Markov Perfect Equilibria in Multi-Mode Differential Games with Endogenous Timing of Mode Transitions

We study Markov perfect equilibria (MPE) of two-player multi-mode differential games with controlled state dynamics, where one player controls the transition between modes. Different types of MPE are characterized distinguishing between delay equilibria, inducing for some initial conditions mode switches after a positive finite delay, and now or never equilibria, under which, depending on the initial condition, a mode switch occurs immediately or never. These results are applied to analyze the MPE of a game capturing the dynamic interaction between two incumbent firms among which one has to decide when to extend its product range by introducing a new product. The market appeal of the new product can be influenced over time by both firms through costly investments. Under a wide range of market introduction costs a now or never equilibrium coexists with a continuum of delay equilibria, each of them inducing a different time of product introduction.

Locomotion Mode Transition Prediction Based on Gait-Event Identification Using Wearable Sensors and Multilayer Perceptrons

People walk on different types of terrain daily; for instance, level-ground walking, ramp and stair ascent and descent, and stepping over obstacles are common activities in daily life. Movement patterns change as people move from one terrain to another. The prediction of transitions between locomotion modes is important for developing assistive devices, such as exoskeletons, as the optimal assistive strategies may differ for different locomotion modes. The prediction of locomotion mode transitions is often accompanied by gait-event detection that provides important information during locomotion about critical events, such as foot contact (FC) and toe off (TO). In this study, we introduce a method to integrate locomotion mode prediction and gait-event identification into one machine learning framework, comprised of two multilayer perceptrons (MLP). Input features to the framework were from fused data from wearable sensors—specifically, electromyography sensors and inertial measurement units. The first MLP successfully identified FC and TO, FC events were identified accurately, and a small number of misclassifications only occurred near TO events. A small time difference (2.5 ms and −5.3 ms for FC and TO, respectively) was found between predicted and true gait events. The second MLP correctly identified walking, ramp ascent, and ramp descent transitions with the best aggregate accuracy of 96.3%, 90.1%, and 90.6%, respectively, with sufficient prediction time prior to the critical events. The models in this study demonstrate high accuracy in predicting transitions between different locomotion modes in the same side’s mid- to late stance of the stride prior to the step into the new mode using data from EMG and IMU sensors. Our results may help assistive devices achieve smooth and seamless transitions in different locomotion modes for those with motor disorders.

Synchronization Mode Transitions Induced by Chaos in Modified Morris-Lecar Neural Systems with Weak Coupling

Based on a modified Morris–Lecar neural model, the synchronization modes transitions between two coupled neurons or star-coupled neural network connected by weak electrical and chemical coupling are respectively investigated. For the two coupled neurons, by increasing the calcium conductivity, it is found that the period-2 synchronization of action potential of neurons is transformed to desynchronization first, and then to period-3 synchronization. By increasing the potassium conductivity, however, the synchronization mode transition is a reversal direction process as mentioned above. The bifurcation analysis of inter-spike interval shows that the synchronization modes transition is induced by the chaos. The stronger the coupling strength is, the smaller the period-2 synchronization region in the parameters plane is, while the larger the period-3 synchronization region will be. For the star-coupled neural network, in the presence of weak electrical coupling, it can exhibit the complete synchronization, desynchronization, and drum head mode states under different parameter values, respectively. In the presence of chemical synapse, however, the completely synchronized state can not be observed in the star-coupled neural network. Our results might provide novel insights into synchronization modes transition and related biological experiments.

Robust flight mode transition control for tail-sitter formation flying with communication delays

In this article, the formation control problem is investigated for a team of unmanned tail-sitters subject to communication delays. A robust distributed and continuous formation control scheme is developed to achieve the desired aggressive time-varying formation flying in flight mode transitions between forward and vertical flights. The proposed control method consists of a translational controller and a rotational controller for each individual tail-sitter to govern the position and attitude motions, respectively. It is proven that the formation system stability can be guaranteed in the presence of communication delays and multiple uncertainties. Simulation results are presented for a team of tail-sitters to illustrate the advantages of the proposed formation flight control algorithm.

An EFT toolbox for baryon and lepton number violating dinucleon to dilepton decays

In this paper we systematically consider the baryon (B) and lepton (L) number violating dinucleon to dilepton decays (pp → ℓ+ℓ′+, pn → $$ {\mathrm{\ell}}^{+}\overline{\nu}^{\prime } $$ ℓ + ν ¯ ′ , nn → $$ \overline{\nu}\overline{\nu}^{\prime } $$ ν ¯ ν ¯ ′ ) with ∆B = ∆L = −2 in the framework of effective field theory. We start by constructing a basis of dimension-12 (dim-12) operators mediating such processes in the low energy effective field theory (LEFT) below the electroweak scale. Then we consider their standard model effective field theory (SMEFT) completions upwards and their chiral realizations in baryon chiral perturbation theory (BχPT) downwards. We work to the first nontrivial orders in each effective field theory, collect along the way the matching conditions, and express the decay rates in terms of the Wilson coefficients associated with the dim-12 operators in the SMEFT and the low energy constants pertinent to BχPT. We find the current experimental limits push the associated new physics scale larger than 1 − 3 TeV, which is still accessible to the future collider searches. Through weak isospin symmetry, we find the current experimental limits on the partial lifetime of transitions pp → ℓ+ℓ′+, pn → $$ {\mathrm{\ell}}^{+}\overline{\nu}^{\prime } $$ ℓ + ν ¯ ′ imply stronger limits on nn → $$ \overline{\nu}\overline{\nu}^{\prime } $$ ν ¯ ν ¯ ′ than their existing lower bounds, which are improved by 2−3 orders of magnitude. Furthermore, assuming charged mode transitions are also dominantly generated by the similar dim-12 SMEFT interactions, the experimental limits on pp → e+e+, e+μ+, μ+μ+ lead to stronger limits on pn → $$ {\mathrm{\ell}}_{\alpha}^{+}{\overline{\nu}}_{\beta } $$ ℓ α + ν ¯ β with α, β = e, μ than their existing bounds. Conversely, the same assumptions help us to set a lower bound on the lifetime of the experimentally unsearched mode pp → e+τ+ from that of pn → $$ {e}^{+}{\overline{\nu}}_{\tau } $$ e + ν ¯ τ , i.e., $$ {\Gamma}_{pp\to {e}^{+}{\tau}^{+}}^{-1}\gtrsim 2\times {10}^{34} $$ Γ pp → e + τ + − 1 ≳ 2 × 10 34 yr.