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Systematic Class of Information Based Architecture Types
Published in Harald Maurer, 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),"
Multi-scale modeling approaches: application in chemo– and immuno–therapies
Published in Issam El Naqa, A Guide to Outcome Modeling in Radiotherapy and Oncology, 2018
where τ(σ) is the cell type associated with cell σ; J() is the surface energy determining the adhesion between two cells; δ is the Kronecker (tensor) product; υ(σ) is the volume of cell σ, V(σ) is the target volume; and λ is a Lagrange multiplier determining the strength of the volume constraint. The Hamiltonian has been modified to control cell behaviors such as chemotaxis, elongation and haptotaxis by using other sub-lattices containing information such as the concentrations of chemicals as shown in Figure 11.5 [482].
Dictionary
Published in Mario P. Iturralde, 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.
Development of reliable quantitative structure–toxicity relationship models for toxicity prediction of benzene derivatives using semiempirical descriptors
Published in Toxicology Mechanisms and Methods, 2023
Ayushi Singh, Sunil Kumar, Archana Kapoor, Parvin Kumar, Ashwani Kumar
The studied dataset was acquired from literature (Lu et al. 2001; Haghdadi and Fatemi 2010). In a study, Lu et al. reported a 50% effective inhibitory concentration of 39 substituted benzenes against S. obliquus after 48 h of exposure. The algae inhibition test was used to determine these values, which were then reported as pEC50. The range of values of pEC50 varied from 2.36 to 5.04. The dataset of 103 NB derivatives and 392 benzene derivatives was taken from the reported work (Schultz and Netzeva 2004; Bellifa and Mekelleche 2016; Castillo-Garit et al. 2016; El-chokrafi 2018). These substituted NB and benzene compounds were discovered to have a 50% effective inhibitory concentration against T. pyriformis, and these values were also determined using an algae inhibition test in the form of pEC50. These derivatives with experimental data were first drawn, standardized, and optimized by Marvin sketch software (version:21.2.0, Chemaxon, open source) and then further optimization of the resulting molecular structures was performed with MOPAC (2016) software version 21.041w (open source) using PM7 semi-empirical Hamiltonians. The gnorm value was set to 0.01 for minimization and descriptors calculation. The models were developed using QSARINS software version 2.2.4 (open source).
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].
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