Implicit in the RNA world hypothesis is that prebiotic RNA synthesis, despite occurring in an environment without biochemical catalysts, produced the long RNA polymers which are essential to the formation of life. In order to investigate the prebiotic formation of long RNA polymers, we consider a general solution of functionally identical monomer units that are capable of bonding to form linear polymers by a step-growth process. Under the assumptions that (1) the solution is well-mixed and (2) bonding/unbonding rates are independent of polymerization state, the concentration of each length of polymer follows the geometric Flory-Schulz distribution. We consider the rate dynamics that produce this equilibrium; connect the rate dynamics, Gibbs free energy of bond formation, and the bonding probability; solve the dynamics in closed form for the representative special case of a Flory-Schulz initial condition; and demonstrate the effects of imposing a maximum polymer length. Afterwards, we derive a lower bound on the error introduced by truncation and compare this lower bound to the actual error found in our simulation. Finally, we suggest methods to connect these theoretical predictions to experimental results.

As one of the most complex systems known to science, modeling brain behavior and function is both fascinating and extremely difficult. Empirical data is increasingly available from ex vivo human brain organoids and surgical samples, as well as in vivo animal models, so the problem of modeling the behavior of large-scale neuronal systems is more relevant than ever. The statistical physics concept of a mean-field model offers a tractable way to bridge the gap between single-neuron and population-level descriptions of neuronal activity, by modeling the behavior of a single representative neuron and extending this to the population. However, existing neural mean-field methods typically either take the limit of small interaction sizes, or are applicable only to the specific neuron models for which they were derived. This paper derives a mean-field model by fitting a transfer function called Refractory SoftPlus, which is simple yet applicable to a broad variety of neuron types. The transfer function is fitted numerically to simulated spike time data, and is entirely agnostic to the underlying neuronal dynamics. The resulting mean-field model predicts the response of a network of randomly connected neurons to a time-varying external stimulus with a high degree of accuracy. Furthermore, it enables an accurate approximate bifurcation analysis as a function of the level of recurrent input. This model does not assume large presynaptic rates or small postsynaptic potential size, allowing mean-field models to be developed even for populations with large interaction terms.

Origami structures have made significant contributions to the field of robotics, offering various advantages. One such advantage is their ability to conserve space by transforming the structure into a compact form. Additionally, many origami structures can be fabricated in a flat state to simplify manufacturing, giving them the potential for large-scale and cost-effective production. Rotational joints play a crucial role in the construction of robotic systems, yet origami rotational joints can suffer from a limited range of motion. We previously theoretically proposed the Self-Lock Joint to address this issue, but it is only partially flat-foldable. This paper presents a novel approach to the 3D printing of modular origami joints, such as the Self-Lock Joint, using 3D-printed plates joined with a fabric layer. The compliance of the fabric can improve the joints semi flat-foldability or even enable it to achieve complete flat-foldability. Furthermore, the rotational motion of the joint is enhanced, allowing for close to 360 degrees of rotational movement. We assess the physical properties of the joint under both loaded and unloaded conditions in order to identify design trade-offs in the physical properties of the joints. Moreover, as a proof of concept, we construct and demonstrate manipulators utilizing these joints. The increase in rotational movement enabled by this fabrication method, coupled with the compliant joints flat-foldability and modular nature, make it a promising candidate for use in a wide range of applications.

We propose a modular architecture for neuromorphic closed-loop control based on bistable relaxation oscillator modules consisting of three spiking neurons each. Like its biological prototypes, this basic component is robust to parameter variation but can be modulated by external inputs. By combining these modules, we can construct a neural state machine capable of generating the cyclic or repetitive behaviors necessary for legged locomotion. A concrete case study for the approach is provided by a modular robot constructed from flexible plastic volumetric pixels, in which we produce a forward crawling gait entrained to the natural frequency of the robot by a minimal system of twelve neurons organized into four modules.