Oscillatory Trajectories Research Articles

Six distinct NFκB signaling codons convey discrete information to distinguish stimuli and enable appropriate macrophage responses

SUMMARYMacrophages initiate inflammatory responses via the transcription factor NFκB. The temporal pattern of NFκB activity determines which genes are expressed and thus, the type of response that ensues. Here, we examined how information about the stimulus is encoded in the dynamics of NFκB activity. We generated an mVenus-RelA reporter mouse line to enable high-throughput live-cell analysis of primary macrophages responding to host- and pathogen-derived stimuli. An information-theoretic workflow identified six dynamical features—termed signaling codons—that convey stimulus information to the nucleus. In particular, oscillatory trajectories were a hallmark of responses to cytokine but not pathogen-derived stimuli. Single-cell imaging and RNA sequencing of macrophages from a mouse model of Sjögren’s syndrome revealed inappropriate responses to stimuli, suggestive of confusion of two NFκB signaling codons. Thus, the dynamics of NFκB signaling classify immune threats through six signaling codons, and signal confusion based on defective codon deployment may underlie the etiology of some inflammatory diseases.

Power and spectral evolution of a Free Electron Laser oscillator with electron beam energy ramping

This work is focused on experiments showing enhancements in power extraction efficiency and spectral control of a W-band Free Electron Laser oscillator (FELo) using ramping of the electron beam energy. The FELo operates at 1.4 MeV with electron beam currents of 1–2 A with pulse duration 10–20 μs. Changing the beam energy post-laser-saturation of the initially unbunched continuous electron beam changes the phase-space oscillation trajectory between the beam energy and trapping ponderomotive wave. This enables very significant increases in output power with just 2% changes in beam energy, cases of 39%, and 100% are presented. Unlike in previous work a variable delay has been introduced between the start of the electron beam and the ramp in electron beam energy such that the effect can be observed unambiguously despite significant system jitter from shot-to-shot. In addition to increasing radiative efficiency, where desirable this could be used to rapidly modulate the power without a need to modify parameters such as the beam current or resonator out-coupling. This effect is shown to pull the locked longitudinal modes up or down depending on the direction of the ramp allowing fine frequency control and influence over mode-competition and mode-hops. To complement the experiments simulations were run to map the full range of beam-energy-ramping against resonator out-coupling and beam current for the experimental system.

A tale of two rhythms: Locked clocks and chaos in biology.

The fundamental mechanisms that control and regulate biological organisms exhibit a surprising level of complexity. Oscillators are perhaps the simplest motifs that produce time-varying dynamics and are ubiquitous in biological systems. It is also known that such biological oscillators interact with each other-for instance, circadian oscillators affect the cell cycle, and somitogenesis clock proteins in adjacent cells affect each other in developing embryos. Therefore, it is vital to understand the effects that can emerge from non-linear interaction between oscillations. Here, we show how oscillations typically arise in biology and take the reader on a tour through the great variety in dynamics that can emerge even from a single pair of coupled oscillators. We explain how chaotic dynamics can emerge and outline the methods of detecting this in experimental time traces. Finally, we discuss the potential role of such complex dynamical features in biological systems.

Conservation laws and spin system modeling through principal component analysis

This paper examines several applications of principal component analysis (PCA) to physical systems. The central result demonstrates that the PCA can identify from the recorded system trajectories conserved quantities that take the form of polynomials in the system variables in an easily programmed and straightforward fashion. In particular, a data record composed of the positions and velocities generated from simulations of two-dimensional harmonic oscillator trajectories is recast into a feature record containing the values of the lowest order atomic polynomials formed from these quantities at each evaluation time. The combinations of the features that are conserved can then be obtained from the principal components of the feature record with the smallest explained variances. Additionally, two features of the application of the PCA to homogeneous periodic spin systems are identified and discussed. The first of these relates to certain characteristic behaviors of the explained variances associated with the principal components of the spin distribution that are found to be artifacts of the boundary geometry. The PCA is then employed to generate synthetic spin realizations with probability distributions in energy-magnetization space that resemble the corresponding input distributions although the associated statistical quantities are not sufficiently accurate.

