Initial Perturbation Research Articles

Discovering Root Causal Genes with High Throughput Perturbations.

Root causal gene expression levels - or root causal genes for short - correspond to the initial changes to gene expression that generate patient symptoms as a downstream effect. Identifying root causal genes is critical towards developing treatments that modify disease near its onset, but no existing algorithms attempt to identify root causal genes from data. RNA-sequencing (RNA-seq) data introduces challenges such as measurement error, high dimensionality and non-linearity that compromise accurate estimation of root causal effects even with state-of-the-art approaches. We therefore instead leverage Perturb-seq, or high throughput perturbations with single cell RNA-seq readout, to learn the causal order between the genes. We then transfer the causal order to bulk RNA-seq and identify root causal genes specific to a given patient for the first time using a novel statistic. Experiments demonstrate large improvements in performance. Applications to macular degeneration and multiple sclerosis also reveal root causal genes that lie on known pathogenic pathways, delineate patient subgroups and implicate a newly defined omnigenic root causal model.

Characterizing structure formation through instance segmentation

Dark matter haloes form from small perturbations to the almost homogeneous density field of the early universe. Although it is known how large these initial perturbations must be to form haloes, it is rather poorly understood how to predict which particles will end up belonging to which halo. However, it is this process that determines the Lagrangian shape of proto-haloes and it is therefore essential to understand their mass, spin, and formation history. We present a machine learning framework to learn how the proto-halo regions of different haloes emerge from the initial density field. We developed one neural network to distinguish semantically which particles become part of any halo and a second neural network that groups these particles by halo membership into different instances. This instance segmentation is done through the Weinberger method, in which the network maps particles into a pseudo-space representation where different instances can easily be distinguished through a simple clustering algorithm. Our model reliably predicts the masses and Lagrangian shapes of haloes object by object, as well as other properties such as the halo-mass function. We find that our model extracts information close to optimally by comparing it to the degree of agreement between two N-body simulations with slight differences in their initial conditions. We publish our model open source and suggest that it can be used to inform analytical methods of structure formation by studying the effect of systematic manipulations of the initial conditions.

Turbulence statistics and transport in compressible mixing driven by spherical implosions with narrowband and broadband initial perturbations

Turbulence statistics and transport in compressible mixing driven by spherical implosions with narrowband and broadband initial perturbations

Outlet boundary condition and mean temperature gradient effects on the minimum acoustics disturbances energy in triggering nonlinear thermoacoustic instability

In this study, we theoretically investigate the impact of outlet boundary conditions and mean temperature gradients on the maximum transient growth rate of acoustical energy and the critical energy required for triggering. Our analysis encompasses open–open and open–closed thermoacoustic systems. The theoretical models developed focus on horizontal ducts with a mean temperature jump over the heat source, employing the modified King's law. By linearizing the unsteady heat release, the nonlinear thermoacoustic equations transform into linearized-delay ones. This approach enables us to predict optimal initial perturbations for linearized-delay and nonlinear systems, corresponding to maximum transient growth rates of acoustic energy over short and long periods, respectively, thus providing insights into critical energy for triggering. We find that a closed outlet leads to higher transient energy growth and a lower critical energy for triggering compared to an open outlet. The increased mean temperature gradient has a “destructive” impact on triggering in open–open systems but a “constructive” effect in open–closed systems. Raising the mean temperature ratio generally increases the critical energy for triggering in the open–open system, whereas it decreases the critical energy in the open–closed system. The critical energy for nonlinear optimal initial perturbations is notably affected by the minimum energy of critical unstable periodic solutions, while the critical energy for linearized-delay optimal initial perturbations is closely tied to the energy level of stable periodic solutions. Due to the transient energy growth rate, the critical energy for nonlinear optimal initial perturbations is significantly lower than that for linearized-delay optimal initial perturbations.

State estimation of a novel brake-by-wire system based on cascade observer

Pressure regulation is the primary function of the brake-by-wire (BBW) system, and its prerequisite is the precise pressure acquisition. In autonomous vehicles(AVs), a higher fail-safe level is required that a backup pressure source is available when the main pressure source fails. So the use of pressure sensors, like the existing method, for pressure regulation will increase the cost of BBW systems in AVs. To meet the requirement of brake redundancy and the cost limit, a novel BBW system with a redundant pressure supply unit is designed and its electro-mechanical-hydraulic model is analyzed in this research. A time-domain observer (TDO) of motor speed is designed based on the periodic characteristics of motor current to get more system information. Next, the robust observer of pressure is proposed based on the existing current sensor and the derived motor speed. Its computational burden is reduced by calculating the matrices offline. The estimator developed in this paper is verified in typical pressure regulation conditions. Experimental results show that the estimation error of the motor speed is within 3% and has the potential to be improved, and the error of pressure is within 0.1 MPa, and the observer exhibits enough robustness under different initial condition perturbations.

