Improved time complexity for spintronic oscillator ising machines compared to a popular classical optimization algorithm for the Max-Cut problem.

Solving certain combinatorial optimization problems like Max-Cut becomes challenging once the graph size and edge connectivity increase beyond a threshold, with brute-force algorithms which solve such problems exactly on conventional digital computers having the bottleneck of exponential time complexity. Hence currently, such problems are instead solved approximately using algorithms like Goemans-Williamson (GW) algorithm, run on conventional computers with polynomial time complexity. Phase binarized oscillators (PBOs), also often known as oscillator Ising machines, have been proposed as an alternative to solve such problems. In this paper, restricting ourselves to the combinatorial optimization problem Max-Cut solved on three kinds of graphs (Mobius Ladder, random cubic, Erdös Rényi) up to 100 nodes, we empirically show that computation time/time to solution (TTS) for PBOs (captured through Kuramoto model) grows at a much lower rate (logarithmically:O(log(N)), with respect to graph sizeN) compared to GW algorithm, for which TTS increases as square of graph size (O(N2)). However, Kuramoto model being a physics-agnostic mathematical model, this time complexity/ TTS trend for PBOs is a general trend and is device-physics agnostic. So for more specific results, we choose spintronic oscillators, known for their high operating frequency (in GHz), and model them through Slavin's model which captures the physics of their coupled magnetization oscillation dynamics. We thereby empirically show that TTS of spintronic oscillators also grows logarithmically with graph size (O(log(N)), while their accuracy is comparable to that of GW. So spintronic oscillators have improved time complexity over GW algorithm. For large graphs, they are expected to compute Max-Cut values much faster than GW algorithm, as well as other oscillators operating at lower frequencies, while maintaining the same level of accuracy.

Nonreciprocal synchronization in embryonic oscillator ensembles.

Synchronization of coupled oscillators is a universal phenomenon encountered across different scales and contexts, e.g., chemical wave patterns, superconductors, and the unison applause we witness in concert halls. The existence of common underlying coupling rules defines universality classes, revealing a fundamental sameness between seemingly distinct systems. Identifying rules of synchronization in any particular setting is hence of paramount relevance. Here, we address the coupling rules within an embryonic oscillator ensemble linked to vertebrate embryo body axis segmentation. In vertebrates, the periodic segmentation of the body axis involves synchronized signaling oscillations in cells within the presomitic mesoderm (PSM), from which somites, the prevertebrae, form. At the molecular level, it is known that intact Notch-signaling and cell-to-cell contact are required for synchronization between PSM cells. However, an understanding of the coupling rules is still lacking. To identify these, we develop an experimental assay that enables direct quantification of synchronization dynamics within mixtures of oscillating cell ensembles, for which the initial input frequency and phase distribution are known. Our results reveal a "winner-takes-it-all" synchronization outcome, i.e., the emerging collective rhythm matches one of the input rhythms. Using a combination of theory and experimental validation, we develop a coupling model, the "Rectified Kuramoto" (ReKu) model, characterized by a phase-dependent, nonreciprocal interaction in the coupling of oscillatory cells. Such nonreciprocal synchronization rules reveal fundamental similarities between embryonic oscillators and a class of collective behaviors seen in neurons and fireflies, where higher-level computations are performed and linked to nonreciprocal synchronization.

Higher central circadian temperature amplitude is associated with greater metabolite rhythmicity in humans.

Robust circadian rhythms are essential for optimal health. The central circadian clock controls temperature rhythms, which are known to organize the timing of peripheral circadian rhythms in rodents. In humans, however, it is unknown whether temperature rhythms relate to the organization of circadian rhythms throughout the body. We assessed core body temperature amplitude and the rhythmicity of 929 blood plasma metabolites across a 40-h constant routine protocol, controlling for behavioral and environmental factors that mask endogenous temperature rhythms, in 23 healthy individuals (mean [± SD] age = 25.4 ± 5.7 years, 5 women). Valid core body temperature data were available in 17/23 (mean [± SD] age = 25.6 ± 6.3 years, 1 woman). Individuals with higher core body temperature amplitude had a greater number of metabolites exhibiting circadian rhythms (R2 = 0.37, p = .009). Higher core body temperature amplitude was also associated with less variability in the free-fitted periods of metabolite rhythms within an individual (R2 = 0.47, p = .002). These findings indicate that a more robust central circadian clock is associated with greater organization of circadian metabolite rhythms in humans. Metabolite rhythms may therefore provide a window into the strength of the central circadian clock.

