Layer-specific population rate coding in a local cortical model with a laminar structure

Uncovering the principle of neural coding is essential for understanding how our mysterious brain works. Recent studies have reported the laminar differences of alpha-beta and gamma rhythms in the sensory cortex, yet it remains unclear about the underlying function role of frequency-dependent interlaminar interactions in neural coding. Using a rate-based network model to simulate the cortical laminar under the external time-varying stimuli, we showed that the physiological specificity of rhythms for layers enables the cortical laminae to preferentially encode information in different frequency ranges. The interplay of the supragranular layer and infragranular layer contributes significantly to improving the neural representation of external time-varying input at the population level. Further investigations revealed the essential role of recurrent connections of the cortical laminae in regulating the population rate coding. In particular, the laminar network optimally encodes the time-varying input at intermediate strengths of intralaminar excitatory–inhibitory circuits and interlaminar connections. Additionally, we verified the crucial role of adaptation in improving population coding by introducing slow dynamics and suppressing the noise-like excitatory activity in the laminar network. These findings highlight the crucial role of frequency-dependent interlaminar interactions in encoding time-varying stimuli and may shed light on the underlying function of cortical structural specificity in neural information processing.

     

The evolution dam problem for a compressible fluid with nonlinear Darcy's law and Dirichlet boundary condition

In this paper, we consider the evolution dam problem (P) related to a compressible fluid flow governed by a generalized nonlinear Darcy's law with Dirichlet boundary conditions on some part of the boundary. We establish existence of a solution for this problem. We choose a convenient regularized problem (P_?) for which we prove the existence and uniqueness of solution using the comparison Lemma 2.1 and the Schauder fixed‐point theorem. Then, we pass to the limit, when ? goes to 0, to get a solution for our problem. Moreover, we will see another approach for the incompressible case where we pass to the limit in (P), when α goes to 0, to get a solution.