A Semiparametric Generalized Exponential Regression Model with a Principled Distance-based Prior for Analyzing Trends in Rainfall

The Western Ghats mountain range holds critical importance in regulating monsoon rainfall across Southern India, with a profound impact on regional agriculture. Here, we analyze daily wet-day rainfall data for the monsoon months between 1901-2022 for the Northern, Middle, and Southern Western Ghats regions. Motivated by an exploratory data analysis, we introduce a semiparametric Bayesian generalized exponential (GE) regression model; despite the underlying GE distribution assumption being well-known in the literature, including in the context of rainfall analysis, no research explored it in a regression setting, as of our knowledge. Our proposed approach involves modeling the GE rate parameter within a generalized additive model framework. An important feature is the integration of a principled distance-based prior for the GE shape parameter; this allows the model to shrink to an exponential regression model that retains the advantages of the exponential family. We draw inferences using the Markov chain Monte Carlo algorithm. Extensive simulations demonstrate that the proposed model outperforms simpler alternatives. Applying the model to analyze the rainfall data over 122 years provides insights into model parameters, temporal patterns, and the impact of climate change. We observe a significant decreasing trend in wet-day rainfall for the Southern Western Ghats region.Comment: 24 pages, 8 figure

On Binary Networked Public Goods Game with Altruism

In the classical Binary Networked Public Goods (BNPG) game, a player can either invest in a public project or decide not to invest. Based on the decisions of all the players, each player receives a reward as per his/her utility function. However, classical models of BNPG game do not consider altruism which players often exhibit and can significantly affect equilibrium behavior. Yu et al. (2021) extended the classical BNPG game to capture the altruistic aspect of the players. We, in this paper, first study the problem of deciding the existence of a Pure Strategy Nash Equilibrium (PSNE) in a BNPG game with altruism. This problem is already known to be NP-Complete. We complement this hardness result by showing that the problem admits efficient algorithms when the input network is either a tree or a complete graph. We further study the Altruistic Network Modification problem, where the task is to compute if a target strategy profile can be made a PSNE by adding or deleting a few edges. This problem is also known to be NP-Complete. We strengthen this hardness result by exhibiting intractability results even for trees. A perhaps surprising finding of our work is that the above problem remains NP-Hard even for bounded degree graphs when the altruism network is undirected but becomes polynomial-time solvable when the altruism network is directed. We also show some results on computing an MSNE and some parameterized complexity results. In summary, our results show that it is much easier to predict how the players in a BNPG game will behave compared to how the players in a BNPG game can be made to behave in a desirable way.Comment: 26 page

Multi-component Fermionic Dark Matter and IceCube PeV scale Neutrinos in Left-Right Model with Gauge Unification

We consider a simple extension of the minimal left-right symmetric model (LRSM) in order to explain the PeV neutrino events seen at the IceCube experiment from a heavy decaying dark matter. The dark matter sector is composed of two fermions: one at PeV scale and the other at TeV scale such that the heavier one can decay into the lighter one and two neutrinos. The gauge annihilation cross sections of PeV dark matter are not large enough to generate its relic abundance within the observed limit. We include a pair of real scalar triplets $\Omega_{L,R}$ which can bring the thermally overproduced PeV dark matter abundance into the observed range through late time decay and consequent entropy release thereby providing a consistent way to obtain the correct relic abundance without violating the unitarity bound on dark matter mass. Another scalar field, a bitriplet under left-right gauge group is added to assist the heavier dark matter decay. The presence of an approximate global $U(1)_X$ symmetry can naturally explain the origin of tiny couplings required for long-lived nature of these decaying particles. We also show, how such an extended LRSM can be incorporated within a non-supersymmetric $SO(10)$ model where the gauge coupling unification at a very high scale naturally accommodate a PeV scale intermediate symmetry, required to explain the PeV events at IceCube.Comment: 33 pages, 9 figures, 4 tables; error in relic density calculation fixed and discussion expanded for better clarity; matches published versio

Constraints on Dark Matter-Neutrino Interaction from 21-cm Cosmology and Forecasts on SKA1-Low

In this article, we have done a thorough investigation of the possible effects of interaction between dark matter (DM) and neutrinos on reionization history. We have constrained the interaction strength using 21 cm Cosmology and found out possible deviations from standard, non-interacting $\Lambda$CDM scenario. Comparing the results with the existing constraints from present cosmological observations reveals that 21 cm observations are more competent to constrain the interaction strength by a few orders of magnitude. We have also searched for prospects of detecting any such interaction in the upcoming 21 cm mission SKA1-Low by doing a forecast analysis and error estimation.Comment: Version considerably modified. To appear in MNRA