Sparse reservoir computing with vertically coupled vortex spin-torque oscillators for time series prediction.

Spin torque nano-oscillators possessing fast nonlinear dynamics and short-term memory functions are potentially able to achieve energy-efficient neuromorphic computing. In this study, we introduce an activation-state controllable spin neuron unit composed of vertically coupled vortex spin torque oscillators and aV-Isource circuit is proposed and used to build an energy-efficient sparse reservoir computing (RC) system to solve nonlinear dynamic system prediction task. Based on micromagnetic and electronic circuit simulation, the Mackey-Glass chaotic time series and the real motor vibration signal series can be predicted by the RC system with merely 20 and 100 spin neuron units, respectively. Further study shows that the proposed sparse reservoir system could reduce energy consumption without significantly compromising performance, and a minimal response from inactivated neurons is crucial for maintaining the system's performance. The accuracy and signal processing speed show the potential of the proposed sparse RC system for high-performance and low-energy neuromorphic computing.

Resilience of the slow component in timescale-separated synchronized oscillators.

Physiological networks are usually made of a large number of biological oscillators evolving on a multitude of different timescales. Phase oscillators are particularly useful in the modelling of the synchronization dynamics of such systems. If the coupling is strong enough compared to the heterogeneity of the internal parameters, synchronized states might emerge where phase oscillators start to behave coherently. Here, we focus on the case where synchronized oscillators are divided into a fast and a slow component so that the two subsets evolve on separated timescales. We assess the resilience of the slow component by, first, reducing the dynamics of the fast one using Mori-Zwanzig formalism. Second, we evaluate the variance of the phase deviations when the oscillators in the two components are subject to noise with possibly distinct correlation times. From the general expression for the variance, we consider specific network structures and show how the noise transmission between the fast and slow components is affected. Interestingly, we find that oscillators that are among the most robust when there is only a single timescale, might become the most vulnerable when the system undergoes a timescale separation. We also find that layered networks seem to be insensitive to such timescale separations.

Acinonyx jubatus-Inspired Quadruped Robotics: Integrating Neural Oscillators for Enhanced Locomotion Control.

This study presents the design, simulation, and prototype creation of a quadruped robot inspired by the Acinonyx jubatus (cheetah), specifically designed to replicate its distinctive walking, trotting, and galloping locomotion patterns. Following a detailed examination of the cheetah's skeletal muscle anatomy and biomechanics, a simplified model of the robot with 12 degrees of freedom was conducted. The mathematical transformation hierarchy model was established, and direct kinematics were simulated. A bio-inspired control approach was introduced, employing a Central Pattern Generator model based on Wilson-Cowan neural oscillators for each limb, interconnected by synaptic weights. This approach assisted in the simulation of oscillatory signals for relative phases corresponding to four distinct gaits in a system-level simulation platform. The design phase was conducted using CAD software (SolidWorks 2018), resulting in a 1:3-scale robot mirroring the cheetah's actual proportions. Movement simulations were performed in a virtual mechanics software environment, leading to the construction of a prototype measuring 35.5 cm in length, 21 cm in width, 27 cm in height (when standing), and weighing approximately 2.1 kg. The experimental validation of the prototype's limb angular positions and trajectories was achieved through the image processing of video-recorded movements, demonstrating a high correlation (0.9025 to 0.9560) in joint angular positions, except for the knee joint, where a correlation of 0.7071 was noted. This comprehensive approach from theoretical analysis to practical implementation showcases the potential of bio-inspired robotics in emulating complex biological locomotion.

Evaluation of Renal Microhemodynamics Heterogeneity in Different Strains and Sexes of Mice.

