs. 39% [61]; odds ratio, 2.64; 95% confidence interval [CI], 1.65 to 4.22; P<0.001). Durable overall response at day 56 was higher in the ruxolitinib group than in the control group (40% [61 patients] vs. 22% [34]; odds ratio, 2.38; 95% CI, 1.43 to 3.94; P<0.001). The estimated cumulative incidence of loss of response at 6 months was 10% in the ruxolitinib group and 39% in the control group. The median failure-free survival was considerably longer with ruxolitinib than with control (5.0 months vs. 1.0 month; hazard ratio for relapse or progression of hematologic disease, non-relapse-related death, or addition of new systemic therapy for acute GVHD, 0.46; 95% CI, 0.35 to 0.60). The median overall survival was 11.1 months in the ruxolitinib group and 6.5 months in the control group (hazard ratio for death, 0.83; 95% CI, 0.60 to 1.15). The most common adverse events up to day 28 were thrombocytopenia (in 50 of 152 patients [33%] in the ruxolitinib group and 27 of 150 [18%] in the control group), anemia (in 46 [30%] and 42 [28%], respectively), and cytomegalovirus infection (in 39 [26%] and 31 [21%]). CONCLUSIONS: Ruxolitinib therapy led to significant improvements in efficacy outcomes, with a higher incidence of thrombocytopenia, the most frequent toxic effect, than that observed with control therapy

Novel Common Genetic Susceptibility Loci for Colorectal Cancer

BACKGROUND: Previous genome-wide association studies (GWAS) have identified 42 loci (P < 5 × 10-8) associated with risk of colorectal cancer (CRC). Expanded consortium efforts facilitating the discovery of additional susceptibility loci may capture unexplained familial risk. METHODS: We conducted a GWAS in European descent CRC cases and control subjects using a discovery-replication design, followed by examination of novel findings in a multiethnic sample (cumulative n = 163 315). In the discovery stage (36 948 case subjects/30 864 control subjects), we identified genetic variants with a minor allele frequency of 1% or greater associated with risk of CRC using logistic regression followed by a fixed-effects inverse variance weighted meta-analysis. All novel independent variants reaching genome-wide statistical significance (two-sided P < 5 × 10-8) were tested for replication in separate European ancestry samples (12 952 case subjects/48 383 control subjects). Next, we examined the generalizability of discovered variants in East Asians, African Americans, and Hispanics (12 085 case subjects/22 083 control subjects). Finally, we examined the contributions of novel risk variants to familial relative risk and examined the prediction capabilities of a polygenic risk score. All statistical tests were two-sided. RESULTS: The discovery GWAS identified 11 variants associated with CRC at P < 5 × 10-8, of which nine (at 4q22.2/5p15.33/5p13.1/6p21.31/6p12.1/10q11.23/12q24.21/16q24.1/20q13.13) independently replicated at a P value of less than .05. Multiethnic follow-up supported the generalizability of discovery findings. These results demonstrated a 14.7% increase in familial relative risk explained by common risk alleles from 10.3% (95% confidence interval [CI] = 7.9% to 13.7%; known variants) to 11.9% (95% CI = 9.2% to 15.5%; known and novel variants). A polygenic risk score identified 4.3% of the population at an odds ratio for developing CRC of at least 2.0. CONCLUSIONS: This study provides insight into the architecture of common genetic variation contributing to CRC etiology and improves risk prediction for individualized screenin