Maximal Perturbations Research Articles

Existence and Relaxation of Solutions for a Differential Inclusion with Maximal Monotone Operators and Perturbations

Existence and Relaxation of Solutions for a Differential Inclusion with Maximal Monotone Operators and Perturbations

Neural Adversarial Attacks with Random Noises

In this paper, we present an approach which relies on the use of random noises to generate adversarial examples of deep neural network classifiers. We argue that existing deterministic attacks, which perform by sequentially applying maximal perturbations on selected components of the input, fail at reaching accurate adversarial examples on real-world large scale datasets. By exploiting a simple Taylor expansion of the expected output probability under the noise perturbation, we introduce noise-based sparse (or L0) targeted and untargeted attacks. Our proposed method, called Voting Folded Gaussian Attack (VFGA), achieves significantly better L0 scores than state-of-the-art L0 attacks (such as SparseFool and Sparse-RS) while being faster on both CIFAR-10 and ImageNet. Moreover, we show that VFGA is also applicable as an L∞ attack and outperforms the state-of-the-art projected gradient attack (PGD) method.

Modulation of H-reflex and V-wave responses during dynamic balance perturbations

Motoneuron excitability is possible to measure using H-reflex and V-wave responses. However, it is not known how the motor control is organized, how the H-reflex and V-wave responses modulate and how repeatable these are during dynamic balance perturbations. To assess the repeatability, 16 participants (8 men, 8 women) went through two, identical measurement sessions with ~ 48 h intervals, where maximal isometric plantar flexion (IMVC) and dynamic balance perturbations in horizontal, anterior–posterior direction were performed. Soleus muscle (SOL) neural modulation during balance perturbations were measured at 40, 70, 100 and 130 ms after ankle movement by using both H-reflex and V-wave methods. V-wave, which depicts the magnitude of efferent motoneuronal output (Bergmann et al. in JAMA 8:e77705, 2013), was significantly enhanced as early as 70 ms after the ankle movement. Both the ratio of M-wave-normalized V-wave (0.022–0.076, p < 0.001) and H-reflex (0.386–0.523, p < 0.001) increased significantly at the latency of 70 ms compared to the latency of 40 ms and remained at these levels at latter latencies. In addition, M-wave normalized V-wave/H-reflex ratio increased from 0.056 to 0.179 (p < 0.001). The repeatability of V-wave demonstrated moderate-to-substantial repeatability (ICC = 0.774–0.912) whereas the H-reflex was more variable showing fair-to-substantial repeatability (ICC = 0.581–0.855). As a conclusion, V-wave was enhanced already at 70 ms after the perturbation, which may indicate that increased activation of motoneurons occurred due to changes in descending drive. Since this is a short time-period for voluntary activity, some other, potentially subcortical responses might be involved for V-wave increment rather than voluntary drive. Our results addressed the usability and repeatability of V-wave method during dynamic conditions, which can be utilized in future studies.

Deciphering the role of alternative splicing as modulators of defense response in the MYMIV- Vigna mungo pathosystem.

Alternative splicing (AS) is a crucial regulatory mechanism that impacts transcriptome and proteome complexity under stressful situations. Although its role in abiotic stresses is somewhat understood, our understanding of the mechanistic regulation of pre-mRNA splicing in plant-pathogen interaction is meagre. To comprehend this unexplored immune reprogramming mechanism, transcriptome profiles of Mungbean Yellow Mosaic India Virus (MYMIV)-resistant and susceptible Vigna mungo genotypes were analysed for AS genes that may underlie the resistance mechanism. Results revealed a repertoire of AS-isoforms accumulated during pathogenic infestation, with intron retention being the most common AS mechanism. Identification of 688 differential alternatively spliced (DAS) genes in the resistant host elucidates its robust antiviral response, whereas 322 DAS genes were identified in the susceptible host. Enrichment analyses confirmed DAS transcripts pertaining to stress, signalling, and immune system pathways have undergone maximal perturbations. Additionally, a strong regulation of the splicing factors has been observed both at transcriptional and post-transcriptional levels. qPCR validation of candidate DAS transcripts with induced expression upon MYMIV-infection demonstrated a competent immune response in the resistant background. The AS-impacted genes resulted either in partial/complete loss of functional domains or altered sensitivity to miRNA-mediated gene silencing. A complex regulatory module, miR7517-ATAF2, has been identified in an aberrantly spliced ATAF2 isoform that exposes an intronic miR7517 binding site, thereby suppressing the negative regulator to enhance defense reaction. The present study establishes AS as a non-canonical immune reprogramming mechanism that operates in parallel, thereby offering an alternative strategy for developing yellow mosaic-resistant V. mungo cultivars. This article is protected by copyright. All rights reserved.

