Gray matter differences associated with menopausal hormone therapy in menopausal women: a DARTEL-based VBM study by Tae-Hoon Kim, ByoungRyun Kim, Youe Ree Kim, Chang-Won Jeong, Young Hwan Lee

“…This cross-sectional study investigated the MHT-related effect on brain morphology and its association with sex hormones in menopausal women by using an optimized diffeomorphic anatomical registration through exponentiated Lie algebra (DARTEL)-based voxel-based morphometry (VBM) method. …”
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Rational matrix differential operators and integrable systems of PDEs by Carpentier, Sylvain,Ph. D.Massachusetts Institute of Technology.

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Poisson traces, D-modules, and symplectic resolutions by Schedler, Travis, Etingof, Pavel I

“…We also explain generalizations to arbitrary Lie algebras of vector fields, connections to the Bernstein–Sato polynomial, relations to two-variable special polynomials such as Kostka polynomials and Tutte polynomials, and a conjectural relationship with deformations of symplectic resolutions. …”
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Qudit-Basis Universal Quantum Computation Using X[superscript (2)] by Niu, Yuezhen, Chuang, Isaac, Shapiro, Jeffrey H

“…Next, we demonstrate qutrit-basis universality by proving that χ[superscript (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[superscript (2)] interactions. …”
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Applications of group theory to few-body physics by Chaudhary, Irfan Ullah, 1970-

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Nilpotent orbits in bad characteristic and the Springer correspondence by Xue, Ting, Ph. D. Massachusetts Institute of Technology

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Modeling and estimating persistent motion with geometric flows by Lin, Dahua, Grimson, Eric, Fisher, John W., III

“…With this in mind, we first introduce the concept of geometric flow that describes motion simultaneously over space and time, and derive a vector space representation based on Lie algebra. We then extend it to model complex motion by combining multiple flows in a geometrically consistent manner. …”
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Exact categories, Koszul duality, and derived analytic algebra by Kelly, J

“…We conclude by defining analytic extensions of the Koszul dual of a Lie algebra in <em>Ind</em>(<em>Ban_k</em>).…”

Algorithmic problems for subsemigroups of infinite groups by Dong, R

“…</p> <p>We apply a large variety of mathematical tools in the study of these problems, ranging from Lie algebra, algebraic geometry and number theory, to combinatorics, graph theory and convex geometry. …”

Quantum groups at q=0, a Tannakian reconstruction theorem for IndBanach spaces, and analytic analogues of quantum groups by Smith, C

“…The quantum co-ordinate algebra A_q(&amp;gfr;) associated to a KacMoody Lie algebra g forms a Hopf algebra whose comodules are direct sums of finite dimensional irreducible U_q(&amp;gfr;) modules. …”

SO(N) gauge theories in 2+1 dimensions by Lau, R

“…This motivates us to compare the physical properties of <i>SO(N</i>) and <i>SU(N</i>) gauge theories between 'group equivalences', which includes Lie algebra equivalences such as <i>SO</i>(6) and <i>SU</i>(4), and particularly a large-<i>N</i> equivalence. …”

On the Applicability of Quantum Machine Learning by Sebastian Raubitzek, Kevin Mallinger

“…Hereby, this paper introduces a novel dataset based on concepts from quantum mechanics using the exponential map of a Lie algebra. This dataset will be made publicly available and contributes a novel contribution to the empirical evaluation of quantum supremacy. …”
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Universal Central Extension of the Tensor Algebra of a Lie Superalgebra and a Commutative Associative Algebra by Malihe Yousofzadeh

“…In 1984, universal central extensions of the algebras of the form  for a unital commutative associative algebra  and a simple finite dimensional Lie algebra , were identified. Then in 2011, the case when  is a basic classical simple Lie superalgebra was studied by K. …”
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Analysis of the presence or absence of atrophy of the subgenual and subcallosal cingulate cortices using voxel-based morphometry on MRI is useful to select prescriptions for patien... by Niida A, Niida R, Matsuda H, Motomura M, Uechi A

“…Akira Niida,1 Richi Niida,2 Hiroshi Matsuda,3 Makoto Motomura,4 Akihiko Uechi5 1Department of Radiology, Nanbu Hospital, Itoman City, Okinawa, Japan; 2Department of Psychiatry, Nanto Clinic, Urasoe City, Okinawa, Japan; 3Integrative Brain Imaging Center, National Center of Neurology and Psychiatry, Kodaira City, Tokyo, Japan; 4Department of Human Sciences, University of the Ryukyus, Nakagami County, Okinawa, Japan; 5Cognitive Neuroscience Research Project, Kansai Gaidai University, Hirakata City, Osaka, Japan Objective: We objectively evaluated the presence or absence of atrophy of the subgenual anterior cingulate cortex (sgACC) and the subcallosal anterior cingulate cortex (scACC), using new voxel-based morphometry (VBM) software employing Statistical Parametric Mapping software v8 and diffeomorphic anatomic registration through an exponentiated lie algebra. We prepared a database covering young-mature adulthood and investigated the clinical usefulness of the evaluation. …”
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Exact solutions of the Cn quantum spin chain by Guang-Liang Li, Panpan Xue, Pei Sun, Hulin Yang, Xiaotian Xu, Junpeng Cao, Tao Yang, Wen-Li Yang

“…We study the exact solutions of quantum integrable model associated with the Cn Lie algebra, with either a periodic or an open one with off-diagonal boundary reflections, by generalizing the nested off-diagonal Bethe ansatz method. …”
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A Screw Theory Approach to Computing the Instantaneous Rotation Centers of Indeterminate Planar Linkages by Juan Ignacio Valderrama-Rodríguez, José M. Rico, J. Jesús Cervantes-Sánchez, Ricardo García-García

“…The method is based on the systematic application of screw theory, isomorphic to the Lie algebra, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>s</mi><mi>e</mi><mo>(</mo><mn>3</mn><mo>)</mo></mrow></semantics></math></inline-formula>, of the Euclidean group, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>E</mi><mo>(</mo><mn>3</mn><mo>)</mo></mrow></semantics></math></inline-formula>, and the invariant symmetric bilinear forms defined on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>s</mi><mi>e</mi><mo>(</mo><mn>3</mn><mo>)</mo></mrow></semantics></math></inline-formula>.…”
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The smallest interacting universe by Modjtaba Shokrian Zini, Adam R. Brown, Michael Freedman

“…This was found in the context of a rather general potential functional F on the space of metrics {g ij } on su $$ \mathfrak{su} $$ (n), the Lie algebra of symmetries. This emergence of qunits through operator-level spontaneous symmetry breaking (SSB) may help us understand why the world seems to consist of myriad interacting degrees of freedom. …”
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Teleparallel Robertson-Walker Geometries and Applications by Alan Albert Coley, Alexandre Landry, Fateme Gholami

“…The set of invariant coframes and their corresponding spin connections that respect the full six dimensional Lie algebra of Robertson–Walker affine symmetries are displayed and discussed. …”
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Análisis Cinemático del Manipulador Paralelo 4-PRUR Mediante la Teoría de Tornillos by Jaime Gallardo-Alvarado, Mario A. Garcia-Murillo

“…To this aim, the robot is treated as a six-degrees-of-freedom parallel manipulator incorporating pseudo kinematic pairs connecting the limbs to the fixed platform and one virtual kinematic chain in order to apply without restrictions the Lie algebra se(3) of the Euclidean group SE(3). The singularity analysis is investigated based on the input-output equation of velocity. …”
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Articulated pose estimation via over-parametrization and noise projection by Brookshire, Jonathan David

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