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Lie algebra

Gwang-Won Kim, Yun-Hyeon Kim, Kwangsung Park, Gwang-Woo Jeong
Cross-sex hormones in female-to-male (FtM) transsexuals play a crucial role in brain plasticity. Morphological study associated with white matter (WM) volume in postoperative FtM transsexuals receiving cross-sex hormones has not been published yet. This study was performed to discriminate the regional WM volume differences between postoperative FtM transsexuals and female controls using voxel-based morphometry (VBM) and further to assess the correlations between regional volume variations and cross-sex hormones...
January 24, 2019: International Journal of Impotence Research
Stefano Maestri, Emanuela Merelli
The successful use of process calculi to specify behavioural models allows us to compare RNA and protein folding processes from a new perspective. We model the folding processes as behaviours resulting from the interactions that nucleotides and amino acids (the elementary units that compose RNAs and proteins respectively) perform on their linear sequences. This approach is intended to provide new knowledge about the studied systems without strictly relying on empirical data. By applying Milner's CCS process algebra to highlight the distinguishing features of the two folding processes, we discovered an abstraction level at which they show behavioural equivalences...
January 24, 2019: Scientific Reports
E Yakaboylu, M Shkolnikov, M Lemeshko
We present an approach to interacting quantum many-body systems based on the notion of quantum groups, also known as q-deformed Lie algebras. In particular, we show that, if the symmetry of a free quantum particle corresponds to a Lie group G, in the presence of a many-body environment this particle can be described by a deformed group, G_{q}. Crucially, the single deformation parameter, q, contains all the information about the many-particle interactions in the system. We exemplify our approach by considering a quantum rotor interacting with a bath of bosons, and demonstrate that extracting the value of q from closed-form solutions in the perturbative regime allows one to predict the behavior of the system for arbitrary values of the impurity-bath coupling strength, in good agreement with nonperturbative calculations...
December 21, 2018: Physical Review Letters
Viktor Szalay, Dominika Viglaska, Michael Rey
The internal-axis system (IAS) of molecules with a large amplitude internal motion (LAM) is determined by integrating the kinematic equation of the IAS by Lie-group and Lie-algebraic methods. Numerical examples on hydrogen peroxide, nitrous acid, and acetaldehyde demonstrate the methods. By exploiting the special product structure of the solution matrix, simple methods are devised for calculating the transformation to the rho-axis system (RAS) along with the value of the parameter ρ characterizing a RAS rotational-LAM kinetic energy operator...
December 28, 2018: Journal of Chemical Physics
Zahra Ghobadi Nejad, Seyed Mehdi Borghei, Soheila Yaghmaei, Atefeh Hasan-Zadeh
Laccase production by indigenous fungus, Phanerochaete chrysosporium, requires solving optimal problems to determine the maximum production of the enzyme within a definite time period and conditions specified in the solid-state fermentation process. For this purpose, parallel to response surface methodology, an analytical approach has been proposed based on the advanced concepts of Poisson geometry and Lie groups, which lead to a system of the Hamiltonian equations. Despite the dating of the Hamiltonian approach to solving biological problems, the novelty of this paper is based on the expression of a Hamiltonian system in notions of Poisson geometry, Lie algebras and symmetry groups and first integrals...
December 18, 2018: Mathematical Biosciences
R R Valiev, G V Baryshnikov, D Sundholm
Magnetically induced current densities have been calculated at the second-order Møller-Plesset perturbation theory (MP2) level for seven hetero[8]circulenes and their dicationic and dianionic forms. Calculations of the magnetic dipole transition moments have also been carried out at the algebraic diagrammatic construction (ADC(2)) and the second-order approximate coupled-cluster (CC2) levels. The calculations show that the degree of aromaticity and the size of the magnetic dipole transition moment of the lowest magnetic-dipole allowed excited state are related...
November 26, 2018: Physical Chemistry Chemical Physics: PCCP
Lee M Thompson
Broken symmetry solutions-solutions to the independent particle model that do not obey all symmetries required by the Hamiltonian-have attracted significant interest for capturing multireference properties with mean-field scaling. However, identification and optimization of broken-symmetry solutions is difficult owing to the non-linear nature of the self-consistent field (SCF) equations, particularly for solutions belonging to low-symmetry subgroups and where multiple broken symmetry solutions are sought. Linearization of SCF solution space results in the Lie algebra, which this work utilizes as a framework for elucidation of the set of solutions that exist at the desired symmetry...
