Systematic Class of Information Based Architecture Types
Harald Maurer in Cognitive Science, 2021
This relationship between probability and harmony is mathematically identical to the relationship between probability and (minus) energy in statistical physics: the Gibbs223 or Boltzmann208 law. This is the basis of the isomorphism between cognition and physics, exploited by harmony theory. In statistical physics, H is called the Hamiltonian function; it measures the energy of a state of a physical system. In physics, T is the temperature of the system. In harmony theory, T is called the computational temperature (Smolensky 1983) of the cognitive system. When the temperature is very high, completions with high harmony are assigned estimated probabilities that are only slightly higher than those assigned to low harmony completions; the environment is treated as more random in the sense that all completions are estimated to have roughly equal probability. When the temperanire is very low, only the completions with highest harmony are given non negligible estimated probabilities (Smolensky 1986a),"
Dictionary
Mario P. Iturralde in Dictionary and Handbook of Nuclear Medicine and Clinical Imaging, 1990
Hamiltonian. (H) The hamiltonian is a mathematical operator used in quantum mechanical treatment of some phenomena (e.g., magnetic resonance). It represents the sum of the kinetic and potential energies of a particle or a system. It can be represented as a function of momentum and position coordinates of the particle. It can be expressed as H = p2/2m + V(r), where p is the momentum operator, V(r) is the potential energy as a function of position operator r, and m is the mass of the particle.
Computational Methods for Bayesian Analysis
Gary L. Rosner, Purushottam W. Laud, Wesley O. Johnson in Bayesian Thinking in Biostatistics, 2021
In physics, the function is called the potential energy that corresponds to the “position,” θ, and the function is called the kinetic energy, which is determined by the “momenta,” δ. Momentum would have physical meaning in a real physical problem, but here it is used as a device, so we do not discuss its meaning. The Hamiltonian function H is termed the total energy.
Frontiers of metal-coordinating drug design
Published in Expert Opinion on Drug Discovery, 2021
Giulia Palermo, Angelo Spinello, Aakash Saha, Alessandra Magistrato
In QM/MM studies of metallo-systems, the metal and its coordination sphere are treated at a higher level of accuracy (QM level), while the remainder of the system is described at the MM (FF) level of theory (Figure 1). Namely, for an inhibitor binding to the metalloenzyme, the QM region should comprise the enzyme’s metal center, the residues coordinating to it, and the inhibitor. In the case of a metallodrug binding an enzyme, the QM region includes the drug and the residues/nucleobases of the protein/nucleic acid directly binding the metal. In the general form of a hybrid QM/MM scheme, Eq. 2, the Hamiltonian
Exploring space-energy matching via quantum-molecular mechanics modeling and breakage dynamics-energy dissipation via microhydrodynamic modeling to improve the screening efficiency of nanosuspension prepared by wet media milling
Published in Expert Opinion on Drug Delivery, 2021
Jing Tian, Fangxia Qiao, Yanhui Hou, Bin Tian, Jianhong Yang
where H is the Hamiltonian operator, Ψ is the wave function, E represents energy, r represents electrons, and R denotes the positions of the electrons relative to the atomic nucleus. Thereinto, the nucleus term was considered in the earliest equation, due to motions of electrons being actually affected by other electrons and nucleus. Subsequently, based on the theory of quantum mechanics methods, it removes the nucleus term from the R term and mainly the parts for electrons are derived. However, the difficulty of this computation increases greatly because of the additional dimension. The density functional theory must be applied to reduce the difficulty because it transforms the three-dimensional wave function equation into a three-dimensional density function [29].
Optimal Control Model and Cost Effectiveness Analysis of Maize Streak Virus Pathogen Interaction with Pest Invasion in Maize Plant
Published in Egyptian Journal of Basic and Applied Sciences, 2020
Haileyesus Tessema Alemneh, Oluwole Daniel Makinde, David Mwangi Theuri
Proof. The adjoint equation and transversality conditions are standard results obtained from Pontryagin’s maximum principle [30]. We differentiate Hamiltonian in Equation (6) with respect to states
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