Distance     Last updated on 2011/2555     12     10, a full moon day;

time     time   AND   1, 2, 3, 4, 5, 6, ... number  = distance; ACT2 and ACT3 stage parallel time calculation is in progress, also see: 2554;

1st to understand static 2-point distance, and then understand n-point distance; 2nd to understand non-static distance between hyperspace1 and hyperspace2, without weight; 3rd to understand non-static weighted distance among ACT2 stage FuzzySVMs in hyperplane1 AND hyperplane2;

Approx. 8 distances available to read, and a Myanmar's imaginary hyperdimensional hyperspace craft's horizontal ACT3 gray scale has been in 5 columns [still do not know the cause of WHY gray scale is not even to left and to right], but still calculating parallel time because natural time slows down in ACT3 stage ... ;

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2-point distance to n-point distance:

Point P1 and point P2 lie on a line L  ;

If point P1 is called A, and point P2 is called B, and then mathematical distance notation can be symbolized/written as AB;

n numbers of points lie in Euclidean space in ACT1 stage was with n dimensions;

n numbers of points P₁, P₂, P₃, P₄, ... , P_n; and those n numbers of points must NOT lie in the same Euclidean space in ACT1 stage was with n - 1 dimensions;

WHERE in xy plane, in ACT1 stage, 1 is abscissa for P1 and 2 is ordinate for P1, 3 is abscissa for P2 and 4 is ordinate for P2. Since point P1 and P2 depend on XY coordinate' same data type, P1 and P2 can be represented as array in computers as P1[x, y], P2[x, y], aka 2 dimensional arrays. After understanding space, and then time WHEN concerns, in simulation, we human beings can only have 2D vision [also see: aspect ratio], therefore, incoming Z as time in 3 dimensional array ... ; However in M theory, 10 dimensional strings have been proposed [Also read Prof. Kaku's Parallel World, for ACT2 and ACT3 stage developments];

IFF AB characteristic is in USB bus testing, for example AB = 10 cm, CD = 14 cm, EF = 24 cm, ... [ testing a port's tolerance by tapping/splitting/sharing/... ] and then notice that USB bus's tolerate distance becomes constraint along with time; Almost all testing boards, bus extenders, modular devices, ... are based on, engineered by distance vs. time, some engineers may say "due to attenuation", some engineers may say "due to resistance", some engineers may say "due to interference", ... , [Time . Space . Action];

ACT3 Distance Calculation, for a Myanmar's imaginary hypercraft's parallel time
1st to understand numerical values in numerology; 2nd to understand syntax vs. semantics logic so that only 3 is essential; 3rd to understand homological 2 and 3 solves 4PP + JUN = 6;3*3 ACT3 vectors and their dimensions must be further developed, a new ACT3 dimension must be developed; For ACT3 simulation developers, develop 3*3 ACT3 vectors, therefore a Myanmar's imaginary hyperdimensional hyperspace crafts can be able to do displacement of number at parallel time. And then, ACT3 distance calculation to prove gray scales simulation scientifically;

ACT3 Heat Distance Simulation, for a Myanmar's imaginary hypercraft's parallel time

After understanding 4 Planets Prediction, and then JUN time, 1st to understand is 1 stick of light, and then sticks as strings must be thoroughly understood; In a Myanmar's imaginary hyperdimensional hyperspace craft, 44 sticks need 4 holes to engineer 1 gravity symbol, but heat in distance has not been tested yet, for example: heat in 24 mm natural time might be diff IFF ACT3 hypercraft went very very very far away from our universe ... ; Therefore, cold and dark room environmental simulation is a must to measure heat in distance, and then ... ; Also read: Oct., 2007 Volume XVII Number 3 LINEAR TECHNOLOGY; Fuzzy Gray Scale Simulation;

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Damerau & Levenshtein distance, 1964:

An extension of Levenshtein distance; In addition to Levenshtein distance, additional recurrence has been computed, aka transposition, and calculated as:

