Explore the vast range of titles available.

Asthma has striking disparities across ancestral groups, but the molecular underpinning of these differences is poorly understood and minimally studied. A goal of the Consortium on Asthma among African-ancestry Populations in the Americas (CAAPA) is to understand multi-omic signatures of asthma focusing on populations of African ancestry. RNASeq and DNA methylation data are generated from nasal epithelium including cases (current asthma, N = 253) and controls (never-asthma, N = 283) from 7 different geographic sites to identify differentially expressed genes (DEGs) and gene networks. We identify 389 DEGs; the top DEG, FN1 , was downregulated in cases (q = 3.26 × 10 −9 ) and encodes fibronectin which plays a role in wound healing. The top three gene expression modules implicate networks related to immune response ( CEACAM5 ; p = 9.62 × 10 −16 and CPA3 ; p = 2.39 × 10 −14 ) and wound healing ( FN1 ; p = 7.63 × 10 −9 ). Multi-omic analysis identifies FKBP5 , a co-chaperone of glucocorticoid receptor signaling known to be involved in drug response in asthma, where the association between nasal epithelium gene expression is likely regulated by methylation and is associated with increased use of inhaled corticosteroids. This work reveals molecular dysregulation on three axes – increased Th2 inflammation, decreased capacity for wound healing, and impaired drug response – that may play a critical role in asthma within the African Diaspora. Here, the authors suggest that molecular dysregulation on three axes may play a critical role in asthma within the African Diaspora. RNASeq and DNA methylation data are generated from nasal epithelium including cases and controls from seven different geographic sites.

We study a class of left-invertible operators which we call weakly concave operators. It includes the class of concave operators and some subclasses of expansive strict $m$-isometries with $m > 2$. We prove a Wold-type decomposition for weakly concave operators. We also obtain a Berger–Shaw-type theorem for analytic finitely cyclic weakly concave operators. The proofs of these results rely heavily on a spectral dichotomy for left-invertible operators. It provides a fairly close relationship, written in terms of the reciprocal automorphism of the Riemann sphere, between the spectra of a left-invertible operator and any of its left inverses. We further place the class of weakly concave operators, as the term $\\mathcal {A}_1$, in the chain $\\mathcal {A}_0 \\subseteq \\mathcal {A}_1 \\subseteq \\ldots \\subseteq \\mathcal {A}_{\\infty }$ of collections of left-invertible operators. We show that most of the aforementioned results can be proved for members of these classes. Subtleties arise depending on whether the index $k$ of the class $\\mathcal {A}_k$ is finite or not. In particular, a Berger–Shaw-type theorem fails to be true for members of $\\mathcal {A}_{\\infty }$. This discrepancy is better revealed in the context of $C^*$- and $W^*$-algebras.

Scientists have unprecedented access to a wide variety of high-quality datasets. These datasets, which are often independently curated, commonly use unstructured spreadsheets to store their data. Standardized annotations are essential to perform synthesis studies across investigators, but are often not used in practice. Therefore, accurately combining records in spreadsheets from differing studies requires tedious and error-prone human curation. These efforts result in a significant time and cost barrier to synthesis research. We propose an information retrieval inspired algorithm, Synthesize, that merges unstructured data automatically based on both column labels and values. Application of the Synthesize algorithm to cancer and ecological datasets had high accuracy (on the order of 85-100%). We further implement Synthesize in an open source web application, Synthesizer (https://github.com/lisagandy/synthesizer). The software accepts input as spreadsheets in comma separated value (CSV) format, visualizes the merged data, and outputs the results as a new spreadsheet. Synthesizer includes an easy to use graphical user interface, which enables the user to finish combining data and obtain perfect accuracy. Future work will allow detection of units to automatically merge continuous data and application of the algorithm to other data formats, including databases.

