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https://read.qxmd.com/read/38489612/lie-algebraic-quantum-phase-reduction
#1
JOURNAL ARTICLE
Wataru Setoyama, Yoshihiko Hasegawa
We introduce a general framework of phase reduction theory for quantum nonlinear oscillators. By employing the quantum trajectory theory, we define the limit-cycle trajectory and the phase according to a stochastic Schrödinger equation. Because a perturbation is represented by unitary transformation in quantum dynamics, we calculate phase response curves with respect to generators of a Lie algebra. Our method shows that the continuous measurement yields phase clusters and alters the phase response curves...
March 1, 2024: Physical Review Letters
https://read.qxmd.com/read/38475190/sensor-fusion-for-underwater-vehicle-navigation-compensating-misalignment-using-lie-theory
#2
JOURNAL ARTICLE
Da Bin Jeong, Nak Yong Ko
This paper presents a sensor fusion method for navigation of unmanned underwater vehicles. The method combines Lie theory into Kalman filter to estimate and compensate for the misalignment between the sensors: inertial navigation system and Doppler Velocity Log (DVL). In the process and measurement model equations, a 3-dimensional Euclidean group (SE(3)) and 3-sphere space (S3) are used to express the pose (position and attitude) and misalignment, respectively. SE(3) contains position and attitude transformation matrices, and S3 comprises unit quaternions...
March 3, 2024: Sensors
https://read.qxmd.com/read/38404806/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-structure-view
#3
JOURNAL ARTICLE
Yilin Zhao, Jieqiong Lin, Xinxin Qi, Dezhi Cao, Fengjun Zhu, Li Chen, Zeshi Tan, Tong Mo, Hongwu Zeng
OBJECTIVES: To investigate the characteristics of brain structure in children with focal cortical dysplasia (FCD)-induced pharmacoresistant epilepsy, and explore the potential mechanisms of cognitive impairment from the view of gray matter alteration. METHODS: 25 pharmacoresistant pediatric patients with pathologically confirmed focal cortical dysplasia (FCD), and 25 gender-matched healthy controls were included in this study. 3.0T MRI data and intelligence tests using the Wechsler Intelligence Scale for Children-Forth Edition (WISC-IV) were generated for all subjects...
February 29, 2024: Heliyon
https://read.qxmd.com/read/38379993/existence-uniqueness-and-galerkin-shifted-legendre-s-approximation-of-time-delays-integrodifferential-models-by-adapting-the-hilfer-fractional-attitude
#4
JOURNAL ARTICLE
Hind Sweis, Nabil Shawagfeh, Omar Abu Arqub
Guaranteeing the uniqueness of the solution will simplify the analysis and provide a clear approximation of the considered problem. This article presents theoretical proof of the presence of a unique solution and leverages approximation for the time delay functions in integrodifferential models in the sense of the Hilfer fractional approach. Once the wellposedness discussion is done, our focus lies on utilizing the Galerkin pseudo-codes based on the OSLPs to generate an approximation by applying GSLM as follows: utilizing the OSLPs to replace the required functions in main Hilfer model, applying the Galerkin pseudo-codes, and transforming Hilfer model into an algebraic system of equations...
February 29, 2024: Heliyon
https://read.qxmd.com/read/38329862/self-supervised-lie-algebra-representation-learning-via-optimal-canonical-metric
#5
JOURNAL ARTICLE
Xiaohan Yu, Zicheng Pan, Yang Zhao, Yongsheng Gao
Learning discriminative representation with limited training samples is emerging as an important yet challenging visual categorization task. While prior work has shown that incorporating self-supervised learning can improve performance, we found that the direct use of canonical metric in a Lie group is theoretically incorrect. In this article, we prove that a valid optimization measurement should be a canonical metric on Lie algebra. Based on the theoretical finding, this article introduces a novel self-supervised Lie algebra network (SLA-Net) representation learning framework...