The Motion of Ions Confined in a Molecular Channel

In order to understand the features governing the motion of ions in a molecular environment the migrational features of Na⁺ and Cl⁻ ions in a molecular channel composed of stacked crown ether 6-CE-18 rings is followed using molecular dynamics, which shows that Na⁺ is subject to a much greater dynamic hindrance than the Cl⁻ ion. The effects of the fluctuating electric fields of the atomic constituents in the channel on the motion of the migrants are investigated by clamping them so as to remove the fluctuations. The dynamic system is simulated both <i>in vacuo</i> and in water. For both it is found that the fluctuating electric fields of the channel and water atoms play a significantly greater role in the ion motions than do fluctuations in the ‘non-bonded’ interactions. The effect of temperature on the dynamics is investigated. Oscillatory trajectories are followed via the force and the potential energy profiles of the system over the timestep range of the molecular dynamics.

Application of Latent Growth Curve modeling to predict individual trajectories during neurofeedback treatment for tinnitus.

Tinnitus is a heterogeneous phenomenon indexed by various EEG oscillatory profiles. Applying neurofeedback (NFB) with the aim of changing these oscillatory patterns not only provides help for those who suffer from the phantom percept, but a promising foundation from which to probe influential factors. The reliable attribution of influential factors that potentially predict oscillatory changes during the course of NFB training may lead to the identification of subgroups of individuals that are more or less responsive to NFB training. The present study investigated oscillatory trajectories of delta (3-4Hz) and individual alpha (8.5-12Hz) during 15 NFB training sessions, based on a Latent Growth Curve framework. First, we found the desired enhancement of alpha, while delta was stable throughout the NFB training. Individual differences in tinnitus-specific variables and general-, as well as health-related quality of life predictors were largely unrelated to oscillatory change prior to and across the training. Only the predictors age and sex at baseline were clearly related to slow-wave delta, particularly so for older female individuals who showed higher delta power values from the start. Second, we confirmed a hierarchical cross-frequency association between the two frequency bands; however, in opposing directions to those anticipated in tinnitus. The establishment of individually tailored NFB protocols would boost this therapy's effectiveness in the treatment of tinnitus. In our analysis, we propose a conceptual groundwork toward this goal of developing more targeted treatment.

Analytical predictor–corrector entry guidance for hypersonic gliding vehicles

Abstract For the entry guidance problem of hypersonic gliding vehicles (HGVs), an analytical predictor–corrector guidance method based on feedback control of bank angle is proposed. First, the relative functions between the velocity, bank angle and range-to-go are deduced, and then, the analytical relation is introduced into the predictor–corrector algorithm, which is used to replace the traditional method to predict the range-to-go via numerical integration. To eliminate the phugoid trajectory oscillation, a method for adding the aerodynamic load feedback into the control loop of the bank angle is proposed. According to the quasi-equilibrium gliding condition, the function of the quasi-equilibrium glide load along with the velocity variation is derived. For each guidance period, the deviation between the real-time load and the quasi-equilibrium gliding load is revised to obtain a smooth reentry trajectory. The simulation results indicate that the guidance algorithm can adapt to the mission requirements of different downranges, and it also has the ability to guide the vehicle to carry out a large range of lateral maneuvers. The feedback control law of the bank angle effectively eliminates the phugoid trajectory oscillation and guides the vehicle to complete a smooth reentry flight. The Monte Carlo test indicated that the guidance precision and robustness are good.

Dynamics and selective temporal focusing of a time truncated Airy pulse in varying dispersive media

We theoretically and numerically investigate the dynamics of a time truncated finite energy Airy pulse (FEAP) under longitudinally varying group velocity dispersion (GVD), which significantly influences the Airy dynamics. Realistic waveguide geometries are proposed that offer linear and oscillating GVD profiles through which one can efficiently control the ballistic Airy trajectory. We observe that a linear spatial variation of GVD may lead to a quasi-linear trajectory of the accelerating Airy pulse with modulated peak power. The impact of the periodic GVD on Airy dynamics is found to be interesting, where FEAP exhibits an oscillatory trajectory with a periodic modulation of peak power. Exploiting the transcendental relation between the modulation strength and period of GVD, we theoretically estimate an optimized length of the waveguide that delivers maximum power at the output. The effect of oscillatory third-order dispersion is dramatic for an Airy pulse, where it experiences successive singularities during its propagation. At singularity, the Airy pulse undergoes a temporal inversion after reaching a focal point. The rich dynamics of FEAP near the singularity point is theoretically investigated by solving the propagation equation. We provide detailed theoretical analyses to achieve selective temporal focusing of FEAP, which may be useful for practical applications. Theoretical results derived in this paper are verified numerically with satisfactory agreements.

