About your first question: You did actually answer yourself; you said:

We are talking about advances in specified fields, not, for example, about advances in biology.

Why didn't you add the article "the" although you were talking about some specific fields advances, in the first time? And about a particular field, in the second time?

The answer is simple: You specified what you were talking about that there wasn't a need for an article to define the two nouns when they have already been defined by what had followed them.

• The same is applied to your main sentence.

About your second question:

... in compiler and virtual machine technologies

If we were to add "the" before those two words, or at least before "compiler" which would refer to "virtual machine technologies" as well because of the conjunction "and", then it would be understood that we are talking about a particular group of compilers and VMs.

Without the article, it is understood as their preceding sentence is about compilers and VMs in general, not ones with some features and properties that have been mentioned/defined before. Otherwise, adding "the" would be necessary.

For example:

Recently, some new virtual machines have been invented. They are different from those regular ones as they have many unique features like: (the features are mentioned here). After running some tests on them, we can say now that the virtual machines have proved their reliability and efficiency that they are ready to get adapted and produced.

I used "the" as I'm only referring to the VMs that have many unique features, not all the VMs in the technology world.

About your first question: You did actually answer yourself; you said:

We are talking about advances in specified fields, not, for example, about advances in biology.

Why didn't you add the article "the" although you were talking about some specific fields advances, in the first time? And about a particular field, in the second time?

The answer is simple: You specified what you were talking about that there wasn't a need for an article to define the two nouns when they have already been defined by what had followed them.

• The same is applied to your main sentence.

About your second question:

... in compiler and virtual machine technologies

If we were to add "the" before those two words, or at least before "compiler" which would refer to "virtual machine technologies" as well because of the conjunction "and", then it would be understood that we are talking about a particular group of compiler and VM technologies.

Without the article, it is understood as their preceding sentence is about compiler and VM technologies in general, not ones with some features and properties that have been mentioned/defined before. Otherwise, adding "the" would be necessary.

For example:

Recently, some new virtual machine technologies have arisen. They are more efficient and productive than those regular ones as they have many unique features like: (the features are mentioned here). We predict that the virtual machine technologies will be introduced to the VM community soon.

I used "the" as I'm only referring to the VM technologies with the new, unique features, not all the VM technologies in the world.