Method for solving waveform sequence-matching problems using multidimensional attractor tokens
First Claim
1. A method for determining a combinatorial identity of a waveform or waveform segment source set from a waveform source multiset space, said waveform source multiset having a plurality of elements comprising the steps of:
- a) configuring a device in at least one of hardware, firmware and software to carry out an attractor process for mapping said waveform source multiset to an attractor space, said attractor process being an iterative process which cause said plurality of elements to converge on one of at least two different behaviors defined within said attractor space as a result of said iterative process, said configuring step including inputting a characterization of the waveform source multiset to input to said device the number of distinct elements of said waveform source multiset;
b) using said device, executing said mapping of said plurality of elements of said waveform source multiset to one or more coordinates of said attractor space;
c) mapping said attractor space coordinates into a target space representation, said target space representation including at least the attractor space coordinates;
d) storing the representation from said target space.
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Abstract
An improved method is provided for solving waveform description, matching and comparison problems using attractor-based processes to extract identity tokens that indicate sequence and subsequence symbol content and order of the waveform or waveform segments. The waveform is described with a suitable alphabet to extract the ontology of the waveform, and syntactical rules are applied to direct pattern extraction using the alphabet. The patterns are extracted in a hierarchical, embedded manner according the global or local maximia and minimia so that the resulting statements are compatible with analysis in catastrophe theory. The attractor processes map the resulting waveform sequence from its original sequence representation space (OSRS) into a hierarchical multidimensional attractor space (HMAS). The HMAS can be configured to represent equivalent symbol distributions within two symbol sequences or perform exact symbol sequence matching. The mapping process results in each sequence being drawn to an attractor in the HMAS. Each attractor within the HMAS forms a unique token for a group of sequences with no overlap between the sequence groups represented by different attractors. The size of the sequence groups represented by a given attractor can be reduced from approximately half of all possible sequences to a much smaller subset of possible sequences. The mapping process is repeated for a given sequence so that tokens are created for the whole sequence and a series of subsequences created by repeatedly removing a symbol or group of symbols from the one end of sequence and then repeating the process from the other end. The resulting string of tokens represents the exact identity of the whole sequence and all its subsequences ordered from each end.
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Citations
116 Claims
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1. A method for determining a combinatorial identity of a waveform or waveform segment source set from a waveform source multiset space, said waveform source multiset having a plurality of elements comprising the steps of:
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a) configuring a device in at least one of hardware, firmware and software to carry out an attractor process for mapping said waveform source multiset to an attractor space, said attractor process being an iterative process which cause said plurality of elements to converge on one of at least two different behaviors defined within said attractor space as a result of said iterative process, said configuring step including inputting a characterization of the waveform source multiset to input to said device the number of distinct elements of said waveform source multiset;
b) using said device, executing said mapping of said plurality of elements of said waveform source multiset to one or more coordinates of said attractor space;
c) mapping said attractor space coordinates into a target space representation, said target space representation including at least the attractor space coordinates;
d) storing the representation from said target space. - View Dependent Claims (2, 3, 4, 5, 6, 7)
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8. A method for recognizing the identity of a family of permutations of a waveform source multiset in a space of waveform multisets containing combinations of set elements, repeat elements, and permutations of those combinations of set elements and repeat elements, all of which set elements, repeat elements and permutations characterize waveforms. said method comprising the steps of:
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a) configuring a device in at least one of hardware, firmware and software to carry out an attractor process for mapping said waveform source multiset to an attractor space, said attractor process being an iterative process which causes said plurality of elements to converge on one of at least two different behaviors defined within said attractor space as a result of said iterative process, said configuring step including inputting a characterization of the waveform source multiset to input to said device the number of distinct elements of said waveform source multiset;