Addressing the existing gaps in our understanding of sex- and strain-dependent disparities in renal microhemodynamics, this study conducted an investigation into the variations in renal function and related biological oscillators. Using the genetically diverse mouse models BALB/c, C57BL/6, and Kunming, which serve as established proxies for the study of renal pathophysiology, we implemented laser Doppler flowmetry conjoined with wavelet transform analyses to interrogate dynamic renal microcirculation. Creatinine, urea, uric acid, glucose, and cystatin C levels were quantified to investigate potential divergences attributable to sex and genetic lineage. Our findings reveal marked sexual dimorphism in metabolite concentrations, as well as strain-specific variances, particularly in creatinine and cystatin C levels. Through the combination of Mantel tests and Pearson correlation coefficients, we delineated the associations between renal functional metrics and microhemodynamics, uncovering interactions in female BALB/c mice for creatinine and uric acid, and in male C57BL/6 mice for cystatin C. Histopathologic examination confirmed an augmented microvascular density in female mice and elucidating variations in the expression of estrogen receptor ß among the strains. These data collectively highlight the influence of both sex and genetic constitution on renal microcirculation, providing an understanding that may inform the etiologic exploration of renal ailments.

Highly reproducible and CMOS-compatible VO2-based oscillators for brain-inspired computing.

With remarkable electrical and optical switching properties induced at low power and near room temperature (68 °C), vanadium dioxide (VO2) has sparked rising interest in unconventional computing among the phase-change materials research community. The scalability and the potential to compute beyond the von Neumann model make VO2 especially appealing for implementation in oscillating neural networks for artificial intelligence applications, to solve constraint satisfaction problems, and for pattern recognition. Its integration into large networks of oscillators on a Silicon platform still poses challenges associated with the stabilization in the correct oxidation state and the ability to fabricate a structure with predictable electrical behavior showing very low variability. In this work, the role played by the different annealing parameters applied by three methods (slow thermal annealing, flash annealing, and rapid thermal annealing), following the vanadium oxide atomic layer deposition, on the formation of VO2 grains is studied and an optimal substrate stack configuration that minimizes variability between devices is proposed. Material and electrical characterizations are performed on the different films and a step-by-step recipe to build reproducible VO2-based oscillators is presented, which is argued to be made possible thanks to the introduction of a hafnium oxide (HfO2) layer between the silicon substrate and the vanadium oxide layer. Up to seven nearly identical VO2-based devices are contacted simultaneously to create a network of oscillators, paving the way for large-scale implementation of VO2 oscillating neural networks.

Temperature compensation through kinetic regulation in biochemical oscillators.

Nearly all circadian clocks maintain a period that is insensitive to temperature changes, a phenomenon known as temperature compensation (TC). Yet, it is unclear whether there is any common feature among different systems that exhibit TC. From a general timescale invariance, we show that TC relies on the existence of certain period-lengthening reactions wherein the period of the system increases strongly with the rates in these reactions. By studying several generic oscillator models, we show that this counterintuitive dependence is nonetheless a common feature of oscillators in the nonlinear (far-from-onset) regime where the oscillation can be separated into fast and slow phases. The increase of the period with the period-lengthening reaction rates occurs when the amplitude of the slow phase in the oscillation increases with these rates while the progression speed in the slow phase is controlled by other rates of the system. The positive dependence of the period on the period-lengthening rates balances its inverse dependence on other kinetic rates in the system, which gives rise to robust TC in a wide range of parameters. We demonstrate the existence of such period-lengthening reactions and their relevance for TC in all four model systems we considered. Theoretical results for a model of the Kai system are supported by experimental data. A study of the energy dissipation also shows that better TC performance requires higher energy consumption. Our study unveils a general mechanism by which a biochemical oscillator achieves TC by operating in parameter regimes far from the onset where period-lengthening reactions exist.

Multilevel Latent Differential Structural Equation Model with Short Time Series and Time-Varying Covariates: A Comparison of Frequentist and Bayesian Estimators.

