The isometric immersion of surfaces with finite total curvature

In this paper, we study the smooth isometric immersion of a complete simply connected surface with a negative Gauss curvature in the three-dimensional Euclidean space. For a surface with a finite total Gauss curvature and appropriate oscillations of the Gauss curvature, we prove the global existence of a smooth solution to the Gauss-Codazzi system and thus establish a global smooth isometric immersion of the surface into the three-dimensional Euclidean space. Based on a crucial observation that some linear combinations of the Riemann invariants decay faster than others, we reformulate the Gauss-Codazzi system as a symmetric hyperbolic system with a partial damping. Such a damping effect and an energy approach permit us to derive global decay estimates and meanwhile control the non-integrable coefficients of nonlinear terms.Comment: 53 pages, 1 figur

Влияние Китайской реформы налога на добавленную стоимость 2009 года на инвестиции и занятость – эмпирический анализ данных Национального налогового исследования

The article analyzes the impact of the 2009 VAT reform in China on investment and employment. This reform was a key step in improving the VAT tax system in the long term, and one of the key measures to structurally reduce taxes in response to the global financial crisis in the short term. The data for this analysis were provided by the “National Tax Survey” jointly conducted by the Chinese Ministry of Finance and State Administration of Taxation. We measured the impact of the VAT reform using the difference-in-differences method: we compared the difference between the experimental group and the control group before and after the reform. There were two kinds of organizations in our control group. The first kind consisted of enterprises that did not pay the VAT and small-scale VAT-paying enterprises that did not subtract the input taxes for fixed assets investment. The second kind comprised organizations that had not been included in pilot experiments before 2009 and foreign-invested corporations that were allowed to deduct the input tax for fixed asset investment before and after 2009. The experimental group consisted of ordinary VAT-paying enterprises that had not been included in the pilot study before 2009 and were affected by the 2009 reform. Our estimations lead us to the conclusion that the VAT tax reform of 2009 significantly enhanced the companies’ physical investment in machinery and equipment, but had no impact on employment. When comparing physical investment and employment in 2007 with 2008 and 2009, we detected a downward trend, which may reflect the impact of the global financial crisis on Chinese business. The total corporate profits and profit margins have little impact on business investment and employment, while the asset size and the tax burden show a significant positive impact. Thus, the reform significantly increased business investment in fixed assets, but had no obvious effect on employment.For citationWang Dehua, Wu Han. The Impact of 2009 VAT Reform on Enterprise Investment and Employment – Empirical Analysis Based on Chinese Tax Survey Data. Journal of Tax Reform. 2019;5(2):166–176. DOI: 10.15826/jtr.2019.5.2.066Article infoReceived May 17, 2019; accepted August 11, 2019В статье анализируется влияние реформы налога на добавленную стоимость, проведенной в Китае в 2009 г., на инвестиции и занятость. В долгосрочной перспективе реформа должна была кардинально улучшить налогообложение добавленной стоимости, а в краткосрочной – ответить структурным снижением налогов на глобальный финансовый кризис. Использованы данные «Национального налогового исследования» проводимого совместно Министерством финансов Китая и Государственной налоговой администрацией. Влияние реформы НДС оценивалось методом «разность-в разностях», путем сравнения экспериментальной и контрольной групп до и после реформы. В контрольную группу были включены два вида организаций. Во-первых, неплательщики НДС и мелкие налогоплательщики, не применяющие вычет входного НДС по инвестициям в основной капитал. Во-вторых, организации, включенные в пилотный эксперимент по НДС до 2009 г. и корпорации с иностранными инвестициями, которым было разрешено вычитать входящий налог для инвестиций в основной капитал до и после 2009 г. В экспериментальную группу включены обычные организации – плательщики НДС, которые не были включены в пилотный эксперимент по НДС до 2009 г., на которых реформа НДС оказала свое воздействие. На основе проведенной оценки был сделан вывод, что реформа НДС значительно увеличила объемы инвестиций в машины и оборудование, но не оказала воздействия на занятость. При этом, сравнение физических объемов инвестиций и занятости в 2007 и 2008–2009 гг. показывает тенденцию показателей к снижению, что отражает влияние на китайский бизнес глобального финансового кризиса. Общая корпоративная прибыль и маржинальная прибыль мало повлияли на инвестиции и занятость, в то время как величина активов и налоговая нагрузка оказали на них значительное положительное влияние. Основным выводом исследования является то, что реформа повлияла на существенное увеличение инвестиций бизнеса в основной капитал, но не оказала заметного влияния на занятость.Для цитированияВан Дэхуа, У Хань. Влияние Китайской реформы налога на добавленную стоимость 2009 года на инвестиции и занятость – эмпирический анализ данных Национального налогового исследования // Journal of Tax Reform. — 2019. — Т. 5, № 2. — С. 166–176. — DOI: 10.15826/jtr.2019.5.2.066Информация о статьеДата поступления 17 мая 2019 г.; дата принятия к печати 11 августа 2019 г

