Periodic Weighted Sums of Binomial Coefficients

Using elementary methods, we establish old and new relations between binomial coefficients, Fibonacci numbers, Lucas numbers, and more.Comment: Currently under review. Substantially revise

Exploration of Sustainable Urban Transportation Development in China through the Forecast of Private Vehicle Ownership

With the acceleration of China&rsquo s urbanization process, the urban transportation problem has become increasingly serious. The rapid expansion of private vehicle ownership, in particular, has become one of the barriers to the realization of sustainable urban transition. This paper applied the Gompertz model to analyze the non-linear relationship between private vehicle ownership and per capita GDP in China using provincial data. In addition, we forecasted private vehicle ownership for 31 Chinese provinces for the period of 2019&ndash 2030 and predicted the time to reach the upper limit of 1000 people vehicle ownership of each province according to different scenarios. The main findings revealed that the number of private vehicles owned in China&rsquo s provinces was in line with &ldquo S&rdquo -shaped development and was currently in the process of accelerated growth. Under the scenario of an annual per capita GDP growth rate of 6%, China&rsquo s private vehicle ownership will reach 246 million, 375 million, and 475 million in 2020, 2025, and 2030, respectively. This indicates that China&rsquo s expansion of private vehicle ownership will generate significant challenges, such as on-road vehicle-related fossil fuel consumption, pollutant emissions, traffic congestion, and scrapped vehicle recycling. These issues will become increasingly prominent. In provinces such as Hubei, Hebei, Hunan, and other central provinces that have a 50&ndash 60% urbanization rate, the large potential for income promotion will significantly stimulate the increase in private vehicle ownership, and the upper limit of 1000 people vehicle ownership in each province will be reached in 2032, 2037, and 2046 with annual per capita GDP growth rates of 8%, 6%, and 4%, respectively. Document type: Articl

Evaluation of Tung Oil (Vernicia fordii (Hemsl.)) for Controlling Termites

In worldwide, the use of chemical pesticides to protect wood has been greatly restricted. In recent years, a large number of researchers devoted to the search for natural, safe and non-polluting bioactive chemical compounds from plants as an alternative to synthetic organic chemical preservative. In Chinese folk, tung oil can be used as paint for wooden furniture to protect them from pests. This study aimed to evaluate the chemical compositions of raw and heated tung oil and their activity against termite. In choice bioassays, weight loss of wood treated with 5% raw or heated tung oil after 4 weeks was significantly less than that of the control group. In no-choice bioassays, there was a significant difference in termite survival and wood weight loss on raw and heated tung oil-treated wood. When tung oil-treatment concentrations increased to 5%, wood weight loss was less than 10%. There was no significant difference in termite survival and wood weight loss between raw and heated tung oil-treated wood. Survival of termites in both tung oil wood treatments was significantly lower than that in the starvation control after 4 weeks. Raw and heated tung oil significantly improved the resistance of pine wood to termites, and have the potential for the development of natural wood preservatives

A Bayesian Updating Scheme for Pandemics: Estimating the Infection Dynamics of COVID-19

Epidemic models play a key role in understanding and responding to the emerging COVID-19 pandemic. Widely used compartmental models are static and are of limited use to evaluate intervention strategies of combatting the pandemic. Applying the technology of data assimilation, we propose a Bayesian updating approach for estimating epidemiological parameters using observable information to assess the impacts of different intervention strategies. We adopt a concise renewal model and propose new parameters by disentangling the reduction of instantaneous reproduction number R_t into mitigation and suppression factors to quantify intervention impacts at a finer granularity. A data assimilation framework is developed to estimate these parameters including constructing an observation function and developing a Bayesian updating scheme. A statistical analysis framework is built to quantify the impacts of intervention strategies by monitoring the evolution of the estimated parameters. We reveal the intervention impacts in European countries and Wuhan and the resurgence risk in the United States

Theoretical foundations of studying criticality in the brain

Criticality is hypothesized as a physical mechanism underlying efficient transitions between cortical states and remarkable information processing capacities in the brain. While considerable evidence generally supports this hypothesis, non-negligible controversies persist regarding the ubiquity of criticality in neural dynamics and its role in information processing. Validity issues frequently arise during identifying potential brain criticality from empirical data. Moreover, the functional benefits implied by brain criticality are frequently misconceived or unduly generalized. These problems stem from the non-triviality and immaturity of the physical theories that analytically derive brain criticality and the statistic techniques that estimate brain criticality from empirical data. To help solve these problems, we present a systematic review and reformulate the foundations of studying brain criticality, i.e., ordinary criticality (OC), quasi-criticality (qC), self-organized criticality (SOC), and self-organized quasi-criticality (SOqC), using the terminology of neuroscience. We offer accessible explanations of the physical theories and statistic techniques of brain criticality, providing step-by-step derivations to characterize neural dynamics as a physical system with avalanches. We summarize error-prone details and existing limitations in brain criticality analysis and suggest possible solutions. Moreover, we present a forward-looking perspective on how optimizing the foundations of studying brain criticality can deepen our understanding of various neuroscience questions

Toward Learning Model-Agnostic Explanations for Deep Learning-Based Signal Modulation Classifiers

Recent advances in deep learning (DL) have brought tremendous gains in signal modulation classification. However, DL-based classifiers lack transparency and interpretability, which raises concern about model's reliability and hinders the wide deployment in real-word applications. While explainable methods have recently emerged, little has been done to explain the DL-based signal modulation classifiers. In this work, we propose a novel model-agnostic explainer, Model-Agnostic Signal modulation classification Explainer (MASE), which provides explanations for the predictions of black-box modulation classifiers. With the subsequence-based signal interpretable representation and in-distribution local signal sampling, MASE learns a local linear surrogate model to derive a class activation vector, which assigns importance values to the timesteps of signal instance. Besides, the constellation-based explanation visualization is adopted to spotlight the important signal features relevant to model prediction. We furthermore propose the first generic quantitative explanation evaluation framework for signal modulation classification to automatically measure the faithfulness, sensitivity, robustness, and efficiency of explanations. Extensive experiments are conducted on two real-world datasets with four black-box signal modulation classifiers. The quantitative results indicate MASE outperforms two state-of-the-art methods with 44.7% improvement in faithfulness, 30.6% improvement in robustness, and 44.1% decrease in sensitivity. Through qualitative visualizations, we further demonstrate the explanations of MASE are more human interpretable and provide better understanding into the reliability of black-box model decisions