b) using said device, executing said mapping of said plurality of elements, N, of said multiset to one or more coordinates in said attractor space;
c) mapping said attractor space coordinates as part of an accumulation of attractor space coordinates into a target space representation, said target space representation including at least the attractor space coordinates, said target space being designed to provide representational structure to the accumulation of attractor space coordinates;
d) removing one or more elements as a group from the waveform source multiset to form a waveform source multiset with N=N−
1 element groups;
e) repeating steps b), c) and d) until N is less than a pre-determined value;
f) mapping said target space representation into an analytic space to determine the source multiset'"'"'s combinatorial identity, said analytic space including at least the attractor space coordinate and an identification of said waveform source multiset;
g) storing a representation of said analytic space. - View Dependent Claims (9, 10, 11, 12)
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13. A method of creating spatial coordinates in a space for describing a waveform comprising:
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mapping a plurality of patterns or embedded parts or fractional parts thereof or any combinations of the same from an original representation space (ORS) of the waveform into a hierarchical multidimensional attractor behavior space (HMBS), to draw the patterns or embedded parts or fractional parts thereof or any combinations of the same, respectively, to a plurality of resultant attractor behaviors in the HMBS, wherein each of the resultant attractor behaviors forms an identity for a group of patterns or embedded parts or fractional parts thereof or any combinations of the same;
mapping each attractor behavior identity to a specific analytical symbol that is part of an analytical symbol scheme;
mapping said analytical symbol to create the spatial coordinates in a space, a group of spaces or a hierarchy of spaces. - View Dependent Claims (14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37)
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38. A method of waveform sequence matching, comprising:
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(a) mapping a plurality of waveform sequences from an original representation space (ORS) comprised of waveform sequences into a hierarchical multidimensional attractor behavior space (HMBS), to draw the waveform sequences respectively to a plurality of attractor behaviors in the HMBS, wherein each of the attractor behaviors forms a unique identity for a given group of said waveform sequences with no overlap between different groups of waveform sequences represented by different attractor behaviors, then mapping the attractor identity to one of a group of analytical symbols that is part of an analytical symbol scheme to provide a token;
(b) creating a first plurality of waveform subsequences of a given one of the waveform sequences by repeatedly removing a waveform sequence element from a first end of the given waveform sequence to create a first waveform multi-set of subsequences;
(c) mapping each of said first plurality of waveform subsequences of said first waveform multi-set into the HMBS to form a plurality of identities;
(d) mapping each of said plurality of identities formed in step (c) to one of said group of analytic symbols to create a first string of analytical symbols for the first waveform multi-set of subsequence;
(e) combining said first string of analytical symbols for said first multi-set of sequences with said token of said given sequence from step (a) to produce a first token string of analytic symbols representing an exact identity of the given sequence and all of the subsequences ordered from the first end of the given sequence;
(f) creating a second plurality of waveform subsequences of said given one of the waveform sequences by repeatedly removing a waveform sequence element from a second end of the given waveform sequence to create a second waveform multi-set of subsequences;
(g) mapping each of said second plurality of waveform subsequences of said second waveform multi-set into the HMBS to form a plurality of identities;
(h) mapping each of said plurality of identities formed in step (g) to one of said group of analytic symbols to create a second string of analytical symbols for the second waveform multi-set of subsequence;
(i) combining said second string of analytical symbols for said second multi-set of sequences with said token of said given sequence from step (a) to produce a second token string of analytic symbols representing an exact identity of the given sequence and all of the subsequences ordered from the second end of the given sequence;
(j) repeating steps (b)-(i) for a plurality of other given waveform sequences from said plurality of waveform sequences to produce a plurality of first and a plurality of second token strings of analytic symbols;
(k) mapping said first and second plurality of token strings of analytical symbols to create a series of spatial coordinates in a hierarchy of spaces; and
(l) evaluating sequence-similarity characteristics of at least two token strings of analytical symbols using said spatial coordinates.