November 21, 2018: Journal of Chemical Physics
Mark P Bogers, Tomáš Brauner
We use Lie-algebraic arguments to classify Lorentz-invariant theories of massless interacting scalars that feature coordinate-dependent redundant symmetries of the Galileon type. We show that such theories are determined, up to a set of low-energy effective couplings, by specifying an affine representation of the Lie algebra of physical, nonredundant internal symmetries and an invariant metric on its target space. This creates an infinite catalog of theories relevant for both cosmology and high-energy physics thanks to their special properties such as enhanced scaling of scattering amplitudes in the soft limit...
October 26, 2018: Physical Review Letters
Ruben Stienstra, Walter D van Suijlekom
We give an operator-algebraic interpretation of the notion of an ideal generated by the unbounded operators associated with the elements of the Lie algebra of a Lie group that implements the symmetries of a quantum system. We use this interpretation to establish a link between Rieffel induction and the implementation of a local Gauss law in lattice gauge theories similar to the method discussed by Kijowski and Rudolph (J Math Phys 43:1796-1808, 2002; J Math Phys 46:032303, 2004).
2018: Letters in Mathematical Physics
Fajun Yu, Li Li, Shuo Feng
A few of discrete integrable coupling systems(DICSs) of previous papers are linear discrete integrable couplings(LDICS). We take a special matrix Lie algebra system(non-semisimple) to construct the Lax pairs, and establish a method for deriving the nonlinear discrete integrable coupling systems(NDICS). From the Lax pairs of the generalized Toda(G-Toda) spectral problem, we can derive a novel NDICS, which is a real NDICS. For the obtained lattice integrable coupling equation, we establish a Darboux transformation (DT) with 4 × 4 Lax pairs, and apply the gauge transformation to a specific equation, then the explicit solutions of the lattice integrable coupling equation are given, which contains discrete soliton solution, breather solution and rogue wave solution...
October 16, 2018: Scientific Reports
Anis Kacem, Zakia Hammal, Mohamed Daoudi, Jeffrey Cohn
Recent breakthroughs in deep learning using automated measurement of face and head motion have made possible the first objective measurement of depression severity. While powerful, deep learning approaches lack interpretability. We developed an interpretable method of automatically measuring depression severity that uses barycentric coordinates of facial landmarks and a Lie-algebra based rotation matrix of 3D head motion. Using these representations, kinematic features are extracted, preprocessed, and encoded using Gaussian Mixture Models (GMM) and Fisher vector encoding...
May 2018: Proceedings of the ... International Conference on Automatic Face and Gesture Recognition
Kristen M Campbell, P Thomas Fletcher
This paper presents an efficient, numerically stable algorithm for parallel transport of tangent vectors in the group of diffeomorphisms. Previous approaches to parallel transport in large deformation diffeomorphic metric mapping (LDDMM) of images represent a momenta field, the dual of a tangent vector to the diffeomorphism group, as a scalar field times the image gradient. This "scalar momenta" constraint couples tangent vectors with the images being deformed and leads to computationally costly horizontal lifts in parallel transport...
September 2017: Graphs in Biomedical Image Analysis, Computational Anatomy and Imaging Genetics: first International Workshop, GRAIL 2017, 6th International Workshop, MFCA 2017, and third International Workshop, MICGen 2017, held in conjunction with MICCAI 2017, Québec
A B Trofimov, I Powis, R C Menzies, D M P Holland, E Antonsson, M Patanen, C Nicolas, C Miron, A D Skitnevskaya, E V Gromov, H Köppel
The valence shell photoelectron spectrum of cis -dichloroethene has been studied both experimentally and theoretically. Photoelectron spectra have been recorded with horizontally and vertically plane polarized synchrotron radiation, thereby allowing the anisotropy parameters, characterizing the angular distributions, to be determined. The third-order algebraic-diagrammatic construction approximation scheme for the one-particle Green's function has been employed to compute the complete valence shell ionization spectrum...
