Slow manifolds within network dynamics encode working memory efficiently and robustly

Working memory is a cognitive function involving the storage and manipulation of latent information over brief intervals of time, thus making it crucial for context-dependent computation. Here, we use a top-down modeling approach to examine network-level mechanisms of working memory, an enigmatic issue and central topic of study in neuroscience. We optimize thousands of recurrent rate-based neural networks on a working memory task and then perform dynamical systems analysis on the ensuing optimized networks, wherein we find that four distinct dynamical mechanisms can emerge. In particular, we show the prevalence of a mechanism in which memories are encoded along slow stable manifolds in the network state space, leading to a phasic neuronal activation profile during memory periods. In contrast to mechanisms in which memories are directly encoded at stable attractors, these networks naturally forget stimuli over time. Despite this seeming functional disadvantage, they are more efficient in terms of how they leverage their attractor landscape and paradoxically, are considerably more robust to noise. Our results provide new hypotheses regarding how working memory function may be encoded within the dynamics of neural circuits.

Phase Space Analysis and Thermodynamics of Interacting Umami Chaplygin Gas in FRW Universe

In this work interacting Umami Chaplygin gas has been studied in flat FRW model of universe in context of it’s thermodynamic and dynamical behaviour. In particular, considering Umami fluid as dark energy interacting with dark matter, irreversible thermodynamics has been studied both for apparent and event horizon as bounding horizon in two separate cases. Also the model has been investigated in purview of dynamical systems analysis by converting the cosmological evolution equations to an autonomous system of ordinary differential equations. With some restrictions on model parameter $$\omega $$ ω and coupling parameter $$\lambda $$ λ , some cosmologically interesting critical points describing late time accelerated evolution of the universe attracted by cosmological constant and accelerated scaling attractor in quintessence era have been found to alleviate coincidence problem.

Pathways connecting the North Brazil Current and the RAPID line

<p>The North Brazil Current is considered a bottleneck in the South Atlantic, responsible for funneling upper-ocean waters into the North Atlantic. This work explores the surface and subsurface pathways that connect the North Brazil Current to the RAPID line. To that extent, observational trajectories from surface drifters and Argo floats are used in conjunction with Markov chain theory and tools from dynamical systems analysis to compute probable pathways. More specifically, these pathways are computed as ensembles of paths transitioning directly between the North Brazil Current and the RAPID line. In addition, simulated trajectories will be used (1) to assess how representative the two-dimensional observational trajectories are of the three-dimensional circulation, and (2) to compute the associated volume transport of different pathways. Preliminary results suggest that two dominant pathways connect the North Brazil Current and the RAPID line. First, is the traditional pathway through the Caribbean Sea and Gulf of Mexico, which carries waters to the Florida Current, and second is a more direct route east of the Caribbean that supplies waters to the Antilles Current and the basin interior.  </p>

Walking droplets through the lens of dynamical systems

Over the past decade the study of fluidic droplets bouncing and skipping (or “walking”) on a vibrating fluid bath has gone from an interesting experiment to a vibrant research field. The field exhibits challenging fluids problems, potential connections with quantum mechanics, and complex nonlinear dynamics. We detail advancements in the field of walking droplets through the lens of Dynamical Systems Theory, and outline questions that can be answered using dynamical systems analysis. The paper begins by discussing the history of the fluidic experiments and their resemblance to quantum experiments. With this physics backdrop, we paint a portrait of the complex nonlinear dynamics present in physical models of various walking droplet systems. Naturally, these investigations lead to even more questions, and some unsolved problems that are bound to benefit from rigorous Dynamical Systems Analysis are outlined.