Package 'AIUQ' reference manual

Title:	Ab Initio Uncertainty Quantification
Description:	Uncertainty quantification and inverse estimation by probabilistic generative models from the beginning of the data analysis. An example is a Fourier basis method for inverse estimation in scattering analysis of microscopy videos. It does not require specifying a certain range of Fourier bases and it substantially reduces computational cost via the generalized Schur algorithm. See the reference: Mengyang Gu, Yue He, Xubo Liu and Yimin Luo (2023), <doi:10.48550/arXiv.2309.02468>.
Authors:	Yue He [aut], Xubo Liu [aut], Mengyang Gu [aut, cre]
Maintainer:	Mengyang Gu <[email protected]>
License:	GPL (>= 3)
Version:	0.5.3
Built:	2024-10-01 06:43:51 UTC
Source:	CRAN

Scattering analysis of microscopy for anisotropic processes

Description

Fast parameter estimation in scattering analysis of microscopy for anisotropic processes, using AIUQ method.

Usage

aniso_SAM(
  intensity = NA,
  intensity_str = "T_SS_mat",
  pxsz = 1,
  sz = c(NA, NA),
  mindt = 1,
  AIUQ_thr = c(1, 1),
  model_name = "BM",
  sigma_0_2_ini = NaN,
  param_initial = NA,
  num_optim = 1,
  msd_fn = NA,
  msd_grad_fn = NA,
  num_param = NA,
  uncertainty = FALSE,
  M = 50,
  sim_object = NA,
  msd_truth = NA,
  method = "AIUQ",
  index_q_AIUQ = NA,
  message_out = TRUE,
  square = FALSE
)
aniso_SAM(
  intensity = NA,
  intensity_str = "T_SS_mat",
  pxsz = 1,
  sz = c(NA, NA),
  mindt = 1,
  AIUQ_thr = c(1, 1),
  model_name = "BM",
  sigma_0_2_ini = NaN,
  param_initial = NA,
  num_optim = 1,
  msd_fn = NA,
  msd_grad_fn = NA,
  num_param = NA,
  uncertainty = FALSE,
  M = 50,
  sim_object = NA,
  msd_truth = NA,
  method = "AIUQ",
  index_q_AIUQ = NA,
  message_out = TRUE,
  square = FALSE
)

Arguments

`intensity`	intensity profile. See 'Details'.
`intensity_str`	structure of the intensity profile, options from ('SST_array','S_ST_mat','T_SS_mat'). See 'Details'.
`pxsz`	size of one pixel in unit of micron, 1 for simulated data
`sz`	frame size of the intensity profile in x and y directions, number of pixels contained in each frame equals sz_x by sz_y.
`mindt`	minimum lag time, 1 for simulated data
`AIUQ_thr`	threshold for wave number selection, numeric vector of two elements with values between 0 and 1. See 'Details'.
`model_name`	fitted model, options from ('BM','OU','FBM','OU+FBM', 'user_defined'), with Brownian motion as the default model. See 'Details'.
`sigma_0_2_ini`	initial value for background noise. If NA, use minimum value of absolute square of intensity profile in reciprocal space.
`param_initial`	initial values for param estimation.
`num_optim`	number of optimization.
`msd_fn`	user defined mean squared displacement(MSD) structure, a function of parameters and lag times. NA if `model_name` is not 'user_defined'.
`msd_grad_fn`	gradient for user defined mean squared displacement structure. If `NA`, then numerical gradient will be used for parameter estimation in `'user_defined'` model.
`num_param`	number of parameters need to be estimated in the intermediate scattering function, need to be non-NA value for user_defined' model.
`uncertainty`	a logical evaluating to TRUE or FALSE indicating whether parameter uncertainty should be computed.
`M`	number of particles. See 'Details'.
`sim_object`	NA or an S4 object of class `simulation`.
`msd_truth`	true MSD or reference MSD value.
`method`	methods for parameter estimation, options from ('AIUQ', 'DDM').
`index_q_AIUQ`	index range for wave number when using AIUQ method. See 'Details'.
`message_out`	a logical evaluating to TRUE or FALSE indicating whether or not to output the message.
`square`	a logical evaluating to TRUE or FALSE indicating whether or not to crop the original intensity profile into square image.

Details

For simulated data using aniso_simulation in AIUQ package, intensity will be automatically extracted from aniso_simulation class.

By default intensity_str is set to 'T_SS_mat', a time by space $\times$ space matrix, which is the structure of intensity profile obtained from aniso_simulation class. For intensity_str='SST_array' , input intensity profile should be a space by space by time array, which is the structure from loading a tif file. For intensity_str='S_ST_mat', input intensity profile should be a space by space $\times$ time matrix.

By default AIUQ_thr is set to c(1,1), uses information from all complete q rings. The first element affects maximum wave number selected, and second element controls minimum proportion of wave number selected. By setting 1 for the second element, if maximum wave number selected is less than the wave number length, then maximum wave number selected is coerced to use all wave number unless user defined another index range through index_q_AIUQ.

If model_name equals 'user_defined', or NA (will coerced to 'user_defined'), then msd_fn and num_param need to be provided for parameter estimation.

Number of particles M is set to 50 or automatically extracted from simulation class for simulated data using simulation in AIUQ package.

By default, using all wave vectors from complete q ring for both AIUQ, unless user defined index range through index_q_AIUQ.

Value

Returns an S4 object of class aniso_SAM.

Author(s)

Yue He [aut], Xubo Liu [aut], Mengyang Gu [aut, cre]

References

Gu, M., He, Y., Liu, X., & Luo, Y. (2023). Ab initio uncertainty quantification in scattering analysis of microscopy. arXiv preprint arXiv:2309.02468.

Gu, M., Luo, Y., He, Y., Helgeson, M. E., & Valentine, M. T. (2021). Uncertainty quantification and estimation in differential dynamic microscopy. Physical Review E, 104(3), 034610.

Cerbino, R., & Trappe, V. (2008). Differential dynamic microscopy: probing wave vector dependent dynamics with a microscope. Physical review letters, 100(18), 188102.

