title: Symmetrical treatment of "Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition", for major depressive disorders.
abstract: BACKGROUND
  We previously presented a group theoretical model that describes psychiatric patient states or clinical data in a graded vector-like format based on modulo groups. Meanwhile, the Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition (DSM-5, the current version), is frequently used for diagnosis in daily psychiatric treatments and biological research. The diagnostic criteria of DSM-5 contain simple binominal items relating to the presence or absence of specific symptoms. In spite of its simple form, the practical structure of the DSM-5 system is not sufficiently systemized for data to be treated in a more rationally sophisticated way. To view the disease states in terms of symmetry in the manner of abstract algebra is considered important for the future systematization of clinical medicine.
  
  
  RESULTS
  We provide a simple idea for the practical treatment of the psychiatric diagnosis/score of DSM-5 using depressive symptoms in line with our previously proposed method. An expression is given employing modulo-2 and -7 arithmetic (in particular, additive group theory) for Criterion A of a 'major depressive episode' that must be met for the diagnosis of 'major depressive disorder' in DSM-5. For this purpose, the novel concept of an imaginary value 0 that can be recognized as an explicit 0 or implicit 0 was introduced to compose the model. The zeros allow the incorporation or deletion of an item between any other symptoms if they are ordered appropriately. Optionally, a vector-like expression can be used to rate/select only specific items when modifying the criterion/scale. Simple examples are illustrated concretely.
  
  
  CONCLUSIONS
  Further development of the proposed method for the criteria/scale of a disease is expected to raise the level of formalism of clinical medicine to that of other fields of natural science.
authors.affiliation: Department of Psychiatry, Tokyo Women's Medical University, Tokyo, Japan.
authors.forename: Jitsuki
authors.initials: J
authors.lastname: Sawamura
authors.affiliation: Depression Prevention Medical Center, Inariyama Takeda Hospital, Kyoto, Japan.
authors.forename: Shigeru
authors.initials: S
authors.lastname: Morishita
authors.affiliation: Department of Psychiatry, Tokyo Women's Medical University, Tokyo, Japan.
authors.forename: Jun
authors.initials: J
authors.lastname: Ishigooka
keywords: Abstract algebra; Criterion; DSM-5; Depression; Diagnosis; Upgrading