Technical questions about local gene co-expression

I am interested to assess the matching
score and the relationship between expression profiles as you did in your
Qian et al 2000 (pubmedid: 11743722) paper, on my own data.
But I need some clarifications if possible.
After normalizing gene expressions using z-score, how did you eliminated
the negative expression levels? In other words, if the expression of each
gene is normalized using z-score, so each gene contains positive and
negative normalized expression levels, so how do you define genes having
negative expression levels?

Normalization was used to calculate the correlation coefficient. Although we will have negative values, we should not interpret them as actual gene expression levels.

To estimate the p-value of each matching score, how did you generated the
random expression profiles? Did you switched two gene expression time points
for each gene or did you permuted the gene expressions for each gene?

We permuted the gene expression for each gene by switching two gene expression time points.

If I wish to determine locally co-expressed genes in different
time-series experiments, can I combine the gene expression profiles from the
different experiments in one matrix as bellow and apply your algorithm on
this new matrix instead of applying the algorithm on the gene expression
profile of each experiment alone?
exp1: exp1_t1, exp1_t2, exp1_t3, exp1_t4
exp2: exp2_t1, exp2_t2, exp2_t3
combined_exp: exp1_t1, exp1_t2, exp1_t3, exp1_t4, exp2_t1, exp2_t2, exp2_t3.

Our algorithm will detect the time delayed relationships. If exp2_t1 is indeed the measurement following exp1_t4, the operation should be fine.