Dynamic uniqueness for stochastic chains with unbounded memory

Christophe Gallesco, Sandro Gallo and Daniel Y. Takahashi

We say that a probability kernel exhibits dynamic uniqueness (DU) if all the stochastic chains starting from a fixed past coincide on the future tail σ-algebra. Our first theorem is a set of properties that are pairwise equivalent to DU which allow us to understand how it compares to other more classical concepts. In particular, we prove that DU is equivalent to a weak-ℓ2 summability condition on the kernel. As a corollary to this theorem, we prove that the Bramson–Kalikow and the long-range Ising models both exhibit DU if and only if their kernels are ℓ2 summable. Finally, if we weaken the condition for DU, asking for coincidence on the future σ-algebra for almost every pair of pasts, we obtain a condition that is equivalent to β-mixing (weak-Bernoullicity) of the compatible stationary chain. As a consequence, we show that a modification of the weak-ℓ2 summability condition on the kernel is equivalent to the β-mixing of the compatible stationary chain.

Post-class naps boost declarative learning in a naturalistic school setting

Thiago Cabral, Natália B. Mota, Lucia Fraga, Mauro Copelli, Mark A. McDaniel and Sidarta Ribeiro

Laboratory evidence of a positive effect of sleep on declarative memory consolidation suggests that naps can be used to boost school learning in a scalable, low-cost manner. The few direct investigations of this hypothesis have so far upheld it, but departed from the naturalistic setting by testing non-curricular contents presented by experimenters instead of teachers. Furthermore, nap and non-nap groups were composed of different children. Here we assessed the effect of post-class naps on the retention of Science and History curricular contents presented by the regular class teacher to 24 students from 5th grade. Retention was repeatedly measured 3–4 days after content learning, with weekly group randomization over 6 consecutive weeks. Contents followed by long naps (>30 min), but not short naps (

Open Science: a NeuroMat video

The NeuroMat scientific dissemination has recently launched another short movie, this time on "open science", the movement to make scientific research, data and dissemination accessible to all levels of an inquiring society, amateur or professional. The video was supported by FAPESP and it also presents RIDC NeuroMat commitment to open science best practices.

The anguish of the mathematician Ludwig Boltzmann - pt 2

The third post by RIDC NeuroMat director, Antonio Galves, at the blog on Science and Mathematics at O Globo was also out this month. It is the second of a series on the laws of thermodynamics and Ludwig Boltzmann.O Globo website, 08/2018. (In Portuguese.)

Potentializing a new generation of NeuroMat researchers

The Research, Innovation and Dissemination Center for Neuromathematics (RIDC NeuroMat) has contributed decisively to the onset of a new generation of researchers. Fifty-five young researchers have been trained at NeuroMat since its inception, in 2013




O Centro de Pesquisa, Inovação e Difusão em Neuromatemática está sediado na Universidade de São Paulo e é financiado pela FAPESP (Fundação de Amparo à Pesquisa do Estado de São Paulo).


Login do usuário



Rua do Matão, 1010 - Cidade Universitária - São Paulo - SP - Brasil. 05508-090. Veja o mapa.

55 11 3091-1717


Contatos de mídia: