Discontinuous Action Research Articles

Correction to: A note on properly discontinuous actions

We correct a mistake appearing in the earlier paper “A note on properly discontinuous actions.”

Human Motion Capture and Recognition Based on Sparse Inertial Sensor

The field of human motion capture technology represents an emergent and multifaceted domain that encapsulates various disciplines, including but not limited to computer graphics, ergonomics, and communication technology. A distinct network platform within its domain has been established to ensure the reliability and stability of data transmission. Moreover, a sink node has been configured to facilitate sensor data reception through two distinct channels. Notably, the simplicity of the measurement system is directly proportional to the limited number of sensors used. This study focuses on accurately estimating uncertain human 3D movements via a sparse arrangement of wearable inertial sensors, utilizing only six sensors within the system. The methodology is based on a time series sequence throughout the motion process, wherein a series of discontinuous actions constitute the sequential motion. Deep learning methodologies, specifically recurrent neural networks, were employed to refine the regression parameters. Our approach integrated both historical and present sensor data to forecast future sensor data. These data were amalgamated into a superposed input vector, which was fed back into a shallow neural network to estimate human motion. Our experimental results demonstrate the viability of this approach: the six sensors could accurately replicate representative poses. This finding carries significant implications for advancing and applying wearable devices within the realm of motion capture, offering the potential for widespread adoption and implementation.

A twin delayed deep deterministic policy gradient-based energy management strategy for a battery-ultracapacitor electric vehicle considering driving condition recognition with learning vector quantization neural network

Deep reinforcement learning algorithms have been widely applied in the energy management of hybrid energy storage systems. However, these deep reinforcement learning algorithms, such as DQN and DDPG, have the problem of discontinuous action space and consistently overestimated Q values. To address this issue, a novel energy management strategy based on a twin delayed deep deterministic policy gradient (TD3) algorithm is proposed for the battery-ultracapacitor electric vehicles in this study. In addition, the driving condition recognition method is integrated into the energy management strategy framework to reduce the training time of the TD3 agent. The detailed implementation steps are as follows. At first, dynamic experiments were performed to establish high-precision models of the battery and ultracapacitor. Secondly, learning vector quantization neural networks are applied to classify driving conditions, namely, urban, suburban and highway conditions. Furthermore, three parallel TD3 agents are trained for urban, suburban and highway conditions, respectively. Finally, the proposed strategy is evaluated under standard driving cycles. The simulation results indicate that compared with the TD3-based strategy, the proposed strategy improves the economy by 1 % and reduces the training time by 34 %, and the economic gap with the dynamic programming-based energy management strategy is narrowed down to 3 %.

A note on properly discontinuous actions

AbstractWe compare various notions of proper discontinuity for group actions. We also discuss fundamental domains and criteria for cocompactness.

Jesus, the Anthropologist: Patterns of Emplotment and Modes of Action in the Parables

This article uses a typology of action framework to analyze a selection of the gospels’ parables. It does so by connecting these parables to A. G. Haudricourt and C. Ferret’s research on the “anthropology of action”. After summarizing Haudricourt’s and Ferret’s results, I relate modes of action to types of emplotment. I select four parables as the basis of my analysis, using J. P. Meier’s findings as a guide for selection. I discern in these four parables four modes of emplotment, which enables me to insert them into larger narrative networks found within the gospels. I locate the corpus of narratives determined this way in the context of Jesus’ time so as to better appreciate how the four modes of emplotment combine into a typology of action shaped by a specific social and cultural context. Within this typology of action, I put a spotlight on the way our corpus’ modes of emplotment make use of “discontinuous actions” (coined by Ferret). “Discontinuous actions” decisively initiate or correct a specified course of events. The stress on this dimension of action applies to the relationships occurring between humans and the natural world, within the social world, and between humans and the supranatural world, thus connecting one order of reality with another.

Equivariant discretizations of diffusions and harmonic functions of bounded growth

For covering spaces and properly discontinuous actions with compatible diffusion operators, we discuss Lyons—Sullivan discretizations of the associated diffusions and harmonic functions of bounded growth.

Equivariant discretizations of diffusions, random walks, and harmonic functions

For covering spaces and properly discontinuous actions with compatible diffusion processes, we discuss Lyons–Sullivan discretizations of the processes and the associated function theory.

