Abstract:
A computer processor converts a symbolic sequence I j  (j=1˜m) into a parallel sequence A(k), in which the suffix j is aligned in the following positional relationship: 
                                       j =   1,   2, . . .   k − 1,   k     j =   k + 1,   k + 2, . . .   k + k − 1,   k + k     :     :     j =   (n − 1)k + 1,   (n − 1)k + 2, . . .   (n − 1)k + k − 1,   (n − 1)k + k     j =   nk + 1,   nk + 2, . . .   nk + k − 1,   nk + k                                
and additional parallel sequences A(k) can be generated by changing k to p, p+r, p+2r, p+3r . . . . Therefore, a set of parallel sequences ΣA(k) can be generated. The parallel sequences may then be visually displayed using different colors for the different symbols in order to reveal at least one latent characteristic existing in the symbolic sequence I j .

Description:
CROSS-REFERENCE 
     This application is a divisional application of U.S. patent application Ser. No. 09/137,162, now U.S. Pat. No. 6,438,496 filed Aug. 20, 1998 which application claims priority to Japanese patent application serial number 9-223908. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to methods and apparatus for manifesting a characteristic or regularity, which is latent and can not ordinarily be recognized by visual inspection, although such characteristic or regularity actually exists in a complicated symbolic sequence, for example, a nucleotide sequence of DNA, an amino acid sequence of a protein, or a digital sequence of decimal expansion of an irrational number and the like. In these sequences, regularity can not be recognized at a glance even when regularity exists therein. The present invention enables recognition of a characteristic or regularity existing within a symbolic sequence, which has not yet been recognized. 
     2. Description of the Related Art 
     Some complicated symbolic sequences contain a characteristic, which has not been recognized by human beings, although the characteristic actually exists. For example, genetic information is represented by a long sequence of symbols. The symbols consist of four different symbols, each indicating one of the four types of nucleotides. A large number of symbols are one-dimensionally aligned. In the study of genetic information, it is extremely important to recognize a certain regularity hidden within the symbolic sequence that represents the genetic information. In addition, if a certain regularity is found in an irrational number, e.g., the number π, and the base of natural logarithm (e), the study of irrational numbers will be enhanced and various developments can be expected in mathematics. 
     For such purpose, various efforts have been made to analyze a symbolic sequence based on a variety of mathematical methods, such as Fourier analysis. However, these efforts have not necessarily accomplished successful results. One problem with conventional analysis methods is that, even if a certain regularity exists within a portion of a very long symbolic sequence, the latent regularity is buried within the entire sequence and can not be recognized when the entire symbolic sequence is analyzed. Since there has been no effective technology for determining in advance as to which part of the sequence that the regularity exists, there are many characteristics or regularity which can not be recognized by conventional analysis methods. 
     SUMMARY OF THE INVENTION 
     An object of the present invention is to provide methods and apparatus which manifest a characteristic or regularity even if such characteristic or regularity exists only in a portion of the entire symbolic sequence, and thereby enable recognition of a characteristic or regularity which has not been previously recognized. 
     Another object of the present invention is to manifest a characteristic or regularity existing throughout the entire sequence. 
     In one embodiment of the present invention, a symbolic sequence I j (j=1˜m) is converted into a parallel sequence A(k) of partial symbolic sequences, in which the suffix j is aligned in the following positional relationship: 
     
       
         
               
               
               
               
               
             
           
               
                   
               
             
             
               
                 j = 
                 1, 
                 2, . . . 
                 k − 1, 
                 k 
               
               
                 j = 
                 k + 1, 
                 k + 2, . . . 
                 k + k − 1, 
                 k + k 
               
               
                 : 
               
               
                 : 
               
               
                 : 
               
               
                 j = 
                 (n − 1)k + 1, 
                 (n − 1)k + 2, . . . 
                 (n − 1)k + k − 1, 
                 (n − 1)k + k 
               
               
                 j = 
                 nk + 1, 
                 nk + 2, . . . 
                 nk + k − 1, 
                 nk + k. 
               