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39. A method of waveform sequence matching comprising:
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a) mapping a first waveform sequence having a plurality of waveform sequence elements from an original representation space (ORS) into a multidimensional attractor behavior space (HMBS), said first waveform sequence converging to one of at least two distinct behaviors in said attractor behavior space, wherein each behavior is assigned to one of unique analytical symbols from an analytical symbol scheme;
b) forming a plurality of first waveform subsequences of said first waveform sequence; and
c) mapping said plurality of first waveform subsequences of said first waveform sequence to said HMBS space to create a plurality of analytical symbols corresponding to the behavior of each waveform subsequence, said analytical symbol assigned to said first waveform sequence and said plurality of analytical symbols assigned to said first waveform subsequences defining together a first analytical symbol string uniquely characterizing said first waveform sequence including said first waveform subsequences;
wherein the step of forming said plurality of first waveform subsequences comprises;
1) removing a waveform sequence element from a first end of the first waveform sequence to produce an initial first waveform subsequence;
2) iteratively repeating step
1) for the produced initial first waveform subsequence to form subsequent first waveform subsequences;
3) removing a symbol from a second end of the first waveform sequence to produce another initial first waveform subsequence;
4) iteratively repeating step
3) for the produced another initial first waveform subsequence to form subsequent other first waveform subsequences,5) said plurality of first waveform subsequences formed by said initial first waveform subsequence, said subsequent first waveform subsequences, said another initial first waveform subsequence and said subsequent other first waveform subsequences;
d) repeating steps a)-c) for a second waveform sequence and second waveform subsequences to obtain a second analytical symbol string;
f) said first and second analytical symbol strings representing an exact identity of the first and second waveform sequences respectively and all waveform subsequences ordered from the first and second ends of the first and second waveform sequences; and
g) comparing the first analytical symbol string with the second analytical symbol string whereby a match may be detected between said first waveform sequence and said second waveform sequence. - View Dependent Claims (40, 41, 42)
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43. A method of waveform sequence matching comprising:
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(a) mapping at least a first and a second waveform sequence having a plurality of waveform sequence elements from an original representation space (ORS) into a multidimensional attractor behavior space (HMBS), each of said first and second waveform sequence converging to one of at least two distinct behaviors in said attractor behavior space, wherein each behavior is assigned to one of unique analytical symbols from an analytical symbol scheme;
(b) forming a plurality of first and second waveform subsequences of said first and second waveform sequences respectively; and
(c) mapping said plurality of first and second waveform subsequences of said first and second waveform sequence to said HMBS space to create a plurality of analytical symbols corresponding to the behavior of each of said plurality of first and second waveform subsequence, said analytical symbol assigned to said first waveform sequence and said plurality of analytical symbols assigned to said first waveform subsequences defining together a first analytical symbol string uniquely characterizing said first waveform sequence including said first waveform subsequences, and said analytical symbol assigned to said second waveform sequence and said plurality of analytical symbols assigned to said second waveform subsequences defining together a second analytical symbol string uniquely characterizing said second waveform sequence including said second waveform subsequences;
wherein the analytic symbols, for each of said first and second analytical symbol strings of said first and second waveform sequences, are obtained by;
(i) taking said waveform sequence elements one at a time for forming analytical sequence elements and, collectively, an analytical sequence, and mapping the analytical sequence to said attractor space;
(ii) taking said waveform sequence elements two at a time for forming analytical sequence elements and, collectively, an analytical sequence, and mapping the analytical sequence to said attractor space;
(iii) taking said waveform sequence elements three at a time for forming analytical sequence elements and, collectively, an analytical sequence, and mapping the analytical sequence to said attractor space;
(iv) removing j sequence elements, where j is an integer initially equal to one, from one end of said waveform subsequence and, for the resulting subsequence, repeating steps (i)-(iii);
(v) iteratively repeating step (iv) at least once for j=j+1 at each iteration, and at most for j equal to the number of sequence elements in said waveform sequence;
(vi) removing k sequence elements, where k is an integer initially equal to one, from the other end of said subsequence and, for the resulting subsequence, repeating steps (i)-(iii); and
(vii) iteratively repeating step (vi) at least once for k=k+1 at each iteration, and at most for k equal to the number of sequence elements in said waveform sequence. - View Dependent Claims (44, 45, 46, 108)
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47. A method of classifying and identifying waveforms comprising the steps of:
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(a) representing the waveform as a series of discrete points, each point having an amplitude value;
