23 papers · ranked by Valyu relevance
Chenming Zhang, Jie Li, Xiaoqiao Yuan, Xi Zhang + 6 more
'Kaiqiang Feng' 'Chenjun Hu' 'Debiao Zhang' 'Yubing Jiao' 'Shah Nawaz Burokur'] Single-axis rotation modulation (SRM) still accumulates errors in the roll axis direction, which leads to the navigation accuracy not meeting the requirements of guided missiles. Compound rotation modulation (CRM) superimposes…
Hongmei Chen, Zhaoyang Wang, Han Sun, Dongbing Gu + 2 more
Rotational modulation improves strapdown inertial navigation system (SINS) by periodically reorienting the inertial measurement unit (IMU) to convert slowly varying sensor errors into manageable, cancelable components. However, existing dual-axis schemes may accumulate large total rotation angles and introduce delayed…
Yabo Wang, Sizhuo Chen, Heng Li, Yueyang Ben + 2 more
'Stephan Sand'] Rotation modulation is a technique that relies on the specific rotation of an inertial measurement unit (IMU) to achieve the self-compensation of device errors. Common rotation schemes are classified into two modes: continuous rotation and a rotation-stop combination. Aiming at the problem of the poor…
Xiaoqiao Yuan, Jie Li, Xi Zhang, Kaiqiang Feng + 4 more
'Debiao Zhang' 'Jing Mi' 'Stefano Lenci'] Rotation modulation (RM) has been widely used in navigation systems to significantly improve the navigation accuracy of inertial navigation systems (INSs). However, the traditional single-axis rotation modulation cannot achieve the modulation of all the constant errors in the…
A. Teplinsky
We show the equivalence of two possible definitions of a rotational interval exchange transformation: by the first one, it is a first return map for a circle rotation onto a union of finite number of circle arcs, and by the second one, it is an interval exchange with a scheme (in the sense of interval rearrangement…
Authors not listed
Conventional molecular simulation approaches are based on calculating the forces acting on individual atoms in a molecular system, followed by numerical integration of the corresponding Newtonian equations of motion. Algorithms such as the Velocity Verlet scheme are typically employed to propagate these dynamics and…
Gang Wu, Xinqiu Fang, Yang Song, Ningning Chen + 5 more
'Jiaxuan Li' 'Fukang Qiao' 'Fernando Caballero Benítez' 'Danilo Tardioli'] The operating attitude of a shearer based on a three-dimensional (3D) space scale is the necessary basic information for realizing intelligent mining. Aiming to address the problem of the insufficient perception accuracy of shearers, in this…
L. Dicks, D. J. Wales
Rotamer Information in Global Optimization of Proteins Authors: ['L. Dicks' 'D. J. Wales'] Rotamers, namely amino acid side chain conformations common to many different peptides, can be compiled into libraries. These rotamer libraries are used in protein modeling, where the limited conformational space occupied by…
Philipp Allgeuer, Sven Behnke
— The parameterisation of rotations in three dimensional Euclidean space is an area of applied mathematics that has long been studied, dating back to the original works of Euler in the 18th century. As such, many ways of parameterising a rotation have been developed over the years. Motivated by the task of representing…
Jakob Tómas Bullerjahn, Balázs Fábián, Gerhard Hummer
Markov-chain Monte Carlo algorithms rely on trial moves that are either rejected or accepted based on certain criteria. Here, we provide an efficient algorithm to generate random rotation matrices in four dimensions (4D) covering an arbitrary pre-defined range of rotation angles. The matrices can be combined with Monte…
Mingxu Hu, Qi Zhang, Jing Yang, Xueming Li
Electron cryo-microscopy (cryoEM) involves the estimation of orientations of projection images or three-dimensional (3D) volumes, and it is therefore important to properly describe and operate spatial rotations. However, the current Euler angle system that is widely adopted in cryoEM has many drawbacks, which limit the…
Jack D. Evans, Simon Krause, Ben L. Feringa
Molecules in gas and liquid states, as well as in solution, exhibit significant and random Brownian motion. Molecules in the solid-state, although strongly immobilized, can still exhibit significant intramolecular dynamics. However, in most framework materials, these intramolecular dynamics are driven by temperature…
Mustafa Özdemir
Elliptical rotation is the motion of a point on an ellipse through some angle about a vector. The purpose of this paper is to examine the generation of elliptical rotations and to interpret the motion of a point on an elipsoid using elliptic inner product and elliptic vector product. To generate an elliptical rotation…
Oliver C. Kiersnowski, Anita Karsa, Stephen J. Wastling, John S. Thornton + 1 more
Quantitative susceptibility mapping (QSM) is increasingly used for clinical research where oblique image acquisition is commonplace but its effects on QSM accuracy are not well understood. The QSM processing pipeline involves defining the unit magnetic dipole kernel, which requires knowledge of the direction of the…
Authors not listed
Light-driven rotary motors allow direct transformation of light energy into unidirectional rotary motion at the nanoscale, giving rise to countless emerging applications in molecular engineering. The key feature enabling the unidirectional rotation and controlling its direction is the motor chirality, an inherently…
Sheng Xu, Amnon Balanov, Tamir Bendory
Accurate orientation estimation is a crucial component of 3D molecular structure reconstruction, both in single-particle cryo-electron microscopy (cryo-EM) and in the increasingly popular field of cryo-electron tomography (cryo-ET). The dominant method, which involves searching for an orientation with maximum…
Angel G Valdenebro
The purpose of this paper is to show that the mathematical treatment of three-dimensional rotations can be simplified, and its geometrical understanding improved, by using the Rodrigues' vector representation. We present a novel geometrical interpretation of the Rodrigues' vector. Based on this interpretation and…
Judith Hoeller, Lin Zhong, Larissa Heinrich, Stephan Saalfeld + 2 more
As we move through the world, we see the same visual scene from different perspectives. But how does the brain encode scene identity invariant to perspective, while remaining sensitive to these transformations? We propose a solution through equivariance, where perspective transformations induce structured changes in…
Feng Lu, Ziqiang Chen
We present algebraic projective geometry definitions of 3D rotations so as to bridge a small gap between the applications and the definitions of 3D rotations in homogeneous matrix form. A general homogeneous matrix formulation to 3D rotation geometric transformations is proposed which suits for the cases when the…
Yukiko Yamauchi, Taichi Uehara, Masafumi Yamashita
Self-organization of a swarm of mobile computing entities in the three-dimensional Euclidean space (3D-space) such as drones and satellites attracts much attention as such systems are required to accomplish more complicated tasks. We consider a swarm of autonomous mobile robots each of which is an anonymous point in…
Authors not listed
This article is the second in a two-part tutorial review on electronic spin-dependent dynamics. In Part I, we presented the fundamental theory within the adiabatic Born– Huang framework that describes the interaction between nuclear motion and the elec- tronic (spin and spatial) degrees of freedom. In particular, we…
Kalistyn H. Burley, Samuel C. Gill, Nathan M. Lim, David Mobley
Molecular simulations are a valuable tool for studying biomolecular motions and thermodynamics. However, such motions can be slow compared to simulation timescales, yet critical. Specifically, adequate sampling of sidechain motions in protein binding pockets proves crucial for obtaining accurate estimates of ligand…
Ty Balduf, Marco Caricato
This work reports the derivation and implementation of the electric dipole-magnetic dipole and electric dipole- electric quadrupole polarizability tensors at density functional theory level with periodic boundary conditions (DFT-PBC). These tensors are combined to evaluate the Buckingham/ Dunn tensor that describes the…