Examples

library(AIUQ)
# Example 1: Estimation for simulated data
set.seed(1)
aniso_sim = aniso_simulation(sz=100,len_t=100, model_name="BM",M=100,sigma_bm=c(0.5,0.3))
show(aniso_sim)
plot_traj(object=aniso_sim)
aniso_sam = aniso_SAM(sim_object=aniso_sim, model_name="BM",AIUQ_thr = c(0.999,0))
show(aniso_sam)
plot_MSD(aniso_sam,msd_truth = aniso_sam@msd_truth)
library(AIUQ)
# Example 1: Estimation for simulated data
set.seed(1)
aniso_sim = aniso_simulation(sz=100,len_t=100, model_name="BM",M=100,sigma_bm=c(0.5,0.3))
show(aniso_sim)
plot_traj(object=aniso_sim)
aniso_sam = aniso_SAM(sim_object=aniso_sim, model_name="BM",AIUQ_thr = c(0.999,0))
show(aniso_sam)
plot_MSD(aniso_sam,msd_truth = aniso_sam@msd_truth)

Anisotropic SAM class

Description

S4 class for fast parameter estimation in scattering analysis of microscopy for anisotropic processes, using either AIUQ or DDM method.

Slots

pxsz: numeric. Size of one pixel in unit of micron with default value 1.
mindt: numeric. Minimum lag time with default value 1.
sz: vector. Frame size of the intensity profile in x and y directions, number of pixels contained in each frame equals sz_x by sz_y.
len_t: integer. Number of time steps.
len_q: integer. Number of wave vector.
q: vector. Wave vector in unit of um^-1.
d_input: vector. Sequence of lag times.
B_est_ini: numeric. Estimation of B. This parameter is determined by the noise in the system. See 'References'.
A_est_ini: vector. Estimation of A(q). Note this parameter is determined by the properties of the imaged material and imaging optics. See 'References'.
I_o_q_2_ori: vector. Absolute square of Fourier transformed intensity profile, ensemble over time.
q_ori_ring_loc_unique_index: list. List of location index of non-duplicate values for each q ring.
model_name: character. Fitted model, options from ('BM','OU','FBM','OU+FBM', 'user_defined').
param_est: matrix. Estimated parameters contained in MSD.
sigma_2_0_est: vector. Estimated variance of background noise.
msd_est: matrix. Estimated MSD.
uncertainty: logical. A logical evaluating to TRUE or FALSE indicating whether parameter uncertainty should be computed.
msd_truth: matrix. True MSD or reference MSD value.
sigma_2_0_truth: vector. True variance of background noise, non NA for simulated data using simulation.
param_truth: matrix. True parameters used to construct MSD, non NA for simulated data using aniso_simulation.
index_q: vector. Selected index of wave vector.
I_q: matrix. Fourier transformed intensity profile with structure 'SS_T_mat'.
AIC: numeric. Akaike information criterion score.
mle: numeric. Maximum log likelihood value.
msd_x_lower: vector. Lower bound of 95% confidence interval of MSD in x directions.
msd_x_upper: vector. Upper bound of 95% confidence interval of MSD in x directions.
msd_y_lower: vector. Lower bound of 95% confidence interval of MSD in y directions.
msd_y_upper: vector. Upper bound of 95% confidence interval of MSD in y directions.
param_uq_range: matrix. 95% confidence interval for estimated parameters.

Author(s)

Yue He [aut], Xubo Liu [aut], Mengyang Gu [aut, cre]

References

Gu, M., He, Y., Liu, X., & Luo, Y. (2023). Ab initio uncertainty quantification in scattering analysis of microscopy. arXiv preprint arXiv:2309.02468.

Gu, M., Luo, Y., He, Y., Helgeson, M. E., & Valentine, M. T. (2021). Uncertainty quantification and estimation in differential dynamic microscopy. Physical Review E, 104(3), 034610.

Cerbino, R., & Trappe, V. (2008). Differential dynamic microscopy: probing wave vector dependent dynamics with a microscope. Physical review letters, 100(18), 188102.

Simulate anisotropic 2D particle movement

Description

Simulate anisotropic 2D particle movement from a user selected stochastic process, and output intensity profiles.

Usage

aniso_simulation(
  sz = c(200, 200),
  len_t = 200,
  M = 50,
  model_name = "BM",
  noise = "gaussian",
  I0 = 20,
  Imax = 255,
  pos0 = matrix(NaN, nrow = M, ncol = 2),
  rho = c(0.95, 0.9),
  H = c(0.4, 0.3),
  sigma_p = 2,
  sigma_bm = c(1, 0.5),
  sigma_ou = c(2, 1.5),
  sigma_fbm = c(2, 1.5)
)
aniso_simulation(
  sz = c(200, 200),
  len_t = 200,
  M = 50,
  model_name = "BM",
  noise = "gaussian",
  I0 = 20,
  Imax = 255,
  pos0 = matrix(NaN, nrow = M, ncol = 2),
  rho = c(0.95, 0.9),
  H = c(0.4, 0.3),
  sigma_p = 2,
  sigma_bm = c(1, 0.5),
  sigma_ou = c(2, 1.5),
  sigma_fbm = c(2, 1.5)
)

Arguments

`sz`	frame size of simulated image with default `c(200,200)`.
`len_t`	number of time steps with default 200.
`M`	number of particles with default 50.
`model_name`	stochastic process simulated, options from ('BM','OU','FBM','OU+FBM'), with default 'BM'.
`noise`	background noise, options from ('uniform','gaussian'), with default 'gaussian'.
`I0`	background intensity, value between 0 and 255, with default 20.
`Imax`	maximum intensity at the center of the particle, value between 0 and 255, with default 255.
`pos0`	initial position for M particles, matrix with dimension M by 2.
`rho`	correlation between successive step and previous step in O-U process, in x, y-directions. A vector of length 2 with values between 0 and 1, default `c(0.95,0.9)`.
`H`	Hurst parameter of fractional Brownian Motion, in x, y-directions. A vector of length 2, value between 0 and 1, default `c(0.4,0.3)`.
`sigma_p`	radius of the spherical particle (3sigma_p), with default 2.
`sigma_bm`	distance moved per time step of Brownian Motion, in x,y-directions. A vector of length 2 with default `c(1,0.5)`.
`sigma_ou`	distance moved per time step of Ornstein–Uhlenbeck process, in x, y-directions. A vector of length 2 with default `c(2,1.5)`.
`sigma_fbm`	distance moved per time step of fractional Brownian Motion, in x, y-directions. A vector of length 2 with default `c(2,1.5)`.

