degrade towards zero

[Matt_T_hat]

I am working on a project that will hopefully be written in several programming langauges and I therefore need to explain useing maths and words only.

The project deals with trust.



We have a trust value let's call it t and a second value indicating the degrees of seperation between the holder of t and the issuer I'll call that d (for deviation).
The target is T the trust I have based on my deviation from the issuer

If t = 10 and d=4 T=6 - T=t-d
However if t=-10 and d=4 T is -6

So I need to cause T to approach zero from either direction based on the value of d.

However I need to also explain a more complex situation where I use D not d where D is some function of my T for my source of t (d=1).

This will allow me to degrade towards 0 values of d fast or slow based the value T placed upon the source (d=1).

If that was not enough it may be possible that the system might record the source for d=1, d=2 and so forth so that D is some function of T for each stage from issuer to d=1 (I'm d=0 and my trust is theoretically unlimited for myself).

because at each stage on the journy the value t is the sum of all the T recorded at that level (degraded towards 0 against time) the value of t that is recieved could be any number at all negative or possative.

The rest of the math I have a hold on: the average biased against T for example is simply a case of multiplying all the t agaisnt the T for that source and deviding by the sum of T.

Degrad to 0 against time should be so similar to the simple solution as mentioned first that I should be able to work it out for myself.

However I am stuck on two points basic degrade towards 0 (I'm sure it should be simple but my mind is stuck) and the complex based upon the T for the final stage of the journy or all of them (or whatever I have).

I hope to goodness that some one followed all that and that a formula can be created that I can attempt to impliment (php first then VB second I'm guessing after that...)

I think I ned a cup of tea

[wossname]

Basicaly you are having sign problems, t can be positive or negative but d is always positive?

If you make d the same sign as t then..... (-10) - (-4) = (-6)

[Matt_T_hat]

Basicaly you are having sign problems, t can be positive or negative but d is always positive?

If you make d the same sign as t then..... (-10) - (-4) = (-6)

In the main yes.

However I would like to create a formula where

10 function 11 is 0
-9 function -22 is 0
10 function 9 is 1
-10 function 9 is -1
etc. etc.

I'm prity sure the answer should involve x*-1 but it's been a very long time since I did all that larking about... what I'm hoping is that the formula can be constructed such that t and d coiuld be anything but T (the result) never crosses 0.

It doesn't even need to be linier such that the larger the value of t the faster towards 0 it travels (so that back in the real worl the more extream a view is the more it takes to sustain that view). So that larger numbers are naturalised back towards x = 0.

I guess I'm trying to create a deviation towards the mean with a mean of 0. I just realy don't want to use the IF function on a mathmatical problem.

sqrt(t^2)-d would do part of it...

Even if I give in and describe a series of if statments or other logic I still must address the issue for somefunction of T against d with repect to ?

any ideas there.

I've set it in my mind like this

Source = (A, B, C)
Subject = (E, F, G)
T (A(1), B(10), C(-1))

I now take the t for E from A who got it from B who got it from C
I now take the t for F from A who got it from B
I now take the t for G from C who got it from B who got it from A

now rather than just asses the d (3,2,3) and drive the value of t towards zero by this factor I wish to also adjust this by some reasonable function of my T for these sources in the first case it should be something like
T(C)/3 + T(B)/2 + T(A)/1 = D

So I guess I have something like

sum(T(n)/d) = D

which then has to be if-then-elsed which seems a shame.

would a percentage reduction function be a reasonable action here?

[Matt_T_hat]

Which leaves me with this rather unified theory

		D = SUM( T(n) / d )
		
		T = (t - D) -> 0
		where D > t :: t = 0
		where t < -1 :: t = t + D
		else t = t - D

[Matt_T_hat]

Any one?

[zaza]

Why don't you just multiply t by 1/d ?

If the abs of the resulting value drops below 1 (such as 10 * (1/11)) then you set your result to 0.


zaza