Return probabilities for certain three-dimensional random walks

1979 ◽  
Vol 16 (1) ◽  
pp. 45-53 ◽  
Author(s):  
D. J. Daley
Keyword(s):  
Random Walks ◽  
Three Dimensional ◽  
Cubic Lattice ◽  
Starting Point

For some three-dimensional random walks on the cubic lattice, the probability of the walk returning to its starting point is given numerically.

Return probabilities for certain three-dimensional random walks

1979 ◽  
Vol 16 (01) ◽  
pp. 45-53 ◽  
Author(s):  
D. J. Daley
Keyword(s):  
Random Walks ◽  
Three Dimensional ◽  
Cubic Lattice ◽  
Starting Point

For some three-dimensional random walks on the cubic lattice, the probability of the walk returning to its starting point is given numerically.

scholarly journals Second sacral sacralalar‐iliac (S2AI) screw placement in adult degenerative scoliosis (ADS) patients: an imaging study

BMC Surgery ◽  
2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Bing Wu ◽  
Kai Song ◽  
Junyao Cheng ◽  
Pengfei Chi ◽  
Zhaohan Wang ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Imaging Study ◽  
Outer Diameter ◽  
Degenerative Scoliosis ◽  
Female Patients ◽  
Lateral Angle ◽  
Adult Degenerative Scoliosis ◽  
Imaging Characteristics ◽  
Starting Point ◽  
Trajectory Length

Abstract Background The imaging characteristics of sacral sacralalar-iliac (S2AI) screw trajectory in adult degenerative scoliosis (ADS) patients will be determined. Methods S2AI screw trajectories were mapped on three-dimensional computed tomography (3DCT) reconstructions of 40 ADS patients. The starting point, placement plane, screw template, and a circle centered at the lowest point of the ilium inner cortex were set on these images. A tangent line from the starting point to the outer diameter of the circle was selected as the axis of the screw trajectory. The related parameters in different populations were analyzed and compared. Results The trajectory length of S2AI screws in ADS patients was 12.00 ± 0.99 cm, the lateral angle was 41.24 ± 3.92°, the caudal angle was 27.73 ± 6.45°, the distance from the axis of the screw trajectory to the iliosciatic notch was 1.05 ± 0.81 cm, the distance from the axis of the screw trajectory to the upper edge of the acetabulum was 1.85 ± 0.33 cm, and the iliac width was 2.12 ± 1.65 cm. Compared with females, the lateral angle of male ADS patients was decreased, but the trajectory length was increased (P < 0.05). Compared to patients without ADS in previous studies, the lateral angle of male patients was larger, the lateral angle of female patients was increased, and the caudal angle was decreased (P < 0.05). Conclusions There is an ideal trajectory of S2AI screws in ADS patients. A different direction should be noticed in the placement of S2AI screws, especially in female patients.

scholarly journals Colourful Poincaré symmetry, gravity and particle actions

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Joaquim Gomis ◽  
Euihun Joung ◽  
Axel Kleinschmidt ◽  
Karapet Mkrtchyan
Keyword(s):  
Field Theory ◽  
Free Particle ◽  
Three Dimensional ◽  
Background Field ◽  
Quantum Field ◽  
Symmetry Factor ◽  
Starting Point ◽  
Poincaré Algebra ◽  
Poincaré Symmetry ◽  
Three Space

Abstract We construct a generalisation of the three-dimensional Poincaré algebra that also includes a colour symmetry factor. This algebra can be used to define coloured Poincaré gravity in three space-time dimensions as well as to study generalisations of massive and massless free particle models. We present various such generalised particle models that differ in which orbits of the coloured Poincaré symmetry are described. Our approach can be seen as a stepping stone towards the description of particles interacting with a non-abelian background field or as a starting point for a worldline formulation of an associated quantum field theory.

scholarly journals Inferring Single-Cell 3D Chromosomal Structures Based on the Lennard-Jones Potential

2021 ◽  
Vol 22 (11) ◽  
pp. 5914
Author(s):  
Mengsheng Zha ◽  
Nan Wang ◽  
Chaoyang Zhang ◽  
Zheng Wang
Keyword(s):  
Single Cell ◽  
Loss Function ◽  
Gaussian Function ◽  
Three Dimensional ◽  
Lennard Jones Potential ◽  
Jones Potential ◽  
Cubic Lattice ◽  
Lennard Jones ◽  
3D Fish ◽  
Well Depth

Reconstructing three-dimensional (3D) chromosomal structures based on single-cell Hi-C data is a challenging scientific problem due to the extreme sparseness of the single-cell Hi-C data. In this research, we used the Lennard-Jones potential to reconstruct both 500 kb and high-resolution 50 kb chromosomal structures based on single-cell Hi-C data. A chromosome was represented by a string of 500 kb or 50 kb DNA beads and put into a 3D cubic lattice for simulations. A 2D Gaussian function was used to impute the sparse single-cell Hi-C contact matrices. We designed a novel loss function based on the Lennard-Jones potential, in which the ε value, i.e., the well depth, was used to indicate how stable the binding of every pair of beads is. For the bead pairs that have single-cell Hi-C contacts and their neighboring bead pairs, the loss function assigns them stronger binding stability. The Metropolis–Hastings algorithm was used to try different locations for the DNA beads, and simulated annealing was used to optimize the loss function. We proved the correctness and validness of the reconstructed 3D structures by evaluating the models according to multiple criteria and comparing the models with 3D-FISH data.

