Prime numbers have fascinated mathematicians since antiquity, with ongoing efforts to uncover both their properties and ever-larger examples. While giant primes rarely aid cryptography, they find use in areas such as locally decodable codes. Large prime-hunting, often brute-force in nature, is conceptually linked to the Riemann Hypothesis and the prime number theorem, which portrays prime distribution as essentially random. This motivates a statistical perspective, with Bayesian methodology providing a natural foundation. We show that the prime number theorem suggests a nonhomogeneous Poisson process for prime counts, yielding primes as waiting times. This process agrees with the prime number theorem, asymptotic results, and prime gap properties. Building on it, we develop a recursive Bayesian theory for large prime prediction and Riemann Hypothesis validation. The approach matches traditional but computationally infeasible non-recursive Bayesian formulations in the limit, and it strongly falsifies the Riemann Hypothesis. Finally, we propose a computational method using Transformation-based MCMC to simulate recursive posterior predictives. A simple change of variable enables simulation of Mersenne prime exponents. With modest computing resources, we identified 259 primes over 140 million, including 184 strong Mersenne candidates corresponding to potential primes with 42--242 million digits.

The study is conducted to evaluate the job satisfaction among the administrative and teaching faculties in higher educational institutions. Many researchers have conducted studies to evaluate differences in job perception between teaching and non-teaching staff. Despite this, none of the studies have explicitly focused on developing a formal mathematical approach for analysis. Thus, this paper aims to identify the job satisfaction parameters among staff in an educational institution by using Multi Criteria Decision Making (MCDM) tools. The factors influencing employee job satisfaction have been ascertained and hierarchically organized through the utilization of the standard deviation methodology. Analytical findings reveal that certain variables, including promotional opportunities, interpersonal relations with colleagues, managerial support, and the department of employment, exert a substantial impact on an individual's level of job satisfaction. The research posits that the strategic implementation of these variables and attributes by organizational management can significantly ameliorate challenges related to employee retention, thereby enhancing overall workforce efficiency.

This paper presents EinsteinPy (version 0.3), a community-developed Python package for gravitational and relativistic astrophysics. Python is a free, easy to use a high-level programming language which has seen a huge expansion in the number of its users and developers in recent years. Specifically, a lot of recent studies show that the use of Python in Astrophysics and general physics has increased exponentially. We aim to provide a very high level of abstraction, an easy to use interface and pleasing user experience. EinsteinPy is developed keeping in mind the state of a theoretical gravitational physicist with little or no background in computer programming and trying to work in the field of numerical relativity or trying to use simulations in their research. Currently, EinsteinPy supports simulation of time-like and null geodesics and calculates trajectories in different background geometries some of which are Schwarzschild, Kerr, and KerrNewmann along with coordinate inter-conversion pipeline. It has a partially developed pipeline for plotting and visualization with dependencies on libraries like Plotly, matplotlib, etc. One of the unique features of EinsteinPy is a sufficiently developed symbolic tensor manipulation utilities which are a great tool in itself for teaching yourself tensor algebra which for many beginner students can be overwhelmingly tricky. EinsteinPy also provides few utility functions for hypersurface embedding of Schwarzschild spacetime which further will be extended to model gravitational lensing simulation.

In India financial markets have existed for many years. A functionally accented, diverse, efficient and flexible financial system is vital to the national objective of creating a market driven, productive and competitive economy. Today markets of varying maturity exist in equity, debt, commodities and foreign exchange. In this work we attempt to generate prediction rules scheme for stock price movement at Bombay Stock Exchange using an important Soft Computing paradigm viz., Rough Fuzzy Multi Layer Perception. The use of Computational Intelligence Systems such as Neural Networks, Fuzzy Sets, Genetic Algorithms, etc. for Stock Market Predictions has been widely established. The process is to extract knowledge in the form of rules from daily stock movements. These rules can then be used to guide investors. To increase the efficiency of the prediction process, Rough Sets is used to discretize the data. The methodology uses a Genetic Algorithm to obtain a structured network suitable for both classification and rule extraction. The modular concept, based on divide and conquer strategy, provides accelerated training and a compact network suitable for generating a minimum number of rules with high certainty values. The concept of variable mutation operator is introduced for preserving the localized structure of the constituting Knowledge Based sub-networks, while they are integrated and evolved. Rough Set Dependency Rules are generated directly from the real valued attribute table containing Fuzzy membership values. The paradigm is thus used to develop a rule extraction algorithm. The extracted rules are compared with some of the related rule extraction techniques on the basis of some quantitative performance indices. The proposed methodology extracts rules which are less in number, are accurate, have high certainty factor and have low confusion with less computation time.

