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The classical Kuramoto model consists of finitely many pairwise coupled oscillators on the circle. In many applications a simple pairwise coupling is not sufficient to describe real-world phenomena as higher-order (or group) interactions…
A parallel program together with the parallel hardware it is running on is not only a vehicle to solve numerical problems, it is also a complex system with interesting dynamical behavior: resynchronization and desynchronization of parallel…
Coupled nonlinear oscillators, e.g., Kuramoto models, are commonly used to analyze electrical power systems. The cage model from statistical mechanics has also been used to describe the dynamics of synchronously connected generation…
Synchronization is crucial for the correct functionality of many natural and man-made complex systems. In this work we characterize the formation of synchronization patterns in networks of Kuramoto oscillators. Specifically, we reveal…
Reservoir computing is a highly efficient machine learning framework for processing temporal data by extracting features from the input signal and mapping them into higher dimensional spaces. Physical reservoir layers have been realized…
Neuronal cultures exhibit a complex activity, bursts, or avalanches, characterized by the coexistence of scale invariance and synchronization, quite stable with the percentage of inhibitory neurons. While this bistable behavior has been…
We propose a two-stage memory retrieval dynamics for modern Hopfield models, termed $\mathtt{U\text{-}Hop}$, with enhanced memory capacity. Our key contribution is a learnable feature map $\Phi$ which transforms the Hopfield energy function…
Studies have been made on the phase transition phenomena of an oscillator network model based on a standard Hebb learning rule like the Hopfield model. The relative phase informations---the in-phase and anti-phase, can be embedded in the…
The increasing difficulty in continued development of digital electronic logic has led to a renewed interest in alternative approaches. Oscillatory computing is one such approach that leverages alternative physical systems and computation…
We investigate the emergence of synchronization in the second-order Kuramoto model with adaptive simplicial interactions on a globally connected network. This inertial Kuramoto framework describes systems, where oscillator frequencies…
Traditional von Neumann architecture based processors become inefficient in terms of energy and throughput as they involve separate processing and memory units, also known as~\textit{memory wall}. The memory wall problem is further…
The primate heteromodal cortex presents an evident functional modularity at a mesoscopic level, with physiological and anatomical evidence pointing to it as likely substrate of long-term memory. In order to investigate some of its…
High-capacity associative memory models, such as Kernel Logistic Regression (KLR) Hopfield networks, have demonstrated strong storage capabilities but typically rely on computationally expensive synchronous updates. This reliance poses a…
SoCs are now designed with their own AI accelerator segment to accommodate the ever-increasing demand of Deep Learning (DL) applications. With powerful MAC engines for matrix multiplications, these accelerators show high computing…
Despite growing interest in synchronization dynamics over "higher-order" network models, optimization theory for such systems is limited. Here, we study a family of Kuramoto models inspired by algebraic topology in which oscillators are…
We propose a dynamical approach to quantum memories using an oscillator-cavity model. This overcomes the known difficulties of achieving high quantum input-output fidelity with storage times long compared to the input signal duration. We…
The Kuramoto model is a system of nonlinear differential equations that models networks of coupled oscillators and is often used to study synchronization among them. It has been observed that if the natural frequencies of the oscillators…
Networks of coupled oscillators are some of the most studied objects in the theory of dynamical systems. Two important areas of current interest are the study of synchrony in highly disordered systems and the modeling of systems with…
The Kuramoto model and its generalizations have been broadly employed to characterize and mechanistically understand various collective dynamical phenomena, especially the emergence of synchrony among coupled oscillators. Despite almost…
Memory is fundamental to intelligence, enabling learning, reasoning, and adaptability across biological and artificial systems. While Transformer architectures excel at sequence modeling, they face critical limitations in long-range context…