Time Uncertainty in Quantum Gravitational Systems

It is generally argued that the combined effect of Heisenberg principle and general relativity leads to a minimum time uncertainty. Most of the analyses supporting this conclusion are based on a perturbative approach to quantization. We consider a simple family of gravitational models, including the Einstein-Rosen waves, in which the (non-linearized) inclusion of gravity changes the normalization of time translations by a monotonic energy-dependent factor. In these circumstances, it is shown that a maximum time resolution emerges non-perturbatively only if the total energy is bounded. Perturbatively, however, there always exists a minimum uncertainty in the physical time.Comment: (4 pages, no figures) Accepted for publication in Physical Review

Hybrid One-Dimensional CNN and DNN Model for Classification Epileptic Seizure

Epilepsy is a common chronic brain disease caused by abnormal neuronal activity and the occurrence of sudden or transient seizures. Electroencephalogram (EEG) is a non-invasive technique commonly used to identify epileptic brain activity. However, visual detection of the EEG is subjective, time consuming, and labour intensive for the neurologist. Therefore, we propose an automatic seizure detection using a combination of one-dimension convolution neural network (1D-CNN) with majority voting and deep neural network (DNN). EEG signals features are extracted using discrete Fourier transform (DFT) and discrete wavelet transform (DWT) which then these features will be selected with XGBoost to minimize features classified with CNN. The proposed method experimental results show that it can detect epilepsy from EEG signals perfectly with an accuracy of 100%. However, the proposed method only yielded classified EEG signals from the University of Bonn Dataset as its results

Some Essays in Growth Theory.

no abstract availableEconomic development;

Efficient numerical methods to solve some reaction-diffusion problems arising in biology

Philosophiae Doctor - PhDIn this thesis, we solve some time-dependent partial differential equations, and systems of such equations, that governs reaction-diffusion models in biology. we design and implement some novel exponential time differencing schemes to integrate stiff systems of ordinary differential equations which arise from semi-discretization of the associated partial differential equations. We split the semi-linear PDE(s) into a linear, which contains the highly stiff part of the problem, and a nonlinear part, that is expected to vary more slowly than the linear part. Then we introduce higher-order finite difference approximations for the spatial discretization. Resulting systems of stiff ODEs are then solved by using exponential time differencing methods. We present stability properties of these methods along with extensive numerical simulations for a number of different reaction-diffusion models, including single and multi-species models. When the diffusivity is small many of the models considered in this work are found to exhibit a form of localized spatiotemporal patterns. Such patterns are correctly captured by our proposed numerical schemes. Hence, the schemes that we have designed in this thesis are dynamically consistent. Finally, in many cases, we have compared our results with those obtained by other researchers