For a matrix a = ( a m , n ) m , n = 1 ∞ with scalar entries, the Dirichlet series kernel κ a is the double Dirichlet series κ a ( s , u ) = ∑ m , n = 1 ∞ a m , n m - s n - u ¯ in the variables s and u ¯ , which is regularly convergent on some right half-plane H ρ . The analytic symbols A n , a = ∑ m = 1 ∞ a m , n m - s , n ⩾ 1 play a central role in the study of the reproducing kernel Hilbert space H a associated with the positive semi-definite kernel κ a . In particular, they form a total subset of H a and provide the formula ∑ n = 1 ∞ ⟨ f , A n , a ⟩ n - s , s ∈ H ρ , for f ∈ H a . We combine the basic theory of Dirichlet series kernels with the Gelfond-Schneider theorem (Hilbert’s seventh problem) to show that any quasi-invariant Dirichlet series kernel κ a ( s , u ) factors as f ( s ) f ( u ) ¯ for some Dirichlet series f on H ρ . In particular, there is no quasi-invariant Dirichlet series kernel κ a if the dimension of H a is bigger than one. This is in strict contrast with the case of the unit disc, where non-factorable quasi-invariant kernels exist in abundance. We further discuss the Dirichlet series kernels κ a invariant under the group T of translation automorphisms of H ρ and construct a family of densely defined T -homogeneous operators in H a , whose adjoints are defined only at the zero vector.

We introduce and study a class of operator tuples in complex Hilbert spaces, which we call spherical tuples. In particular, we characterize spherical multi-shifts, and more generally, multiplication tuples on RKHS. We further use these characterizations to describe various spectral parts including the Taylor spectrum. We also find a criterion for the Schatten Sp-class membership of cross-commutators of spherical m-shifts. We show, in particular, that cross-commutators of non-compact spherical m-shifts cannot belong to Sp for p ≤ m. We specialize our results to some well-studied classes of multi-shifts. We prove that the cross-commutators of a spherical joint m-shift, which is a q-isometry or a 2-expansion, belongs to Sp if and only if p > m. We further give an example of a spherical jointly hyponormal 2-shift, for which the cross-commutators are compact but not in Sp for any p < ∞.

We used a deeply sequenced dataset of 910 individuals, all of African descent, to construct a set of DNA sequences that is present in these individuals but missing from the reference human genome. We aligned 1.19 trillion reads from the 910 individuals to the reference genome (GRCh38), collected all reads that failed to align, and assembled these reads into contiguous sequences (contigs). We then compared all contigs to one another to identify a set of unique sequences representing regions of the African pan-genome missing from the reference genome. Our analysis revealed 296,485,284 bp in 125,715 distinct contigs present in the populations of African descent, demonstrating that the African pan-genome contains ~10% more DNA than the current human reference genome. Although the functional significance of nearly all of this sequence is unknown, 387 of the novel contigs fall within 315 distinct protein-coding genes, and the rest appear to be intergenic. Assembly of a pan-genome from 910 humans of African descent identifies 296.5 Mb of novel DNA mapping to 125,715 distinct contigs. This African pan-genome contains ~10% more DNA than the current human reference genome.

A rooted directed tree T = ( V , E ) with root root can be extended to a directed graph T ∞ = ( V ∞ , E ∞ ) by adding a vertex ∞ to V and declaring each vertex in V as a parent of ∞ . One may associate with the extended directed tree T ∞ a family of semigroup structures ⊔ b with extreme ends being induced by the join operation ⊔ and the meet operation ⊓ from lattice theory (corresponding to b = root and b = ∞ respectively). Each semigroup structure among these leads to a family of densely defined linear operators W λ u ( b ) acting on ℓ 2 ( V ) , which we refer to as weighted join operators at a given base point b ∈ V ∞ with prescribed vertex u ∈ V . The extreme ends of this family are weighted join operators W λ u ( root ) and weighted meet operators W λ u ( ∞ ) . In this paper, we systematically study the weighted join operators on rooted directed trees. We also present a more involved counterpart of weighted join operators W λ u ( b ) on rootless directed trees T . In the rooted case, these operators are either finite rank operators, diagonal operators or rank one perturbations of diagonal operators. In the rootless case, these operators are either possibly infinite rank operators, diagonal operators or (possibly unbounded) rank one perturbations of diagonal operators. In both cases, the class of weighted join operators overlaps with the well-studied classes of complex Jordan operators and n -symmetric operators. An important half of this paper is devoted to the study of rank one extensions W f , g of weighted join operators W λ u ( b ) on rooted directed trees, where f ∈ ℓ 2 ( V ) and g : V → C is unspecified. Unlike weighted join operators, these operators are not necessarily closed. We provide a couple of compatibility conditions involving the weight system λ u and g to ensure closedness of W f , g . These compatibility conditions are intimately related to whether or not an associated discrete Hilbert transform is well-defined. We discuss the role of the Gelfand-triplet in the realization of the Hilbert space adjoint of W f , g . Further, we describe various spectral parts of W f , g in terms of the weight system and the tree data. We also provide sufficient conditions for W f , g to be a sectorial operator (resp. an infinitesimal generator of a quasi-bounded strongly continuous semigroup). In case T is leafless, we characterize rank one extensions W f , g , which admit compact resolvent. Motivated by the above graph-model, we also take a brief look into the general theory of rank one non-selfadjoint perturbations.