Continuous-time modeling using differential equations is a promising technique to model change processes with longitudinal data. Among ways to fit this model, the Latent Differential Structural Equation Modeling (LDSEM) approach defines latent derivative variables within a structural equation modeling (SEM) framework, thereby allowing researchers to leverage advantages of the SEM framework for model building, estimation, inference, and comparison purposes. Still, a few issues remain unresolved, including performance of multilevel variations of the LDSEM under short time lengths (e.g., 14 time points), particularly when coupled multivariate processes and time-varying covariates are involved. Additionally, the possibility of using Bayesian estimation to facilitate the estimation of multilevel LDSEM (M-LDSEM) models with complex and higher-dimensional random effect structures has not been investigated. We present a series of Monte Carlo simulations to evaluate three possible approaches to fitting M-LDSEM, including: frequentist single-level and two-level robust estimators and Bayesian two-level estimator. Our findings suggested that the Bayesian approach outperformed other frequentist approaches. The effects of time-varying covariates are well recovered, and coupling parameters are the least biased especially using higher-order derivative information with the Bayesian estimator. Finally, an empirical example is provided to show the applicability of the approach.

Cardioid oscillator-based pattern generator for imitating the time-ratio-asymmetrical behavior of the lower limb exoskeleton.

Introduction: Periodicity, self-excitation, and time ratio asymmetry are the fundamental characteristics of the human gait. In order to imitate these mentioned characteristics, a pattern generator with four degrees of freedom is proposed based on cardioid oscillators developed by the authors. Method: The proposed pattern generator is composed of four coupled cardioid oscillators, which are self-excited and have asymmetric time ratios. These oscillators are connected with other oscillators through coupled factors. The dynamic behaviors of the proposed oscillators, such as phase locking, time ratio, and self-excitation, are analyzed via simulations by employing the harmonic balance method. Moreover, for comparison, the simulated trajectories are compared with the natural joint trajectories measured in experiments. Results and discussion: Simulation and experimental results show that the behaviors of the proposed pattern generator are similar to those of the natural lower limb. It means the simulated trajectories from the generator are self-excited without any additional inputs and have asymmetric time ratios. Their phases are locked with others. Moreover, the proposed pattern generator can be applied as the reference model for the lower limb exoskeleton controlling algorithm to produce self-adjusted reference trajectories.

Noise-induced synchrony of two-neuron motifs with asymmetric noise and uneven coupling.

Synchronous dynamics play a pivotal role in various cognitive processes. Previous studies extensively investigate noise-induced synchrony in coupled neural oscillators, with a focus on scenarios featuring uniform noise and equal coupling strengths between neurons. However, real-world or experimental settings frequently exhibit heterogeneity, including deviations from uniformity in coupling and noise patterns. This study investigates noise-induced synchrony in a pair of coupled excitable neurons operating in a heterogeneous environment, where both noise intensity and coupling strength can vary independently. Each neuron is an excitable oscillator, represented by the normal form of Hopf bifurcation (HB). In the absence of stimulus, these neurons remain quiescent but can be triggered by perturbations, such as noise. Typically, noise and coupling exert opposing influences on neural dynamics, with noise diminishing coherence and coupling promoting synchrony. Our results illustrate the ability of asymmetric noise to induce synchronization in such coupled neural oscillators, with synchronization becoming increasingly pronounced as the system approaches the excitation threshold (i.e., HB). Additionally, we find that uneven coupling strengths and noise asymmetries are factors that can promote in-phase synchrony. Notably, we identify an optimal synchronization state when the absolute difference in coupling strengths is maximized, regardless of the specific coupling strengths chosen. Furthermore, we establish a robust relationship between coupling asymmetry and the noise intensity required to maximize synchronization. Specifically, when one oscillator (receiver neuron) receives a strong input from the other oscillator (source neuron) and the source neuron receives significantly weaker or no input from the receiver neuron, synchrony is maximized when the noise applied to the receiver neuron is much weaker than that applied to the source neuron. These findings reveal the significant connection between uneven coupling and asymmetric noise in coupled neuronal oscillators, shedding light on the enhanced propensity for in-phase synchronization in two-neuron motifs with one-way connections compared to those with two-way connections. This research contributes to a deeper understanding of the functional roles of network motifs that may serve within neuronal dynamics.

