Exact variational dynamics of the multimode Bose-Hubbard model based on 
SU(M)
 coherent states

AbstractWe prove that the flow of the discrete nonlinear Schrödinger equation (DNLS) is the mean field limit of the quantum dynamics of the Bose–Hubbard model for N interacting particles. In particular, we show that the Wick symbol of the annihilation operators evolved in the Heisenberg picture converges, as N becomes large, to the solution of the DNLS. A quantitative $$L^p$$ L p -estimate, for any $$p \ge 1$$ p ≥ 1 , is obtained with a linear dependence on time due to a Gaussian measure on initial data coherent states.

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Thermodynamics of the Two-Dimensional Hubbard Model Based on the Exact Two-Body S-Matrix

Brazilian Journal of Physics ◽

10.1007/s13538-012-0068-z ◽

2012 ◽

Vol 42 (1-2) ◽

pp. 28-40

Author(s):

André LeClair

Keyword(s):

Hubbard Model ◽

Two Dimensional ◽

Model Based ◽

S Matrix

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SUPERCONDUCTING COHERENT STATES FOR AN EXTENDED HUBBARD MODEL

International Journal of Modern Physics B ◽

10.1142/s0217979203023094 ◽

2003 ◽

Vol 17 (27) ◽

pp. 4859-4866

Author(s):

F. MADOURI ◽

Y. HASSOUNI ◽

M. EL BAZ

Keyword(s):

Hubbard Model ◽

Coherent States ◽

Extended Hubbard Model ◽

Quantum Symmetry ◽

Energy Expectation

An extended Hubbard model with phonons is considered. q-coherent states relative to the superconducting quantum symmetry of the model are constructed and their properties studied. It is shown that they can have energy expectation lower than eigenstates constructed via conventional processes and that they exhibit ODLRO.

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Representation, abstraction, and simple-minded sophisticates

Behavioral and Brain Sciences ◽

10.1017/s0140525x19002942 ◽

2020 ◽

Vol 43 ◽

Author(s):

Peter Dayan

Keyword(s):

Decision Theory ◽

Predictive Coding ◽

Bayesian Decision Theory ◽

Bayesian Decision ◽

Model Based ◽

Model Free

Abstract Bayesian decision theory provides a simple formal elucidation of some of the ways that representation and representational abstraction are involved with, and exploit, both prediction and its rather distant cousin, predictive coding. Both model-free and model-based methods are involved.

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Quantitative Model-Based Image Analysis of NuMa Distribution Links Nuclear Organization with Cell Phenotype

Microscopy and Microanalysis ◽

10.1017/s1431927600028968 ◽

2001 ◽

Vol 7 (S2) ◽

pp. 578-579

Author(s):

David W. Knowles ◽

Sophie A. Lelièvre ◽

Carlos Ortiz de Solόrzano ◽

Stephen J. Lockett ◽

Mina J. Bissell ◽

...

Keyword(s):

Image Analysis ◽

Mammary Epithelial Cells ◽

Nuclear Organization ◽

Critical Role ◽

Quantitative Model ◽

Mammary Epithelial ◽

Cell Phenotype ◽

Proliferating Cells ◽

Mitotic Apparatus ◽

Model Based

The extracellular matrix (ECM) plays a critical role in directing cell behaviour and morphogenesis by regulating gene expression and nuclear organization. Using non-malignant (S1) human mammary epithelial cells (HMECs), it was previously shown that ECM-induced morphogenesis is accompanied by the redistribution of nuclear mitotic apparatus (NuMA) protein from a diffuse pattern in proliferating cells, to a multi-focal pattern as HMECs growth arrested and completed morphogenesis . A process taking 10 to 14 days.To further investigate the link between NuMA distribution and the growth stage of HMECs, we have investigated the distribution of NuMA in non-malignant S1 cells and their malignant, T4, counter-part using a novel model-based image analysis technique. This technique, based on a multi-scale Gaussian blur analysis (Figure 1), quantifies the size of punctate features in an image. Cells were cultured in the presence and absence of a reconstituted basement membrane (rBM) and imaged in 3D using confocal microscopy, for fluorescently labeled monoclonal antibodies to NuMA (fαNuMA) and fluorescently labeled total DNA.

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