               
                   
               
             
          
         
       
     
     In the alternative, the positional relationship may be represented as follows: 
     
       
         
               
               
               
               
               
             
           
               
                   
               
             
             
               
                 j = 
                 1, 
                 2, . . . 
                 k − 1, 
                 k 
               
               
                 j = 
                 k + k, 
                 k + k − 1, . . . 
                 k + 2, 
                 k + 1 
               
               
                 : 
               
               
                 : 
               
               
                 j = 
                 (n − 1)k + k, 
                 (n − 1)k + k − 1, . . . 
                 (n − 1)k + 2, 
                 (n − 1)k + 1 
               
               
                 j = 
                 nk + 1, 
                 nk + 2, . . . 
                 nk + k − 1, 
                 nk + k. 
               
               
                   
               
             
          
         
       
     
     Herein, k represents an integer of 2 or more, n represents an integer such that nk&lt;m≦nk+k, and when the suffix j is m+1 or more, the result is ignored. 
     Then, the converted parallel sequence A(k) is output using one or more means for expressing the output selected from color hue, color lightness and color saturation and from sound interval, sound tone and sound volume. 
     “Equidistant Letter Sequences in the Book of Genesis” (Doron Witztum, Eliyahu Rips and Yoav Rosenberg, Statistical Science 1994, Vol. 9, No. 3, page 429-438) introduces a technology in which a code hidden in a one-dimensional letter sequence is decoded by converting the one-dimensional letter sequence into a parallel sequence A(k) of partial symbolic sequences. In this known technology, words having meanings must be extracted from the parallel sequence A(k) of partial symbolic sequences, and this known method can not be used for sequences other than letter sequences. Further, when searching for a certain regularity in a symbolic sequence, which symbolic sequence appears to be irregular at a glance and which is often the case in the fields of natural science, inconsistency, (i.e., regularity can not be recognized unless the regularity has been identified in advance), can not be solved. 
     In the present invention described above, since a parallel sequence A(k) of partial symbolic sequences is output using one or more expression means selected from color hue, color lightness and color saturation and from sound interval, sound tone and sound volume, even if the regularity is not known in advance, that regularity is manifested by a pattern of color hue, color lightness or color saturation or sound interval, sound tone or sound volume and can be easily recognized. 
     In another embodiment of the present invention, a one-dimensional symbolic sequence I j (j=1˜m) is converted into a parallel sequence A(k) of partial symbolic sequences, in which the suffix j is aligned in the following positional relationship: 
     
       
         
               
               
               
               
               
             
           
               
                   
               
             
             
               
                 j = 
                 1, 
                 2, . . . 
                 k − 1, 
                 k 
               
               
                 j = 
                 k + 1, 
                 k + 2, . . . 
                 k + k − 1, 
                 k + k 
               
               
                 : 
               
               
                 : 
               
               
                 : 
               
               
                 j = 
                 (n − 1)k + 1, 
                 (n − 1)k + 2, . . . 
                 (n − 1)k + k − 1, 
                 (n − 1)k + k 
               
               
                 j = 
                 nk + 1, 
                 nk + 2, . . . 
                 nk + k − 1, 
                 nk + k. 
               
               
                   
               
             
          
         
       
     
     In the alternative, the positional relationship may be represented as follows: 
     
       
         
               
               
               
               
               
             
           
               
                   
               
             
             
               
                 j = 
                 1, 
                 2, . . . 
                 k − 1, 
                 k 
               
               
                 j = 
                 k + k, 
                 k + k − 1, . . . 
                 k + 2, 
                 k + 1 
               
               
                 : 
               
               
                 : 
               
               
                 : 
               
               
                 j = 
                 (n − 1)k + k, 
                 (n − 1)k + k − 1, . . . 
                 (n − 1)k + 2, 
                 (n − 1)k + 1 
               
               
                 j = 
                 nk + 1, 
                 nk + 2, . . . 
                 nk + k − 1, 
                 nk + k. 
               
