Rank 3 Quadratic Generators of Veronese Embeddings

Let $L$ be a very ample line bundle on a projective scheme $X$ defined over an algebraically closed field $\Bbbk$ with ${\rm char}~\Bbbk \neq 2$. We say that $(X,L)$ satisfies property $\mathsf{QR}(k)$ if the homogeneous ideal of the linearly normal embedding $X \subset \mathbb{P}H^0 (X,L)$ can be generated by quadrics of rank $\leq k$. Many classical varieties such as Segre-Veronese embeddings, rational normal scrolls and curves of high degree satisfy property $\mathsf{QR}(4)$. In this paper, we first prove that if ${\rm char}~\Bbbk \neq 3$ then $(\mathbb{P}^n , \mathcal{O}_{\mathbb{P}^n} (d))$ satisfies property $\mathsf{QR}(3)$ for all $n \geq 1$ and $d \geq 2$. We also investigate an asymptotic behavior of property $\mathsf{QR}(3)$ for any projective scheme. Namely, we prove that $(i)$ if $X \subset \mathbb{P} H^0 (X,L)$ is $m$-regular then $(X,L^d )$ satisfies property $\mathsf{QR}(3)$ for all $d \geq m$ and $(ii)$ if $A$ is an ample line bundle on $X$ then $(X,A^d )$ satisfies property $\mathsf{QR}(3)$ for all sufficiently large even number $d$. These results provide an affirmative evidence for the expectation that property $\mathsf{QR}(3)$ holds for all sufficiently ample line bundles on $X$, as in the cases of Green-Lazarsfeld's condition $\mathrm{N}_p$ and Eisenbud-Koh-Stillman's determininantal presentation in [EKS88]. Finally, when ${\rm char}~\Bbbk = 3$ we prove that $(\mathbb{P}^n , \mathcal{O}_{\mathbb{P}^n} (2))$ fails to satisfy property $\mathsf{QR}(3)$ for all $n \geq 3$.Comment: 24 page

A Comparison of Flare Forecasting Methods. III. Systematic Behaviors of Operational Solar Flare Forecasting Systems

A workshop was recently held at Nagoya University (31 October – 02 November 2017), sponsored by the Center for International Collaborative Research, at the Institute for Space-Earth Environmental Research, Nagoya University, Japan, to quantitatively compare the performance of today’s operational solar flare forecasting facilities. Building upon Paper I of this series (Barnes et al. 2016), in Paper II (Leka et al. 2019) we described the participating methods for this latest comparison effort, the evaluation methodology, and presented quantitative comparisons. In this paper we focus on the behavior and performance of the methods when evaluated in the context of broad implementation differences. Acknowledging the short testing interval available and the small number of methods available, we do find that forecast performance: 1) appears to improve by including persistence or prior flare activity, region evolution, and a human “forecaster in the loop”; 2) is hurt by restricting data to disk-center observations; 3) may benefit from long-term statistics, but mostly when then combined with modern data sources and statistical approaches. These trends are arguably weak and must be viewed with numerous caveats, as discussed both here and in Paper II. Following this present work, we present in Paper IV a novel analysis method to evaluate temporal patterns of forecasting errors of both types (i.e., misses and false alarms; Park et al. 2019). Hence, most importantly, with this series of papers we demonstrate the techniques for facilitating comparisons in the interest of establishing performance-positive methodologies

Ruggedness and Interlaboratory Studies for Asphalt Mixture Performance Tester (AMPT) Cyclic Fatigue Test: Phase \u2161 Report

DTFH6117C00037This report highlights findings from Phase \u2161 of a project designed to develop precision statements for cyclic fatigue testing using an asphalt mixture performance tester (AMPT). These standards include American Association of State Highway and Transportation Officials (AASHTO) TP 107-22 and AASHTO TP 133-21, which apply to 100-mm-diameter and 38-mm-diameter test specimens, respectively.(1,2) Seven laboratories participated in an interlaboratory study of the AMPT cyclic fatigue tests designed according to ASTM E691-20 and ASTM C670-15(4,5) . Researchers in these laboratories conducted dynamic modulus and cyclic fatigue testing of three mixtures for each specimen geometry. The results were used to establish repeatability and reproducibility precision limits for damage characteristic curve and failure criterion results of the AMPT cyclic fatigue tests; these limits reflect the variation in test results that will be exceeded with a probability of 5 percent if the test is executed properly. The researchers introduced a refined functional data metric to capture the variation in damage characteristic curve results. All precision limits were defined as a function of the mixture nominal maximum aggregate size (NMAS) except the failure criterion reproducibility, which did not follow a consistent trend with respect to NMAS. The established repeatability limits quantify the acceptable variation among three test determinations (specimens) obtained within a laboratory on a single material. The reproducibility limits quantify the acceptable variation between average test results of two laboratories conducted on the same material

Relative contributions of the host genome, microbiome, and environment to the metabolic profile