Fabrication of endothelialized tube in collagen gel as starting point for self-developing capillary-like network to construct three-dimensional organs in vitro

2006 ◽  
Vol 95 (1) ◽  
pp. 1-7 ◽  
Author(s):  
Takayuki Takei ◽  
Shinji Sakai ◽  
Tsutomu Ono ◽  
Hiroyuki Ijima ◽  
Koei Kawakami
Keyword(s):  
Three Dimensional ◽  
Collagen Gel ◽  
Starting Point

Epitaxial Ni nanoparticles on CaF2(001), (110) and (111) surfaces studied by three-dimensional RHEED, GIXD and GISAXS reciprocal-space mapping techniques

2017 ◽  
Vol 50 (3) ◽  
pp. 830-839 ◽  
Author(s):  
S. M. Suturin ◽  
V. V. Fedorov ◽  
A. M. Korovin ◽  
N. S. Sokolov ◽  
A. V. Nashchekin ◽  
...  
Keyword(s):  
Lattice Structure ◽  
Three Dimensional ◽  
Grazing Incidence ◽  
High Energy ◽  
Reciprocal Space ◽  
Mapping Technique ◽  
Face Centered Cubic ◽  
X Ray ◽  
Cubic Lattice ◽  
Face Centered

The development of growth techniques aimed at the fabrication of nanoscale heterostructures with layers of ferroic 3dmetals on semiconductor substrates is very important for their potential usage in magnetic media recording applications. A structural study is presented of single-crystal nickel island ensembles grown epitaxially on top of CaF2/Si insulator-on-semiconductor heteroepitaxial substrates with (111), (110) and (001) fluorite surface orientations. The CaF2buffer layer in the studied multilayer system prevents the formation of nickel silicide, guides the nucleation of nickel islands and serves as an insulating layer in a potential tunneling spin injection device. The present study, employing both direct-space and reciprocal-space techniques, is a continuation of earlier research on ferromagnetic 3dtransition metals grown epitaxially on non-magnetic and magnetically ordered fluorides. It is demonstrated that arrays of stand-alone faceted nickel islands with a face-centered cubic lattice can be grown controllably on CaF2surfaces of (111), (110) and (001) orientations. The proposed two-stage nickel growth technique employs deposition of a thin seeding layer at low temperature followed by formation of the islands at high temperature. The application of an advanced three-dimensional mapping technique exploiting reflection high-energy electron diffraction (RHEED) has proved that the nickel islands tend to inherit the lattice orientation of the underlying fluorite layer, though they exhibit a certain amount of {111} twinning. As shown by scanning electron microscopy, grazing-incidence X-ray diffraction (GIXD) and grazing-incidence small-angle X-ray scattering (GISAXS), the islands are of similar shape, being faceted with {111} and {100} planes. The results obtained are compared with those from earlier studies of Co/CaF2epitaxial nanoparticles, with special attention paid to the peculiarities related to the differences in lattice structure of the deposited metals: the dual-phase hexagonal close-packed/face-centered cubic lattice structure of cobalt as opposed to the single-phase face-centered cubic lattice structure of nickel.

Path Planning for Spheres in Three Dimensional Environments With Low Interference Index

1994 ◽  
Author(s):  
Duane W. Storti ◽  
Debasish Dutta
Keyword(s):  
Path Planning ◽  
Free Path ◽  
Configuration Space ◽  
Local Knowledge ◽  
Three Dimensional ◽  
Target Point ◽  
Planning Problem ◽  
Spherical Object ◽  
Starting Point ◽  
Path Planning Problem

Abstract We consider the path planning problem for a spherical object moving through a three-dimensional environment composed of spherical obstacles. Given a starting point and a terminal or target point, we wish to determine a collision free path from start to target for the moving sphere. We define an interference index to count the number of configuration space obstacles whose surfaces interfere simultaneously. In this paper, we present algorithms for navigating the sphere when the interference index is ≤ 2. While a global calculation is necessary to characterize the environment as a whole, only local knowledge is needed for path construction.

