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The striped patterns in rocks, characterized by thin dark bands and thick light bands, are a result of the natural processes that have shaped the rocks through in situ metamorphism. Notably, the dark and light bands are composed of similar minerals, with the dark bands containing additional trapped materials such as fluid pockets or extra mineral grains. Here we employed the Gray-Scott Reaction Diffusion model to investigate the interaction between two sets of virtual chemicals, denoted as 'u' and 'v'. The differing diffusion and reaction rates of 'u' and 'v' chemical orders lead to the formation of 180 degree out-of-phase chemical domains, resulting in striped patterns. Utilizing the Gray-Scott model in this manner, we gain valuable insights into the early microscopic stages of these geologically significant striped patterns in metamorphic rocks., Comment: 13 Pages, 4 figures

Electroencephalogram (EEG) is a very promising and widely implemented procedure to study brain signals and activities by amplifying and measuring the post-synaptical potential arising from electrical impulses produced by neurons and detected by specialized electrodes attached to specific points in the scalp. It can be studied for detecting brain abnormalities, headaches, and other conditions. However, there are limited studies performed to establish a smart decision-making model to identify EEG's relation with the mood of the subject. In this experiment, EEG signals of 28 healthy human subjects have been observed with consent and attempts have been made to study and recognise moods. Savitzky-Golay band-pass filtering and Independent Component Analysis have been used for data filtration.Different neural network algorithms have been implemented to analyze and classify the EEG data based on the mood of the subject. The model is further optimised by the usage of Blackman window-based Fourier Transformation and extracting the most significant frequencies for each electrode. Using these techniques, up to 96.01% detection accuracy has been obtained.

Theories with higher derivatives involve linear instabilities in the Hamiltonian commonly known as Ostrogradski ghosts and can be viewed as a very serious problem during quantization. To cure {this} , we have considered the properties of antilinearty that can be found inherently in the non-Hermitian Hamiltonians. Owing to the existence of antilinearity, we can construct an operator, called the $V$-operator, which acts as an intertwining operator between the Hamiltonian and its hermitian conjugate. We have used this $V$-operator to remove the linear momenta term from the higher derivative Hamiltonian by making it non-Hermitian in the first place via an isospectral similarity transformation. The final form of the Hamiltonian is free from the Ostrogradski ghosts under some restriction on the mass term., Comment: 12 pages, Latex, updated version

Ghost fields in quantum field theory have been a long-standing problem. Specifically, theories with higher derivatives involve ghosts that appear in the Hamiltonian in the form of linear momenta term, which is commonly known as the Ostrogradski ghost. Higher derivative theories may involve both types of constraints i.e. first class and second class. Interestingly, these higher derivative theories may have non-Hermitian Hamiltonian respecting $\mathcal{PT}-$symmetries. In this paper, we have considered the $\mathcal{PT}-$symmetric nature of the extended Maxwell-Chern-Simon's theory and employed the second class constraints to remove the linear momenta terms causing the instabilities. We found that the removal is not complete rather conditions arise among the coefficients of the operator ${Q}$., Comment: 11 page, Latex

The Ostrogradski ghost problem that appears in higher derivative theories containing constraints has been considered here. Specifically we have considered systems where only the second class constraints appear. For these kind of systems, it is not possible to gauge away the linear momenta that cause the instability. To solve this issue, we have considered the PT symmetric aspects of the theory. As an example we have considered the Galilean invariant Chern Simons model in $2+1$ D which is a purely second class system. By solving the constraints, in the reduced phasespace, we have derived the \p similarity transformed Hamiltonian and putting conditions on we found that the final form of the Hamiltonian is free from any linear momenta and bounded from below., Comment: 13 pages, Latex, Subsection added

While teaching introductory programming courses for over a decade in reputed institutions we have experienced that several factors play significant role in developing problem solving skills and program development skills in students. There are certain types of difficulties that are encountered by the beginners. These difficulties vary in their nature. Beginners find difficulties with the programming language that they use, the compilers that they use and so on. These difficulties if not overcome proves detrimental to their career as professional engineers at a later stage. This paper focuses on the various types of difficulties that a novice programmer faces while learning programming and tries to find out ways to overcome them., Comment: 7 pages

This paper is an extensive survey of literature on complex network communities and clustering. Complex networks describe a widespread variety of systems in nature and society especially systems composed by a large number of highly interconnected dynamical entities. Complex networks like real networks can also have community structure. There are several types of methods and algorithms for detection and identification of communities in complex networks. Several complex networks have the property of clustering or network transitivity. Some of the important concepts in the field of complex networks are small-world and scale-robustness, degree distributions, clustering, network correlations, random graph models, models of network growth, dynamical processes on networks, etc. Some current areas of research on complex network communities are those on community evolution, overlapping communities, communities in directed networks, community characterization and interpretation, etc. Many of the algorithms or methods proposed for network community detection through clustering are modified versions of or inspired from the concepts of minimum-cut based algorithms, hierarchical connectivity based algorithms, the original GirvanNewman algorithm, concepts of modularity maximization, algorithms utilizing metrics from information and coding theory, and clique based algorithms., Comment: 15 pages, Review article