# Question on omission of "by" and location of modifiers

I am a nonnative graduate student writing science related journals. Whenever I write related papers, there are always confusing parts, so I put up a questionnaire to clarify this. What I'm confused about is (i) to use or not to use the word by, and (ii) the arrangement of the modifiers. Please look at the following four sentences I made:

• Case 1: To use the word by and to place the modifier before the main clause.

To this end, by leveraging Lagrangian duality and stochastic optimization theories, we develop a novel algorithm, whereby the original problem is decomposed into a series of subproblems, one for each time slot.

• Case 2: Not to use the word by and to place the modifier before the main clause.

To this end, leveraging Lagrangian duality and stochastic optimization theories, we develop a novel algorithm, whereby the original problem is decomposed into a series of subproblems, one for each time slot.

• Case 3: To use the word by and to place the modifier after the main clause.

To this end, we develop a novel algorithm by leveraging Lagrangian duality and stochastic optimization theories, whereby the original problem is decomposed into a series of subproblems, one for each time slot.

• Case 4: Not to use the word by and to place the modifier after the main clause.

To this end, we develop a novel algorithm leveraging Lagrangian duality and stochastic optimization theories, whereby the original problem is decomposed into a series of subproblems, one for each time slot.

I really want to know how they are different. Do they all have the same meaning? If not, how are they different?

Thanks for your interest in my question.

This question is largely about adverbials- about how they are formed, and where to place them. Placement of an adverbial is relatively flexible: it can follow the main clause, or precede it to give emphasis to the adverbial. If it precedes the main clause, we normally insert a comma between the adverbial and the main clause.

We can get there faster by bus.
By bus, we can get there faster. - emphasising the adverbial

In cases 1 and 2, the adverbial precedes the main clause, which gives emphasis to the adverbial. In cases 3 and 4, the adverbial follows the main clause.

In cases 1 and 3, your adverbial is a prepositional phrase beginning with by. In this context, it indicates how something is being done- the method.

In cases 2 and 4, your adverbial is a participle phrase beginning with leveraging. This indicates that two things are happening at the same time, but does not indicate that one is the method for achieving the other.

When the subject of the participial phrase directly precedes the pp, we don't add a comma, but if the subject of the pp is at the beginning of the main clause, we add a comma. In this case, if you consider that we are leveraging, a comma is required. If you consider that the algorithm is leveraging, no comma is required.

If you want to emphasise the relationship between the algorithm and the leveraging, you should consider using a relative clause: this also gives a more natural sentence flow.

To this end, we develop a novel algorithm that leverages Lagrangian duality and stochastic optimization theories, whereby the original problem is decomposed into a series of subproblems, one for each time slot.

Note that "to this end" and "whereby..." are also adverbials. That, plus the length of the sentence, makes me think that you are trying a little too hard to fit everything into one sentence.

• Thank you for a very good explanation. Based on your teaching, I think that the case 1 is the most correct since WE use those theories to develop the algorithm. (In fact, I tried to explain it concisely in one sentence, but it is too difficult for me, who uses Korean as my mother tongue. TT) Mar 7, 2021 at 13:18