A Note on Cyclic Codes from APN Functions

Cyclic codes, as linear block error-correcting codes in coding theory, play a vital role and have wide applications. Ding in \cite{D} constructed a number of classes of cyclic codes from almost perfect nonlinear (APN) functions and planar functions over finite fields and presented ten open problems on cyclic codes from highly nonlinear functions. In this paper, we consider two open problems involving the inverse APN functions $f(x)=x^{q^m-2}$ and the Dobbertin APN function $f(x)=x^{2^{4i}+2^{3i}+2^{2i}+2^{i}-1}$. From the calculation of linear spans and the minimal polynomials of two sequences generated by these two classes of APN functions, the dimensions of the corresponding cyclic codes are determined and lower bounds on the minimum weight of these cyclic codes are presented. Actually, we present a framework for the minimal polynomial and linear span of the sequence $s^{\infty}$ defined by $s_t=Tr((1+\alpha^t)^e)$, where $\alpha$ is a primitive element in $GF(q)$. These techniques can also be applied into other open problems in \cite{D}

Cosmic constraint on the unified model of dark sectors with or without a cosmic string fluid in the varying gravitational constant theory

Observations indicate that most of the universal matter are invisible and the gravitational constant $G(t)$ maybe depends on the time. A theory of the variational $G$ (VG) is explored in this paper, with naturally producing the useful dark components in universe. We utilize the observational data: lookback time data, model-independent gamma ray bursts, growth function of matter linear perturbations, type Ia supernovae data with systematic errors, CMB and BAO to restrict the unified model (UM) of dark components in VG theory. Using the best-fit values of parameters with the covariance matrix, constraints on the variation of $G$ are $(\frac{G}{G_{0}})_{z=3.5}\simeq 1.0015^{+0.0071}_{-0.0075}$ and $(\frac{\dot{G}}{G})_{today}\simeq -0.7252^{+2.3645}_{-2.3645}\times 10^{-13} yr^{-1}$, the small uncertainties around constants. Limit on the equation of state of dark matter is $w_{0dm}=0.0072^{+0.0170}_{-0.0170}$ with assuming $w_{0de}=-1$ in unified model, and dark energy is $w_{0de}=-0.9986^{+0.0011}_{-0.0011}$ with assuming $w_{0dm}=0$ at prior. Restriction on UM parameters are $B_{s}=0.7442^{+0.0137+0.0262}_{-0.0132-0.0292}$ and $\alpha=0.0002^{+0.0206+0.0441}_{-0.0209-0.0422}$ with $1\sigma$ and $2\sigma$ confidence level. In addition, the effect of a cosmic string fluid on unified model in VG theory are investigated. In this case it is found that the $\Lambda$CDM ($\Omega_{s}=0$, $\beta=0$ and $\alpha=0$) is included in this VG-UM model at $1\sigma$ confidence level, and the larger errors are given: $\Omega_{s}=-0.0106^{+0.0312+0.0582}_{-0.0305-0.0509}$ (dimensionless energy density of cosmic string), $(\frac{G}{G_{0}})_{z=3.5}\simeq 1.0008^{+0.0620}_{-0.0584}$ and $(\frac{\dot{G}}{G})_{today}\simeq -0.3496^{+26.3135}_{-26.3135}\times 10^{-13}yr^{-1}$.Comment: 17 pages,4 figure

Review of \u3cem\u3eLabor of Love: Gestational Surrogacy and the Work of Making Babies\u3c/em\u3e. Heather Jacobson. Reviewed by Yanfeng Xu.

