Schizophrenic speech as a disordered trajectory in a collapsed cognitive 'Small-World'

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.