Unperturbed Dynamics Research Articles

High-order state transition polynomial with time expansion based on differential algebra

In this study, a high-order state transition polynomial with time expansion (STP-T) method is developed to propagate an initial orbital state around its reference value to a variable final time based on the differential algebra (DA) technique. STP-T is a high-order Taylor polynomial of the final orbital state expanded around the reference initial state and reference propagation time. Since the final state usually shows different nonlinearity with respect to different components of initial state and propagation time, a weighted-order scheme is combined with STP-T, which enables the STP-T to have higher orders on the components with higher nonlinearity and lower orders on the components with lower nonlinearity. Then, an error estimation method is presented, which can a priori provide the error profiles of a STP-T and is useful for selecting a proper order and determining the corresponding valid ranges of displacements. Finally, the STP-T method is tested for orbit propagation under three typical orbital dynamics: the unperturbed Keplerian dynamics, the J2 perturbed two-body dynamics, and the nonlinear relative dynamics. The numerical simulation results indicate that the STP-T supplies a good approximation of the final state within certain valid ranges of initial state and propagation time, the a priori estimated error is close to the exact error in sense of trend and magnitude, and the computational cost can be significantly saved by the weighted-order scheme without loss of accuracy.

Observability analysis and autonomous navigation for two satellites with relative position measurements

The autonomous navigation of multi-satellite systems using only on-board measurements is a fundamental task in many space missions. The main purpose of this study is to establish new methods for the autonomous orbit determination of a dual satellite system using relative position measurements only. A novel concept, k-order local weak observability, is proposed. Based on unperturbed Kepler orbit dynamics and J2-perturbed orbit dynamics respectively, sufficient and necessary conditions of k-order local weak observability are mathematically proved for the autonomous navigation system. Observability-based modified EKF, modified UKF, and modified SDREF are presented and used as navigation algorithms. Simulation results illustrate the performance of the developed navigation algorithms in comparison with the traditional EKF, UKF, and SDREF.

Desynchronization of the Germinal Center Dynamics and Remodeling of the Tumor Microenvironment Characterize KMT2D-Driven Lymphomagenesis

Follicular lymphoma (FL) is a prototypical example of germinal center (GC) derived B-cell lymphoma. Using a mouse model recapitulating the sporadic occurrence of the FL hallmark BCL2/IGH translocation in healthy individuals, our previous work demonstrated that FL genesis is a dynamic process that requires multiple re-entries of BCL2+ memory B-cells into the GC to ultimately accumulate in lymphoid organs. In line with this, using single-cell gene expression analysis of human FL vs normal GC B-cells, we recently discovered that FL cells are not ‘frozen’ at a particular GC maturation stage but instead exhibit a major desynchronization of the GC-specific expression program (Milpied et al. Nat Immunol in press). Since KMT2D loss-of-function mutations and BCL2 translocations are the 2 main alterations in FL, we hypothesized these 2 genetic events might explain the GC program desynchronization we observe in humans.To explore the in vivo consequences of Kmt2d inactivation with Bcl2 overexpression in regulating GC/memory dynamics, we transduced bone marrow progenitors carrying B-cell-specific conditional Cd19-Cre Kmt2dflox/flox alleles with a retrovirus encoding human BCL2 or reporter alone, followed by iv transplantation into lethally irradiated WT recipients. Only double-mutant Kmt2d-/-Bcl2+ mice manifested with GC-derived lymphomas in chronically challenged animals, recapitulating histological and phenotypic features associated with human FL progression from early preneoplastic lesions to overt FL-like tumors. We used integrative single-cell analysis of surface phenotype (10-color panel), gene expression (88-gene panel by microfluidic RT-qPCR) and IGH clonality to deconvolute cellular heterogeneity of flow-sorted GC and memory B-cells after acute (day 10) or chronic T-cell dependent immunization in double-mutant vs. single Bcl2+, Kmt2d-/- or WT mice, retaining >4000 cells for downstream analysis. Populations of WT GC B-cells were molecularly heterogeneous and spanned a cyclic continuum of transitional B-cell states polarized between the light and dark zone where synchronized expression of gene modules characterized mouse GC functional identity. In acute responses, single and double-mutant mice formed GC similar to control chimera mice, and single GC B-cells from all genotypes clustered together with WT GCs, suggesting unperturbed GC transcriptional dynamics upon first antigen encounter. However, preneoplastic/tumoral Kmt2d-/-Bcl2+ mice after chronic challenge showed massive GC hyperplasia and single B-cells expressed a distinct transcriptional signature that clustered separately from WT GC or memory cells. Specifically, murine lymphoma B-cells sorted with a GC-like phenotype accumulated in transitional cell states where the synchrony of most GC-specific co-expression patterns was progressively lost whereas expression of cytokines (Lta) or surface markers linked to GC to memory transition (Gpr183, Cxcr3) became markedly expressed, indicating that Kmt2d-deficient lymphomas were not blocked at a particular GC stage.Given the importance of T-cell help for the fate ‘decisions’ of GC-to-memory B-cells, we further explored whether tumor cell-intrinsic factors may affect immune cell phenotypes thereby supporting the GC gene expression desynchronization. Using flow cytometry, we found that Kmt2d inactivation instructed a progressive remodeling of the tumor microenvironment with an increased recruitment of CD4+ T-follicular helper (TFH) (n=21, p<0.01). Using droplet-based single-cell RNA-seq to profile total spleens from 2 WT mice and 2 lymphomas (>9000 cells), we revealed a TFH cluster with an activation signature distinct from normal TFH and a concomitant expansion of exhausted CD8+ T-cells strongly co-expressing inhibitory receptors (Lag3, Tim3, Pdcd1), thereby indicating that Kmt2d inactivation in B-cells may favor lymphoma formation by shaping the FL tumor supportive niche and contributing to immune evasion.In summary, our integrative single-cell analyses in murine lymphomas revealed that Kmt2d mutations in FL not only instruct B-cell intrinsic effects involving the desynchronization of the normal GC expression program, but also trigger a concomitant re-education of a tumor-supportive immune microenvironment, establishing for the first time a key link between the most frequent epigenetic alteration and the FL microenvironment. DisclosuresSalles:F. Hoffmann-La Roche Ltd: Consultancy, Honoraria, Research Funding; Celgene: Honoraria, Other: Advisory Board, Research Funding; Janssen: Honoraria, Other: Advisory Board; Novartis: Consultancy, Honoraria; Takeda: Honoraria; Servier: Honoraria, Other: Advisory Board; Epizyme: Honoraria; Merck: Honoraria; BMS: Honoraria, Other: Advisory Board; Morphosys: Honoraria; Acerta: Honoraria; Amgen: Honoraria; Gilead: Honoraria, Other: Advisory Board; Pfizer: Honoraria; Servier: Honoraria; Abbvie: Honoraria.