Review of: Heather Jacobson, Labor of Love: Gestational Surrogacy and the Work of Making Babies. Rutgers University Press (2016), 201 pages, $19.99 (paperback)

The Weight Distributions of Cyclic Codes and Elliptic Curves

Cyclic codes with two zeros and their dual codes as a practically and theoretically interesting class of linear codes, have been studied for many years. However, the weight distributions of cyclic codes are difficult to determine. From elliptic curves, this paper determines the weight distributions of dual codes of cyclic codes with two zeros for a few more cases

Transit Use for Single-parent Households: Evidence from Maryland

Single parents face unique transportation barriers in their lives. Although helping single parents obtain private vehicles (e.g., car donation programs) would be a potential solution, we cannot ignore the high expense of maintaining and operating a vehicle, which may impose a heavy financial burden on single-parent families and constrain their ability to access opportunities and services. In contrast, public transit could be a more accessible and affordable transportation mode that benefits single-parent families. This study examined the association between public transit use and single parents using 2017 National Household Travel Survey and American Community Survey data for Maryland, United States. Using zero-inflated negative binomial (ZINB) regression, we found that single parents used transit more than the average resident, and census block groups with more single-parent families had more transit commuters, holding other demographic and socioeconomic variables constant. This association was more significant in large metropolitan and urban areas than the state average. The findings highlight the vital role of public transit in single parents\u27 daily travel. We discussed policy implications related to helping single parents access opportunities and services

Transmission of H7N9 influenza virus in mice by different infective routes.

BackgroundOn 19 February 2013, the first patient infected with a novel influenza A H7N9 virus from an avian source showed symptoms of sickness. More than 349 laboratory-confirmed cases and 109 deaths have been reported in mainland China since then. Laboratory-confirmed, human-to-human H7N9 virus transmission has not been documented between individuals having close contact; however, this transmission route could not be excluded for three families. To control the spread of the avian influenza H7N9 virus, we must better understand its pathogenesis, transmissibility, and transmission routes in mammals. Studies have shown that this particular virus is transmitted by aerosols among ferrets.MethodsTo study potential transmission routes in animals with direct or close contact to other animals, we investigated these factors in a murine model.ResultsViable H7N9 avian influenza virus was detected in the upper and lower respiratory tracts, intestine, and brain of model mice. The virus was transmissible between mice in close contact, with a higher concentration of virus found in pharyngeal and ocular secretions, and feces. All these biological materials were contagious for naïve mice.ConclusionsOur results suggest that the possible transmission routes for the H7N9 influenza virus were through mucosal secretions and feces

室内植物表型平台及性状鉴定研究进展和展望

Plant phenomics is under rapid development in recent years, a research field that is progressing towards integration, scalability, multi-perceptivity and high-throughput analysis. Through combining remote sensing, Internet of Things (IoT), robotics, computer vision, and artificial intelligence techniques such as machine learning and deep learning, relevant research methodologies, biological applications and theoretical foundation of this research domain have been advancing speedily in recent years. This article first introduces the current trends of plant phenomics and its related progress in China and worldwide. Then, it focuses on discussing the characteristics of indoor phenotyping and phenotypic traits that are suitable for indoor experiments, including yield, quality, and stress related traits such as drought, cold and heat resistance, salt stress, heavy metals, and pests. By connecting key phenotypic traits with important biological questions in yield production, crop quality and Stress-related tolerance, we associated indoor phenotyping hardware with relevant biological applications and their plant model systems, for which a range of indoor phenotyping devices and platforms are listed and categorised according to their throughput, sensor integration, platform size, and applications. Additionally, this article introduces existing data management solutions and analysis software packages that are representative for phenotypic analysis. For example, ISA-Tab and MIAPPE ontology standards for capturing metadata in plant phenotyping experiments, PHIS and CropSight for managing complicated datasets, and Python or MATLAB programming languages for automated image analysis based on libraries such as OpenCV, Scikit-Image, MATLAB Image Processing Toolbox. Finally, due to the importance of extracting meaningful information from big phenotyping datasets, this article pays extra attention to the future development of plant phenomics in China, with suggestions and recommendations for the integration of multi-scale phenotyping data to increase confidence in research outcomes, the cultivation of cross-disciplinary researchers to lead the next-generation plant research, as well as the collaboration between academia and industry to enable world-leading research activities in the near future