``The reason that this is called a linear function is because the output is formed from a linear combination of the inputs.''Example 2
``Thus a given state s is defined by a set of values for each of the random variables that define the state space of the problem: we have s = {X1, ..., Xn}.''Example 3
``We consider the architectural style of the system, the structures and properties of the components that comprise the system and the interrelationships between them.''Example 4
``Essentially, what has happened is that as of July this year (2003) the University adopted the uPortal framework for an initial test run on the usability and functionality of employing a portal system as the main `web-top' for a number of staff-related information needs and tasks.''
``or:The reason thatThis is called a linear functionisbecause the output is formed from a linear combination of the inputs.''
``Personally, I don't mind the "formed from". It's redundant but to me it makes the sentence a little more vivid. (This can probably be explained by the different grammatical roles of "formed from" and "combination" (if they do have different roles) but I don't know enough about grammar. Please mail me if you do.)The reason thatThis is called a linear functionisbecause the output isformed froma linear combination of the inputs.''
In addition to the stylistic problems with this sentence, there is also a semantic problem. It's not clear what the author intended to explain: what a function is, or what "linear" means, or what a linear function is. If the sentence is supposed to explain what a linear function is, it does not do a very good job because it does not explain what "linear" means. Instead, it just uses the word "linear" in the explanation. This is a bit like saying "A linear function is a function that is linear", which does not explain very much! The sentence doesn't really explain what a function is either, although it touches on the idea that outputs are somehow determined by inputs.
Example 2. The initial version wrongly suggests each random variable is a set, and is very awkward. A better version is:
``Thus a given state s is defined by a set ofExample 3. In the following I've added new text in bold.values for each of therandom variablesthat define the state space of the problem:we haves = {X1, ..., Xn}.''
``We consider the architectureExample 4al styleof the system, the structures and properties oftheits componentsthat comprise the systemand theirinterrelationshipsbetween them.''
``I still don't like the better version, especially the last part. The following more substantial change doesn't have quite all the details of the original but I find it far more readable.Essentially, what has happened is thatas of Julythis year (2003)the University adoptedtheuPortalframeworkfor an initial testrunon the usability and functionality ofemployinga portal system as the main `web-top' for a number of staff-related information needs and tasks.''
``In July 2003 the University started initial evaluation of the usability and functionality of uPortal as the main `web-top' for some staff information and tasks.''An even more tidy version, with pretty much the same content, is:
``In July 2003 the University started initial evaluation ofthe usability and functionality ofuPortal as the main `web-top' for some staff information and tasks.''