Accurate measurement of the Hubble constant from standard sirens such as the gravitational wave (GW) sources with electromagnetic counterparts relies on the robust peculiar velocity correction of the redshift of the host galaxy. We show in this work that the peculiar velocity of the host galaxies exhibits a correlation with the properties of the host galaxy primarily such as its stellar mass and this correlation also evolves with redshift. As the galaxies of higher stellar mass tend to form in galaxies with higher halo masses which are located in spatial regions having a non-linear fluctuation in the density field of the matter distribution, the root mean square (RMS) peculiar velocity of more massive galaxies is higher. As a result, depending on the formation channel of the binary compact objects, the peculiar velocity contamination to the galaxies will be different. The variation in the peculiar velocity of the host galaxies can lead to a significant variation in the estimation of the Hubble constant inferred using sources such as Binary Neutron Stars (BNSs). For the network of GW detectors such as LIGO-Virgo-KAGRA (LVK), LVK+LIGO-India, and Cosmic Explorer+Einstein Telescope, the variation in the precision of Hubble constant inferred from 10 bright siren events can vary from $\sim 5.4 - 6\%$, $\sim 4.5 - 5.3\%$ and $\sim 1.1 - 2.7\%$ respectively. The impact of such a correlation between peculiar velocity and stellar mass on the inference of the Hubble constant is not only limited to GW sources but also applicable to type-Ia supernovae.

Advancements in technologies related to working with omics data require novel computation methods to fully leverage information and help develop a better understanding of human diseases. This paper studies the effects of introducing graph contrastive learning to help leverage graph structure and information to produce better representations for downstream classification tasks for multi-omics datasets. We present a learnining framework named Multi-Omics Graph Contrastive Learner(MOGCL) which outperforms several aproaches for integrating multi-omics data for supervised learning tasks. We show that pre-training graph models with a contrastive methodology along with fine-tuning it in a supervised manner is an efficient strategy for multi-omics data classification.

Solar activities have significant impact on the member of the solar systems including earth. As earth is a planet with its own magnetic field, solar emissions with magnetic fields do interact with the earth's own magnetic field to create geo-magnetic disturbances. Substorms are geo-magnetic disturbances of shorter duration (few hours or less) which are mainly concentrated in the auroral region and originates due to the ionospheric current injection at high latitudes. Supersubstorm are intense substorms as identified by peak activities in geo-magnetic indices. In this thesis, we have investigated the energy dynamics during the supersubstorm and analyzed the relation of the energy components with different geo-magnetic indices and interplanetary magnetic field (IMF) components. In particular, the solar wind energy levels and the energy coupled into the magnetosphere as captured by the Akasofu parameter are studied. A qualitative analysis of the computed energy and its relationship with different geo-magnetic indices is presented. Correlation and cross-correlation analysis have been used to get insights into the nature of the relationship between the energy components and indices. This for example uncovered the negative relationship between the solar wind energy and the Akasofu parameter. A summary analysis of the supersubstorm event in comparison with the quiet phases are made. This has led to insights for example showing the higher energy levels during supersubstorm and different energy ratios (Akasofu parameter divided by the solar wind energy) existing for different supersubstorm.

Atomically thin semiconductors have versatile future applications in the information and communication technologies for the ultimate miniaturization of electronic components. In particular, the ongoing research demands not only a large-scale synthesis of pristine quality monolayer MoS2 but also advanced nanofabrication and characterization methods for investigation of intrinsic device performances. Here, we conduct a meticulous investigation of the fast transient charge trapping mechanisms in field-effect transistors (FETs) of high-quality CVD MoS2 monolayers grown by a salt-driven method. To unfold the intrinsic transistor behavior, an amplitude sweep pulse I~V methodology is adapted with varying pulse widths. A significant increase in the field-effect mobility up to ~100% is achieved along with a hysteresis-free transfer characteristic by applying the shortest pulse. Moreover, to correlate these results, a single pulse time-domain drain current analysis is carried out to unleash the fast and slow transient charge trapping phenomena. Furthermore, rigorous density functional theory (DFT) calculations are implemented to inspect the effects of the Schottky barrier and metal-induced gap states between drain/source electrode and MoS2 for the superior carrier transport. Our findings on the controllable transient charge trapping mechanisms for estimation of intrinsic field-effect mobility and hysteresis-free transfer characteristic in salt-assisted CVD-grown MoS2 FETs will be beneficial for future device applications in complex memory, logic, and sensor systems.

