Large deviations for extreme eigenvalues of deformed Wigner random matrices

We present a large deviation principle at speed N for the largest eigenvalue of some additively deformed Wigner matrices. In particular this includes Gaussian ensembles with full-rank general deformation. For the non-Gaussian ensembles, the deformation should be diagonal, and we assume that the laws of the entries have sharp sub-Gaussian Laplace transforms and satisfy certain concentration properties. For these latter ensembles we establish the large deviation principle in a restricted range $(-\infty, x_c)$, where $x_c$ depends on the deformation only and can be infinite.Comment: We thank Alice Guionnet and Ofer Zeitouni for explaining that one assumption in an early version of this paper was superfluou

Extremal statistics of quadratic forms of GOE/GUE eigenvectors

We consider quadratic forms of deterministic matrices $A$ evaluated at the random eigenvectors of a large $N \times N$ GOE or GUE matrix, or equivalently evaluated at the columns of a Haar-orthogonal or Haar-unitary random matrix. We prove that, as long as the deterministic matrix has rank much smaller than $\sqrt{N}$, the distributions of the extrema of these quadratic forms are asymptotically the same as if the eigenvectors were independent Gaussians. This reduces the problem to Gaussian computations, which we carry out in several cases to illustrate our result, finding Gumbel or Weibull limiting distributions depending on the signature of $A$. Our result also naturally applies to the eigenvectors of any invariant ensemble.Comment: Fixed small gap in application of main theorem to finding Weibull statistics, via short argument in new Section 3.6. Results unchanged. 39 pages, 5 figure

Interpreting scores on multiple sclerosis-specific patient reported outcome measures (the PRIMUS and U-FIS)

BACKGROUND: The PRIMUS is a Multiple Sclerosis (MS)-specific suite of outcome measures including assessments of QoL (PRIMUS QoL, scored 0-22) and activity limitations (PRIMUS Activities, scored 0-30). The U-FIS is a measure of fatigue impact (scored 0-66). These measures have been fully validated previously using an MS sample with mixed diagnoses. The aim of the present study was to validate the measures further in a specifically Relapse Remitting MS (RRMS) sample and to provide preliminary evidence of the responder definitions (RD; also known as minimal important difference) for these instruments. METHODS: Data were derived from a multi-country efficacy trial of MS patients with assessments at baseline and 12 months. Baseline data were used to assess the internal reliability and validity of the measures. Both anchor-based and distribution-based approaches were employed for estimating RD. Anchor-based estimates were based on published RD values for the EQ-5D and were assessed for those improving and deteriorating separately. Distribution-based estimates were based on standard error of measurement (SEM), change score equivalent to 0.30, and change score equivalent to 0.50, effect sizes (ES). RESULTS: The sample included 911 RRMS patients (67.3% female, age mean (SD) 36.2 (8.4) years, duration of MS mean (SD) 4.8 (5.2) years). Results showed that the PRIMUS and U-FIS had good internal consistency. Appropriate correlations were observed with comparator instruments and both measures were able to distinguish between participants based on Expanded Disability Status Scale scores and time since diagnosis. The anchor-based and distribution-based RD estimates were: PRIMUS Activities range = 1.2-2.3, PRIMUS QoL range = 1.0-2.2, and U-FIS range = 2.4-7.0. CONCLUSIONS: The results show that the PRIMUS and U-FIS are valid instruments for use with RRMS patients. The analyses provide preliminary information on how to interpret scores on the scales. These data will be useful for assessing treatment efficacy and for powering clinical studies. TRIAL REFERENCE NUMBER: ClinicalTrials.gov Identifier NCT00340834

Universality for the global spectrum of random inner-product kernel matrices in the polynomial regime