Pseudo-linear inertial navigation algorithm

A new method is illustrated for processing the output of a set of triad orthogonal rate gyros and accelerometers to reconstruct vehicle navigation parameters (attitude, velocity, and position). The paper introduces two vectors with dimensions 4 × 1 as velocity and position quaternions. The navigation equations for strapdown systems are nonlinear but after using these parameters, the navigation equations are converted into a pseudo-linear system. The new set of navigation equations has an analytical solution and the state transition matrix is used to solve the linear time-varying differential equations through time series. The navigation parameters are updated using the new formulation for strapdown navigation equations. Finally, the quaternions of velocity and position are converted into the original position and velocity vectors. The combination of the coning motion and a translational oscillatory trajectory is used to evaluate the accuracy of the proposed algorithm. The simulations show significant improvement in the accuracy of the inertial navigation system, which is achieved through the mentioned algorithm.

Eco-Driving Algorithm with a Moving Bottleneck on a Single-Lane Road

Eco-driving strategies have been applied to smooth traffic flow and reduce greenhouse gas emissions along with air pollution. In this paper, we propose an eco-driving strategy to reduce traffic oscillation and smooth trajectories for connected vehicles following a moving bottleneck on a single-lane road. The eco-driving strategy, which leverages vehicle-to-vehicle (V2V) communications, designs advisory speed limits for each following vehicle through a control algorithm. The algorithm is based on the prediction of the following vehicle trajectories dictated by a moving bottleneck. The following vehicle trajectories are obtained by analytically solving the moving bottleneck problem in which the moving bottleneck speeds vary over time. In addition, the bounded acceleration rate is imposed in car-following behavior. The benefits of this strategy are demonstrated by applying it to four scenarios with different bottleneck movements. By simulating the scenarios with Newell’s car-following model with bounded acceleration and VT-Micro emission model, we find that both speed fluctuations and emissions are reduced with the algorithm in the scenarios in which the moving bottleneck has a constant speed, accelerates, decelerates and stops-and-goes. The results indicate that the proposed eco-driving algorithm can smooth traffic flow behind a moving bottleneck.

Three-dimensional dynamics of fluid-conveying pipe simultaneously subjected to external axial flow

In this paper, the instability and three-dimensional (3-D) nonlinear dynamics of a supported pipe subjected concurrently to internal and external axial flows are investigated, for the flow velocity of internal fluid being either steady or pulsatile. For that purpose, a 3-D version of nonlinear governing equations for two perpendicular lateral displacements of the pipe are derived by the use of extended Hamilton's principle. Unlike previous two-dimensional (2-D) versions of governing equation for a supported pipe subjected concurrently to external and internal axial flows, this new 3-D version of governing equations is capable of predicting the non-planar motions of the pipe. Based on linear analyses, it is shown that buckling instability may occur for an internal steady fluid flow while parametric instability can be generated by an internal pulsatile flow. In the nonlinear analyses, the nonlinear dynamics of the pipe with various internal and external flow velocities for different pulsating frequencies and amplitudes are represented by means of bifurcation diagrams, time traces, phase portraits, oscillation trajectories, power spectral density (PSD) diagrams and Poincaré maps. Some interesting dynamical behaviors, including periodic, quasi-periodic and chaotic motions, are detected in a wide range of pulsating frequency of interest. In many cases, non-planar motions of the pipe may be induced by fluid flows. These non-planar motions, however, need to be determined by using the present 3-D theoretical model instead of previously used 2-D ones for supported pipes subjected concurrently to internal and external axial flows.

The high forecasting complexity of stochastically perturbed periodic orbits limits the ability to distinguish them from chaos