Dynamic Behavior Analysis of a Rotating Smooth and Discontinuous Oscillator with Irrational Nonlinearity

This paper focuses on a novel rotating mechanical model which provides a cylindrical example of transition from smooth to discontinuous dynamics. The remarkable feature of the proposed system is a cylindrical dynamical system with strongly irrational nonlinearity exhibiting both smooth and discontinuous characteristics due to the geometry configuration. By using nonlinear dynamical technique, the unperturbed dynamics of the proposed system are studied including the irrational restoring force, stability of equilibria, Hamiltonian function and phase portraits. Note that a pair of double heteroclinic-like orbits connecting two non-standard saddle points are proposed in discontinuous case. For the perturbed system, we introduce a cylindrical approximate system for which the analytical solutions can be obtained successfully to reflect the nature of the original system without barrier of the irrationalities. Melnikov method is employed to detect the chaotic thresholds for the double heteroclinic orbits under the perturbation of viscous damping and external harmonic forcing in smooth regime. Finally, numerical simulations show the efficiency of the proposed method and demonstrate the predicated periodic solution and chaotic attractors. It is found that a good degree of correlation is demonstrated in the bifurcation diagram, the phase portraits of periodic solution, the chaotic attractor’ structures and the Lyapunov characteristics between the original system and approximate system.

Association between stride time fractality and gait adaptability during unperturbed and asymmetric walking

