Daily mean PM\(_{2.5}\) concentrations in Hyderabad routinely exceed both the 24-hour (\(60\,\mu\text{g/m}^3\)) and the annual (\(40\,\mu\text{g/m}^3\)) National Ambient Air Quality Standards, motivating the development of transparent and inexpensive descriptive models of their seasonal behaviour. To this end, we develop and calibrate a parsimonious first-order linear ordinary differential equation (ODE) that describes the daily evolution of ambient PM\(_{2.5}\) as the balance between a seasonally varying emission source \(E(t)=E_{0}+A\cos(2\pi(t-\varphi)/365)\) and a wind-driven first-order removal \(\lambda(t)=\alpha v(t)+\lambda_{0}\). The five parameters are estimated by Differential Evo... More >

The modern era is characterized by rapid advancements in technology, wherein the design and topology of interconnection networks play a pivotal role in enabling efficient communication systems. The analysis of topological and structural characteristics of interconnection networks, however, remains a challenging task. Graph theory facilitates this process by enabling analytical and efficient solutions through the use of numerical parameters known as topological descriptors. These descriptors have proven to be highly significant, with applications spanning computer science, chemistry, biology, and related domains. This paper deals with the evaluation of topological descriptors for an $n$-dimen... More >

This paper develops a dynamical systems model of an economy with recursively self-improving artificial intelligence and financialization. The model features quadratic self-amplification in both AI capability ($\lambda A^2$) and financial capital ($\gamma_F K_f^2$), coupled through investment flows. It is shown that under mild conditions, the system exhibits a finite-time singularity where AI capability, AI capital, and financial capital diverge. Near the singularity, the wealth ratio between capital owners and workers diverges super-exponentially, with financialization amplifying the exponent by a factor $\gamma_F/\eta$. Introducing taxes on AI returns ($\tau_{ai}$) and financial gains ($\ta... More >