Backward Dynamics Research Articles

Asymmetric nucleation processes in spontaneous mode switch of active matter

Flocking and vortical are two typical motion modes in active matter. Although it is known that the two modes can spontaneously switch between each other in a finite-size system, the switching dynamics remain elusive. In this work, by computer simulation of a two-dimensional Vicsek-like system with 1000 particles, we find from the perspective of the classical nucleation theory that the forward and backward switching dynamics are asymmetric: going from flocking to vortical is a one-step nucleation process, while the opposite is a two-step nucleation process, with the system staying in a metastable state before reaching the final flocking state.

Improving world models for robot arm grasping with backward dynamics prediction

Improving world models for robot arm grasping with backward dynamics prediction

Speeds of convergence for petals of semigroups of holomorphic functions

We study the backward dynamics of one-parameter semigroups of holomorphic self-maps of the unit disk. More specifically, we introduce the speeds of convergence for petals of the semigroup, namely the total, orthogonal, and tangential speeds. These are analogous to speeds of convergence introduced by Bracci, yet profoundly different due to the nature of backward dynamics. Results are extracted on the asymptotic behavior of speeds of petals, depending on the type of the petal. We further discuss the asymptotic behavior of the hyperbolic distance along non-regular backward orbits.

The angular derivative problem for petals of one-parameter semigroups in the unit disk

We study the angular derivative problem for petals of one-parameter semigroups of holomorphic self-maps of the unit disk. For hyperbolic petals, we prove a necessary and sufficient condition for the conformality of the petal in terms of the intrinsic hyperbolic geometry of the petal and the backward dynamics of the semigroup. For parabolic petals, we characterize conformality of the petal in terms of the asymptotic behaviour of the Koenigs function at the Denjoy–Wolff point.

Backward dynamics of non-expanding maps in Gromov hyperbolic metric spaces

We study the interplay between the backward dynamics of a non-expanding self-map f of a proper geodesic Gromov hyperbolic metric space X and the boundary regular fixed points of f in the Gromov boundary as defined in [8]. To do so, we introduce the notion of stable dilation at a boundary regular fixed point of the Gromov boundary, whose value is related to the dynamical behavior of the fixed point. This theory applies in particular to holomorphic self-maps of bounded domains Ω⊂⊂Cq, where Ω is either strongly pseudoconvex, convex finite type, or pseudoconvex finite type with q=2, and solves several open problems from the literature. We extend results of holomorphic self-maps of the disc D⊂C obtained by Bracci and Poggi-Corradini in [14,27,28]. In particular, with our geometric approach we are able to answer a question, open even for the unit ball Bq⊂Cq (see [5,26]), namely that for holomorphic parabolic self-maps any escaping backward orbit with bounded step always converges to a point in the boundary.

Large deviations and conditioning for chaotic non-invertible deterministic maps: analysis via the forward deterministic dynamics and the backward stochastic dynamics

The large deviation properties of trajectory observables for chaotic non-invertible deterministic maps as studied recently by Smith (2022 Phys. Rev. E 106 L042202) and by Gutierrez et al (2023 arXiv:2304.13754) are revisited in order to analyze in detail the similarities and the differences with the case of stochastic Markov chains. More concretely, we focus on the simplest example displaying the two essential properties of local stretching and global folding, namely the doubling map xt+1=2xt[mod1] on the real-space interval x∈[0,1[ that can also be analyzed via the decomposition x=∑l=1+∞σl2l into binary coefficients σl=0,1 . The large deviation properties of trajectory observables can be studied either via deformations of the forward deterministic dynamics or via deformations of the backward stochastic dynamics. Our main conclusions concerning the construction of the corresponding Doob canonical conditioned processes are: (i) non-trivial conditioned dynamics can be constructed only in the backward stochastic perspective where the reweighting of existing transitions is possible, and not in the forward deterministic perspective; (ii) the corresponding conditioned steady state is not smooth on the real-space interval x∈[0,1[ and can be better characterized in the binary space σl=1,2,..,+∞ . As a consequence, the backward stochastic dynamics in the binary space are also the most appropriate framework to analyze higher levels of large deviations, and we obtain the explicit large deviations at level 2 for the probability of the empirical density of long backward trajectories.

