Holomorphic subgraph reduction of higher-point modular graph forms

Modular graph forms are a class of modular covariant functions which appear in the genus-one contribution to the low-energy expansion of closed string scattering amplitudes. Modular graph forms with holomorphic subgraphs enjoy the simplifying property that they may be reduced to sums of products of modular graph forms of strictly lower loop order. In the particular case of dihedral modular graph forms, a closed form expression for this holomorphic subgraph reduction was obtained previously by D'Hoker and Green. In the current work, we extend these results to trihedral modular graph forms. Doing so involves the identification of a modular covariant regularization scheme for certain conditionally convergent sums over discrete momenta, with some elements of the sum being excluded. The appropriate regularization scheme is identified for any number of exclusions, which in principle allows one to perform holomorphic subgraph reduction of higher-point modular graph forms with arbitrary holomorphic subgraphs.Comment: 38 pages; v2: publication versio

Heterotic-string amplitudes at one loop: modular graph forms and relations to open strings

We investigate one-loop four-point scattering of non-abelian gauge bosons in heterotic string theory and identify new connections with the corresponding open-string amplitude. In the low-energy expansion of the heterotic-string amplitude, the integrals over torus punctures are systematically evaluated in terms of modular graph forms, certain non-holomorphic modular forms. For a specific torus integral, the modular graph forms in the low-energy expansion are related to the elliptic multiple zeta values from the analogous open-string integrations over cylinder boundaries. The detailed correspondence between these modular graph forms and elliptic multiple zeta values supports a recent proposal for an elliptic generalization of the single-valued map at genus zero.Comment: 57+22 pages, v2: references updated, version published in JHE

Geometric deep learning and equivariant neural networks

We survey the mathematical foundations of geometric deep learning, focusing on group equivariant and gauge equivariant neural networks. We develop gauge equivariant convolutional neural networks on arbitrary manifolds M using principal bundles with structure group K and equivariant maps between sections of associated vector bundles. We also discuss group equivariant neural networks for homogeneous spaces M= G/ K , which are instead equivariant with respect to the global symmetry G on M . Group equivariant layers can be interpreted as intertwiners between induced representations of G, and we show their relation to gauge equivariant convolutional layers. We analyze several applications of this formalism, including semantic segmentation and object detection networks. We also discuss the case of spherical networks in great detail, corresponding to the case M= S2= SO (3) / SO (2) . Here we emphasize the use of Fourier analysis involving Wigner matrices, spherical harmonics and Clebsch–Gordan coefficients for G= SO (3) , illustrating the power of representation theory for deep learning

HEAL-SWIN: A Vision Transformer On The Sphere

High-resolution wide-angle fisheye images are becoming more and more important for robotics applications such as autonomous driving. However, using ordinary convolutional neural networks or vision transformers on this data is problematic due to projection and distortion losses introduced when projecting to a rectangular grid on the plane. We introduce the HEAL-SWIN transformer, which combines the highly uniform Hierarchical Equal Area iso-Latitude Pixelation (HEALPix) grid used in astrophysics and cosmology with the Hierarchical Shifted-Window (SWIN) transformer to yield an efficient and flexible model capable of training on high-resolution, distortion-free spherical data. In HEAL-SWIN, the nested structure of the HEALPix grid is used to perform the patching and windowing operations of the SWIN transformer, resulting in a one-dimensional representation of the spherical data with minimal computational overhead. We demonstrate the superior performance of our model for semantic segmentation and depth regression tasks on both synthetic and real automotive datasets. Our code is available at https://github.com/JanEGerken/HEAL-SWIN.Comment: Main body: 10 pages, 7 figures. Appendices: 4 pages, 2 figure