While cracking is a complex dynamics that involves material intrinsic properties like grain shape and size distribution, elastic properties of grain and cementing materials, and extrinsic properties of loading, in this work, the focus has been to check the dependence on the elastic properties of the bonding material. A 3-dimensional disordered system was constructed from spherical balls of varying radii that were chosen randomly from a log-normal distribution. The growth of micro-cracks with increasing compressive strain was monitored till the limit of the percolation crack. The two parameters varied were the bond stiffness constant and the bond strength of the material. Two distinct regimes of cracking rates were observed across a critical strain $\epsilon_{knee}$ that manifested as a knee in the cumulative crack-strain plot. The critical strain $\epsilon_{knee}$ and the strain at the percolation point $\epsilon_{perc}$ showed a power law dependence on the elastic property of the bond material. Individual micro-cracks were observed to grow sharply to a maximum value $N^{k_{b}}_{max}$, after which the number of new micro-cracks decreased, showing a long tail. The maximum $N^{k_{b}}_{max}$ was found to correspond to the strain $\epsilon_{knee}$, thus indicating that pre-$N^{k_{b}}_{max}$ cracking brittle, followed by ductile cracking behaviour of system. Lastly, we show that there exists a robust relation between $\epsilon_{knee}$ and $\epsilon_{perc}$ that is a power-law where the exponent is a function of the material elastic property. As $\epsilon_{knee}$ can be determined from acoustic signals associated with micro-cracks, our proposed relation can act as a warning towards critical strain resulting in crack percolation.

In this paper, we will analyze the gravitational collapse in the framework of gravity's rainbow. We will demonstrate that the position of the horizon for a particle inside the black hole depends on the energy of that particle. It will also be observe that the position of the horizon for a particle falling radially into the black hole also depends on its energy. Thus, it is possible for a particle coming from outside to interact with a particle inside the black, and take some information outside the black hole. This is because for both these particles the position of horizon is different. So, even though the particle from inside the black hole is in its own horizon, it is not in the horizon of the particle coming from outside. Thus, we will demonstrate that in gravity's rainbow information can get out of a black hole.

A quantum algorithm to solve the parity problem is better than its most efficient classical counter- part with a separation that is polynomial in the number of queries. This was shown by E. Bernstein and U. Vazirani and was one of the earliest indications that the quantum information processing can outperform the classical one by a significant margin. The problem and its solution both is usually stated for a 2-level system since we generally work with bits/qubits. However, many works have been done generalizing known quantum computing techniques to higher level systems. Following this, we look at a generalization of the Bernstein-Vazirani algorithm implemented on a general qudit system.

In this paper, we characterize the positive integers $n$ for which intersection graph of ideals of $\mathbb{Z}_n$ is perfect.

We apply the notion of \emph{optimality} of measurements for state determination(tomography) as originally given by Wootters and Fields to \emph{weak value tomography} of \emph{pure states}. They defined measurements to be optimal if they 'minimised' the effects of statistical errors. For technical reasons they actually maximised the state averaged information, precisely quantified as the negative logarithm of 'error volume'. In this paper we optimise both the state averaged information as well as error volumes. We prove, for Hilbert spaces of arbitrary (finite) dimensionality, that varieties of weak value measurements are optimal when the post-selected bases are \emph{mutually unbiased} with respect to the eigenvectors of the observable being measured. We prove a number of important results about the geometry of state spaces when expressed through the weak values as coordinates. We derive an expression for the Ka\"ehler potential for the N-dimensional case with the help of which we give an exact treatment of the arbitrary-spin case.

Considering that the ultrahigh energy (UHE) upgoing muon neutrino events around the PeV energy region observed by the IceCube are due to the decay of super heavy dark matter to neutrinos, we constrain the mass of the decaying dark matter and its decay lifetime using the IceCube analysis of these neutrinos in the PeV region. The theoretical fluxes are computed by adpoting the procedure given in the reference [1,2], where the DGLAP numerical evolutions of QCD cascades as well as electroweak corrections are included for evolving the decay process of the super heavy dark matter. Our results indicate that to explain the IceCube events around PeV region the decaying dark matter mass $m_\chi$ would be $\sim 5 \times 10^{7}$ GeV with the decay lifetime $\tau \sim 7 \times 10^{28}$ sec.

Integral geometry uses four geometric invariants -- the Minkowski functionals -- to characterize certain subsets of 3-dimensional space. The question was, how is the fluid flow in a 3-dimensional porous system related to these invariants? In this work, we systematically study the dependency of permeability on the geometrical characteristics of two categories of 3-dimensional porous systems generated: (i) stochastic and (ii) deterministic. For the stochastic systems, we investigated both normal and log-normal size distribution of grains. For the deterministic porous systems, we checked for a cubic and a hexagonal arrangement of grains of equal size. Our studies reveal that for any 3-dimensional porous system, ordered or disordered, permeability $k$ follows a unique scaling relation with the Minkowski functionals: (a) volume of the pore space, (b) integral mean curvature, (c) Euler Characteristic and (d) critical cross-sectional area of the pore space. The cubic and the hexagonal symmetrical systems formed the upper and lower bounds of the scaling relations, respectively. The disordered systems lay between these bounds. Moreover, we propose a combinatoric $F$ that weaves together the four Minkowski functionals and follows a power-law scaling with permeability. The scaling exponent is independent of particle size and distribution and has a universal value of $0.428$ for 3-dimensional porous systems built of spherical grains.