(b) selecting the global maximum and global minimum points according to their amplitude values within the waveform, said waveform defined between right and left terminator points that bound the waveform, said terminator points having amplitude values;
(c) assigning a symbol from an alphabet of symbols to represent the selected global maximum, global minimum and terminator points, said symbol assigned to characterize said points based on amplitude values of adjacent ones of said global maximum, global minimum and terminator points, while ignoring all other points;
(d) dividing the waveform into regions according to the selected global maximum and global minimum points and the terminator points;
(e) within each region, selecting a local maximum and minimum points according to their amplitude values;
(f) within each region, assigning a symbol from said alphabet of symbols to represent the selected local maximum and local minimum points, said symbol assigned to characterize said points based on amplitude values of adjacent ones of said local maximum, said local minimum, said global maximum, said global minimum, and said terminator points, if any, while ignoring all other points;
(g) forming a first sequence of symbols by combining the assigned symbols formed in steps (c) and (f);
(h) forming a multiset of sequences of symbols by taking subsets of said first sequence;
(i) mapping said first sequence and said multiset of sequences with an attractor process, said attractive process being an iterative process which causes each of said first sequence and each sequence of said multiset of sequences to converge on one of at least two different behaviors;
(j) representing each of said at least two behaviors with a token value;
(k) concatenating said token values corresponding to said first sequence and said multiset of sequences to produce a token value sequence corresponding to said waveform;
(l) repeating steps (a) through (k) for at least one other waveform; and
(m) classifying or identifying said waveform and said at least one other waveform by ordering and comparing their token value sequences. - View Dependent Claims (48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58)
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59. A method of classifying and identifying waveforms comprising the steps of:
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(a) representing the waveform as a series of discrete points, each point having an amplitude value;
(b) selecting the global maximum and global minimum points according to their amplitude values within the waveform, said waveform defined between right and left terminator points that bound the waveform, said terminator points having amplitude values;
(c) assigning a symbol from an alphabet of symbols to represent the selected global maximum, global minimum and terminator points, said symbol assigned to characterize said points based on amplitude values of adjacent ones of said global maximum, global minimum and terminator points, while ignoring all other points;
(d) selecting the next global maximum and next global minimum points according to their amplitude values;
(e) assigning a symbol from said alphabet of symbols to represent the selected next global maximum and next global minimum points, said symbol assigned to characterize said points based on amplitude values of adjacent ones of said next global maximum, said next global minimum, said global maximum, said global minimum, and said terminator points, if any, while ignoring all other points;
(f) forming a first sequence of symbols by combining the assigned symbols formed in steps c) and e);
(g) forming a multiset of sequences of symbols by taking subsets of said first sequence;
(h) mapping said first sequence and said multiset of sequences with an attractor process, said attractive process being an iterative process which causes each of said first sequence and each sequence of said multiset of sequences to converge on one of at least two different behaviors;
(i) representing each of said at least two behaviors with a token value;
(j) concatenating said token values corresponding to said first sequence and said multiset of sequences to produce a token value sequence corresponding to said waveform;
(k) repeating steps (a) through (j) for at least one other waveform; and
(l) classifying or identifying said waveform and said at least one other waveform by ordering and comparing their token value sequences. - View Dependent Claims (60, 61, 62, 63, 64, 65, 66, 67, 68, 69)
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70. A method of classifying and identifying a statistical distribution between parameter A and parameter B comprising the steps of:
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(a) dividing parameter A into regions;
(b) setting j=2 (c) dividing the parameter B space into j regions;
(d) counting the number of points for each of the regions of parameter A that fall within each of the j regions of parameter B;
(e) setting j=2×
j and repeating steps (d) at least one time;
(f) representing the counted number of points from step (d) for each of the regions as a first sequence of numbers;
(g) forming multisets of the first sequence by taking subsets of the first sequence;
(h) mapping said first sequence and said multiset of sequences with an attractor process, said attractive process being an iterative and contractive process which causes each of said first sequence and each sequence of said multiset of sequences to converge on one of at least two different behaviors;
(i) representing each of said at least two behaviors with a token value;
(j) concatenating said token values corresponding to said first sequence and said multiset of sequences to produce a token value sequence corresponding to said waveform;
(k) repeating steps (a) through (j) for at least one other statistical distribution; and
(l) classifying or identifying said statistical distribution and said at least one other statistical distribution by ordering and comparing their token value sequences.
