Additive Perturbations Research Articles

Iterative Algorithms for Assessing Network Resilience Against Structured Perturbations

This article studies network resilience against structured additive perturbations to its topology. We consider dynamic networks modeled as linear time-invariant systems subject to perturbations of bounded energy satisfying specific sparsity and entry-wise constraints. Given an energy level, the structured pseudospectral abscissa captures the worst-possible perturbation an adversary could employ to destabilize the network, and the structured stability radius is the maximum energy in the structured perturbation that the network can withstand without becoming unstable. Building on a novel characterization of the worst-case structured perturbation, we propose iterative algorithms that efficiently compute the structured pseudospectral abscissa and structured stability radius. We provide theoretical guarantees of the local convergence of the algorithms and illustrate their efficacy and accuracy on several network examples.

An adaptive observer for uncertain linear time-varying systems with unknown additive perturbations

In this paper we are interested in the problem of adaptive state observation of linear time-varying (LTV) systems where the system and the input matrices depend on unknown time-varying parameters. It is assumed that these parameters satisfy some known LTV dynamics, but with unknown initial conditions. Moreover, the state equation is perturbed by an additive signal generated from an exosystem with uncertain constant parameters. Our main contribution is to propose a globally convergent state observer that requires only a weak excitation assumption on the system, which is satisfied in the present context of regulation.

Estimations and Control of Julia Sets of the SIS Model Perturbed by Noise.

The estimations and control of Julia sets of the SIS(susceptible-infectious-susceptible) model under noise perturbation are studied. At first, a discrete SIS model is introduced, and the effects of additive and multiplicative noises on the fractal characteristics of the SIS model are discussed. Then, estimations of the Julia sets of the SIS model under additive and multiplicative noise perturbations are given, respectively. At last, the feedback control method is used to set appropriate controllers to realize control of the Julia set, and the influence of noise on the Julia set of the SIS model is reduced. The reason why this method is effective is also explained.

Dynamically Computing Adversarial Perturbations for Recurrent Neural Networks

Convolutional and recurrent neural networks (RNNs) have been widely used to achieve state-of-the-art performance on classification tasks. However, it has also been noted that these networks can be manipulated adversarially with relative ease, by carefully crafted additive perturbations to the input. Though several experimentally established prior works exist on crafting and defending against attacks, it is also desirable to have rigorous theoretical analyses to illuminate conditions under which such adversarial inputs exist. This article provides both the theory and supporting experiments for real-time attacks. The focus is specifically on recurrent architectures and inspiration is drawn from dynamical systems’ theory to naturally cast this as a control problem, allowing dynamic computation of adversarial perturbations at each timestep of the input sequence, thus resembling a feedback controller. Illustrative examples are provided to supplement the theoretical discussions.

Quantitative results for banded Toeplitz matrices subject to random and deterministic perturbations

We consider the eigenvalues of a fixed, non-normal matrix subject to a small additive perturbation. In particular, we consider the case when the fixed matrix is a banded Toeplitz matrix, where the bandwidth is allowed to grow slowly with the dimension, and the perturbation matrix is drawn from one of several different random matrix ensembles. We establish a number of non-asymptotic results for the eigenvalues of this model, including a local law and a rate of convergence in Wasserstein distance of the empirical spectral measure to its limiting distribution. In addition, we define the classical locations of the eigenvalues and prove a rigidity result showing that, on average, the eigenvalues concentrate closely around their classical locations. While proving these results we also establish a number of auxiliary results that may be of independent interest, including a quantitative version of the Tao–Vu replacement principle, a general least singular value bound that applies to adversarial models, and a description of the limiting empirical spectral measure for random multiplicative perturbations.

On Disturbance Rejection for a Class of Underactuated Hamiltonian Systems

In this work, the problem of additive perturbations is studied for a class of port Control Hamiltonian (PCH) systems. The considered class of Hamiltonian systems includes underactuated systems, which continue to be an important open study area. The starting point of the used methodology begins by considering that a previous tracking control has already made the equilibrium point of the error dynamic system asymptotically stable. The Integral Control (IC) reported in cite{ortega2012robust} and cite{ferguson2017integral} are implemented in the PCH class system so that it can reject the constant additive perturbations and conserves the Hamiltonian system structure. The results are compared and tested in a studied case with the system application of the Permanente Magnet Synchronous Motor (PMSM), and the MATLAB Simulink simulations obtained are exposed to compare the performance of both controls.

