Age-related changes in functional hemispheric asymmetry : an fMRI study. by Heng, Gladys Jiamin

“…Grey matter atrophy was accounted for by using the grey matter probability maps created from Diffeomorphic Anatomical Registration Through Exponentiated Lie Algebra (DARTEL) as covariates in analyses and AveLI was used to provide a quantitative measurement of functional lateralization. …”
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Derivations of some classes of Leibniz algebras by Ahmed I, Al-Nashri Al-Hossain

“…Leibniz algebra is a generalization of Lie algebra. The class of Leibniz algebras in dimensional two and three has been classified by Loday and Omirov, respectively. …”
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Gauging the higher-spin-like symmetries by the Moyal product by M. Cvitan, P. Dominis Prester, S. Giaccari, M. Paulišić, I. Vuković

“…The off-shell definition is based on fields defined on a 2d-dimensional master space equipped with a symplectic structure, where the infinite dimensional Lie algebra of gauge transformations is given by the Moyal commutator. …”
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The computation of Lie point symmetry generators, modulational instability, classification of conserved quantities, and explicit power series solutions of the coupled system by Waqas Ali Faridi, Abdullahi Yusuf, Ali Akgül, Ferdous M.O. Tawfiq, Fairouz Tchier, Rawya Al-deiakeh, Tukur A. Sulaiman, Ahmed M. Hassan, Wen-Xiu Ma

“…The suggested approach produces the six dimensional Lie algebra, where translation symmetries in space and time are associated to mass conservation and conservation of energy respectively, the other symmetries are scaling or dilation. …”
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N $$ \mathcal{N} $$ = 2 Conformal SYM theories at large N $$ \mathcal{N} $$ by M. Beccaria, M. Billò, F. Galvagno, A. Hasan, A. Lerda

“…We exploit both recursive methods in the so-called full Lie algebra approach and the more standard Cartan sub-algebra approach based on the eigenvalue distribution. …”
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Scale robust point matching‐Net: End‐to‐end scale point matching using Lie group by Xin Wang, Hui Ding, Guangwei Zhao, Yaxin Peng, Chaomin Shen

“…It is conducted by Lie group linearisation representation with the constraints of parameters under the corresponding basis of Lie algebra. SRPM‐Net preserves the structure of the solution and avoids degeneration. …”
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Computational approach in obtaining analytic solutions of a generalized nonlinear breaking soliton equation with applications in engineering and physics by Oke Davies Adeyemo, Chaudry Masood Khalique

“…Lie group theory is utilized to generate an 11-dimensional Lie algebra associated with the equation under consideration and in addition one parametric group of transformations related to the algebra is calculated. …”
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Conformal embeddings of affine vertex algebras in minimal W-algebras II: decompositions by Adamović, Dražen, Kac, Victor G, Möseneder Frajria, Pierluigi, Papi, Paolo, Perše, Ozren

“…In almost all cases when g♮ is a semisimple Lie algebra, we show that, for a suitable conformal level k, Wk(g, θ) is isomorphic to an extension of Vk(g♮) by its simple module. …”
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Theory of Trotter Error with Commutator Scaling by Andrew M. Childs, Yuan Su, Minh C. Tran, Nathan Wiebe, Shuchen Zhu

“…Whereas previous work achieves similar goals for systems with geometric locality or Lie-algebraic structure, our approach holds, in general. …”
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Robust Terminal Sliding Mode Control on SE(3) for Gough–Stewart Flight Simulator Motion Platform with Payload Uncertainty by Binhai Xie, Shuling Dai

“…With exponential coordinates for configuration error and adjoint operator on Lie algebra <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="fraktur">se</mi><mo>(</mo><mn>3</mn><mo>)</mo></mrow></semantics></math></inline-formula>, the robust control strategy is designed to guarantee almost global finite-time convergence over state space through the Lyapunov stability theory. …”
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Generalization of Geyer’s commutation relations with respect to the orthogonal group in even dimensions by Yu. A. Markov, M. A. Markova

