The Lagrangian formalism is developed for the population dynamics of interacting species that are described by several well-known models. The formalism is based on standard Lagrangians, which represent differences between the physical kinetic and potential energy-like terms. A method to derive these Lagrangians is presented and applied to selected theoretical models of the population dynamics. The role of the derived Lagrangians and the energy-like terms in the population dynamics is investigated, and it is shown that the obtained standard Lagrangians can be used to study oscillatory behavior of the models and the period of their oscillations, which may have ecological and environmental implications. These and other physical and biological insights gained from the derived standard Lagrangians are discussed.

Non-standard Lagrangians do not display any discernible energy-like terms, yet they give the same equations of motion as standard Lagrangians, which have easily identifiable energy-like terms. A new method to derive non-standard Lagrangians for second-order nonlinear differential equations with damping is developed and the limitations of this method are explored. It is shown that the limitations do not exist only for those nonlinear dynamical systems that can be converted into linear ones. The obtained results are applied to selected population dynamics models for which non-standard Lagrangians and their corresponding null Lagrangians and gauge functions are derived, and their roles in the population dynamics are discussed.

Retiring coal power plants can reduce air pollution and health damages. However, the spatial distribution of those impacts remains unclear due to complex power system adjustments and pollution chemistry and transport. Focusing on coal retirements in Pennsylvania (PA), we analyze six counterfactual scenarios for 2019 that differ in retirement targets (e.g., reducing 50% of coal-based installed capacity vs. generation) and priorities (e.g., closing plants with higher cost, closer to Environmental Justice Areas, or with higher CO₂ emissions). Using a power system model of the PJM Interconnection, we find that coal retirements in PA shift power generation across PA and the Rest of PJM region leading to scenario-varying changes in the plant-level release of several air pollutants. Due to air pollution chemistry and transport and socio-demographics, these changes in turn give rise to a reduction of 10 to 182 PM_2.5-attributable deaths in PJM across the six scenarios, with most reductions occurring in PA. Scenarios that reduce more coal power generation yield greater aggregate health benefits due to air quality improvements in PA and adjacent downwind regions. In addition, vulnerable populations—in both PA and Rest of PJM—benefit most in scenarios that prioritize plant closures in PA near Environmental Justice Areas. These results demonstrate the importance of considering cross-regional linkages and socio-demographics in designing equitable retirement strategies.

In the past decade, targeted therapies for solid tumors, including non-small cell lung cancer (NSCLC), have advanced significantly, offering tailored treatment options for patients. However, individuals without targetable mutations pose a clinical challenge, as they may not respond to standard treatments like immune-checkpoint inhibitors (ICIs) and novel targeted therapies. While the mechanism of action of ICIs seems promising, the lack of a robust response limits their widespread use. Although the expression levels of programmed death ligand 1 (PD-L1) on tumor cells are used to predict ICI response, identifying new biomarkers, particularly those associated with the tumor microenvironment (TME), is crucial to address this unmet need. Recently, inflammatory cytokines such as interleukin-1 beta (IL-1β) have emerged as a key area of focus and hold significant potential implications for future clinical practice. Combinatorial approaches of IL-1β inhibitors and ICIs may provide a potential therapeutic modality for NSCLC patients without targetable mutations. In this review, we discuss the role of IL-1β in NSCLC, its involvement in inflammatory pathways, and explore its potential role in the treatment of NSCLC.