               
                   
               
             
          
         
       
     
     Further, when p represents a natural number from 2 to less than m, r represents any natural number, the above-described conversion is repeated by changing k to p, p+r, p+2r, p+3r, . . . in order to obtain parallel sequences of partial symbolic sequences: A(p), A(p+r), A(p+2r), A(p+3r) . . . Then, the resulting parallel sequences: A(p), A(p+r), A(p+2r), A(p+3r) . . . are further parallel-positioned in order to generate a set of parallel sequences ΣA(k). Then, the set of parallel sequences ΣA(k) is output. Herein, n represents an integer such that nk&lt;m≦nk+k, and when the suffix j is m+1 or more, the result is ignored. 
     In this case, a parallel sequence generated by parallel-positioning p partial symbolic sequences, a parallel sequence generated by parallel-positioning p+r partial symbolic sequences, and parallel sequences generated by parallel-positioning of similar increasing numbers of partial symbolic sequences, are all parallel-positioned. In this processing, if regularity of period length α is hidden in the symbolic sequence, such regularity is remarkably manifested in a parallel sequence A(α) generated by parallel-positioning of partial symbolic sequences of a number of α. 
     If α falls within p, p+r, p+2r, p+3r, . . . rows, the regularity having period length α is manifested in a parallel sequence of partial symbolic sequences of an analogous number to α. Therefore, increment r regarding the number of the partial symbolic sequences is not necessarily required to be one, and it may advantageously be any natural number. In this case, when the increment r is smaller, the characteristic is more easily manifested. 
     In this embodiment, regularity of an unknown period length is manifested in a parallel sequence of partial symbolic sequences of some number, and recognition of the characteristic becomes easy. 
     In the above-described method, each symbol is preferably expressed by a combination of color hue, color lightness and color saturation. In this embodiment, as a result of the manifestation of the characteristic hidden in the symbolic sequence through visual means, a more comprehensive understanding of the characteristic hidden in the symbolic sequence is possible, and various applications and developments utilizing the characteristic are made possible. Further, the resulting visual pattern is a pattern including mixed regularity and irregularity that was not previously known, and a visual pattern of which design itself has utility can be designed. 
     Each symbol may be expressed by a combination of sound interval, sound tone and sound volume. By expressing the parallel sequence as a combination of sound interval, sound tone and sound volume, a unique audio pattern is created and the characteristic of the symbolic sequence can be recognized through auditory means. 
     One symbol may be removed from the original symbolic sequence at an interval of k-1 (namely, at every k) in order to generate a symbolic sequence. The present method is then applied to this extracted symbolic sequence. If a regularity of period length k is hidden in the original symbolic sequence, the regularity is manifested and appears remarkably. 
     One symbol may be removed from the original symbolic sequence at an interval of kq-1 (namely, at every kq) in order to generate a symbolic sequence. The present method is then applied to this extracted symbolic sequence. If a regularity of period length kq is hidden in the original symbolic sequence, the regularity is manifested and appears remarkably. 
     Further, when any of the above-described methods are conducted by changing k to p, p+r, p+2r . . . , a set of parallel sequences ΣA(k) is generated, including a parallel sequence A(p) generated by parallel-positioning p partial symbolic sequences, a parallel sequence A(p+r) generated by parallel-positioning p+r partial symbolic sequences, and parallel sequences generated by parallel-positioning similar increasing numbers of partial symbolic sequences. A regularity of period length α appears remarkably in a parallel sequence A(α) formed by parallel-positioning of k (=α) partial symbolic sequences. Therefore, a characteristic or regularity of unknown period length is manifested, and recognition of the characteristic or regularity becomes easy. 
     According to this method, even if the period length α of regularity or characteristic exists between p, p+r, p+2r, . . . rows, the characteristic or regularity is manifested in a parallel sequence formed by parallel-positioning partial sequences of a number approximately equal to α, and increment r is not necessarily required to be one. Therefore, the characteristic may be manifested using small amounts of data processing by selecting increment r according to the particular situation. 
     Further, by outputting the analyzed results using color and/or sound, expressions suitable for the particular situation and observer become possible, and the characteristic can be more easily recognized. The resulting color and/or sound pattern will be an interesting pattern in which regularity and irregularity are mixed, and the present method also can be utilized as a designing method. 
     In particular, when the initiation point of regularity is situated at an analysis initiation position, a pattern having a parabolic shape clearly appears, and a regularity having a long period length is manifested clearly, within the set of parallel sequences ΣA(k). 
     The present invention will be recognized more successfully by reading the descriptions of the following examples with reference to the drawings. 
    