February 8, 2024: IEEE Transactions on Neural Networks and Learning Systems
https://read.qxmd.com/read/38177434/theory-of-overparametrization-in-quantum-neural-networks
#6
JOURNAL ARTICLE
Martín Larocca, Nathan Ju, Diego García-Martín, Patrick J Coles, Marco Cerezo
The prospect of achieving quantum advantage with quantum neural networks (QNNs) is exciting. Understanding how QNN properties (for example, the number of parameters M) affect the loss landscape is crucial to designing scalable QNN architectures. Here we rigorously analyze the overparametrization phenomenon in QNNs, defining overparametrization as the regime where the QNN has more than a critical number of parameters Mc allowing it to explore all relevant directions in state space. Our main results show that the dimension of the Lie algebra obtained from the generators of the QNN is an upper bound for Mc , and for the maximal rank that the quantum Fisher information and Hessian matrices can reach...
June 2023: Nature computational science
https://read.qxmd.com/read/38171318/quantum-state-complexity-meets-many-body-scars
#7
JOURNAL ARTICLE
Sourav Nandy, Bhaskar Mukherjee, Arpan Bhattacharyya, Aritra Banerjee
Scar eigenstates in a many-body system refers to a small subset of non-thermal finite energy density eigenstates embedded into an otherwise thermal spectrum. This novel non-thermal behaviour has been seen in recent experiments simulating a one-dimensional PXP model with a kinetically-constrained local Hilbert space realized by a chain of Rydberg atoms. We probe these small sets of special eigenstates starting from particular initial states by computing the spread complexity associated to time evolution of the PXP hamiltonian...
January 3, 2024: Journal of Physics. Condensed Matter: An Institute of Physics Journal
https://read.qxmd.com/read/38169487/modular-geodesics-and-wedge-domains-in-non-compactly-causal-symmetric-spaces
#8
JOURNAL ARTICLE
Vincenzo Morinelli, Karl-Hermann Neeb, Gestur Ólafsson
We continue our investigation of the interplay between causal structures on symmetric spaces and geometric aspects of Algebraic Quantum Field Theory. We adopt the perspective that the geometric implementation of the modular group is given by the flow generated by an Euler element of the Lie algebra (an element defining a 3-grading). Since any Euler element of a semisimple Lie algebra specifies a canonical non-compactly causal symmetric space <mml:math xmlns:mml="https://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>M</mml:mi><mml:mo>=</mml:mo><mml:mi>G</mml:mi><mml:mo>/</mml:mo><mml:mi>H</mml:mi></mml:mrow></mml:math>, we turn in this paper to the geometry of this flow...
2024: Annals of global analysis and geometry
https://read.qxmd.com/read/38136507/bosonic-representation-of-matrices-and-angular-momentum-probabilistic-representation-of-cyclic-states
#9
JOURNAL ARTICLE
Julio A López-Saldívar, Olga V Man'ko, Margarita A Man'ko, Vladimir I Man'ko
The Jordan-Schwinger map allows us to go from a matrix representation of any arbitrary Lie algebra to an oscillator (bosonic) representation. We show that any Lie algebra can be considered for this map by expressing the algebra generators in terms of the oscillator creation and annihilation operators acting in the Hilbert space of quantum oscillator states. Then, to describe quantum states in the probability representation of quantum oscillator states, we express their density operators in terms of conditional probability distributions (symplectic tomograms) or Husimi-like probability distributions...
December 6, 2023: Entropy
https://read.qxmd.com/read/38039889/motifhub-detection-of-trans-acting-dna-motif-group-with-probabilistic-modeling-algorithm
#10
JOURNAL ARTICLE
Zhe Liu, Hiu-Man Wong, Xingjian Chen, Jiecong Lin, Shixiong Zhang, Shankai Yan, Fuzhou Wang, Xiangtao Li, Ka-Chun Wong
BACKGROUND: Trans-acting factors are of special importance in transcription regulation, which is a group of proteins that can directly or indirectly recognize or bind to the 8-12 bp core sequence of cis-acting elements and regulate the transcription efficiency of target genes. The progressive development in high-throughput chromatin capture technology (e.g., Hi-C) enables the identification of chromatin-interacting sequence groups where trans-acting DNA motif groups can be discovered...
