A self-exciting point process with cyclic component, trend component, triggering function, and response function

2021 ◽  
Author(s):  
Hasih Pratiwi ◽  
Winda Haryanto ◽  
Sri Subanti ◽  
I. Wayan Mangku ◽  
Kiki Ferawati
Keyword(s):  
Point Process ◽  
Response Function ◽  
Cyclic Component ◽  
Trend Component

scholarly journals Sensitivity of the resting-state haemodynamic response function estimation to autonomic nervous system fluctuations

2016 ◽  
Vol 374 (2067) ◽  
pp. 20150190 ◽  
Author(s):  
Guo-Rong Wu ◽  
Daniele Marinazzo
Keyword(s):  
Point Process ◽  
Response Function ◽  
Neural Activity ◽  
Resting State ◽  
Process Analysis ◽  
Low Frequency ◽  
Cardiac Activity ◽  
Haemodynamic Response ◽  
Design Matrix ◽  
Bold Signal

The haemodynamic response function (HRF) is a key component of the blood oxygen level-dependent (BOLD) signal, providing the mapping between neural activity and the signal measured with functional magnetic resonance imaging (fMRI). Most of the time the HRF is associated with task-based fMRI protocols, in which its onset is explicitly included in the design matrix. On the other hand, the HRF also mediates the relationship between spontaneous neural activity and the BOLD signal in resting-state protocols, in which no explicit stimulus is taken into account. It has been shown that resting-state brain dynamics can be characterized by looking at sparse BOLD ‘events’, which can be retrieved by point process analysis. These events can be then used to retrieve the HRF at rest. Crucially, cardiac activity can also induce changes in the BOLD signal, thus affecting both the number of these events and the estimation of the haemodynamic response. In this study, we compare the resting-state haemodynamic response retrieved by means of a point process analysis, taking the cardiac fluctuations into account. We find that the resting-state HRF estimation is significantly modulated in the brainstem and surrounding cortical areas. From the analysis of two high-quality datasets with different temporal and spatial resolution, and through the investigation of intersubject correlation, we suggest that spontaneous point process response durations are associated with the mean interbeat interval and low-frequency power of heart rate variability in the brainstem.

Measurement of a wandering signal amid noise

1967 ◽  
Vol 4 (1) ◽  
pp. 90-102 ◽  
Author(s):  
E. J. Hannan
Keyword(s):  
Seasonal Variation ◽  
Difference Equation ◽  
Unit Circle ◽  
Response Function ◽  
Stationary Process ◽  
Stochastic Integral ◽  
Trend Component ◽  
The Difference

A formula is given for the response function of a filter which extracts a signal generated by a non-stationary process from amid noise. The non-stationarity is due to the presence of zeros on the unit circle of the function characterising the difference equation generating the signal. The signal is broken into a trend component and a stochastic integral in which t occurs only through the factor exp it λ and it is shown that the filter which optimally extracts the latter perfectly represents the former. The considerations cover the case of a vector series. Applications to problems in seasonal variation measurement are indicated.

Measurement of a wandering signal amid noise

1967 ◽  
Vol 4 (01) ◽  
pp. 90-102 ◽  
Author(s):  
E. J. Hannan
Keyword(s):  
Seasonal Variation ◽  
Difference Equation ◽  
Unit Circle ◽  
Response Function ◽  
Stationary Process ◽  
Stochastic Integral ◽  
Trend Component ◽  
The Difference

A formula is given for the response function of a filter which extracts a signal generated by a non-stationary process from amid noise. The non-stationarity is due to the presence of zeros on the unit circle of the function characterising the difference equation generating the signal. The signal is broken into a trend component and a stochastic integral in which t occurs only through the factor exp it λ and it is shown that the filter which optimally extracts the latter perfectly represents the former. The considerations cover the case of a vector series. Applications to problems in seasonal variation measurement are indicated.

Habitat use of toothed whales in a marine protected area based on point process models

2019 ◽  
Vol 609 ◽  
pp. 239-256 ◽  
Author(s):  
TL Silva ◽  
G Fay ◽  
TA Mooney ◽  
J Robbins ◽  
MT Weinrich ◽  
...  
Keyword(s):  
Habitat Use ◽  
Point Process ◽  
Protected Area ◽  
Marine Protected Area ◽  
Process Models ◽  
Point Process Models

On the generation and origin of I/f noise

1999 ◽  
Vol 4 ◽  
pp. 87-96 ◽  
Author(s):  
B. Kaulakys ◽  
T. Meškauskas
Keyword(s):  
Point Process ◽  
Solvable Model ◽  
Autoregressive Process ◽  
Wide Range ◽  
Occurrence Times

Simple analytically solvable model exhibiting 1/f spectrum in any desirably wide range of frequency is analysed. The model consists of pulses (point process) whose interevent times obey an autoregressive process with small damping. Analysis and generalizations of the model indicate to the possible origin of 1/f noise, i.e. random increments between the occurrence times of particles or pulses resulting in the clustering of the pulses.

Connected-Tube MPP Model for Unsupervised 3D Fiber Detection

2020 ◽  
Vol 2020 (14) ◽  
pp. 305-1-305-6
Author(s):  
Tianyu Li ◽  
Camilo G. Aguilar ◽  
Ronald F. Agyei ◽  
Imad A. Hanhan ◽  
Michael D. Sangid ◽  
...  
Keyword(s):  
Composite Material ◽  
Point Process ◽  
Marked Point ◽  
Experimental Results ◽  
Marked Point Process ◽  
Fiber Reinforced Composite ◽  
Reinforced Composite ◽  
Proposed Model ◽  
Cylinder Model ◽  
Reinforced Composite Material

In this paper, we extend our previous 2D connected-tube marked point process (MPP) model to a 3D connected-tube MPP model for fiber detection. In the 3D case, a tube is represented by a cylinder model with two spherical areas at its ends. The spherical area is used to define connection priors that encourage connection of tubes that belong to the same fiber. Since each long fiber can be fitted by a series of connected short tubes, the proposed model is capable of detecting curved long tubes. We present experimental results on fiber-reinforced composite material images to show the performance of our method.

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