2018 Global CESI-MS Symposium - Poster Submission requiring confirmation. Primary Presenters Name
Dr Shane Lawrence
Presenters Title
Consultant Researcher
Organisation Name
University of Cambridge and Senstechse
Address
Street Address : 9 Victoria Way Street Address Line 2 : Melbourn Royston City : Royston State/Province : Herts Postal/Zip Code : SG86FE
Phone Number
(0044) 1763264066
Email
[email protected]
Poster title
Category
An Advanced Method of Assessing Experimental Results Distribution. Metabolomics
Introduction
It is often necessary when experimental results are obtained to devise a method of determining the mathematical distribution of results to eanble a future method of assessing the relative inportance of the results obtained.
Methods
These results when translated into data distribution curves are usually defined as Type curves where particular sorts of graphical distribution. For example if bell shaped and J shaped curves are excluded by means of a defined boundary,only distribution curves of another type possibly hyperbolic,are encompassed within the boundary.
Preliminary Data
Firstly the upper boundary of a Pearson representation; y=yo/2 + yo(1+x/a)2 + yo(x/a1)2 + yo(1-x/a2)m2/2 + (1+(x2/a1a2))/2 Below this boundary we have mainly Type 1 distributions with Type 2 distributions at the x=0 position at B2=2.5. This immediately gives a limit. Defining a lower boundary by extension as y=yo.e-g/x-p/2 + yo(1+x/a)m/2 which is a combination of the standard lower boundary for Type 1 distribution 8\b2-15B1-36=0 below which values of Type 9 distribution; y = yoe-vtan-1/9(1+x2/a2)-m Between these boundaries the distributions that can be considered as applicable for our experimental data distribution
are enclosed. Novel Aspect
We can see the advantages of the advanced Pearson method taking shape.With an upper boundary defined we can progress to define the lower boundary etc.
Development of boundaries and inner region of Pearson representations of experimental results distribution. _________________________________________________________ 1) Standard Pearson Graphical Representations. ___________________________________
The standard Pearson graphical representations or Pearson curves are generally defined as originating in the function; y = f(x)
1dy/ydx = -(x+a)/Co+C1x+C2x2 origin x at mean;
dependent on constants CoC1C2 related to moments of curve; ur = integ.l1l2 xrf(x) dx if
¬ = u2
B1 = u3sq/u2sq
for constants ; Co = rsq(4B2-3B1)/2(5B2-6B1-q) C1 = ¬sqrtB1(B2+3)/2(5B2-6P1-9) C2 = 2B2-3B1-6/2(5B2-6B1-9) for nth moment and (uo = 1,u1 = 0) where 1 and 1z are permeable at lower limit and upper limit for x. Then diagrammatically assigning B1,B2 to residual axis gives different area curve or point in a phase associated with a particular sort of curve.
2) Extension of Standard Pearson Graphical Representation. _____________________________________________
To consider an upper boundary of B2B1-1=0 above which B1B2 is a point of no real meaning,while u8 is above and inside the area defined by 8B2-15B1-36=0 at the bottom of the graphical representation. If functions that define bell shaped and J shaped curves are excluded from this consideration then we can introduce the acceptable varieties of Type curves. For example at our upper boundary of B2B1-1=0 becomes the upper limit of Type 1 curve as defined by;
y=yo(1+x/a1)m1 (1-x/a2)m2.m1m2+ve limit of x is -a
