Toric varieties with ample tangent bundle

We give a simple combinatorial proof of the toric version of Mori's theorem that the only $n$-dimensional smooth projective varieties with ample tangent bundle are the projective spaces $\mathbb{P}^n$.Comment: 7 pages, 2 figure

Schur positivity of difference of products of derived Schur polynomials

To any Schur polynomial $s_{\lambda}$ one can associated its derived polynomials $s_{\lambda}{(i)}$ $i=0,\ldots,|\lambda|$ by the rule $$s_{\lambda}(x_1+t,\ldots,x_n+t) = \sum_i s_{\lambda}^{(i)}(x_1,\ldots,x_n) t^i.$$ We conjecture that $$(s_{\lambda}^{(i)})^2 - s_{\lambda}^{(i-1)} s_{\lambda}^{(i+1)}$$ is always Schur positive and prove this when $i=1$ for rectangles $\lambda = (k^\ell)$, for hooks $\lambda = (k, 1^{\ell -1})$, and when $\lambda = (k,k,1)$ or $\lambda = (3,2^{k-1})$.Comment: 20 pages, 18 figure

DEVELOPMENT AND EVALUATION OF A SMARTPHONE VIRTUAL SEATING COACH APPLICATION TO FACILITATE POWERED SEAT FUNCTION USAGE FOR POWERED WHEELCHAIR USERS

Powered wheelchairs with powered seat functions (PSFs) are prescribed for wheelchair users who are unable to adjust their postures or manage their seating pressure independently because of motor and/ or sensory impairments. However, a novice powered-wheelchair user might not have appropriate or sufficient training on using PSFs due to the limited time in clinics or complex situations in real-life environments. The Human Engineering Research Laboratories have developed the Virtual Seating Coach (VSC) which records PSF usage and reminds users to adjust their PSFs. This research project was to develop a smartphone virtual seating coach (SVSC) and investigate several improvements. The SVSC used low-cost accelerometers to detect the seating angles which decreased the complexity of the sensor installation. By using the smartphone for information display and integrating the electronic components into the phone holder, the SVSC significantly decreased the dimension and increased the clearance of the whole system. A usability study has been conducted from five powered wheelchair users and five rehabilitation professionals to gather their feedback and refine the SVSC. In order to overcome the limitation of the internal storage in the system and enable the PSF usage to be reviewed by clinicians in real time, a prototype web service was constructed for data storage and data visualization. This web service allowed the SVSC to upload the daily PSF usage data from different users and provided the longitudinal PSF data plots for review. Ten powered wheelchair users were recruited for a three-week in-home trial to evaluate the effectiveness of SVSC. The compliance rate of performing repositioning exercise has increased around 44% after the intervention of the SVSC. The results also show that the users’ attention and decision toward the reminders can be predicted by context factors collected from the smartphones’ sensors (around 80% and 75% accuracy respectively). Furthermore, the negative correlation between the frequency of using PSFs and the wheelchair discomfort indicate the need for dynamic seating posture and suggested that the SVSC could implement this functionality to remind users to change their seating angle periodically to improve wheelchair comfort

DACH1 suppresses breast cancer as a negative regulator of CD44.

Dachshund homolog 1 (DACH1), a key cell fate determination factor, contributes to tumorigenesis, invasion, metastasis of human breast neoplasm. However, the exact molecular mechanisms for the anti-tumor roles of DACH1 in breast carcinoma are still lack of extensive understanding. Herein, we utilized immunohistochemistry (IHC) staining and public microarray data analysis showing that DACH1 was higher in normal breast, low-grade and luminal-type cancer in comparison with breast carcinoma, high-grade and basal-like tumors respectively. Additionally, both correlation analysis of public databases of human breast carcinoma and IHC analysis of mice xenograft tumors demonstrated that DACH1 inversely related to cancer stem cells (CSCs) markers, epithelial-mesenchymal transition (EMT) inducers and basal-enriched molecules, while cluster of differentiation 44 (CD44) behaved in an opposite manner. Furthermore, mice transplanted tumor model indicated that breast cancer cells Met-1 with up-regulation of DACH1 were endowed with remarkably reduced potential of tumorigenesis. Importantly, meta-analysis of 19 Gene Expression Omnibus (GEO) databases of breast cancer implicated that patients with higher DACH1 expression had prolonged time to death, recurrence and metastasis, while CD44 was a promising biomarker predicting worse overall survival (OS) and metastasis-free survival (MFS). Collectively, our study indicated that CD44 might be a novel target of DACH1 in breast carcinoma

Rapid Determination of Saponins in the Honey-Fried Processing of Rhizoma Cimicifugae by Near Infrared Diffuse Reflectance Spectroscopy.

