The brain exhibits capabilities of fast incremental learning from few noisy examples, as well as the ability to associate similar memories in autonomously-created categories and to combine contextual hints with sensory perceptions. Together with sleep, these mechanisms are thought to be key components of many high-level cognitive functions. Yet, little is known about the underlying processes and the specific roles of different brain states. In this work, we exploited the combination of context and perception in a thalamo-cortical model based on a soft winner-take-all circuit of excitatory and inhibitory spiking neurons. After calibrating this model to express awake and deep-sleep states with features comparable with biological measures, we demonstrate the model capability of fast incremental learning from few examples, its resilience when proposed with noisy perceptions and contextual signals, and an improvement in visual classification after sleep due to induced synaptic homeostasis and association of similar memories.

Depleted metals have been produced since many centuries ago. Probably the most famous examples from ancient times are the so-called Tumbaga gold artifacts, whose production was introduced by the pre-Colombian civilizations. Tumbaga-like structures have been identified also in modern nanotechnological materials. In both cases, but specially for the ancient Tumbaga, due to their preciousness, their characterization should be obtained by non-destructive analysis. Several analytical protocols have been developed, some of them non-destructive, such as those based on X-ray Fluorescence, but the results obtained do not always allow for a reliable identification of Tumbaga with respect to gilding or single alloy samples. Besides the capability to distinguish between different structures of the sample, it is also important to obtain a quantitative estimation of its composition. In order to meet this demand, a new approach based on X-ray Fluorescence coupled to Monte Carlo simulations is proposed. It allows one to distinguish easily between the three manufacturing techniques and to quantify the composition of the sample without any destructive sampling. It constitutes a new tool for the study of complex alloy structures. The protocol is applied here to some ancient Tumbaga gold samples and is described in detail, comparing the results to those obtained with other techniques.

In this paper we consider some nodal solutions of the H\'enon problem in the unit disc with Dirichlet boundary conditions and we show that they are quasiradial, that is to say they are nonradial, they have two nodal regions and their nodal line does not touch the boundary of the disc.