A virtual PGLr\mathrm{PGL}_r-SLr\mathrm{SL}_r correspondence for projective surfaces

For a smooth projective surface $X$ satisfying $H_1(X,\mathbb{Z}) = 0$ and $w \in H^2(X,\mu_r)$, we study deformation invariants of the pair $(X,w)$. Choosing a Brauer-Severi variety $Y$ (or, equivalently, Azumaya algebra $\mathcal{A}$) over $X$ with Stiefel-Whitney class $w$, the invariants are defined as virtual intersection numbers on suitable moduli spaces of stable twisted sheaves on $Y$ constructed by Yoshioka (or, equivalently, moduli spaces of $\mathcal{A}$-modules of Hoffmann-Stuhler). We show that the invariants do not depend on the choice of $Y$. Using a result of de Jong, we observe that they are deformation invariants of the pair $(X,w)$. For surfaces with $h^{2,0}(X) > 0$, we show that the invariants can often be expressed as virtual intersection numbers on Gieseker-Maruyama-Simpson moduli spaces of stable sheaves on $X$. This can be seen as a $\mathrm{PGL}_r$-$\mathrm{SL}_r$ correspondence. As an application, we express $\mathrm{SU}(r) / \mu_r$ Vafa-Witten invariants of $X$ in terms of $\mathrm{SU}(r)$ Vafa-Witten invariants of $X$. We also show how formulae from Donaldson theory can be used to obtain upper bounds for the minimal second Chern class of Azumaya algebras on $X$ with given division algebra at the generic point.Comment: 47 page

Gopakumar-Vafa invariants via vanishing cycles

In this paper, we propose an ansatz for defining Gopakumar-Vafa invariants of Calabi-Yau threefolds, using perverse sheaves of vanishing cycles. Our proposal is a modification of a recent approach of Kiem-Li, which is itself based on earlier ideas of Hosono-Saito-Takahashi. We conjecture that these invariants are equivalent to other curve-counting theories such as Gromov-Witten theory and Pandharipande-Thomas theory. Our main theorem is that, for local surfaces, our invariants agree with PT invariants for irreducible one-cycles. We also give a counter-example to the Kiem-Li conjectures, where our invariants match the predicted answer. Finally, we give examples where our invariant matches the expected answer in cases where the cycle is non-reduced, non-planar, or non-primitive.Comment: 63 pages, many improvements of the exposition following referee comments, final version to appear in Inventione

Thermal Instability and Photoionized X-ray Reflection in Accretion Disks

We study the X-ray illumination of an accretion disk. We relax the simplifying assumption of constant gas density used in most previous studies; instead we determine the density from hydrostatic balance. It is found that the thermal ionization instability prevents the illuminated gas from attaining temperatures at which the gas is unstable. In particular, the uppermost layers of the X-ray illuminated gas are found to be almost completely ionized and at the local Compton temperature ($\sim 10^7 - 10^8$ K); at larger depths, the gas temperature drops abruptly to form a thin layer with $T\sim 10^6$ K, while at yet larger depths it decreases sharply to the disk effective temperature. We find that most of the Fe K$\alpha$ line emission and absorption edge are produced in the coolest, deepest layers, while the Fe atoms in the hottest, uppermost layers are generally almost fully ionized, hence making a negligible contribution to reprocessing features in $\sim 6.4-10$ keV energy range. We provide a summary of how X-ray reprocessing features depend on parameters of the problem. The results of our self-consistent calculations are both quantitatively and qualitatively different from those obtained using the constant density assumption. Therefore, we conclude that X-ray reflection calculations should always utilize hydrostatic balance in order to provide a reliable theoretical interpretation of observed X-ray spectra of AGN and GBHCs.Comment: Submitted to ApJ; 16 pages plus 13 figure

