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Density functional theory (DFT) exploits an independent-particle-system construction to replicate the densities and current of an interacting system. This construction is used here to access the exact effective potential and bias of…

The spatial distribution of income shapes the structure and organisation of cities and its understanding has broad societal implications. Despite an abundant literature, many issues remain unclear. In particular, all definitions of…

Evolutionary dynamics and patterns of molecular evolution are strongly influenced by selection on linked regions of the genome, but our quantitative understanding of these effects remains incomplete. Recent work has focused on predicting…

We present an explicit unified stochastic model of fluctuations in population size due to random birth, death, density-dependent competition and environmental fluctuations. Stochastic dynamics provide insight into small populations,…

Density functional theory (DFT) stands as a cornerstone method in computational quantum chemistry and materials science due to its remarkable versatility and scalability. Yet, it suffers from limitations in accuracy, particularly when…

Mobility is a fundamental feature of human life, and through it our interactions with the world and people around us generate complex and consequential social phenomena. Social segregation, one such process, is increasingly acknowledged as…

Homophily and heterophobia, the tendency for people with similar characteristics to preferentially interact with (or avoid) each other are pervasive in human social networks. Here, we develop an extension of the mathematical theory of urban…

Nuclear density functional theory (DFT) is one of the main theoretical tools used to study the properties of heavy and superheavy elements, or to describe the structure of nuclei far from stability. While on-going efforts seek to better…

In two-strategy decision-making problems, individuals often imitate the highest earners or choose either the common or rare strategy. Individuals who benefit from the common strategy are conformists, whereas those who profit by choosing the…

The effects of demographic stochasticity in the long term behaviour of endemic infectious diseases have been considered for long as a necessary addition to an underlying deterministic theory. The latter would explain the regular behaviour…

Resource allocation plays a central role in many networked systems such as smart grids, communication networks and urban transportation systems. In these systems, many constraints have physical meaning and having feasible allocation is…

In binary decision-making, individuals often choose either the rare or the common action. In the framework of evolutionary game theory, the best-response update rule can be used to model this dichotomy. Those who prefer the common action…

Mean-field theories have proven to be efficient tools for exploring diverse phases of matter, complementing alternative methods that are more precise but also more computationally demanding. Conventional mean-field theories often fall short…

The driving force of the dynamical system can be decomposed into the gradient of a potential landscape and curl flux (current). The fluctuation-dissipation theorem (FDT) is often applied to near equilibrium systems with detailed balance.…

Deep-learning density functional theory (DFT) shows great promise to significantly accelerate material discovery and potentially revolutionize materials research. However, current research in this field primarily relies on data-driven…

A fundamental assumption of the dynamical density functional theory (DDFT) of colloidal systems is that a grand-canonical free energy functional may be employed to generate the thermodynamic driving forces. Using one-dimensional hard-rods…

This work addresses a longstanding theoretical discrepancy using Density Functional Theory (DFT) with experimental observations of CO binding trends on electrocatalytically relevant metals for the CO2 reduction reaction (CO2RR). By…

We will discuss the key concepts in density functional theory (DFT), how it can be used to model experimental data, and consider how the synergy between DFT and experiment can give significant insights. The discussion will centre on the…

This paper presents a quantitative framework for forecasting immigrant integration using immigrant density as the single driver. By comparing forecasted integration estimates based on data collected up to specific periods in time, with…

Cities are characterized by the coexistence of general aggregate patterns, along with many local variations. This poses challenges for analyses of urban phenomena, which tend to be either too aggregated or too local, depending on the…