Correlations in bivariate point processes: some biological applications

1996 ◽  
Vol 28 (2) ◽  
pp. 330-330
Author(s):  
Guillermo Ayala ◽  
Amelia Simó
Keyword(s):  
Monte Carlo ◽  
Point Processes ◽  
Intensity Function ◽  
Childhood Leukaemia ◽  
Biological Applications ◽  
Point Patterns ◽  
Palm Distribution ◽  
Correlation Measures ◽  
The Cross ◽  
Random Labelling

Let (Φ1 Φ2) be a bivariate point process. Let be the probability that (Φ1 Φ2) - (0, s) (the process without the 0 and s points) verify U when we have a point of <1>1 in the origin and a point of Φ2 in s. This is the reduced cross Palm distribution. Some correlation measures for bivariate point processes based on this reduced cross Palm distribution are proposed. Their estimators and expressions under the independence and the random labelling hypothesis are considered. The differences and improvements with respect to the cross intensity function and its integrated version, the cross function (Stoyan et al. 1987), are studied. Some Monte Carlo tests for testing the independence and the random labelling hypothesis are proposed. They are applied to real bivariate point patterns: positions of hickories and maples in the Lansing Woods (Diggle 1983) and cases and controls of childhood leukaemia and lymphoma in North Humberside (Cuzick and Edwards 1990).

Correlations in bivariate point processes: some biological applications

1996 ◽  
Vol 28 (02) ◽  
pp. 330
Author(s):  
Guillermo Ayala ◽  
Amelia Simó
Keyword(s):  
Monte Carlo ◽  
Point Processes ◽  
Intensity Function ◽  
Childhood Leukaemia ◽  
Biological Applications ◽  
Point Patterns ◽  
Palm Distribution ◽  
Correlation Measures ◽  
The Cross ◽  
Random Labelling

Let (Φ1 Φ2) be a bivariate point process. Let be the probability that (Φ1 Φ2) - (0, s) (the process without the 0 and s points) verify U when we have a point of &lt;1&gt;1 in the origin and a point of Φ2 in s. This is the reduced cross Palm distribution. Some correlation measures for bivariate point processes based on this reduced cross Palm distribution are proposed. Their estimators and expressions under the independence and the random labelling hypothesis are considered. The differences and improvements with respect to the cross intensity function and its integrated version, the cross function (Stoyan et al. 1987), are studied. Some Monte Carlo tests for testing the independence and the random labelling hypothesis are proposed. They are applied to real bivariate point patterns: positions of hickories and maples in the Lansing Woods (Diggle 1983) and cases and controls of childhood leukaemia and lymphoma in North Humberside (Cuzick and Edwards 1990).

scholarly journals Neural Decoding Using a Parallel Sequential Monte Carlo Method on Point Processes with Ensemble Effect

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Kai Xu ◽  
Yiwen Wang ◽  
Fang Wang ◽  
Yuxi Liao ◽  
Qiaosheng Zhang ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Point Process ◽  
Goodness Of Fit ◽  
Point Processes ◽  
Sequential Monte Carlo ◽  
Neuronal Response ◽  
Position Estimation ◽  
Monte Carlo Algorithm ◽  
Sequential Monte Carlo Method ◽  
Proposed Model

Sequential Monte Carlo estimation on point processes has been successfully applied to predict the movement from neural activity. However, there exist some issues along with this method such as the simplified tuning model and the high computational complexity, which may degenerate the decoding performance of motor brain machine interfaces. In this paper, we adopt a general tuning model which takes recent ensemble activity into account. The goodness-of-fit analysis demonstrates that the proposed model can predict the neuronal response more accurately than the one only depending on kinematics. A new sequential Monte Carlo algorithm based on the proposed model is constructed. The algorithm can significantly reduce the root mean square error of decoding results, which decreases 23.6% in position estimation. In addition, we accelerate the decoding speed by implementing the proposed algorithm in a massive parallel manner on GPU. The results demonstrate that the spike trains can be decoded as point process in real time even with 8000 particles or 300 neurons, which is over 10 times faster than the serial implementation. The main contribution of our work is to enable the sequential Monte Carlo algorithm with point process observation to output the movement estimation much faster and more accurately.