{TRUE}

if ( i > 1 AND j > 1 AND string[ i ] = string [ j - 1 ] AND string[ i - 1 ] = string [ j ] ) then

2d_array [ i, j ] := is going to be assigned min (

2d_array [ i, j ],

2d_array [ i - 2, j - 2 ] + cost

)

Damerau & Levenshtein distance is aka edit distance. Can be used in natural language processing; Cannot be used in Metric tree;

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Damerau & Levenshtein distance between string and string can be written as:

declare integer 2d_array [ 0 .. length_of_string, 0 .. length_of_string ] /*** 2D table */

declare integer i, j, cost /*** defined variable */

integer Damerau_Levenshtein_distance (character_data_type string [ 1 .. length_of_string ], character_data_type string [ 1 .. length_of_string ] )

/*** WHERE d table contains length_of_string + 1 rows AND length_of_string columns */

For i from 0 to length_of_string

2d_array [ i, 0 ]  := is going to be assigned i

For j from 0 to length_of_string

2d_array [ 0, j ]  := is going to be assigned j

For i from 1 to length_of_string   For j from 1 to length_of_string

If string[ i ] = string[ j ] then

cost := is going to be assigned 0

else

cost := is going to be assigned 1

2d_array [ i, j ] := is going to be assigned min (parameterA, parameterB, parameterC) /*** 3 parameters */ WHERE parameterA is 2d_array [ i - 1, j ] + 1 for deletion, parameterB is 2d_array [ i, j - 1] + 1 for insertion, parameterC is 2d_array [ i - 1, j - 1 ] + cost for substitution

if ( i > 1 AND j > 1 AND string[ i ] = string [ j - 1 ] AND string[ i - 1 ] = string [ j ] ) then

2d_array [ i, j ] := is going to be assigned min (parameterD, parameterE) /*** 2 parameters */ WHERE parameterD is 2d_array [ i, j ] for transposition, parameterE is 2d_array [ i - 2, j - 2 ] + cost for transposition

return 2d_array [return_parameterX, return_parameterY] /*** 2 return_integer_parameters after function integer Damerau_Levenshtein_distance () is called */ WHERE return_parameterX is length_of_string, and return_parameterY is length_of_string

/*** also read: invariant correctness, longest common subsequence problem, upper bound and lower bound, ... , for THIS distance; */

{TRUE} ;

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Fuzzy distance, Foundations of Soft Case-Based Reasoning, Pal & Shiu, 2004:

WHERE corresponding objects "not subjects" in different coordinates, and those objects' locations can be represented as set of real numbers, and those sets are needed to be ordered [also see: Orbit] therefore must be weighted;

FuzzySVMs' traveling journeys can be collected as {F_journey (journey = 1, 2, 3, 4, 5, 6, ...)  and notice that journey 1, 2, 3, 4, 5, 6, ... n can become N Euclidean distances;

Therefore N Euclidean distances can be represented as:

distance_without_weight = { Ed₁, Ed₂, Ed₃, Ed₄, ... , Ed_N };

For each Ed i^th , dimensional vector (n + 1) can be represented as:

Ed_i = (xyz_i1, xyz_i2, xyz_i3, xyz_i4, ... , xyz_iN, θ_i);

WHERE xyz_ij corresponds to fuzzy member functions of

F_journey ( 1 〱= j 〱= n ) AND θ_i corresponds 〉Dimensional Time.Space.Action's

action ( i = 1, 2, 3, 4, 5, 6, ... , N);

For each F_journey  ( 1 〱= j 〱= n ),

Weight W_journey ( W_journey Є [ O, 1] );

Weighted distance:

Wd_AȢ = Wd ( Ed_1A, Ed_1Ȣ ) = [ _{journey = 1}Σⁿ W²_journey (X_Ajourney - XȢ_journey)²  ]^1/2

aka (  _{journey = 1}Σⁿ W²_journey X²_journey )^1/2 ;

WHERE X²_journey = (X_Ajourney - XȢ_journey)^2;

