Bayesian reasoning with emotional material in patients with schizophrenia.

Delusions are one of the most classical symptoms described in schizophrenia. However, despite delusions are often emotionally charged, they have been investigated using tasks involving non-affective material, such as the Beads task. In this study we compared 30 patients with schizophrenia experiencing delusions with 32 matched controls in their pattern of responses to two versions of the Beads task within a Bayesian framework. The two versions of the Beads task consisted of one emotional and one neutral, both with ratios of beads of 60:40 and 80:20, considered, respectively, as the “difficult” and “easy” variants of the task. Results indicate that patients showed a greater deviation from the normative model, especially in the 60:40 ratio, suggesting that more inaccurate probability estimations are more likely to occur under uncertainty conditions. Additionally, both patients and controls showed a greater deviation in the emotional version of the task, providing evidence of a reasoning bias modulated by the content of the stimuli. Finally, a positive correlation between patients’ deviation and delusional symptomatology was found. Impairments in the 60:40 ratio with emotional content was related to the amount of disruption in life caused by delusions. These results contribute to the understanding of how cognitive mechanisms interact with characteristics of the task (i.e., ambiguity and content) in the context of delusional thinking. These findings might be used to inform improved intervention programs in the domain of inferential reasoning.post-print700 K

Lagrangian Curves in a 4-dimensional affine symplectic space

Lagrangian curves in R4 entertain intriguing relationships with second order deformation of plane curves under the special affine group and null curves in a 3-dimensional Lorentzian space form. We provide a natural affine symplectic frame for Lagrangian curves. It allows us to classify La- grangrian curves with constant symplectic curvatures, to construct a class of Lagrangian tori in R4 and determine Lagrangian geodesic

Discrete moving frames on lattice varieties and lattice based multispace

In this paper, we develop the theory of the discrete moving frame in two different ways. In the first half of the paper, we consider a discrete moving frame defined on a lattice variety and the equivalence classes of global syzygies that result from the first fundamental group of the variety. In the second half, we consider the continuum limit of discrete moving frames as a local lattice coalesces to a point. To achieve a well-defined limit of discrete frames, we construct multispace, a generalization of the jet bundle that also generalizes Olver’s one dimensional construction. Using interpolation to provide coordinates, we prove that it is a manifold containing the usual jet bundle as a submanifold. We show that continuity of a multispace moving frame ensures that the discrete moving frame converges to a continuous one as lattices coalesce. The smooth frame is, at the same time, the restriction of the multispace frame to the embedded jet bundle. We prove further that the discrete invariants and syzygies approximate their smooth counterparts. In effect, a frame on multispace allows smooth frames and their discretisations to be studied simultaneously. In our last chapter we discuss two important applications, one to the discrete variational calculus, and the second to discrete integrable systems. Finally, in an appendix, we discuss a more general result concerning equicontinuous families of discretisations of moving frames, which are consistent with a smooth frame

Cell-autonomous role of Notch, an epidermal growth factor homologue, in sensory organ differentiation in Drosophila.

The gene Notch (N) codes for a transmembrane protein with an extracellular domain that has homologies to epidermal growth factors and an intracellular domain that could be involved in signal transduction. N null alleles cause the transformation of most epidermal cells into neuroblasts in central and peripheral nervous systems. Alleles of the same gene, called Abruptex (Ax), that map to the extracellular domain of N protein cause the absence of adult sensory organs. Both types of alleles show cell autonomy in mosaic analysis carried out in the last stages of the formation of adult sensory organs. The phenotypes are different: cells lacking N gene products differentiate as sensory organ mother cells early and as its neural sublineage later, whereas in the homozygous Ax condition epidermal cells do not enter the sensory organ mother cell pathway. The results indicate that N gene products act internally in the cell, probably as receptors of intercellular signals both in sensory organ mother cell singularization and in fate specification of its daughter cells. Ax mutations behave as an excess of N+ function in this signal transduction process. N proteins modified by these mutations act as constitutively activated