Imitation learning by state-only distribution matching

Imitation Learning from observation describes policy learning in a similar way to human learning. An agent’s policy is trained by observing an expert performing a task. Although many state-only imitation learning approaches are based on adversarial imitation learning, one main drawback is that adversarial training is often unstable and lacks a reliable convergence estimator. If the true environment reward is unknown and cannot be used to select the best-performing model, this can result in bad real-world policy performance. We propose a non-adversarial learning-from-observations approach, together with an interpretable convergence and performance metric. Our training objective minimizes the Kulback-Leibler divergence (KLD) between the policy and expert state transition trajectories which can be optimized in a non-adversarial fashion. Such methods demonstrate improved robustness when learned density models guide the optimization. We further improve the sample efficiency by rewriting the KLD minimization as the Soft Actor Critic objective based on a modified reward using additional density models that estimate the environment’s forward and backward dynamics. Finally, we evaluate the effectiveness of our approach on well-known continuous control environments and show state-of-the-art performance while having a reliable performance estimator compared to several recent learning-from-observation methods.

Forward and backward recall dynamics.

Although possible to recall in both forward and backward order, recall proceeds most naturally in the order of encoding. Prior studies ask whether and how forward and backward recall differ. We reexamine this classic question by studying recall dynamics while varying the predictability and timing of forward and backward cues. Although overall accuracy did not differ by recall direction, recall dynamics highlight key distinctions. Forward recall exhibits a modest advantage for correct transitions following errors, independent of cueing predictability and list length. Without consistent directional cueing, participants initiate backward recall more accurately, but this effect reverses with predictable directional cues. Following omissions, participants commit more fill-in errors in backward recall. Our findings implicate an asymmetric, cue-dependent retrieval process underlying forward and backward recall, with relative contributions of primacy and recency depending on directional predictability. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Convergence to closed-form distribution for the backward [formula omitted] at some random times and the phase transition at [formula omitted

We study a one-dimensional SDE that we obtain by performing a random time change of the backward Loewner dynamics in H. The stationary measure for this SDE has a closed-form expression. We show the convergence towards its stationary measure for this SDE, in the sense of random ergodic averages. The precise formula of the density of the stationary law gives a phase transition at the value κ=8 from integrability to non-integrability, that happens at the same value of κ as the change in behavior of the SLEκ trace from non-space filling to space-filling curve. Using convergence in total variation for the law of this diffusion towards stationarity, we identify families of random times on which the law of the arguments of points under the backward SLEκ flow converge to a closed form expression measure. For κ=4, this gives precise characterization for the random times on which the law of the arguments of points under the backward SLEκ flow converge to the uniform law.

Neural Abstraction-Based Controller Synthesis and Deployment

Abstraction-based techniques are an attractive approach for synthesizing correct-by-construction controllers to satisfy high-level temporal requirements. A main bottleneck for successful application of these techniques is the memory requirement, both during controller synthesis (to store the abstract transition relation) and in controller deployment (to store the control map). We propose memory-efficient methods for mitigating the high memory demands of the abstraction-based techniques using neural network representations . To perform synthesis for reach-avoid specifications, we propose an on-the-fly algorithm that relies on compressed neural network representations of the forward and backward dynamics of the system. In contrast to usual applications of neural representations, our technique maintains soundness of the end-to-end process. To ensure this, we correct the output of the trained neural network such that the corrected output representations are sound with respect to the finite abstraction. For deployment, we provide a novel training algorithm to find a neural network representation of the synthesized controller and experimentally show that the controller can be correctly represented as a combination of a neural network and a look-up table that requires a substantially smaller memory. We demonstrate experimentally that our approach significantly reduces the memory requirements of abstraction-based methods. We compare the performance of our approach with the standard abstraction-based synthesis on several models. For the selected benchmarks, our approach reduces the memory requirements respectively for the synthesis and deployment by a factor of 1.31× 10 5 and 7.13× 10 3 on average, and up to 7.54× 10 5 and 3.18× 10 4 . Although this reduction is at the cost of increased off-line computations to train the neural networks, all the steps of our approach are parallelizable and can be implemented on machines with higher number of processing units to reduce the required computational time.