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71. A method of classifying and identifying a statistical distribution between parameter A and parameter B comprising the steps of:
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(a) dividing parameter A into regions;
(b) dividing the parameter B space into j regions;
(c) counting the number of points for each of the regions of parameter A that fall within each of the j regions of parameter B;
(d) representing the counted number of points from step (c) for each of the regions as a first sequence of numbers;
(e) forming multisets of the first sequence by taking subsets of the first sequence;
(f) mapping said first sequence and said multiset of sequences with an attractor process, said attractive process being an iterative and contractive process which causes each of said first sequence and each sequence of said multiset of sequences to converge on one of at least two different behaviors;
(g) representing each of said at least two behaviors with a token value;
(h) concatenating said token values corresponding to said first sequence and said multiset of sequences to produce a token value sequence corresponding to said waveform;
(i) repeating steps (a) through (h) for at least one other statistical distribution; and
(j) classifying or identifying said statistical distribution and said at least one other statistical distribution by ordering and comparing their token value sequences.
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72. A method of waveform comparison comprising:
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(a) mapping, through an attractor process, at least first and second waveform sequence source multisets, from an original representation space (ORS) into an attractor behavior space;
(i) each of said at least first and second waveform sequence source multisets being a plurality of subsets of a first and second waveform sequence and each subset having a plurality of waveform sequence elements;
(ii) said attractor process being an iterative process which causes first and second waveform sequences source multisets in the ORS to converge to at least two distinct behaviors in said attractor behavior space;
(iii) wherein each behavior in said attractor behavior space is assigned a distinct symbol from a symbol scheme, (iv) said mapping resulting in a first and second token string, each consisting of a series of said symbols, corresponding to said first and second waveform sequence source multisets respectively;
(b) mapping, through said attractor process and into said attractor behavior space, a plurality of first and second waveform subsequences source mutisets of said first and second waveform sequences respectively, (i) said plurality of first and second waveform subsequence source multisets each being a plurality of subsets of a different one of a plurality of first and second waveform subsequence of said first and second waveform sequence and each having a number of waveform sequence elements;
(ii) said mapping resulting in a plurality of first and second subsequence token strings, each consisting of a series of said symbols, corresponding to said plurality of first and second waveform subsequence source multisets respectively; and
(c) comparing said first token string and said plurality of first subsequence token strings with said second token string and said plurality of second subsequence token strings to determine a match among said first and second waveform sequence source multisets and said plurality of first and second waveform subsequences source multisets. - View Dependent Claims (73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93)
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94. A method of waveform comparison comprising:
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(a) mapping, through an attractor process, a first waveform sequence source multiset, from an original representation space (ORS) into an attractor behavior space;
(i) said first waveform sequence source multisets being a plurality of subsets of a first waveform sequence and each subset having a plurality of waveform sequence elements;
(ii) said attractor process being an iterative and contractive process which causes first waveform sequences source multisets in the ORS to converge to at least two distinct behaviors in said attractor behavior space;
(iii) wherein each behavior in said attractor behavior space is assigned a distinct symbol from a symbol scheme, (iv) said mapping resulting in a first token string consisting of a series of said symbols, corresponding to said first waveform sequence source multisets respectively;
(b) mapping, through said attractor process and into said attractor behavior space, a plurality of first waveform subsequences source mutisets of said first waveform sequences respectively, (i) said plurality of first waveform subsequence source multisets being a plurality of subsets of a different one of a plurality of a first waveform subsequence of said first waveform sequence and each having a number of waveform sequence elements;
(ii) said mapping resulting in a plurality of first subsequence token strings, each consisting of a series of said symbols, corresponding to said plurality of first waveform subsequence source multisets respectively; and
(c) mapping, through an attractor process, a second waveform sequence source multiset, from an original representation space (ORS) into an attractor behavior space;
(i) said second waveform sequence source multisets being a plurality of subsets of a second waveform sequence and each subset having a plurality of waveform sequence elements;
(ii) said attractor process being an iterative and contractive process which causes second waveform sequences source multisets in the ORS to converge to at least two distinct behaviors in said attractor behavior space;
(iii) wherein each behavior in said attractor behavior space is assigned a distinct symbol from said symbol scheme, (iv) said mapping resulting in a second token string consisting of a series of said symbols, corresponding to said second waveform sequence source multisets respectively;
(d) mapping, through said attractor process and into said attractor behavior space, a plurality of second waveform subsequences source mutisets of said second waveform sequences respectively, (i) said plurality of second waveform subsequence source multisets being a plurality of subsets of a different one of a plurality of a second waveform subsequence of said second waveform sequence and each having a number of waveform sequence elements;
(ii) said mapping resulting in a plurality of second subsequence token strings, each consisting of a series of said symbols, corresponding to said plurality of second waveform subsequence source multisets respectively; and
(e) comparing said first token string and said plurality of first subsequence token strings with said second token string and said plurality of second subsequence token strings respectively to determine a match among said first and second waveform sequence source multisets and said plurality of first and second waveform subsequences source multisets.
