Motivic coaction on generalized hypergeometric functions by Kamlesh, D

“…There has also been recent progress, of which I am a part, that was made in collaboration with Hadleigh Frost, Martijn Hidding, Carlos Rodriguez, Oliver Schlotterer and Bram Verbeek, where we bridge the two approaches mentioned above to give a Lie algebraic reformulation of the coaction conjecture as well as applications of the new approach to computing the single-valued (trivial monodromy) map for hypergeometric functions. …”

Twisted coadmissible equivariant D-modules on rigid analytic spaces by Mathers, R

“…The first section contains results on the structure of the dual nilpotent cone of a semisimple Lie algebra g over an algebraically closed field K of positive characteristic p. …”

Structure of classical W-algebras by Suh, Uhi Rinn

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Altered Brain Morphometry in Cerebral Small Vessel Disease With Cerebral Microbleeds: An Investigation Combining Univariate and Multivariate Pattern Analyses by Jing Li, Hongwei Wen, Hongwei Wen, Shengpei Wang, Shengpei Wang, Yena Che, Nan Zhang, Lingfei Guo

“…Both univariate analysis and multivariate pattern analysis (MVPA) approaches were applied to investigate differences in brain morphometry among groups.ResultsIn univariate analysis, GMV and WMV differences were compared among groups using voxel-based morphometry (VBM) with diffeomorphic anatomical registration through exponentiated lie algebra (DARTEL). Compared to healthy controls, the CSVD-c group and CSVD-n group showed significantly lower GMV than the control group in similar brain clusters, mainly including the right superior frontal gyrus (medial orbital), left anterior cingulate gyrus, right inferior frontal gyrus (triangular part) and left superior frontal gyrus (medial), while the CSVD-n group also showed significantly lower WMV in the cluster of the left superior frontal gyrus (medial). …”
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To explore the potential mechanisms of cognitive impairment in children with MRI-negative pharmacoresistant epilepsy due to focal cortical dysplasia: A pilot study from gray matter... by Yilin Zhao, Jieqiong Lin, Xinxin Qi, Dezhi Cao, Fengjun Zhu, Li Chen, Zeshi Tan, Tong Mo, Hongwu Zeng

“…Voxel-based morphometry (VBM)-diffeomorphic anatomical registration through exponentiated lie algebra (DARTEL) and surface-based morphometry (SBM) analyses were performed to analyze gray matter volume and cortical structure. …”
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Independent and additive contribution of white matter hyperintensities and Alzheimer’s disease pathology to basal forebrain cholinergic system degeneration by Christine Kindler, Neeraj Upadhyay, Zeynep Bendella, Franziska Dorn, Vera C. Keil, Gabor C. Petzold

“…We assessed the white matter hyperintensity burden within the cholinergic projection pathways using the Cholinergic Pathways Hyperintensities Scale (CHIPS), and applied probabilistic anatomical maps for the analysis of CBFN volumes, i.e. the Ch1-3 compartment and the Ch4 cell group (nucleus basalis of Meynert), by diffeomorphic anatomical registration using exponentiated lie algebra analysis of voxel-based morphometry. Using multiple linear regression analyses, we explored correlations between regional gray matter volumes and the extent of white matter hyperintensities or CBFN volumes in both groups. …”
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Generalised Uncertainty Relations for Angular Momentum and Spin in Quantum Geometry by Matthew J. Lake, Marek Miller, Shi-Dong Liang

“…We show that this also gives rise to a rescaled Lie algebra for generalised spin operators, together with associated subalgebras that are analogous to those for orbital angular momentum. …”
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Riemann–Hilbert Problems, Polynomial Lax Pairs, Integrable Equations and Their Soliton Solutions by Vladimir Stefanov Gerdjikov, Aleksander Aleksiev Stefanov

“…Step 1 involves several assumptions: the choice of the Lie algebra <i>g</i> underlying <i>L</i>, as well as its dependence on the spectral parameter, typically linear or quadratic in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>λ</mi></semantics></math></inline-formula>. …”
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Kelvin Notation for Stabilizing Elastic-Constant Inversion Notation Kelvin pour stabiliser l'inversion de constantes élastiques by Dellinger J., Vasicek D., Sondergeld C.

“…The rotational parameters are defined using a Lie-algebra representation that avoids the artificial degeneracies and coordinate-system bias that can occur with standard polar representations. …”
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Alternative Derivation of the Non-Abelian Stokes Theorem in Two Dimensions by Seramika Ariwahjoedi, Freddy Permana Zen

“…For a given loop <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula> embedded in a manifold <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">M</mi></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="bold-italic">H</mi><mfenced separators="" open="(" close=")"><mi>γ</mi><mo>,</mo><mi mathvariant="script">O</mi></mfenced></mrow></semantics></math></inline-formula> is an element of a Lie group <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">G</mi></semantics></math></inline-formula>; the curvature <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="bold-italic">R</mi><mfenced open="(" close=")"><mi>σ</mi></mfenced><mo>∈</mo><mi mathvariant="fraktur">g</mi></mrow></semantics></math></inline-formula> is an element of the Lie algebra of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">G</mi></semantics></math></inline-formula>. …”
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Patterns of regional gray matter loss at different stages of schizophrenia: A multisite, cross-sectional VBM study in first-episode and chronic illness by Ulysses S. Torres, Fabio L.S. Duran, Maristela S. Schaufelberger, José A.S. Crippa, Mario R. Louzã, Paulo C. Sallet, Caroline Y.O. Kanegusuku, Helio Elkis, Wagner F. Gattaz, Débora P. Bassitt, Antonio W. Zuardi, Jaime Eduardo C. Hallak, Claudia C. Leite, Claudio C. Castro, Antonio Carlos Santos, Robin M. Murray, Geraldo F. Busatto

“…Image processing and analyses were conducted using Statistical Parametric Mapping (SPM8) software with the diffeomorphic anatomical registration through exponentiated Lie algebra (DARTEL) algorithm. Group effects on regional gray matter (GM) volumes were investigated through whole-brain voxel-wise comparisons using General Linear Model Analysis of Co-variance (ANCOVA), always including total GM volume, scan protocol, age and gender as nuisance variables. …”
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The Interactions of molecules with the electromagnetic field by Woolley, R, Woolley, R.G.

“…With a suitable lagrangian and the use of the Coulomb gauge condition to define a specific Lie algebra for the dynamical variables, the hamiltonian that finally emerges is the required generalization of the multipole hamiltonian. …”

Extended Hamilton–Jacobi Theory, Symmetries and Integrability by Quadratures by Sergio Grillo, Juan Carlos Marrero, Edith Padrón

“…To do that, we give, for some elements <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ξ</mi></semantics></math></inline-formula> of the Lie algebra <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">g</mi></semantics></math></inline-formula> of <i>G</i>, an explicit expression up to quadratures of the exponential curve <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo form="prefix">exp</mo><mfenced separators="" open="(" close=")"><mi>ξ</mi><mspace width="0.166667em"></mspace><mi>t</mi></mfenced></mrow></semantics></math></inline-formula>, different to that appearing in the literature for matrix Lie groups. …”
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