The relation between Rossby wave-breaking events and low-level weather systems

Abstract. Rossby wave-breaking events describe the last stage in the life cycle of baroclinic atmospheric disturbances. These breaking events can strongly influence large-scale circulation and are also related to weather extremes such as heat waves, blocking, and extreme precipitation events. Nonetheless, a complete understanding of the synoptic-scale dynamics involved with the breaking events is still absent. For example, it is not clear how well the theoretical life cycle experiments, which use a specified initial perturbation with a single zonal wavenumber and a prescribed simplified initial zonal jet, capture the life cycle of real-atmosphere weather systems. Here we combine a storm-tracking technique together with a wave-breaking detection algorithm to examine how upper-level wave breaking and surface weather systems are related in the North Atlantic during winter. These datasets allow us to examine whether upper-level wave breaking and low-level weather systems always occur simultaneously and if we can identify preferred relations between the surface weather system type (cyclone or anticyclone) and the type of the upper-level breaking event (cyclonic or anticyclonic wave breaking denoted CWB or AWB, respectively). We find that in the North Atlantic, most weather systems are associated with AWB and/or CWB at some point during their lifetime, while only few cyclones and anticyclones do not involve any upper-level wave breaking (roughly 11 % and 15 %, respectively). Our results imply that composites of cyclones and anticyclones involve a mixture of different types of life cycles, depending on whether they involve CWB or AWB, as well as their position relative to the Rossby wave-breaking (RWB) center. Moreover, the system characteristics (including actual and relative positions, intensities, and displacements) differ depending on the associated breaking type. We distinguish between “same-pairing” cases (i.e., cyclone with CWB and anticyclones with AWB) and “opposite-pairing” cases (i.e., cyclones with AWB and anticyclones with CWB). Compositing the cyclones and anticyclones based on this criterion, we find that in similar pairings the surface system is positioned so that its associated upper-level winds would enhance the breaking (the anomalous circulation is in the same direction as the background shear), but, for opposite pairings, the upper-level winds associated with the surface system do not act to enhance the breaking which occurs in the direction of the background shear. A better understanding of the different life cycles of real-atmosphere cyclones and anticyclones and the upper-level breaking they involve is important for exploring the relation between storm tracks and slowly varying weather regimes and how they are mediated by RWB events.

Direct numerical simulation of laminar, transitional and turbulent radially inward flow between closely spaced corotating disks

This study describes direct numerical simulation (DNS) of radially inward spiralling corotating disk flow with a narrow disk spacing, using the open source solver Nek5000 and the supercomputer SuperMUC-NG at Leibniz Supercomputing Centre. Knowledge about laminar and turbulent regime boundaries in this flow scenario is important for modelling and performance prediction of friction turbines. Simulations are performed in differently sized sections of the flat annulus that is formed by two opposing corotating disk surfaces. Three sets of operating conditions are covered, from the laminar, transitional and turbulent region of a previously determined stability chart respectively. Directly downstream of the inlet boundary, the flow is artificially perturbed with a random body force acting normal to the disk surfaces. Fourier analysis of the DNS flow field reveals that the artificial perturbation is dampened across all wavenumbers for the laminar conditions, while at the transitional conditions a small range of modes is weakly amplified towards the outlet. The identified unstable modes were previously correctly predicted by linear stability analysis. Comparison to experimental velocity profile measurements from a previous study at the same transitional operating conditions suggests strongly perturbed flow during the experiment. For inflow conditions leading to turbulent flow, average velocity profiles from DNS coincide with those from experiment and from commercial fluid simulation software with turbulence modelling (ANSYS CFX). Close to the walls, turbulent dissipation and turbulent kinetic energy distributions do not agree with the ANSYS CFX results. Friction Reynolds number settles at about 118 after turbulent flow has developed from the initial perturbation. Two point correlations and corresponding energy spectra are presented.