Value

Returns an S4 object of class anisotropic_simulation.

Author(s)

Yue He [aut], Xubo Liu [aut], Mengyang Gu [aut, cre]

References

Gu, M., He, Y., Liu, X., & Luo, Y. (2023). Ab initio uncertainty quantification in scattering analysis of microscopy. arXiv preprint arXiv:2309.02468.

Gu, M., Luo, Y., He, Y., Helgeson, M. E., & Valentine, M. T. (2021). Uncertainty quantification and estimation in differential dynamic microscopy. Physical Review E, 104(3), 034610.

Cerbino, R., & Trappe, V. (2008). Differential dynamic microscopy: probing wave vector dependent dynamics with a microscope. Physical review letters, 100(18), 188102.

Examples

library(AIUQ)
# -------------------------------------------------
# Example 1: Simple diffusion for 200 images with
#            200 by 200 pixels and 50 particles
# -------------------------------------------------
aniso_sim_bm = aniso_simulation()
show(aniso_sim_bm)

# -------------------------------------------------
# Example 2: Simple diffusion for 100 images with
#            100 by 100 pixels and slower speed
# -------------------------------------------------
aniso_sim_bm = aniso_simulation(sz=100,len_t=100,sigma_bm=c(0.5,0.1))
show(aniso_sim_bm)

# -------------------------------------------------
# Example 3: Ornstein-Uhlenbeck process
# -------------------------------------------------
aniso_sim_ou = aniso_simulation(model_name="OU")
show(aniso_sim_ou)
library(AIUQ)
# -------------------------------------------------
# Example 1: Simple diffusion for 200 images with
#            200 by 200 pixels and 50 particles
# -------------------------------------------------
aniso_sim_bm = aniso_simulation()
show(aniso_sim_bm)

# -------------------------------------------------
# Example 2: Simple diffusion for 100 images with
#            100 by 100 pixels and slower speed
# -------------------------------------------------
aniso_sim_bm = aniso_simulation(sz=100,len_t=100,sigma_bm=c(0.5,0.1))
show(aniso_sim_bm)

# -------------------------------------------------
# Example 3: Ornstein-Uhlenbeck process
# -------------------------------------------------
aniso_sim_ou = aniso_simulation(model_name="OU")
show(aniso_sim_ou)

Anisotropic simulation class

Description

S4 class for anisotropic 2D particle movement simulation.

Details

intensity should has structure 'T_SS_mat', matrix with dimension len_t by sz $\times$ sz.

pos should be the position matrix with dimension M $\times$ len_t. See bm_particle_intensity, ou_particle_intensity, fbm_particle_intensity, fbm_ou_particle_intensity.

Slots

sz: vector. Frame size of the intensity profile, number of pixels contained in each frame equals sz[1] by sz[2].
len_t: integer. Number of time steps.
noise: character. Background noise, options from ('uniform','gaussian').
model_name: character. Simulated stochastic process, options from ('BM','OU','FBM','OU+FBM').
M: integer. Number of particles.
pxsz: numeric. Size of one pixel in unit of micron, 1 for simulated data.
mindt: numeric. Minimum lag time, 1 for simulated data.
pos: matrix. Position matrix for particle trajectory, see 'Details'.
intensity: matrix. Filled intensity profile, see 'Details'.
num_msd: matrix. Numerical mean squared displacement (MSD).
param: matrix. Parameters used to construct MSD.
theor_msd: matrix. Theoretical MSD.
sigma_2_0: vector. Variance of background noise.

Author(s)

Yue He [aut], Xubo Liu [aut], Mengyang Gu [aut, cre]

References

Gu, M., He, Y., Liu, X., & Luo, Y. (2023). Ab initio uncertainty quantification in scattering analysis of microscopy. arXiv preprint arXiv:2309.02468.

Gu, M., Luo, Y., He, Y., Helgeson, M. E., & Valentine, M. T. (2021). Uncertainty quantification and estimation in differential dynamic microscopy. Physical Review E, 104(3), 034610.

Cerbino, R., & Trappe, V. (2008). Differential dynamic microscopy: probing wave vector dependent dynamics with a microscope. Physical review letters, 100(18), 188102.

Compute observed dynamic image structure function

Description

Compute observed dynamic image structure function (Dqt) using object of SAM class.

Usage

get_dqt(object, index_q = NA)
get_dqt(object, index_q = NA)

Arguments

`object`	an S4 object of class `SAM`
`index_q`	wavevector range used for computing Dqt

Value

A matrix of observed dynamic image structure function with dimension len_q by len_t-1.

Author(s)

Yue He [aut], Xubo Liu [aut], Mengyang Gu [aut, cre]

References

Gu, M., He, Y., Liu, X., & Luo, Y. (2023). Ab initio uncertainty quantification in scattering analysis of microscopy. arXiv preprint arXiv:2309.02468.

Gu, M., Luo, Y., He, Y., Helgeson, M. E., & Valentine, M. T. (2021). Uncertainty quantification and estimation in differential dynamic microscopy. Physical Review E, 104(3), 034610.

Cerbino, R., & Trappe, V. (2008). Differential dynamic microscopy: probing wave vector dependent dynamics with a microscope. Physical review letters, 100(18), 188102.

Examples

## Not run: 
library(AIUQ)
sim_bm = simulation(len_t=100,sz=100,sigma_bm=0.5)
show(sim_bm)
sam = SAM(sim_object = sim_bm)
show(sam)
Dqt = get_dqt(object=sam)

## End(Not run)
## Not run: 
library(AIUQ)
sim_bm = simulation(len_t=100,sz=100,sigma_bm=0.5)
show(sim_bm)
sam = SAM(sim_object = sim_bm)
show(sam)
Dqt = get_dqt(object=sam)

## End(Not run)

Compute empirical intermediate scattering function

Description

Compute empirical intermediate scattering function (ISF) using object of SAM class.

Usage

get_isf(object, index_q = NA, msd_truth = NA)
get_isf(object, index_q = NA, msd_truth = NA)

Arguments

`object`	an S4 object of class `SAM`
`index_q`	wavevector range used for computing ISF
`msd_truth`	true or reference MSD

Value

A matrix of empirical intermediate scattering function with dimension len_q by len_t-1.

