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In this work we demonstrate a high sensitivity atomic gradiometer capable of operation in earth-field level environments. We apply a light-pulse sequence at four times the Larmor frequency to achieve gradiometer sensitivity <20 fT/cm/$\sqrt{\rm Hz}$ at the finite field strength of 22 $\mu$T. The experimental timing sequence can be tuned to the field magnitude of interest. Our one dimensional all-optical gradiometer performs a differential measurement between two regions of a single vapor cell on a 4 cm baseline. Our results pave the way for extensions to operation in higher dimensions, vector sensitivity, and more advanced gradiometers.

We demonstrate a transversely polarized spin-exchange pumped noble gas comagnetometer which suppresses systematic errors from longitudinal polarization. Rb atoms as well as $^{131}$Xe and $^{129}$Xe nuclei are simultaneously polarized perpendicular to a pulsed bias field. Both Xe isotopes' nuclear magnetic resonance conditions are simultaneously satisfied by frequency modulation of the pulse repetition rate. The Rb atoms detect the Xe precession. We highlight the importance of magnetometer phase shifts when performing comagnetometry. For detection of non-magnetic spin-dependent interactions the sensing bandwidth is 1 Hz, the white-noise level is 7 $\mu$Hz /$\sqrt{\text{Hz}}$, and the bias stability is $\approx1$ $\mu$Hz.

Due to its popularity and availability, social media data may present a new way to identify individuals who are experiencing mental illness. By analysing blog content, this study aimed to investigate the associations between linguistic features and symptoms of depression, generalised anxiety, and suicidal ideation. This study utilised a longitudinal study design. Individuals who blogged were invited to participate in a study in which they completed fortnightly mental health questionnaires including the PHQ9 and GAD7 for a period of 36 weeks. Linguistic features were extracted from blog data using the LIWC tool. Bivariate and multivariate analyses were performed to investigate the correlations between the linguistic features and mental health scores between subjects. We then used the multivariate regression model to predict longitudinal changes in mood within subjects. A total of 153 participants consented to taking part, with 38 participants completing the required number of questionnaires and blog posts during the study period. Between-subject analysis revealed that several linguistic features, including tentativeness and non-fluencies, were significantly associated with depression and anxiety symptoms, but not suicidal thoughts. Within-subject analysis showed no robust correlations between linguistic features and changes in mental health score. This study provides further support for the relationship between linguistic features within social media data and symptoms of depression and anxiety. The lack of robust within-subject correlations indicate that the relationship observed at the group level may not generalise to individual changes over time., Comment: 29 pages, 6 figures

We place new limits on potential T- and P- violating monopole-dipole interactions between unpolarized nucleons and neutrons using dual species magnetic resonance in polarzed Xe gas. Free-induction decay transients with relaxation times ~20 s allow high precision measurements of the NMR frequencies, whose ratios cancel magnetic fluctuations. The new limits on the product gsgp improve on previous laboratory work by 2 orders of magnitude., Comment: revised version accepted by PRL

Let $\Gamma$ be a group and $r_n(\Gamma)$ the number of its $n$-dimensional irreducible complex representations. We define and study the associated representation zeta function $\calz_\Gamma(s) = \suml^\infty_{n=1} r_n(\Gamma)n^{-s}$. When $\Gamma$ is an arithmetic group satisfying the congruence subgroup property then $\calz_\Gamma(s)$ has an ``Euler factorization". The "factor at infinity" is sometimes called the "Witten zeta function" counting the rational representations of an algebraic group. For these we determine precisely the abscissa of convergence. The local factor at a finite place counts the finite representations of suitable open subgroups $U$ of the associated simple group $G$ over the associated local field $K$. Here we show a surprising dichotomy: if $G(K)$ is compact (i.e. $G$ anisotropic over $K$) the abscissa of convergence goes to 0 when $\dim G$ goes to infinity, but for isotropic groups it is bounded away from 0. As a consequence, there is an unconditional positive lower bound for the abscissa for arbitrary finitely generated linear groups. We end with some observations and conjectures regarding the global abscissa.

We consider the abelian group $PT$ generated by quasi-equivalence classes of pretriangulated DG categories with relations coming from semi-orthogonal decompositions of corresponding triangulated categories. We introduce an operation of "multiplication" $\bullet$ on the collection of DG categories which makes this abelian group into a commutative ring. A few applications are considered: representability of "standard" functors between derived categories of coherent sheaves on smooth projective varieties and a construction of an interesting motivic measure., Comment: 33 pages