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95. A method of waveform comparison comprising:
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(a) representing a first waveform as a first series of discrete points, each point having a value, a first waveform sequence source multiset being at least a portion of said first series of discrete points and a plurality of subsets of said portion of said first series of discrete points, and each subset having a plurality of said discrete points as waveform sequence elements;
(i) mapping, through an iterative and contractive process, said first waveform sequence source multiset into an attractor behavior space having at least two distinct behaviors with each behavior assigned a distinct symbol;
(ii) said mapping resulting in a first token string consisting of a series of said symbols, corresponding to said first waveform sequence source multisets;
(b) representing a second waveform as a second series of discrete points, each point having a value, a second waveform sequence source multiset being at least a portion of said second series of discrete points and a plurality of subsets of said portion of said second series of discrete points, and each subset having a plurality of said discrete points as waveform sequence elements;
(i) mapping, through said iterative and contractive process, said second waveform sequence source multiset into said attractor behavior space;
(ii) said mapping resulting in a second token string consisting of a series of said symbols, corresponding to said second waveform sequence source multisets;
(c) comparing said first token string and with said second token string to determine a match among said first and second waveform sequence source multisets. - View Dependent Claims (96, 97, 98, 99)
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100. A method of waveform comparison comprising:
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(a) representing a first waveform as a first series of discrete points;
(b) mapping, said first waveform through an iterative and contractive process, to obtain a first token based on the results of the iterative and contractive process;
(c) representing a second waveform as a second series of discrete points, (d) mapping, said second waveform through said iterative and contractive process, to obtain a second token based on the results of the iterative and contractive process, said first and second tokens each being one or a plurality of symbols;
(e) comparing said first token and with said second token to determine a match among said first and second waveforms.
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101. A method of comparing at least a first and second waveform comprising the steps of:
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(a) representing the first waveform as a series of discrete points;
(b) setting k initially equal to “
first”
where k is an ordinal number;
(c) selecting a k plurality of points based on a k resolution examination of said series of discrete points,;
(d) assigning symbols from an alphabet of symbols to represent the k plurality of points at said k resolution examination;
(e) incrementing k such that k=k+1;
(f) repeating steps (c) and (d) at least once;
(g) forming a sequence of symbols by combining the assigned symbols formed in steps (d);
(h) forming a plurality of said subsequences of symbols by taking subsets of said sequence of symbols;
(i) mapping said sequence and said plurality of subsequences with an iterative, contractive process which causes said sequence and each of said plurality of subsequences to converge on one of at least two different behaviors;
(j) representing each of said at least two behaviors with a token value;
(k) concatenating said token values corresponding to said sequence and said plurality of subsequences to produce a first token value sequence corresponding to said first waveform;
(l) representing the second waveform as a series of discrete points;
(m) repeating steps (b) through (k) for said second waveform to produce a second token value sequence corresponding to said second waveform; and
(n) comparing said first and second waveforms by comparing the first and second token value sequences. - View Dependent Claims (102, 103, 104)
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105. A method of comparing at least a first and second waveform comprising the steps of:
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(a) representing the first waveform as a series of discrete points;
(b) setting k initially equal to “
first”
where k is an ordinal number;
(c) selecting a k plurality of points based on a k resolution examination of said series of discrete points;
(d) assigning symbols from an alphabet of symbols to represent the k plurality of points at said k resolution examination;
(e) incrementing k such that k=k+1;
(f) repeating steps (c) and (d) at least once;
(g) forming a sequence of symbols by combining the assigned symbols formed in steps (d);
(h) mapping said sequence with an iterative, contractive process which causes said sequence to converge on one of at least two different behaviors, and assigning a first token indicative of said behavior;
(i) representing the second waveform as a series of discrete points;
(j) setting m initially equal to “
first”
where m is an ordinal number;
(k) selecting a m plurality of points based on a m resolution examination of said series of discrete points;
