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Abstract INTRODUCTIONVascular damage in Alzheimer's disease (AD) has shown conflicting findings particularly when analyzing longitudinal data. We introduce white matter hyperintensity (WMH) longitudinal morphometric analysis (WLMA) that quantifies WMH expansion as the distance from lesion voxels to a region of interest boundary. METHODSWMH segmentation maps were derived from 270 longitudinal fluid‐attenuated inversion recovery (FLAIR) ADNI images. WLMA was performed on five data‐driven WMH patterns with distinct spatial distributions. Amyloid accumulation was evaluated with WMH expansion across the five WMH patterns. RESULTSThe preclinical group had significantly greater expansion in the posterior ventricular WM compared to controls. Amyloid significantly associated with frontal WMH expansion primarily within AD individuals. WLMA outperformed WMH volume changes for classifying AD from controls primarily in periventricular and posterior WMH. DISCUSSIONThese data support the concept that localized WMH expansion continues to proliferate with amyloid accumulation throughout the entirety of the disease in distinct spatial locations. 

Abstract ObjectiveNeurodegenerative conditions often manifest radiologically with the appearance of premature aging. Multiple sclerosis (MS) biomarkers related to lesion burden are well developed, but measures of neurodegeneration are less well‐developed. The appearance of premature aging quantified by machine learning applied to structural MRI assesses neurodegenerative pathology. We assess the explanatory and predictive power of “brain age” analysis on disability in MS using a large, real‐world dataset. MethodsBrain age analysis is predicated on the over‐estimation of predicted brain age in patients with more advanced pathology. We compared the performance of three brain age algorithms in a large, longitudinal dataset (>13,000 imaging sessions from >6,000 individual MS patients). Effects of MS, MS disease course, disability, lesion burden, and DMT efficacy were assessed using linear mixed effects models. ResultsMS was associated with advanced predicted brain age cross‐sectionally and accelerated brain aging longitudinally in all techniques. While MS disease course (relapsing vs. progressive) did contribute to advanced brain age, disability was the primary correlate of advanced brain age. We found that advanced brain age at study enrollment predicted more disability accumulation longitudinally. Lastly, a more youthful appearing brain (predicted brain age less than actual age) was associated with decreased disability. InterpretationBrain age is a technically tractable and clinically relevant biomarker of disease pathology that correlates with and predicts increasing disability in MS. Advanced brain age predicts future disability accumulation. 

Abstract We establish a theory of noncommutative (NC) functions on a class of von Neumann algebras with a particular direct sum property, e.g.,$$B({\mathcal H})$$. In contrast to the theory’s origins, we do not rely on appealing to results from the matricial case. We prove that the$$k{\mathrm {th}}$$directional derivative of any NC function at a scalar point is ak-linear homogeneous polynomial in its directions. Consequences include the fact that NC functions defined on domains containing scalar points can be uniformly approximated by free polynomials as well as realization formulas for NC functions bounded on particular sets, e.g., the NC polydisk and NC row ball. 

We consider pairs of anti-commuting [Formula: see text]-by-[Formula: see text] Hermitian matrices that are chosen randomly with respect to a Gaussian measure. Generically such a pair decomposes into the direct sum of [Formula: see text]-by-[Formula: see text] blocks on which the first matrix has eigenvalues [Formula: see text] and the second has eigenvalues [Formula: see text]. We call [Formula: see text] the skew spectrum of the pair. We derive a formula for the probability density of the skew spectrum, and show that the elements are repelling. 

Jury and Martin establish an analogue of the classical inner-outer factorization of Hardy space functions. They show that every function $f$in a Hilbert function space with a normalized complete Pick reproducing kernel has a factorization of the type $f=\mathrm{\phi <\#comment/>}g$, where $g$is cyclic, $\mathrm{\phi <\#comment/>}$is a contractive multiplier, and $\Vert <\#comment/>f\Vert <\#comment/>=\Vert <\#comment/>g\Vert <\#comment/>$. In this paper we show that if the cyclic factor is assumed to be what we call free outer, then the factors are essentially unique, and we give a characterization of the factors that is intrinsic to the space. That lets us compute examples. We also provide several applications of this factorization.