arXiv subjects

Dipak Patra

Publications and source records attributed to Dipak Patra.

6 recordsLinked to original sources

arXiv2026

Parametric bootstrap simultaneous confidence interval based on doubly type-II censoring

Parametric bootstrap and fiducial generalized methods are proposed to construct simultaneous confidence intervals (SCIs) for all pairwise mean differences of several two-parameter exponential distributions, based on doubly censored samples. Both methods have been shown to have correct asymptotic coverage probabilities. Simulation studies are conducted to compare the performance of the two proposed methods. The usefulness of our proposed procedure is illustrated with two examples.

math.ST↗

arXiv2024

Modeling contagious disease spreading

An understanding of the disease spreading phenomenon based on a mathematical model is extremely needed for the implication of the correct policy measures to contain the disease propagation. Here, we report a new model namely the Ising-SIR model describing contagious disease spreading phenomena including both airborne and direct contact disease transformations. In the airborne case, a susceptible agent can catch the disease either from the environment or its infected neighbors whereas in the second case, the agent can be infected only through close contact with its infected neighbors. We have performed Monte Carlo simulations on a square lattice using periodic boundary conditions to investigate the dynamics of disease spread. The simulations demonstrate that the mechanism of disease spreading plays a significant role in the growth dynamics and leads to different growth exponent. In the direct contact disease spreading mechanism, the growth exponent is nearly equal to two for some model parameters which agrees with earlier empirical observations. In addition, the model predicts various types of spatiotemporal patterns that can be observed in nature.

cond-mat.stat-mech↗

arXiv2024

Growth of Science: How long will the United States uphold its position?

Policymakers often assess the growth of science in a country and compare it with that of other countries to set future planning for scientific research focusing on the sustainable development and economic growth of the country. Here, we study the growth of science for the period of 1996-2020 corresponding to the top fifty countries with the highest publications in 2020. It is found that the annual growth rates of scientific and technical journal publications exhibit Taylor's power law behavior indicating the dependence of the variance on the mean growth rate and the distributions of annual growth rates follow skew-symmetric distributions. Furthermore, we have computed the entropy based on annual publication numbers among the countries to assess the spatial disparity in the system. The entropy is found to increase mostly linear with time reducing the disparity among the countries. By performing the linear regression analysis, we predict that around the year 2046, all the countries excluding China may equally contribute towards the growth of science. We have also assessed the stability of the current USA ranking by computing the entropy between the USA and other countries. Based on the regression analysis, it is estimated that three potential countries such as Indonesia, India, and Iran may take the ranks ahead of the USA around the years 2024, 2029, and 2041 respectively.

physics.soc-ph↗

arXiv2024

Similarities among top one day batters: physics-based quantification

Assessment of the performance of a player in any sport is very much needed to determine the ranking of players and make a solid team with the best players. Besides these, fans, journalists, sports persons, and sports councils often analyse the performances of current and retired players to identify the best players of all time. Here, we study the performance of all-time top batters in one-day cricket using physics-based statistical methods. The batters are selected in this study who possess either higher total runs or a high number of centuries. It is found that the total runs increases linearly with the innings number at the later stage of the batter carrier, and the runs rate estimated from the linear regression analysis also increases linearly with the average runs. The probability of non-scoring innings is found to be a negligibly small number (i.e., $\leq 0.1$ ) for each batter. Furthermore, based on innings-wise runs, we have computed the six-dimensional probability distribution vector for each player. Two components of the probability distribution vector vary linearly with average runs. The component representing the probability of scoring runs less than 50 linearly decreases with the average runs. In contrast, the probability of scoring runs greater than or equal to 100 and less than 150 linearly increases with the average runs. We have also estimated the entropy to assess the diversity of a player. Interestingly, the entropy varies linearly with the average runs, giving rise to two clusters corresponding to the old and recent players. Furthermore, the angle between two probability vectors is calculated for each pair of players to measure the similarities among the players. It is found that some of the players are almost identical to each other.

physics.soc-ph↗

arXiv2024

Determination of the mean center of a region: A physics-based approach

The mean center of a geographical region, including continents and countries, has been mostly determined to study the trend of population migration, the shift of economic hubs, and the spatial change of extreme climate events. However, the determination of the mean center is a formidable task as it deals with the curvature of the earth's surface. Here, we report a physics-based model to determine the mean center of a region. Our method provides the analytical expression for the location of the mean center for both flat and curved spaces, such as straight lines, circles, planes, three-dimensional space, cylinders, and spheres. Some of these expressions are often used to compute the center of mass of the physical system. Therefore, the implication of our model in the physical system extends the general validity of the model. Furthermore, we have computed various mean centers of India, such as the geographical, population, and crime centers. We have also assessed the year-wise movement of the crime center and found a spatial trend towards the north.

physics.soc-ph↗

arXiv2022

Observation of banded spherulite in a pure compound by rhythmic growth

Banded spherulitic growth of crystal is observed in some materials with spherically symmetric growth front and periodic radial variation of birefringence. This variation of birefringence in quasi two dimensional geometry produces concentric interference colour bands when viewed through crossed polarisers. In most materials, the banded spherulites are found to be formed by radially oriented periodically twisted fibrillar crystallites. Here, we report the formation of banded spherulites due to the rhythmic growth of concentric crystallite-rich and crystallite-poor bands for a pure compound consisting of strongly polar rod like molecules. The compound exhibits coexistence of untwisted fibrillar crystallites and an amorphous phase in its most stable solid state. On sufficient supercooling of the sample from its melting point, the banded spherulites are formed with a periodic variation of composition of untwisted radially aligned fibrillar crystallites and an amorphous solid phase. We have developed a time dependent Ginzburg-Landau model to account for the observed banded spherulitic growth.

cond-mat.mtrl-sci↗