A long-standing question in applications of dynamical systems theory is how to distinguish noisy signals from chaotic steady states. Information-theoretic measures hold promise to resolve this problem. We apply two such measures to numerically computed phase-space trajectories of continuous-state nonlinear oscillators: forecasting or statistical complexity, which quantifies the minimum memory required for the optimal prediction of discrete observables, and the entropy rate, which quantifies their intrinsic unpredictability. We estimate empirical generating partitions to obtain discrete observables faithfully representing continuous-state chaotic time series. We focus on the problem of distinguishing stochastically perturbed periodic orbits from chaotic attractors that exist at nearby parameter values, in a region of the parameter space where a strange invariant set exists. We find that a stochastically perturbed, stable, high-period ( $$p=15$$ ) orbit of a periodically driven Duffing oscillator admits high values of both information measures, making it difficult to distinguish it from chaotic states at adjacent parameters, even with small noise. However, for a low-period ( $$p=3$$ ) orbit, such a distinction becomes easier, as both measures admit considerably lower values compared to a chaotic attractor at a nearby parameter. Furthermore, the forecasting complexity of the selected periodic orbits increases with noise as they undergo a transition to “noise-induced chaos.” For sufficiently high noise levels, our ability to distinguish chaos from noise depends on model-order selection when estimating forecasting complexity and also on the exact choice of discrete observables used to encode phase-space trajectories.

ON OSCILLATIONS DESCRIBING A GENERALIZED DIFFERENTIAL RELAY EQUATION

The motion of an oscillatory system with one degree of freedom, described by the generalized Rayleigh differential equation, is considered. The generalization is achieved by replacing the cubic term, which expresses the dissipative strength of the equation of motion, by a power term with an arbitrary positive exponent. To study the oscillatory process involved the method of energy balance. Using it, an approximate differential equation of the envelope of the graph of the oscillatory process is compiled and its analytical solution is constructed from which it follows that quasilinear frictional self-oscillations are possible only when the exponent is greater than unity. The value of the amplitude of the self-oscillations in the steady state also depends on the value of the indicator. A compact formula for calculating this amplitude is derived. In the general case, the calculation involves the use of a gamma function table. In the case when the exponent is three, the amplitude turned out to be the same as in the asymptotic solution of the Rayleigh equation that Stoker constructed. The amplitude is independent of the initial conditions. Self-oscillations are impossible if the exponent is less than or equal to unity, since depending on the initial deviation of the system, oscillations either sway (instability of the movement is manifested) or the range decreases to zero with a limited number of cycles, which is usually observed with free oscillations of the oscillator with dry friction. These properties of the oscillatory system are also confirmed by numerical computer integration of the differential equation of motion for specific initial data. In the Maple environment, the oscillator trajectories are constructed for various values of the nonlinearity index in the expression of the viscous resistance force and a corresponding comparative analysis is carried out, which confirms the adequacy of approximate analytical solutions.

Force Sensing with an Optomechanical Self-Oscillator

Ultra-high-frequency nanomechanical resonators (${f}_{m}&gt;300$ MHz) can increase our capacity to study fast physical phenomena, for example by measuring forces. Their extreme stiffness is also a chance to access molecular forces in the subpicometer low amplitude of motion limit, but it makes them hard to drive and control. Here we analyze a method to optomechanically sense a force field with an ultra-high-frequency and stiff mechanical resonator, where back-action optical forces set the resonator into a self-sustained stable oscillator trajectory. After elucidating the experimental conditions to obtain optimal resolution, we carry out controlled experiments where the oscillator senses an optical force generated by a secondary laser. We analyze and model our results, and illustrate the concrete advantage of the method in the measurement of such a weak force, which would otherwise remain undetected by the undriven probe. We establish the thermodynamical limits of the approach, and finally connect it to the class of feedback-controlled problems, clarifying its assets and limitations.

Dynamical Learning of Dynamics.

The ability of humans and animals to quickly adapt to novel tasks is difficult to reconcile with the standard paradigm of learning by slow synaptic weight modification. Here, we show that fixed-weight neural networks can learn to generate required dynamics by imitation. After appropriate weight pretraining, the networks quickly and dynamically adapt to learn new tasks and thereafter continue to achieve them without further teacher feedback. We explain this ability and illustrate it with a variety of target dynamics, ranging from oscillatory trajectories to driven and chaotic dynamical systems.

Magnetic control over the zitterbewegung of exciton–polaritons

The effect of the zitterbewegung consisting in trembling of trajectory of propagating particles may, in principle, be found in a variety of physical systems characterized by split kinetic energy dispersion branches. However, in a majority of material systems the effect is too weak to be observable. Specially designed semiconductor heterostructures representing optical microcavities with embedded quantum wells allow observing the zitterbewegung of exciton–polaritons that are optical cavity modes strongly hybridized with excitons in quantum wells. Here we show that external magnetic fields applied in the plane of the microcavity amplify this effect and allow for tuning the amplitude and the period of oscillations of polariton trajectories, thus being a convenient tool of control. These results pave the way towards realization of ballistic polariton transistors based on the spin–orbit effect, conceptually similar to Datta-and-Das transistors.

