EuclidNet: Deep Visual Reasoning for Constructible Problems in Geometry

In this paper, we present a deep learning-based framework for solving geometric construction problems through visual reasoning, which is useful for automated geometry theorem proving. Constructible problems in geometry often ask for the sequence of straightedge-and-compass constructions to construct a given goal given some initial setup. Our EuclidNet framework leverages the neural network architecture Mask R-CNN to extract the visual features from the initial setup and goal configuration with extra points of intersection, and then generate possible construction steps as intermediary data models that are used as feedback in the training process for further refinement of the construction step sequence. This process is repeated recursively until either a solution is found, in which case we backtrack the path for a step-by-step construction guide, or the problem is identified as unsolvable. Our EuclidNet framework is validated on complex Japanese Sangaku geometry problems, demonstrating its capacity to leverage backtracking for deep visual reasoning of challenging problems.Comment: Accepted by 2nd MATH-AI Workshop at NeurIPS'2

MotionEditor: Editing Video Motion via Content-Aware Diffusion

Existing diffusion-based video editing models have made gorgeous advances for editing attributes of a source video over time but struggle to manipulate the motion information while preserving the original protagonist's appearance and background. To address this, we propose MotionEditor, a diffusion model for video motion editing. MotionEditor incorporates a novel content-aware motion adapter into ControlNet to capture temporal motion correspondence. While ControlNet enables direct generation based on skeleton poses, it encounters challenges when modifying the source motion in the inverted noise due to contradictory signals between the noise (source) and the condition (reference). Our adapter complements ControlNet by involving source content to transfer adapted control signals seamlessly. Further, we build up a two-branch architecture (a reconstruction branch and an editing branch) with a high-fidelity attention injection mechanism facilitating branch interaction. This mechanism enables the editing branch to query the key and value from the reconstruction branch in a decoupled manner, making the editing branch retain the original background and protagonist appearance. We also propose a skeleton alignment algorithm to address the discrepancies in pose size and position. Experiments demonstrate the promising motion editing ability of MotionEditor, both qualitatively and quantitatively.Comment: 18 pages, 15 figures. Project page at https://francis-rings.github.io/MotionEditor

Sound Velocities of Stishovite at Simultaneous High Pressure and High Temperature Suggest an Eclogite-Rich Layer Beneath the Hawaii Hotspot

Compressional and shear wave velocities of polycrystalline stishovite (SiO2) have been measured at simultaneous high pressures and temperatures up to 14.5 GPa and 800°C. By fitting velocities to the finite strain equations, the elastic moduli and density were determined to be KS0 = 306.6(46) GPa, KS′ = 4.92(10), ∂KS/∂T = −0.024(1) GPa/K, G0 = 229.0(34) GPa, G′ = 1.07(10), ∂G/∂T = −0.017(1) GPa/K, ρ0 = 4.287(2) g/cm3. Our modeling suggested that, in the eclogite, coesite-stishovite transition can increase P and S wave velocities by 2.4% and 3.5%, respectively. A comparison between geophysical observations and our model shows that the coesite-stishovite phase transition in the eclogite can potentially be responsible for the occurrence of the X discontinuity beneath Hawaii. In addition, our current results suggest an eclogite-rich layer between 340 and 450 km depth beneath Hawaii. The eclogite concentration at the top and bottom of the layer is 41–55 vol% and >77 vol%, respectively

Research Progress of Glucansucrase from Lactic Acid Bacteria

Glucansucrase (EC.2.4.5.1) is a class of α-glucosyltransferases, mainly produced by lactic acid bacteria such as Leuconostoc, Streptococcus and Lactobacillus. The structure and catalytic mechanism of glucansucrase are diverse, and it is an important tool enzyme for the biosynthesis of exopolysaccharide. This article mainly reviews the source, classification, structure and reaction mechanism of glucansucrase and the effects of medium composition, culture conditions on the production of glucansucrase, with a focus on the optimization methods, separation and purification processes, and enzymatic properties of glucansucrase, and prospects for its development trend. This article aims to provide reference for the research of glucansucrase in related fields

Genetic prediction of the causal relationship between schizophrenia and tumors: a Mendelian randomized study

