It has been hypothesized that a Theory of Mind (ToM) deficit could be a vulnerability marker for psychosis. Recent studies, however, have shown ToM deficits in affective relapses of bipolar disorder as well as in the euthymic phase. This study analyzes the relationship between ToM and a previous history of psychotic symptoms in bipolar disorder. ToM,… (More)
A scheme for solving Whitham hierarchies satisfying a special class of string equations is presented. The τ-function of the corresponding solutions is obtained and the differential expressions of the underlying Virasoro constraints are characterized. Illustrative examples of exact solutions of Whitham hierarchies are derived and applications to conformal… (More)
Solutions of the Riemann-Hilbert problem implementing the twisto-rial structure of the dispersionless Toda (dToda) hierarchy are obtained. Two types of string equations are considered which characterize solutions arising in hodograph sectors and integrable structures of two-dimensional quantum gravity and Laplacian growth problems.
We show that the quantum field theoretical formulation of the τ-function theory has a geometrical interpretation within the classical transformation theory of conjugate nets. In particular, we prove that i) the partial charge transformations preserving the neutral sector are Laplace transformations, ii) the basic vertex operators are Lévy and adjoint Lévy… (More)
A class of exact solutions of the dispersionless Toda hierarchy constrained by a string equation is obtained. These solutions represent deformations of analytic curves with a finite number of nonzero harmonic moments. The corresponding τ-functions are determined and the emergence of cusps is studied.
A scheme for solving quasiclassical string equations is developped to prove that genus-zero Whitham hierarchies describe the deformations of planar domains determined by rational conformal maps. This property is applied in normal matrix models to show that deformations of simply-connected supports of eigenvalues under changes of coupling constants are… (More)
In this work we derive potential symmetries for ordinary differential equations. By using these potential symmetries we find that the order of the ODE can be reduced even if this equation does not admit point symmetries. Moreover, in the case for which the ODE admits a group of point symmetries, we find that the potential symmetries allow us to perform… (More)
A ¯ ∂-formalism for studying dispersionless integrable hierarchies is applied to the dKP hierarchy. Connections with the theory of qua-siconformal mappings on the plane are described and some clases of explicit solutions of the dKP hierarchy are presented.
Critical points of semiclassical expansions of solutions to the dispersionful Toda hierarchy are considered and a double scaling limit method of regularization is formulated. The analogues of the critical points characterized by the strong conditions in the Hermitian matrix model are analyzed and the property of doubling of equations is proved. A wide… (More)
It is proved that the system of string equations of the dispersionless 2-Toda hierarchy which arises in the planar limit of the hermitian matrix model also underlies certain processes in Hele-Shaw flows.