Author(s)

Yue He [aut], Xubo Liu [aut], Mengyang Gu [aut, cre]

References

Gu, M., He, Y., Liu, X., & Luo, Y. (2023). Ab initio uncertainty quantification in scattering analysis of microscopy. arXiv preprint arXiv:2309.02468.

Gu, M., Luo, Y., He, Y., Helgeson, M. E., & Valentine, M. T. (2021). Uncertainty quantification and estimation in differential dynamic microscopy. Physical Review E, 104(3), 034610.

Cerbino, R., & Trappe, V. (2008). Differential dynamic microscopy: probing wave vector dependent dynamics with a microscope. Physical review letters, 100(18), 188102.

Examples

## Not run: 
library(AIUQ)
sim_bm = simulation(len_t=100,sz=100,sigma_bm=0.5)
show(sim_bm)
sam = SAM(sim_object = sim_bm)
show(sam)
ISF = get_isf(object=sam)

## End(Not run)
## Not run: 
library(AIUQ)
sim_bm = simulation(len_t=100,sz=100,sigma_bm=0.5)
show(sim_bm)
sam = SAM(sim_object = sim_bm)
show(sam)
ISF = get_isf(object=sam)

## End(Not run)

Compute modeled dynamic image structure function

Description

Compute modeled dynamic image structure function (Dqt) using object of SAM class.

Usage

modeled_dqt(object, index_q = NA, uncertainty = FALSE)
modeled_dqt(object, index_q = NA, uncertainty = FALSE)

Arguments

`object`	an S4 object of class `SAM`
`index_q`	wavevector range used for computing Dqt
`uncertainty`	logic evalution

Value

A matrix of modeled dynamic image structure function with dimension len_q by len_t-1.

Author(s)

Yue He [aut], Xubo Liu [aut], Mengyang Gu [aut, cre]

References

Gu, M., He, Y., Liu, X., & Luo, Y. (2023). Ab initio uncertainty quantification in scattering analysis of microscopy. arXiv preprint arXiv:2309.02468.

Gu, M., Luo, Y., He, Y., Helgeson, M. E., & Valentine, M. T. (2021). Uncertainty quantification and estimation in differential dynamic microscopy. Physical Review E, 104(3), 034610.

Cerbino, R., & Trappe, V. (2008). Differential dynamic microscopy: probing wave vector dependent dynamics with a microscope. Physical review letters, 100(18), 188102.

Examples

library(AIUQ)
sim_bm = simulation(len_t=100,sz=100,sigma_bm=0.5)
show(sim_bm)
sam = SAM(sim_object = sim_bm)
show(sam)
modeled_Dqt = modeled_dqt(object=sam)
library(AIUQ)
sim_bm = simulation(len_t=100,sz=100,sigma_bm=0.5)
show(sim_bm)
sam = SAM(sim_object = sim_bm)
show(sam)
modeled_Dqt = modeled_dqt(object=sam)

Compute modeled intermediate scattering function

Description

Compute modeled intermediate scattering function (ISF) using object of SAM class.

Usage

modeled_isf(object, index_q = NA)
modeled_isf(object, index_q = NA)

Arguments

`object`	an S4 object of class `SAM`
`index_q`	wavevector range used for computing ISF

Value

A matrix of modeled intermediate scattering function with dimension len_q by len_t-1.

Author(s)

Yue He [aut], Xubo Liu [aut], Mengyang Gu [aut, cre]

References

Gu, M., He, Y., Liu, X., & Luo, Y. (2023). Ab initio uncertainty quantification in scattering analysis of microscopy. arXiv preprint arXiv:2309.02468.

Gu, M., Luo, Y., He, Y., Helgeson, M. E., & Valentine, M. T. (2021). Uncertainty quantification and estimation in differential dynamic microscopy. Physical Review E, 104(3), 034610.

Cerbino, R., & Trappe, V. (2008). Differential dynamic microscopy: probing wave vector dependent dynamics with a microscope. Physical review letters, 100(18), 188102.

Examples

library(AIUQ)
sim_bm = simulation(len_t=100,sz=100,sigma_bm=0.5)
show(sim_bm)
sam = SAM(sim_object = sim_bm)
show(sam)
modeled_ISF = modeled_isf(object=sam)
library(AIUQ)
sim_bm = simulation(len_t=100,sz=100,sigma_bm=0.5)
show(sim_bm)
sam = SAM(sim_object = sim_bm)
show(sam)
modeled_ISF = modeled_isf(object=sam)

Plot 2D intensity

Description

Function to plot 2D intensity profile for a certain frame, default is to plot the first frame. Input can be a matrix (2D) or an array (3D).

Usage

plot_intensity(
  intensity,
  intensity_str = "T_SS_mat",
  frame = 1,
  sz = NA,
  title = NA,
  color = FALSE
)
plot_intensity(
  intensity,
  intensity_str = "T_SS_mat",
  frame = 1,
  sz = NA,
  title = NA,
  color = FALSE
)

Arguments

`intensity`	intensity profile
`intensity_str`	structure of the intensity profile, options from ('SST_array','S_ST_mat','T_SS_mat', 'SS_T_mat'). See 'Details'.
`frame`	frame index
`sz`	frame size of simulated image with default `c(200,200)`.
`title`	main title of the plot. If `NA`, title is "intensity profile for frame n" with n being the frame index in `frame`.
`color`	a logical evaluating to TRUE or FALSE indicating whether a colorful plot is generated

Details

By default intensity_str is set to 'T_SS_mat', a time by space $\times$ space matrix, which is the structure of intensity profile obtained from simulation class. For intensity_str='SST_array' , input intensity profile should be a space by space by time array, which is the structure from loading a tif file. For intensity_str='S_ST_mat', input intensity profile should be a space by space $\times$ time matrix. For intensity_str='SS_T_mat', input intensity profile should be a space $\times$ space by time matrix.

Value

2D plot in gray scale (or with color) of selected frame.

Author(s)

Yue He [aut], Xubo Liu [aut], Mengyang Gu [aut, cre]

Examples

library(AIUQ)
sim_bm = simulation(sz=100,len_t=100,sigma_bm=0.5)
show(sim_bm)
plot_intensity(sim_bm@intensity, sz=sim_bm@sz)

library(AIUQ)
sim_bm = simulation(sz=100,len_t=100,sigma_bm=0.5)
show(sim_bm)
plot_intensity(sim_bm@intensity, sz=sim_bm@sz)

Plot estimated MSD with uncertainty from SAM class

Description

Function to plot estimated MSD with uncertainty from SAM class, versus true mean squared displacement(MSD) or given reference values.

