This document describes in detail the ARTphone
model simulated in Pitt, Myung and Altieri (in press, *Psychonomic** Bulletin
& Review*). The schematic diagram
of the model shown in the figure below is implemented via a system of
differential equations. The basic model equations are derived from Grossberg, Boardman and Cohen (1997), to which the reader
is directed for other details not described here.

Figure 1. Schematic
illustration of ARTPhone simulated in Pitt, Myung and Altieri (in press).

Each working memory node receives a phoneme input pulse over
a determined time interval

1.
I_{j}(t) = 0.1 if a_{j}_{ }< t < b_{j} and 0 otherwise

where the time interval (a_{j}, b_{j}) represents the duration of the phoneme input to
the j-th working memory node, and 0.1
indicates the magnitude. Items in working
memory interact with all items in short-term memory (phonemes, biphones, words) via bidirectional
(bottom-up and top-down) excitatory connections between them. Let x_{j}(t) be the activity at time t of the j-th
phoneme node in working memory, and its activity is governed by the following
differential equation

2.
dx_{j}(t)/dt = *g*
[(b - x_{j}(t))(*I*_{j}(t) + k S_{k} y_{k}(t) w_{kj}(t)) – ax_{j}(t)]

In this equation, y_{k}(t) represents the activity of the k-th
phoneme, bi-phone or word node in short-term memory, w_{kj}(t) represents the activity
of the top-down connection weight from y_{k} to x_{j}, and *g*,
b, k and a are
positive constants.

Items in short-term memory are ‘category nodes’
corresponding to phonemes, bi-phones or words. Let y_{k}(t) be the activity of the k-th
node in a short-term memory layer, and its activity is governed by the equation
below

3.
dy_{k}(t)/dt = *g*
[(b – y_{k}(t))(S_{j} m_{j }q_{j}(t) v_{jk}(t) – dy_{k}(t) - eS_{i} y_{i}(t) - hS_{i} z_{i}(t)]

In the above equation, the thresholded
signal q_{j}(t)
is defined as *q*_{j}*(t) = max(x _{j}(t) - *

The following equations describe the transmitter dynamics of the connection weights between layers

4.
dw_{kj}(t)/dt
= V(1 – w_{kj}(t))
– h(y_{k}(t))
w_{kj}(t) (top-down transmitter)

5.
dv_{jk}(t)/dt
= V(1 – v_{jk}(t))
– h(q_{j}(t))
v_{jk}(t) (bottom-up transmitter)

In each equation, V represents the transmitter rate, and the transmitter
inactivation rate function h(x) is given by the equation h(x) = lx + mx^{2}.

The parameter values were derived from Grossberg
et al (1997). The table below shows the values incorporated into our ARTphone model. Additions include the top-down modulating
parameter k, the phonotactic
probability parameter m_{j}, and e
& h, the inhibition parameters.

Parameter |
Description |
Value |

a |
Decay |
0.50 |

b |
Maximum activation |
1.0 |

k |
Top-down modulation |
0.20 |

d |
Decay |
0.28 |

g |
Threshold |
0.10 |

z |
Transmitter rate |
0.10 |

l |
Transmitter inactivation |
0.10 |

m |
Transmitter inactivation |
2.20 |

g |
Gain control |
1.10 |

e |
Lateral inhibition |
(variable) |

h |
Masking inhibition |
(variable) |

m |
Phonotactic
probability effects |
(variable) |

(^{#}:
For the specific m_{j}
values, see the appendix of Pitt, Myung & Altieri (in press).)

Grossberg, S., Boardman, I. & Cohen, M. (1997). Neural dynamics of variable-rate speech categorization. *Journal of Experimental Psychology: Human
Perception and Performance, 23(2),* 481 – 503.

Pitt, M. A., Myung,
J. I. & Altieri, N. (2007). Modeling
the work recognition data of Vitevitch and Luce
(1998): Is it ARTful? *Psychonomic** Bulletin & Review, 14, *442-448.
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