Asymptotic properties of the equilibrium probability of identity in a geographically structured population

1977 ◽  
Vol 9 (2) ◽  
pp. 268-282 ◽  
Author(s):  
Stanley Sawyer
Keyword(s):  
Nearest Neighbor ◽  
Asymptotic Properties ◽  
Higher Dimensions ◽  
Two Dimensions ◽  
Three Dimensions ◽  
One Dimension ◽  
Order Zero ◽  
Structured Population ◽  
Equilibrium Probability ◽  
Migration Law

Let I(x, u) be the probability that two genes found a vector distance x apart are the same type in an infinite-allele selectively-neutral migration model with mutation rate u. The creatures involved inhabit an infinite of colonies, are diploid and are held at N per colony. Set in one dimension and in higher dimensions, where σ2 is the covariance matrix of the migration law (which is assumed to have finite fifth moments). Then in one dimension, in two dimensions, and in three dimensions uniformly for Here C0 is a constant depending on the migration law, K0(y) is the Bessel function of the second kind of order zero, and are the eigenvalues of σ2. For symmetric nearest-neighbor migrations, in one dimension and log mi in two. For is known in one dimension and C0 does not appear. In two dimensions, These results extend and make more precise earlier work of Malécot, Weiss and Kimura and Nagylaki.

Asymptotic properties of the equilibrium probability of identity in a geographically structured population

1977 ◽  
Vol 9 (02) ◽  
pp. 268-282 ◽  
Author(s):  
Stanley Sawyer
Keyword(s):  
Nearest Neighbor ◽  
Asymptotic Properties ◽  
Higher Dimensions ◽  
Two Dimensions ◽  
Three Dimensions ◽  
One Dimension ◽  
Order Zero ◽  
Structured Population ◽  
Equilibrium Probability ◽  
Migration Law

Let I(x, u) be the probability that two genes found a vector distance x apart are the same type in an infinite-allele selectively-neutral migration model with mutation rate u. The creatures involved inhabit an infinite of colonies, are diploid and are held at N per colony. Set in one dimension and in higher dimensions, where σ2 is the covariance matrix of the migration law (which is assumed to have finite fifth moments). Then in one dimension, in two dimensions, and in three dimensions uniformly for Here C 0 is a constant depending on the migration law, K0 (y) is the Bessel function of the second kind of order zero, and are the eigenvalues of σ2. For symmetric nearest-neighbor migrations, in one dimension and log m i in two. For is known in one dimension and C 0 does not appear. In two dimensions, These results extend and make more precise earlier work of Malécot, Weiss and Kimura and Nagylaki.

scholarly journals Averaging over Narain moduli space

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Alexander Maloney ◽  
Edward Witten
Keyword(s):  
Einstein Gravity ◽  
Two Dimensions ◽  
Three Dimensions ◽  
One Dimension ◽  
Simons Theory ◽  
Two Dimensional ◽  
Dual Theory ◽  
Recent Developments ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract Recent developments involving JT gravity in two dimensions indicate that under some conditions, a gravitational path integral is dual to an average over an ensemble of boundary theories, rather than to a specific boundary theory. For an example in one dimension more, one would like to compare a random ensemble of two-dimensional CFT’s to Einstein gravity in three dimensions. But this is difficult. For a simpler problem, here we average over Narain’s family of two-dimensional CFT’s obtained by toroidal compactification. These theories are believed to be the most general ones with their central charges and abelian current algebra symmetries, so averaging over them means picking a random CFT with those properties. The average can be computed using the Siegel-Weil formula of number theory and has some properties suggestive of a bulk dual theory that would be an exotic theory of gravity in three dimensions. The bulk dual theory would be more like U(1)2D Chern-Simons theory than like Einstein gravity.

Assessing the Validity of SWAT as a Workload Measurement Instrument

1983 ◽  
Vol 27 (2) ◽  
pp. 124-128 ◽  
Author(s):  
Stephen P. Boyd
Keyword(s):  
Mental Workload ◽  
Measurement Instrument ◽  
Two Dimensions ◽  
The Other ◽  
Three Dimensions ◽  
One Dimension ◽  
Implicit Assumption ◽  
Workload Measurement ◽  
Positive Correlations ◽  
High Level

The Subjective Workload Asssessment Technique (SWAT) carries with it the implicit assumption that people can accurately predict the amount of mental workload they would experience under various levels of three component dimensions. Research suggests that the perceptions of these dimensions may not be independent. This study was designed to measure the subjective interactions between the dimensions used in SKAT. Mental workload was generated using a text editing task in which the dimensions were manipulated independently. Results revealed significant positive correlations between the subjective levels of the three dimensions. That is, when a subject experienced a high level of one dimension, s/he also tended to rate the other two dimensions high. It may be unreasonable to assume that people can accurately predict the magnitude of these interactions when performing the ranking process which is used to derive the workload scale.