We consider certain large random matrices, called random inner-product kernel matrices, which are essentially given by a nonlinear function $f$ applied entrywise to a sample-covariance matrix, $f(X^TX)$, where $X \in \mathbb{R}^{d \times N}$ is random and normalized in such a way that $f$ typically has order-one arguments. We work in the polynomial regime, where $N \asymp d^\ell$ for some $\ell > 0$, not just the linear regime where $\ell = 1$. Earlier work by various authors showed that, when the columns of $X$ are either uniform on the sphere or standard Gaussian vectors, and when $\ell$ is an integer (the linear regime $\ell = 1$ is particularly well-studied), the bulk eigenvalues of such matrices behave in a simple way: They are asymptotically given by the free convolution of the semicircular and Mar\v{c}enko-Pastur distributions, with relative weights given by expanding $f$ in the Hermite basis. In this paper, we show that this phenomenon is universal, holding as soon as $X$ has i.i.d. entries with all finite moments. In the case of non-integer $\ell$, the Mar\v{c}enko-Pastur term disappears (its weight in the free convolution vanishes), and the spectrum is just semicircular.Comment: 43 pages, no figure

Dynamic association between perfusion and white matter integrity across time since injury in Veterans with history of TBI.

ObjectiveCerebral blood flow (CBF) plays a critical role in the maintenance of neuronal integrity, and CBF alterations have been linked to deleterious white matter changes. Although both CBF and white matter microstructural alterations have been observed within the context of traumatic brain injury (TBI), the degree to which these pathological changes relate to one another and whether this association is altered by time since injury have not been examined. The current study therefore sought to clarify associations between resting CBF and white matter microstructure post-TBI.Methods37 veterans with history of mild or moderate TBI (mmTBI) underwent neuroimaging and completed health and psychiatric symptom questionnaires. Resting CBF was measured with multiphase pseudocontinuous arterial spin labeling (MPPCASL), and white matter microstructural integrity was measured with diffusion tensor imaging (DTI). The cingulate cortex and cingulum bundle were selected as a priori regions of interest for the ASL and DTI data, respectively, given the known vulnerability of these regions to TBI.ResultsRegression analyses controlling for age, sex, and posttraumatic stress disorder (PTSD) symptoms revealed a significant time since injury × resting CBF interaction for the left cingulum (p < 0.005). Decreased CBF was significantly associated with reduced cingulum fractional anisotropy (FA) in the chronic phase; however, no such association was observed for participants with less remote TBI.ConclusionsOur results showed that reduced CBF was associated with poorer white matter integrity in those who were further removed from their brain injury. Findings provide preliminary evidence of a possible dynamic association between CBF and white matter microstructure that warrants additional consideration within the context of the negative long-term clinical outcomes frequently observed in those with history of TBI. Additional cross-disciplinary studies integrating multiple imaging modalities (e.g., DTI, ASL) and refined neuropsychiatric assessment are needed to better understand the nature, temporal course, and dynamic association between brain changes and clinical outcomes post-injury

Community structure of soil fungi in a novel perennial crop monoculture, annual agriculture, and native prairie reconstruction

The use of perennial crop species in agricultural systems may increase ecosystem services and sustainability. Because soil microbial communities play a major role in many processes on which ecosystem services and sustainability depend, characterization of soil community structure in novel perennial crop systems is necessary to understand potential shifts in function and crop responses. Here, we characterized soil fungal community composition at two depths (0–10 and 10–30 cm) in replicated, long-term plots containing one of three different cropping systems: a tilled three-crop rotation of annual crops, a novel perennial crop monoculture (Intermediate wheatgrass, which produces the grain Kernza®), and a native prairie reconstruction. The overall fungal community was similar under the perennial monoculture and native vegetation, but both were distinct from those in annual agriculture. The mutualist and saprotrophic community subsets mirrored differences of the overall community, but pathogens were similar among cropping systems. Depth structured overall communities as well as each functional group subset. These results reinforce studies showing strong effects of tillage and sampling depth on soil community structure and suggest plant species diversity may play a weaker role. Similarities in the overall and functional fungal communities between the perennial monoculture and native vegetation suggest Kernza® cropping systems have the potential to mimic reconstructed natural systems

Eye Tracking Reveals Abnormal Visual Preference for Geometric Images as an Early Biomarker of an Autism Spectrum Disorder Subtype Associated With Increased Symptom Severity