    
     
       BRIEF EXPLANATION OF THE DRAWINGS 
         FIG. 1  shows a set of parallel sequences ΣA(k) generated from a nucleotide sequence of human genomic DNA. 
         FIG. 2  depicts the positional relationship of suffix j in FIG.  1 . 
         FIG. 3  shows a set of parallel sequences ΣA(k) generated from a numerical sequence π. 
         FIG. 4  shows a set of parallel sequences ΣA(k) generated from a circulating numerical sequence having a period length of 18 (symbolic sequence). 
         FIG. 5  shows a set of parallel sequences ΣA(k) generated from a circulating numerical sequence having a period length of 12 (symbolic sequence). 
         FIG. 6  shows a portion of the set of parallel sequences ΣA(k) generated from the amino acid sequence of the muscle protein myosin. 
         FIG. 7  shows another portion of the set of parallel sequences ΣA(k) generated from the amino acid sequence of the muscle protein myosin. 
         FIG. 8  shows another portion of the set of parallel sequences ΣA(k) generated from the amino acid sequence of the muscle protein myosin. 
         FIG. 9  shows the positions of the vowel ‘O’ appearing in ‘Genji Monogatari’. 
         FIG. 10  depicts the conversion of a symbolic sequence having 100 symbols into a set of parallel sequences ΣA(k). 
         FIG. 11  explains pre-treatments for symbolic sequences. 
         FIG. 12  depicts another example of converting a symbolic sequence into a set of parallel sequences ΣA(k). 
         FIG. 13  shows a set of parallel sequences ΣA(k) generated from the cDNA sequence of a G protein β subunit. 
         FIG. 14  represents extraction of symbolic sequence I from a symbolic sequence M by changing the initial point. 
         FIG. 15  shows an example in which a parabolic pattern appears in the set of parallel sequences ΣA(k) generated from a genomic DNA sequence of baker&#39;s yeast. 
         FIG. 16  shows another positioning (reciprocal) pattern for generating a parallel sequence A(k). 
         FIG. 17  shows a set of parallel sequences ΣA(k) generated from a circulating sequence having a period length of 100. 
         FIG. 18  represents an apparatus for performing the methods of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Experimental examples embodying the present invention will be described below. 
       FIG. 1  represents an experimental example for processing a symbolic sequence I j  that represents a nucleotide sequence of human genomic DNA. A symbolic sequence I j  representing the nucleotide sequence of human genomic DNA is typically represented as a one-dimensional sequence of an enormous number of symbols, each symbol indicating one of the four types of nucleotides (i.e., ATGC), and a certain regularity hidden therein is recognized as useful information. Therefore, it is an important object of genetic study to find regularity, or to identify a portion of the sequence that includes the regularity. 
       FIG. 1  represents a processed result output using color, and the four types of symbols (ATGC) are, respectively, expressed by four different colors, i.e., red, blue, green and yellow. Thus,  FIG. 1  is expressed using four colors. Further,  FIG. 1  represents the result when the present method is performed using the parameters of p=5 and r=1. 
     An example of a parallel sequence A( 17 ) in which k=17 is shown in  FIG. 2 , in which longitudinal partial symbolic sequences C 1 , C 2 , C 3  . . . C 17  are extracted from a symbolic sequence I j  at every k and aligned longitudinally. Then, the longitudinal sequences are laterally aligned to form a parallel sequence A( 17 ). In columns C 1 , C 2 , C 3  . . . , the values of symbol suffixes j that will be extracted are shifted by one. This rule is common to all k values and to all partial symbolic sequences C. 
     In this example, a symbol group extracted at every k is placed longitudinally (i.e., in columns) to form a longitudinal partial symbolic sequence, and the longitudinal partial symbolic sequences are laterally placed. However, the longitudinal to lateral relationship may be reversed, and a symbol group extracted at every k may be placed laterally to form a lateral partial symbolic sequence, and the lateral partial symbolic sequences may be longitudinally placed. 
