We perform a late-time cosmological study, we compare the performance of two Dirac-Born-Infeld (DBI) type k-essence scalar field extensions of the model to the standard framework and a scenario using the Chevallier-Polarski-Linder (CPL) equation of state parametrization. We solve background dynamics numerically as functions of redshift and incorporate them into a Bayesian inference pipeline accelerated by machine learning. We use a Flax-based surrogate emulator to replace repeated direct integrations of the ODE system, reducing computational cost. A hybrid scheme that combines stochastic variational inference (SVI) with No-U-Turn Hamiltonian Monte Carlo constrains cosmological parameters using the Pantheon+SH0ES Type Ia supernova sample, DESI BAO (DR2) data, and cosmic chronometer measurements without CMB-based priors. In both DBI k-essence formulations, present-day dark energy equations of state are consistent with cosmic acceleration, indicating a -like regime with a modest redshift dependence. The model is marginally favored by conventional model selection measures such as , AIC, BIC, and DIC, which are based on goodness of fit and penalized. However, Bayesian predictive measures like WAIC and PSIS-LOO show no significant differences between , , and DBI k-essence scenarios. All have similar model weights and out-of-sample predictive performance for the datasets. Thus, DBI k-essence models mimic the success of the classic paradigm while allowing controlled, redshift-dependent deviations from a strict cosmological constant that are consistent with present late-time observations.
Eylee Jung et.al[1] had conjectured that P_max=1/2 is a necessary and sufficient condition for the perfect two-party teleportation, and consequently, the Groverian measure of entanglement for the entanglement resource must be 1/√(2) . It is also known that prototype W state is not useful for standard teleportation. Agrawal and Pati[2] have successfully executed perfect (standard) teleportation with non-prototype W state. Aligned with the protocol mentioned in[2], we have considered here Star type tripartite states and have shown that perfect teleportation is suitable with such states. Moreover, we have taken the linear superposition of non-prototype W state and its spin-flipped version and shown that it belongs to Star class. Also, standard teleportation is possible with these states. It is observed that genuine tripartite entanglement is not necessary requirement for a state to be used as a channel for successful standard teleportation. We have also shown that these Star class states are P_max=1/4 states and their Groverian entanglement is √(3)/2 , thus concluding that Jung conjecture is not a necessary condition.
Millimetre-wave (mm-Wave) communication, spanning 30-300 GHz, suffers from strong atmospheric attenuation due to water vapour and oxygen absorption. These effects are highly variable, influenced by temperature and humidity, which determine the location of atmospheric “window frequencies (fwindows)”, regions of reduced attenuation essential for high-capacity wireless links. This study examines the seasonal and geographical variability of these windows across 14 Pacific tropical countries during July–August and January–February, using a refined Millimetre Wave Propagation Model (MPM) up to 200 GHz. Three deep learning models, Long Short-Term Memory (LSTM), Convolutional Neural Network (CNN), and Recurrent Neural Network (RNN) were tested to predict window frequencies at 30 GHz, 94 GHz, and 140 GHz from temperature and water vapour density data. Results show that the RNN consistently achieved the highest accuracy (R² > 0.98, RMSE < 0.015 dB/km), outperforming CNN and LSTM. While CNN proved competitive in cooler conditions, LSTM exhibited greater sensitivity to seasonal shifts. The findings highlight that atmospheric windows are dynamic rather than static, with significant seasonal and spatial variations. The study confirms that window frequencies are not fixed but dynamically modulated by climatic parameters, especially in humid tropical zones. The RNN model’s superior performance is attributed to its ability to capture temporal dependencies in meteorological inputs. Larger training sets (80–20 split) enhanced generalization and reduced prediction errors across all models. The proposed RNN-based framework offers a robust, climate-adaptive solution for real-time spectrum allocation, supporting energy efficiency, resilience, and sustainability in future mm-Wave communication networks.