High Dimensional Inference With Random Maximum A-Posteriori Perturbations

This paper presents a new approach, called perturb-max, for high-dimensional statistical inference in graphical models that is based on applying random perturbations followed by optimization. This framework injects randomness into maximum a-posteriori (MAP) predictors by randomly perturbing the potential function for the input. A classic result from extreme value statistics asserts that perturb-max operations generate unbiased samples from the Gibbs distribution using high-dimensional perturbations. Unfortunately, the computational cost of generating so many high-dimensional random variables can be prohibitive. However, when the perturbations are of low dimension, sampling the perturb-max prediction is as efficient as MAP optimization. This paper shows that the expected value of perturb-max inference with low dimensional perturbations can be used sequentially to generate unbiased samples from the Gibbs distribution. Furthermore the expected value of the maximal perturbations is a natural bound on the entropy of such perturb-max models. A measure concentration result for perturb-max values shows that the deviation of their sampled average from its expectation decays exponentially in the number of samples, allowing effective approximation of the expectation.

Structured maximal perturbations for Hamiltonian eigenvalue problems

We discuss the effect of structure-preserving perturbations on complex or real Hamiltonian eigenproblems and characterize the structured worst-case effect perturbations. We derive explicit expressions for the maximal Hamiltonian perturbations.

1084 EXPERIMENTAL INVESTIGATION OF THE SINGLE RIB EFFECT ON SEPARATION REGION BEHIND THE BACK-FACING STEP

This work is aimed at experimental investigation of the single rib effect on the recirculation region behind the backfacing step. Measurements were carried out by the PIV method. The experiments were performed at Reynolds number Re = 15000 in the rectangular working channel of 21 X 150 mm and length of 1 m. At the distance of 600 mm from the channel inlet there was the back-facing step of the constant height H=9 mm. Rib height d and distance to the back-facing step S were varied (d from 3 to 6 mm and S from 0 to 77 mm). According to measurements, in this case the following interaction mechanism between separated flows occurs: if there is a rib in the channel in front of the step, the boundary layer separates. Depending on the distance between the rib and the step in the channel the flow will attach in front of the step or behind it. In our experiments the flow attached at S/D >7.5 and Δ=3mm and S/Δ > 10 at Δ= 6mm. In the case when the flow attaches in front of the step, the recirculation zone behind the step decreases to 35%. This relates to the fact that the flow separated behind a rib influences the mixing layer behind the step and intensifies the mixing processes, what finally leads to reduction in the length of recirculation zone. When S/Δ < 7.5, the recirculation zone behind the back-facing step increases, and in the limit case of S/Δ = 0 (the rib is at the step edge) becomes 60% larger for Δ= 3mm. We should note the general tendency of interaction between the separated flows of different scales. A rib changes the typical profile of longitudinal average velocities and mean-root velocity pulsations behind the back-facing step. For the studied configurations it was not enough time for velocity profiles and profiles of velocity pulsations to be restored to the values, corresponding to the separated flow behind the step without a rib. Maximal perturbations within the initial region of separated flow development behind the step were observed at the distance from the wall, corresponding to the coordinate of rib top. In general, the experimental data agree with experimental results of Miau et al., 1991 for S/Δ=12 and calculation results of Neumann, Wengle, 2004. The mechanism of interference for the separated flows of different scales is discussed in detail in the current study.

Strongly quasibounded maximal monotone perturbations for the Berkovits–Mustonen topological degree theory

Let X be a real reflexive Banach space with dual X ∗ . Let L : X ⊃ D ( L ) → X ∗ be densely defined, linear and maximal monotone. Let T : X ⊃ D ( T ) → 2 X ∗ , with 0 ∈ D ( T ) and 0 ∈ T ( 0 ) , be strongly quasibounded and maximal monotone, and C : X ⊃ D ( C ) → X ∗ bounded, demicontinuous and of type ( S + ) w.r.t. D ( L ) . A new topological degree theory has been developed for the sum L + T + C . This degree theory is an extension of the Berkovits–Mustonen theory (for T = 0 ) and an improvement of the work of Addou and Mermri (for T : X → 2 X ∗ bounded). Unbounded maximal monotone operators with 0 ∈ D ˚ ( T ) are strongly quasibounded and may be used with the new degree theory.

