## dog_01

WMWorking Modelswww.iModel.org/wm

## Overview

This 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

## Parameters

These 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

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)kerneland themask. The mask is a Gaussian centered on timetcentand having SDtsig. The kernel may be one of several filters, defined by the parametertfilter, 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.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 Gaussianamp2- amplitude of surround Gaussiancs_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 Filter

The kernel may be one of several filters, controlled by the parametertfilter, 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 A2:284-299).f(t) = (kt)and the following additional parameters control the shape:^{n}e^{-kt}[1/n! - (kt)^{2}/(n+2)!]

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 Generation

dog_01models also require a <spike_gen> object that defines the method of spike generation from the final filter output.

## Model Outputs

## Model Components

The following commands allow users to extract information about the DoG filter itself:

write_3d_filter[outfile] - write the DoG filter to 3D data filewrite_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 Responses

The following response types can be requested:

spikes- spike timeswrite_3d_response[outfile] - write response to 3D data filewrite_raw[outfile] - write output of linear DoG filter (before spikes)

## Models of This Type