Evolutionary homology on coupled dynamical systems with applications to protein flexibility analysis.

While the spatial topological persistence is naturally constructed from a radius-based filtration, it has hardly been derived from a temporal filtration. Most topological models are designed for the global topology of a given object as a whole. There is no method reported in the literature for the topology of an individual component in an object to the best of our knowledge. For many problems in science and engineering, the topology of an individual component is important for describing its properties. We propose evolutionary homology (EH) constructed via a time evolution-based filtration and topological persistence. Our approach couples a set of dynamical systems or chaotic oscillators by the interactions of a physical system, such as a macromolecule. The interactions are approximated by weighted graph Laplacians. Simplices, simplicial complexes, algebraic groups and topological persistence are defined on the coupled trajectories of the chaotic oscillators. The resulting EH gives rise to time-dependent topological invariants or evolutionary barcodes for an individual component of the physical system, revealing its topology-function relationship. In conjunction with Wasserstein metrics, the proposed EH is applied to protein flexibility analysis, an important problem in computational biophysics. Numerical results for the B-factor prediction of a benchmark set of 364 proteins indicate that the proposed EH outperforms all the other state-of-the-art methods in the field.

Identification and Physiological Significance of Temporal Nfκb Signaling Codewords Deployed by Macrophages to Classify Immune Threats

Inflammatory pathologies often involve dysregulated macrophage functions. In health, macrophages are immune sentinels that initiate inflammatory responses via the transcription factor NFkB. The temporal pattern of NFkB activity determines which genes are expressed, but how such temporal signaling code works in primary immune cells remains unexplored. For this study, we developed tools to enable high-throughput analysis of live, primary macrophages responding to host- and pathogen-derived stimuli. An information-theoretic workflow identified six dynamical features that constitute codewords that convey stimulus information to the nucleus. In particular, oscillatory trajectories are a hallmark of the responses to host cytokine TNF. Remarkably, examining macrophages derived from a systemic autoimmune disease model suggests that confusion of two NFkB signaling codewords, and thus miscoding of TNF as a pathogen-derived stimulus, may underlie sporadic inflammatory pathology. Overall, this study identifies six codewords of the temporal NFkB signaling code for classifying immune threats and demonstrates their biological significance.

Revisiting the tangential oscillations of the tool to form the microrelief of the workpiece surface

The article is focused on the possibilities of using the tangential oscillations of the tool to form a microrelief of the workpiece surface. The diagram of the cutting tool oscillation trajectory during vibrational turning is presented. The scheme for calculation of the values of two tangential oscillation components is presented. The photos of the surfaces obtained by machining of the workpieces with the use of vibrational turning are provided. The results of the surface microgeometry modeling under the turning with tangential oscillations imposition of the tool are given. The dependence of the surface microgeometry height on the workpiece rotation speed and the tool oscillation frequency is determined. The factors which influence on the workpiece surface microgeometry formation are specified.

Direct electron acceleration by chirped laser pulse in a cylindrical plasma channel**Project supported by the National Natural Science Foundation of China (Grant Nos. 11865014, 11765017, 11764039, 11475027, 11274255, and 11305132),the Natural Science Foundation of Gansu Province of China (Grant No. 17JR5RA076), the Scientific Research Project of Gansu Higher Education of China (Grant No. 2016A-005), the Natural Science Foundation of Education

We study the dynamics of single electron in an inhomogeneous cylindrical plasma channel during the direct acceleration by linearly polarized chirped laser pulse. By adjusting the parameters of the chirped laser pulse and the plasma channel, we obtain the energy gain, trajectory, dephasing rate and unstable threshold of electron oscillation in the channel. The influences of the chirped factor and inhomogeneous plasma density distribution on the electron dynamics are discussed in depth. We find that the nonlinearly chirped laser pulse and the inhomogeneous plasma channel have strong coupled influence on the electron dynamics. The electron energy gain can be enhanced, the instability threshold of the electron oscillation can be lowered, and the acceleration length can be shortened by chirped laser, while the inhomogeneity of the plasma channel can reduce the amplitude of the chirped laser.