Using a joint statistical analysis, we test a four-dimensional FLWR model embedded in a five-dimensional bulk based on the Nash-Greene embedding theorem. Performing a Markov Chain Monte Carlo (MCMC) modelling, we combine observational data sets as those of the recent ``Gold 2018'' growth data, the best-fit Planck2018/$\Lambda$CDM parameters on the Cosmic Microwave Background (CMB), the Baryon Acoustic Oscillations (BAO) measurements, the Pantheon Supernovae type Ia and the Hubble parameter data with redshift ranging from $0.01 < z < 2.3$ to impose restrictions on the model. From linear Nash-Green fluctuations of the metric, we obtain the related perturbed equations in longitudinal Newtonian gauge to obtain the evolution of growth matter. We show that a mild alleviation is obtained from the $\sigma$ tension between the growth amplitude factor and the matter content $(\sigma_8$-$\Omega_m)$ of the observations from CMB and Large Scale Structure (LSS) probes with degeneracies on the parameters. We also apply the Om(z) diagnosis to distinguish the model from $\Lambda$CDM. The Akaike Information Criterion (AIC) is used and we find a relative statistical consistence of the present model with both $\Lambda$CDM and $w$CDM models up to 1$\%$ of percentage difference at early times.

The Hubble parameter H(z), as a function of redshift, is modified by the presence of a new term originated from the extrinsic curvature in an embedded space-time. Assuming an asymptotic expansion factor $a\sim 0$ or, equivalently $z\rightarrow \infty$, it is obtained a nearly resemblance of the present model ($\beta$-model) with quintessence $w$CDM model with $H(z)\sim H_{wCDM}(z)$ at background level. In conjunction with $\Lambda$CDM, we test the models using a pack of recent datasets like that of the ``Gold 2018'' growth data, the best-fit Planck2018/$\Lambda$CDM parameters on the Cosmic Microwave Background (CMB), the Baryon Acoustic Oscillations (BAO) measurements, the Pantheon Supernovae type Ia and the Hubble parameter data with redshift ranging from $0.01 < z < 2.3$. Performing the Akaike Information Criterion (AIC) to ascertain the statistical viability of the model from Jeffreys' scale, we apply a joint likelihood analysis to the data with the Markov Chain Monte Carlo (MCMC) method. We find that the present model is in very good agreement with observations with a close statistical equivalence with the $\Lambda$CDM and $w$CDM cosmologies at 1-$\sigma$ level. We also show that a mild alleviation of the $\sigma$ tension between the growth amplitude factor and the matter content $(\sigma_8$-$\Omega_m)$ of the observations from CMB and Large Scale Structure (LSS) probes. A comparison of the aforementioned full pack of data in MCMC chains is made with the resulting MCMC from Pantheon SNIa+$H(z)$ in order to analyse the sensitivity of the models and how they respond to a cosmography analysis on the evolution of $H(z)$ and the deceleration parameter $q(z)$. In this sense, we find that only the $\beta$-model can be unaffected to the variations of the previous datasets due to its several minima in the likelihood (degeneracies) of the related parameters with an overall percentage relative difference only up to 4$\%$.

An analysis of the performance of Automatic Dependent Surveillance-Broadcast (ADS-B) data received from the Grand Forks, North Dakota International Airport was carried out in this study. The purpose was to understand the vulnerabilities of Universal Access Transceiver (UAT) ADS-B system and recognize the effects on present and future Air Traffic Control (ATC) operation. The Federal Aviation Administration (FAA) mandated all the General Aviation aircraft to be equipped with ADS-B. The aircraft flying within United States and below the transition altitude (18,000 feet) are more likely to install an UAT ADS-B. At present unmanned aircraft systems (UAS) and autonomous air traffic control (ATC) towers are being integrated into the aviation industry and UAT ADS-B is a basic sensor for both class 1 and class 2 Detect and Avoid (DAA) systems. As a fundamental component of future surveillance system, the anomalies and vulnerabilities of ADS-B system need to be identified to enable a fully utilized airspace with enhanced situational awareness. The data received was archived in GDL-90 format, which was parsed into readable data. The anomaly detection of ADS-B messages was based on the FAA ADS-B performance assessment report. The data investigation revealed ADS-B message suffered from different anomalies including drop out; missing payload; data jump; low confident data and altitude discrepancy. Among those studied, the most severe was drop out and 32.49% of messages suffered from this anomaly. Dropout is an incident where ADS-B failed to update within a specified rate. Considering the potential danger being imposed, an in-depth analysis was carried out to characterize message dropout. Three flight parameters were selected to investigate their effect on drop out. Statistical analysis was carried out and Friedman Statistical Test identified that altitude affected drop out more than any other flight parameters.

We consider the propagation of electromagnetic waves in the Friedman – Lemaître – Robertson – Walker metric. The exact solutions for plane and spherical wave are written down. The corresponding redshift, amplitude change, and dispersion are discussed. We also speculate about the connection of the electromagnetic wave equation to the Klein–Gordon equation.