August 21, 2018: Journal of Chemical Physics
Chenxi Li, Zelin Shi, Yunpeng Liu, Tianci Liu, Lingyun Xu
This paper considers the joint geometric and photometric image registration problem. The inverse compositional (IC) algorithm and the efficient second-order minimization (ESM) algorithm are two typical efficient methods applied to the geometric registration problem. Their efficiency stems from the utilization of the group structure of geometric transformations. To allow for photometric variations, the dual IC algorithm (DIC) proposed by Bartoli performs joint geometric and photometric image registration by extending the IC algorithm...
December 2018: IEEE Transactions on Image Processing: a Publication of the IEEE Signal Processing Society
Lin Wu, Fuqing Zhou, Yue Zhang, Jian Li, Hongmei Kuang, Jie Zhan, Dechang Peng, Laichang He, Xianjun Zeng, Honghan Gong
Disrupted white matter structure has been established in patients with diffuse axonal injury (DAI), but morphological changes in gray matter and local intrinsic activity in the short and midterm (before 6 months) have not been documented in DAI patients. We hypothesized that regionally selective atrophy observed in deep gray matter in the short-term and mid-term periods in patients with mild-to-moderate DAI, local atrophy, and/or dysfunction would be related to clinical characteristics. We evaluated the changes in regional density and synchronization in 18 DAI patients separately using Diffeomorphic Anatomical Registration through Exponentiated Lie algebra-enhanced voxel-based morphometry and regional homogeneity (ReHo)...
October 17, 2018: Neuroreport
Andrea Insinga, Bjarne Andresen, Peter Salamon, Ronnie Kosloff
We show that the inability of a quantum Otto cycle to reach a limit cycle is connected with the propagator of the cycle being noncompact. For a working fluid consisting of quantum harmonic oscillators, the transition point in parameter space where this instability occurs is associated with a non-Hermitian degeneracy (exceptional point) of the eigenvalues of the propagator. In particular, a third-order exceptional point is observed at the transition from the region where the eigenvalues are complex numbers to the region where all the eigenvalues are real...
June 2018: Physical Review. E
Yinyan Zhang, Shuai Li, Xiaoping Liu
In this paper, the receding horizon near-optimal tracking control problem about a class of continuous-time nonlinear systems with fully unknown dynamics is considered. The main challenges of this problem lie in two aspects: 1) most existing systems only restrict their considerations to the state feedback part while the input channel parameters are assumed to be known. This paper considers fully unknown system dynamics in both the state feedback channel and the input channel and 2) the optimal control of nonlinear systems requires the solution of nonlinear Hamilton-Jacobi-Bellman equations...
December 2018: IEEE Transactions on Neural Networks and Learning Systems
Joy Christian
The exceptional Lie group E 8 plays a prominent role in both mathematics and theoretical physics. It is the largest symmetry group associated with the most general possible normed division algebra, namely, that of the non-associative real octonions, which-thanks to their non-associativity-form the only possible closed set of spinors (or rotors) that can parallelize the 7-sphere. By contrast, here we show how a similar 7-sphere also arises naturally from the algebraic interplay of the graded Euclidean primitives, such as points, lines, planes and volumes, which characterize the three-dimensional conformal geometry of the ambient physical space, set within its eight-dimensional Clifford-algebraic representation...
May 2018: Royal Society Open Science
Léon Brenig
A global framework for treating nonlinear differential dynamical systems is presented. It rests on the fact that most systems can be transformed into the quasi-polynomial format. Any system in this format belongs to an infinite equivalence class characterized by two canonical forms, the Lotka-Volterra (LV) and the monomial systems. Both forms allow for finding total or partial integrability conditions, invariants and dimension reductions of the original systems. The LV form also provides Lyapunov functions and systematic tools for stability analysis...
July 28, 2018: Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
Raphael F Ribeiro, Joel Yuen-Zhou
Explorations of the consequences of the Jahn-Teller (JT) effect remain active in solid-state and chemical physics. In this topical review we revisit the class of JT models which exhibit continuous vibronic symmetries. A treatment of these systems is given in terms of their algebraic properties. In particular, the compact symmetric spaces corresponding to JT models carrying a vibronic Lie group action are identified, and their invariants used to reduce their adiabatic potential energy surfaces into orbit spaces of the corresponding Lie groups...
August 22, 2018: Journal of Physics. Condensed Matter: An Institute of Physics Journal
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