Additive decompositions for rings of modular forms

We study rings of integral modular forms for congruence subgroups as modules over the ring of integral modular forms for the full modular group. In many cases these modules are free or decompose at least into well-understood pieces. We apply this to characterize which rings of modular forms are Cohen--Macaulay and to prove finite generation results. These theorems are based on decomposition results about vector bundles on the compactified moduli stack of elliptic curves.Comment: Complete revision. Comments welcome. arXiv admin note: text overlap with arXiv:1609.0926

Dear Wife : the Civil War letters of Chester K. Leach

Occasional paper (University of Vermont. Center for Research on Vermont) ; no. 20

Prevalence and Social Inequality in Youth Loneliness in the UK.

Using data from the English arm of the Health Behaviour in School-aged Children (HBSC) study, we examined the prevalence of loneliness for school-aged adolescents and how it is linked to social inequalities. The HBSC study collects data from 11-, 13-, and 15-year-olds, and is repeated every four years, allowing the exploration of prevalence rates of loneliness pre COVID-19 pandemic for comparison. We also explored whether loneliness was associated with socio-economic status (SES) and linked to academic attainment and health complaints. The total sample was 14,077 from 156 schools in England. Findings revealed a stable prevalence rate of 8.2% for loneliness from 2006 to 2014. We also found, across all survey years, (1) those aged 15 years were significantly lonelier than younger peers, (2) those who reported lower SES were lonelier than their more well-off peers, and (3) higher loneliness was associated with being '"below average" academically and reporting more health complaints. Conclusions: These prevalence data enable researchers, policymakers, and others to make comparisons with prevalence rates during the COVID-19 pandemic to explore whether there have been increases in loneliness among school-aged adolescents. Loneliness was consistently related to social inequalities, suggesting that targeted interventions that include whole systems changes are needed

IMAC capture of recombinant protein from unclarified mammalian cell feed streams

Fusion-tag affinity chromatography is a key technique in recombinant protein purification. Current methods for protein recovery from mammalian cells are hampered by the need for feed stream clarification. We have developed a method for direct capture using immobilized metal affinity chromatography (IMAC) of hexahistidine (His6) tagged proteins from unclarified mammalian cell feed streams. The process employs radial flow chromatography with 300-500 μm diameter agarose resin beads that allow free passage of cells but capture His-tagged proteins from the feed stream; circumventing expensive and cumbersome centrifugation and/or filtration steps. The method is exemplified by Chinese Hamster Ovary (CHO) cell expression and subsequent recovery of recombinant His-tagged carcinoembryonic antigen (CEA); a heavily glycosylated and clinically relevant protein. Despite operating at a high NaCl concentration necessary for IMAC binding, cells remained over 96% viable after passage through the column with host cell proteases and DNA detected at ∼8 U/mL and 2 ng/μL in column flow-through, respectively. Recovery of His-tagged CEA from unclarified feed yielded 71% product recovery. This work provides a basis for direct primary capture of fully glycosylated recombinant proteins from unclarified mammalian cell feed streams. Biotechnol. Bioeng. 2015;9999: 1-11. © 2015 The Authors. Biotechnology and Bioengineering Published by Wiley Periodicals, Inc

Linear polarization sensitivity of SeGA detectors

Parity is a key observable in nuclear spectroscopy. Linear polarization measurements of $\gamma$-rays are a probe to access the parities of energy levels. Utilizing the segmentation of detectors in the Segmented Germanium Array (SeGA) at the NSCL and analyzing the positions of interaction therein allows the detectors to be used as Compton polarimeters. Unlike other segmented detectors, SeGA detectors are irradiated from the side to utilize the transversal segmentation for better Doppler corrections. Sensitivity in such an orientation has previously been untested. A linear polarization sensitivity $Q \approx 0.14$ has been measured in the 350-keV energy range for SeGA detectors using $\alpha$-$\gamma$ correlations from a \nuc{249}{Cf} source.Comment: 7 pages, 9 figure

Novel Mechanism of Supersolid of Ultracold Polar Molecules in Optical Lattices

We study the checkerboard supersolid of the hard-core Bose-Hubbard model with the dipole-dipole interaction. This supersolid is different from all other supersolids found in lattice models in the sense that superflow paths through which interstitials or vacancies can hop freely are absent in the crystal. By focusing on repulsive interactions between interstitials, we reveal that the long-range tail of the dipole-dipole interaction have the role of increasing the energy cost of domain wall formations. This effect produces the supersolid by the second-order hopping process of defects. We also perform exact quantum Monte Carlo simulations and observe a novel double peak structure in the momentum distribution of bosons, which is a clear evidence for supersolid. This can be measured by the time-of-flight experiment in optical lattice systems