AbstractBackgroundClinically and biologically, autism spectrum disorder (ASD) is heterogeneous. Unusual patterns of visual preference as indexed by eye tracking are hallmarks; however, whether they can be used to define an early biomarker of ASD as a whole or leveraged to define a subtype is unclear. To begin to examine this issue, large cohorts are required.MethodsA sample of 334 toddlers from six distinct groups (115 toddlers with ASD, 20 toddlers with ASD features, 57 toddlers with developmental delay, 53 toddlers with other conditions [e.g., premature birth, prenatal drug exposure], 64 toddlers with typical development, and 25 unaffected toddlers with siblings with ASD) was studied. Toddlers watched a movie containing geometric and social images. Fixation duration and number of saccades within each area of interest and validation statistics for this independent sample were computed. Next, to maximize power, data from our previous study (n = 110) were added for a total of 444 subjects. A subset of toddlers repeated the eye-tracking procedure.ResultsAs in the original study, a subset of toddlers with ASD fixated on geometric images >69% of the time. Using this cutoff, sensitivity for ASD was 21%, specificity was 98%, and positive predictive value was 86%. Toddlers with ASD who strongly preferred geometric images had 1) worse cognitive, language, and social skills relative to toddlers with ASD who strongly preferred social images and 2) fewer saccades when viewing geometric images. Unaffected siblings of ASD probands did not show evidence of heightened preference for geometric images. Test-retest reliability was good. Examination of age effects suggested that this test may not be appropriate with children >4 years old.ConclusionsEnhanced visual preference for geometric repetition may be an early developmental biomarker of an ASD subtype with more severe symptoms

Abiotic and biotic context dependency of perennial crop yield

A grant from the One-University Open Access Fund at the University of Kansas was used to defray the author's publication fees in this Open Access journal. The Open Access Fund, administered by librarians from the KU, KU Law, and KUMC libraries, is made possible by contributions from the offices of KU Provost, KU Vice Chancellor for Research & Graduate Studies, and KUMC Vice Chancellor for Research. For more information about the Open Access Fund, please see http://library.kumc.edu/authors-fund.xml.Perennial crops in agricultural systems can increase sustainability and the magnitude of ecosystem services, but yield may depend upon biotic context, including soil mutualists, pathogens and cropping diversity. These biotic factors themselves may interact with abiotic factors such as drought. We tested whether perennial crop yield depended on soil microbes, water availability and crop diversity by testing monocultures and mixtures of three perennial crop species: a novel perennial grain (intermediate wheatgrass—Thinopyrum intermedium-- that produces the perennial grain Kernza®), a potential perennial oilseed crop (Silphium intregrifolium), and alfalfa (Medicago sativa). Perennial crop performance depended upon both water regime and the presence of living soil, most likely the arbuscular mycorrhizal (AM) fungi in the whole soil inoculum from a long term perennial monoculture and from an undisturbed native remnant prairie. Specifically, both Silphium and alfalfa strongly benefited from AM fungi. The presence of native prairie AM fungi had a greater benefit to Silphium in dry pots and alfalfa in wet pots than AM fungi present in the perennial monoculture soil. Kernza did not benefit from AM fungi. Crop mixtures that included Kernza overyielded, but overyielding depended upon inoculation. Specifically, mixtures with Kernza overyielded most strongly in sterile soil as Kernza compensated for poor growth of Silphium and alfalfa. This study identifies the importance of soil biota and the context dependence of benefits of native microbes and the overyielding of mixtures in perennial crops.Perennial Agricultural Project sponsored by the Malone Family Land Preservation FoundationNational Science Foundation (DEB-1556664, DEB- 1738041, OIA 1656006

Synthesis and Incorporation of Unnatural Amino Acids To Probe and Optimize Protein Bioconjugations

The utilization of unnatural amino acids (UAAs) in bioconjugations is ideal due to their ability to confer a degree of bioorthogonality and specificity. In order to elucidate optimal conditions for the preparation of bioconjugates with UAAs, we synthesized 9 UAAs with variable methylene tethers (2-4) and either an azide, alkyne, or halide functional group. All 9 UAAs were then incorporated into green fluorescent protein (GFP) using a promiscuous aminoacyl-tRNA synthetase. The different bioconjugations were then analyzed for optimal tether length via reaction with either a fluorophore or a derivatized resin. Interestingly, the optimal tether length was found to be dependent on the type of reaction. Overall, these findings provide a better understanding of various parameters that can be optimized for the efficient preparation of bioconjugates