Let $\Omega $ be a compact subset of $\mathbb {C}$ and let A be a unital simple, separable $C^*$-algebra with stable rank one, real rank zero, and strict comparison. We show that, given a Cu-morphism ${\alpha :\mathrm { Cu}(C(\Omega ))\to \mathrm {Cu}(A)}$ with , there exists a homomorphism $\phi : C(\Omega )\to A$ such that $\mathrm {Cu}(\phi )=\alpha $. Moreover, if $K_1(A)$ is trivial, then $\phi $ is unique up to approximate unitary equivalence. We also give classification results for maps from a large class of $C^*$-algebras to A in terms of the Cuntz semigroup.

We introduce and study the weak Glimm property for $\mathrm{C}^{*}$-algebras, and also a property we shall call (HS$_0$). We show that the properties of being nowhere scattered and residual (HS$_0$) are equivalent for any $\mathrm{C}^{*}$-algebra. Also, for a $\mathrm{C}^{*}$-algebra with the weak Glimm property, the properties of being purely infinite and weakly purely infinite are equivalent. It follows that for a $\mathrm{C}^{*}$-algebra with the weak Glimm property such that the absolute value of every nonzero, square-zero, element is properly infinite, the properties of being (weakly, locally) purely infinite, nowhere scattered, residual (HS$_0$), residual (HS$_{\text {t}}$), and residual (HI) are all equivalent, and are equivalent to the global Glimm property. This gives a partial affirmative answer to the global Glimm problem, as well as certain open questions raised by Kirchberg and Rørdam.

Inhibitory control plays an important role in children’s cognitive and socioemotional development, including their psychopathology. It has been established that contextual factors such as socioeconomic status (SES) and parents’ psychopathology are associated with children’s inhibitory control. However, the relations between the neural correlates of inhibitory control and contextual factors have been rarely examined in longitudinal studies. In the present study, we used both event-related potential (ERP) components and time-frequency measures of inhibitory control to evaluate the neural pathways between contextual factors, including prenatal SES and maternal psychopathology, and children’s behavioral and emotional problems in a large sample of children (N = 560; 51.75% females; Mage = 7.13 years; Rangeage = 4–11 years). Results showed that theta power, which was positively predicted by prenatal SES and was negatively related to children’s externalizing problems, mediated the longitudinal and negative relation between them. ERP amplitudes and latencies did not mediate the longitudinal association between prenatal risk factors (i.e., prenatal SES and maternal psychopathology) and children’s internalizing and externalizing problems. Our findings increase our understanding of the neural pathways linking early risk factors to children’s psychopathology.

The clay fractions of Jurassic marls in the Great Estuarine Group in southern Isle of Skye are composed of mixed-layered illite-smectite (I-S) with large percentages (>85%) of illite layers, kaolinite, and generally smaller amounts of chlorite. These marls have not been buried to the depths normally required to convert smectite to illite-rich I-S, so it is possible that the conversion was in response to heat and hydrothermal fluids from nearby early Tertiary igneous activity ∼55 Ma ago. The large percentages of illite layers in I-S, the Środoń intensity ratios, and the Kübler index values appear to be consistent with the formation of diagenetic I-S as a result of relatively brief heating caused by igneous activity. The Jurassic rocks in southern Skye contain a secondary chemical remanent magnetization (CRM) that resides in magnetite and formed at approximately the same time as the Tertiary igneous rocks on Skye. K-Ar age values for I-S based on illite age analysis have been determined to test the hypothesis that the CRM was acquired coincidently with the smectite-to-illite conversion. However, linear extrapolation of K-Ar age vs. percentage of 2M1 polytype (detrital illite) from one marl (EL-6) yields an estimate for the age of diagenetic illite of 106 Ma, which is close to the measured age of the finest subfraction (108 Ma). These estimated and measured age values, however, could be substantially greater than the true age of the diagenetic illite in I-S because of the presence of detrital 1Md illite that was recycled from early Paleozoic shales and whose abundance relative to the diagenetic I-S may have been enhanced because the diagenetic fluid had a low K/Na ratio, limiting the amount of diagenetic illite formed. Nevertheless, most of the illite in the Elgol marls (80% or more in the finest fractions) must be diagenetic and probably formed in response to the early Tertiary magmatism.