Design of oscillatory neural networks by machine learning.

We demonstrate the utility of machine learning algorithms for the design of oscillatory neural networks (ONNs). After constructing a circuit model of the oscillators in a machine-learning-enabled simulator and performing Backpropagation through time (BPTT) for determining the coupling resistances between the ring oscillators, we demonstrate the design of associative memories and multi-layered ONN classifiers. The machine-learning-designed ONNs show superior performance compared to other design methods (such as Hebbian learning), and they also enable significant simplifications in the circuit topology. We also demonstrate the design of multi-layered ONNs that show superior performance compared to single-layer ones. We argue that machine learning can be a valuable tool to unlock the true computing potential of ONNs hardware.

Small and Simple Systems That Favor the Arrow of Time.

The 2nd law of thermodynamics yields an irreversible increase in entropy until thermal equilibrium is achieved. This irreversible increase is often assumed to require large and complex systems to emerge from the reversible microscopic laws of physics. We test this assumption using simulations and theory of a 1D ring of N Ising spins coupled to an explicit heat bath of N Einstein oscillators. The simplicity of this system allows the exact entropy to be calculated for the spins and the heat bath for any N, with dynamics that is readily altered from reversible to irreversible. We find thermal-equilibrium behavior in the thermodynamic limit, and in systems as small as N=2, but both results require microscopic dynamics that is intrinsically irreversible.

Information Geometry Theoretic Measures for Characterizing Neural Information Processing from Simulated EEG Signals.

In this work, we explore information geometry theoretic measures for characterizing neural information processing from EEG signals simulated by stochastic nonlinear coupled oscillator models for both healthy subjects and Alzheimer's disease (AD) patients with both eyes-closed and eyes-open conditions. In particular, we employ information rates to quantify the time evolution of probability density functions of simulated EEG signals, and employ causal information rates to quantify one signal's instantaneous influence on another signal's information rate. These two measures help us find significant and interesting distinctions between healthy subjects and AD patients when they open or close their eyes. These distinctions may be further related to differences in neural information processing activities of the corresponding brain regions, and to differences in connectivities among these brain regions. Our results show that information rate and causal information rate are superior to their more traditional or established information-theoretic counterparts, i.e., differential entropy and transfer entropy, respectively. Since these novel, information geometry theoretic measures can be applied to experimental EEG signals in a model-free manner, and they are capable of quantifying non-stationary time-varying effects, nonlinearity, and non-Gaussian stochasticity presented in real-world EEG signals, we believe that they can form an important and powerful tool-set for both understanding neural information processing in the brain and the diagnosis of neurological disorders, such as Alzheimer's disease as presented in this work.

A dynamical computational model of theta generation in hippocampal circuits to study theta-gamma oscillations during neurostimulation.

Neurostimulation of the hippocampal formation has shown promising results for modulating memory but the underlying mechanisms remain unclear. In particular, the effects on hippocampal theta-nested gamma oscillations and theta phase reset, which are both crucial for memory processes, are unknown. Moreover, these effects cannot be investigated using current computational models, which consider theta oscillations with a fixed amplitude and phase velocity. Here, we developed a novel computational model that includes the medial septum, represented as a set of abstract Kuramoto oscillators producing a dynamical theta rhythm with phase reset, and the hippocampal formation, composed of biophysically realistic neurons and able to generate theta-nested gamma oscillations under theta drive. We showed that, for theta inputs just below the threshold to induce self-sustained theta-nested gamma oscillations, a single stimulation pulse could switch the network behavior from non-oscillatory to a state producing sustained oscillations. Next, we demonstrated that, for a weaker theta input, pulse train stimulation at the theta frequency could transiently restore seemingly physiological oscillations. Importantly, the presence of phase reset influenced whether these two effects depended on the phase at which stimulation onset was delivered, which has practical implications for designing neurostimulation protocols that are triggered by the phase of ongoing theta oscillations. This novel model opens new avenues for studying the effects of neurostimulation on the hippocampal formation. Furthermore, our hybrid approach that combines different levels of abstraction could be extended in future work to other neural circuits that produce dynamical brain rhythms.