Identifying parent bodies of meteorites among near-Earth asteroids

ABSTRACT Meteorites provide an important source of information about the formation and composition of asteroids, because the level of accuracy of studies and analyses performed in a laboratory cannot be achieved by any ground- or space-based observation. To better understand what asteroid types a meteorite represents, it is crucial to identify the body they originated from. In this paper, we aim to determine possible parent bodies for the known meteorite falls among the known population of near-Earth asteroids (NEAs). By using the similarity criterion DN, based on geocentric quantities, we found 20 possible NEA–meteorite pairs. By performing additional numerical simulations of the backward dynamics, we found that 12 of these pairs may be associated with a possible separation event from the progenitor NEA, while the remaining 8 pairs appear to be ambiguous or random associations. The most interesting are the Pribram and Neuschwanstein meteorites, which are dynamically associated with (482488) 2012 SW20 with a common separation age dating back to about 20–30 kyr ago, and the Motopi Pan meteorite, which has three candidate parent bodies: (454100) 2013 BO73, 2017 MC3, and 2009 FZ4. The average time of separation between our meteorite list and the progenitor body appears to be about 10 kyr, a time consistent with what is expected from the collision frequency of small NEAs. Based on our results, we suggest that about 25 per cent of meteorites do not originate in the main belt, but mainly from little collision events happening between NEAs in the inner Solar system.

Stochastic Entropy Production: Fluctuation Relation and Irreversibility Mitigation in Non-unital Quantum Dynamics

In this work, we study the stochastic entropy production in open quantum systems whose time evolution is described by a class of non-unital quantum maps. In particular, as in Phys Rev E 92:032129 (2015), we consider Kraus operators that can be related to a nonequilibrium potential. This class accounts for both thermalization and equilibration to a non-thermal state. Unlike unital quantum maps, non-unitality is responsible for an unbalance of the forward and backward dynamics of the open quantum system under scrutiny. Here, concentrating on observables that commute with the invariant state of the evolution, we show how the non-equilibrium potential enters the statistics of the stochastic entropy production. In particular, we prove a fluctuation relation for the latter and we find a convenient way of expressing its average solely in terms of relative entropies. Then, the theoretical results are applied to the thermalization of a qubit with non-Markovian transient, and the phenomenon of irreversibility mitigation, introduced in Phys Rev Res 2:033250 (2020), is analyzed in this context.

On global dynamics of type-K competitive Kolmogorov differential systems

This paper deals with global asymptotic behaviour of the dynamics for N-dimensional type-K competitive Kolmogorov systems of differential equations defined in the first orthant. It is known that the backward dynamics of such systems is type-K monotone. Assuming the system is dissipative and the origin is a repeller, it is proved that there exists a compact invariant set Σ which separates the basin of repulsion of the origin and the basin of repulsion of infinity and attracts all the non-trivial orbits. There are two closed sets S H and S V , their restriction to the interior of the first orthant are -dimensional hypersurfaces, such that the asymptotic dynamics of the type-K system in the first orthant can be described by a system on either S H or S V : each trajectory in the interior of the first orthant is asymptotic to one in S H and one in S V . Geometric and asymptotic features of the global attractor Σ are investigated. It is proved that the partition holds such that and . Thus, Σ0 contains all the ω-limit sets for all interior trajectories of any type-K subsystems and the closure as a subset of Σ is invariant and the upper boundary of the basin of repulsion of the origin. This Σ has the same asymptotic feature as the modified carrying simplex for a competitive system: every nontrivial trajectory below Σ is asymptotic to one in Σ and the ω-limit set is in Σ for every other nontrivial trajectory.

Instantaneous and Averaged Volatility in Two-Side Filtration Model of Financial Asset Pricing

A two-factor approach to asset pricing based on averaged historical and instantaneous volatility defined by a marginal investor’s beliefs and herding behaviour is proposed. For the two-side filtration, backward SDE-defined stochastic dynamics under the risk-neutral probability measure is determined by a target price distribution at given horizon with parameters averaged over a subset of active market agents. For the current price at market equilibrium and instantaneous volatility, the distribution of acceptable price of risk is obtained. The found implied volatility dependencies on strike and maturity are corresponding to the historical data for options by <xref>Carr and Wu (2016)</xref>. The liquidity discount for bonds and options is derived. A generalized solution for the FBSDE and a partial solution for the stochastic terminal conditions are found. The developed two-factor approach is well-suited to deep learning pricing algorithms.

DETONATE: Nonlinear Dynamic Evolution Modeling of Time-dependent 3-dimensional Point Cloud Profiles

Modeling the evolution of a 3D profile over time as a function of heterogeneous input data and the previous time steps’ 3D shape is a challenging, yet fundamental problem in many applications. We introduce a novel methodology for the nonlinear modeling of dynamically evolving 3D shape profiles. Our model integrates heterogeneous, multimodal inputs that may affect the evolvement of the 3D shape profiles. We leverage the forward and backward temporal dynamics to preserve the underlying temporal physical structures. Our approach is based on the Koopman operator theory for high-dimensional nonlinear dynamical systems. We leverage the theoretical Koopman framework to develop a deep learning-based framework for nonlinear, dynamic 3D modeling with consistent temporal dynamics. We evaluate our method on multiple high-dimensional and short-term dependent problems, and it achieves accurate estimates, while also being robust to noise.