Target electron removal in C5+ + H collision

2021 ◽  
Author(s):  
Saed J Al Atawneh ◽  
Karoly Tokesi
Keyword(s):  
Monte Carlo ◽  
Cross Sections ◽  
Dominant Role ◽  
Correction Term ◽  
Theoretical Data ◽  
Model Potential ◽  
Classical Trajectory ◽  
Projectile Energy ◽  
Collision Dynamics ◽  
The Cross

Abstract We present target ionization and charge exchange cross sections in a collision between C5+ ion and H atom. We treat the collision dynamics classically using a four-body classical trajectory Monte Carlo (CTMC) and a four-body quasi-classical Monte Carlo (QCTMC) model when the Heisenberg correction term is added to the standard CTMC model via model potential. The calculations were performed in the projectile energy range between 1.0 keV/amu and 10 MeV/amu. We found that the cross sections obtained by the QCTMC model are higher than that of the cross sections calculated by the standard CTMC model and these cross sections are closer to the previous experimental and theoretical data. Moreover, for the case of ionization, we show that the interaction between the projectile and the target electrons plays a dominant role in the enhancement of the cross sections at lower energies.

On the statistics of the linked stress release model

2001 ◽  
Vol 38 (A) ◽  
pp. 176-187 ◽  
Author(s):  
Mark Bebbington ◽  
David S. Harte
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Numerical Analysis ◽  
Large Scale ◽  
Point Processes ◽  
Information Criterion ◽  
Stress Release ◽  
Stress Release Model ◽  
Using Data ◽  
Release Model

The paper reviews the formulation of the linked stress release model for large scale seismicity together with aspects of its application. Using data from Taiwan for illustrative purposes, models can be selected and verified using tools that include Akaike's information criterion (AIC), numerical analysis, residual point processes and Monte Carlo simulation.

scholarly journals On the weak convergence of stochastic processes with embedded point processes

1988 ◽  
Vol 20 (2) ◽  
pp. 473-475 ◽  
Author(s):  
Panagiotis Konstantopoulos ◽  
Jean Walrand
Keyword(s):  
Stochastic Process ◽  
Weak Convergence ◽  
Stochastic Processes ◽  
Point Process ◽  
Real Line ◽  
Continuous Time ◽  
Point Processes ◽  
Mixing Condition ◽  
The Real ◽  
Palm Distribution

We consider a stochastic process in continuous time and two point processes on the real line, all jointly stationary. We show that under a certain mixing condition the values of the process at the points of the second point process converge weakly under the Palm distribution with respect to the first point process, and we identify the limit. This result is a supplement to two other known results which are mentioned below.

scholarly journals EVALUASI NUMERIK PENDUGA FUNGSI NILAI HARAPAN DAN FUNGSI RAGAM PROSES POISSON MAJEMUK DENGAN INTENSITAS EKSPONENSIAL FUNGSI LINEAR

2018 ◽  
Vol 17 (2) ◽  
pp. 157
Author(s):  
S. UTAMI ◽  
I W. MANGKU ◽  
I G. P. PURNABA
Keyword(s):  
Monte Carlo ◽  
Confidence Intervals ◽  
Observation Interval ◽  
Compound Poisson Process ◽  
Intensity Function ◽  
Significance Level ◽  
Variance Functions ◽  
Mean And Variance ◽  
The Mean ◽  
Strongly Consistent

<em>Performances of estimators for the mean and variance functions of a compound Poisson process having intensity obtained as an exponential of linear function are investigated using Monte Carlo simulations. The intensity function of this process is assumed to be </em>𝑒𝑥𝑝(𝛼+𝛽𝑠) <em>with </em>0&lt;𝛽&lt;<em>∞</em>, <em>where </em>𝛽 <em>is assumed to be known. In [8], estimators of the mean and variance functions of this process have been constructed and have been proved to be unbiased, weakly and strongly consistent. The objectives of this research are to check distributions of these estimators using Monte Carlo simulation and to check the convergence to </em>1−𝛼 <em>of the probabilities that the parameters are contained in the confidence intervals constructed in [11]. Results of the research are as follows. Distribution of estimators for the mean and variance functions are approximately normal. For a given significance level </em>𝛼<em>, the larger the size of observation interval, the closer the probabilities that the parameters are contained in the confidence intervals to </em>1−𝛼<em>.</em>

scholarly journals Monte Carlo with determinantal point processes

2020 ◽  
Vol 30 (1) ◽  
pp. 368-417 ◽  
Author(s):  
Rémi Bardenet ◽  
Adrien Hardy
Keyword(s):  
Monte Carlo ◽  
Point Processes ◽  
Determinantal Point Processes
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