     In  FIG. 1 , B 16  remarkably shows that a repeating pattern having a period length of 16 exists in a portion of the nucleotide sequence. Based upon the pattern B 16 , one can learn that there is a possibility that useful information exists in this portion, and this portion is an area that is valuable for detailed analysis. B 17  and B 16  represent the same regularity. The regularity of period length 16 appears as vertical stripes in B 16 , and appears as inclined stripes in B 17 . The inclined stripes in B 17  form a pattern that declines towards the left side. B 18  also represents the same regularity, and the inclination of the stripes in B 18  is closer to horizontal than in B 17 . The same regularity is also shown in a parallel sequence A( 19 ) in which k=19. However, in this case, the inclination is almost horizontal, and extraction of characteristic becomes increasingly difficult. 
     Regularity of period length α appears vertically and is expressed most remarkably in A(α) in which k (=α) partial symbolic sequences are parallel-positioned. However, the regularity also appears in a parallel sequence of partial symbolic sequences in which k=α+1 and k=α+2. Therefore, it is confirmed that the increment r is not necessarily required to be 1. 
     A 18  shows regularity of period length 18, and the same regularity is shown as pattern A 17  and the parallel sequence A( 17 ) in which k=17 declines towards the rights side, and shown as pattern A 19  and the parallel sequence A( 19 ) in which k=19 declines towards the left side. 
     In addition, many remarkable patterns appear in  FIG. 1 , and characteristics hidden in a nucleotide sequence of human genomic DNA can be recognized from these patterns. 
     The initial number p in the set of parallel sequences of partial symbolic sequences may be any natural number, and in  FIG. 1 , p=5. The increment r is not limited to 1, and it may be 2 or more. When r is smaller, characteristics always can be found, and when r is larger, data processing is reduced. The increment r is not required to be constant, and it is preferable to select the increment r according to the particular situation. 
       FIG. 18  represents an apparatus for performing the above-described processing method, and in this apparatus, a symbolic sequence I j  that will be analyzed is stored in memory apparatus  181 . Apparatus  182  converts the symbolic sequence Ij into a parallel sequence A(k), apparatus  183  generates the set of parallel sequences ΣA(k) in which a plurality of parallel sequences A(k) obtained by changing the value of k are parallel-positioned, and apparatus  184  outputs the set of parallel sequences ΣA(k). Apparatus  182  and  183  may be a computer and apparatus  184  may be a color printer. When the set of parallel sequences ΣA(k) is output using sound, a sound synthesizer may be used as apparatus  184 . 
       FIG. 1  is preferably expressed with a time lapse according to processing speed of the symbolic sequence. For example in  FIG. 1 , color corresponding to I 1  is first expressed on the left upper summits of A( 5 ) to A( 21 ), and the further expressions of I 2 , I 3 , I 4  . . . are effected in succession. By using this change in time, characteristics are more easily recognized, and also in the case of output by sound, output with a time lapse is effective. When output with a time lapse is conducted, characteristics are recognized using the changes in sound. 
       FIG. 3  exemplifies a result obtained by processing the symbolic sequence of π(i.e., the numerical sequence), and the 10 symbols (i.e., numbers  0  to  9 ) are expressed using 10 equally divided colors within the spectrum from a violet to red.  FIG. 3  shows that specific symbols (numbers) tend to appear frequently within a specific range. 
     When noise input is processed as a row of a symbolic sequence and this symbolic sequence is processed to obtain a similar pattern as in  FIG. 3 , it becomes possible to extract a characteristic existing in the noise and to extract only meaningful sound included in the noise. Further, it is known that the pattern shown in  FIG. 3  can be used, for example, as a ground pattern for securities, and this complicated ground pattern can be specified by a one-dimensional symbolic sequence. 
       FIG. 4  represents a result obtained by processing a circulating numerical sequence of period length 18, and various patterns can be drawn according to the number k of a partial symbolic sequences to be fractionated. Various textile patterns can be designed by this pattern creating technology.  FIG. 5  represents a processed result of a circulating numerical sequence of period length  12 , and it is confirmed that different patterns from those of  FIG. 4  can be made. According to this method, the complicated pattern shown in FIG.  3  and the regular patterns shown in  FIGS. 4 and 5  can be designed by the same method. Further, various patterns that impart completely different impressions can be produced by changing the corresponding relationships of symbols and colors. 
