STDP-based associative memory formation and retrieval.

Spike-timing-dependent plasticity (STDP) is a biological process in which the precise order and timing of neuronal spikes affect the degree of synaptic modification. While there has been numerous research focusing on the role of STDP in neural coding, the functional implications of STDP at the macroscopic level in the brain have not been fully explored yet. In this work, we propose a neurodynamical model based on STDP that renders storage and retrieval of a group of associative memories. We showed that the function of STDP at the macroscopic level is to form a "memory plane" in the neural state space which dynamically encodes high dimensional data. We derived the analytic relation between the input, the memory plane, and the induced macroscopic neural oscillations around the memory plane. Such plane produces a limit cycle in reaction to a similar memory cue, which can be used for retrieval of the original input.

An STDP-based encoding method for associative and composite data.

Spike-timing-dependent plasticity(STDP) is a biological process of synaptic modification caused by the difference of firing order and timing between neurons. One of neurodynamical roles of STDP is to form a macroscopic geometrical structure in the neuronal state space in response to a periodic input by Susman et al. (Nat. Commun. 10(1), 1-9 2019), Yoon, & Kim. Stdp-based associative memory formation and retrieval. arXiv:2107.02429v2 (2021). In this work, we propose a practical memory model based on STDP which can store and retrieve high dimensional associative data. The model combines STDP dynamics with an encoding scheme for distributed representations and is able to handle multiple composite data in a continuous manner. In the auto-associative memory task where a group of images are continuously streamed to the model, the images are successfully retrieved from an oscillating neural state whenever a proper cue is given. In the second task that deals with semantic memories embedded from sentences, the results show that words can recall multiple sentences simultaneously or one exclusively, depending on their grammatical relations.

PDE-guided reservoir computing for image denoising with small data.

While network-based techniques have shown outstanding performance in image denoising in the big data regime requiring massive datasets and expensive computation, mathematical understanding of their working principles is very limited. Not to mention, their relevance to traditional mathematical approaches has not attracted much attention. Therefore, we suggest how reservoir computing networks can be strengthened in combination with conventional partial differential equation (PDE) methods for image denoising, especially in the small data regime. Given image data, PDEs generate sequential datasets enhancing desired image features, which provide the network with a better guideline for training in reservoir computing. The proposed procedure, reservoir computing in collaboration with PDEs (RCPDE), offers a synergetic combination of data-driven network-based methods and mathematically well-established PDE methods. It turns out that RCPDE outperforms both the usual reservoir computing and existing PDE approaches in image denoising. Furthermore, RCPDE also excels deep neural networks such as a convolutional neural network both in quality and in time in the small data regime. We believe that RCPDE reveals the great potential of reservoir computing in collaboration with various mathematically justifiable dynamics for better performance as well as for better mathematical understanding.

Critical neuromorphic computing based on explosive synchronization.

Synchronous oscillations in neuronal ensembles have been proposed to provide a neural basis for the information processes in the brain. In this work, we present a neuromorphic computing algorithm based on oscillator synchronization in a critical regime. The algorithm uses the high-dimensional transient dynamics perturbed by an input and translates it into proper output stream. One of the benefits of adopting coupled phase oscillators as neuromorphic elements is that the synchrony among oscillators can be finely tuned at a critical state. Especially near a critical state, the marginally synchronized oscillators operate with high efficiency and maintain better computing performances. We also show that explosive synchronization that is induced from specific neuronal connectivity produces more improved and stable outputs. This work provides a systematic way to encode computing in a large size coupled oscillator, which may be useful in designing neuromorphic devices.

Recurrent synchronization of coupled oscillators with spontaneous phase reformation.

Self-organizing and spontaneous breaking are seemingly opposite phenomena and hardly captured in a single model. We develop a second order Kuramoto model with phase-induced damping which shows phase locking together with spontaneous synchrony breaking and reformation. In a relatively large regime where the interacting force and the damping ratio are of the same order, the dynamics of the oscillators alternates in an irregular cycle of synchronization, formation-breaking, and reorganization. While the oscillators keep coming back to phase-locked states, their phase distribution repeatedly reforms. Also, the interevent time between bursty deviation from the synchronization states follows a power-law distribution, which implies that the synchronized states are maintained near a tipping point.

