"thus I need" is correct and usable in written English.
You can use it to start a sentence when you want to emphasize that there is a need for something after a previous statement or explanation. Example: I have searched everywhere, thus I need some assistance to find the missing document.
Upon my return, thus, I needed to combine the ones I'd missed with the ones opening during the rush.
He told me that I was a role model to young children and thus I almost needed to have a 'home accent' and a 'school accent'".
Thus, because P i needs to be computed redundantly by every process, even if it has just one alignment site belonging to partition i, we need to minimize the number of partitions for which a process calculates the likelihood.
Thus, I do not need to retract the actual claim I made in 1963…" Somewhat similar arguments are given by Redhead (1993, 114) and by Debs and Redhead (2007, 87 92).
It is also worth considering how much the warp and woof of the messianic and antinomian that underlies much of Scholem's historiography of Kabbala is born from, and serves, his Zionism, In an interview a short time before his death he admitted that he believed his work was already "dated" and thus, I assume, in need of revision and revaluation.
Thus, I expect that the need for people with scientific (and engineering) expertise in the field of patent mapping is on the increase.
Thus, the initiator peer p i needs to deliver a message to peers in the set P D = 3 through peers in P D = 2 and P D = 1).
Thus, I have two takeaways: We need to grow our small-business sector to create a more resilient economy, and SaaS companies are well-positioned to cater to the technology needs of small businesses and to weather the economic storm (see "Top Eight SaaS Stocks").
Thus as a teacher, I need to guide the majority of the students as well as the minority into a learning environment in which they are comfortable.
I thus need to formulate proxies for the shock in (2) that can capture the change.