       FIGS. 6 through 8  represent results obtained by processing a symbolic sequence which shows an amino acid sequence of a protein myosin of an adductor muscle of a scallop. In  FIGS. 6  to  8 , basic residues are shown in blue, polar residues are shown in green, acidic residues are shown in red, and hydrophobic residues are shown in yellow. In  FIG. 6 , a remarkable yellow longitudinal stripe appears in a parallel sequence in which k=7, and the existence of regularity having a period length of 7 was found. This regularity of hydrophobic residues having a period length of 7 corresponds to an α-helix, and by this method, the existence of an α-helix can be recognized and the existing position thereof can be identified. This α-helix is manifested as yellow longitudinal stripes in the parallel sequences in which k=7, 14, 28 and 35, and is manifested as yellow diagonal lines in the parallel sequences in which, for example, k=22, 27 and 29. 
       FIG. 9  represents an example expressing dots in positions where the vowel ‘O’ appears in the novel Genji Monogatari, and was prepared by applying the present method to a symbolic sequence of a row of vowels. The left side represents the analysis result of the chapter entitled Kiritsubo, and the right side represents the analysis result of the chapter entitled Hahakigi. There is manifested a characteristic that appears at a high frequency for the vowel ‘O’ within this specific portion of the document, and as low in other specific portions. By this method, extraction of characteristics in alphabet information becomes easy. 
       FIG. 10  schematically represents processing contents of a symbolic sequence I j  (j=1 to 100). 
     When the period length of regularity to be extracted is known in advance, it will be easily recognized whether the regularity of the known period length k really exists, and in the case of existence, where it exists, by generating a parallel sequence A(k) in which partial symbolic sequences obtained by division into k fractions are parallel-positioned. 
     Even when the period length is not known, the regularity of the unknown period length is manifested at some location in the set of parallel sequences. 
       FIG. 11  represents an example of pre-processing for a symbolic sequence that will be processed. When the portion of the symbolic sequence J shown under (A) is processed, the part shown under (B) will be the entire symbolic sequence I according to the present method. Further, when one symbol is specified by a combination of a plurality of symbols, this method is applied for the symbolic sequence identified by the combination of a plurality of symbols, for example, as shown in (C). In the alternative, one symbol can be obtained from symbols of order  123  in a symbolic sequence K. Then, one symbol can be obtained from symbols of order  234  in a symbolic sequence K, This procedure is repeated to effect conversion into one symbolic sequence I, and converted symbol I is processed using the present method, such as in the case of calculating a moving average. Further, as shown in (E), for a symbolic sequence existing in a symbolic sequence at specific period, a symbolic sequence of this period can first be extracted, and the present method is then applied to the extracted symbolic sequence. 
     Instead of this method, processing as exemplified in  FIG. 12  may be effected. In this method, one symbol is extracted at every kq for a partial symbolic sequence of longitudinal direction. In the case shown in this drawing, the result is obtained by effecting the method and changing k to  2 ,  3 ,  4  . . . and q is fixed at  5 . This result corresponds to the same result when a symbol of an order of  5 · 10 · 15  . . . is first extracted The extracted sequence is then separated into k partial symbolic sequences, and the resulting partial sequences are parallel-positioned to generate a parallel sequence. By this method, it is possible to manifest regularity further hidden in a symbolic sequence that is hidden in a symbolic sequence L (shown in (E) of FIG.  11 ). 
