[A short paragraph on normal seating position ends:] Children typically lose normal riding position because of their lighter weight which allows them to move more easily during a collision. A certain study has shown that an unrestrained child may occupy one of thirteen likely positions at the moment of air bag deployment.
Shortly after these positions were identified research was done to determine the potential danger of each position to the child. Researchers determined that the most dangerous positions for a child at the moment of airbag inflation were those positions in which the child's head was near the instrument panel.  In these cases, research has shown that the force of airbag inflation is great enough to cause fatal neck or brain injuries.  Even in ideal conditions airbags may be dangerous to children since their smaller frame cannot tolerate the same level of stress as adults. 
[Here is an alternative which inserts more materials, most of which I happen to know the author knows.] During air bag inflation, children can reach 13 non-normal positions; those near the instrument panel are the most dangerous. Crash tests appropriate for children required the design of smaller and lighter weight dummies with joints more flexibility than those of adults. All those features -- size, lightness and joint flexibility -- lead, in crash tests, to the discovery of thirteen positions that the dummies reached. In contrast adults dummies reached none of those non-normal-seating positions. Of the thirteen, six had the child's head near the instrument panel. For these, the proximity to the initial force of the expanding airbag, initially 200 mph, caused fatal neck or brain injuries. If fact, crash test data estimates that x percent of five-year old children would suffer injuries. However even for the remaining 1-x percent, the children were less able to withstand the strain of the airbag inflation and suffer serious, if not fatal injuries. Indeed only z percent wearing seat belts were estimated to escape serious or fatal injuries from air-bag inflation in crashes
The observed wobble of a distant star could be caused by an orbiting planet. If so, it is then possible to deduce the orbital period. With the use of Keppler's laws, the orbital radius can be found. The mass of the world is found by using center of mass principle.
The observed oscillatory wobble of a well-characterized star can be analyzed to give the properties of its presumed planet. Identifying the wobble period with the planet's orbital period yields, via Keppler's Law, the planet's orbital radius. Three features of the star can be deduced: from the red shift its distance; from the luminosity its mass; and from the angular width of the wobble the actual size of the wobble. Combining the latter two with the fact that the star-planet pair must orbit about its center of mass yields an estimate of the mass of the planet.
If an astronomer watches a star wobble for some time, the orbital period can be determined. The astronomer simply notes how long it takes the star to transverse the wobble and then knows that is the orbital period of the planet.
An astronomer interprets the period of the star wobble as the period of the planet orbiting the star.
[or] The period of the star wobble is the orbital period of the planet orbiting the star.
[Last two sentences of a paragraph.] The highly radioactive material is removed first and stored in NRC approved containers or sent to a waste facility for disposal. The structure at the facility and the remaining equipment is decontaminated for unconditional use using various methods. [Next paragraph goes on to described some of the various methods.]
The highly radioactive material is removed first and either stored in NRC approved containers or sent to a waste facility for disposal. The remaining equipment and the structure of the facility are then decontaminated for `unconditional use' -- that is, so they are below NRC-set radiation levels.
[Last sentence in paper in a paragraph talking about the slow acceptance of special relativity.] However, after many more years of experiment relativity's success have become so ingrained that almost a century later
[A] practically every physicist takes [B] what was once a revolutionary step [C] for granted
Subsequent, repeated, successful tests of relativity have lead almost a century later to
-> practically every physicist taking for granted what was once a revolutionary step.
[or] -> what was once a revolutionary step being taken for granted by practically every physicist.
[Last three sentences of introduction which up to now has very generally discussed orientation of birds without mentioning any mechanism.] At this point, it seems as though a single, universal applicable mechanism for this phenomena does not exist. The orientational mechanism could be a very complex one, drawing off of the most ideal stimulus in a particular environment. The answer is still out there.
[Instead should introduce the topic strings that will be features in subsequent paragraphs.] Three proposed mechanisms -- inertial navigation, sun-arc navigation, and magnetic-field orientation -- offer some insight but each has a serious flaw. It seems unlikely that a single, universally applicable mechanism exists. More likely the orientational mechanism is complex, taking advantage in each environment of the most useful stimulus.
[After this sentence in abstract:] These and other brain attributes researchers would like to simulate with computers.
Here I focus on the amazingly hard test for computer mimicry set by the brain's ability at sure pattern recognition and to learn different patterns.
Here I focus on the amazingly hard test for computer mimicry set by the brain's ability both to surely recognize known patterns and to quickly learn new patterns.
[or] Computer mimicry of the brain must match its ability both to recognize known patterns and to learn new ones.
Is its topic sentence in best place? [This is next to last paragraph in paper. The last sentence of the preceding paragraph is:] The most popular explanation suggests there was a huge explosion, the Big Bang.
With the theory of the Big Bang, scientists obtain insight into the evolution of the matter that we know today. Much of this evolution would have occurred immediately after the explosion. Within a second of the Big Bang, the theory predicts a sequential development of elementary particles, followed by nuclei, and then atoms. "Once atoms were in existence the door was open for the formation of larger complexes and eventually stars and galaxies" [Tefit, p. 49] As a consequence, the time periods following the explosion are divided into several periods based on the existence of a new form of matter due to the cooling of the universe.
Within a second of the Big Bang, the theory predicts a sequential development of elementary particles, followed by nuclei, and then atoms. "Once atoms were in existence the door was open for the formation of larger complexes and eventually stars and galaxies" [Tefit, p. 49] Big Bang theory has provided scientists with much of the current insight into the evolution of the matter.
... then go onto concluding paragraph.