Isolation and exploitation of minority: Game theoretical analysis.

We investigate various group-size distributions occurring in a situation where each group's resource is exposed to appropriation by other groups. The amount of appropriation depends on the size difference between groups. Our work focuses on the cases where the entire community isolates a small group or even an individual to maximize its gain. While people's basic motivation to form a group can be understood based on the group-size effect on multiplying a collective asset, sensitive factors that induce a asymmetric group distribution are the group efficiency and the ratio of secured assets to assets pending in a competition. We show that social rejection to a minor group may occur when the group efficiency is relatively low and their asset is severely exposed to possible appropriation.

Surfactant effects on droplet dynamics and deposition patterns: a lattice gas model.

A coarse-grained lattice gas model is developed to study pattern forming processes in drying drops containing surfactant. By performing Monte Carlo simulations of the model, the coupled dynamics of surfactant and liquid evaporation and the resulting oscillatory dynamics at the contact line are elucidated. We show that the coupled drop dynamics and the resulting final deposition patterns can be altered by adsorption kinetics. For slow adsorption rates, surfactant molecules recirculate along with colloidal particles and the area covered by the surfactant on the surface grows from the contact line as the initial concentration of the surfactant increases. This leads to coffee-ring patterns with wide rim areas upon drying or to multi-ring patterns depending on the surfactant concentration. For fast adsorption rates, a surfactant skin covers the entire surface area during the early phase of evaporation. This suppresses the coffee ring effect, and uniform patterns are obtained independent of surfactant concentration. The results suggest that the distribution of surfactant on the surface is critical in determining final deposition patterns and that understanding of the skin-forming process of the surfactant on the surface can help in manipulating the delicate pattern forming process of particles in evaporating drops.

Maximum Power Game as a Physical and Social Extension of Classical Games.

We consider an electric circuit in which the players participate as resistors and adjust their resistance in pursuit of individual maximum power. The maximum power game(MPG) becomes very complicated in a circuit which is indecomposable into serial/parallel components, yielding a nontrivial power distribution at equilibrium. Depending on the circuit topology, MPG covers a wide range of phenomena: from a social dilemma in which the whole group loses to a well-coordinated situation in which the individual pursuit of power promotes the collective outcomes. We also investigate a situation where each player in the circuit has an intrinsic heat waste. Interestingly, it is this individual inefficiency which can keep them from the collective failure in power generation. When coping with an efficient opponent with small intrinsic resistance, a rather inefficient player gets more power than efficient one. A circuit with multiple voltage inputs forms the network-based maximum power game. One of our major interests is to figure out, in what kind of the networks the pursuit for private power leads to greater total power. It turns out that the circuits with the scale-free structure is one of the good candidates which generates as much power as close to the possible maximum total.

A simple model of ostracism formation.

We study formation of ostracism in a society from a game theoretical perspective. The dynamics of group formation is complicated in that the choices of the individuals and the form of the groups mutually affect each other in the process. A suggested simple model shows that individual efforts to increase his/her own sense of belonging is responsible for both growth of groups and creation of an outcast. Once a person happens to get behind in synchronizing with others, tendency to alienate him may grow among others, possibly making him left out in the end. Alienating minority occurs even when there is a penalty for disliking and people are encouraged to favor others. Considering that the target is accidentally picked, we can understand ostracism as an inherent part of the group formation, rather than a result of specific discrepancy among people. Another finding is that a single individual who seeks for unconditional unification of the society ("philanthropist") likely invites his/her own isolation from the society, while the existence of such person generally promotes coalition of others.

A probability generating function method for stochastic reaction networks.

In this paper we present a probability generating function (PGF) approach for analyzing stochastic reaction networks. The master equation of the network can be converted to a partial differential equation for PGF. Using power series expansion of PGF and Padé approximation, we develop numerical schemes for finding probability distributions as well as first and second moments. We show numerical accuracy of the method by simulating chemical reaction examples such as a binding-unbinding reaction, an enzyme-substrate model, Goldbeter-Koshland ultrasensitive switch model, and G(2)/M transition model.