     When a set of parallel sequences of partial symbolic sequences is generated as described above, various methods can be utilized to express the result. For example, the symbol may be expressed by color, the symbol may be expressed by variations in color density and the symbol may be expressed by a character (two dimensional pattern). Further, the resulting lines and rows of symbols may also be expressed by sound. In this case, a chord is formed by an arrangement of symbols along the line direction, and an arrangement in a row direction is expressed by changing this chord over time. By this procedure, it becomes possible to recognize a characteristic existing in a symbolic sequence using sound. 
     The present invention is useful for analyzing various symbolic sequences, and useful for analyzing a nucleotide sequence of DNA, a nucleotide sequence of RNA, an amino acid sequence of a protein, a numerical sequence, an alphabet sequence, a sound sequence and the like. By this analysis, it becomes possible to identify an existing position of useful information and to extract useful information. Further, when this method is applied to two symbolic sequences, which can not be distinguished at a glance, characteristics are manifested, and the identity can be easily determined. In this sense, characteristics and regularity manifested using this method are not restricted to a repeating pattern having a certain period, and characteristics found in a distribution of appearing sequence are also manifested. Further, the increment r in the number of partial symbolic sequences is not necessarily required to be 1, and further, it is not required to be a constant number. By effecting this method according to k 1 , k 2 , k 3  . . . distributing irregularly, characteristics existing in two or more symbolic sequences are manifested, and the identity is easily determined. 
       FIG. 13  represents the analysis result of a cDNA sequence of a G protein β subunit, and represents the result when the set of parallel sequences ΣA(k) is generated by setting p equal to 5. In  FIG. 13 , GCTA are expressed by 4 colors and three different color zones are apparent. 
     The boundary  101  of the color zones corresponds approximately to the position of j=281, and the boundary  102  of the color zones corresponds approximately to the position of j=1303. In this case, it is known that a coding range exists within the range from j=281 to j=1303, and it is recognized that the coding range is easily identified using visual means in this method. 
       FIG. 14  represents a procedure for generating a symbolic sequence I from a one-dimensional symbolic sequence M by changing the initial point. For example, symbolic sequence  16  to be processed is a symbolic sequence obtained by extraction of M( 6 ) and the following. 
     When the present invention is performed on symbolic sequences I 1 , I 2 , I 3 , I 4  . . . thus extracted in order to generate the set of parallel sequences ΣA(k), a clear pattern may be visualized in the set of parallel sequences ΣA(k) corresponding to a specific I. 
       FIG. 15  represents one example thereof, in which a plurality of parabolic lines  151 ,  152 ,  153  . . . appear. 
     As a result of intensive study of this phenomenon, it has been recognized that the above-described line group appears when the initiation point of regularity coincides with the initiation point of the symbolic sequence to be processed. Consequently, it has been determined that the initiation point of regularity can be identified by utilizing the appearance of a line group. 
     Further, it was also determined that the appearance gap of a group of lines  151 ,  152 ,  153  . . . and other group of lines  161 ,  162 ,  163  . . . corresponds to regularity of an extremely long period, and it has also been recognized that the regularity of an extremely long period can be recognized by utilizing a line group. 
     It has been recognized that the above-described pattern also appears by alternately reversing the sequential direction of the partial symbolic sequences in a lateral direction (reciprocal positioning pattern).  FIG. 16  represents a positional relationship for generating parallel sequences A(k) by alternately reversing the sequential direction of the partial symbolic sequences along the lateral direction.  FIG. 17  represents an example in which a circulating sequence having a period of 100 is converted into a set of parallel sequences ΣA(k) having the positional relationship as shown in  FIG. 16 , and a clear line group appeared. 
     The above-described explanations are only some specific examples and the present invention can be used in various ways within the attached claims.