Related papers: Complete integrability of information processing b…
Scaling analysis exploiting timescale separation has been one of the most important techniques in the quantitative analysis of nonlinear dynamical systems in mathematical and theoretical biology. In the case of enzyme catalyzed reactions,…
We analyze the dynamics of an algorithm for approximate inference with large Gaussian latent variable models in a student-teacher scenario. To model nontrivial dependencies between the latent variables, we assume random covariance matrices…
Understanding a complex system entails capturing the non-trivial collective phenomena that arise from interactions between its different parts. Information theory is a flexible and robust framework to study such behaviours, with several…
Quantum mechanical equations of motion are strictly linear in state descriptors, such as wavefunctions and density matrices, but equations describing chemical kinetics and hydrodynamics may be non-linear in concentrations. This…
Equilibrium statistical mechanics is intended to link the microscopic dynamics of particles to the thermodynamic laws for macroscopic quantities. However, the modern statistical theory is faced with significant difficulties, as applied to…
The past two decades have seen a revolution in statistical physics, generalizing it to apply to systems of arbitrary size, evolving while arbitrarily far from equilibrium. Many of these new results are based on analyzing the dynamics of the…
Biochemical systems are inherently stochastic, particularly those with small-molecule populations. The spatial distribution of molecules plays a critical role and requires the inclusion of spatial coordinates in their analysis. Stochastic…
During the last decade, a large number of different numerical methods have been proposed to tackle the automatic identification and quantification in {\gamma}-ray spectrometry. However, the lack of common benchmarks, including datasets,…
Extensive cooperation among unrelated individuals is unique to humans, who often sacrifice personal benefits for the common good and work together to achieve what they are unable to execute alone. The evolutionary success of our species is…
Due to the equivalence of the statistical ensembles thermostatic properties of physical systems with short-range interactions can be calculated in different ensembles leading to the same physics. In particular, the ensemble equivalence…
In this work we review some recent development in the mathematical modelling of quantitative sociology by means of statistical mechanics. After a short pedagogical introduction to static and dynamic properties of many body systems, we…
Sensitivity analysis of biochemical reactions aims at quantifying the dependence of the reaction dynamics on the reaction rates. The computation of the parameter sensitivities, however, poses many computational challenges when taking…
The two-body potential of systems with long-range interactions decays at large distances as $V(r)\sim 1/r^\alpha$, with $\alpha\leq d$, where $d$ is the space dimension. Examples are: gravitational systems, two-dimensional hydrodynamics,…
All ensembles of statistical mechanics are equivalent in the sense that they give the equivalent thermodynamic functions in the thermodynamic limit. However, when investigating microscopic structures in the first-order phase transition…
Classical swarm models, exemplified by the Cucker--Smale framework, provide foundational insights into collective alignment but exhibit fundamental limitations in capturing the adaptive, heterogeneous behaviours intrinsic to living systems.…
Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics…
The formalism of statistical mechanics can be generalized by starting from more general measures of information than the Shannon entropy and maximizing those subject to suitable constraints. We discuss some of the most important examples of…
Simplified stochastic models are widely used in the study of frequency-resolved noise propagation in biochemical reaction networks, a common measure being the coherence between random fluctuations in molecule number trajectories. Such…
The central philosophy of statistical mechanics (stat-mech) and random-matrix theory of complex systems is that while individual instances are essentially intractable to simulate, the statistical properties of random ensembles obey simple…
An exact approach to compute physical properties for general multi-electronic-state (MES) systems in thermal equilibrium is presented. The approach is extended from our recent progress on path integral molecular dynamics (PIMD) [J. Chem.…