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The state space or phase space is the geometric space in which the axes are the state variables. The system state can be represented as a vector , the state vector . If the dynamical system is linear, time-invariant, and finite-dimensional, then the differential and algebraic equations may be written in matrix form.
In the simpler case, switching state-space models are defined based on a switching variable which evolves independent of the hidden variable. The probabilistic model of such variant of SKF is as the following: [10] [This section is badly written: It does not explain the notation used below.]
Dynamic models, [86] [87] Bayesian belief networks, [88] Fisher information, [89] and fuzzy cognitive maps [90] have been used as a tool to explore the phase space where regime shifts are likely to happen and understand the dynamics that govern dynamic thresholds. Models are useful oversimplifications of reality, whose limits are given by the ...
The SAFT equation of state was developed using statistical mechanical methods (in particular the perturbation theory of Wertheim [12]) to describe the interactions between molecules in a system. [ 1 ] [ 13 ] [ 14 ] The idea of a SAFT equation of state was first proposed by Walter G. Chapman and by Chapman et al. in 1988 and 1989.
A water model is defined by its geometry, together with other parameters such as the atomic charges and Lennard-Jones parameters. In computational chemistry, a water model is used to simulate and thermodynamically calculate water clusters, liquid water, and aqueous solutions with explicit solvent.
MSM is a stochastic volatility model [10] [11] with arbitrarily many frequencies. MSM builds on the convenience of regime-switching models, which were advanced in economics and finance by James D. Hamilton. [12] [13] MSM is closely related to the Multifractal Model of Asset Returns. [14]
Chaotic Liquid State Machine The liquid (i.e. reservoir) of a Chaotic Liquid State Machine (CLSM), [ 20 ] [ 21 ] or chaotic reservoir, is made from chaotic spiking neurons but which stabilize their activity by settling to a single hypothesis that describes the trained inputs of the machine.
Markov switching multifractal – model of asset returns Weighted planar stochastic lattice – mathematical structure sharing some of the properties both of lattices and of graphs Pages displaying wikidata descriptions as a fallback