UniGlyph is a constructed language (conlang) designed to create a universal transliteration system using a script derived from seven-segment characters. The goal of UniGlyph is to facilitate cross-language communication by offering a flexible and consistent script that can represent a wide range of phonetic sounds. This paper explores the design of UniGlyph, detailing its script structure, phonetic mapping, and transliteration rules. The system addresses imperfections in the International Phonetic Alphabet (IPA) and traditional character sets by providing a compact, versatile method to represent phonetic diversity across languages. With pitch and length markers, UniGlyph ensures accurate phonetic representation while maintaining a small character set. Applications of UniGlyph include artificial intelligence integrations, such as natural language processing and multilingual speech recognition, enhancing communication across different languages. Future expansions are discussed, including the addition of animal phonetic sounds, where unique scripts are assigned to different species, broadening the scope of UniGlyph beyond human communication. This study presents the challenges and solutions in developing such a universal script, demonstrating the potential of UniGlyph to bridge linguistic gaps in cross-language communication, educational phonetics, and AI-driven applications.

We study the fluctuations in the brightness temperature of 21-cm signal $\delta T_{21}$ at the dark ages ($z\sim100$) with a dark matter candidate in Inter Doublet Model (IDM). We then explore the effects of different fractions of IDM dark matter on $\delta T_{21}$ signal. The IDM dark matter masses are chosen in few tens of GeV region as well as in the high mass region beyond 500 GeV. It has been observed that the $\delta T_{21}$ signal is more sensitive in the dark matter mass range of $70 - 80$ GeV. A lower bound on annihilation cross-section for this dark matter is also obtained analyzing the $\delta T_{21}$ signal. This is found to lie within the range $6.5 \times 10^{-29} \,\, \rm{cm^3 / sec} \leq \langle\sigma v\rangle \leq 4.88\times 10^{-26}\,\, \rm{cm^ 3 / sec}$ for the IDM dark matter mass range $10 \, {\rm GeV} \leq m_{\chi}\leq 990 \,{\rm GeV}$.

We report the numerical results for the steady state income or wealth distribution $P(m)$ and the resulting inequality measures (Gini $g$ and Kolkata $k$ indices) in the kinetic exchange models of market dynamics. We study the variations of $P(m)$ and of the indices $g$ and $k$ with the saving propensity $\lambda$ of the agents, with two different kinds of trade (kinetic exchange) dynamics. In the first case, the exchange occurs between randomly chosen pairs of agents and in the next, one of the agents in the chosen pair is the poorest of all and the other agent is randomly picked up from the rest of the population (where, in the steady state, a self-organized poverty level or SOPL appears). These studies have also been made for two different kinds of saving behaviors. One, where each agent has the same value of $\lambda$ (constant over time) and the other where $\lambda$ for each agent can take two values (0 and 1), changing randomly over a fraction of time \rho(<1) of choosing $\lambda = 1$. We find that the inequality decreases with increasing savings ($\lambda$); inequality indices ($g$ and $k$) decrease and SOPL increases with increasing $\lambda$, indicating possible applications in economic policy making.

The primordial heavy or superheavy dark matter that could be created during the reheating or preheating stage of the Universe can undergo QCD cascade decay process to produce leptons or $\gamma$ as end products. Although these could be rare decays, the energy involved in such decay process can influence 21-cm signal of hyperfine transition of neutral hydrogen during the reionization era. We explore in this work, possible multimessenger signals of such heavy dark matter decays. One of which could be the source of ultra high energy neutrino (of $\sim$ PeV energy regime) signals at IceCube detector whereas the other signal attributes to the cooling/heating of the baryons by the exchange of energy involved in this decay process and its consequent influence on 21-cm signal. The effect of evaporation of primordial black holes and baryon scattering with light cold dark matter are also included in relation to the evolution of the 21-cm signal temperature and their influence are also discussed.

In this paper, we propose a novel quantum computing approach to solve the real-world problem of optimizing transportation in bustling Kathmandu city. The transportation system in Kathmandu is chaotic, with no central authority controlling the transportation. We leverage this chaotic feature in our quantum optimization procedure. The quantum chaos theory's Wigner-Dyson distribution surfaced as the most effective bus spacing distribution for a bus driver to maximize their profit. We investigate the statistical properties of the buses with real-time GPS bus location data and optimize bus spacing and interval distribution around the 27 km circular ring road in Kathmandu. Using tools like quantum simulation, eigenvalue distributions, and output wave function analysis, we show that such optimal bus spacing distribution could be achieved.