Waveform level adversarial example generation for joint attacks against both automatic speaker verification and spoofing countermeasures

Adversarial examples crafted to deceive Automatic Speaker Verification (ASV) systems have attracted a lot of attention when studying the vulnerability of ASV. However, real-world ASV systems usually work together with spoofing countermeasures (CM) to exclude fake voices generated by text-to-speech (TTS) or voice conversion (VC). The deployment of CM would reduce the capability of the adversarial samples on deceiving ASV. Although additional perturbations against CM may be generated and put on the crafted adversarial examples against ASV to yield new adversarial examples against both ASV and CM, those additional perturbations would however hinder the examples’ adversarial effectiveness on ASV. In this paper, a novel joint approach is proposed to generate adversarial examples by considering attacking ASV and CM simultaneously. For any voice from TTS, VC or a real-world speaker, our crafted adversarial perturbations will turn its original labels on CM and speaker ID to bonafide and some target speaker ID, correspondingly. In our approach, a differentiable front-end is introduced to replace the conventional hand-crafted time–frequency feature extractor. Perturbations can thus be estimated by updating the gradients of the joint objective of ASV and CM on the waveform variables. The proposed method has demonstrated a 99.3% success rate on white-box logical access attacks to deceive ASV and CM simultaneously, which outperforms the baselines of 65.3% and 36.7%. Furthermore, transferability on black-box and physical settings has also been validated.

Regularization of multiplicative SDEs through additive noise

We investigate the regularizing effect of certain additive continuous perturbations on SDEs with multiplicative fractional Brownian motion (fBm). Traditionally, a Lipschitz requirement on the drift and diffusion coefficients is imposed to ensure existence and uniqueness of the SDE. We show that suitable perturbations restore existence, uniqueness and regularity of the flow for the resulting equation, even when both the drift and the diffusion coefficients are distributional, thus extending the program of regularization by noise to the case of multiplicative SDEs. Our method relies on a combination of the nonlinear Young formalism developed by Catellier and Gubinelli (Stochastic Process. Appl. 126 (2016) 2323–2366), and stochastic averaging estimates recently obtained by Hairer and Li (Ann. Probab. 48 (2020) 1826–1860).

Climate and edaphic factors drive soil enzyme activity dynamics and tolerance to Cd toxicity after rewetting of dry soil

The intense drying-rewetting cycle due to climate change can affect soil microbial community composition and function, resulting in long-term consequences for belowground carbon and nutrient dynamics. However, how climatic and edaphic factors influence the responses of enzymes to rewetting and their responses to additional perturbation (e.g., heavy metal pollution) after the drying-rewetting history are not well understood. In this study, we collected 18 surface soils from farmlands across various climate zones in China. We chose dehydrogenase (DHA) and alkaline phosphomonoesterase (ALP) as representative intracellular and extracellular enzymes, respectively, and investigated their tolerance to additional perturbation by adding metal ions (i.e., Cd2+) upon rewetting. In all soils, rewetting increased DHA activities but did not affect ALP activities compared to air-dried soils. Rewetting increased the tolerances of DHA and ALP to Cd stress, suggesting that the drying-rewetting history may reduce the susceptibility of soil enzymes to additional disturbance. The results demonstrate that differentiating enzymes based on their location in the soil will improve our ability to assess the stress response of microbial communities to drastic fluctuations in soil moisture, thereby better predicting the legacy of climate change on microbial function in soils contaminated with heavy metals.