Usage

plot_MSD(object, msd_truth = NA, title = NA, log10 = TRUE)
plot_MSD(object, msd_truth = NA, title = NA, log10 = TRUE)

Arguments

`object`	an S4 object of class `SAM`
`msd_truth`	a vector/matrix of true MSD or reference MSD value, default is `NA`
`title`	main title of the plot. If `NA`, title is "model_name" with `model_name` being a field in `SAM` class representing fitted model.
`log10`	a logical evaluating to TRUE or FALSE indicating whether a plot in log10 scale is generated

Value

A plot of estimated MSD with uncertainty versus truth/reference values.

Author(s)

Yue He [aut], Xubo Liu [aut], Mengyang Gu [aut, cre]

References

Gu, M., He, Y., Liu, X., & Luo, Y. (2023). Ab initio uncertainty quantification in scattering analysis of microscopy. arXiv preprint arXiv:2309.02468.

Gu, M., Luo, Y., He, Y., Helgeson, M. E., & Valentine, M. T. (2021). Uncertainty quantification and estimation in differential dynamic microscopy. Physical Review E, 104(3), 034610.

Examples

library(AIUQ)

## Simulate BM and get estimated parameters with uncertainty using BM model
# Simulation
set.seed(1)
sim_bm = simulation(sz=100,len_t=100,sigma_bm=0.5)
show(sim_bm)

# AIUQ method: fitting using BM model
sam = SAM(sim_object=sim_bm, uncertainty=TRUE,AIUQ_thr=c(0.999,0))
show(sam)

plot_MSD(object=sam, msd_truth=sam@msd_truth) #in log10 scale
plot_MSD(object=sam, msd_truth=sam@msd_truth,log10=FALSE) #in real scale

library(AIUQ)

## Simulate BM and get estimated parameters with uncertainty using BM model
# Simulation
set.seed(1)
sim_bm = simulation(sz=100,len_t=100,sigma_bm=0.5)
show(sim_bm)

# AIUQ method: fitting using BM model
sam = SAM(sim_object=sim_bm, uncertainty=TRUE,AIUQ_thr=c(0.999,0))
show(sam)

plot_MSD(object=sam, msd_truth=sam@msd_truth) #in log10 scale
plot_MSD(object=sam, msd_truth=sam@msd_truth,log10=FALSE) #in real scale

Plot 2D particle trajectory

Description

Function to plot the particle trajectory after the simulation class has been constructed.

Usage

plot_traj(object, title = NA)
plot_traj(object, title = NA)

Arguments

`object`	an S4 object of class `simulation`
`title`	main title of the plot. If `NA`, title is "model_name with M particles" with `model_name` and `M` being field in `simulation` class.

Value

2D plot of particle trajectory for a given simulation from simulation class.

Author(s)

Yue He [aut], Xubo Liu [aut], Mengyang Gu [aut, cre]

Examples

library(AIUQ)
sim_bm = simulation(sz=100,len_t=100,sigma_bm=0.5)
show(sim_bm)
plot_traj(sim_bm)
library(AIUQ)
sim_bm = simulation(sz=100,len_t=100,sigma_bm=0.5)
show(sim_bm)
plot_traj(sim_bm)

Scattering analysis of microscopy

Description

Fast parameter estimation in scattering analysis of microscopy, using either AIUQ or DDM method.

Usage

SAM(
  intensity = NA,
  intensity_str = "T_SS_mat",
  pxsz = 1,
  sz = c(NA, NA),
  mindt = 1,
  AIUQ_thr = c(1, 1),
  model_name = "BM",
  sigma_0_2_ini = NaN,
  param_initial = NA,
  num_optim = 1,
  msd_fn = NA,
  msd_grad_fn = NA,
  num_param = NA,
  uncertainty = FALSE,
  M = 50,
  sim_object = NA,
  msd_truth = NA,
  method = "AIUQ",
  index_q_AIUQ = NA,
  index_q_DDM = NA,
  message_out = TRUE,
  A_neg = "abs",
  square = FALSE,
  output_dqt = FALSE,
  output_isf = FALSE,
  output_modeled_isf = FALSE,
  output_modeled_dqt = FALSE
)
SAM(
  intensity = NA,
  intensity_str = "T_SS_mat",
  pxsz = 1,
  sz = c(NA, NA),
  mindt = 1,
  AIUQ_thr = c(1, 1),
  model_name = "BM",
  sigma_0_2_ini = NaN,
  param_initial = NA,
  num_optim = 1,
  msd_fn = NA,
  msd_grad_fn = NA,
  num_param = NA,
  uncertainty = FALSE,
  M = 50,
  sim_object = NA,
  msd_truth = NA,
  method = "AIUQ",
  index_q_AIUQ = NA,
  index_q_DDM = NA,
  message_out = TRUE,
  A_neg = "abs",
  square = FALSE,
  output_dqt = FALSE,
  output_isf = FALSE,
  output_modeled_isf = FALSE,
  output_modeled_dqt = FALSE
)

