Segregation at a Single Trap in the Presence of Fields

1992 ◽  
Vol 290 ◽  
Author(s):  
Haim Taitelbaum ◽  
George H. Weiss
Keyword(s):  
Nearest Neighbor ◽  
Distance Measure ◽  
Random Systems ◽  
Hard Core ◽  
Reaction Rates ◽  
Transition Rates ◽  
Constant Bias ◽  
Random Transition ◽  
Anomalous Reaction ◽  
Global Bias

AbstractThere have been a number of recent investigations of segregation properties of diffusing particles in the presence of a single static trap in low dimensions. We study these properties when the diffusing particles are subject to different forms of external fields: global constant bias, random bias fields (Sinai model) and random transition rates. We discuss two measures of segregation, the distances from the trap either to the point at which the concentration profile reaches a specified fraction of its bulk value, or to the nearest unreacted particle. For the cases of global bias (both away from, and towards the trap) and random fields, we found that both measures of segregation have the same asymptotic temporal behavior, while for random transition rates they differ. We explain this difference by relating the nearest-neighbor distance measure to properties of hard-core diffusion in these systems. We also found anomalous spatial shapes for the profile in the vicinity of the trap in the random systems, as well as anomalous reaction rates.

scholarly journals Infinitely divisible random transition probabilities with application to dependent Markov chains

1984 ◽  
Vol 25 (4) ◽  
pp. 463-472
Author(s):  
Peter L. Chesson
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
White Noise ◽  
Transition Probabilities ◽  
Transition Probability ◽  
Transition Rates ◽  
Infinitely Divisible ◽  
Random Transition ◽  
Transition Probability Matrices ◽  
Probability Matrices

AbstractRandom transition probability matrices with stationary independent factors define “white noise” environment processes for Markov chains. Two examples are considered in detail. Such environment processes can be used to construct several Markov chains which are dependent, have the same transition probabilities and are jointly a Markov chain. Transition rates for such processes are evaluated. These results have application to the study of animal movements.

The Statistical Analysis of a Distribution of Activity Points in Relation to Surface-Like Elements

1988 ◽  
Vol 20 (5) ◽  
pp. 609-620 ◽  
Author(s):  
A Okabe ◽  
T Yoshikawa ◽  
A Fujii ◽  
K Oikawa
Keyword(s):  
Statistical Analysis ◽  
Probability Density Function ◽  
Nearest Neighbor ◽  
Distance Measure ◽  
Computational Method ◽  
Spatial Dependency ◽  
Neighbor Distance ◽  
High Class ◽  
Apartment Buildings ◽  
Nearest Neighbor Distance

The objective of this paper is to formulate a statistical method of testing the hypothesis that the distribution of activity points (such as retail stores) is independent of location of ‘surface-like’ infrastructural elements (such as parks). In order to do this, first, the probability density function of a distance from a random point to the nearest surface-like element is derived. Second, through the use of this function, a measure, R, of spatial dependency on the surface-like elements is defined as the ratio of the average nearest-neighbor distance to the expected average nearest-neighbor distance. This measure is an extension of the ordinary nearest-neighbor distance measure frequently referred to in geography and ecology. Third, the statistical use of measure R is shown. Fourth, as this measure is difficult to compute geometrically, the computational method of calculating the value of R is developed. Last, by use of this method, a test is conducted to decide whether or not the distribution of high-class apartment buildings in Setagaya, Tokyo, is affected by the location of big parks.

Glauber dynamics in the Ising chain with random transition rates

1989 ◽  
Vol 135 (1) ◽  
pp. 17-19 ◽  
Author(s):  
J.M. Nunes Da Silva ◽  
E.J.S. Jage
Keyword(s):  
Glauber Dynamics ◽  
Transition Rates ◽  
Ising Chain ◽  
Random Transition

Nearest Neighbor Distance Distribution in Hard-Core Point Processes

2016 ◽  
Vol 20 (9) ◽  
pp. 1872-1875 ◽  
Author(s):  
Akram Al-Hourani ◽  
Robin J. Evans ◽  
Sithamparanathan Kandeepan
Keyword(s):  
Point Processes ◽  
Nearest Neighbor ◽  
Hard Core ◽  
Distance Distribution ◽  
Neighbor Distance ◽  
Core Point ◽  
Nearest Neighbor Distance

scholarly journals Comparison of Different Approaches for Measuring Tibial Cartilage Thickness

2017 ◽  
Vol 14 (2) ◽  
Author(s):  
Jennifer Maier ◽  
Marianne Black ◽  
Serena Bonaretti ◽  
Bastian Bier ◽  
Bjoern Eskofier ◽  
...  
Keyword(s):  
Nearest Neighbor ◽  
Distance Measure ◽  
Thickness Distribution ◽  
Weight Bearing ◽  
Correlation Coefficients ◽  
Cartilage Thickness ◽  
Tibial Cartilage ◽  
Normal Vectors ◽  
Field Lines

AbstractOsteoarthritis is a degenerative disease affecting bones and cartilage especially in the human knee. In this context, cartilage thickness is an indicator for knee cartilage health. Thickness measurements are performed on medical images acquired in-vivo. Currently, there is no standard method agreed upon that defines a distance measure in articular cartilage. In this work, we present a comparison of different methods commonly used in literature. These methods are based on nearest neighbors, surface normal vectors, local thickness and potential field lines. All approaches were applied to manual segmentations of tibia and lateral and medial tibial cartilage performed by experienced raters. The underlying data were contrast agent-enhanced cone-beam C-arm CT reconstructions of one healthy subject’s knee. The subject was scanned three times, once in supine position and two times in a standing weight-bearing position. A comparison of the resulting thickness maps shows similar distributions and high correlation coefficients between the approaches above 0.90. The nearest neighbor method results on average in the lowest cartilage thickness values, while the local thickness approach assigns the highest values. We showed that the different methods agree in their thickness distribution. The results will be used for a future evaluation of cartilage change under weight-bearing conditions.