Vortices over bathymetry

There are numerous examples of long-lived, surface-intensified anticyclones over submarine depressions and troughs in the ocean. These often co-exist with a large-scale cyclonic circulation. The latter is predicted by existing barotropic theory but the anticyclone is not. We extend one such theory, which minimizes enstrophy while conserving energy, to two fluid layers. This yields a bottom-intensified flow with cyclonic circulation over a depression. The solution is steady, an enstrophy minimum and stable. When the Lagrange multiplier, $\lambda$ , is near zero, the total potential vorticity (PV) becomes homogenized, in both layers. For positive $\lambda$ , the surface PV is anticyclonic and strongest at intermediate energies. In quasi-geostrophic numerical simulations with a random initial perturbation PV, the bottom-intensified cyclonic flow always emerges. Vortices evolve independently in the layers and vortex mergers are asymmetric over the depression; cyclones are preferentially strained out at depth while only anticyclones merge at the surface. Both asymmetries are linked to the topographic flow. The deep cyclones feed the bottom-intensified cyclonic circulation while the asymmetry at the surface is only apparent after that circulation has spun up. The result of the surface merger asymmetry is often a lone anticyclone above the depression. This occurs primarily at intermediate energies, when the surface PV predicted by the theory is strongest. Similar results obtain in a full complexity ocean model but with a more pronounced asymmetry in surface vortex mergers and, with bottom friction, significant bottom flow beneath the central anticyclone.

On the representation of solution for the perturbed quasi-linear controlled neutral functional-differential equation with the discontinuous initial condition

Abstract The analytic relation between solutions of the original Cauchy problem and a corresponding perturbed problem is established. In the representation formula of solution, the effects of the discontinuous initial condition and perturbation of the initial data are revealed.

Decay of the compressible Navier-Stokes equations with hyperbolic heat conduction

This paper is concerned with the global well-posedness and large-time behavior of the compressible Navier-Stokes equations with hyperbolic heat conduction, where the heat flux is assumed to satisfy Cattaneo's law. When the initial perturbation is small and regular, we establish the global existence of the classical solution without any additional assumption on the relaxation time τ. Furthermore, assuming the initial perturbation belongs to a negative Sobolev space, we obtain the optimal time-decay rates of the high-order spatial derivatives of solutions by using a pure energy method instead of complicated spectral analysis. It is also observed that the heat flux, due to its damping structure, decays to the motionless state at a faster time-decay rate compared to density, velocity, and temperature.

Global stability of viscous contact wave for compressible Navier–Stokes equations with temperature‐dependent transport coefficients and large data

We are concerned with the large‐time behavior of the viscous contact wave for a one‐dimensional compressible Navier–Stokes equations whose transport coefficients depend on the temperature. It is shown that if the adiabatic exponent satisfies a suitable inequality and strength is small enough, the unique solution global in time to ideal polytropic gas exists and asymptotically tends toward the viscous contact wave under large initial perturbation for any . Subsequently, we also prove that the large‐time asymptotic stability of the contact wave has a uniform convergence rate under initial data. Our results improve ‐rate in [F. Huang, Z. Xin, and T. Yang, Adv. Math. 219 (2008), 1246–1297] which studied the constant coefficients Navier–Stokes system. The proofs are given by the elementary energy estimate and anti‐derivative method.

Time decay of solutions for compressible isentropic non-Newtonian fluids

In this paper, we consider the Cauchy problem of a compressible Navier–Stokes system of Eills-type non-Newtonian fluids. We investigate the time decay properties of classical solutions for the compressible non-Newtonian fluid equations. More specifically, we construct a new linearized system in terms of a combination of the solutions, and then we investigate the long-time behavior of the Cauchy problem for the three-dimensional isentropic compressible Eills-type non-Newtonian fluids with an initial perturbation.

Initial and Transient Growth of Symmetric Instability

Abstract The mechanism of initial and transient perturbations of symmetric instability (SI) in a hydrostatic flow with lateral shear is analyzed by applying the generalized stability analysis. It is well known that the SI’s most rapidly growing motion is along isopycnals, and the growth rates consist of growing, neutral, and decaying modes. The eigenvectors of these three modes are not orthogonal to each other, hence the initial and transient perturbations bear little resemblance to the normal mode. Our findings indicate that the emergence of normal modes occurs within a time span of 1–3 inertial periods, which we refer to as the transient state. The overall growth of perturbation energy is divided into three components: geostrophic shear production (GSP), lateral shear production (LSP), and meridional buoyancy flux (MB). During the transient state, the perturbation energy is partly driven by MB, contrary to the normal mode which has zero MB. The relative energy contribution is evaluated through the ratio to GSP. While the MB-to-GSP ratio of the initial mode is higher than that of the normal mode, the LSP-to-GSP ratio remains constant. In the absence of the fastest-growing normal mode, MB can serve as the predominant initial energy source. The precise transition in the energy regime is contingent upon the geostrophic Richardson number and Rossby number. Significance Statement Fronts can be unstable to instabilities, which generate disturbance growth and lead to the mixing of water masses. We wanted to understand the initial and transient development of disturbance growth leading to the well-known exponentially growing state. While the exponentially growing disturbance is dominant in the long run, the disturbance growth may not have enough time to achieve the exponentially growing state. We find that the initial disturbance growth bears little resemblance to the exponentially growing state. Capturing the complete spectrum of front evolution remains challenging, and observations have thus far been limited to short-term records. The insights learned from this study can aid in better characterizing the disturbance growth captured in these short-term records.