Presidential elections can be forecast using information from political and economic conditions, polls, and a statistical model of changes in public opinion over time. However, these “knowns” about how to make a good presidential election forecast come with many unknowns due to the challenges of evaluating forecast calibration and communication. We highlight how incentives may shape forecasts, and particularly forecast uncertainty, in light of calibration challenges. We illustrate these challenges in creating, communicating, and evaluating election predictions, using the Economist and Fivethirtyeight forecasts of the 2020 election as examples, and offer recommendations for forecasters and scholars.

It is shown that the colored isomorphism class of a unital, simple, $\mathcal {Z}$-stable, separable amenable C$^*$-algebra satisfying the universal coefficient theorem is determined by its tracial simplex.

A category structure for ordered Bratteli diagrams is proposed in which isomorphism coincides with the notion of equivalence of Herman, Putnam, and Skau. It is shown that the natural one-to-one correspondence between the category of Cantor minimal systems and the category of simple properly ordered Bratteli diagrams is in fact an equivalence of categories. This gives a Bratteli–Vershik model for factor maps between Cantor minimal systems. We give a construction of factor maps between Cantor minimal systems in terms of suitable maps (called premorphisms) between the corresponding ordered Bratteli diagrams, and we show that every factor map between two Cantor minimal systems is obtained in this way. Moreover, solving a natural question, we are able to characterize Glasner and Weiss’s notion of weak orbit equivalence of Cantor minimal systems in terms of the corresponding C*-algebra crossed products.

We show that the property of a C*-algebra that all its Hilbert modules have a frame, in the case of σ-unital C*-algebras, is preserved under Rieffel–Morita equivalence. In particular, we show that a σ-unital continuous-trace C*-algebra with trivial Dixmier–Douady class, all of whose Hilbert modules admit a frame, has discrete spectrum. We also show this for the tensor product of any commutative C*-algebra with the C*-algebra of compact operators on any Hilbert space.

A category structure for Bratteli diagrams is proposed and a functor from the category of $\text{AF}$ algebras to the category of Bratteli diagrams is constructed. Since isomorphism of Bratteli diagrams in this category coincides with Bratteli’s notion of equivalence, we obtain in particular a functorial formulation of Bratteli’s classification of $\text{AF}$ algebras (and at the same time, of Glimm’s classification of $\text{UHF}$ algebras). It is shown that the three approaches to classification of $\text{AF}$ algebras, namely, through Bratteli diagrams, $\text{K}$ -theory, and a certain natural abstract classifying category, are essentially the same from a categorical point of view.

Let $\theta \,\in \,\left[ 0,\,1 \right]$ be any irrational number. It is shown that the extended rotation algebra ${{B}_{\theta }}$ introduced by the authors in J. Reine Angew. Math. 665(2012), pp. 1–71, is always an $\text{AF}$ algebra.

Copy number variants (CNVs) are structural changes in chromosomes that result in deletions, duplications, inversions or translocations of large DNA segments. Eleven confirmed CNV loci have been identified as rare but important risk factors in schizophrenia. These CNVs are also associated with other neurodevelopmental disorders and medical/physical comorbidities. Although the penetrance of the CNVs for schizophrenia (the chance that CNV carriers will develop the disorder) is modest, the penetrance of CNVs for any early-onset developmental disorder (e.g. intellectual disability or autism) is much higher. Testing for CNVs is now affordable and being used in clinical genetics and neurodevelopmental disorders clinics. It is possible that testing will be expanded to psychiatric clinics. This article provides a clinically relevant overview of recent CNV findings in schizophrenia and related disorders.

Let $X$ be a compact metric space. A lower bound for the radius of comparison of the ${{\text{C}}^{*}}$ -algebra $\text{C}\left( X \right)$ is given in terms of ${{\dim}_{\mathbb{Q}}}\,X$ , where ${{\dim}_{\mathbb{Q}}}\,X$ is the cohomological dimension with rational coefficients. If ${{\dim}_{\mathbb{Q}}}\,X\,=\,\dim\,X\,=\,d$ , then the radius of comparison of the ${{\text{C}}^{*}}$ -algebra $C\left( X \right)$ is $\max \left\{ 0,\,\left( d\,-\,1 \right)/\,2\,-\,1 \right\}$ if $d$ is odd, and must be either ${d}/{2}\;\,-\,1$ or ${d}/{2}\;\,-\,2$ if $d$ is even (the possibility ${d}/{2}\;\,-\,1$ does occur, but we do not know if the possibility ${d}/{2}\;\,-\,2$ can also occur).