Numerical Analysis of the Deterministic Stresses Associated to Impeller-Tongue Interactions in a Single Volute Centrifugal Pump

2019 ◽  
Vol 141 (9) ◽  
Author(s):  
J. M. Fernández Oro ◽  
J. González ◽  
R. Barrio Perotti ◽  
M. Galdo Vega
Keyword(s):  
Numerical Analysis ◽  
Numerical Model ◽  
Centrifugal Pump ◽  
Turbulence Intensity ◽  
Three Dimensional ◽  
Relevant Information ◽  
Three Dimensional Flow ◽  
Deterministic Analysis ◽  
Starting Point ◽  
Flow Features

In this paper, a deterministic stress decomposition is applied over the numerical three-dimensional flow solution available for a single volute centrifugal pump. The numerical model has proven in previous publications its robustness to obtain the impeller to volute-tongue flow interaction, and it is now used as starting point for the current research. The main objective has been oriented toward a detailed analysis of the lack of uniformity in the flow that the volute tongue promotes on the blade-to-blade axisymmetric pattern. Through this analysis, the fluctuation field may be retrieved and main interaction sources have been pinpointed. The results obtained with the deterministic analysis become of paramount interest to understand the different flow features found in a typical centrifugal pump as a function of the flow rate. Moreover, this postprocessing tool provides an economic and easy procedure for designers to compare the different deterministic terms, also giving relevant information on the unresolved turbulence intensity scales. Complementarily, a way to model the turbulent effects in a systematic way is also presented, comparing their impact on the performance with respect to deterministic sources in a useful framework, that may be applied for similar kinds of pumps.

scholarly journals Structure of human dual-specificity phosphatase 7, a potential cancer drug target

2015 ◽  
Vol 71 (6) ◽  
pp. 650-656 ◽  
Author(s):  
George T. Lountos ◽  
Brian P. Austin ◽  
Joseph E. Tropea ◽  
David S. Waugh
Keyword(s):  
Catalytic Domain ◽  
Three Dimensional ◽  
Mitogen Activated Protein Kinase ◽  
Cancer Drug ◽  
Dual Specificity Phosphatase ◽  
Dual Specificity ◽  
Starting Point ◽  
Mitogen Activated Protein ◽  
Dual Specificity Phosphatases

Human dual-specificity phosphatase 7 (DUSP7/Pyst2) is a 320-residue protein that belongs to the mitogen-activated protein kinase phosphatase (MKP) subfamily of dual-specificity phosphatases. Although its precise biological function is still not fully understood, previous reports have demonstrated that DUSP7 is overexpressed in myeloid leukemia and other malignancies. Therefore, there is interest in developing DUSP7 inhibitors as potential therapeutic agents, especially for cancer. Here, the purification, crystallization and structure determination of the catalytic domain of DUSP7 (Ser141–Ser289/C232S) at 1.67 Å resolution are reported. The structure described here provides a starting point for structure-assisted inhibitor-design efforts and adds to the growing knowledge base of three-dimensional structures of the dual-specificity phosphatase family.

scholarly journals MRI Study on Tibial Nerve of the Ankle Canal and Its Branches: A method of multiplanar reconstruction with 3D-FIESTA-C sequences

2020 ◽  
Author(s):  
Yan Zhang ◽  
Xucheng He ◽  
Juan Li ◽  
Ju Ye ◽  
Wenjuan Han ◽  
...  
Keyword(s):  
Tibial Nerve ◽  
Three Dimensional ◽  
The Body ◽  
Multiplanar Reconstruction ◽  
Medial Malleolus ◽  
Cross Sectional ◽  
Medial Plantar Nerve ◽  
Lateral Plantar Nerve ◽  
Good Imaging ◽  
Starting Point

Abstract Background The display of tibial nerve and its branches in the ankle canal is helpful for the diagnosis of local lesions and compression, and also for clinical observation and surgical planning.The aim of this study was to investigate the feasibility of three-dimensional dual-excitation balanced steady-state free precession sequence (3D-FIESTA-C) multiplanar reconstruction (MPR) display of tibial nerve and its branches of the ankle canal. Methods The subjects were 20 healthy volunteers (40 ankles), aged 22–50, with no history of ankle joint desease. 3D-FIESTA-C sequence was used in the 3.0t magnetic resonance equipment for imaging. During the scanning, each foot was at a 90-degree angle to the tibia.The tibial nerve of the ankle canal and its branches were displayed and measured at the same level through multiplanar reconstruction. Results Most of the tibial nerve bifurcation points were located in the ankle canal (57.5%), few (42.5%) were located at the proximal end of the ankle canal, and none was found away from the distal end. The bifurcation between the medial plantar nerve and the lateral plantar nerve is on the line between the tip of the medial malleolus and the calcaneus, and it’s angle is between 6° and 35°.The average cross-sectional diameter of the medial plantar nerve is about mm, and the lateral plantar nerve about mm. In MPR images, the display rates of both the medial calcaneal nerve and the subcalcaneal nerve were 100%, and the starting point of the subcalcaneal nerve was always at the distal end of the starting point of the medial calcaneal nerve. In 55% of cases, there were more than 2 medial calcaneal nerve innervations. Conclusion The 3D-FIESTA-C MPR can display the morphological features and positions of tibial nerve and its branches and the bifurcation point’s projection position on the body surface can be marked. This method not only benefited the imaging diagnosis of tibial nerve and branch-related lesions of the ankle canal, but also provided a good imaging basis to plan the clinical operation of the ankle canal and avoid surgical injury.

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