Novel AlkB Dioxygenases—Alternative Models for In Silico and In Vivo Studies

Background: ALKBH proteins, the homologs of Escherichia coli AlkB dioxygenase, constitute a direct, single-protein repair system, protecting cellular DNA and RNA against the cytotoxic and mutagenic activity of alkylating agents, chemicals significantly contributing to tumor formation and used in cancer therapy. In silico analysis and in vivo studies have shown the existence of AlkB homologs in almost all organisms. Nine AlkB homologs (ALKBH1–8 and FTO) have been identified in humans. High ALKBH levels have been found to encourage tumor development, questioning the use of alkylating agents in chemotherapy. The aim of this work was to assign biological significance to multiple AlkB homologs by characterizing their activity in the repair of nucleic acids in prokaryotes and their subcellular localization in eukaryotes. Methodology and Findings: Bioinformatic analysis of protein sequence databases identified 1943 AlkB sequences with eight new AlkB subfamilies. Since Cyanobacteria and Arabidopsis thaliana contain multiple AlkB homologs, they were selected as model organisms for in vivo research. Using E. coli alkB2 mutant and plasmids expressing cyanobacterial AlkBs, we studied the repair of methyl methanesulfonate (MMS) and chloroacetaldehyde (CAA) induced lesions in ssDNA, ssRNA, and genomic DNA. On the basis of GFP fusions, we investigated the subcellular localization of ALKBHs in A. thaliana and established its mostly nucleo-cytoplasmic distribution. Some of the ALKBH proteins were found to change their localization upon MMS treatment. Conclusions: Our in vivo studies showed highly specific activity of cyanobacterial AlkB proteins towards lesions and nucleic acid type. Subcellular localization and translocation of ALKBHs in A. thaliana indicates a possible role for these proteins in the repair of alkyl lesions. We hypothesize that the multiplicity of ALKBHs is due to their involvement in the metabolism of nucleo-protein complexes; we find their repair by ALKBH proteins to be economical and effective alternative to degradation and de novo synthesis

Neurobeachin, a Regulator of Synaptic Protein Targeting, Is Associated with Body Fat Mass and Feeding Behavior in Mice and Body-Mass Index in Humans

Neurobeachin (Nbea) regulates neuronal membrane protein trafficking and is required for the development and functioning of central and neuromuscular synapses. In homozygous knockout (KO) mice, Nbea deficiency causes perinatal death. Here, we report that heterozygous KO mice haploinsufficient for Nbea have higher body weight due to increased adipose tissue mass. In several feeding paradigms, heterozygous KO mice consumed more food than wild-type (WT) controls, and this consumption was primarily driven by calories rather than palatability. Expression analysis of feeding-related genes in the hypothalamus and brainstem with real-time PCR showed differential expression of a subset of neuropeptide or neuropeptide receptor mRNAs between WT and Nbea+/− mice in the sated state and in response to food deprivation, but not to feeding reward. In humans, we identified two intronic NBEA single-nucleotide polymorphisms (SNPs) that are significantly associated with body-mass index (BMI) in adult and juvenile cohorts. Overall, data obtained in mice and humans suggest that variation of Nbea abundance or activity critically affects body weight, presumably by influencing the activity of feeding-related neural circuits. Our study emphasizes the importance of neural mechanisms in body weight control and points out NBEA as a potential risk gene in human obesity

The Magnitude of Global Marine Species Diversity

Background: The question of how many marine species exist is important because it provides a metric for how much we do and do not know about life in the oceans. We have compiled the first register of the marine species of the world and used this baseline to estimate how many more species, partitioned among all major eukaryotic groups, may be discovered. Results: There are ∼226,000 eukaryotic marine species described. More species were described in the past decade (∼20,000) than in any previous one. The number of authors describing new species has been increasing at a faster rate than the number of new species described in the past six decades. We report that there are ∼170,000 synonyms, that 58,000–72,000 species are collected but not yet described, and that 482,000–741,000 more species have yet to be sampled. Molecular methods may add tens of thousands of cryptic species. Thus, there may be 0.7–1.0 million marine species. Past rates of description of new species indicate there may be 0.5 ± 0.2 million marine species. On average 37% (median 31%) of species in over 100 recent field studies around the world might be new to science. Conclusions: Currently, between one-third and two-thirds of marine species may be undescribed, and previous estimates of there being well over one million marine species appear highly unlikely. More species than ever before are being described annually by an increasing number of authors. If the current trend continues, most species will be discovered this century

Search for the doubly charmed baryon Ω cc +

Abstract: A search for the doubly charmed baryon Ωcc+ with the decay mode Ωcc+ → Ξc+K−π+ is performed using proton-proton collision data at a centre-of-mass energy of 13 TeV collected by the LHCb experiment from 2016 to 2018, corresponding to an integrated luminosity of 5.4 fb−1. No significant signal is observed within the invariant mass range of 3.6 to 4.0GeV/c2. Upper limits are set on the ratio R of the production cross-section times the total branching fraction of the Ωcc+ → Ξc+K−π+ decay with respect to the Ξcc++→Λc+K−π+π+ decay. Upper limits at 95% credibility level for R in the range 0.005 to 0.11 are obtained for different hypotheses on the Ωcc+ mass and lifetime in the rapidity range from 2.0 to 4.5 and transverse momentum range from 4 to 15 GeV/c