Cleft Extensions and Quotients of Twisted Quantum Doubles

Given a pair of finite groups $F, G$ and a normalized 3-cocycle $\omega$ of $G$, where $F$ acts on $G$ as automorphisms, we consider quasi-Hopf algebras defined as a cleft extension $\Bbbk^G_\omega\#_c\,\Bbbk F$ where $c$ denotes some suitable cohomological data. When $F\rightarrow \overline{F}:=F/A$ is a quotient of $F$ by a central subgroup $A$ acting trivially on $G$, we give necessary and sufficient conditions for the existence of a surjection of quasi-Hopf algebras and cleft extensions of the type $\Bbbk^G_\omega\#_c\, \Bbbk F\rightarrow \Bbbk^G_\omega\#_{\overline{c}} \, \Bbbk \overline{F}$. Our construction is particularly natural when $F=G$ acts on $G$ by conjugation, and $\Bbbk^G_\omega\#_c \Bbbk G$ is a twisted quantum double $D^{\omega}(G)$. In this case, we give necessary and sufficient conditions that Rep($\Bbbk^G_\omega\#_{\overline{c}} \, \Bbbk \overline{G}$) is a modular tensor category.Comment: LaTex; 14 page

Electronic state spectroscopy of C₂Cl₄

The VUV spectrum of C2Cl4 is reported in the energy range 3.8-10.8 eV (325-115 nm). Several photoabsorption features are observed for the first time, including a very weak low-lying band which is provisionally attributed to a π → π* triplet transition. Recent ab initio calculations of the molecule’s electronic transitions [Arulmozhiraja et al. J. Chem. Phys. 129 (2008) 174506] provide the basis for the present assignments below 8.5 eV. An extended ndπ series is proposed to account for several higher-energy Rydberg bands. The identification of vibrational structure, dominated by symmetric C=C and CCl2 stretching in excitations from the HOMO, largely agrees with previous spectroscopic studies. The present absolute photoabsorption cross sections cover a wider energy range than the previous measurements and are used to calculate UV photolysis lifetimes of this aeronomic molecule at altitudes between 20 and 50 km

Arginine mutation alters binding of a human monoclonal antibody to antigens linked to systemic lupus erythematosus and the antiphospholipid syndrome

Objective: Previous studies have shown the importance of somatic mutations and arginine residues in the complementarity-determining regions (CDRs) of pathogenic anti-double-stranded DNA (anti-dsDNA) antibodies in human and murine lupus, and in studies of murine antibodies, a role of mutations at position 53 in VH CDR2 has been demonstrated. We previously demonstrated in vitro expression and mutagenesis of the human IgG1 monoclonal antibody B3. The present study was undertaken to investigate, using this expression system, the importance of the arginine residue at position 53 (R53) in B3 VH. Methods: R53 was altered, by site-directed mutagenesis, to serine, asparagine, or lysine, to create 3 expressed variants of VH. In addition, the germline sequence of the VH3-23 gene (from which B3 VH is derived) was expressed either with or without arginine at position 53. These 5 new heavy chains, as well as wild-type B3 VH, were expressed with 4 different light chains, and the resulting antibodies were assessed for their ability to bind to nucleosomes, -actinin, cardiolipin, ovalbumin, 2-glycoprotein I (2GPI), and the N-terminal domain of 2GPI (domain I), using direct binding assays. Results: The presence of R53 was essential but not sufficient for binding to dsDNA and nucleosomes. Conversely, the presence of R53 reduced binding to -actinin, ovalbumin, 2GPI, and domain I of 2GPI. The combination B3 (R53S) VH/B3 VL bound human, but not bovine, 2GPI. Conclusion: The fact that the R53S substitution significantly alters binding of B3 to different clinically relevant antigens, but that the alteration is in opposite directions depending on the antigen, implies that this arginine residue plays a critical role in the affinity maturation of antibody B3

"Non-metabolizable" glucose analogue shines new light on primingmechanisms: Triggering of microbial metabolism

The rhizosphere and detritusphere are characterized by increased carbon availability, including low-molecular weight organic substances. Such easily biodegradable organic substances can change the mineralization rates of pre-existing soil organic matter, a phenomenon termed priming. Priming of soil organic matter decomposition has attracted much research interest, yet a conclusive mechanistic explanation remains elusive. One proposal is that low molecular weight organic substances might “trigger” an acceleration of microbial metabolism. For the first time, we applied a glucose analogue to soil to demonstrate triggering of microbial metabolism, and to estimate its relative contribution to priming. “Non-metabolizable” glucose analogues have been widely used in pure culture studies to mimic glucose, but never in soil biochemistry. We hypothesized that analogue molecules will elicit a metabolic response in microorganisms despite limited catabolism, and thereby confirm the proposed triggering. The effect of 14C-labeled 3-O-methyl-D-glucose (OMG) – a common “non-metabolizable” glucose analogue – on soil organic matter mineralization was compared to that of 14C-labeled D-glucose. OMG was mineralized, but its mineralization was initially impeded and substantially delayed, relative to glucose. OMG caused brief but strong priming in the first 24 h, increasing unlabeled CO2 efflux by 173%, 89% and 36% above control for additions of 0.49, 2.4 and 4.9 mmol OMG g-1 soil, respectively. In contrast, glucose caused low or negative priming on the first day. On the first day after OMG addition, a negative correlation between priming and OMG mineralization indicated that triggering is a valid mechanism of microbial activation during a famine-feast transition, but is short-lived. Glucose mineralization peaked on the second day for medium and high additions, coinciding with peaks in positive priming. Maximum substrate mineralization also coincided with peaks in priming for medium and high OMG levels, but these occurred 9 and 11 days after addition, respectively. This revealed non-triggering priming mechanisms, which contributed most to priming and were closely coupled to substrate mineralization. By separating energy- and substrate-dependent metabolic processes from triggering processes, the glucose analogue 3-O-methyl-D-glucose enabled triggering to be demonstrated, but triggering by glucose occurs without contributing greatly to priming