scholarly journals Hydrodynamic Limit for a Type of Exclusion Process with Slow Bonds in Dimension d ≥ 2

2011 ◽  
Vol 48 (2) ◽  
pp. 333-351 ◽  
Author(s):  
Tertuliano Franco ◽  
Adriana Neumann ◽  
Glauco Valle
Keyword(s):  
Exchange Rate ◽  
Nearest Neighbor ◽  
Exclusion Process ◽  
Hard Core ◽  
Inner Product ◽  
Permeable Membrane ◽  
System Of Particles ◽  
Discrete Torus ◽  
The Exchange Rate ◽  
Hydrodynamical Behavior

Let Λ be a connected closed region with smooth boundary contained in the d-dimensional continuous torus Td. In the discrete torus N-1TdN, we consider a nearest-neighbor symmetric exclusion process where occupancies of neighboring sites are exchanged at rates depending on Λ in the following way: if both sites are in Λ or Λc, the exchange rate is 1; if one site is in Λ and the other site is in Λc, and the direction of the bond connecting the sites is ej, then the exchange rate is defined as N-1 times the absolute value of the inner product between ej and the normal exterior vector to ∂Λ. We show that this exclusion-type process has a nontrivial hydrodynamical behavior under diffusive scaling and, in the continuum limit, particles are not blocked or reflected by ∂Λ. Thus, the model represents a system of particles under hard-core interaction in the presence of a permeable membrane which slows down the passage of particles between two complementary regions.

scholarly journals Hydrodynamic Limit for a Type of Exclusion Process with Slow Bonds in Dimension d ≥ 2

2011 ◽  
Vol 48 (02) ◽  
pp. 333-351 ◽  
Author(s):  
Tertuliano Franco ◽  
Adriana Neumann ◽  
Glauco Valle
Keyword(s):  
Exchange Rate ◽  
Nearest Neighbor ◽  
Exclusion Process ◽  
Hard Core ◽  
Inner Product ◽  
Permeable Membrane ◽  
System Of Particles ◽  
Discrete Torus ◽  
The Exchange Rate ◽  
Hydrodynamical Behavior

Let Λ be a connected closed region with smooth boundary contained in the d-dimensional continuous torus T d . In the discrete torus N -1 T d N , we consider a nearest-neighbor symmetric exclusion process where occupancies of neighboring sites are exchanged at rates depending on Λ in the following way: if both sites are in Λ or Λc, the exchange rate is 1; if one site is in Λ and the other site is in Λc, and the direction of the bond connecting the sites is e j , then the exchange rate is defined as N -1 times the absolute value of the inner product between e j and the normal exterior vector to ∂Λ. We show that this exclusion-type process has a nontrivial hydrodynamical behavior under diffusive scaling and, in the continuum limit, particles are not blocked or reflected by ∂Λ. Thus, the model represents a system of particles under hard-core interaction in the presence of a permeable membrane which slows down the passage of particles between two complementary regions.

scholarly journals Combining SDAE Network with Improved DTW Algorithm for Similarity Measure of Ultra-Weak FBG Vibration Responses in Underground Structures

Sensors ◽  
2020 ◽  
Vol 20 (8) ◽  
pp. 2179
Author(s):  
Sheng Li ◽  
Xiang Zuo ◽  
Zhengying Li ◽  
Honghai Wang ◽  
Lizhi Sun
Keyword(s):  
Similarity Measure ◽  
Nearest Neighbor ◽  
Distance Measure ◽  
Integrated Approach ◽  
Structural Vibration ◽  
Distributed Monitoring ◽  
Underground Structures ◽  
Long Distance ◽  
Vibration Responses ◽  
Weak Fbg

Quantifying structural status and locating structural anomalies are critical to tracking and safeguarding the safety of long-distance underground structures. Given the dynamic and distributed monitoring capabilities of an ultra-weak fiber Bragg grating (FBG) array, this paper proposes a method combining the stacked denoising autoencoder (SDAE) network and the improved dynamic time wrapping (DTW) algorithm to quantify the similarity of vibration responses. To obtain the dimensionality reduction features that were conducive to distance measurement, the silhouette coefficient was adopted to evaluate the training efficacy of the SDAE network under different hyperparameter settings. To measure the distance based on the improved DTW algorithm, the one nearest neighbor (1-NN) classifier was utilized to search the best constraint bandwidth. Moreover, the study proposed that the performance of different distance metrics used to quantify similarity can be evaluated through the 1-NN classifier. Based on two one-dimensional time-series datasets from the University of California, Riverside (UCR) archives, the detailed implementation process for similarity measure was illustrated. In terms of feature extraction and distance measure of UCR datasets, the proposed integrated approach of similarity measure showed improved performance over other existing algorithms. Finally, the field-vibration responses of the track bed in the subway detected by the ultra-weak FBG array were collected to determine the similarity characteristics of structural vibration among different monitoring zones. The quantitative results indicated that the proposed method can effectively quantify and distinguish the vibration similarity related to the physical location of structures.

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