WM Working Models www.iModel.org/wm
OverviewThis is a linear filter difference of Gaussians (DoG) model. The center and surround are each represented by a 2-D Gaussian function multiplied by a temporal filter.
Configuring the Model
ParametersThese parameters set the basic simulation settings:
The next set of parameters define the center and surround of the spatial DoG filters and the shape of the temporal filter. The temporal filter is generated by multiplying two functions, which we refer to as the kernel and the mask. The mask is a Gaussian centered on time tcent and having SD tsig. The kernel may be one of several filters, defined by the parameter tfilter, described below. The Gaussian mask reshapes the temporal kernel, for example, in can be used to balance out positive and negative lobes or to cut short a long tail.
- sscale - spatial resolution (degrees/pixel)
- tscale - temporal resolution (samples per second)
- xn - filter x-axis spatial extent (pixels)
- yn - filter y-axis spatial extent (pixels)
- tn - duration of the model (sampling units)
The model can be made transient in two ways, either by using a transient temporal filter or by having spike rate adaptation (setting a positive adaptation conductance value).
- sig1 - SD of center Gaussian (deg) (n.b. Set to -1 for delta-function model)
- sig2 - SD of surround Gaussian (deg)
- amp1 - amplitude of center Gaussian
- amp2 - amplitude of surround Gaussian
- cs_x - [0.0] offset of surround x-coord. w.r.t. center (deg)
- cs_y - [0.0] offset of surround y-coord. w.r.t. center (deg)
- cs_delay - Surround delay (time units of the model, set by tscale)
- tcent - [0.0] center time of multiplicative Gaussian mask (ms).
- tsig - SD of multiplicative Gaussian mask (ms). Used to control balance of positive and negative lobes.
- tab_k - Adelson and Bergen temporal filter 'k'
- tab_n - Adelson and Bergen temporal filter 'n'
- tdelay - [0.0] Retinal latency (sec)
- tfilter - ['ab'] use only the default value for models of type 'dog_01'.
- power - [1.0] raise the response to a power, before spike generation.
Temporal FilterThe kernel may be one of several filters, controlled by the parameter tfilter, which defaults to 'ab'. The following is a list of possible options and the parameters needed to define them:
- ab - This function was used by Adelson and Bergen, 1985 (J Opt Soc Am A 2:284-299).f(t) = (kt)n e-kt [1/n! - (kt)2/(n+2)!]and the following additional parameters control the shape:
- tab_k - 'k' in the equation above. Multiplying 't', this controls the horizontal scaling.
- tab_n - 'n' in the equation above
- wa - A function used by Watson and Ahumada (1985).f(t) = a*[f1(t) - b*f2(t)] u(t) fi(t) = ---------------- (t/tau_i)^(n_i - 1) exp(-t/tau_i) tau_i (n_i - 1)! u(t) is the unit step function.
- dexp - a combination of decaying exponentials
- delta - delta function (1 at time zero)
- tfilt_01 - customized filter.
Spike Generationdog_01 models also require a <spike_gen> object that defines the method of spike generation from the final filter output.
Model ComponentsThe following commands allow users to extract information about the DoG filter itself:
- write_3d_filter [outfile] - write the DoG filter to 3D data file
- write_dog_temporal [outfile] - write the temporal filters used to build the DoG. This includes the biphasic temporal kernel and the Gaussian mask, which multiplies the biphasic kernel to adjust the size of the positive and negative lobes.
- write_trace_filter [outfile] [xi] [yi] [ti] - plot one line of the DoG filter along the dimension whose index (x1, yi, or ti) is set to -1. Use the other indices to select the coordinates of the line.
Model ResponsesThe following response types can be requested:
- spikes - spike times
- write_3d_response [outfile] - write response to 3D data file
- write_raw [outfile] - write output of linear DoG filter (before spikes)
Models of This Type