I Wonder Where My Old Gal Is To-night

https://digitalcommons.library.umaine.edu/mmb-vp/1732/thumbnail.jp

Patterns of primes in joint Sato--Tate distributions

For $j=1,2$, let $f_j(z) = \sum_{n=1}^{\infty} a_{j}(n) e^{2\pi i nz}$ be a holomorphic, non-CM cuspidal newform of even weight $k_j \ge 2$ with trivial nebentypus. For each prime $p$, let $\theta_{j}(p)\in[0,\pi]$ be the angle such that $a_j(p) = 2p^{(k-1)/2} \cos \theta_{j}(p)$. The now-proven Sato--Tate conjecture states that the angles $(\theta_j(p))$ equidistribute with respect to the measure $d\mu_{\mathrm ST} = \frac{2}{\pi}\sin^2\theta\,d\theta$. We show that, if $f_1$ is not a character twist of $f_2$, then for subintervals $I_1,I_2 \subset [0,\pi]$, there exist infinitely many bounded gaps between the primes $p$ such that $\theta_1(p) \in I_1$ and $\theta_2(p) \in I_2$. We also prove a common generalization of the bounded gaps with the Green--Tao theorem.Comment: 28 page

From mental disorder to shared understanding: a non-categorical approach to support individuals with distress in primary care.

This article argues that, rather than aiming for a psychiatric diagnosis, generalist professionals such as those working in primary care, as well as in other hospital and community settings, should use a non-diagnostic framework when encountering distress. The conceptual and empirical limitations of the psychiatric diagnostic system and evidence that psychological phenomena are dimensional suggest the need for an alternative approach; one that might also address problems of overdiagnosis and overmedication.1 There are three key problems with the current Diagnostic Statistical Manual (DSM) and International Classification of Diseases (ICD) systems of psychiatric classification. The process can be stigmatising; diagnoses are not adequate representations of reality; and they are inadequate for informing an individualised management plan. The current categorical diagnostic system encourages the patient to understand their distress as a disease, rather than as an understandable response to current problems, genetic inheritance, and past experience of trauma, loss, and problematic attachments. Although some patients are comforted by labels, we propose that a more scientifically valid and individualised assessment can provide a deeper understanding, a sense of being understood, and access to specialised services and benefits if required

Longitudinal associations between incident lumbar spine MRI findings and chronic low back pain or radicular symptoms: retrospective analysis of data from the longitudinal assessment of imaging and disability of the back (LAIDBACK)

BACKGROUND: There are few longitudinal cohort studies examining associations between incident MRI findings and incident spine-related symptom outcomes. Prior studies do not discriminate between the two distinct outcomes of low back pain (LBP) and radicular symptoms. To address this gap in the literature, we conducted a secondary analysis of existing data from the Longitudinal Assessment of Imaging and Disability of the Back (LAIDBACK). The purpose of this study was to examine the association of incident lumbar MRI findings with two specific spine-related symptom outcomes: 1) incident chronic bothersome LBP, and 2) incident radicular symptoms such as pain, weakness, or sensation alterations in the lower extremity. METHODS: The original LAIDBACK study followed 123 participants without current LBP or sciatica, administering standardized MRI assessments of the lumbar spine at baseline and at 3-year follow-up, and collecting information on participant-reported spine-related symptoms and signs every 4 months for 3 years. These analyses examined bivariable and multivariable associations between incident MRI findings and symptom outcomes (LBP and radicular symptoms) using logistic regression. RESULTS: Three-year cumulative incidence of new MRI findings ranged between 2 and 8%, depending on the finding. Incident annular fissures were associated with incident chronic LBP, after adjustment for prior back pain and depression (adjusted odds ratio [OR] 6.6; 95% confidence interval [CI] 1.2-36.9). All participants with incident disc extrusions (OR 5.4) and nerve root impingement (OR 4.1) reported incident radicular symptoms, although associations were not statistically significant. No other incident MRI findings showed large magnitude associations with symptoms. CONCLUSIONS: Even when applying more specific definitions for spine-related symptom outcomes, few MRI findings showed large magnitude associations with symptom outcomes. Although incident annular fissures, disc extrusions, and nerve root impingement were associated with incident symptom outcomes, the 3-year incidence of these MRI findings was extremely low, and did not explain the vast majority of incident symptom cases

Generalized Appell connection sequences

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/22378/1/0000827.pd

Posttraumatic Stress Disorder and Impaired Autonomic Modulation in Male Twins

BACKGROUND: Posttraumatic stress disorder (PTSD) has been linked to increased morbidity. An inflexibility of the autonomic nervous system may be the underlying mechanism. We aimed to assess whether PTSD and combat trauma exposure are associated with lower heart rate variability (HRV), a measure of autonomic function and a predictor of death. METHODS: We measured HRV by power spectral analysis on 24-hour ambulatory ECG in 459 middle-aged veteran male twins. Combat trauma was assessed with the combat exposure scale, and current and remitted PTSD with the Structured Clinical Interview for Psychiatry Disorders. Mixed-effects regression models were used to test associations of PTSD and HRV between and within twin pairs. RESULTS: Of all twins, 211 had combat exposure, 31 had current PTSD, and 43 had remitted PTSD. Current PTSD was inversely associated with very-low frequency (VLF) and low frequency (LF) HRV both in individual twins and within 20 pairs discordant for current PTSD. Twins with current PTSD had a 49% lower LF HRV than their brothers without PTSD (p<0.001). Remitted PTSD was not associated with HRV. Results were robust to adjustment for depression and other risk factors. Combat exposure was inversely associated with most HRV frequencies, but this association mostly diminished after adjustment for current PTSD. CONCLUSION: In middle-aged veteran men, combat exposure and current PTSD are associated with measures of autonomic inflexibility previously shown to have prognostic significance. The negative health impact of combat exposure on autonomic function is mediated largely through PTSD and may reverse with remission of PTSD

Semiclassical universality of parametric spectral correlations

We consider quantum systems with a chaotic classical limit that depend on an external parameter, and study correlations between the spectra at different parameter values. In particular, we consider the parametric spectral form factor $K(\tau,x)$ which depends on a scaled parameter difference $x$. For parameter variations that do not change the symmetry of the system we show by using semiclassical periodic orbit expansions that the small $\tau$ expansion of the form factor agrees with Random Matrix Theory for systems with and without time reversal symmetry.Comment: 18 pages, no figure