Related papers: Augmented Transition Path Theory for Sequences of …
Real-world scenarios demand reasoning about process, more than final outcome prediction, to discover latent causal chains and better understand complex systems. It requires the learning algorithms to offer both accurate predictions and…
Beyond their use as numerical tools, quantum trajectories can be ascribed a degree of reality in terms of quantum measurement theory. In fact, they arise naturally from considering continuous observation of a damped quantum system. A…
Atypical, rare trajectories of dynamical systems are important: they are often the paths for chemical reactions, the haven of (relative) stability of planetary systems, the rogue waves that are detected in oil platforms, the structures that…
Agent-based models are a natural choice for modeling complex social systems. In such models simple stochastic interaction rules for a large population of individuals can lead to emergent dynamics on the macroscopic scale, for instance a…
We study the rate of activated motion over multiple barriers, in particular the correlated double-jump of an adatom diffusing on a missing-row reconstructed Platinum (110) surface. We develop a Transition Path Theory, showing that the…
The pathway is a biological term that refers to a series of interactions between molecules in a cell that causes a certain product or a change in the cell. Pathway analysis is a powerful method for gene expression analysis. Through pathway…
Influence theory is a foundational theory of physics that is not based on traditional empirically defined concepts, such as positions in space and time, mass, energy, or momentum. Instead, the aim is to derive these concepts, and their…
Transition state or minimum energy path finding methods constitute a routine component of the computational chemistry toolkit. Standard analysis involves trajectories conventionally plotted in terms of the relative energy to the initial…
Recent advances in reaction prediction have achieved near-saturated accuracy on standard benchmarks (e.g., USPTO), yet most state-of-the-art models formulate the task as a one-shot mapping from reactants to products, offering limited…
The dominant reaction pathway (DRP) is a rigorous framework to microscopically compute the most probable trajectories, in non-equilibrium transitions. In the low-temperature regime, such dominant pathways encode the information about the…
In the development of equations of state for polyatomic molecules, thermodynamic perturbation theory (TPT) is widely used to calculate the change in free energy due to chain formation. TPT is a simplification of a more general and exact…
The rates of chemical reactions are not absolute but their magnitude depends upon the relative speeds of the moving observers. This has been proved by unifying theories of chemical kinetics, which are transition state theory, collision…
The modelling of linear and nonlinear reaction-subdiffusion processes is more subtle than normal diffusion and causes different phenomena. The resulting equations feature a spatial Laplacian with a temporal memory term through a time…
The mathematical formulation of the model for molecular movement of single motor proteins driven by cyclic biochemical reactions in an aqueous environment leads to a drifted Brownian motion characterized by coupled diffusion equations. In…
We apply quantum rate theory to calculate the transition rates as hydrogen or deuterium atoms escape from a vacancy trap in iron into a neighbouring metastable site. We determine transition rates and corresponding activation energies over a…
Phase separation is the thermodynamic process that explains how droplets form in multicomponent fluids. These droplets can provide controlled compartments to localize chemical reactions, and reactions can also affect the droplets' dynamics.…
This paper proposes a graph-based approach to representing spatio-temporal trajectory data that allows an effective visualization and characterization of city-wide traffic dynamics. With the advance of sensor, mobile, and Internet of Things…
The pathway idea is a way of going from one family of functions to another family of functions and yet another family of functions through a parameter in the model so that a switching mechanism is introduced into the model through a…
Thermodynamics of trajectories promises to make possible the thorough analysis of the dynamical properties of an open quantum system, a sought-after goal in modern physics. Unfortunately, calculation of the relevant quantities presents…
These lecture notes cover basic automata-theoretic concepts and logical formalisms for the modeling and verification of concurrent and distributed systems. Many of these concepts naturally extend the classical automata and logics over…