Genus Two Partition and Correlation Functions for Fermionic Vertex Operator Superalgebras I

We define the partition and $n$-point correlation functions for a vertex operator superalgebra on a genus two Riemann surface formed by sewing two tori together. For the free fermion vertex operator superalgebra we obtain a closed formula for the genus two continuous orbifold partition function in terms of an infinite dimensional determinant with entries arising from torus Szeg\"o kernels. We prove that the partition function is holomorphic in the sewing parameters on a given suitable domain and describe its modular properties. Using the bosonized formalism, a new genus two Jacobi product identity is described for the Riemann theta series. We compute and discuss the modular properties of the generating function for all $n$-point functions in terms of a genus two Szeg\"o kernel determinant. We also show that the Virasoro vector one point function satisfies a genus two Ward identity.Comment: A number of typos have been corrected, 39 pages. To appear in Commun. Math. Phy

Vertex operator algebras of rank 2 - the Mathur-Mukhi-Sen theorem revisited

Let $V$ be a strongly regular vertex operator algebra and let $\frak{ch}_V$ be the space spanned by the characters of the irreducible $V$-modules.\ It is known that $\frak{ch}_V$ is the space of solutions of a so-called \emph{modular linear differential equation (MLDE)}.\ In this paper we obtain a near-classification of those $V$ for which the corresponding MLDE is irreducible and monic of order $2$.\ As a consequence we derive the complete classification when $V$ has exactly two simple modules.\ It turns out that $V$ is either one of four affine Kac-Moody algebras of level $1$, or the Yang-Lee Virasoro model of central charge ${-}22/5$.\ Our proof establishes new connections between the characters of $V$ and Gauss hypergeometric series, and puts the finishing touches to work of Mathur, Mukhi and Sen who first considered this problem forty years ago

A COMPARISON OF JAPANESE FINALISTS TO OTHER FINALISTS IN THE 100 m SWIMMING RACES AT THE SYDNEY OLYMPIC GAMES

The purpose of this study was to compare the performance in 100 m swimming events at the Sydney Olympics between Japanese finalists and finalists from the other nations. The data collated by the B~omechanicsD epartment of the Australian lnstitute of Sport was used for this purpose. Swimming events were divided into four phases and the time taken to perform each phase was measured for 48 finalists. Although three Japanese swimmer performances were superior in the free swimming phase, their placing did not reflect this because of inferior performances in the start and turn. In contrast, the opposite situation arose with three other Japanese swimmers. These results suggest that not only the free swimming phase but also the starting and turning phases are important in determining race results in 100 m swimming events in international competition

Case studies: US-Japan comparison of attachment transmission

Today, attachment research has become increasingly more quantitative and complex, utilizing extremely sophisticated statistical analyses often based on enormous synthesized datasets across the globe (Verhage et al., 2016). This marks a significant advancement in the attachment field in particular and developmental fields in general. However, this phenomenon arguably restricts the ability to visualize interactions of each parent-child dyad, on which the relationship quality is assessed. Notably, the Adult Attachment Interview (AAI) and the Strange Situation Procedure (SSP) are the most validated, widely-used attachment measures world-wide, known to predict attachment transmission. This paper demonstrates the qualitative presentation of attachment transmission data, comparing samples from the US and Japan. We present case studies for each main attachment category through AAI excerpts, SSP behavioral summaries, and the expected transmission process. We also compare case studies cross-culturally to confirm the universality of attachment phenomena as well as to explore any cultural differences that may affect attachment expressions

Averaging rheological quantities in descriptions of soft glassy materials

Many mean-field models have been introduced to describe the mechanical behavior of glassy materials. They often rely on averages performed over distributions of elements or states. We here underline that averaging is a more intricate procedure in mechanics than in more classical situations such as phase transitions in magnetic systems. This leads us to modify the predictions of the recently proposed SGR model for soft glassy materials, for which we suggest that the viscosity should diverge at the glass transition temperature $T_g$ with an exponential form $\eta \sim \exp(\frac{A}{T-T_g})$.Comment: 4 pages, Latex, 1 eps figur