Human locomotion is an inherently complex activity that requires the coordination and control of neurophysiological and biomechanical degrees of freedom across various spatiotemporal scales. Locomotor patterns must constantly be altered in the face of changing environmental or task demands, such as heterogeneous terrains or obstacles. Variability in stride times occurring at short time scales (e.g., 5–10 strides) is statistically correlated to larger fluctuations occurring over longer time scales (e.g., 50–100 strides). This relationship, known as fractal dynamics, is thought to represent the adaptive capacity of the locomotor system. However, this has not been tested empirically. Thus, the purpose of this study was to determine if stride time fractality during steady state walking associated with the ability of individuals to adapt their gait patterns when locomotor speed and symmetry are altered. Fifteen healthy adults walked on a split-belt treadmill at preferred speed, half of preferred speed, and with one leg at preferred speed and the other at half speed (2:1 ratio asymmetric walking). The asymmetric belt speed condition induced gait asymmetries that required adaptation of locomotor patterns. The slow speed manipulation was chosen in order to determine the impact of gait speed on stride time fractal dynamics. Detrended fluctuation analysis was used to quantify the correlation structure, i.e., fractality, of stride times. Cross-correlation analysis was used to measure the deviation from intended anti-phasing between legs as a measure of gait adaptation. Results revealed no association between unperturbed walking fractal dynamics and gait adaptability performance. However, there was a quadratic relationship between perturbed, asymmetric walking fractal dynamics and adaptive performance during split-belt walking, whereby individuals who exhibited fractal scaling exponents that deviated from 1/f performed the poorest. Compared to steady state preferred walking speed, fractal dynamics increased closer to 1/f when participants were exposed to asymmetric walking. These findings suggest there may not be a relationship between unperturbed preferred or slow speed walking fractal dynamics and gait adaptability. However, the emergent relationship between asymmetric walking fractal dynamics and limb phase adaptation may represent a functional reorganization of the locomotor system (i.e., improved interactivity between degrees of freedom within the system) to be better suited to attenuate externally generated perturbations at various spatiotemporal scales.

Robustness of Synchrony in Complex Networks and Generalized Kirchhoff Indices.

In network theory, a question of prime importance is how to assess network vulnerability in a fast and reliable manner. With this issue in mind, we investigate the response to external perturbations of coupled dynamical systems on complex networks. We find that for specific, nonaveraged perturbations, the response of synchronous states depends on the eigenvalues of the stability matrix of the unperturbed dynamics, as well as on its eigenmodes via their overlap with the perturbation vector. Once averaged over properly defined ensembles of perturbations, the response is given by new graph topological indices, which we introduce as generalized Kirchhoff indices. These findings allow for a fast and reliable method for assessing the specific or average vulnerability of a network against changing operational conditions, faults, or external attacks.

Using Perturbed Underdamped Langevin Dynamics to Efficiently Sample from Probability Distributions

In this paper we introduce and analyse Langevin samplers that consist of perturbations of the standard underdamped Langevin dynamics. The perturbed dynamics is such that its invariant measure is the same as that of the unperturbed dynamics. We show that appropriate choices of the perturbations can lead to samplers that have improved properties, at least in terms of reducing the asymptotic variance. We present a detailed analysis of the new Langevin sampler for Gaussian target distributions. Our theoretical results are supported by numerical experiments with non-Gaussian target measures.

On the Design of Nonlinear Distributed Control Protocols for Platooning Systems

In this letter, we introduce a novel sufficient condition for the stability of acyclic directed networks subject to time- and state-dependent disturbances. Such a condition, which essentially characterizes the behavior of the network in terms of the solutions of its unperturbed dynamics, is applied to address the problem of designing distributed control protocols for vehicle platooning. Specifically, we show how it can be used to design both linear and nonlinear distributed control protocols for the stable platooning of a network of automated vehicles. We illustrate the effectiveness of our approach via a representative example.

Network Formation under Heterogeneous Costs: The Multiple Group Model

It is widely recognized that the shape of networks influences both individual and aggregate behavior. This raises the question which types of networks are likely to arise. Our paper fits into the literature that addresses this question. The paper continues on the work of Galeotti, Goyal and Kamphorst (2003). In their paper they investigate a model of network formation, where players are divided into groups. The costs of a link between any pair of players are increasing in the distance between the groups that these players belong to. They apply the solution concept of minimal curb sets to the case of two groups. In this paper we give a full characterization of the networks induced by a minimal curb set for any number of groups. To do so, we show that in our multiple group model each minimal curb set is a so-called super-tight curb set, that is a minimal curb set satisfying the condition that in each state of the set every player has the same best reply. From the proof it follows that every recurrent class of an unperturbed best reply dynamics is a minimal (super-tight) curb set and reversely. From this result we obtain the characterization of the types of networks that may arise in a minimal curb set. We show that such networks may have features that can not occur in networks with at most two groups. Nevertheless, local centrality and center-sponsorship are still important characteristics of the networks in minimal curb sets.

Leading birds by their beaks: the response of flocks to external perturbations

We study the asymptotic response of polar ordered active fluids (‘flocks’) to small external aligning fields h. The longitudinal susceptibility diverges, in the thermodynamic limit, like as . In finite systems of linear size L, saturates to a value . The universal exponents ν and γ depend only on the spatial dimensionality d, and are related to the dynamical exponent z and the ‘roughness exponent’ α characterizing the unperturbed flock dynamics. Using a well supported conjecture for the values of these two exponents, we obtain , in d = 2 and , in d = 3. These values are confirmed by our simulations.

Periodic thermodynamics of open quantum systems.

