Schizophrenic speech as a disordered trajectory in a collapsed cognitive ‘‘Small-World’’ Eduardo Mizraji * , Juan C. Valle-Lisboa Grupo de Modelizacio ´n de Sistemas Cognitivos, Seccio ´n Biofı ´sica, Facultad de Ciencias, Universidad de la Repu ´blica, Montevideo, Uruguay Received 26 June 2006; accepted 7 July 2006 Summary New theoretical instruments, as goal-directed neural networks models and geometric representations based on semantic graphs, open new approaches for our understanding of the schizophrenic speech. The neuropathologic disorders of the schizophrenia can be simulated using neural models, and these models can eventually explain the origin of goal confusion and incoherence in the schizophrenic discourse trajectory. Moreover, these models are useful to evaluate the different hypothesis about the pathogenic mechanisms of the disease. At the same time, a geometric representation of the trajectory of the speech can be obtained from real data. Our conjecture is that a context-dependent graph can be constructed in order to explore if, when the disease became more severe, a transition from a quasi ordered graph to a nearly completely random graph occurs. Plausibly, there exists a wide region where the graph has the properties of a ‘‘small-world’’. This kind of analyses could be potentially carried out using data coming from the spontaneous speech of schizophrenic patients, and can help to evaluate the progress of the disease. At the same time, these geometrical representations could help to evaluate the effect of treatments.  c 2006 Elsevier Ltd. All rights reserved. Introduction The full understanding of a complex pathological process as Schizophrenia requires the harmonic connection between data coming from very differ- ent observation levels [10]. These levels run from the genetic mechanisms that partially program the neural connectivity to language production, passing through the neurochemistry of synaptic transmission, the development of different classes of neural memories and the generation of thought processes. Schizophrenic speech is an observable manifesta- tion of the complex pathophysiology of schizophre- nia, and its analysis provides us at the same time with diagnostic cues and the possibility to evaluate the therapeutic progresses [1,6]. Recent results in the theory of communication networks give new mathematical and geometric instruments to approach the problems involved in schizophrenic speech. The hypotheses described in what follows, is an attempt in that direction. 0306-9877/$ - see front matter  c 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.mehy.2006.07.014 * Corresponding author. Address: Seccio ´n Biofı ´sica, Facultad de Ciencias, UdelaR, Casilla de Correos 6695, Montevideo 11000, Uruguay. Tel.: +5982 525 86 18. E-mail addresses: mizraj@fcien.edu.uy (E. Mizraji), juancvl@fcien.edu.uy (J.C. Valle-Lisboa). Medical Hypotheses (2007) 68, 347–352 http://intl.elsevierhealth.com/journals/mehy