Critical intensities of Boolean models with different underlying convex shapes

2002 ◽  
Vol 34 (01) ◽  
pp. 48-57
Author(s):  
Rahul Roy ◽  
Hideki Tanemura
Keyword(s):  
Unit Area ◽  
Higher Dimensions ◽  
Boolean Model ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Boolean Models ◽  
Regular Polytope ◽  
Minimum Value ◽  
Critical Intensity ◽  
Poisson Boolean Model

We consider the Poisson Boolean model of percolation where the percolating shapes are convex regions. By an enhancement argument we strengthen a result of Jonasson (2000) to show that the critical intensity of percolation in two dimensions is minimized among the class of convex shapes of unit area when the percolating shapes are triangles, and, for any other shape, the critical intensity is strictly larger than this minimum value. We also obtain a partial generalization to higher dimensions. In particular, for three dimensions, the critical intensity of percolation is minimized among the class of regular polytopes of unit volume when the percolating shapes are tetrahedrons. Moreover, for any other regular polytope, the critical intensity is strictly larger than this minimum value.

scholarly journals Diffusion and Superdiffusion in Lattice Models for Colliding Particles with Stored Momentum

2019 ◽  
Vol 177 (6) ◽  
pp. 1240-1262
Author(s):  
Edward Crane ◽  
Sean Ledger ◽  
Bálint Tóth
Keyword(s):  
Initial Conditions ◽  
Mean Square Displacement ◽  
Lattice Models ◽  
Higher Dimensions ◽  
Two Dimensions ◽  
Discrete Models ◽  
One Dimension ◽  
Logarithmic Correction ◽  
Mean Square ◽  
The Mean

Abstract We introduce two discrete models of a collection of colliding particles with stored momentum and study the asymptotic growth of the mean-square displacement of an active particle. We prove that the models are superdiffusive in one dimension (with power law correction) and diffusive in three and higher dimensions. In two dimensions we demonstrate superdiffusivity (with logarithmic correction) for certain anisotropic initial conditions.

PROJECTED ENTANGLED STATES: PROPERTIES AND APPLICATIONS

2006 ◽  
Vol 20 (30n31) ◽  
pp. 5142-5153 ◽  
Author(s):  
F. VERSTRAETE ◽  
M. WOLF ◽  
D. PÉREZ-GARCÍA ◽  
J. I. CIRAC
Keyword(s):  
Numerical Algorithms ◽  
Higher Dimensions ◽  
Two Dimensions ◽  
One Dimension ◽  
Entangled States ◽  
Matrix Product ◽  
Many Body ◽  
Many Body Systems ◽  
Dimension One

We present a new characterization of quantum states, what we call Projected Entangled-Pair States (PEPS). This characterization is based on constructing pairs of maximally entangled states in a Hilbert space of dimension D2, and then projecting those states in subspaces of dimension d. In one dimension, one recovers the familiar matrix product states, whereas in higher dimensions this procedure gives rise to other interesting states. We have used this new parametrization to construct numerical algorithms to simulate the ground state properties and dynamics of certain quantum-many body systems in two dimensions.

scholarly journals Edge detection with meta-lens: from one dimension to three dimensions

Nanophotonics ◽  
2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Mu Ku Chen ◽  
Yue Yan ◽  
Xiaoyuan Liu ◽  
Yongfeng Wu ◽  
Jingcheng Zhang ◽  
...  
Keyword(s):  
Edge Detection ◽  
Light Field ◽  
Imaging System ◽  
Detection System ◽  
Two Dimensions ◽  
Three Dimensions ◽  
One Dimension ◽  
Visible Range ◽  
Depth Information ◽  
Lens Array

Abstract Meta-lens has successfully been developed for a variety of optical functions. We demonstrate a light-field edge detection imaging system with a gallium nitride achromatic meta-lens array. It enables edge detection from one dimension to three dimensions. The designed meta-lens array consists of 60 by 60 achromatic meta-lenses, which operate in the visible range from 400 to 660 nm. All of the light field information of objects in the scene can be captured and computed. The focused edge images from one dimension to three dimensions are extracted with depth estimation by image rendering. Three dimensions edge detection is two dimensions edge imaging with depth information. The focused edge images can be obtained by the sub-image reconstruction of the light field image. Our multidimensional edge detection system by achromatic meta-lens array brings novel advantages, such as broadband detection, data volume reduction, and device miniaturization capacity. Results of our experiments show new insight into applications of biological diagnose and robotic vision.