The thermodynamics of quantum systems coupled to periodically modulated heat baths and work reservoirs is developed. By identifying affinities and fluxes, the first and the second law are formulated consistently. In the linear response regime, entropy production becomes a quadratic form in the affinities. Specializing to Lindblad dynamics, we identify the corresponding kinetic coefficients in terms of correlation functions of the unperturbed dynamics. Reciprocity relations follow from symmetries with respect to time reversal. The kinetic coefficients can be split into a classical and a quantum contribution subject to an additional constraint, which follows from a natural detailed balance condition. This constraint implies universal bounds on efficiency and power of quantum heat engines. In particular, we show that Carnot efficiency cannot be reached whenever quantum coherence effects are present, i.e., when the Hamiltonian used for work extraction does not commute with the bare system Hamiltonian. For illustration, we specialize our universal results to a driven two-level system in contact with a heat bath of sinusoidally modulated temperature.

Intrinsic limitation of cavity-enhanced Faraday detection of spin noise in quantum wells and quantum dots

Spin noise spectroscopy is a quite attractive experimental tool for studying unperturbed spin dynamics and magnetic resonance in semiconductor nanostructures. However in some cases its practical interest maybe severely limited by the weakness of the spin noise signal to be detected. In this paper we examine by how much the detection of spin noise of magnetic atoms or of nuclei, in quantum wells or quantum dots, can be improved by making use of cavity-enhanced Faraday rotation. The conditions for optimized cavities are first determined. In reflection geometry it corresponds to tune the cavity to the critical point of impedance matching. It is shown that even for optimized cavities the enhancement in spin noise detection is intrinsically limited by absorption. It turns out that the cavity effect improves the spin noise detection only when the inhomogeneous broadening of the involved optical resonance is large compared to its radiative broadening.

Communication: Fully coherent quantum state hopping.

In this paper, we describe a new and fully coherent stochastic surface hopping method for simulating mixed quantum-classical systems. We illustrate the approach on the simple but unforgiving problem of quantum evolution of a two-state quantum system in the limit of unperturbed pure state dynamics and for dissipative evolution in the presence of both stationary and nonstationary random environments. We formulate our approach in the Liouville representation and describe the density matrix elements by ensembles of trajectories. Population dynamics are represented by stochastic surface hops for trajectories representing diagonal density matrix elements. These are combined with an unconventional coherent stochastic hopping algorithm for trajectories representing off-diagonal quantum coherences. The latter generalizes the binary (0,1) "probability" of a trajectory to be associated with a given state to allow integers that can be negative or greater than unity in magnitude. Unlike existing surface hopping methods, the dynamics of the ensembles are fully entangled, correctly capturing the coherent and nonlocal structure of quantum mechanics.

Adapted random perturbations for non-uniformly expanding maps

We obtain stochastic stability of C2 non-uniformly expanding one-dimensional endomorphisms, requiring only that the first hyperbolic time map be Lp-integrable for p &gt; 3. We show that, under this condition (which depends only on the unperturbed dynamics), we can construct a random perturbation that preserves the original hyperbolic times of the unperturbed map and, therefore, to obtain non-uniform expansion for random orbits. This ensures that the first hyperbolic time map is uniformly integrable for all small enough noise levels, which is known to imply stochastic stability. The method enables us to obtain stochastic stability for a class of maps with infinitely many critical points. For higher dimensional endomorphisms, a similar result is obtained, but under stronger assumptions.

Tension is required but not sufficient for focal adhesion maturation without a stress fiber template

Focal adhesion composition and size are modulated in a myosin II-dependent maturation process that controls adhesion, migration, and matrix remodeling. As myosin II activity drives stress fiber assembly and enhanced tension at adhesions simultaneously, the extent to which adhesion maturation is driven by tension or altered actin architecture is unknown. We show that perturbations to formin and α-actinin 1 activity selectively inhibited stress fiber assembly at adhesions but retained a contractile lamella that generated large tension on adhesions. Despite relatively unperturbed adhesion dynamics and force transmission, impaired stress fiber assembly impeded focal adhesion compositional maturation and fibronectin remodeling. Finally, we show that compositional maturation of focal adhesions could occur even when myosin II-dependent cellular tension was reduced by 80%. We propose that stress fiber assembly at the adhesion site serves as a structural template that facilitates adhesion maturation over a wide range of tensions. This work identifies the essential role of lamellar actin architecture in adhesion maturation.