Holomorphic anomaly equations and the Igusa cusp form conjecture

Let $S$ be a K3 surface and let $E$ be an elliptic curve. We solve the reduced Gromov-Witten theory of the Calabi-Yau threefold $S \times E$ for all curve classes which are primitive in the K3 factor. In particular, we deduce the Igusa cusp form conjecture. The proof relies on new results in the Gromov-Witten theory of elliptic curves and K3 surfaces. We show the generating series of Gromov-Witten classes of an elliptic curve are cycle-valued quasimodular forms and satisfy a holomorphic anomaly equation. The quasimodularity generalizes a result by Okounkov and Pandharipande, and the holomorphic anomaly equation proves a conjecture of Milanov, Ruan and Shen. We further conjecture quasimodularity and holomorphic anomaly equations for the cycle-valued Gromov-Witten theory of every elliptic fibration with section. The conjecture generalizes the holomorphic anomaly equations for ellliptic Calabi-Yau threefolds predicted by Bershadsky, Cecotti, Ooguri, and Vafa. We show a modified conjecture holds numerically for the reduced Gromov-Witten theory of K3 surfaces in primitive classes.Comment: 68 page

Improving Management of Natural Resources for Sustainable Rainfed Agriculture in Ringnodia Micro-watershed

The current productivity of rainfed lands in Madhya Pradesh, India is about 1.0 t ha-1 although there is scope to obtain >3 t ha-1. To assess and evaluate the potential of improved soil, water, and nutrient management options through integrated watershed management at Ringnodia in Indore in western Madhya Pradesh, a micro-watershed of 390 ha was delineated. Soybean is a major crop during the rainy season and yield of <1 t ha-1 is obtained in the micro-watershed. Landholdings in the watershed are generally small. The input use is low with little soil and water conservation measures in vogue among farmers. About 30–40% of the total rainfall is lost through runoff, carrying productive soils and nutrients while crops experienced drought stress in the rainy as well as postrainy seasons. With a critical advisory support from scientists, the watershed farmers could augment water storage capacity in the village through construction of percolation/storage tanks and renovation of existing ponds. For safe disposal of water from the watershed, waterways were developed and wire mesh bound boulder structures were constructed to reduce soil loss and runoff. These water storage structures could store up to 30 ha-m water representing about 70% of total runoff from 100 ha cultivated area and thus reduce runoff and soil losses. This increased groundwater recharge, which manifested in increased water table in most wells including the abandoned ones. The scenario analysis suggested various cropping options for enhanced yield with limited irrigation (soybean-wheat) or under rainfed conditions (pigeonpea/sorghum intercrop). Sorghum/pigeonpea intercrop was, however, less popular amongst the farmers. The introduction of extra-short-duration pigeonpea opened avenues for diversification and its adoption is likely to increase. Under rainfed conditions, double cropping could be practiced in two out of three postrainy seasons. Soybean yields increased marginally by gypsum application and also by planting on mini-ridges. The medium-duration chickpea cultivar JG 218 gave higher yield than short-duration cultivars ICCV 2 and ICCC 37 indicating sufficient moisture for the traditional types. Pests were the major yield reducers in soybean and adoption of integrated pest management options nearly tripled soybean yield. In another micro-watershed at the College of Agriculture, Indore interaction between land and water conservation measures and efficient cropping systems was examined. Soybean/pigeonpea strip crop and soybean-wheat systems were more productive than soybean-chickpea and soybean-linseed systems. Chickpea and wheat could easily be established with minimum tillage when planted in moist seed zone at 15 cm depth after the harvest of soybea

Evaluation of a New Balloon Catheter for Difficult Calcified Lesions in Infrainguinal Arterial Disease: Outcome of a Multicenter Registry

