Investigation of Eigenmode-Based Coupled Oscillator Solver Applied to Ising Spin Problems

We evaluate a coupled oscillator solver by applying it to square lattice (N × N) Ising spin problems for N values up to 50. The Ising problems are converted to a classical coupled oscillator model that includes both positive (ferromagnetic-like) and negative (antiferromagnetic-like) coupling between neighboring oscillators (i.e., they are reduced to eigenmode problems). A map of the oscillation amplitudes of lower-frequency eigenmodes enables us to visualize oscillator clusters with a low frustration density (unfrustrated clusters). We found that frustration tends to localize at the boundary between unfrustrated clusters due to the symmetric and asymmetric nature of the eigenmodes. This allows us to reduce frustration simply by flipping the sign of the amplitude of oscillators around which frustrated couplings are highly localized. For problems with N = 20 to 50, the best solutions with an accuracy of 96% (with respect to the exact ground state) can be obtained by simply checking the lowest ~N/2 candidate eigenmodes.

Optimal Closed-loop Deep Brain Stimulation with Multi-Contact Electrodes

Deep brain stimulation (DBS) is a well-established treatment option for a variety of neurological disorders, including Parkinson’s disease (PD) and essential tremor (ET). It is widely believed that the efficacy, efficiency and side-effects of the treatment can be improved by stimulating ‘closed-loop’, according to the symptoms of a patient. Multi-contact electrodes powered by independent current sources are a recent development in DBS technology which allow for greater precision when targeting one or more pathological regions but, in order to realise the potential of such systems, algorithms must be developed to deal with their increased complexity. This motivates the need to understand how applying DBS to multiple regions (or neural populations) can affect the efficacy and efficiency of the treatment. On the basis of a theoretical model, our paper aims to address the question of how to best apply DBS to multiple neural populations to maximally desynchronise brain activity. Using a coupled oscillator model, we derive analytical expressions which predict how the symptom severity should change as a result of applying stimulation. On the basis of these expressions we derive an algorithm describing when the stimulation should be delivered to individual contacts. Remarkably, these expressions also allow us to determine the conditions for when stimulation using information from individual contacts is likely to be advantageous. Using numerical simulation, we demonstrate that our methods have the potential to be both more effective and efficient than existing methods found in the literature.

Tunable THz Graphene Filter Based on Cross-In-Square-Shaped Resonators Metasurface

The tunable terahertz (THz) Fano-resonant filter based on hybrid metal-graphene metamaterial was proposed. The optical parameters of metasurface with unit cell in the form of a cross-shaped graphene sheet in the center of a square gold ring were simulated by the finite element method using a surface conductivity model of a graphene monolayer. The narrowband modulation of the transmission by varying the Fermi level of the graphene and the position of graphene cross inside the metal ring was demonstrated. Simulation results were well explained theoretically using a three-coupled oscillator model. The proposed device can be used as a narrowband filter in wireless THz communication systems and sensing applications.

Evidence for a Coupled Oscillator Model of Endocrine Ultradian Rhythms

Whereas long-period temporal structures in endocrine dynamics have been well studied, endocrine rhythms on the scale of hours are relatively unexplored. The study of these ultradian rhythms (URs) has remained nascent, in part, because a theoretical framework unifying ultradian patterns across systems has not been established. The present overview proposes a conceptual coupled oscillator network model of URs in which oscillating hormonal outputs, or nodes, are connected by edges representing the strength of node-node coupling. We propose that variable-strength coupling exists both within and across classic hormonal axes. Because coupled oscillators synchronize, such a model implies that changes across hormonal systems could be inferred by surveying accessible nodes in the network. This implication would at once simplify the study of URs and open new avenues of exploration into conditions affecting coupling. In support of this proposed framework, we review mammalian evidence for (1) URs of the gut-brain axis and the hypothalamo-pituitary-thyroid, -adrenal, and -gonadal axes, (2) UR coupling within and across these axes; and (3) the relation of these URs to body temperature. URs across these systems exhibit behavior broadly consistent with a coupled oscillator network, maintaining both consistent URs and coupling within and across axes. This model may aid the exploration of mammalian physiology at high temporal resolution and improve the understanding of endocrine system dynamics within individuals.