Background Metabolic syndrome is as a well-known risk factor for cardiovascular disease, which is associated with both genetic and environmental factors. Recently, the microbiome composition has been shown to affect the development of metabolic syndrome. Thus, it is expected that the complex interplay among host genetics, the microbiome, and environmental factors could affect metabolic syndrome. Objective To evaluate the relative contributions of genetic, microbiome, and environmental factors to metabolic syndrome using statistical approaches. Methods Data from the prospective Korean Association REsource project cohort (N = 8476) were used in this study, including single-nucleotide polymorphisms, phenotypes and lifestyle factors, and the urine-derived microbial composition. The effect of each data source on metabolic phenotypes was evaluated using a heritability estimation approach and a prediction model separately. We further experimented with various types of metagenomic relationship matrices to estimate the phenotypic variance explained by the microbiome. Results With the heritability estimation, five of the 11 metabolic phenotypes were significantly associated with metagenome-wide similarity. We found significant heritability for fasting glucose (4.8%), high-density lipoprotein cholesterol (4.9%), waist-hip ratio (7.7%), and waist circumference (5.6%). Microbiome compositions provided more accurate estimations than genetic factors for the same sample size. In the prediction model, the contribution of each source to the prediction accuracy varied for each phenotype. Conclusion The effects of host genetics, the metagenome, and environmental factors on metabolic syndrome were minimal. Our statistical analysis suffers from a small sample size, and the measurement error is expected to be substantial. Further analysis is necessary to quantify the effects with better accuracy.N

A Controllable Agent by Subgoals in Path Planning Using Goal-Conditioned Reinforcement Learning

The aim of path planning is to search for a path from the starting point to the goal. Numerous studies, however, have dealt with a single predefined goal. That is, an agent who has completed learning cannot reach other goals that have not been visited in the training. In the present study, we propose a novel reinforcement learning (RL) framework for an agent reachable to any subgoal as well as the final goal in path planning. To do this, we utilize goal-conditioned RL and propose bidirectional memory editing to obtain various bidirectional trajectories of the agent. Bidirectional memory editing can generate various behavior and subgoals of the agent from the limited trajectory. Then, the generated subgoals and behaviors of the agent are trained on the policy network so that the agent can reach any subgoals from any starting point. In addition, we present reward shaping for the short path of the agent to reach the goal. In the experimental result, the agent was able to reach the various goals that had never been visited by the agent during the training. We confirmed that the agent could perform difficult missions, such as a round trip, and the agent used the shorter route with reward shaping

Development of Precipitation-Strengthened Al0.8NbTiVM (M = Co, Ni) Light-Weight Refractory High-Entropy Alloys

Single-phase solid-solution refractory high-entropy alloys (RHEAs) have been receiving significant attention due to their excellent mechanical properties and phase stability at elevated temperatures. Recently, many studies have been reported regarding the precipitation-enhanced alloy design strategy to further improve the mechanical properties of RHEAs at elevated temperatures. In this study, we attempted to develop precipitation-hardened light-weight RHEAs via addition of Ni or Co into Al0.8NbTiV HEA. The added elements were selected due to their smaller atomic radius and larger mixing enthalpy, which is known to stimulate the formation of precipitates. The addition of the Ni or Co leads to the formation of the sigma precipitates with homogeneous distribution. The formation and homogeneous distribution of sigma particles plays a critical role in improvement of yield strength. Furthermore, the Al0.8NbTiVM0.2 (M = Co, Ni) HEAs show excellent specific yield strength compared to single-phase AlNbTiV and NbTiVZr RHEA alloys and conventional Ni-based superalloy (Inconel 718) at elevated temperatures

Role of an unclassified Lachnospiraceae in the pathogenesis of type 2 diabetes: a longitudinal study of the urine microbiome and metabolites

Recent investigations have revealed that the human microbiome plays an essential role in the occurrence of type 2 diabetes (T2D). However, despite the importance of understanding the involvement of the microbiota throughout the body in T2D, most studies have focused specifically on the intestinal microbiota. Extracellular vesicles (EVs) have been recently found to provide important evidence regarding the mechanisms of T2D pathogenesis, as they act as key messengers between intestinal microorganisms and the host. Herein, we explored microorganisms potentially associated with T2D by tracking changes in microbiota-derived EVs from patient urine samples collected three times over four years. Mendelian randomization analysis was conducted to evaluate the causal relationships among microbial organisms, metabolites, and clinical measurements to provide a comprehensive view of how microbiota can influence T2D. We also analyzed EV-derived metagenomic (N = 393), clinical (N = 5032), genomic (N = 8842), and metabolite (N = 574) data from a prospective longitudinal Korean community-based cohort. Our data revealed that GU174097_g, an unclassified Lachnospiraceae, was associated with T2D (beta = -189.13; p = 0.00006), and it was associated with the ketone bodies acetoacetate and 3-hydroxybutyrate (r = -0.0938 and -0.0829, respectively; p = 0.0022 and 0.0069, respectively). Furthermore, a causal relationship was identified between acetoacetate and HbA1c levels (beta = 0.0002; p = 0.0154). GU174097_g reduced ketone body levels, thus decreasing HbA1c levels and the risk of T2D. Taken together, our findings indicate that GU174097_g may lower the risk of T2D by reducing ketone body levels. Diabetes: a little help from the microbiome A microbe that may help protect against type II diabetes has been detected by examining extracellular vesicles (EVs), tiny membrane-wrapped packages secreted by human cells and by the bacteria making up the microbiome. Examining EVs allows researchers to sample microbial populations other than the intensively studied intestinal microbiome. Sungho Won, Seoul National University, and Geum-Sook Hwang, Korea Basic Science Institute, Seoul, and coworkers studied the microbial EVs in urine samples collected from South Korean subjects over four years. They identified a previously unclassified bacterial species in the family Lachnospiraceae that was associated with lower risk of developing type II diabetes. Further investigation showed that these bacteria may break down ketone bodies, metabolic byproducts that signal disrupted sugar metabolism leading to diabetes. These results contribute to understanding how the microbiome contributes to metabolic health and disease.N