November 25, 2023: Computers in Biology and Medicine
https://read.qxmd.com/read/37915991/generalized-teleparallel-de-sitter-geometries
#11
JOURNAL ARTICLE
A A Coley, A Landry, R J van den Hoogen, D D McNutt
Theories of gravity based on teleparallel geometries are characterized by the torsion, which is a function of the coframe, derivatives of the coframe, and a zero curvature and metric compatible spin-connection. The appropriate notion of a symmetry in a teleparallel geometry is that of an affine symmetry. Due to the importance of the de Sitter geometry and Einstein spaces within General Relativity, we shall describe teleparallel de Sitter geometries and discuss their possible generalizations. In particular, we shall analyse a class of Einstein teleparallel geometries which have a 4-dimensional Lie algebra of affine symmetries, and display two one-parameter families of explicit exact solutions...
2023: European Physical Journal. C, Particles and Fields
https://read.qxmd.com/read/37745006/lipschitz-carnot-carath%C3%A3-odory-structures-and-their-limits
#12
JOURNAL ARTICLE
Gioacchino Antonelli, Enrico Le Donne, Sebastiano Nicolussi Golo
In this paper we discuss the convergence of distances associated to converging structures of Lipschitz vector fields and continuously varying norms on a smooth manifold. We prove that, under a mild controllability assumption on the limit vector-fields structure, the distances associated to equi-Lipschitz vector-fields structures that converge uniformly on compact subsets, and to norms that converge uniformly on compact subsets, converge locally uniformly to the limit Carnot-Carathéodory distance. In the case in which the limit distance is boundedly compact, we show that the convergence of the distances is uniform on compact sets...
2023: Journal of Dynamical and Control Systems
https://read.qxmd.com/read/37744678/higher-polynomial-identities-for-mutations-of-associative-algebras
#13
JOURNAL ARTICLE
Murray R Bremner, Jose Brox, Juana Sánchez-Ortega
We study polynomial identities satisfied by the mutation product <mml:math xmlns:mml="https://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>x</mml:mi><mml:mi>p</mml:mi><mml:mi>y</mml:mi><mml:mo>-</mml:mo><mml:mi>y</mml:mi><mml:mi>q</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:math> on the underlying vector space of an associative algebra A , where p ,  q are fixed elements of A . We simplify known results for identities in degree 4, proving that only two identities are necessary and sufficient to generate them all; in degree 5, we show that adding one new identity suffices; in degree 6, we demonstrate the existence of a significant number of new identities, which induce us to conjecture that the variety generated by mutation algebras of associative algebras is not finitely based...
2023: Results in mathematics
https://read.qxmd.com/read/37739375/extreme-spontaneous-deformations-of-active-crystals
#14
JOURNAL ARTICLE
Xia-Qing Shi, Fu Cheng, Hugues Chaté
We demonstrate that two-dimensional crystals made of active particles can experience extremely large spontaneous deformations without melting. Using particles mostly interacting via pairwise repulsive forces, we show that such active crystals maintain long-range bond order and algebraically decaying positional order, but with an exponent η not limited by the 1/3 bound given by the (equilibrium) KTHNY theory. We rationalize our findings using linear elastic theory and show the existence of two well-defined effective temperatures quantifying respectively large-scale deformations and bond-order fluctuations...
September 8, 2023: Physical Review Letters
https://read.qxmd.com/read/37706775/computing-aberration-coefficients-for-plane-symmetric-reflective-systems-a-lie-algebraic-approach
#15
JOURNAL ARTICLE
A Barion, M J H Anthonissen, J H M Ten Thije Boonkkamp, W L IJzerman
We apply the Lie algebraic method to reflecting optical systems with plane-symmetric freeform mirrors. Using analytical ray-tracing equations, we construct an optical map. The expansion of this map gives us the aberration coefficients in terms of initial ray coordinates. The Lie algebraic method is applied to treat aberrations up to arbitrary order. The presented method provides a systematic and rigorous approach to the derivation, treatment, and composition of aberrations in plane-symmetric systems. We give the results for second- and third-order aberrations and apply them to three single-mirror examples...