Generalized Carleson perturbations of elliptic operators and applications

We extend in two directions the notion of perturbations of Carleson type for the Dirichlet problem associated to an elliptic real second-order divergence-form (possibly degenerate, not necessarily symmetric) elliptic operator. First, in addition to the classical perturbations of Carleson type, that we call additive Carleson perturbations, we introduce scalar-multiplicative and antisymmetric Carleson perturbations, which both allow non-trivial differences at the boundary. Second, we consider domains which admit an elliptic PDE in a broad sense: we count as examples the 1-sided NTA (a.k.a. uniform) domains satisfying the capacity density condition, the 1-sided chord-arc domains, the domains with low-dimensional Ahlfors-David regular boundaries, and certain domains with mixed-dimensional boundaries; thus our methods provide a unified perspective on the Carleson perturbation theory of elliptic operators. Our proofs do not introduce sawtooth domains or the extrapolation method. We also present several applications to some Dahlberg-Kenig-Pipher operators, free-boundary problems, and we provide a new characterization of A ∞ A_{\infty } among elliptic measures.

Moment based model predictive control for linear systems: Additive perturbations case

AbstractIn this article, we present a novel linear model predictive control (MPC) strategy for controlling uncertain dynamical systems. The moment based MPC strategy is based on the (centralized) moments of the stochastic cost and constraint functions. We show that moment based MPC formulations yield computationally tractable predictive control problems, due to the explicit analytic expressions of the moments and linearity in the dynamics. This article considers (i) the output regulation MPC configuration, where the output is steered towards a reference and state vector is not correctly accessible to the controller at the decision instants; (ii) the moment based MPC formulation with uncertainties that are non‐Gaussian random variables, and (iii) bound and polytopic constraints in the uncertain MPC problem subject to either Gaussian disturbances or uncertainties with symmetric distributions. We demonstrate the effectiveness of the proposed MPC technique on simulation examples such as a double integrator system and a quadruple tank system.

Hybrid nonfragile intermediate observer-based T-S fuzzy attitude control for flexible spacecraft with input saturation

This paper investigates a hybrid nonfragile intermediate observer-based T-S fuzzy attitude control strategy subject to multi-source complex disturbances to achieve integrated attitude stabilization and vibration suppression for the flexible spacecraft. A refined T-S fuzzy model for flexible spacecraft is introduced to represent the nonlinear characteristics in large-angle attitude maneuver. Then a hybrid nonfragile observer with coexisting additive and multiplicative perturbations is designed to estimate state information and disturbance simultaneously. Consequently, based on the closed-loop system, the quadratic stability and robust H∞ performance are proved via the Lyapunov stability analysis with corresponding conditions in terms of linear matrix inequalities (LMIs). It is worth mentioning that different from the limiter directly used in much literature, input saturation is disposed as a disturbance during the proof to satisfy the stability requirements. Finally, numerical simulations of a flexible spacecraft attitude control system are performed which demonstrate the effectiveness and superiority of the proposed control strategy.

Current Understanding of Molecular Pathophysiology of Heart Failure With Preserved Ejection Fraction.

Heart Failure (HF) is the most common cause of hospitalization in the Western societies. HF is a heterogeneous and complex syndrome that may result from any dysfunction of systolic or diastolic capacity. Abnormal diastolic left ventricular function with impaired relaxation and increased diastolic stiffness is characteristic of heart failure with preserved ejection fraction (HFpEF). HFpEF accounts for more than 50% of all cases of HF. The prevalence increases with age: from around 1% for those aged <55 years to >10% in those aged 70 years or over. Nearly 50% of HF patients have HFrEF and the other 50% have HFpEF/HFmrEF, mainly based on studies in hospitalized patients. The ESC Long-Term Registry, in the outpatient setting, reports that 60% have HFrEF, 24% have HFmrEF, and 16% have HFpEF. To some extent, more than 50% of HF patients are female. HFpEF is closely associated with co-morbidities, age, and gender. Epidemiological evidence suggests that HFpEF is highly represented in older obese women and proposed as ‘obese female HFpEF phenotype’. While HFrEF phenotype is more a male phenotype. In addition, metabolic abnormalities and hemodynamic perturbations in obese HFpEF patients appear to have a greater impact in women then in men (Sorimachi et al., European J of Heart Fail, 2022, 22). To date, numerous clinical trials of HFpEF treatments have produced disappointing results. This outcome suggests that a “one size fits all” approach to HFpEF may be inappropriate and supports the use of tailored, personalized therapeutic strategies with specific treatments for distinct HFpEF phenotypes. The most important mediators of diastolic stiffness are the cardiomyocytes, endothelial cells, and extracellular matrix (ECM). The complex physiological signal transduction networks that respond to the dual challenges of inflammatory and oxidative stress are major factors that promote the development of HFpEF pathologies. These signalling networks contribute to the development of the diseases. Inhibition and/or attenuation of these signalling networks also delays the onset of disease. In this review, we discuss the molecular mechanisms associated with the physiological responses to inflammation and oxidative stress and emphasize the nature of the contribution of most important cells to the development of HFpEF via increased inflammation and oxidative stress.