ObjectiveA model of Near Infrared Diffuse Reflectance Spectroscopy (NIR-DRS) was established for the first time to determine the content of Shengmaxinside I in the honey-fried processing of Rhizoma Cimicifugae.MethodsShengmaxinside I content was determined by high-performance liquid chromatography (HPLC), and the data of the honey-fried processing of Rhizoma Cimicifugae samples from different batches of different origins by NIR-DRS were collected by TQ Analyst 8.0. Partial Least Squares (PLS) analysis was used to establish a near-infrared quantitative model.ResultsThe determination coefficient R² was 0.9878. The Cross-Validation Root Mean Square Error (RMSECV) was 0.0193%, validating the model with a validation set. The Root Mean Square Error of Prediction (RMSEP) was 0.1064%. The ratio of the standard deviation for the validation samples to the standard error of prediction (RPD) was 5.5130.ConclusionThis method is convenient and efficient, and the experimentally established model has good prediction ability, and can be used for the rapid determination of Shengmaxinside I content in the honey-fried processing of Rhizoma Cimicifugae

Scalar Induced Gravitational Waves from Finslerian Inflation and Pulsar Timing Arrays Observations

The recent data from NANOGrav provide strong evidence of the existence of the \acp{SGWB}. We investigate \acp{SIGW} from Finslerian inflation as a potential source of stochastic gravitational wave background. Small-scale ($\lesssim$1 Mpc) statistically anisotropic primordial scalar perturbations can be generated in Finslerian inflation. The second order \acp{SIGW} from Finslerian inflation are also anisotropic on small scales. After spatially averaging the small-scale anisotropic \acp{SIGW}, we obtain the large-scale isotropic \acp{SGWB}. We find that the parameters of small-scale anisotropic primordial power spectrum generated by Finslerian inflation affect the \acp{PTA} observations of large-scale isotropic gravitational wave background

The Impact on the Brazilian Economy of the Olympic Games in Rio De Janeiro in 2016

Purpose: This study aims to examine the influence of channel power and influence strategy, in terms of non-coercive strategies, on sanitary equipment manufacturers' relationships with channel members and channel performance.   Theoretical framework: The study is based on the literature on channel relationships, which suggests that using an influence strategy can contribute to managing the relationship with the channel members and benefit organization performance.   Design/Methodology/Approach:  In this study, we sampled from a sanitary equipment manufacturer's channel strategy. We used survey data to examine the effect of channel management strategies from sanitary equipment manufacturers on distributors.   Findings: The finding indicates that a supplier using economic power tends to adopt non-coercive strategies. In addition, economic power and non-coercive strategies positively affect the continuity of the relationship with distributors. Relationship continuity between manufacturers and distributors positively impacts whole channel performance.   Originality/Value: This study sampled the distributors in the sanitary equipment industry, a market in which the consumers are not knowledgeable about the products. Most consumers base their purchase decisions heavily on the channel member’s recommendations. Therefore, how to manage the relationship with the channel members is critical to understand.   Research, Practical & Social implications: Distributors are regarded as an extension of the company's sales capabilities. Channels have always held an essential position in the industry. Maintaining relationships between distributors and improving channel performance is a critical question in distribution management

Stanford-ORB: A Real-World 3D Object Inverse Rendering Benchmark

We introduce Stanford-ORB, a new real-world 3D Object inverse Rendering Benchmark. Recent advances in inverse rendering have enabled a wide range of real-world applications in 3D content generation, moving rapidly from research and commercial use cases to consumer devices. While the results continue to improve, there is no real-world benchmark that can quantitatively assess and compare the performance of various inverse rendering methods. Existing real-world datasets typically only consist of the shape and multi-view images of objects, which are not sufficient for evaluating the quality of material recovery and object relighting. Methods capable of recovering material and lighting often resort to synthetic data for quantitative evaluation, which on the other hand does not guarantee generalization to complex real-world environments. We introduce a new dataset of real-world objects captured under a variety of natural scenes with ground-truth 3D scans, multi-view images, and environment lighting. Using this dataset, we establish the first comprehensive real-world evaluation benchmark for object inverse rendering tasks from in-the-wild scenes, and compare the performance of various existing methods.Comment: NeurIPS 2023 Datasets and Benchmarks Track. The first two authors contributed equally to this work. Project page: https://stanfordorb.github.io