(Contravariant) Koszul duality for DG algebras

A DG algebras $A$ over a field $k$ with $H(A)$ connected and $H_{<0}(A)=0$ has a unique up to isomorphism DG module $K$ with $H(K)\cong k$. It is proved that if $H(A)$ is degreewise finite, then RHom_A(?,K): D^{df}_{+}(A)^{op} \equiv D_{df}^{+}}(RHom_A(K,K)) is an exact equivalence of derived categories of DG modules with degreewise finite-dimensional homology. It induces an equivalences of $D^{df}_{b}(A)^{op}$ and the category of perfect DG $RHom_A(K,K)$-modules, and vice-versa. Corresponding statements are proved also when $H(A)$ is simply connected and $H^{<0}(A)=0$.Comment: 33 page

Nonlocal long-range synchronization of planar Josephson junction arrays

We study arrays of planar Nb Josephson junctions with contacts to intermediate electrodes, which allow measurements of individual junctions and, thus, provide an insight into intricate array dynamics. We observe a robust phase-locking of arrays, despite a significant inter-junction separation. Several unusual phenomena are reported, such as a bi-stable critical current with re-entrant superconductivity upon switching of nearby junctions; and incorrect Shapiro steps, occurring at mixing frequencies between the external RF radiation and the internal Josephson frequency in nearby junctions. Our results reveal a surprisingly strong and long-range inter-junction interaction. It is attributed to nonlocality of planar junction electrodynamics, caused by the long-range spreading of stray electromagnetic fields. The nonlocality greatly enhances the high-frequency interjunction coupling and enables large-scale synchronization. Therefore, we conclude that planar geometry is advantageous for realization of coherent Josephson electronics.Comment: 8 pages, 5 figure

Nebuliser therapy in the intensive care unit

The relationship between identity, lived experience, sexual practices and the language through which these are conveyed has been widely debated in sexuality literature. For example, ‘coming out’ has famously been conceptualised as a ‘speech act’ (Sedgwick 1990) and as a collective narrative (Plummer 1995), while a growing concern for individuals’ diverse identifications in relations to their sexual and gender practices has produced interesting research focusing on linguistic practices among LGBT-identified individuals (Leap 1995; Kulick 2000; Cameron and Kulick 2006; Farqhar 2000). While an explicit focus on language remains marginal to literature on sexualities (Kulick 2000), issue of language use and translation are seldom explicitly addressed in the growing literature on intersectionality. Yet intersectional perspectives ‘reject the separability of analytical and identity categories’ (McCall 2005:1771), and therefore have an implicit stake in the ‘vernacular’ language of the researched, in the ‘scientific’ language of the researcher and in the relationship of continuity between the two. Drawing on literature within gay and lesbian/queer studies and cross-cultural studies, this chapter revisits debates on sexuality, language and intersectionality. I argue for the importance of giving careful consideration to the language we choose to use as researchers to collectively define the people whose experiences we try to capture. I also propose that language itself can be investigated as a productive way to foreground how individual and collective identifications are discursively constructed, and to unpack the diversity of lived experience. I address intersectional complexity as a methodological issue, where methodology is understood not only as the methods and practicalities of doing research, but more broadly as ‘a coherent set of ideas about the philosophy, methods and data that underlie the research process and the production of knowledge’ (McCall 2005:1774). My points are illustrated with examples drawn from my ethnographic study on ‘lesbian’ identity in urban Russia, interspersed with insights from existing literature. In particular, I aim to show that an explicit focus on language can be a productive way to explore the intersections between the global, the national and the local in cross-cultural research on sexuality, while also addressing issues of positionality and accountability to the communities researched

Spaces with Noetherian cohomology

Is the cohomology of the classifying space of a p-compact group, with Noetherian twisted coefficients, a Noetherian module? This note provides, over the ring of p-adic integers, such a generalization to p-compact groups of the Evens-Venkov Theorem. We consider the cohomology of a space with coefficients in a module, and we compare Noetherianity over the field with p elements, with Noetherianity over the p-adic integers, in the case when the fundamental group is a finite p-group.Comment: 12 page

Schreier rewriting beyond the classical setting

Using actions of free monoids and free associative algebras, we establish some Schreier-type formulas involving the ranks of actions and the ranks of subactions in free actions or Grassmann-type relations for the ranks of intersections of subactions of free actions. The coset action of the free group is used to establish the generalization of the Schreier formula to the case of subgroups of infinite index. We also study and apply large modules over free associative algebras in the spirit of the paper Olshanskii, A. Yu.; Osin, D.V., Large groups and their periodic quotients, Proc. Amer. Math. Soc., 136 (2008), 753 - 759.Comment: 17 page

Colliding scalar pulses in the Einstein-Gauss-Bonnet gravity

We numerically investigated how the nonlinear dynamics depends on the dimensionality and on the higher-order curvature corrections in the form of Gauss-Bonnet (GB) terms, with a model of colliding scalar pulses in plane-symmetric space-time. We observed that a collision of large scalar pulses will produce a large-curvature region, of which the magnitude depends on αGB. The normal corrections (αGB > 0) work for avoiding the appearance of singularity, although it is inevitable

A Coordinated Effort to Manage Soybean Rust in North America: A Success Story in Soybean Disease Monitoring

Existing crop monitoring programs determine the incidence and distribution of plant diseases and pathogens and assess the damage caused within a crop production region. These programs have traditionally used observed or predicted disease and pathogen data and environmental information to prescribe management practices that minimize crop loss (3,69). Monitoring programs are especially important for crops with broad geographic distribution or for diseases that can cause rapid and great economic losses. Successful monitoring programs have been developed for several plant diseases, including downy mildew of cucurbits, Fusarium head blight of wheat, potato late blight, and rusts of cereal crops (13,36,51,80)

S-duality as a beta-deformed Fourier transform

An attempt is made to formulate Gaiotto's S-duality relations in an explicit quantitative form. Formally the problem is that of evaluation of the Racah coefficients for the Virasoro algebra, and we approach it with the help of the matrix model representation of the AGT-related conformal blocks and Nekrasov functions. In the Seiberg-Witten limit, this S-duality reduces to the Legendre transformation. In the simplest case, its lifting to the level of Nekrasov functions is just the Fourier transform, while corrections are related to the beta-deformation. We calculate them with the help of the matrix model approach and observe that they vanish for beta=1. Explicit evaluation of the same corrections from the U_q(sl(2)) infinite-dimensional representation formulas due to B.Ponsot and J.Teshner remains an open problem.Comment: 21 page