The Mechanism of Downregulated Interstitial Fluid Drainage Following Neuronal Excitation.

The drainage of brain interstitial fluid (ISF) has been observed to slow down following neuronal excitation, although the mechanism underlying this phenomenon is yet to be elucidated. In searching for the changes in the brain extracellular space (ECS) induced by electrical pain stimuli in the rat thalamus, significantly decreased effective diffusion coefficient (DECS) and volume fraction (α) of the brain ECS were shown, accompanied by the slowdown of ISF drainage. The morphological basis for structural changes in the brain ECS was local spatial deformation of astrocyte foot processes following neuronal excitation. We further studied aquaporin-4 gene (APQ4) knockout rats in which the changes of the brain ECS structure were reversed and found that the slowed DECS and ISF drainage persisted, confirming that the down-regulation of ISF drainage following neuronal excitation was mainly attributable to the release of neurotransmitters rather than to structural changes of the brain ECS. Meanwhile, the dynamic changes in the DECS were synchronized with the release and elimination processes of neurotransmitters following neuronal excitation. In conclusion, the downregulation of ISF drainage following neuronal excitation was found to be caused by the restricted diffusion in the brain ECS, and DECS mapping may be used to track the neuronal activity in the deep brain

COVID-Dynamic: A Large-Scale Longitudinal Study of Socioemotional and Behavioral Change Across the Pandemic

The COVID-19 pandemic has caused enormous societal upheaval globally. In the US, beyond the devastating toll on life and health, it triggered an economic shock unseen since the great depression and laid bare preexisting societal inequities. The full impacts of these personal, social, economic, and public-health challenges will not be known for years. To minimize societal costs and ensure future preparedness, it is critical to record the psychological and social experiences of individuals during such periods of high societal volatility. Here, we introduce, describe, and assess the COVID-Dynamic dataset, a within-participant longitudinal study conducted from April 2020 through January 2021, that captures the COVID-19 pandemic experiences of \u3e1000 US residents. Each of 16 timepoints combines standard psychological assessments with novel surveys of emotion, social/political/moral attitudes, COVID-19-related behaviors, tasks assessing implicit attitudes and social decision-making, and external data to contextualize participants’ responses. This dataset is a resource for researchers interested in COVID-19-specific questions and basic psychological phenomena, as well as clinicians and policy-makers looking to mitigate the effects of future calamities

Interdigitated Back‐Contacted Carbon Nanotube–Silicon Solar Cells

Carbon/silicon heterojunctions provide a new perspective for silicon solar cells and in particular those made from carbon nanotubes (CNTs) have already achieved industrial-level power conversion efficiency and device size when using organic passivation and a back-junction design. However, the current state of the art device geometry for silicon photovoltaics is the interdigitated back contact (IBC) cell and this has yet to be demonstrated for CNT/Si solar cells due to the complexity of fabricating the required patterns. Herein, IBC-CNT solar cells are demonstrated via the simple spin coating of a conductive hole-selective passivating film and the evaporation of buried silicon oxide/magnesium electron-selective contacts for both polarities. The CNT coverage area fraction (fCNT) and the gap between the two polarities are optimized to minimize electrical shading loss and ensure high photocarrier collection. Large-area (4.76 cm2) highly efficient (17.53%) IBC-CNT solar cells with a Voc of 651 mV and Jsc of 40.56 mA cm−2 are demonstrated and are prepared with one alignment step for the CNT/Si contact, and photolithographic-free and room-temperature processes. These performance parameters are among the best for solution-processed dopant-free IBC schemes and indicate the feasibility of using low-dimensional carbon materials in IBC solar cells

Association of miR-196a2 and miR-27a polymorphisms with gestational diabetes mellitus susceptibility in a Chinese population