Aberrant NOVA1 function disrupts alternative splicing in early stages of amyotrophic lateral sclerosis

Amyotrophic lateral sclerosis (ALS) is a fatal disease characterized by aberrant alternative splicing (AS). Nuclear loss and cytoplasmic accumulation of the splicing factor TDP-43 in motor neurons (MN) are hallmarks of ALS at late stages of the disease. However, it is unknown if altered AS is present before TDP-43 pathology occurs. Here, we investigate altered AS and its origins in early stages of ALS using human induced pluripotent stem cell-derived motor neurons (MNs) from sporadic and familial ALS patients. We find high levels of the RNA-binding proteins NOVA1, NOVA2, and RBFOX2 in the insoluble protein fractions and observe that AS events in ALS-associated MNs are enriched for binding sites of these proteins. Our study points to an early disrupted function of NOVA1 that drives AS changes in a complex fashion, including events caused by a consistent loss of NOVA1 function. NOVA1 exhibits increased cytoplasmic protein levels in early stage MNs without TDP-43 pathology in ALS postmortem tissue. As nuclear TDP-43 protein level depletes, NOVA1 is reduced. Potential indications for a reduction of NOVA1 also came from mice over-expressing TDP-43 lacking its nuclear localization signal and iPSC-MN stressed with puromycin. This study highlights that additional RBP-RNA perturbations in ALS occur in parallel to TDP-43.

CC-CERT: A Probabilistic Approach to Certify General Robustness of Neural Networks

In safety-critical machine learning applications, it is crucial to defend models against adversarial attacks --- small modifications of the input that change the predictions. Besides rigorously studied $\ell_p$-bounded additive perturbations, semantic perturbations (e.g. rotation, translation) raise a serious concern on deploying ML systems in real-world. Therefore, it is important to provide provable guarantees for deep learning models against semantically meaningful input transformations. In this paper, we propose a new universal probabilistic certification approach based on Chernoff-Cramer bounds that can be used in general attack settings. We estimate the probability of a model to fail if the attack is sampled from a certain distribution. Our theoretical findings are supported by experimental results on different datasets.

Dynamical effects of inflation in ensemble‐based data assimilation under the presence of model error

AbstractCovariance inflation is one of the necessary tools enabling the success of ensemble Kalman filters (EnKFs) in high‐dimensional spaces and in the presence of model error. Inflation maintains the ensemble variance to a sufficiently large value, counteracting the variance damping at analysis times and its underestimation arising from model and sampling errors. In this work, we investigate the effect of inflation on the dynamics of the EnKF ensemble. When the focus is on the recursive full cycle forecast–analysis–forecast, an apparently counterintuitive effect of multiplicative inflation appears in the span of the ensemble in the EnKF. In particular, we demostrate that multiplicative inflation changes the alignment of ensemble anomalies on to weakly stable backward Lyapunov vectors. Whereas the ensemble is expected to collapse on to the subspace corresponding to the unstable portions of the Lyapunov spectrum, the use of multiplicative inflation contributes to the retention of anomalies beyond that subspace. Given that the presence of model error implies that the analysis error is no longer fully confined in the local unstable subspace, this feature of multiplicative inflation is of paramount importance for optimal filtering. We propose hybrid schemes, whereby additive perturbations complement multiplicative inflation by suitably increasing the dimension of the subspace spanned by the ensemble. The use of hybrid schemes improves analysis root‐mean‐squared error in the Lorenz 96 model compared with the use of multiplicative inflation alone, emphasizing the role of model dynamics when designing additive inflation schemes.