The operator Cauchy dual to a $2$-hyperexpansive operator $T$, given by $T'\\equiv T(T^*T)^{-1}$, turns out to be a hyponormal contraction. This simple observation leads to a structure theorem for the $C^*$-algebra generated by a $2$-hyperexpansion, and a version of the Berger–Shaw theorem for $2$-hyperexpansions. As an application of the hyperexpansivity version of the Berger–Shaw theorem, we show that every analytic $2$-hyperexpansive operator with finite-dimensional cokernel is unitarily equivalent to a compact perturbation of a unilateral shift.

Let T\\mathbf {T} be a pair of commuting hyponormal operators satisfying the so-called quasitriangular property \\[ dimker(T−λ)≥dimker(T−λ)∗,\\textrm {dim} \\; \\textrm {ker} \\; (\\mathbf {T}-\\boldsymbol \\lambda ) \\ge \\textrm {dim} \\; \\textrm {ker} \\; (\\mathbf {T} - {\\boldsymbol \\lambda })^*, \\] for every λ\\boldsymbol \\lambda in the Taylor spectrum σ(T)\\sigma (\\mathbf {T}) of T\\mathbf {T}. We prove that the Weyl spectrum of T\\mathbf {T}, ω(T)\\omega (\\mathbf {T}), satisfies the identity \\[ ω(T)=σ(T)∖π00(T),\\omega (\\mathbf {T})=\\sigma (\\mathbf {T}) \\setminus \\pi _{00}(\\mathbf {T}), \\] where π00(T)\\pi _{00}(\\mathbf {T}) denotes the set of isolated eigenvalues of finite multiplicity. Our method of proof relies on a (strictly 22-variable) fact about the topological boundary of the Taylor spectrum; as a result, our proof does not hold for dd-tuples of commuting hyponormal operators with d>2d>2.

Abstract Context Thyroid nodule ultrasound-based risk stratification schemas rely on the presence of high-risk sonographic features. However, some malignant thyroid nodules have benign appearance on thyroid ultrasound. New methods for thyroid nodule risk assessment are needed. Objective We investigated polygenic risk score (PRS) accounting for inherited thyroid cancer risk combined with ultrasound-based analysis for improved thyroid nodule risk assessment. Methods The convolutional neural network classifier was trained on thyroid ultrasound still images and cine clips from 621 thyroid nodules. Phenome-wide association study (PheWAS) and PRS PheWAS were used to optimize PRS for distinguishing benign and malignant nodules. PRS was evaluated in 73 346 participants in the Colorado Center for Personalized Medicine Biobank. Results When the deep learning model output was combined with thyroid cancer PRS and genetic ancestry estimates, the area under the receiver operating characteristic curve (AUROC) of the benign vs malignant thyroid nodule classifier increased from 0.83 to 0.89 (DeLong, P value = .007). The combined deep learning and genetic classifier achieved a clinically relevant sensitivity of 0.95, 95% CI [0.88-0.99], specificity of 0.63 [0.55-0.70], and positive and negative predictive values of 0.47 [0.41-0.58] and 0.97 [0.92-0.99], respectively. AUROC improvement was consistent in European ancestry-stratified analysis (0.83 and 0.87 for deep learning and deep learning combined with PRS classifiers, respectively). Elevated PRS was associated with a greater risk of thyroid cancer structural disease recurrence (ordinal logistic regression, P value = .002). Conclusion Augmenting ultrasound-based risk assessment with PRS improves diagnostic accuracy.