Short-term Wind Speed Prediction Based on Improved Auto Encoder

In order to improve the wind power consumption level of the new power system with new energy as the main body, it is necessary to accurately predict the wind speed. The key is to refine the dynamic trend of the wind power system and the potential physical structure in the wind speed sequence. Firstly, on the basis of the library Koopman dynamics theory and the encoder structures, a physically constrained spatio-temporal neural network is built, which generates the linear evolution moment of the nonlinear variables of the wind farm. Secondly, the system trend is approximated by the linear evolution matrix, and the forward and backward dynamics are fully considered in the prediction process. Then, the bidirectional correlation prediction mechanism and the cost function adapted to different objects are set to reduce the requirements for the reversibility and stability of the prediction sequence. Meanwhile, the hidden vector of feature space is visualized to show the feature interval dependency in the system. Finally, the effectiveness of the proposed method is verified by the wind speed measurement data of Prince Mountain in Beipiao. The results show that the proposed method has high prediction accuracy, strong generalization ability, and high interpretability for strong random and strong fluctuation wind speed series.

Paradoxical simulation results of chaos-like chattering in the bouncing ball system

This paper reports and investigates paradoxical simulation results of the bouncing ball system. Chaos-like motion of the bouncing ball system with intermittent chattering (Zeno behavior) is observed in simulations if the relative acceleration of the table exceeds a critical value. However, one can show that this is theoretically impossible. A detailed analysis is given by looking at the backward and forward dynamics of grazing solutions. It is shown in detail that a self-similar structure appears if the relative acceleration of the table exceeds the critical value.

Analysis of a mathematical model for the transmission dynamics of human melioidosis

A deterministic model for the transmission dynamics of melioidosis disease in human population is designed and analyzed. The model is shown to exhibit the phenomenon of backward bifurcation, where a stable disease-free equilibrium co-exists with a stable endemic equilibrium when the basic reproduction number [Formula: see text] is less than one. It is further shown that the backward bifurcation dynamics is caused by the reinfection of individuals who recovered from the disease and relapse. The existence of backward bifurcation implies that bringing down [Formula: see text] to less than unity is not enough for disease eradication. In the absence of backward bifurcation, the global asymptotic stability of the disease-free equilibrium is shown whenever [Formula: see text]. For [Formula: see text], the existence of at least one locally asymptotically stable endemic equilibrium is shown. Sensitivity analysis of the model, using the parameters relevant to the transmission dynamics of the melioidosis disease, is discussed. Numerical experiments are presented to support the theoretical analysis of the model. In the numerical experimentations, it has been observed that screening and treating individuals in the exposed class has a significant impact on the disease dynamics.

Dynamics of a Discrete Nonlinear Prey–Predator Model

The dynamics of a discrete nonlinear prey–predator model is studied. The local dynamical results are obtained on asymptotic properties of fixed points and Neimark–Sacker bifurcations. Then global dynamics is studied by finding invariant sets. Also some achievements on attraction are shown for certain trivial invariant sets including a shadowing type result, and estimates on boundedness of orbits. Some ergodic type results are also derived. Certain issues are extended to systems with impulses by showing the influence of impulses on dynamics. Moreover, backward dynamics is investigated as well. All these results are derived analytically and numerical computations are presented to support them.

Structure of resonance eigenfunctions for chaotic systems with partial escape.

Physical systems are often neither completely closed nor completely open, but instead are best described by dynamical systems with partial escape or absorption. In this paper we introduce classical measures that explain the main properties of resonance eigenfunctions of chaotic quantum systems with partial escape. We construct a family of conditionally invariant measures with varying decay rates by interpolating between the natural measures of the forward and backward dynamics. Numerical simulations in a representative system show that our classical measures correctly describe the main features of the quantum eigenfunctions: their multifractal phase-space distribution, their product structure along stable and unstable directions, and their dependence on the decay rate. The (Jensen-Shannon) distance between classical and quantum measures goes to zero in the semiclassical limit for long- and short-lived eigenfunctions, while it remains finite for intermediate cases.