This article highlights a connection between Diophantine approximation and the lower Assouad dimension by using information about the latter to show that the Hausdorff dimension of the set of badly approximable points that lie in certain non-conformal fractals, known as self-affine sponges, is bounded below by the dynamical dimension of these fractals. The results, which are the first to advance beyond the conformal setting, encompass both the case of Sierpiński sponges/carpets (also known as Bedford–McMullen sponges/carpets) and the case of Barański carpets.

This article explores the use of an information-entropy-based gene clustering method for genomic island detection in MRSA.

Article verifying a conjecture of Vershik by showing that Hall’s universal countable locally finite group can be embedded as a dense subgroup in the isometry group of the Urysohn space and in the automorphism group of the random graph. It shows the same for all automorphism groups of known infinite ultraextensive spaces.

Article discusses how a Cantor series expansion for a real number x with respect to a basic sequence Q=(q), where qi≥2, is a generalization of the base b expansion to an infinite sequence of bases. The authors show that for any basic sequence the set of distribution normal numbers is Π03-complete, and if Q is 1-divergent then the sets of normal and ratio normal numbers are Π03-complete.

Article describes how the Tirilman spaces were introduced by Casazza and Shura as variations of the spaces constructed by Tzafriri. We prove that all subsymmetric basic sequences in the dual space are equivalent to its canonical subsymmetic but not symmetric basis.

This article predicts that marine-derived bacteria should inhibit Vibrio pathogens and may be a source of unique antibiotic compounds.

Article describes how the authors plant to deal with orientation preserving homeomorphisms and, more specifically, diffeomorphisms of the unit circle S1. By employing the recurrence method worked out in Pawelec the authors provide effective lower estimates of the proper-dimensional Hausdorff measure of minimal sets of circle homeomorphisms that are not conjugate to any rotation.

Article describes how a set of reals is universally Baire if all of its continuous preimages in topological spaces have the Baire property. The authors show that over some mild large cardinal theory, sealing is equiconsistent with LSA-over-uB.

Article studies radial solutions of ∆u + K(r)f(u) = 0 on the exterior of the ball of radius R > 0 centered at the origin in ℝᶰ where f is odd with f < 0 on (0, β), f > 0 on (β, δ), f ≡ 0 for u > δ, and where the function K(r) is assumed to be positive and K(r) → 0 as r → ∞.

This article studies radial solutions of Δu + K(r)ƒ(u) = 0 on the exterior of the ball of radius R > 0, BR, centered at the origin in ℝN with u = 0 on @BR where ƒ is odd with ƒ < 0 on (0; β), ƒ > 0 on (β;∞), f(u) ~ uᵖ with 0 < p < 1 for large u and K(r) ~ r⁻ᵅ for large r.

This article proves the existence of radial solutions of Δu + K(r)ƒ(u) = 0 on the exterior of the ball, of radius R, centered at the origin in ℝᴺ such that limᵣ→∞u(r) = 0 if R > 0 is sufficiently small.

Article proving the existence of infinitely many radial solutions of ∆𝓊+𝐾(𝓇) ƒ (𝓊) = 0 on the exterior of the ball of radius R > 0, BR, centered at the origin in ℝᴺ with u = 0 on ∂BR and lim/r→∞ 𝓊(𝓇) = 0 where N > 2, f is odd with f < 0 on (0, β), f > 0 on (β, ∞), f is superlinear for large u, ƒ(𝓊) ∼ −1/(|𝓊|𝘲⁻¹𝓊) with 0 < q < 1 for small u, and 0 < 𝐾(𝓇) ≤ 𝐾₁/r∝ with 𝑁 + q(𝑁 − 2) < ∝ < 2(𝑁− 1) for large r.

Article proves the existence of an infinite number of radial solutions to ∆u+K(r)f(u) = 0 on ℝᶰ such that limᵣ →∞ u(r) = 0 with prescribed number of zeros on the exterior of the ball of radius R > 0 where f is odd with f < 0 on (0, β), f > 0 on (β, ∞) with f superlinear for large u, and K(r) ∼ r ⁻ᵅ with α > 2(N − 1).

This article proves the existence of an infinite number of radial solutions of Δu+K(r)ƒ(u) = 0, one with exactly n zeros for each nonnegative integer n on the exterior of the ball of radius R > 0, Bʀ, centered at the origin in ℝᴺ with u = 0 on ∂Bʀ and limᵣ→∞u(r) = 0 where N > 2, f is odd with ƒ < 0 on (0; β), ƒ > 0 on (β;∞), ƒ(u) ~ uᵖ with 0 < p < 1 for large u and K(r) ~ r-α with 0 < α < 2 for large r.

This article identifies the principal features in Foias’ original proof and streamlines them into a general result. The result gives further evidence to the observation that the connection between the sequence with initial seed the Foias constant and the Prime Number Theorem must be fortuitous.

Article presents an overview of the data sets and the contributions analyzing data related to human lipid-related phenotypes, DNA methylation, and single-nucleotide markers in a study involving a pharmaceutical intervention.

In this article, the authors propose a statistical method by Testing an Optimally Weighted Combination of Multiple traits (TOW-CM) to test the association between multiple traits and multiple variants in a genomic region (a gene or pathway). They investigate the performance of the proposed method through extensive simulation studies. Their simulation studies show that the proposed method has correct type I error rates and is either the most powerful test or comparable with the most powerful tests. Additionally, they illustrate the usefulness of TOW-CM based on a COPDGene study.

Article proposes a powerful and computationally efficient gene-based association test, called Overall. Using extended Simes procedure, Overall aggregates information from three types of traditional gene-based association tests and also incorporates expression quantitative trait locus (eQTL) information into a gene-based association test using GWAS summary statistics. The results show that this newly developed method can identify more significant genes than other methods.

Article describes how gene-based association tests provide a useful alternative and complement to the usual single marker association tests, especially in genome-wide association studies (GWAS). The authors propose a test named OWC based on summary statistics from GWAS data.

Article describes how anthracyclines are highly effective in treating cancer, despite increased risk of cardiomyopathy. This study examined gene-level associations with cardiomyopathy among cancer survivors using whole-exome sequencing data.

Article describes the high-quality, 887-Mb genome of jojoba assembled into 26 chromosomes with 23,490 protein-coding genes.

Article describes how anthracycline-related cardiomyopathy is a leading cause of premature death in childhood cancer survivors. The authors interrogated differentially expressed genes (DEGs) to identify genetic variants serving regulatory functions or genetic variants not easily identified when using genomewide array platforms.

Article reveal that the systemic transcriptomic response of plants to excess light stress is extensive in the context of systemic acquired acclimation and involves an early (2 min) and transient stage of transcript expression that includes thousands of genes.

This article proves the existence of an infinite number of radial solutions to Δu + K(r)ƒ(u) = 0 with a nonlinear boundary condition on the exterior of the ball of radius R centered at the origin in ℝᴺ.