(l) assigning symbols from said alphabet of symbols to represent the m plurality of points at said m resolution examination;
(m) incrementing m such that m=m+1;
(n) repeating steps (k) and (l) at least once;
(o) forming a sequence of symbols by combining the assigned symbols formed in steps (l);
(p) mapping said sequence with an iterative, contractive process which causes said sequence to converge on one of at least two different behaviors, and assigning a second token indicative of said behavior;
(q) comparing said first and second waveforms by comparing the first and second tokens. - View Dependent Claims (106)
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107. A method of waveform sequence matching comprising:
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(a) mapping a first waveform sequence having a plurality of waveform sequence elements from an original representation space (ORS) into a multidimensional attractor behavior space (HMBS), said first waveform sequence converging to one of at least two distinct behaviors in said attractor behavior space, wherein each behavior is assigned to one of unique analytical symbols from an analytical symbol scheme;
(b) forming a plurality of first waveform subsequences of said first waveform sequence; and
(c) mapping said plurality of first waveform subsequences of said first waveform sequence to said HMBS space to create a plurality of analytical symbols corresponding to the behavior of each waveform subsequence, said analytical symbol assigned to said first waveform sequence and said plurality of analytical symbols assigned to said first waveform subsequences defining together a first analytical symbol string uniquely characterizing said first waveform sequence including said first waveform subsequences;
(d) repeating steps (a)-(c) for a second waveform sequence and second waveform subsequences to obtain a second analytical symbol string;
(e) said first and second analytical symbol strings representing an exact identity of the first and second waveform sequences respectively and all waveform subsequences ordered from the first and second ends of the first and second waveform sequences; and
(f) comparing the first analytical symbol string with the second analytical symbol string whereby a match may be detected between said first waveform sequence and said second waveform sequence.
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109. A method of waveform comparison comprising:
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(a) representing a waveform as a series of discrete points;
(b) mapping said waveform representation through an iterative and contractive process to obtain a token string based on the results of the iterative and contractive process;
(c) comparing said token string with stored token strings from previously mapped waveform representations to determine a match between said token string and said stored token strings.
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110. A method of waveform comparison comprising:
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(a) mapping a waveform representation through an iterative and contractive process to obtain a token string based on the results of the iterative and contractive process;
(b) comparing said token string with stored token strings from previously mapped waveforms representations to determine a match between said token string and said stored token strings.
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111. Apparatus for waveform comparison comprising:
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(a) a device for mapping a waveform representation through an iterative and contractive process to obtain a token string based on the results of the iterative and contractive process;
(b) a comparator for comparing said token string with stored token strings from previously mapped waveform representations to determine a match between said token string and said stored token strings. - View Dependent Claims (112, 113)
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114. Apparatus for waveform comparison comprising:
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(a) means for mapping a waveform representation through an iterative and contractive process to obtain a token string based on the results of the iterative and contractive process;
(b) means for comparing said token string with stored token strings from previously mapped waveform representations to determine a match between said token string and said stored token strings.
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115. Apparatus comprising:
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(a) a device for mapping a plurality of waveform representations through an iterative and contractive process to obtain a plurality of token strings each of which is based on the results of the iterative and contractive process; and
(b) a storage device for storing said token strings.
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116. Apparatus comprising:
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(a) means for mapping a plurality of waveform representations through an iterative and contractive process to obtain a plurality of token strings each of which is based on the results of the iterative and contractive process; and
(b) means for storing said token strings
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Specification