Hippocampal theta oscillations have been implicated in working memory and attentional process, which might be useful for the brain-machine interface (BMI). To further elucidate the properties of the hippocampal theta oscillations that can be used in BMI, we investigated hippocampal theta oscillations during a two-lever choice task. During the task body-restrained rats were trained with a food r...

The theta band oscillation in the hippocampus and medial entorhinal cortex carries a strong correlation with free movement throughout an environment. Recently several models of these oscillations and their relationship to spatially modulated cells in the hippocampus and entorhinal cortex have started to emerge. One area of focus in theta research has been how the speed of movement modulates the...

Abstract Given $$E_0, E_1, E, F$$ E 0 , 1 F rearrangement invariant spaces, $$a, \mathrm {b}, {b}_0, {b}_1$$ a b slowly varying functions and $$0\le \theta _0<...

In this paper, we introduce a new class of set-valued mappings which is called MD-type mappings. This class of mappings is a set-valued case of a class of the D-type mappings. The class of D-type mappings is a generalization of nonexpansive mappings that recently introduced by Kaewkhao and Sokhuma. The class of MD-type mappings includes upper semi-continuous Suzuki type mappings, upper semi-con...

Inspired by a question of Lovász, we introduce a hierarchy of nested semidefinite relaxations of the convex hull of real solutions to an arbitrary polynomial ideal, called theta bodies of the ideal. For the stable set problem in a graph, the first theta body in this hierarchy is exactly Lovász’s theta body of the graph. We prove that theta bodies are, up to closure, a version of Lasserre’s rela...

Inspired by a question of Lovász, we introduce a hierarchy of nested semidefinite relaxations of the convex hull of real solutions to an arbitrary polynomial ideal, called theta bodies of the ideal. For the stable set problem in a graph, the first theta body in this hierarchy is exactly Lovász’s theta body of the graph. We prove that theta bodies are, up to closure, a version of Lasserre’s rela...

Abstract The well-known $$\mathcal {E}$$ E -set introduced by Hayman in 1960 is a countable collection of Euclidean discs the complex plane, whose subtending angles at origin have finite sum. An important special case an known as R -set, for which sum diameters finite. These sets appear numerous papers theori...

The intermediate dimensions of a set $\Lambda$, elsewhere denoted by $\dim\_{\theta}\Lambda$, interpolate between its Hausdorff and box using the parameter $\theta\in\[0,1]$. For Bedford–McMullen carpet $\Lambda$ with distinct dimensions, we show that $\dim\_{\theta}\Lambda$ is strictly less than dimension for every $\theta<1$. Moreover, derivative upper bound positive at $\theta=1$. This answe...