Different Initial Condition Perturbation Methods for Convection-Permitting Ensemble Forecasting over South China during the Rainy Season

Abstract In this study, downscaling, ensemble data assimilation, time lagging, and their combination were used to generate initial condition (IC) perturbations for 12-h convection-permitting ensemble forecasting for heavy-rainfall events over South China during the rainy season in 2013–20. These events were classified as weak- and strong-forcing cases based on synoptic-scale forcing during the presummer rainy season and as landfalling tropical cyclone (TC) cases. This study investigated the impacts of various IC perturbation methods on multiscale characteristics of perturbations and the forecast performance for both nonprecipitation and precipitation variables. These perturbation methods represented different source IC uncertainties and thus differed in multiscale characteristics of perturbations in vertical structures, horizontal distributions, and time evolution. The combination of various IC perturbation methods evidently increased perturbations or spreads of precipitation in both magnitude and location and thus improved the forecast-error estimation. Such an improvement was most and least evident for TC cases during the early and late forecasts, respectively, and was more evident for strong- than weak-forcing cases beyond 6 h. The combination of various IC perturbation methods generally improved both the ensemble-mean and probabilistic forecasts with case-dependent improvements. For heavy rainfall forecasting, 1–6-h improvements were most prominent for TC cases in terms of discrimination and accuracy, while 7–12-h improvements were least prominent for weak-forcing cases in terms of reliability and accuracy. In particular, the improvements in predicting weak-forcing cases increased with spatial errors. In contrast, for strong-forcing cases, the improvements were least and most prominent before and beyond 6 h, respectively. Significance Statement Precipitation forecasting for heavy-rainfall events over South China in the rainy season is still challenging due to large uncertainties. Convection-permitting ensemble forecasting is expected to address such uncertainties to improve forecasts of heavy rainfall. However, it is not yet clear how to optimally design convection-permitting ensembles by implementing perturbations in initial conditions (ICs). This study investigates the impacts of various IC perturbation methods on convection-permitting ensemble forecasting over South China in the rainy season. Various IC perturbation methods show discrepant multiscale characteristics of perturbations, which generally complement each other when these perturbations are combined. The added values of combining various IC perturbation methods in forecasting are confirmed for most variables. However, such values are case dependent, with the largest values for tropical cyclone cases during the early forecasts and for the presummer rainy season cases with strong synoptic-scale forcing during late forecasts. Thus, it is still essential to further improve the combination of various types of IC perturbation methods.

Feedback Stabilization of a Two-Fluid Surface Tension System Modeling the Motion of a Soap Bubble at Low Reynolds Number: The Two-Dimensional Case

The aim of this paper is to design a feedback operator for stabilizing in infinite time horizon a system modeling the interactions between a viscous incompressible fluid and the deformation of a soap bubble. The latter is represented by an interface separating a bounded domain of mathbb {R}^2 into two connected parts filled with viscous incompressible fluids. The interface is a smooth perturbation of the 1-sphere, and the surrounding fluids satisfy the incompressible Stokes equations in time-dependent domains. The mean curvature of the surface defines a surface tension force which induces a jump of the normal trace of the Cauchy stress tensor. The response of the fluids is a velocity trace on the interface, governing the time evolution of the latter, via the equality of velocities. The data are assumed to be sufficiently small, in particular the initial perturbation, that is the initial shape of the soap bubble is close enough to a circle. The control function is a surface tension type force on the interface. We design it as the sum of two feedback operators: one is explicit, the second one is finite-dimensional. They enable us to define a control operator that stabilizes locally the soap bubble to a circle with an arbitrary exponential decay rate, up to translations, and up to non-contact with the outer boundary.