Training Robust Deep Models for Time-Series Domain: Novel Algorithms and Theoretical Analysis

Despite the success of deep neural networks (DNNs) for real-world applications over time-series data such as mobile health, little is known about how to train robust DNNs for time-series domain due to its unique characteristics compared to images and text data. In this paper, we fill this gap by proposing a novel algorithmic framework referred as RObust Training for Time-Series (RO-TS) to create robust deep models for time-series classification tasks. Specifically, we formulate a min-max optimization problem over the model parameters by explicitly reasoning about the robustness criteria in terms of additive perturbations to time-series inputs measured by the global alignment kernel (GAK) based distance. We also show the generality and advantages of our formulation using the summation structure over time-series alignments by relating both GAK and dynamic time warping (DTW). This problem is an instance of a family of compositional min-max optimization problems, which are challenging and open with unclear theoretical guarantee. We propose a principled stochastic compositional alternating gradient descent ascent (SCAGDA) algorithm for this family of optimization problems. Unlike traditional methods for time-series that require approximate computation of distance measures, SCAGDA approximates the GAK based distance on-the-fly using a moving average approach. We theoretically analyze the convergence rate of SCAGDA and provide strong theoretical support for the estimation of GAK based distance. Our experiments on real-world benchmarks demonstrate that RO-TS creates more robust deep models when compared to adversarial training using prior methods that rely on data augmentation or new definitions of loss functions. We also demonstrate the importance of GAK for time-series data over the Euclidean distance.

Singular boundary conditions for Sturm–Liouville operators via perturbation theory

AbstractWe show that all self-adjoint extensions of semibounded Sturm–Liouville operators with limit-circle endpoint(s) can be obtained via an additive singular form-bounded self-adjoint perturbation of rank equal to the deficiency indices, say $d\in \{1,2\}$ . This characterization generalizes the well-known analog for semibounded Sturm–Liouville operators with regular endpoints. Explicitly, every self-adjoint extension of the minimal operator can be written as $$ \begin{align*} \boldsymbol{A}_{ {}_{\scriptstyle \Theta}}=\boldsymbol{A}_0+\mathbf{B}\Theta\mathbf{B}^*, \end{align*} $$ where $\boldsymbol {A}_0$ is a distinguished self-adjoint extension and $\Theta $ is a self-adjoint linear relation in $\mathbb {C}^d$ . The perturbation is singular in the sense that it does not belong to the underlying Hilbert space but is form-bounded with respect to $\boldsymbol {A}_0$ , i.e., it belongs to $\mathcal {H}_{-1}(\boldsymbol {A}_0)$ , with possible “infinite coupling.” A boundary triple and compatible boundary pair for the symmetric operator are constructed to ensure that the perturbation is well defined and self-adjoint extensions are in a one-to-one correspondence with self-adjoint relations $\Theta $ .The merging of boundary triples with perturbation theory provides a more holistic view of the operator’s matrix-valued spectral measures: identifying not just the location of the spectrum, but also certain directional information.As an example, self-adjoint extensions of the classical Jacobi differential equation (which has two limit-circle endpoints) are obtained, and their spectra are analyzed with tools both from the theory of boundary triples and perturbation theory.