Arguments

`intensity`	intensity profile. See 'Details'.
`intensity_str`	structure of the intensity profile, options from ('SST_array','S_ST_mat','T_SS_mat'). See 'Details'.
`pxsz`	size of one pixel in unit of micron, 1 for simulated data
`sz`	frame size of the intensity profile in x and y directions, number of pixels contained in each frame equals sz_x by sz_y.
`mindt`	minimum lag time, 1 for simulated data
`AIUQ_thr`	threshold for wave number selection, numeric vector of two elements with values between 0 and 1. See 'Details'.
`model_name`	fitted model, options from ('BM','OU','FBM','OU+FBM', 'user_defined'), with Brownian motion as the default model. See 'Details'.
`sigma_0_2_ini`	initial value for background noise. If NA, use minimum value of absolute square of intensity profile in reciprocal space.
`param_initial`	initial values for param estimation.
`num_optim`	number of optimization.
`msd_fn`	user defined mean squared displacement(MSD) structure, a function of parameters and lag times. NA if `model_name` is not 'user_defined'.
`msd_grad_fn`	gradient for user defined mean squared displacement structure. If `NA`, then numerical gradient will be used for parameter estimation in `'user_defined'` model.
`num_param`	number of parameters need to be estimated in the intermediate scattering function, need to be non-NA value for user_defined' model.
`uncertainty`	a logical evaluating to TRUE or FALSE indicating whether parameter uncertainty should be computed.
`M`	number of particles. See 'Details'.
`sim_object`	NA or an S4 object of class `simulation`.
`msd_truth`	true MSD or reference MSD value.
`method`	methods for parameter estimation, options from ('AIUQ','DDM_fixedAB','DDM_estAB').
`index_q_AIUQ`	index range for wave number when using AIUQ method. See 'Details'.
`index_q_DDM`	index range for wave number when using DDM method. See 'Details'.
`message_out`	a logical evaluating to TRUE or FALSE indicating whether or not to output the message.
`A_neg`	controls modification for negative A(q), options from ('abs','zero'), with setting negative A(q) to its absolute value as the default.
`square`	a logical evaluating to TRUE or FALSE indicating whether or not to crop the original intensity profile into square image.
`output_dqt`	a logical evaluating to TRUE or FALSE indicating whether or not to compute observed dynamic image structure function(Dqt).
`output_isf`	a logical evaluating to TRUE or FALSE indicating whether or not to compute empirical intermediate scattering function(ISF).
`output_modeled_isf`	a logical evaluating to TRUE or FALSE indicating whether or not to compute modeled intermediate scattering function(ISF).
`output_modeled_dqt`	a logical evaluating to TRUE or FALSE indicating whether or not to compute modeled dynamic image structure function(Dqt).

Details

For simulated data using simulation in AIUQ package, intensity will be automatically extracted from simulation class.

If model_name equals 'user_defined', or NA (will coerced to 'user_defined'), then msd_fn and num_param need to be provided for parameter estimation.

Number of particles M is set to 50 or automatically extracted from simulation class for simulated data using simulation in AIUQ package.

By default, using all wave vectors from complete q ring, unless user defined index range through index_q_AIUQ or index_q_DDM.

Value

Returns an S4 object of class SAM.

Author(s)

Yue He [aut], Xubo Liu [aut], Mengyang Gu [aut, cre]

References

Gu, M., He, Y., Liu, X., & Luo, Y. (2023). Ab initio uncertainty quantification in scattering analysis of microscopy. arXiv preprint arXiv:2309.02468.

Gu, M., Luo, Y., He, Y., Helgeson, M. E., & Valentine, M. T. (2021). Uncertainty quantification and estimation in differential dynamic microscopy. Physical Review E, 104(3), 034610.

Cerbino, R., & Trappe, V. (2008). Differential dynamic microscopy: probing wave vector dependent dynamics with a microscope. Physical review letters, 100(18), 188102.

Examples

library(AIUQ)
# Example 1: Estimation for simulated data
sim_bm = simulation(len_t=100,sz=100,sigma_bm=0.5)
show(sim_bm)
sam = SAM(sim_object = sim_bm)
show(sam)
library(AIUQ)
# Example 1: Estimation for simulated data
sim_bm = simulation(len_t=100,sz=100,sigma_bm=0.5)
show(sim_bm)
sam = SAM(sim_object = sim_bm)
show(sam)

SAM class

Description

S4 class for fast parameter estimation in scattering analysis of microscopy, using either AIUQ or DDM method.

Slots

pxsz: numeric. Size of one pixel in unit of micron with default value 1.
mindt: numeric. Minimum lag time with default value 1.
sz: vector. Frame size of the intensity profile in x and y directions, number of pixels contained in each frame equals sz_x by sz_y.
len_t: integer. Number of time steps.
len_q: integer. Number of wave vector.
q: vector. Wave vector in unit of um^-1.
d_input: vector. Sequence of lag times.
B_est_ini: numeric. Estimation of B. This parameter is determined by the noise in the system. See 'References'.
A_est_ini: vector. Estimation of A(q). Note this parameter is determined by the properties of the imaged material and imaging optics. See 'References'.
I_o_q_2_ori: vector. Absolute square of Fourier transformed intensity profile, ensemble over time.
q_ori_ring_loc_unique_index: list. List of location index of non-duplicate values for each q ring.
model_name: character. Fitted model, options from ('BM','OU','FBM','OU+FBM', 'user_defined').
param_est: vector. Estimated parameters contained in MSD.
sigma_2_0_est: numeric. Estimated variance of background noise.
msd_est: vector. Estimated MSD.
uncertainty: logical. A logical evaluating to TRUE or FALSE indicating whether parameter uncertainty should be computed.
msd_lower: vector. Lower bound of 95% confidence interval of MSD.
msd_upper: vector. Upper bound of 95% confidence interval of MSD.
msd_truth: vector. True MSD or reference MSD value.
sigma_2_0_truth: vector. True variance of background noise, non NA for simulated data using simulation.
param_truth: vector. True parameters used to construct MSD, non NA for simulated data using simulation.
index_q: vector. Selected index of wave vector.
Dqt: matrix. Dynamic image structure function D(q,delta t).
ISF: matrix. Empirical intermediate scattering function f(q,delta t).
I_q: matrix. Fourier transformed intensity profile with structure 'SS_T_mat'.
AIC: numeric. Akaike information criterion score.
mle: numeric. Maximum log likelihood value.
param_uq_range: matrix. 95% confidence interval for estimated parameters.
modeled_Dqt: matrix. Modeled dynamic image structure function D(q,delta t).
modeled_ISF: matrix. Modeled intermediate scattering function f(q,delta t).

Author(s)

Yue He [aut], Xubo Liu [aut], Mengyang Gu [aut, cre]

References

Gu, M., He, Y., Liu, X., & Luo, Y. (2023). Ab initio uncertainty quantification in scattering analysis of microscopy. arXiv preprint arXiv:2309.02468.

Gu, M., Luo, Y., He, Y., Helgeson, M. E., & Valentine, M. T. (2021). Uncertainty quantification and estimation in differential dynamic microscopy. Physical Review E, 104(3), 034610.

Cerbino, R., & Trappe, V. (2008). Differential dynamic microscopy: probing wave vector dependent dynamics with a microscope. Physical review letters, 100(18), 188102.

