scholarly journals Shift vector as the geometric origin of beam shifts

2019 ◽  
Vol 100 (20) ◽  
Author(s):  
Li-kun Shi ◽  
Justin C. W. Song
Keyword(s):  
Shift Vector ◽  
Geometric Origin

scholarly journals The geometric origin of perspectivist science in G.W. Leibniz. Analysis based on unpublished manuscripts

2021 ◽  
Author(s):  
Ricardo Rodríguez Hurtado ◽  
Juan A. Nicolás ◽  
Javier Echeverría Ezponda
Keyword(s):  
Geometric Origin ◽  
Unpublished Manuscripts

Mean Shift Segmentation Algorithm Based on Hybridized Bacterial Chemotaxis

2012 ◽  
Vol 468-471 ◽  
pp. 2019-2023
Author(s):  
Yan Ling Li ◽  
Gang Li
Keyword(s):  
Mean Shift ◽  
Bacterial Chemotaxis ◽  
Local Maximum ◽  
Optimization Methods ◽  
Segmentation Algorithm ◽  
Global Maximum ◽  
Stochastic Local Search ◽  
Shift Vector ◽  
Operation Algorithm ◽  
Maximum Minimum

Mean shift, like other gradient ascent optimization methods, is susceptible to local maximum/minimum, and hence often fails to find the desired global maximum/minimum. For this reason, mean shift segmentation algorithm based on hybridized bacterial chemotaxis (HBC) is proposed in this paper. In HBC, particle swarm operation algorithm(PSO) is introduced before bacterial chemotaxis(BC) works. And PSO is firstly introduced to execute the global search, and then stochastic local search works by BC. Meanwhile, elitism preservation is used in the paper in order to improve the efficiency of the new algorithm. After mean shift vector is optimized using HBC algorithm, the optimal mean shift vector is updated using mean shift procedure. Experimental results show that new algorithm not only has higher convergence speed, but also can achieve more robust segmentation results.

scholarly journals Geometric Origin of Superfluidity in the Lieb-Lattice Flat Band

2016 ◽  
Vol 117 (4) ◽  
Author(s):  
Aleksi Julku ◽  
Sebastiano Peotta ◽  
Tuomas I. Vanhala ◽  
Dong-Hee Kim ◽  
Päivi Törmä
Keyword(s):  
Flat Band ◽  
Geometric Origin ◽  
Lieb Lattice

scholarly journals Einstein-aether theory in Weyl integrable geometry

2020 ◽  
Vol 80 (12) ◽  
Author(s):  
Andronikos Paliathanasis ◽  
Genly Leon ◽  
John D. Barrow
Keyword(s):  
Gravitational Field ◽  
Field Equation ◽  
Scalar Field ◽  
Field Model ◽  
Affine Connection ◽  
Dynamical Evolution ◽  
Field Equations ◽  
Gravitational Field Equation ◽  
Gravitational Field Equations ◽  
Geometric Origin

AbstractWe study the Einstein-aether theory in Weyl integrable geometry. The scalar field which defines the Weyl affine connection is introduced in the gravitational field equation. We end up with an Einstein-aether scalar field model where the interaction between the scalar field and the aether field has a geometric origin. The scalar field plays a significant role in the evolution of the gravitational field equations. We focus our study on the case of homogeneous and isotropic background spacetimes and study their dynamical evolution for various cosmological models.

Langevin field equations: Properties and renormalization

2021 ◽  
pp. 857-874
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Integral Representation ◽  
Langevin Equation ◽  
Gauge Theories ◽  
Homogeneous Spaces ◽  
Brst Symmetry ◽  
Integral Representations ◽  
Constraint Equations ◽  
Dynamic Action ◽  
Geometric Origin ◽  
Field Integral

Langevin equations for fields have been proposed to describe the dynamics of critical phenomena, or as an alternative method of quantization, which could be useful in cases where ordinary methods lead to difficulties, like in gauge theories. Some of their general properties will be described here. For a number of problems, in particular related to perturbation theory, it is more convenient to work with an action and a field integral than with the equation directly, because standard methods of quantum field theory (QFT) then become available. For this purpose, one can associate a field integral representation, involving a dynamic action to the Langevin equation. The dynamic action can be interpreted as generated by the Langevin equation, considered as a constraint equation. Quite generally, the integral representation of constraint equations, including stochastic equations, leads to an action that has a Slavnov–Taylor (ST) symmetry and, in a different form, has an anticommuting type Becchi–Rouet–Stora–Tyutin (BRST) symmetry, a symmetry that involves anticommuting parameters. This symmetry has no geometric origin, but is merely a consequence of associating a specific form of integral representations to the constraint equations. This symmetry is used in a number of different examples to prove the renormalizability of non-Abelian gauge theories, or to prove the geometric stability of models defined on homogeneous spaces under renormalization. In this chapter, it is used to prove Ward-Takahashi (WT) identities, and to determine how the Langevin equation renormalizes.

scholarly journals Equiaffine Braneworld

Galaxies ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 73
Author(s):  
Fan Zhang
Keyword(s):  
Differential Geometry ◽  
Dark Energy ◽  
Second Fundamental Form ◽  
The Second Fundamental Form ◽  
Lorentzian Metric ◽  
Euclidean Hypersurface ◽  
Higher Dimensional ◽  
Extrinsic Geometry ◽  
Geometric Origin ◽  
Spacetime Metric

Higher dimensional theories, wherein our four dimensional universe is immersed into a bulk ambient, have received much attention recently, and the directions of investigation had, as far as we can discern, all followed the ordinary Euclidean hypersurface theory’s isometric immersion recipe, with the spacetime metric being induced by an ambient parent. We note, in this paper, that the indefinite signature of the Lorentzian metric perhaps hints at the lesser known equiaffine hypersurface theory as being a possibly more natural, i.e., less customized beyond minimal mathematical formalism, description of our universe’s extrinsic geometry. In this alternative, the ambient is deprived of a metric, and the spacetime metric becomes conformal to the second fundamental form of the ordinary theory, therefore is automatically indefinite for hyperbolic shapes. Herein, we advocate investigations in this direction by identifying some potential physical benefits to enlisting the help of equiaffine differential geometry. In particular, we show that a geometric origin for dark energy can be proposed within this framework.

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