The mean value of variable | ||

Empty set | ||

Denotes a unit vector; | ||

A vector norm; ; also, cardinality of a set | ||

Denotes symmetric difference of two sets | ||

Denotes vector direct product, a.k.a. dyadic; , | ||

A scalar product of two vectors, a.k.a. dot product; | ||

A set of objects; | ||

A matrix or a vector filled with zeros | ||

One of the two superstates in two-state kinetic model | ||

Approximation to the inverse Hessian matrix, | ||

Set of all the nodes adjacent to node | ||

Set of all the nodes connected to node via incoming edges | ||

Set of all the nodes connected to node via outgoing edges | ||

One of the two superstates in two-state kinetic model | ||

Binary Lennard-Jones liquid with atoms in a periodic cell | ||

Square matrix, columns of which are eigenvectors | ||

A chain graph with nodes | ||

Endpoint separation | ||

th displacement in magnitude of an atom between structures and | ||

A set of edges | ||

Probability of escape from starting from in a single step | ||

Energy barrier corresponding to the reverse reaction | ||

Energy barrier corresponding to the forward reaction | ||

Set of all minima connected to the final endpoint | ||

Frequency distribution function | ||

An arbitrary graph with nodes | ||

Hessian matrix evaluated at point | ||

A set containing all the minima that do not belong to | ||

A complete graph with nodes | ||

Lagrangian function | ||

-atom Lennard-Jones cluster | ||

The set of all possible values of the control variable | ||

Number of atoms; number of nodes in a graph | ||

Cooperativity index | ||

Number of frames or points sampled along a path | ||

Number of images in a band | ||

Participation index | ||

Participation index evaluated using the endpoints alone | ||

Displacement overlap evaluated for atoms using displacements | ||

means holds for some constants | ||

Transition probability matrix | ||

Equilibrium occupation probability of state | ||

Occupation probability of state at time | ||

Probability of transition from state to state | ||

Pathway probability | ||

A random graph with nodes | ||

-dimensional rotation matrix about axis , | ||

The set of all real numbers | ||

Set of all minima connected to the starting endpoint | ||

Total probability of escape from if started at node | ||

Sum of weights of all pathways connecting and and confined to | ||

Temperature | ||

Displacement overlap evaluated for atoms using displacements | ||

Mean escape time from graph if started at node | ||

Set of all minima that do not belong to | ||

A set of feasible points contained in the neighbourhood of | ||

Potential energy functional; also, a set of graph nodes | ||

-dimensional vector of velocities[1]This vector and the other vectors defined here are column vectors. | ||

Spring potential | ||

Weight of the shortest path ; | ||

The set of whole numbers; | ||

Product of branching probabilities associated with path | ||

-dimensional vector representing a point in configuration space | ||

Pathway ensemble | ||

A state that belongs to a superstate | ||

Pathway nonlinearity index | ||

A state that belongs to a superstate | ||

Energy barrier asymmetry index | ||

Eigenvector | ||

A determinant [33] (a scalar-valued function) of matrix | ||

Integrated path length for atom ; also, degree of node | ||

Displacement of atom between structures and | ||

Directed edge that describes a transition from node to node | ||

A parameter in LJ potential (the depth of the potential energy well) | ||

Small positive parameter | ||

Number of atomic degrees of freedom | ||

Objective function of a vector argument | ||

-dimensional gradient vector of the true potential | ||

Kurtosis of a distribution evaluated using moments about the mean | ||

Kurtosis of a distribution evaluated using moments about the origin | ||

Spring gradient vector component parallel to the path | ||

Spring gradient vector component perpendicular to the path | ||

-dimensional gradient vector of the spring potential | ||

True gradient vector component parallel to the path | ||

True gradient vector component perpendicular to the path | ||

Indices; range and meaning may vary depending on the context | ||

Boltzmann's constant | ||

Rate constant for transitions from state to state | ||

Spring force constant | ||

Length of path | ||

Eigenvalue | ||

Atomic mass | ||

th moment of a distribution function about the mean | ||

th moment of a distribution function about the origin | ||

Time parameter of a discrete-time stochastic process | ||

means holds for all constants [1]Otherwise known as an upper bound that is not asymptotically tight. | ||

Search direction vector | ||

Path length asymmetry index | ||

Three-dimensional Cartesian coordinates vector of atom for structure | ||

Integrated path length | ||

A parameter in the LJ potential ( is the pair equilibrium separation) | ||

| -dimensional tangent vector | |

Mean waiting time in state before escape | ||

Time | ||

Time integration step | ||

A matrix or vector transpose | ||

Step size | ||

th graph node | ||

Weight of the undirected edge connecting nodes and | ||

th component of vector | ||

A pathway | ||

Vectors; dimensionality and meaning may vary depending on the context |