 have started an elimination diet.
I would appreciate any advice on how to deal with this, and finding out if other kids have been officially tested. Does anyone know about Fructose Malabsorption?
Yes a fructose test!
You could look into the Sue Dengate Failsafe diet. It’s an elimination diet. Elimination is the best and most accurate way to find out exactly what the tolerances are, which are very different to allergies. Good luck.
Whereabouts did you have the breath test done? I had it done myself, but when I tried to book him in they said he was too young!
How old is your son my daughter had a fructose test and she was five all they have to do is drink a liquid and then breathe into a tube every 15minutes for 2 hours.
Just be careful doing this as you want to make sure that your son is getting enough nutrients from a balanced diet to help him grow. However if he is showing signs of allergies I would talk to a specialist nutritionalist or similar to get professional advice.
Most Dieticians/Nutritionists have a Medicare Provider Number but there a few that don’t. If your GP refers you, be sure to ask if he/she has one. Some that don’t give strict diets for various conditions and give the impression that the diet is for life. That is not always correct and some can cause organ damage.
When they were trying to determine one particular food my little niece was allergic to she was not allowed to eat any of it for 3 weeks, then re-try it. Your little one may have a slight allergy to several foods, which eaten near to each other (e,g, within a week of each other in my brother’s case) he showed reactions to. He went to an Allergist when he was old enough. He was only fairly young but I can’t remember how old he was. These are only suggestions from personal experience within my family.
Fructose is the sugar in fruit. There may be vegetables that he can get the same vitamins from………Like other suggestions I hope this helps in the interim.
You definitely need constructive professional advice and treatment. I wish you well in solving both your problems.
Hi, my advice would be to see a nutritionist/dietitian. I am gluten and lactose sensitive, and also have been put on a low fodmap diet also try and restrict my sugar as well. The nutritionist/dietitian that I went to was great and they monitor what food to eliminate or if a food can be reintroduced.
Being young you don’t want your son to be missing out on vital nutrients and experts in the field can help you through your sons journey. Also see if your GP can do a plan for your son, so as to cut costs at the nutritionist/dietitian.
All the very best of luck to you and your son and I wish you both well.I want to calculate the average of a set of circular data. For example, I might have several samples from the reading of a compass. The problem of course is how to deal with the wraparound. The same algorithm might be useful for a clockface.
The actual question is more complicated - what do statistics mean on a sphere or in an algebraic space which "wraps around", e.g. the additive group mod n. The answer may not be unique, e.g. the average of 359 degrees and 1 degree could be 0 degrees or 180, but statistically 0 looks better.
This is a real programming problem for me and I'm trying to make it not look like just a Math problem.
Compute unit vectors from the angles and take the angle of their average.
This question is examined in detail in the book: "Statistics On Spheres", Geoffrey S. Watson, University of Arkansas Lecture Notes in the Mathematical Sciences, 1983 John Wiley & Sons, Inc. as mentioned at http://catless.ncl.ac.uk/Risks/7.44.html#subj4 by Bruce Karsh.
The method given by starblue is computationally equivalent, but his reasons are clearer and probably programmatically more efficient, and also work well in the zero case, so kudos to him.
The subject is now explored in more detail on Wikipedia, and with other uses, like fractional parts.
I see the problem - for example, if you have a 45' angle and a 315' angle, the "natural" average would be 180', but the value you want is actually 0'.
I think Starblue is onto something. Just calculate the (x, y) cartesian coordinates for each angle, and add those resulting vectors together. The angular offset of the final vector should be your required result.
I'm ignoring for now that a compass heading starts at north, and goes clockwise, whereas "normal" cartesian coordinates start with zero along the X axis, and then go anti-clockwise. The maths should work out the same way regardless.
The answer ( (a + b) mod 360 ) / 2 is WRONG. For angles 350 and 2, the closest point is 356, not 176.
The unit vector and trig solutions may be too expensive.
ackb is right that these vector based solutions cannot be considered true averages of angles, they are only an average of the unit vector counterparts. However, ackb's suggested solution does not appear to mathematically sound.
The following is a solution that is mathematically derived from the goal of minimising (angle[i] - avgAngle)^2 (where the difference is corrected if necessary), which makes it a true arithmetic mean of the angles.
First, we need to look at exactly which cases the difference between angles is different to the difference between their normal number counterparts. Consider angles x and y, if y >= x - 180 and y <= x + 180, then we can use the difference (x-y) directly. Otherwise, if the first condition is not met then we must use (y+360) in the calculation instead of y. Corresponding, if the second condition is not met then we must use (y-360) instead of y. Since the equation of the curve we are minimising only changes at the points where these inequalities change from true to false or vice versa, we can separate the full [0,360) range into a set of segments, separated by these points. Then, we only need to find the minimum of each of these segments, and then the minimum of each segment's minimum, which is the average.
Here's an image demonstrating where the problems occur in calculating angle differences. If x lies in the gray area then there will be a problem.
To minimise a variable, depending on the curve, we can take the derivative of what we want to minimise and then we find the turning point (which is where the derivative = 0).
This alone is not quite enough to get the minimum, while it works for normal values, that has an unbounded set, so the result will definitely lie within set's range and is therefore valid. We need the minimum within a range (defined by the segment). If the minimum is less than our segment's lower bound then the minimum of that segment must be at the lower bound (because quadratic curves only have 1 turning point) and if the minimum is greater than our segment's upper bound then the segment's minimum is at the upper bound. After we have the minimum for each segment, we simply find the one that has the lowest value for what we're minimising (sum((b[i]-x)^2) + sum(((c[i]-360)-b)^2) + sum(((d[i]+360)-c)^2)).
Here is an image to the curve, which shows how it changes at the points where x=(a[i]+180)%360. The data set is in question is {65,92,230,320,250}.
Here is an implementation of the algorithm in Java, including some optimisations, its complexity is O(nlogn). It can be reduced to O(n) if you replace the comparison based sort with a non comparison based sort, such as radix sort.
The arithmetic mean of a set of angles may not agree with your intuitive idea of what the average should be. For example, the arithmetic mean of the set {179,179,0,181,181} is 216 (and 144). The answer you immediately think of is probably 180, however it is well known that the arithmetic mean is heavily affected by edge values. You should also remember that angles are not vectors, as appealing as that may seem when dealing with angles sometimes.
This algorithm does of course also apply to all quantities that obey modular arithmetic (with minimal adjustment), such as the time of day.
I would also like to stress that even though this is a true average of angles, unlike the vector solutions, that does not necessarily mean it is the solution you should be using, the average of the corresponding unit vectors may well be the value you actually should to be using.
The "true" average, i.e. (a + b) / 2 % 360.
The angle that points "between" the two others while staying in the same semicircle, e.g. for 355 and 5, this would be 0, not 180. To do this, you need to check if the difference between the two angles is larger than 180 or not. If so, increment the smaller angle by 360 before using the above formula.
I don't see how the second alternative can be generalized for the case of more than two angles, though.
Two common choices of metric are the Frobenius and the Riemann metrics. For the Frobenius metric, a direct formula exists that corresponds to the usual notion of average bearing in circular statistics