Global solutions to the bipolar non-isentropic Euler-Maxwell system in the Besov framework

ABSTRACT This paper investigates the bipolar non-isentropic compressible Euler-Maxwell system in R 3 and T 3 . For both problems, we establish the global existence of smooth solutions in the general Besov spaces, which covers the usual Sobolev spaces with higher regularity and the critical Besov space, when the initial perturbations around the constant states are small enough. As a byproduct, we obtain the large-time asymptotic behavior of the global solutions near the equilibrium state in the general Besov spaces with relatively lower regularity. The proof is based on the technical Fourier frequency-localization method developed through the Littlewood-Paley theory, but some new development and technique are proposed for treating the strong coupling and nonlinearity for the bipolar non-isentropic case.

The periodic N breather anomalous wave solution of the Davey–Stewartson equations; first appearance, recurrence, and blow up properties

The integrable focusing Davey–Stewartson (DS) equations, multidimensional generalizations of the focusing cubic nonlinear Schrödinger equation, provide ideal mathematical models for describing analytically the dynamics of dimensional anomalous (rogue) waves (AWs). In this paper (i) we construct the N-breather AW solution of Akhmediev type of the DS1 and DS2 equations, describing the nonlinear interaction of N unstable modes over the constant background solution. (ii) For the simplest multidimensional solution of DS2 we construct its limiting subcases, and we identify the constraint on its arbitrary parameters giving rise to blow up at finite time. (iii) We use matched asymptotic expansions to describe the relevance of the constructed AW solutions in the spatially doubly periodic Cauchy problem of DS2 for small initial perturbations of the background, in the case of one and two unstable modes. We also show, in the case of two unstable modes, that (i) no blow up takes place generically, although the AW amplitude can be arbitrarily large; (ii) the excellent agreement of our formulas, expressed in terms of elementary functions of the initial data, with numerical experiments.

Decay rates of the highest order spatial derivatives for solutions of compressible Hall MHD system with or without Coulomb force

In this thesis, we study the decay rates of the highest order (M-th order) spatial derivatives for solutions of both compressible Hall MHD system and that with Coulomb force by a pure energy method inspired by Guo and Wang (2012)[12] and Gao, Li and Yao (2023)[9]. When the norm of H3 for the initial perturbation is small enough, and the norms of both HM(M≥3) and H˙−α(α∈[0,32)) for that only need to be bounded, we first prove the decay rates of compressible Hall MHD system in L2 are (1+t)−(M+α)2. And then affected by the Coulomb force, for compressible Hall MHD system with Coulomb force, we obtain the decay rates are (1+t)−(M+α)2 for α∈[12,32) and (1+t)12[(14−12α)−(M+α)] for α∈[0,12), which are consistent with the decay estimates for compressible MHD system with Coulomb force. In particular, the results improve the original decay rates (1+t)−(M−1+α)2 established by Xu et al. (2016)[46] and Tan, Tong and Wang (2015)[31].

Amplitude modulation and surface wave generation in a complex plasma monolayer.

The response of a two-dimensional plasma crystal to an externally imposed initial perturbation has been explored using molecular dynamics (MD) simulations. A two-dimensional (2D) monolayer of micron-sized charged particles (dust) is formed in the plasma environment under certain conditions. The particles interacting via Yukawa pair potential are confined in the vertical (z[over ̂]) direction by an external parabolic confinement potential, which mimics the combined effect of gravity and the sheath electric field typically present in laboratory dusty plasma experiments. An external perturbation is introduced in the medium by displacing a small central region of particles in the vertical direction. The displaced particles start to oscillate in the vertical direction, and their dynamics get modulated through a parametric decay process generating beats. It has also been shown that the same motion is excited in the dynamics of unperturbed particles. A simple theoretical model is provided to understand the origin of the beat motions of particles. Additionally, in our simulations, concentric circular wavefronts propagating radially outward are observed on the surface of the monolayer. The physical mechanism and parametric dependence of the observed phenomena are discussed in detail. This research sheds light on the medium's ability to exhibit macroscopic softness, a pivotal characteristic of soft matter, while sustaining surface wave modes. Our findings are also relevant to other strongly coupled systems, such as colloids and classical one-component plasmas.

Global classical solution of the Cauchy problem to the 3D Benjamin–Bona–Mahony–Burgers-type equation with nonlocal control constraints

Abstract This article focuses on the Cauchy problem of the Benjamin–Bona–Mahony–Burgers (BBMB) equation with nonlocal control constraints in ℝ 3 {\mathbb{R}^{3}} . We employ the Phragmén–Lindelöf decomposition method and Green’s function to investigate global classical solutions and their long-term behaviors, including optimal estimates for finite density initial perturbation. Additionally, optimal solutions near the minimal mass ground state are analyzed.