scholarly journals MMFO: modified moth flame optimization algorithm for region based RGB color image segmentation

2020 ◽  
Vol 10 (1) ◽  
pp. 196
Author(s):  
Varshali Jaiswal ◽  
Varsha Sharma ◽  
Sunita Varma
Keyword(s):  
Image Segmentation ◽  
Optimization Algorithm ◽  
Color Image ◽  
Color Space ◽  
Region Growing ◽  
Two Dimensions ◽  
Color Image Segmentation ◽  
Three Dimensions ◽  
One Dimension ◽  
Moth Flame Optimization Algorithm

<span lang="EN-US">Region-based color image segmentation is elementary steps in image processing and computer vision. Color image segmentation is a region growing approach in which RGB color image is divided into the different cluster based on their pixel properties. The region-based color image segmentation has faced the problem of multidimensionality. The color image is considered in five-dimensional problems, in which three dimensions in color (RGB) and two dimensions in geometry (luminosity layer and chromaticity layer). In this paper, L*a*b color space conversion has been used to reduce the one dimension and geometrically it converts in the array hence the further one dimension has been reduced. This paper introduced an improved algorithm MMFO (Modified Moth Flame Optimization) Algorithm for RGB color image Segmentation which is based on bio-inspired techniques for color image segmentation. The simulation results of MMFO for region based color image segmentation are performed better as compared to PSO and GA, in terms of computation times for all the images. The experiment results of this method gives clear segments based on the different color and the different no. of clusters is used during the segmentation process.</span>

scholarly journals Universal non-Hermitian skin effect in two and higher dimensions

2021 ◽  
Author(s):  
Kai Zhang ◽  
Zhensen Yang ◽  
Chen Fang
Keyword(s):  
Skin Effect ◽  
Physical Phenomenon ◽  
Higher Dimensions ◽  
Three Dimensions ◽  
One Dimension ◽  
Finite Area ◽  
Open Chain ◽  
Kondo Insulators ◽  
Boundary Spectrum ◽  
Weyl Semimetals

Abstract Skin effect, experimentally discovered in one dimension, describes the physical phenomenon that on an open chain, an extensive number of eigenstates of a non-Hermitian hamiltonian are localized at the end(s) of the chain. Here in two and higher dimensions, we establish a theorem that the skin effect exists, if and only if periodic-boundary spectrum of the hamiltonian covers a finite area on the complex plane. This theorem establishes the universality of the effect, because the above condition is satisfied in almost every generic non-Hermitian hamiltonian, and, unlike in one dimension, is compatible with all spatial symmetries. We propose two new types of skin effect in two and higher dimensions: the corner-skin effect where all eigenstates are localized at one corner of the system, and the geometry-dependent-skin effect where skin modes disappear for systems of a particular shape, but appear on generic polygons. An immediate corollary of our theorem is that any non-Hermitian system having exceptional points (lines) in two (three) dimensions exhibits skin effect, making this phenomenon accessible to experiments in photonic crystals, Weyl semimetals, and Kondo insulators.

scholarly journals Is there supersymmetric Lee–Yang fixed point in three dimensions?

2021 ◽  
pp. 2150176
Author(s):  
Yu Nakayama
Keyword(s):  
Field Theory ◽  
Phase Transition ◽  
Fixed Point ◽  
Higher Dimensions ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Natural Question ◽  
First Order ◽  
Conformal Bootstrap ◽  
First Order Transition

The supersymmetric Lee–Yang model is arguably the simplest interacting supersymmetric field theory in two dimensions, albeit nonunitary. A natural question is if there is an analogue of supersymmetric Lee–Yang fixed point in higher dimensions. The absence of any [Formula: see text] symmetry (except for fermion numbers) makes it impossible to approach it by using perturbative [Formula: see text] expansions. We find that the truncated conformal bootstrap suggests that candidate fixed points obtained by the dimensional continuation from two dimensions annihilate below three dimensions, implying that there is no supersymmetric Lee–Yang fixed point in three dimensions. We conjecture that the corresponding phase transition, if any, will be the first-order transition.

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