Properly discontinuous actions versus uniform embeddings

Whenever a finitely generated group G acts properly discontinuously by isometries on a metric space X , there is an induced uniform embedding (a Lipschitz and uniformly proper map) \rho\colon G \rightarrow X given by mapping G to an orbit. We study when there is a difference between a finitely generated group G acting properly on a contractible n -manifold and uniformly embedding into a contractible n -manifold. For example, Kapovich and Kleiner showed that there are torsion-free hyperbolic groups that uniformly embed into a contractible 3 -manifold but do not act on a contractible 3 -manifold. We show that k -fold products of certain examples do not act on contractible 3k -manifolds.

Systems theory and analysis of the implementation of non pharmaceutical policies for the mitigation of the COVID-19 pandemic

We utilize systems theory in the study of the implementation of non pharmaceutical strategies for the mitigation of the COVID-19 pandemic. We present two models. The first one is a model of predictive control with receding horizon and discontinuous actions of unknown costs for the implementation of adaptive triggering policies during the disease. This model is based on a periodic assessment of the peak of the pandemic (and, thus, of the health care demand) utilizing the latest data about the transmission and recovery rate of the disease. Consequently, the model seems to be suitable for discontinuous, non-mechanical (i.e. human) actions with unknown effectiveness, like those applied in the case of COVID-19. Secondly, we consider a feedback control problem in order to contain the pandemic at the capacity of the NHS (National Health System). As input parameter we consider the value $ p $ that reflects the intensity-effectiveness of the measures applied and as output the predicted maximum of infected people to be treated by NHS. The feedback control regulates $ p $ so that the number of infected people is manageable. Based on this approach, we address the following questions: (a) the limits of improvement of this approach; (b) the effectiveness of this approach; (c) the time horizon and timing of the application.

Neuro-learning-based adaptive control for state-constrained strict-feedback systems with unknown control direction

A neural networks (NNs)-based learning policy is proposed for strict-feedback nonlinear systems with asymmetric full-state constraints and unknown gain directions. A state-constrained function is introduced such that the proposed adaptive control policy works for systems with constraints or without constraints in a unified structure. Furthermore, the unified state-constrained function can also deal with symmetric and asymmetric constraints without changing adaptive structures, which also avoids discontinuous actions. With Nussbaum gain technique and NNs-based approximation technique, the proposed control method can also effectively deal with the unknown signs of control gains, and matched and mismatched uncertainties are also solved by NN approximation technique. According to the Lyapunov theory, the tracking errors can be proved to be semi-globally uniformly ultimately bounded (SGUUB). Finally the effectiveness of the proposed scheme is validated by numerical simulations.

Uncertainty in classical systems (with a local, non-stochastic, non-chaotic origin)

Decisions made by two (or more) independent players in a dynamical system can result in an indeterminable, yet non-stochastic, outcome. The mechanism can be presented as a thought experiment in which two pilots attempt to steer a spacecraft but, in stabilizing its pitch and yaw, lose all knowledge of its forward motion. It is useful to think of this pilots’ dilemma as a classical analogue of Schrödinger’s ‘cat in a box’ thought experiment. In both, the outcome of a life or death scenario is indeterminate until it is directly observed, but in place of the probabilistic radioactive source in Schrödinger’s problem, the discontinuous action of the pilots’ decisions create the classical indeterminacy. We discuss the wider implications of the phenomenon, such as predicting indeterminate scenarios in optimal transport or other network problems. The behaviour only becomes apparent when a system’s dynamics is sufficiently taken into account.

Coarse quotients by group actions and the maximal Roe algebra

For a finitely generated group [Formula: see text] acting on a metric space [Formula: see text], Roe defined the warped space [Formula: see text], which one can view as a kind of large scale quotient of [Formula: see text] by the action of [Formula: see text]. In this paper, we generalize this notion to the setting of actions of arbitrary groups on large scale spaces. We then restrict our attention to what we call coarsely discontinuous actions by coarse equivalences and show that for such actions the group [Formula: see text] can be recovered as an appropriately defined automorphism group [Formula: see text] when [Formula: see text] satisfies a large scale connectedness condition. We show that for a coarsely discontinuous action of a countable group [Formula: see text] on a discrete bounded geometry metric space [Formula: see text] there is a relation between the maximal Roe algebras of [Formula: see text] and [Formula: see text], namely that there is a ∗-isomorphism [Formula: see text], where [Formula: see text] is the ideal of compact operators. If [Formula: see text] has Property A and [Formula: see text] is amenable, then [Formula: see text] has Property A, and thus the maximal Roe algebra and full crossed product can be replaced by the usual Roe algebra and reduced crossed product respectively in the above equation.

