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In an effort to continue the pioneering work of Harary in USA and Flament in France, we have undertaken to develop, on an experimental basis, a formalized theory of systems of beliefs and their modifications. This theory uses the psycho-social concepts of theories of cognitive consistency and of the tools of discrete mathematics, such as rewriting and intervals within graphs. The axioms and rewriting rules are elaborated from experimental data, and we demonstrate that the system we have built has the property of termination. This result is in accordance with experimental observations that show that every subject having an inconsistent system of beliefs (i.e., one containing contradictions) makes this system evolve towards consistency to reach a simple, consistent reference framework.

Introduction: Despite extensive testing, the efficacy of low-frequency (1 Hz) repetitive transcranial magnetic stimulation (rTMS) of temporo-parietal targets for the treatment of auditory verbal hallucinations (AVH) in patients with schizophrenia is still controversial, but promising results have been reported with both high-frequency and neuronavigated rTMS. Here, we report a double-blind sham-controlled study to assess the efficacy of high-frequency (20 Hz) rTMS applied over a precise anatomical site in the left temporal region using neuronavigation., Methods: Fifty-nine of 74 randomized patients with schizophrenia or schizoaffective disorders (DSM-IV R) were treated with rTMS or sham treatment and fully evaluated over 4 weeks. The rTMS target was determined by morphological MRI at the crossing between the projection of the ascending branch of the left lateral sulcus and the superior temporal sulcus (STS)., Results: The primary outcome was response to treatment, defined as a 30% decrease of the Auditory Hallucinations Rating Scale (AHRS) frequency item, observed at 2 successive evaluations. While there was no difference in primary outcome between the treatment groups, the percentages of patients showing a decrease of more than 30% of AHRS score (secondary outcome) did differ between the active (34.6%) and sham groups (9.1%) (P = .016) at day 14., Discussion: This controlled study reports negative results on the primary outcome but demonstrates a transient effect of 20 Hz rTMS guided by neuronavigation and targeted on an accurate anatomical site for the treatment of AVHs in schizophrenia patients.