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Abstract The nonlinear interaction between the tip of a scanning probe microscope (SPM) and a sample is manifested in the emergence of bifurcations and unstable branches in the frequency response of a driven cantilever. While extensively investigated theoretically, exploring the unstable branch in an actual SPM experiment is lacking so far, reflecting the broader challenge in studying mechanical nanojunction oscillators under strongly varying external forces. Here we demonstrate experimental tracking of unstable periodic orbits between two saddle-node bifurcation points in the attractive regime, revealing the full set of stationary oscillatory states. This is achieved by a minimally invasive control scheme based on fast adaptive phase extraction and Fourier discretisation of the tip dynamics. Stabilization of unstable branches of oscillating AFM cantilevers opens avenues for novel experimental modes, potentially enabling ultrasensitive surface detection at considerably large amplitudes with minimal tip-surface interaction, new insights in tip-surface interaction mechanisms, as well as new AFM modes enabling arbitrary setpoint choice while inherently avoiding discontinuities.

Background: Deep brain stimulation (DBS) targeting globus pallidus internus (GPi) is a recognised therapy for drug-refractory dystonia. However, the mechanisms underlying this effect are not fully understood. This study explores how pallidal DBS alters spatiotemporal pattern formation of neuronal dynamics within the cerebellar cortex in a dystonic animal model, the dtsz hamster. Methods: We conducted in vitro analysis using a high-density microelectrode array (HD-MEA) in the cerebellar cortex. For investigating the spatiotemporal pattern, mean firing rates (MFR), interspike intervals (ISI), spike amplitudes, and cerebellar connectivity among healthy control hamsters, dystonic dtsz hamsters, DBS- and sham-DBS-treated dtsz hamsters were analysed. A nonlinear data-driven method characterised the low-dimensional representation of the patterns in MEA data. Results: Our HD-MEA recordings revealed reduced MFR and spike amplitudes in the dtsz hamsters compared to healthy controls. Pallidal DBS induced network-wide effects, normalising MFR, spike amplitudes, and connectivity measures in hamsters, thereby countervailing these electrophysiological abnormalities. Additionally, network analysis showed neural activity patterns organised into communities, with higher connectivity in both healthy and DBS groups compared to dtsz. Conclusions: These findings suggest that pallidal DBS exerts some of its therapeutic effects on dystonia by normalising neuronal activity within the cerebellar cortex. Our findings of reduced MFR and spike amplitudes in the dtsz hamsters could be a hint of a decrease in neuronal fibres and synaptic plasticity. Treatment with pallidal DBS led to cerebellar cortical activity similar to healthy controls, displaying the network-wide impact of local stimulation.

Abstract A large-scale biophysical network model for the isolated striatal body is developed to optimise potential intrastriatal deep brain stimulation applied to, e.g. obsessive-compulsive disorder. The model is based on modified Hodgkin–Huxley equations with small-world connectivity, while the spatial information about the positions of the neurons is taken from a detailed human atlas. The model produces neuronal spatiotemporal activity patterns segregating healthy from pathological conditions. Three biomarkers were used for the optimisation of stimulation protocols regarding stimulation frequency, amplitude and localisation: the mean activity of the entire network, the frequency spectrum of the entire network (rhythmicity) and a combination of the above two. By minimising the deviation of the aforementioned biomarkers from the normal state, we compute the optimal deep brain stimulation parameters, regarding position, amplitude and frequency. Our results suggest that in the DBS optimisation process, there is a clear trade-off between frequency synchronisation and overall network activity, which has also been observed during in vivo studies.

The striatum as part of the basal ganglia is central to both motor, and cognitive functions. Here, we propose a large-scale biophysical network for this part of the brain, using modified Hodgkin-Huxley dynamics to model neurons, and a connectivity informed by a detailed human atlas. The model shows different spatio-temporal activity patterns corresponding to lower (presumably normal) and increased cortico-striatal activation (as found in, e.g., obsessive-compulsive disorder), depending on the intensity of the cortical inputs. By applying equation-free methods, we are able to perform a macroscopic network analysis directly from microscale simulations. We identify the mean synaptic activity as the macroscopic variable of the system, which shows similarity with local field potentials. The equation-free approach results in a numerical bifurcation and stability analysis of the macroscopic dynamics of the striatal network. The different macroscopic states can be assigned to normal/healthy and pathological conditions, as known from neurological disorders. Finally, guided by the equation-free bifurcation analysis, we propose a therapeutic close loop control scheme for the striatal network.

An important question in computational neuroscience is how to improve the efficacy of deep brain stimulation by extracting information from the underlying connectivity structure. Recent studies also highlight the relation of structural and functional connectivity in disorders such as Parkinson’s disease. Exploiting the structural properties of the network, we identify nodes of strong influence, which are potential targets for Deep Brain Stimulation (DBS). Simulating the volume of the tissue activated, we confirm that the proposed targets are reported as optimal targets (sweet spots) to be beneficial for the improvement of motor symptoms. Furthermore, based on a modularity algorithm, network communities are detected as set of nodes with high-interconnectivity. This allows to localise the neural activity, directly from the underlying structural topology. For this purpose, we build a large scale computational model that consists of the following elements of the basal ganglia network: subthalamic nucleus (STN), globus pallidus (external and internal parts) (GPe-GPi), extended with the striatum, thalamus and motor cortex (MC) areas, integrating connectivity from multimodal imaging data. We analyse the network dynamics under Healthy, Parkinsonian and DBS conditions with the aim to improve DBS treatment. The dynamics of the communities define a new functional partition (or segregation) of the brain, characterising Healthy, Parkinsonian and DBS treatment conditions.

Summary: Non-pharmacological interventions (NPIs), principally social distancing, in combination with effective vaccines, aspire to develop a protective immunity shield against pandemics and particularly against the COVID-19 pandemic. In this study, an agent-based network model with small-world topology is employed to find optimal policies against pandemics, including social distancing and vaccination strategies. The agents’ states are characterized by a variation of the SEIR model (susceptible, exposed, infected, recovered). To explore optimal policies, an equation-free method is proposed to solve the inverse problem of calibrating an agent’s infection rate with respect to the vaccination efficacy. The results show that prioritizing the first vaccine dose in combination with mild social restrictions, is sufficient to control the pandemic, with respect to the number of deaths. Moreover, for the same mild number of social contacts, we find an optimal vaccination ratio of 0.85 between older people of ages >65 compared to younger ones.

The motion of pedestrians is a paradigmatic phenomenon to study collective human behavior. We propose a model-free approach to analyze the movement of pedestrians in experiments and get a quantitative understanding of crowd dynamics. Using concepts from control and analysis of dynamical systems, we set up a scheme which allows us to identify dynamical unstable signatures in pedestrian flows. These signatures are the building blocks for crowd control and soft management of people and thus result in a fundamental understanding of collective human behavior. Our approach is entirely data driven, and we provide a proof of concept using field and laboratory experiments. In addition, this methodology provides, based on experimental observations, quantitative benchmarks to judge the quality of mathematical models for pedestrian motion.