Show scattering analysis of microscopy for anisotropic processes (aniso_SAM) object

Description

Function to print the aniso_SAM class object after the aniso_SAM model has been constructed.

Usage

show.aniso_sam(object)
show.aniso_sam(object)

Arguments

object

an S4 object of class aniso_SAM

Value

Show a list of important parameters in class aniso_SAM.

Author(s)

Yue He [aut], Xubo Liu [aut], Mengyang Gu [aut, cre]

References

Gu, M., He, Y., Liu, X., & Luo, Y. (2023). Ab initio uncertainty quantification in scattering analysis of microscopy. arXiv preprint arXiv:2309.02468.

Gu, M., Luo, Y., He, Y., Helgeson, M. E., & Valentine, M. T. (2021). Uncertainty quantification and estimation in differential dynamic microscopy. Physical Review E, 104(3), 034610.

Examples

library(AIUQ)

## Simulate BM and get estimated parameters using BM model
# Simulation
aniso_sim_bm = aniso_simulation(sz=100,len_t=100,sigma_bm=c(0.5,0.3))
show(aniso_sim_bm)

# AIUQ method: fitting using BM model
aniso_sam = aniso_SAM(sim_object=aniso_sim_bm, AIUQ_thr=c(0.99,0))
show(aniso_sam)

library(AIUQ)

## Simulate BM and get estimated parameters using BM model
# Simulation
aniso_sim_bm = aniso_simulation(sz=100,len_t=100,sigma_bm=c(0.5,0.3))
show(aniso_sim_bm)

# AIUQ method: fitting using BM model
aniso_sam = aniso_SAM(sim_object=aniso_sim_bm, AIUQ_thr=c(0.99,0))
show(aniso_sam)

Show anisotropic simulation object

Description

Function to print the aniso_simulation class object after the aniso_simulation model has been constructed.

Usage

show.aniso_simulation(object)
show.aniso_simulation(object)

Arguments

object

an S4 object of class aniso_simulation

Value

Show a list of important parameters in class aniso_simulation.

Author(s)

Yue He [aut], Xubo Liu [aut], Mengyang Gu [aut, cre]

References

Gu, M., He, Y., Liu, X., & Luo, Y. (2023). Ab initio uncertainty quantification in scattering analysis of microscopy. arXiv preprint arXiv:2309.02468.

Gu, M., Luo, Y., He, Y., Helgeson, M. E., & Valentine, M. T. (2021). Uncertainty quantification and estimation in differential dynamic microscopy. Physical Review E, 104(3), 034610.

Examples

library(AIUQ)

# Simulate simple diffusion for 100 images with 100 by 100 pixels
aniso_sim_bm = aniso_simulation(sz=100,len_t=100,sigma_bm=c(0.5,0.1))
show(aniso_sim_bm)
library(AIUQ)

# Simulate simple diffusion for 100 images with 100 by 100 pixels
aniso_sim_bm = aniso_simulation(sz=100,len_t=100,sigma_bm=c(0.5,0.1))
show(aniso_sim_bm)

Show scattering analysis of microscopy (SAM) object

Description

Function to print the SAM class object after the SAM model has been constructed.

Usage

show.sam(object)
show.sam(object)

Arguments

object

an S4 object of class SAM

Value

Show a list of important parameters in class SAM.

Author(s)

Yue He [aut], Xubo Liu [aut], Mengyang Gu [aut, cre]

References

Gu, M., He, Y., Liu, X., & Luo, Y. (2023). Ab initio uncertainty quantification in scattering analysis of microscopy. arXiv preprint arXiv:2309.02468.

Gu, M., Luo, Y., He, Y., Helgeson, M. E., & Valentine, M. T. (2021). Uncertainty quantification and estimation in differential dynamic microscopy. Physical Review E, 104(3), 034610.

Examples

library(AIUQ)

## Simulate BM and get estimated parameters using BM model
# Simulation
sim_bm = simulation(sz=100,len_t=100,sigma_bm=0.5)
show(sim_bm)

# AIUQ method: fitting using BM model
sam = SAM(sim_object=sim_bm)
show(sam)

library(AIUQ)

## Simulate BM and get estimated parameters using BM model
# Simulation
sim_bm = simulation(sz=100,len_t=100,sigma_bm=0.5)
show(sim_bm)

# AIUQ method: fitting using BM model
sam = SAM(sim_object=sim_bm)
show(sam)

Show simulation object

Description

Function to print the simulation class object after the simulation model has been constructed.

Usage

show.simulation(object)
show.simulation(object)

Arguments

object

an S4 object of class simulation

Value

Show a list of important parameters in class simulation.

Author(s)

Yue He [aut], Xubo Liu [aut], Mengyang Gu [aut, cre]

References

Gu, M., He, Y., Liu, X., & Luo, Y. (2023). Ab initio uncertainty quantification in scattering analysis of microscopy. arXiv preprint arXiv:2309.02468.

Gu, M., Luo, Y., He, Y., Helgeson, M. E., & Valentine, M. T. (2021). Uncertainty quantification and estimation in differential dynamic microscopy. Physical Review E, 104(3), 034610.

Examples

library(AIUQ)

# Simulate simple diffusion for 100 images with 100 by 100 pixels
sim_bm = simulation(sz=100,len_t=100,sigma_bm=0.5)
show(sim_bm)
library(AIUQ)

# Simulate simple diffusion for 100 images with 100 by 100 pixels
sim_bm = simulation(sz=100,len_t=100,sigma_bm=0.5)
show(sim_bm)

Simulate 2D particle movement

Description

Simulate 2D particle movement from a user selected stochastic process, and output intensity profiles.