Direct numerical simulation of interaction between a stationary crossflow instability and forward-facing steps

The interaction between forward-facing steps of several heights and a pre-existing critical stationary crossflow instability of a swept-wing boundary layer is analysed. Direct numerical simulations (DNS) are performed of the incompressible three-dimensional laminar base flow and the stationary distorted flow that arise from the interaction between an imposed primary stationary crossflow perturbation and the steps. These DNS are complemented with solutions of the linear and the nonlinear parabolised stability equations, used towards identifying the influence of linearity and non-parallelism near the step. A fully stationary solution of the Navier–Stokes equations is enforced numerically, in order to isolate the mechanisms pertaining to the interaction of the stationary disturbance with the step. Results provide insight into the salient modifications of the base laminar boundary layer due to the step, and the response of the incoming crossflow instability to these changes. The fundamental spanwise Fourier mode of the disturbance field gradually lifts up as it approaches the step and passes over it. The flow environment around the step is characterised by a sudden spanwise modulation of the base-flow streamlines. Additional stationary perturbation structures are induced at the step, which manifest in the form of spanwise-aligned velocity streaks near the wall. Shortly downstream of the step, the fundamental component of the crossflow perturbation maintains a rather constant amplification for the smallest steps studied. For the largest step, however, the fundamental crossflow perturbation is stabilised significantly shortly downstream of the largest step. This surprising result is ascribed to a modulation of the kinetic energy transfer between the base flow and the fundamental perturbation field, which is brought forward as a new step interaction mechanism. Possible non-modal growth effects at the step are discussed. Furthermore, the results from DNS indicate significant amplification of the high-order harmonic crossflow components downstream of the step.

Abstract 838: Loss of Arp2/3 activity promotes anchorage independent growth in KRAS;TP53-mutated human bronchial epithelial cells

Abstract Mutated KRAS and TP53 are well recognized drivers of multiple human cancers including lung cancer, the leading cause of cancer-associated deaths. Yet, directly targeting mutated KRAS or restoring wildtype p53 levels in KRAS/p53-mutated tumors still remains a therapeutic challenge. A rational alternative approach involves targeting potentiators of KRAS;p53-driven tumorigenesis, which represents one of the research ambitions pioneered by the National Cancer Institute (NCI) RAS initiative to meet this challenge. Therefore, we aimed to identify genes, that when lost, potentiate cellular transformation of a non-transformed KRAS;TP53-mutated human bronchial epithelial cell line (HBEC-KP). To address this question, a genome-wide selection experiment was performed using CRISPR/Cas9. Anchorage-independent (AI) growth, a hallmark of cancer, was selected as a phenotypic readout for one experiment. Without additional genetic perturbation, wildtype HBEC-KP cells were incapable of AI growth. Only certain mutants were capable of supporting colony formation in soft agar. These clones were isolated and the integrated small guide RNAs (sgRNAs) were identified. Genes that are targeted by the sgRNAs were then individually knocked out for validation. Through this approach, we discovered that loss of ARPC3 is sufficient for promoting AI growth in the HBEC-KP cells. This contribution to AI growth is attributed to the role that ARPC3 plays in regulating Arp2/3 activity, as inactivating the Arp2/3 complex using a small molecule inhibitor, CK666 also promoted colony growth in the HBEC-KP cells. We determined that ARPC3 loss was not sufficient to drive AI – in the absence of KRAS activation and p53 loss colony growth was not observed. This indicates the essential role that mutated KRAS and/or p53 play to support AI. To test if mutated KRAS is essential for the phenotype, the Arp2/3 complex was inactivated in KRAS-mutated HBECs, which supported AI growth. This suggests that mutated KRAS and loss of Arp2/3 activity are sufficient for driving AI growth in HBECs. However, combined loss of p53 and ARPC3 failed to drive the phenotype, implicating that mutated KRAS is required. In addition, the Arp2/3 complex is essential for maintaining lamellipodial shape via actin filament network and cell motility, which was validated in our HBEC-KP-ARPC3 knockout cells. However, this protein complex is also known to promote AI growth and development of various cancers, as opposed to acting as a suppressor for growth. Multiple mechanisms that lead to this growth phenotype are currently being explored. Clinical relevance is also being closely examined to further understand the role of the Arp2/3 complex in cancer. Citation Format: Chennan Li, Andrea L. Kasinski. Loss of Arp2/3 activity promotes anchorage independent growth in KRAS;TP53-mutated human bronchial epithelial cells [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2022; 2022 Apr 8-13. Philadelphia (PA): AACR; Cancer Res 2022;82(12_Suppl):Abstract nr 838.