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Lie algebra

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...
May 9, 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
Murphy Yuezhen Niu, Isaac L Chuang, Jeffrey H Shapiro
We prove that universal quantum computation can be realized-using only linear optics and χ^{(2)} (three-wave mixing) interactions-in any (n+1)-dimensional qudit basis of the n-pump-photon subspace. First, we exhibit a strictly universal gate set for the qubit basis in the one-pump-photon subspace. Next, we demonstrate qutrit-basis universality by proving that χ^{(2)} Hamiltonians and photon-number operators generate the full u(3) Lie algebra in the two-pump-photon subspace, and showing how the qutrit controlled-Z gate can be implemented with only linear optics and χ^{(2)} interactions...
April 20, 2018: Physical Review Letters
Deokjong Lee, Kee Namkoong, Junghan Lee, Young-Chul Jung
Attention-deficit/hyperactivity disorder (ADHD) is commonly comorbid with Internet gaming disorder (IGD). Although childhood ADHD symptoms may decline during late brain maturation, structural alterations in some brain areas may persist into adulthood. This study investigated whether young adults with IGD and a history of childhood ADHD symptoms had gray matter volume (GMV) alterations that were distinct from subjects without a history of childhood ADHD. As an exploratory investigation, we conducted a whole-brain voxel-based morphometry with the diffeomorphic anatomical registration using an exponentiated Lie algebra algorithm and applied an uncorrected threshold at the voxel level for multiple comparisons...
May 11, 2018: Brain Imaging and Behavior
Jan-Michael Mewes
The origin of the thermally-activated delayed fluorescence (TADF) of three organic emitters is investigated, focusing on the nature of the lowest excited states, their transition properties, as well as the role of the environment. For this purpose, the algebraic-diagrammatic construction for the polarization propagator at second order of perturbation theory [ADC(2)], time-dependent density-functional theory in the Tamm-Dancoff approximation (TDA) and unrestricted Kohn-Sham DFT in combination with the maximum-overlap method (ΔDFT) are employed...
May 9, 2018: Physical Chemistry Chemical Physics: PCCP
Marius Crainic, João Nuno Mestre
We present some features of the smooth structure and of the canonical stratification on the orbit space of a proper Lie groupoid. One of the main features is that of Morita invariance of these structures-it allows us to talk about the canonical structure of differentiable stratified space on the orbispace (an object analogous to a separated stack in algebraic geometry) presented by the proper Lie groupoid. The canonical smooth structure on an orbispace is studied mainly via Spallek's framework of differentiable spaces, and two alternative frameworks are then presented...
2018: Letters in Mathematical Physics
Pedro Frejlich, Ioan Mărcuț
Poisson transversals are submanifolds in a Poisson manifold which intersect all symplectic leaves transversally and symplectically. In this communication, we prove a normal form theorem for Poisson maps around Poisson transversals. A Poisson map pulls a Poisson transversal back to a Poisson transversal, and our first main result states that simultaneous normal forms exist around such transversals, for which the Poisson map becomes transversally linear, and intertwines the normal form data of the transversals...
2018: Letters in Mathematical Physics
Gwyn Bellamy, Travis Schedler
We prove a conjecture which expresses the bigraded Poisson-de Rham homology of the nilpotent cone of a semisimple Lie algebra in terms of the generalized (one-variable) Kostka polynomials, via a formula suggested by Lusztig. This allows us to construct a canonical family of filtrations on the flag variety cohomology, and hence on irreducible representations of the Weyl group, whose Hilbert series are given by the generalized Kostka polynomials. We deduce consequences for the cohomology of all Springer fibers...
2018: Letters in Mathematical Physics
Pavel Etingof, Travis Schedler
We survey the theory of Poisson traces (or zeroth Poisson homology) developed by the authors in a series of recent papers. The goal is to understand this subtle invariant of (singular) Poisson varieties, conditions for it to be finite-dimensional, its relationship to the geometry and topology of symplectic resolutions, and its applications to quantizations. The main technique is the study of a canonical D-module on the variety. In the case the variety has finitely many symplectic leaves (such as for symplectic singularities and Hamiltonian reductions of symplectic vector spaces by reductive groups), the D-module is holonomic, and hence, the space of Poisson traces is finite-dimensional...
2018: Letters in Mathematical Physics
J Komatsu, I Matsunari, M Samuraki, K Shima, M Noguchi-Shinohara, K Sakai, T Hamaguchi, K Ono, H Matsuda, M Yamada
BACKGROUND AND PURPOSE: Although Diffeomorphic Anatomical Registration Through Exponentiated Lie Algebra (DARTEL) has been introduced as an alternative to conventional voxel-based morphometry, there are scant data available regarding the optimal image-processing settings. The aim of this study was to optimize image-processing and ROI settings for the diagnosis of Alzheimer disease using DARTEL. MATERIALS AND METHODS: Between May 2002 and August 2014, we selected 158 patients with Alzheimer disease and 198 age-matched healthy subjects; 158 healthy subjects served as the control group against the patients with Alzheimer disease, and the remaining 40 served as the healthy data base...
February 1, 2018: AJNR. American Journal of Neuroradiology
Alexis Arnaudon, Alex L De Castro, Darryl D Holm
We derive and study stochastic dissipative dynamics on coadjoint orbits by incorporating noise and dissipation into mechanical systems arising from the theory of reduction by symmetry, including a semidirect product extension. Random attractors are found for this general class of systems when the Lie algebra is semi-simple, provided the top Lyapunov exponent is positive. We study in details two canonical examples, the free rigid body and the heavy top, whose stochastic integrable reductions are found and numerical simulations of their random attractors are shown...
2018: Journal of Nonlinear Science
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