IntroductionMiR-196a2 and miR-27a play a key role in the regulation of the insulin signaling pathway. Previous studies have indicated that miR-27a rs895819 and miR-196a2 rs11614913 have a strong association with type 2 diabetes (T2DM), but very few studies have investigated their role in gestational diabetes mellitus (GDM).MethodsA total of 500 GDM patients and 502 control subjects were enrolled in this study. Using the SNPscan™ genotyping assay, rs11614913 and rs895819 were genotyped. In the data treatment process, the independent sample t test, logistic regression and chi-square test were used to evaluate the differences in genotype, allele, and haplotype distributions and their associations with GDM risk. One-way ANOVA was conducted to determine the differences in genotype and blood glucose level.ResultsThere were obvious differences in prepregnancy body mass index (pre-BMI), age, systolic blood pressure (SBP), diastolic blood pressure (DBP) and parity between GDM and healthy subjects (P < 0.05). After adjusting for the above factors, the miR-27a rs895819 C allele was still associated with an increased risk of GDM (C vs. T: OR=1.245; 95% CI: 1.011-1.533; P = 0.039) and the TT-CC genotype of rs11614913-rs895819 was related to an increased GDM risk (OR=3.989; 95% CI: 1.309-12.16; P = 0.015). In addition, the haplotype T-C had a positive interaction with GDM (OR=1.376; 95% CI: 1.075-1.790; P=0.018), especially in the 18.5 ≤ pre-BMI < 24 group (OR=1.403; 95% CI: 1.026-1.921; P=0.034). Moreover, the blood glucose level of the rs895819 CC genotype was significantly higher than that of the TT and TC genotypes (P < 0.05). The TT-CC genotype of rs11614913-rs895819 showed that the blood glucose level was significantly higher than that of the other genotypes.DiscussionOur findings suggest that miR-27a rs895819 is associated with increased GDM susceptibility and higher blood glucose levels

Rankitect: Ranking Architecture Search Battling World-class Engineers at Meta Scale

Neural Architecture Search (NAS) has demonstrated its efficacy in computer vision and potential for ranking systems. However, prior work focused on academic problems, which are evaluated at small scale under well-controlled fixed baselines. In industry system, such as ranking system in Meta, it is unclear whether NAS algorithms from the literature can outperform production baselines because of: (1) scale - Meta ranking systems serve billions of users, (2) strong baselines - the baselines are production models optimized by hundreds to thousands of world-class engineers for years since the rise of deep learning, (3) dynamic baselines - engineers may have established new and stronger baselines during NAS search, and (4) efficiency - the search pipeline must yield results quickly in alignment with the productionization life cycle. In this paper, we present Rankitect, a NAS software framework for ranking systems at Meta. Rankitect seeks to build brand new architectures by composing low level building blocks from scratch. Rankitect implements and improves state-of-the-art (SOTA) NAS methods for comprehensive and fair comparison under the same search space, including sampling-based NAS, one-shot NAS, and Differentiable NAS (DNAS). We evaluate Rankitect by comparing to multiple production ranking models at Meta. We find that Rankitect can discover new models from scratch achieving competitive tradeoff between Normalized Entropy loss and FLOPs. When utilizing search space designed by engineers, Rankitect can generate better models than engineers, achieving positive offline evaluation and online A/B test at Meta scale.Comment: Wei Wen and Kuang-Hung Liu contribute equall

Isometric Immersions and Compensated Compactness

A fundamental problem in differential geometry is to characterize intrinsic metrics on a two-dimensional Riemannian manifold ${\mathcal M}^2$ which can be realized as isometric immersions into $\R^3$. This problem can be formulated as initial and/or boundary value problems for a system of nonlinear partial differential equations of mixed elliptic-hyperbolic type whose mathematical theory is largely incomplete. In this paper, we develop a general approach, which combines a fluid dynamic formulation of balance laws for the Gauss-Codazzi system with a compensated compactness framework, to deal with the initial and/or boundary value problems for isometric immersions in $\R^3$. The compensated compactness framework formed here is a natural formulation to ensure the weak continuity of the Gauss-Codazzi system for approximate solutions, which yields the isometric realization of two-dimensional surfaces in $\R^3$. As a first application of this approach, we study the isometric immersion problem for two-dimensional Riemannian manifolds with strictly negative Gauss curvature. We prove that there exists a $C^{1,1}$ isometric immersion of the two-dimensional manifold in $\R^3$ satisfying our prescribed initial conditions. TComment: 25 pages, 6 figue