Structural Dynamics of Clamshell Rotation during the Incipient Relaxation Process of Photodissociated Carbonmonoxy Myoglobin: Statistical Analysis by the Perturbation Ensemble Method

The structural dynamics of the clamshell rotation of photodissociated carbonmonoxy myoglobin, which is expected to be important for hemoglobin allostery, is investigated by the perturbation ensemble method. In this method, many pairs of perturbed and unperturbed molecular dynamics trajectories are ensemble-averaged to cancel out thermal noises and to detect subtle changes. The number of MD trajectory pairs, in this work 2000 pairs, should be determined to obtain physical properties of interest with statistically meaningful precisions. The calculated structural changes after 20 ps of the photodissociation are consistent with those by time-resolved X-ray diffraction at 100 ps delay time. In the heme proximal side region including the F and H helices, both helices displaced in the proximal direction. Meanwhile, in the heme distal side region including E and A helices, both helices moved toward the heme group after photodissociation. These proximal and distal side displacements occur on a fast time scale (almost complete within 3 ps) and are consistent with the clamshell rotation. Moreover, it was found that the ensemble-averaged structural dynamics of the photodissociated MbCO is independent of the amount of initial excess vibrational energy of the heme, or the difference of excitation photon wavelength. These results provide atomistic details on the functionally important dynamics of the clamshell rotation. Application of the present methodology to Hb will give new insight into the incipient stereochemical mechanism of hemoglobin allostery.

Geometric shadowing in slow–fast Hamiltonian systems

We study a class of slow–fast Hamiltonian systems with any finite number of degrees of freedom, but with at least one slow one and two fast ones. At ε = 0 the slow dynamics is frozen. We assume that the frozen system (i.e. the unperturbed fast dynamics) has families of hyperbolic periodic orbits with transversal heteroclinics.For each periodic orbit we define an action J. This action may be viewed as an action Hamiltonian (in the slow variables). It has been shown in Brännström and Gelfreich (2008 Physica D 237 2913–21) that there are orbits of the full dynamics which shadow any finite combination of forward orbits of J for a time t = O(ε−1).We introduce an assumption on the actions of periodic orbits which enables us to shadow any continuous curve (of arbitrary length) in the slow phase space for any time. The slow dynamics shadows the curve as a purely geometrical object, thus the time on the slow dynamics has to be reparametrized.

In situRamsey interferometry and diffraction echo with an atomic Fermi gas

We report on the observation of Bragg diffraction of a spin-polarized ultracold $^{6}\mathrm{Li}$ Fermi gas and demonstrate a Ramsey-type matter-wave interferometer. Suppression of $s$-wave collisions by the Pauli principle allows for unperturbed dynamics of the atoms in the trap for longer than $2\phantom{\rule{0.3em}{0ex}}\mathrm{s}$. Employing an echo pulse sequence, we observe coherent superpositions of momentum states which do not show any sign of decoherence during the experimentally limited observation time of $100\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$. In contrast, significant decoherence is observed in the presence of a cold cloud of $^{87}\mathrm{Rb}$ atoms. The experiment demonstrates the feasibility of high-resolution atomic interferometry with applications for precision measurements in small volumes and near surfaces.

NETWORK FORMATION UNDER HETEROGENEOUS COSTS: THE MULTIPLE GROUP MODEL

It is widely recognized that the shape of networks influences both individual and aggregate behavior. This raises the question which types of networks are likely to arise. In this paper we investigate a model of network formation, where players are divided into groups and the costs of a link between any pair of players are increasing in the distance between the groups that these players belong to. We give a full characterization of the networks induced by a minimal curb set for any number of groups. To do so, we show that in our multiple group model each minimal curb set is a so-called super-tight curb set, that is a minimal curb set satisfying the condition that in each state of the set every player has the same best reply. From the proof it follows that every recurrent class of an unperturbed best reply dynamics is a minimal (super-tight) curb set and reversely, which yields the characterization result. We show that in case of multiple groups networks in minimal curb sets may have features that can not occur in networks with at most two groups. Nevertheless, local centrality and center-sponsorship are still important characteristics of the networks in minimal curb sets.

Resonant Forcing of Chaotic Dynamics

We study resonances of multidimensional chaotic map dynamics. We use the calculus of variations to determine the additive forcing function that induces the largest response, that is, the greatest deviation from the unperturbed dynamics. We include the additional constraint that only select degrees of freedom be forced, corresponding to a very general class of problems in which not all of the degrees of freedom in an experimental system are accessible to forcing. We find that certain Lagrange multipliers take on a fundamental physical role as the efficiency of the forcing function and the effective forcing experienced by the degrees of freedom which are not forced directly. Furthermore, we find that the product of the displacement of nearby trajectories and the effective total forcing function is a conserved quantity. We demonstrate the efficacy of this methodology with several examples.