Effectiveness of Walker's Cancellation Theorem

Walker's Cancellation theorem for abelian groups tells us that if $A$ is finitely generated and $G$ and $H$ are such that $A \oplus G \cong A \oplus H$, then $G \cong H$. Michael Deveau showed that the theorem can be effectivized, but not uniformly. In this paper, we expand on Deveau's initial analysis to show that the complexity of uniformly outputting an index of an isomorphism between $G$ and $H$, given indices for $A$, $G$, $H$, the isomorphism between $A \oplus G$ and $A \oplus H$, and the rank of $A$, is $\mathbf{0'}$.Comment: 12 page

One-bit Supervision for Image Classification: Problem, Solution, and Beyond

This paper presents one-bit supervision, a novel setting of learning with fewer labels, for image classification. Instead of training model using the accurate label of each sample, our setting requires the model to interact with the system by predicting the class label of each sample and learn from the answer whether the guess is correct, which provides one bit (yes or no) of information. An intriguing property of the setting is that the burden of annotation largely alleviates in comparison to offering the accurate label. There are two keys to one-bit supervision, which are (i) improving the guess accuracy and (ii) making good use of the incorrect guesses. To achieve these goals, we propose a multi-stage training paradigm and incorporate negative label suppression into an off-the-shelf semi-supervised learning algorithm. Theoretical analysis shows that one-bit annotation is more efficient than full-bit annotation in most cases and gives the conditions of combining our approach with active learning. Inspired by this, we further integrate the one-bit supervision framework into the self-supervised learning algorithm which yields an even more efficient training schedule. Different from training from scratch, when self-supervised learning is used for initialization, both hard example mining and class balance are verified effective in boosting the learning performance. However, these two frameworks still need full-bit labels in the initial stage. To cast off this burden, we utilize unsupervised domain adaptation to train the initial model and conduct pure one-bit annotations on the target dataset. In multiple benchmarks, the learning efficiency of the proposed approach surpasses that using full-bit, semi-supervised supervision.Comment: ACM TOMM. arXiv admin note: text overlap with arXiv:2009.0616

Nocaviogua A and B: two lipolanthines from root-nodule-associated Nocardia sp.

Nocaviogua A (1) and B (2), two lipolanthines featuring a non-canonical avionin (Avi)-containing macrocycle and a long acyl chain, were identified from the mutualistic actinomycete Nocardia sp. XZ19_369, which was isolated from the nodules of sea buckthorn collected in Tibet. Their planar structures were elucidated via extensive analyses of 1D and 2D NMR, as well as HRMS data. The absolute configurations were fully elucidated by advanced Marfey’s analysis and GIAO NMR calculations, representing the first time that the configurations of this family of lipolanthines have been determined. Nocaviogua A (1) exhibited weak cytotoxicity against human chronic uveal melanoma cells (UM92-1), non-small cell lung cancer (NCI-H2170), and breast cancer (MDA-MB-231). Our work provides valuable information on this burgeoning class of lipolanthines for further investigations

Evidence based on Mendelian randomization and colocalization analysis strengthens causal relationships between structural changes in specific brain regions and risk of amyotrophic lateral sclerosis

BackgroundAmyotrophic lateral sclerosis (ALS) is a neurodegenerative disease characterized by the degeneration of motor neurons in the brain and spinal cord with a poor prognosis. Previous studies have observed cognitive decline and changes in brain morphometry in ALS patients. However, it remains unclear whether the brain structural alterations contribute to the risk of ALS. In this study, we conducted a bidirectional two-sample Mendelian randomization (MR) and colocalization analysis to investigate this causal relationship.MethodsSummary data of genome-wide association study were obtained for ALS and the brain structures, including surface area (SA), thickness and volume of subcortical structures. Inverse-variance weighted (IVW) method was used as the main estimate approach. Sensitivity analysis was conducted detect heterogeneity and pleiotropy. Colocalization analysis was performed to calculate the posterior probability of causal variation and identify the common genes.ResultsIn the forward MR analysis, we found positive associations between the SA in four cortical regions (lingual, parahippocampal, pericalcarine, and middle temporal) and the risk of ALS. Additionally, decreased thickness in nine cortical regions (caudal anterior cingulate, frontal pole, fusiform, inferior temporal, lateral occipital, lateral orbitofrontal, pars orbitalis, pars triangularis, and pericalcarine) was significantly associated with a higher risk of ALS. In the reverse MR analysis, genetically predicted ALS was associated with reduced thickness in the bankssts and increased thickness in the caudal middle frontal, inferior parietal, medial orbitofrontal, and superior temporal regions. Colocalization analysis revealed the presence of shared causal variants between the two traits.ConclusionOur results suggest that altered brain morphometry in individuals with high ALS risk may be genetically mediated. The causal associations of widespread multifocal extra-motor atrophy in frontal and temporal lobes with ALS risk support the notion of a continuum between ALS and frontotemporal dementia. These findings enhance our understanding of the cortical structural patterns in ALS and shed light on potentially viable therapeutic targets