The N-Oscillator Born-Kuhn Model: An In-Depth Analysis of Chiro-Optical Properties in Complex Chiral Systems.

A comprehensive theory is developed for the chiral optical response of two configurations of the N-oscillator Born-Kuhn model (NOBK): the helically stacked and the corner stacked models. In the helical NOBK model, there is always a chiral response regardless of the value of N, whereas in the corner NOBK, only configurations with even N demonstrate a chiral response. Generally, the magnitudes of optical rotatory dispersion (ORD) and circular dichroism (CD) increase with N when the parameters of each oscillator are fixed. In cases of weak coupling, the spectral shapes of ORD and CD remain invariant, while strong coupling significantly alters the spectral shapes. For large damping, the spectral amplitude becomes smaller, and the spectral features become broader. In the presence of small damping, strong coupling introduces degeneracy in the coupled oscillator system, leading to multiple spectral features in both ORD and CD across the entire spectral region. This simple model can not only help in the design of tunable chiral metamaterials but also enhance our understanding of chiro-optical responses in structures with different configurations.

Analyzing nonlinear oscillations with He's frequency-amplitude method and numerical comparison in jet engine vibration system.

In this study, we describe and successfully solve a jet engine vibration equation using a straightforward tool known as the He's frequency-amplitude Method (HFAM). The jet engine vibration system demonstrates diverse applications across aerospace, power generation, industrial machinery, transportation, marine propulsion, energy optimization, defense, and aviation training. Utilizing HFAM, we derive periodic solutions in a general form for this system, considering various cases dependent on damping and driving forces. The obtained results highlight the effectiveness of HFAM as a distinct and straightforward technique for nonlinear equations. By comparing the solutions with numerical results obtained using the fourth-order Runge-Kutta method, we demonstrate the excellent accuracy of our solutions.

Ultra-Low Current 10 nm Spin Hall Nano-Oscillators.

Nano-constriction based spin Hall nano-oscillators (SHNOs) are at the forefront of spintronics research for emerging technological applications, such as oscillator-based neuromorphic computing and Ising Machines. However, their miniaturization to the sub-50 nm width regime results in poor scaling of the threshold current. Here, it shows that current shunting through the Si substrate is the origin of this problem and studies how different seed layers can mitigate it. It finds that an ultra-thin Al2 O3 seed layer and SiN (200 nm) coated p-Si substrates provide the best improvement, enabling us to scale down the SHNO width to a truly nanoscopic dimension of 10 nm, operating at threshold currents below 30 µ $\umu$ A. In addition, the combination of electrical insulation and high thermal conductivity of the Al2 O3 seed will offer the best conditions for large SHNO arrays, avoiding any significant temperature gradients within the array. The state-of-the-art ultra-low operational current SHNOs hence pave an energy-efficient route to scale oscillator-based computing to large dynamical neural networks of linear chains or 2D arrays.

The physiology of coordination: self-resolving diverse affinities via the sparse order in relevant noise.

Living systems at any given moment enact a very constrained set of end-directed and contextually appropriate actions that are self-initiated from among innumerable possible alternatives. However, these constrained actions are not necessarily because the system has reduced its sensitivities to themselves and their surroundings. Quite the contrary, living systems are continually open to novel and unanticipated stimulations that require a physiology of coordination. To address these competing demands, this paper offers a novel heuristic model informed by neuroscience, systems theory, biology and sign study to explain how organisms situated in diverse, complex and ever-changing environments might draw upon the sparse order made available by 'relevant noise'. This emergent order facilitates coordination, habituation and, ultimately, understanding of the world and its relevant affordances. Inspired by the burgeoning field of coordination dynamics and physiologist Denis Noble's concept of 'biological relativity', this model proposes a view of coordination on the neuronal level that is neither sequential nor stochastic, but instead implements a causal logic of phasic alignment, such that an organism's learned and inherited sets of diverse biological affinities and sympathies can be resolved into a continuous and complex range of patterns that will implement the kind of novel orientations and radical generativity required of such organisms to adaptively explore their environments and to learn from their experiences.