On the uniqueness of the Browder degree

We consider the topological degree theory for maximal monotone perturbations of mappings of class (S + ) originally introduced by F. Browder in 1983. In the original construction it is implicitly assumed that the maximal monotone part is at least densely defined. The construction itself remains valid without this assumption. However, for the proof of the uniqueness of the degree the assumption is crucial. We shall recall the construction of the degree and show how the stabilization of the degree can be obtained directly, thus avoiding a series of technical lemmas used by F. Browder. The main result of this paper is the proof for the uniqueness of the degree in the general case. We also discuss the class of admissible homotopies, which may be quite narrow in case the domain of the maximal monotone part is not densely defined.

Early onset of stabilizing strategies for gait and obstacles: Older adults with Down syndrome

Our goal was to examine the gait patterns of older adults with Down syndrome (DS) for precocious stabilizing adaptations during comfortable over-ground walking and in more challenging conditions. Twelve participants with DS and 12 with typical development (TD) were matched for height, weight and age (range 35–62 years). We used a six-camera motion capture system to assess foot trajectories over obstacles. Participants first walked at their preferred speed over a 5.3 m instrumented gait mat (unperturbed condition). Subsequent walking trials included perturbations mid-walkway: (a) minimal obstacle to step over (12 cm high), (b) moderate obstacle to step onto with both feet and then off (standard step), and (c) maximum obstacle to step onto with only one foot and over with the other (standard step). Adults with DS walked slower with shorter, wider strides while spending more time in both stance and double support. These adaptations increased during the moderate and maximal perturbations. They stepped with the minimal perturbation obstacle further forward in their crossing step and produced a lower, flatter trajectory of the lead foot, with less dorsiflexion at crossing. This strategy decreased trailing toe clearance but did not alter leading heel clearance. The combined effects of ligamentous laxity, low tone, obesity, inactivity and physiological decrements associated with aging lead to these stability-enhancing adaptations at a younger chronological age in adults with DS. We believe intervention to increase overall stability will be beneficial in helping adults with DS maintain optimal functional mobility and health.

Topological degree for (S)++-mappings with maximal monotone perturbations and its applications to variational inequalities

Topological degree for (S)++-mappings with maximal monotone perturbations and its applications to variational inequalities

Topological degree for (S) [formula omitted]-mappings with maximal monotone perturbations and its applications to variational inequalities

This paper is concerned with the topological degree for mappings of class (S) + with maximal monotone perturbations. Several results and remarks concerning the evaluation of this degree are given. In particular, it is shown that the local degree for the generalized gradient of nonsmooth functional at the local minimizer is equal to one. As applications, two examples of elliptic variational inequalities are given, where the multiple existence of solutions is discussed.

Robust performance of systems with affine parameter uncertainty and convex analysis

In this note, we consider SISO plant families with affine parameter uncertainties in the numerator and denominator of their transfer function. It is assumed that the controller has been chosen, and a bound on sensitivity is given. For a nominal plant satisfying the performance criteria we provide a formula for the maximal allowable perturbations of the parameters maintaining the performance criteria.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Computation of nonconservative stability perturbation bounds for systems with nonlinearly correlated uncertainties

Consideration is given to the problem of robust stability analysis of linear dynamic systems with uncertain physical parameters entering as polynomials in the state equation matrices. A method is proposed giving necessary and sufficient conditions for computing the uncertain system stability margin in parameter space, which provides a measure of maximal parameter perturbations preserving stability of the perturbed system around a known, stable, nominal system. A globally convergent optimization algorithm that enables solutions to the problem to be obtained is presented. Using the polynomial structure of the problem, the algorithm generates a convergent sequence of interval estimates of the global extremum. These intervals provide a measure of the accuracy of the approximating solution achieved at each step of the iterative procedure. Some numerical examples are reported, showing attractive features of the algorithm from the point of view of computational burden and convergence behavior. >