What pattern can be learned from the data of RNA seq counts and HiC matrix?
This seems to me to be two independent pieces of data. mRNA seq allows one (in case of linear amplification) to quantify message RNA transcripts of genes of interest. that is, how many copies of mRNA for given gene are in the cell at the moment. It is ultimately, how active this gene is. In neurons different genes will be more active, than in epithelial cells, and vice versa. Genetic expression pattern provides identity of the cell.

Hi-C method, closely related to chromosome conformation capture answers question: what genes are physically interact in the nucleus via stabilizing proteins (e.g. enhcancers). There is more in the video, but general idea is that it allows you to see how genes positioned inside intricate chromatin. Since many genetic elements might physically interact via, for example, enhancers, 3C/Hi-C allows detection of such interactions. Or, at least, quantification of correlation between physical positions of two genes.

Now, the only direct connection between mRNA seq and Hi-C that I can draw is following logic: actively transcribed genes are located in expanded, less tense regions of chromatin. Hence, it will be hard to crosslink genes in such regions and correlation going to be low. Silent genes, if they are located closely in nucleus will be cross-linked with high probability, because chromatin is denser around non-transcribed genes.