Usage

simulation(
  sz = c(200, 200),
  len_t = 200,
  M = 50,
  model_name = "BM",
  noise = "gaussian",
  I0 = 20,
  Imax = 255,
  pos0 = matrix(NaN, nrow = M, ncol = 2),
  rho = 0.95,
  H = 0.3,
  sigma_p = 2,
  sigma_bm = 1,
  sigma_ou = 2,
  sigma_fbm = 2
)
simulation(
  sz = c(200, 200),
  len_t = 200,
  M = 50,
  model_name = "BM",
  noise = "gaussian",
  I0 = 20,
  Imax = 255,
  pos0 = matrix(NaN, nrow = M, ncol = 2),
  rho = 0.95,
  H = 0.3,
  sigma_p = 2,
  sigma_bm = 1,
  sigma_ou = 2,
  sigma_fbm = 2
)

Arguments

`sz`	frame size of simulated image with default `c(200,200)`.
`len_t`	number of time steps with default 200.
`M`	number of particles with default 50.
`model_name`	stochastic process simulated, options from ('BM','OU','FBM','OU+FBM'), with default 'BM'.
`noise`	background noise, options from ('uniform','gaussian'), with default 'gaussian'.
`I0`	background intensity, value between 0 and 255, with default 20.
`Imax`	maximum intensity at the center of the particle, value between 0 and 255, with default 255.
`pos0`	initial position for M particles, matrix with dimension M by 2.
`rho`	correlation between successive step and previous step in O-U process, value between 0 and 1, with default 0.95.
`H`	Hurst parameter of fractional Brownian Motion, value between 0 and 1, with default 0.3.
`sigma_p`	radius of the spherical particle (3sigma_p), with default 2.
`sigma_bm`	distance moved per time step in Brownian Motion, with default 1.
`sigma_ou`	distance moved per time step in Ornstein–Uhlenbeck process, with default 2.
`sigma_fbm`	distance moved per time step in fractional Brownian Motion, with default 2.

Value

Returns an S4 object of class simulation.

Author(s)

Yue He [aut], Xubo Liu [aut], Mengyang Gu [aut, cre]

References

Gu, M., He, Y., Liu, X., & Luo, Y. (2023). Ab initio uncertainty quantification in scattering analysis of microscopy. arXiv preprint arXiv:2309.02468.

Gu, M., Luo, Y., He, Y., Helgeson, M. E., & Valentine, M. T. (2021). Uncertainty quantification and estimation in differential dynamic microscopy. Physical Review E, 104(3), 034610.

Cerbino, R., & Trappe, V. (2008). Differential dynamic microscopy: probing wave vector dependent dynamics with a microscope. Physical review letters, 100(18), 188102.

Examples

library(AIUQ)
# -------------------------------------------------
# Example 1: Simple diffusion for 200 images with
#            200 by 200 pixels and 50 particles
# -------------------------------------------------
sim_bm = simulation()
show(sim_bm)

# -------------------------------------------------
# Example 2: Simple diffusion for 100 images with
#            100 by 100 pixels and slower speed
# -------------------------------------------------
sim_bm = simulation(sz=100,len_t=100,sigma_bm=0.5)
show(sim_bm)

# -------------------------------------------------
# Example 3: Ornstein-Uhlenbeck process
# -------------------------------------------------
sim_ou = simulation(model_name="OU")
show(sim_ou)
library(AIUQ)
# -------------------------------------------------
# Example 1: Simple diffusion for 200 images with
#            200 by 200 pixels and 50 particles
# -------------------------------------------------
sim_bm = simulation()
show(sim_bm)

# -------------------------------------------------
# Example 2: Simple diffusion for 100 images with
#            100 by 100 pixels and slower speed
# -------------------------------------------------
sim_bm = simulation(sz=100,len_t=100,sigma_bm=0.5)
show(sim_bm)

# -------------------------------------------------
# Example 3: Ornstein-Uhlenbeck process
# -------------------------------------------------
sim_ou = simulation(model_name="OU")
show(sim_ou)

Simulation class

Description

S4 class for 2D particle movement simulation.

Details

intensity should has structure 'T_SS_mat', matrix with dimension len_t by sz $\times$ sz.

pos should be the position matrix with dimension M $\times$ len_t. See bm_particle_intensity, ou_particle_intensity, fbm_particle_intensity, fbm_ou_particle_intensity.

Slots

sz: vector. Frame size of the intensity profile, number of pixels contained in each frame equals sz[1] by sz[2].
len_t: integer. Number of time steps.
noise: character. Background noise, options from ('uniform','gaussian').
model_name: character. Simulated stochastic process, options from ('BM','OU','FBM','OU+FBM').
M: integer. Number of particles.
pxsz: numeric. Size of one pixel in unit of micron, 1 for simulated data.
mindt: numeric. Minimum lag time, 1 for simulated data.
pos: matrix. Position matrix for particle trajectory, see 'Details'.
intensity: matrix. Filled intensity profile, see 'Details'.
num_msd: vector. Numerical mean squared displacement (MSD).
param: vector. Parameters for simulated stochastic process.
theor_msd: vector. Theoretical MSD.
sigma_2_0: vector. Variance of background noise.

Author(s)

Yue He [aut], Xubo Liu [aut], Mengyang Gu [aut, cre]

References

Gu, M., He, Y., Liu, X., & Luo, Y. (2023). Ab initio uncertainty quantification in scattering analysis of microscopy. arXiv preprint arXiv:2309.02468.

Gu, M., Luo, Y., He, Y., Helgeson, M. E., & Valentine, M. T. (2021). Uncertainty quantification and estimation in differential dynamic microscopy. Physical Review E, 104(3), 034610.

Cerbino, R., & Trappe, V. (2008). Differential dynamic microscopy: probing wave vector dependent dynamics with a microscope. Physical review letters, 100(18), 188102.

Package 'AIUQ'

Help Index

Scattering analysis of microscopy for anisotropic processes

Description

Usage

Arguments

Details

Value

Author(s)

References

Examples

Anisotropic SAM class

Description

Slots

Author(s)

References

Simulate anisotropic 2D particle movement

Description

Usage

Arguments

Value

Author(s)

References

Examples

Anisotropic simulation class

Description

Details

Slots

Author(s)

References

Compute observed dynamic image structure function

Description

Usage

Arguments

Value

Author(s)

References

Examples

Compute empirical intermediate scattering function

Description

Usage

Arguments

Value

Author(s)

References

Examples

Compute modeled dynamic image structure function

Description

Usage

Arguments

Value

Author(s)

References

Examples

Compute modeled intermediate scattering function

Description

Usage

Arguments

Value

Author(s)

References

Examples

Plot 2D intensity

Description

Usage

Arguments

Details

Value

Author(s)

Examples

Plot estimated MSD with uncertainty from SAM class

Description

Usage

Arguments

Value

Author(s)

References

Examples

Plot 2D particle trajectory

Description