BackgroundPatients with schizophrenia are at a higher risk of developing cancer. However, the causal relationship between schizophrenia and different tumor types remains unclear.MethodsUsing a two-sample, two-way Mendelian randomization method, we used publicly available genome-wide association analysis (GWAS) aggregate data to study the causal relationship between schizophrenia and different cancer risk factors. These tumors included lung adenocarcinoma, lung squamous cell carcinoma, small-cell lung cancer, gastric cancer, alcohol-related hepatocellular cancer, tumors involving the lungs, breast, thyroid gland, pancreas, prostate, ovaries and cervix, endometrium, colon and colorectum, and bladder. We used the inverse variance weighting (IVW) method to determine the causal relationship between schizophrenia and different tumor risk factors. In addition, we conducted a sensitivity test to evaluate the effectiveness of the causality.ResultsAfter adjusting for heterogeneity, evidence of a causal relationship between schizophrenia and lung cancer risk was observed (odds ratio [OR]=1.001, 95% confidence interval [CI], 1.000–1.001; P=0.0155). In the sensitivity analysis, the causal effect of schizophrenia on the risk of lung cancer was consistent in both direction and degree. However, no evidence of causality or reverse causality between schizophrenia and other tumors was found.ConclusionThis study elucidated a causal relationship between the genetic predictors of schizophrenia and the risk of lung cancer, thereby providing a basis for the prevention, pathogenesis, and treatment of schizophrenia in patients with lung cancer

Longitudinal measurement invariance of the Child Problematic Trait Inventory in older Chinese children

The Child Problematic Traits Inventory (CPTI) is a newly developed informant-rated instrument to measure psychopathic traits during early childhood. The aim of this study was to examine the longitudinal measurement invariance of the CPTI in a group of Chinese schoolchildren. Mothers of 585 children aged 8 to 12 years (50% girls) completed the CPTI twice with one-year interval. Confirmatory factor analyses showed that the CPTI had strict invariance (i.e., equality of factor patterns, loadings, intercepts, and item uniqueness) across time. Furthermore, the internal consistencies for the CPTI subscales were good at both time points and the stability coefficients over time were moderate. Findings suggest that, in children aged 8 to 12 years old, changes in CPTI scores across time can be attributed to actual changes in the child’s psychopathic personality

Exploring risk factors for autoimmune diseases complicated by non-hodgkin lymphoma through regulatory T cell immune-related traits: a Mendelian randomization study

BackgroundThe effect of immune cells on autoimmune diseases (ADs) complicated by non-Hodgkin lymphoma (NHL) has been widely recognized, but a causal relationship between regulatory T cell (Treg) immune traits and ADs complicated by NHL remains debated.MethodsAggregate data for 84 Treg-related immune traits were downloaded from the Genome-Wide Association Study (GWAS) catalog, and GWAS data for diffuse large B-cell lymphoma (DLBCL; n=315243), follicular lymphoma (FL; n=325831), sjögren’s syndrome (SS; n=402090), rheumatoid arthritis (RA; n=276465), dermatopolymyositis (DM; n=311640), psoriasis (n=407876), atopic dermatitis (AD; n=382254), ulcerative colitis (UC; n=411317), crohn’s disease(CD; n=411973) and systemic lupus erythematosus (SLE; n=307587) were downloaded from the FinnGen database. The inverse variance weighting (IVW) method was mainly used to infer any causal association between Treg-related immune traits and DLBCL, FL, SS, DM, RA, Psoriasis, AD, UC, CD and SLE, supplemented by MR-Egger, weighted median, simple mode, and weighted mode. Moreover, we performed sensitivity analyses to assess the validity of the causal relationships.ResultsThere was a potential genetic predisposition association identified between CD39+ CD8br AC, CD39+ CD8br % T cell, and the risk of DLBCL (OR=1.51, p<0.001; OR=1.25, p=0.001) (adjusted FDR<0.1). Genetic prediction revealed potential associations between CD25++ CD8br AC, CD28- CD25++ CD8br % T cell, CD39+ CD8br % CD8br, and the risk of FL (OR=1.13, p=0.022; OR=1.28, p=0.042; OR=0.90, p=0.016) (adjusted FDR>0.1). Furthermore, SLE and CD exhibited a genetically predicted potential association with the CD39+ CD8+ Tregs subset. SS and DM were possibly associated with an increase in the quantity of the CD4+ Tregs subset; RA may have reduced the quantity of the CD39+ CD8+ Tregs subset, although no causal relationship was identified. Sensitivity analyses supported the robustness of our findings.ConclusionsThere existed a genetically predicted potential association between the CD39+ CD8+ Tregs subset and the risk of DLBCL, while SLE and CD were genetically predicted to be potentially associated with the CD39+ CD8+ Tregs subset. The CD39+ CD8+ Tregs subset potentially aided in the clinical diagnosis and treatment of SLE or CD complicated by DLBCL