Weighted Similarity Measurement:

WSM_AȢ = 1 / ( 1 + positive constant カ Weighted distance Wd_AȢ );

Mapping 〱Fuzzy_journey X Fuzzy_journey 〉[ O, infinity ],

WHERE point p_journey of distance follows:

            point p_journey ( A, Ȣ) = O IFF A = Ȣ;Also see: 2-point distance

            point p_journey ( A, Ȣ ) = point p_journey ( Ȣ, A );

            point p_journey ( A, Ȣ ) 〱= less than or equal to point p_journey ( A, C ) + point p_journey ( C, Ȣ );n-point

IFF A AND Ȣ are real numbers,

point p_journey ( A, Ȣ ) = | A - Ȣ |;

IFF string AND string are intervals,

point p_journey ( string, string ) = max_{AЄstring, ȢЄstring} | A - Ȣ |;

Thus weighted fuzzy distance:

 = カsquare root of √ ( _{journey = 1}Σⁿ W²_journey  point p²_journey ( Ed_1A, Ed_1Ȣ ) );

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Hamming & Levenshtein distance:

In data communication, WHEN error detection and error correction are needed, Hamming & Levenshtein distance is used.

Levenshtein distance, aka Edit distance

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Jaro & Winkler distance, 1999:

Distance d_j = ( m / 3a) + (m / 3b) + ((m - t ) / 3m) WHERE matching characters are m; length_of_string and length_of_string are a and b; numbers of transpositions is t; AND any 2 characters in string1 and string2 must not farther than max (( a, b ) / 2) - 1;

Length of common prefixes l with prefix constant scale factor p prompt Jaro & Winkler distance for string and string can be calculated with weighted as:

d_w = d_j + ( l * p * (1 - d_j ))

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k-NN algorithm & k-Nearest Neighbor calculation:

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millibar ( distance) GDC, using artificial intelligence ... ;

pore-pore distance, [Progress in Transmission Electron Microscopy 2; Applications in Materials Science; Xiao-Feng Zhang; Ze Zhang; Tsinghua University Press and Springer-Verlag Berlin Heidelberg; 2001]

In ACT2 stage, distance has been defined by time and number Eastern Thought must be understood 1st, WHEN time has been 4 planets prediction's 2*7, and JUN time 2*5, WHERE space can be defined by locations, WHAT number has been by depth and structure as [A, B, C, D, E, ... ] numbers; Surface study in material engineering in ACT1 stage, by electron microscopes, silicate ions' circle characteristic in 5nm ~ 6nm, and those circles seem larger if those circles are near/close to particle's surface, and those circles seem smaller if those circles are longer/farther to particle's surface, WHERE pore's axis must be parallel to particle's surface; The285 distance WHICH initializes "those circles seem larger if those circles are near/close to particle's surface" is called/defined as pore-pore distance in ACT1 stage;

Before understanding carbon nano wall, pore-pore distance must be understood; Carbon study such as C60 and above number+ i.e. C70, C76, ... are aka carbon nanotubes, and ACT3 artificial light, ACT2 gravity7water2, ACT2 gravity2water7, ... must be understood thoroughly.

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A Myanmar's imaginary ACT3 hyperdimensional distance

Consider the following table, and then draw/draft a fully connected / fully distributed connection, and then whether full moon day, or no moon day, or up JUN, or middle JUN, or down JUN, ... ; For ACT2, ACT3 Monbusho grant awarded developers, develop D number for next generation children, ... ;

...

WHICH spectrum of66 location in95 distance, to be 3D Display, without eye-glasses ... ;

For Monbusho level developers, also see: AI global characters IQ;

Develop D number, DEE, Water Clock, ... until ACT3 number 31 can be solved scientifically ... ;

Also see: ri distance;

^_ IFF distance in95 time, aka Quality; 4PP+JUN=6;
^_ IFF power at12 distances (♯ c meter; ♯ m meter; ♯ ... ) electromagnetic induction OR magnetic resonance; solar tree;
 

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