Intersections of homogeneous Cantor sets and beta-expansions

Let $\Gamma_{\beta,N}$ be the $N$-part homogeneous Cantor set with $\beta\in(1/(2N-1),1/N)$. Any string $(j_\ell)_{\ell=1}^\N$ with $j_\ell\in\{0,\pm 1,...,\pm(N-1)\}$ such that $t=\sum_{\ell=1}^\N j_\ell\beta^{\ell-1}(1-\beta)/(N-1)$ is called a code of $t$. Let $\mathcal{U}_{\beta,\pm N}$ be the set of $t\in[-1,1]$ having a unique code, and let $\mathcal{S}_{\beta,\pm N}$ be the set of $t\in\mathcal{U}_{\beta,\pm N}$ which make the intersection $\Gamma_{\beta,N}\cap(\Gamma_{\beta,N}+t)$ a self-similar set. We characterize the set $\mathcal{U}_{\beta,\pm N}$ in a geometrical and algebraical way, and give a sufficient and necessary condition for $t\in\mathcal{S}_{\beta,\pm N}$. Using techniques from beta-expansions, we show that there is a critical point $\beta_c\in(1/(2N-1),1/N)$, which is a transcendental number, such that $\mathcal{U}_{\beta,\pm N}$ has positive Hausdorff dimension if $\beta\in(1/(2N-1),\beta_c)$, and contains countably infinite many elements if $\beta\in(\beta_c,1/N)$. Moreover, there exists a second critical point $\alpha_c=\big[N+1-\sqrt{(N-1)(N+3)}\,\big]/2\in(1/(2N-1),\beta_c)$ such that $\mathcal{S}_{\beta,\pm N}$ has positive Hausdorff dimension if $\beta\in(1/(2N-1),\alpha_c)$, and contains countably infinite many elements if $\beta\in[\alpha_c,1/N)$.Comment: 23 pages, 4 figure

Drought events and their effects on vegetation productivity in China

Many parts of the world have experienced frequent and severe droughts during the last few decades. Most previous studies examined the effects of specific drought events on vegetation productivity. In this study, we characterized the drought events in China from 1982 to 2012 and assessed their effects on vegetation productivity inferred from satellite data. We first assessed the occurrence, spatial extent, frequency, and severity of drought using the Palmer Drought Severity Index (PDSI). We then examined the impacts of droughts on China\u27s terrestrial ecosystems using the Normalized Difference Vegetation Index (NDVI). During the period 1982–2012, China\u27s land area (%) experiencing drought showed an insignificant trend. However, the drought conditions had been more severe over most regions in northern parts of China since the end of the 1990s, indicating that droughts hit these regions more frequently due to the drier climate. The severe droughts substantially reduced annual and seasonal NDVI. The magnitude and direction of the detrended NDVI under drought stress varied with season and vegetation type. The inconsistency between the regional means of PDSI and detrended NDVI could be attributed to different responses of vegetation to drought and the timing, duration, severity, and lag effects of droughts. The negative effects of droughts on vegetation productivity were partly offset by the enhancement of plant growth resulting from factors such as lower cloudiness, warming climate, and human activities (e.g., afforestation, improved agricultural management practices)

Quantum-enhanced radiometry via approximate quantum error correction

By exploiting the exotic quantum states of a probe, it is possible to realize efficient sensors that are attractive for practical metrology applications and fundamental studies. Similar to other quantum technologies, quantum sensing is suffering from noises and thus the experimental developments are hindered. Although theoretical schemes based on quantum error correction (QEC) have been proposed to combat noises, their demonstrations are prevented by the stringent experimental requirements, such as perfect quantum operations and the orthogonal condition between the sensing interaction Hamiltonian and the noise Lindbladians. Here, we report an experimental demonstration of a quantum enhancement in sensing with a bosonic probe with different encodings, by exploring the large Hilbert space of the bosonic mode and developing both the approximate QEC and the quantum jump tracking approaches. In a practical radiometry scenario, we attain a 5.3 dB enhancement of sensitivity, which reaches $9.1\times10^{-4}\,\mathrm{Hz}^{-1/2}$ when measuring the excitation population of a receiver mode. Our results demonstrate the potential of quantum sensing with near-term quantum technologies, not only shedding new light on the quantum advantage of sensing by revealing its difference from other quantum applications, but also stimulating further efforts on bosonic quantum technologies.Comment: 8 pages, 4 figure

Cyclooxygenase inhibitors use is associated with reduced risk of esophageal adenocarcinoma in patients with Barrett's esophagus: A meta-analysis

Background: Esophageal adenocarcinoma (EAC) has high mortality and is increasing in incidence. Barrett's esophagus (BE) increases the risk for EAC. Studies have reported inconsistent findings on the association between use of cyclooxygenase (COX) inhibitors and the risk of neoplastic progression in BE patients. Therefore, we performed a meta-analysis to investigate this association. Methods: A meta-analysis was undertaken among a total of 9 observational studies using fixed- and random-effects models, comprising 5446 participants; 605 had EAC or high-grade dysplasia (HGD). Results: Overall, COX inhibitors use was associated with a reduced risk of EAC/HGD among BE patients (relative risk (RR)=0.64, 95% confidence interval (CI)=0.53-0.77). Aspirin use also reduced the risk of EAC/HGD (RR=0.63, 95% CI=0.43-0.94), as well as non-aspirin COX inhibitors (RR=0.50, 95% CI=0.32-0.78). The chemopreventive effect seemed to be independent of duration response. Conclusions: Cyclooxygenase inhibitors use is associated with a reduced risk of developing EAC in patients with BE. Both low-dose aspirin and non-aspirin COX inhibitors are associated with a reduced risk of neoplasia. More well-designed randomised controlled trials are needed to increase our understanding of the chemopreventive effect of COX inhibitors

Research on a Heat-supply Network Dispatching System Based on Geographical Information System (GIS)

In order to reduce heating systematic operation and maintenance expenses, aimed at the current standards of a heat-supply network based on GIS, combine with a national program of 'tenth-five-year-plan', the authors have developed a Heat-supply Network Dispatching System (HNDS). The system, based on Oracle database and Mapgis 6.5, compiles with Visual C++ software. With computer and communication techniques, the system dynamic inspects parameters and information of a heat-supply network, achieves real-time dispatching and automatic information management. Based on a relief map, the system combines data on inspection equipment with those of the heat-supply network, intuitively displays the state of inspected equipment and the heat-supply network. Using the models of forecast and analysis, the system is reasonably configured for each heat supply dispatch system. Results applied to demonstration projects prove that the system possesses characteristics of stability and security

Study of a Fault Analysis System for a Heat Supply Network Based on GIS

Conventional methods cannot satisfy the request of the layout and operation management in a heating system. The geographical information system (GIS) in a heat supply network can realize information conformity and information share roundly, which makes management of information improve to a new level in district heating. When fault of the heat supply network occurs, the traditional methods make fault reaction time long and the efficiency low, and enlarge the fault harm. The system of fault analysis in a heat supply network based on GIS mainly simulates and calculates according to various fault conditions. By selection of valve shut-off schemes in fault conditions and simulation of various fault conditions, the fault treatment scheme can be optimized. The results of simulation can be shown in the GIS graphics with the aid of advanced image display function of GIS. The application of this system brings great significance to heating system on the management enhancing, fault number-reducing, quick decision-making and influence area diminishing in case of fault