Design of a Continuous Signal Generator Based on Sliding Mode Control of Three-Phase AC-DC Power Converters

In recent years, hundreds of technical papers have been published which describe the use of sliding mode control (SMC) techniques for power electronic equipment and electrical drives. SMC with discontinuous control actions has the potential to circumvent parameter variation effects with low implementation complexity. The problem of controlling time-varying DC loads has been studied in literature if three-phase input voltage sources are available. The conventional approach implies the design of a three-phase AC/DC converter with a constant output voltage. Then, an additional DC/DC converter is utilized as an additional stage in the output of the converter to generate the required voltage for the load. A controllable AC/DC converter is always used to have a high quality of the consumed power. The aim of this study is to design a controlled continuous signal generator based on the sliding mode control of a three-phase AC-DC power converter, which yields the production of continuous variations of the output DC voltage. A sliding mode current tracking system is designed with reference phase currents proportional to the source voltage. The proportionality time-varying gain is selected such that the output voltage is equal to the desired time function. The proposed new topology also offers the capability to get rid of the additional DC/DC power converter and produces the desired time-varying control function in the output of AC/DC power converter. The effectiveness of the proposed control design is demonstrated through a wide range of MATLAB/Simulink simulations.

Finite element modelling of discontinuous action potential propagation in larval zebrafish and human cardiac tissue

Recently the larval zebrafish has emerged as a model organism which is used to assist in the studies of human cardiac electrophysiology. Although they share many similar electrophysiological characteristics, it has been found that the conduction velocity (CV) of action potential (AP) propagation in larval zebrafish heart is up to two orders of magnitude smaller than in the adult mammalian heart. To address this difference, we have developed three dimensional discrete models of larval zebrafish ventricular fibres (LZVF) in order to simulate AP propagation, taking into account the cellular nature of the tissues and intercellular conduction via gap junctions. Since our ultimate goal is to simulate a whole larval zebrafish heart, we have used the phenomenological Fitzhugh Nagumo (FHN) equations to describe transmembrane currents, and manually adjusted the FHN parameters, to fit published AP shapes for larval zebrafish ventricular cells. This has the benefit of reduced computational load compared to approaches based on biophysical ion current models. We have created models for 48 and 72 h post fertilisation LZVF tissue using published AP and cell size data for zebrafish embryos and used mammalian values for passive electrical parameters. Using the gap junction resistivity per myocyte as an adjustable parameter, we were able to obtain CVs in both of our LZVF models which agree with experimental observations. In order to validate our approach, we have applied it to a human ventricular fibre (HVF) model similar in structure and parameters to other models of the mammalian heart, but adjusting the FHN parameters to fit published AP shapes for human ventricular cells. We find good agreement with the human models. The gap junction resistivities used in the LZVF models are significantly higher than in the HVF case and are consistent with a lower density of gap junctions connecting cells.

The Planar Cayley Graphs are Effectively Enumerable I: Consistently Planar Graphs

We obtain an effective enumeration of the family of finitely generated groups admitting a faithful, properly discontinuous action on some 2-manifold contained in the sphere. This is achieved by introducing a type of group presentation capturing exactly these groups. Extending this in a companion paper, we find group presentations capturing the planar finitely generated Cayley graphs. Thus we obtain an effective enumeration of these Cayley graphs, yielding in particular an affirmative answer to a question of Droms et al.

Affine actions with Hitchin linear part

Properly discontinuous actions of a surface group by affine automorphisms of $\mathbb R^d$ were shown to exist by Danciger-Gueritaud-Kassel. We show, however, that if the linear part of an affine surface group action is in the Hitchin component, then the action fails to be properly discontinuous. The key case is that of linear part in $\mathsf{SO}(n,n-1)$, so that the affine action is by isometries of a flat pseudo-Riemannian metric on $\mathbb R^d$ of signature $(n,n-1)$. Here, the translational part determines a deformation of the linear part into $\mathsf{PSO}(n,n)$-Hitchin representations and the crucial step is to show that such representations are not Anosov in $\mathsf{PSL}(2n,\mathbb R)$ with respect to the stabilizer of an $n$-plane. We also prove a negative curvature analogue of the main result, that the action of a surface group on the pseudo-Riemannian hyperbolic space of signature $(n,n-1)$ by a $\mathsf{PSO}(n,n)$-Hitchin representation fails to be properly discontinuous.