“…Abstract A connection between the deformed Duffin–Kemmer–Petiau (DKP) algebra and an extended system of the parafermion trilinear commutation relations for the creation and annihilation operators $$a^{\pm }_{k}$$ a k ± and for an additional operator $$a_{0}$$ a 0 obeying para-Fermi statistics of order 2 based on the Lie algebra $${\mathfrak {s}}{\mathfrak {o}}(2M+2)$$ s o ( 2 M + 2 ) is established. …”
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Quantum control with noisy fields: computational complexity versus sensitivity to noise by S Kallush, M Khasin, R Kosloff

“…The present study considers a paradigm of control, where the Lie-algebraic structure of the control Hamiltonian is fixed, while the size of the system increases with the dimension of the Hilbert space representation of the algebra. …”
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Supersymmetric localization in AdS5 and the protected chiral algebra by Federico Bonetti, Leonardo Rastelli

“…Localization yields Chern-Simons theory on AdS 3 with gauge algebra gF $$ {\mathfrak{g}}_F $$, whose boundary dual is the affine Lie algebra g^F $$ {\widehat{\mathfrak{g}}}_F $$. We comment on the generalization to the full bulk theory. …”
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Koszul Information Geometry and Souriau Geometric Temperature/Capacity of Lie Group Thermodynamics by Frédéric Barbaresco

“…In covariant Souriau model, Gibbs equilibriums states are indexed by a geometric parameter, the Geometric (Planck) Temperature, with values in the Lie algebra of the dynamical Galileo/Poincaré groups, interpreted as a space-time vector, giving to the metric tensor a null Lie derivative. …”
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Stratified hyperkähler spaces and Nahm's equations by Mayrand, M

“…We then focus on an interesting family of examples whose stratification structure can be described explicitly by combinatorial data associated with the root system of a complex semisimple Lie algebra.</p> <p>Leaving stratified spaces aside, we investigate how Nahm's equations, which are non-linear systems of ODEs, can generate groupoid structures by concatenation of paths, in a manner analogous to the fundamental groupoid of a topological space.…”

Ventral striatum and stuttering: Robust evidence from a case-control study applying DARTEL by Christian Montag, Benjamin Bleek, Martin Reuter, Thilo Müller, Bernd Weber, Jennifer Faber, Sebastian Markett

“…Therefore, the present study contrasted a comparably larger sample of n = 36 people who stutter with n = 34 control persons and applied the state of the art DARTEL algorithm (Diffeomorphic Anatomical Registration Through Exponentiated Lie algebra) to analyze the available brain data. In the present data set stuttering was associated with higher gray matter volume of the right caudate and putamen region of the basal ganglia in patients. …”
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A Variety of New Traveling Wave Packets and Conservation Laws to the Nonlinear Low-Pass Electrical Transmission Lines via Lie Analysis by Muhammad Bilal Riaz, Jan Awrejcewicz, Adil Jhangeer, Muhammad Junaid-U-Rehman

“…The resulting equations concede two-dimensional Lie algebra. Then, we have to find the commutation relation of the entire vector field and observe that the obtained generators make an abelian algebra. …”
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Non Abelian T-duality in Gauged Linear Sigma Models by Nana Cabo Bizet, Aldo Martínez-Merino, Leopoldo A. Pando Zayas, Roberto Santos-Silva

“…We solve the equations of motion for an SU(2) gauged group with a choice of a particular Lie algebra direction of the vector superfield. This direction covers a non-Abelian sector that can be described by a family of Abelian dualities. …”
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Quantum robust control theory for Hamiltonian and control field uncertainty by Andrew Koswara, Vaibhav Bhutoria, Raj Chakrabarti

“…To provide guidelines as to the types of quantum control systems and control objectives for which asymptotic robustness analysis is important for accuracy, we introduce methods for assessing the Lie algebraic depth of quantum control systems, and illustrate through examples drawn from quantum information processing how such accurate methods for quantification of robustness to noise and uncertainty are more important for control strategies that exploit higher order quantum pathways. …”
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Bifurcation Theory, Lie Group-Invariant Solutions of Subalgebras and Conservation Laws of a Generalized (2+1)-Dimensional BK Equation Type II in Plasma Physics and Fluid Mechanics by Oke Davies Adeyemo, Lijun Zhang, Chaudry Masood Khalique

“…We achieve a five-dimensional Lie algebra of the equation through Lie group analysis. …”
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