June 1, 2023: Journal of the Optical Society of America. A, Optics, Image Science, and Vision
https://read.qxmd.com/read/37687903/joint-calibration-method-for-robot-measurement-systems
#16
JOURNAL ARTICLE
Lei Wu, Xizhe Zang, Guanwen Ding, Chao Wang, Xuehe Zhang, Yubin Liu, Jie Zhao
Robot measurement systems with a binocular planar structured light camera (3D camera) installed on a robot end-effector are often used to measure workpieces' shapes and positions. However, the measurement accuracy is jointly influenced by the robot kinematics, camera-to-robot installation, and 3D camera measurement errors. Incomplete calibration of these errors can result in inaccurate measurements. This paper proposes a joint calibration method considering these three error types to achieve overall calibration...
August 26, 2023: Sensors
https://read.qxmd.com/read/37683148/self-dual-gravity-and-color-kinematics-duality-in-ads_-4
#17
JOURNAL ARTICLE
Arthur Lipstein, Silvia Nagy
We show that self-dual gravity in Euclidean four-dimensional anti-de Sitter space (AdS_{4}) can be described by a scalar field with a cubic interaction written in terms of a deformed Poisson bracket, providing a remarkably simple generalization of the Plebanski action for self-dual gravity in flat space. This implies a novel symmetry algebra in self-dual gravity, notably an AdS_{4} version of the so-called kinematic algebra. We also obtain the three-point interaction vertex of self-dual gravity in AdS_{4} from that of self-dual Yang-Mills by replacing the structure constants of the Lie group with the structure constants of the new kinematic algebra, implying that self-dual gravity in AdS_{4} can be derived from self-dual Yang-Mills in this background via a double copy...
August 25, 2023: Physical Review Letters
https://read.qxmd.com/read/37601291/spline-in-compression-approximation-of-order-of-accuracy-three-four-for-second-order-non-linear-ivps-on-a-graded-mesh
#18
REVIEW
R K Mohanty, Bishnu Pada Ghosh
A spline-in-compression method, implicit in nature, for computing numerical solution of second order nonlinear initial-value problems (IVPs) on a mesh not necessarily equidistant is discussed. The proposed estimation has been derived directly from consistency condition which is third-order accurate. For scientific computation, we use monotonically descending step lengths. The suggested method is applicable to a wider range of physical problems including the problems which are singular in nature. This is possible due to off-step discretization employed in the spline technique...
December 2023: MethodsX
https://read.qxmd.com/read/37581013/a-lie-bracket-for-the-momentum-kernel
#19
JOURNAL ARTICLE
Hadleigh Frost, Carlos R Mafra, Lionel Mason
We prove results for the study of the double copy and tree-level colour/kinematics duality for tree-level scattering amplitudes using the properties of Lie polynomials. We show that the ' S -map' that was defined to simplify super-Yang-Mills multiparticle superfields is in fact a Lie bracket. A generalized KLT map from Lie polynomials to their dual is obtained by studying our new Lie bracket; the matrix elements of this map yield a recently proposed 'generalized KLT matrix', and this reduces to the usual KLT matrix when its entries are restricted to a basis...
2023: Communications in mathematical physics
https://read.qxmd.com/read/37566835/kinematic-lie-algebras-from-twistor-spaces
#20
JOURNAL ARTICLE
Leron Borsten, Branislav Jurčo, Hyungrok Kim, Tommaso Macrelli, Christian Saemann, Martin Wolf
We analyze theories with color-kinematics duality from an algebraic perspective and find that any such theory has an underlying BV^{▪}-algebra, extending the ideas of Reiterer [A homotopy BV algebra for Yang-Mills and color-kinematics, arXiv:1912.03110.]. Conversely, we show that any theory with a BV^{▪}-algebra features a kinematic Lie algebra that controls interaction vertices, both on shell and off shell. We explain that the archetypal example of a theory with a BV^{▪}-algebra is Chern-Simons theory, for which the resulting kinematic Lie algebra is isomorphic to the Schouten-Nijenhuis algebra on multivector fields...
July 28, 2023: Physical Review Letters
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