### t

``` Decision-making: choosing under uncertainty
 The spontaneous activity in dense networks
Work done in collaboration with:
Víctor de Lafuente (Instituto de Neurobiología, UNAM, Mexico)
Ranulfo Romo
(Instituto de Fisiología Celular, UNAM, Mexico)
A) Spike trains, firing rate, auto- and cross-covariance functions, spike-count covariance
B) Experimental results on a detection task. Decision –making and uncertainty
C) Correlated variability in a decision–making task
D) Temporal uncertainty gives rise to an internal phenomenon.
Inter-Spike-Interval
SPIKE TRAIN
t₁
t₆
t=0
SPIKE-COUNT
t=T
N(T) = 6
for small Δt, N(t) is 0 or 1
r (t)
trial l
P (t) = Prob(spike in [t, t+Δt]) = r(t) Δt
P (t) = (# spikes) / (# trials)
t=0
Δt
t=T
r(t) : probability density of 1 spike
r(t)
instantaneous firing rate
RT
R : Tasa de disparo media.
(temporal and trial average)
σN : spike-count standard deviation
(index i is the neuron label)
For small Δt, N(t) is either 0 or 1
N(t)
Pi (t) = Prob(spike in [t, t+Δt]) = r(t) Δt
trial l
Pi (t, t’) = Prob( spike in [t, t+Δt]; spike in [t’, t’+Δt] )
Pi (t, t’) = (# “coincidences”) / (# trials) ≈ O(Δt²)
Auto-covariance function (ACF):
“excess probability density” with respect to independent events:
Ci (t, t’) = (Pi (t, t’) - Pi (t) Pi (t’)) / (Δt²) = Pi (t, t’) / (Δt²) – ri (t) ri (t’)
Ci (t, t’)
N(t’)
)- r(t’)
- r(t)
r(t) r(t’)
Pi (t) = Prob(spike neuron i in [t, t+Δt]) = ri(t) Δt
(similarly for neuron j)
Pi,j (t, t’) = Prob( spike neuron i in [t, t+Δt]; spike neuron j in [t’, t’+Δt] )
Pi,j (t, t’) = (# “coincidences in the pair of neurons”) / (# trials) ≈ O(Δt²)
Cross-covariance function (CCF):
“excess probability density” with respect to random independent events:
Ci j (t, t’) = (Pi,j (t, t’) - Pi (t) Pj (t’)) / (Δt²) = Pi,j (t, t’) / (Δt²) – ri (t) rj (t’)
Ci j (t, t’)
- ri (t)
tik’ )
tik’ ) --rj (t’)
ri (t) rj (t’)
ni(t; T)
número de espigas en una ventana temporal de tamaño T, obtenida en el
ensayo t, dividida por T.
Su media en L ensayos es la tasa media de disparo
(no escribimos la dependencia en T)
La covarianza entre ni y nj
El coeficiente de correlación entre ni y nj
(varía entre +1 y -1)
(notar que Cov(ni , ni) es la varianza de ni, definida previamente)
A) Spike trains, firing rate, auto- and cross-covariance functions, spike-count covariance
B) Experimental results on a detection task. Decision–making and uncertainty
C) Correlated variability in a decision–making task
D) Temporal uncertainty gives rise to an internal phenomenon.




The monkey has to detect a vibrating stimulus, which is present only in half of the trials.
When it is applied, often its amplitude is rather weak.
The stimulation time is not fixed.
The monkey reports his decision after a 3-second delay period
de Lafuente & Romo, Nature Neuroscience 8: 1698; 2005
 Spontaneous activity
 Evoked activity
 Persistent activity
sensory area
trials
prefrontal area
time
timetime
 Irregularity
 Variability
 correlated variability
The representation of the stimulus gradually transforms from a parametric one to an
all-or-none response that does not depend on the amplitude but only on whether the
subject felt or missed the stimulus.
de Lafuente & Romo, PNAS, 2006
The arrival time of the stimulus is unknown and its presence is often ambiguous,
because it can be weak or absent.
Neural integration is problematic, because if it starts too soon, noise will dominate the
process; if it starts too late, part of the signal will be lost.
A) Spike trains, firing rate, auto- and cross-covariance functions, spike-count covariance
B) Experimental results on a detection task. Decision–making and uncertainty
C) Correlated variability in a decision–making task
D) Temporal uncertainty gives rise to an internal phenomenon.
F Carnevale, V de Lafuente, R Romo y N Parga , PNAS 109: 18938–18943 (2012)
Internal signal correlates neural populations and biases perceptual decision reports
F Carnevale, V de Lafuente, R Romo y N Parga , PNAS 109: 18938–18943 (2012)
Internal signal correlates neural populations and biases perceptual decision reports
F Carnevale, V de Lafuente, R Romo y N Parga , PNAS 109: 18938–18943 (2012)
Internal signal correlates neural populations and biases perceptual decision reports
Noise correlations are modulated during the trial in a conditiondependent manner
They can be weak (0.05 at the end of the delay period)
The distribution of correlation coefficients is wide
Weak correlations are not due to low ring rates.
A) Spike trains, firing rate, auto- and cross-covariance functions, spike-count covariance
B) Experimental results on a detection task. Decision –making and uncertainty
C) Correlated variability in a decision–making task
D) Temporal uncertainty gives rise to an internal phenomenon.
KD
KD
KD
KD
Firing rates and noise correlations suggest the existence of an
internal dynamics effect.
This effect affects the subject's choice
It fluctuates from trial-to-trial and it is common to several
neurons.
```