The purpose of this study was to assess the technical performance and immediate procedure outcome of a new balloon catheter in the treatment of calcified lesions in infrainguinal arterial disease. Seventy-five patients with infrainguinal arterial disease were prospectively entered into the registry. The catheter (ReeKross Clearstream, Ireland) is a 5- to 6-Fr balloon catheter with a rigid shaft intended for enhanced pushability. Only technical procedural outcome was recorded. Treated calcified lesions (range: 5–30 cm), assessed angiographically, were located in the superficial femoral, popliteal, and crural arteries. In 67 patients the lesion was an occlusion. Guidewire passage occurred subintimally in 68 patients. In 24 patients a standard balloon catheter was chosen as first treatment catheter: 5 failed to cross the lesion, 8 balloons ruptured, and in 11 patients there was an inadequate dilatation result. In only one of the five patients did subsequent use of the ReeKross catheter also fail in lesion crossing. The ReeKross was successful as secondary catheter in the other 23 cases. In 50 patients the ReeKross was used as primary catheter. In total the ReeKross crossed the lesions in 74 patients. After passage and dilatation with this catheter in 73 patients (1 failed true-lumen reentry), 19 had >30% residual lesions, of which 11 were not treated and 8 were successfully stented. No ReeKross balloons ruptured. We conclude that in the treatment of difficult calcified lesions in arterial stenotic or occlusive disease, the choice of a high-pushability angioplasty catheter, with more calcification-resistant balloon characteristics, like the ReeKross, warrants consideration

Conformational landscapes of DNA polymerase I and mutator derivatives establish fidelity checkpoints for nucleotide insertion

The fidelity of DNA polymerases depends on conformational changes that promote the rejection of incorrect nucleotides before phosphoryl transfer. Here, we combine single-molecule FRET with the use of DNA polymerase I and various fidelity mutants to highlight mechanisms by which active-site side chains influence the conformational transitions and free-energy landscape that underlie fidelity decisions in DNA synthesis. Ternary complexes of high fidelity derivatives with complementary dNTPs adopt mainly a fully closed conformation, whereas a conformation with a FRET value between those of open and closed is sparsely populated. This intermediate-FRET state, which we attribute to a partially closed conformation, is also predominant in ternary complexes with incorrect nucleotides and, strikingly, in most ternary complexes of low-fidelity derivatives for both correct and incorrect nucleotides. The mutator phenotype of the low-fidelity derivatives correlates well with reduced affinity for complementary dNTPs and highlights the partially closed conformation as a primary checkpoint for nucleotide selection

CAMK2-Dependent Signaling in Neurons Is Essential for Survival

Ca2+/calmodulin-dependent protein kinase II (CAMK2) is a key player in synaptic plasticity and memory formation. Mutations in Camk2a or Camk2b cause intellectual disability in humans, and severe plasticity and learning deficits in mice, indicating unique functions for each isoform. However, considering the high homology between CAMK2A and CAMK2B, it is conceivable that for critical functions, one isoform compensates for the absence of the other, and that the full functional spectrum of neuronal CAMK2 remains to be revealed.Here we show that germline as well as adult deletion of both CAMK2 isoforms in male or female mice is lethal. Moreover, Ca2+-dependent activity as well as autonomous activity of CAMK2 is essential for survival. Loss of both CAMK2 isoforms abolished LTP, whereas synaptic transmission remained intact. The double-mutants showed no gross morphological changes of the brain, and in contrast to the long-considered role for CAMK2 in the structural organization of the postsynaptic density (PSD), deletion of both CAMK2 isoforms did not affect the biochemical composition of the PSD. Together, these results reveal an essential role for CAMK2 signaling in early postnatal development as well as the mature brain, and indicate that the full spectrum of CAMK2 requirements cannot be revealed in the single mutants because of partial overlappin

Establishing accretion flares from massive black holes as a major source of high-energy neutrinos

High-energy neutrinos have thus far been observed in coincidence with time-variable emission from three different accreting black holes: a gamma-ray flare from a blazar (TXS 0506+056), an optical transient following a stellar tidal disruption (AT2019dsg), and an optical outburst from an active galactic nucleus (AT2019fdr). Here we present a unified explanation for the latter two of these sources: accretion flares that reach the Eddington limit. A signature of these events is a luminous infrared reverberation signal from circumnuclear dust that is heated by the flare. Using this property we construct a sample of similar sources, revealing a third event coincident with a PeV-scale neutrino. This sample of three accretion flares is correlated with high-energy neutrinos at a significance of 3.7 sigma. Super-Eddington accretion could explain the high particle acceleration efficiency of this new population.Comment: 46 pages, 11 figures, 3 table