Target detection method based on optical fiber fence

The intrusion alarm system of fiber optic fence perimeter realizes the early warning of intrusion by sensing the vibration of the defense area. How to detect the intrusion correctly, improve the system alarm accuracy and reduce the false alarm rate is the key problem to be explored. In view of the large amplitude of the jump of the intrusion signal and the discontinuous action process, and the disturbance generated by the environment is generally random and disorderly. In this paper, the method based on mean filtering and contrast detection is adopted to detect the intrusion signal. Through the actual data verification, this method can accurately realize the alarm of the intrusion signal and has strong robustness.

Relationship between Flow Behavior and Microstructure Evolution during Isothermal Compression of near β Titanium Alloy Ti-55531 with Acicular Starting Microstructure

Near β titanium alloy Ti-55531 with an acicular starting microstructure was isothermally compressed at 750–825 °C and 10−3−1 s−1. The microstructure evolution and its influence on the flow behavior of yielding and softening were investigated. Discontinuous or continuous yielding depends on the hindrance to the dislocation motion coming from the β grain boundary or α phase. At higher temperatures, the hindrance mainly comes from the β grain boundary. Its discontinuous action, including the piling-up and subsequent loosening of dislocations at the β grain boundary, leads to discontinuous yielding. At lower temperatures, the continuous hindrance to the dislocation motion, which is exerted by the β grain boundary and acicular α, causes continuous yielding. Sequentially, the substructures in acicular α are evolved from high-density dislocations or local shear bands, which depend on the orientation relationship between β and α. Then, the β matrix edges into the acicular α along substructure boundaries. The higher strain rate decreases the deformation time to carry out the fragmentation of acicular α, while the higher temperature decreases the dislocation density due to the recovery of β, which does not benefit the substructure formation and subsequent fragmentation of acicular α. Therefore, the retardation of acicular fragmentation and the as-resulted decreased flow softening rate are observed.

Numerical Analysis of Prestressed UHPC Lightened Member

UHPC (ultra-high-performance concrete) is one of the essential elements in the development and research of new modern concrete structures. It is a material showing all the positive qualities in terms of the design efficiency and construction process. In this paper, we analyze the behavior of prestressed UHPC I-beam with lightened web that is loaded by four-point bending test. Two variants of I-beam were used for the analysis. The first variant is beam with a continuous thin web and the second variant is beam with lightened web, which is analogous to castellated steel I-profiles, commonly used types of steel beams with larger span. Although these are relatively small specimens, light beam analysis can be extrapolated for large span structures, especially bridges. In case of structures of larger magnitude with precast members of UHPC, a certain amount of discontinuous action cannot be avoided, which is the case of using a lightened beam with openings across the entire height of the web. Application of prestressed tendons ensures sufficient resistance for bending action; members are designed so failure occurs by shear response.

Free and Properly Discontinuous Actions of Groups on Homotopy 2n-spheres

Let G be a group acting freely, properly discontinuously and cellularly on some finite dimensional CW-complex Σ(2n) which has the homotopy type of the 2n-sphere 𝕊2n. Then, that action induces a homomorphism G → Aut(H2n(Σ(2n))). We classify all pairs (G, φ), where G is a virtually cyclic group and φ: G → Aut(ℤ) is a homomorphism, which are realizable in the way above and the homotopy types of all possible orbit spaces as well. Next, we consider the family of all groups which have virtual cohomological dimension one and which act on some Σ(2n). Those groups consist of free groups and semi-direct products F ⋊ ℤ2 with F a free group. For a group G from the family above and a homomorphism φ: G → Aut(ℤ), we present an algebraic criterion equivalent to the realizability of the pair (G, φ). It turns out that any realizable pair can be realized on some Σ(2n) with dim Σ(2n) ≤ 2n + 1.