Zero Gradient Research Articles

Quantifying and Exploiting Adversarial Vulnerability: Gradient-Based Input Pre-Filtering for Enhanced Performance in Black-Box Attacks

We investigate the vulnerability of inputs in an adversarial setting and demonstrate that certain samples are more susceptible to adversarial perturbations compared to others. Specifically, we employ a simple yet effective approach to quantify the adversarial vulnerability of inputs, which relies on the clipped gradients of the loss with respect to the input. Our observations indicate that inputs with a low percentage of zero gradient components tend to be more vulnerable to attacks. These findings are supported by a theoretical explanation on a linear model and empirical evidence on deep neural networks. Across all datasets we tested, we find that inputs with the lowest zero gradient percentage, on average, exhibit 34.5% more susceptibility to adversarial attacks than randomly selected inputs. Additionally, we demonstrate that the zero gradient percentage, as a metric, transfers across different model architectures. Finally, we propose a novel black-box attack pipeline that enhances the efficiency of conventional query-based black-box attacks and show that input pre-filtering based on ZGP can boost the attack success rates, particularly under low perturbation levels. On average, across all datasets we test, our approach outperforms the conventional shadow model-based and query-based black-box attack pipelines by 44.9% and 30.4%, respectively.

Zero gradient sum algorithm of arbitrary initial value with constraints and communication delay based on directed graph

The distributed convex optimisation issue with inequality constraints and box constraints on the directed communication topology is examined in this paper. In the case of the communication delay between agents, we propose a piecewise zero-gradient-sum triggered control algorithm that allows arbitrary initial values. Using the log-barrier penalty method, we only need to study an unconstrained approximation problem of the original problem. Firstly, each agent's state converges to the optimal value of the related local objective function in a fixed time. Simultaneously, the upper bound of fixed time in this paper is smaller than some existing results. Then, in the case of communication delay, time-triggered and event-triggered methods with non-uniform sampling interval are proposed in this paper, which make the communication cost lower and the application broader. Using the Lyapunov function method, the sufficient conditions for each agent's state to converge to the optimal point are given, and the Zeno behaviour is excluded. Finally, to confirm the algorithm's effectiveness, we provide two numerical examples and one machine learning example as demonstrations.

Computing complete solution sets for approximate four-bar path synthesis

The approximate path synthesis of four-bar linkages has been framed and solved with many different optimization techniques. Here we present a polynomial objective that is invariant to the number of approximate design positions selected, and a solution technique capable of finding all minima. The invariance property caps compute time despite increasing the size of input task specification data. This is performed by collecting a variable amount of task data into an invariable number of polynomial coefficients, called moments, before numerical optimization begins. The minima are found by applying the method of random monodromy loops to the zero gradient polynomial system of the aforementioned objective. This procedure finds all critical points, including the local and global minimum, and provides an in-process estimate of the percentage of critical points found. We applied our methodology to four-bar path synthesis problems of various computational scales by altering dimensional pre-specifications. The most general case was estimated to have 1,820,238 ± 3810 critical points, while pre-specification of one or two ground pivots yielded 26,052 and 503 roots, respectively, as validated by a trace test. The results are applied to a variety of examples.

Analyzing the acoustic wave propagation characteristics in discontinuous bifurcated waveguide

This article examines the dispersion characteristics and energy distribution in different regions of the bifurcated waveguide with vertical step discontinuities. In this research study, we have considered mathematical model of noise reduction devices, specifically analyzing the acoustic wave propagation problem in a bifurcated waveguide with elastic membrane outer plates and rigid inner plates. Mode-matching (MM) technique is employed to match the eigenfunctions at the interface and analyzed the reflection and transmission amplitudes in all regions. Through MM scheme an infinite system of equations has been obtained for these boundary conditions by dividing the structure into three regions and finding dispersion relations and eigenfunctions using separation of variables and the corresponding orthogonality relations. Because of the flexible nature of the boundary surfaces, the acquired eigenfunctions and the dispersion relation do not satisfy the standard orthogonality relation. To resolve this difficulty, we have established a modified orthogonality relation to take into account the flexible nature of the boundary surfaces. With the implication of physical connections, the uniqueness of the problem has been ensured, and zero displacement and zero gradient edge conditions on bending surfaces have been considered to present results. Energy expressions are obtained showing how the energy is distributed in different sections of the waveguide, which is consistent with the energy conservation law. Finally, the numerical discussion illustrates the quantitative behavior of the physical parameters and summarizes the significant contribution of the study by presenting graphical data.

Infrared radiative switching with thermally and electrically tunable transition metal oxides-based plasmonic grating

Plasmonic and phase transition has been blended to gain the infrared radiative switching which is tunable with temperature or voltage supply. This is applied via vanadium dioxide, tungsten trioxide, and molybdenum trioxide as transition metal oxides (TMO). The metallic phase at high temperature or colored state contributes in magnetic polariton (MP) excitation, producing broad absorptance. The TMO-based sub-layer is integrated underneath the grating fully supporting MP resonance. In contrast, this underlayer leads to producing the narrowband absorptance originated from concept of zero contrast grating (ZCG). The zero gradient in refractive index at the output plane of the grating cause transmission of light in broad wavelength range. With introduction of reflective silver underlayer, those transmitted through the grating are reflected back. However, there exists the near-zero narrowband transmission peaks in ZCG. This undergoes transformation to narrowband absorptance. In addition, another absorptance peak can be induced due to phonon modes at insulating phase. The MP resonance at metallic phase is characterized with inductor-capacitor (LC) circuit and the narrowband absorptance peaks are characterized with phase shift from the Fabry–Perot round trip (FP-RT) eigenequation from high contrast grating (HCG). The work expands the usage of transition metal oxides in infrared region with larger contrast.

Derivation via Hamilton's principle of a new shallow-water model using a color function for the macroscopic description of partial wetting phenomena

This paper presents a new shallow-water type model suitable for the simulation of partially wetting liquid films without the need for very fine resolution of the contact line phenomena, which is particularly suitable for industrial applications. This model is based on the introduction of a color function, propagated at the averaged velocity of the bulk flow, and equal to one where there is a liquid film and zero in the dry zone, which implies a non zero gradient only at the interface. This approach has the advantage of easily locating the interface, allowing to model macroscopically the forces acting at the contact line, which is essential for the simulation of partial wetting phenomena. The formal derivation of this model is based on the principle of least action known as Hamilton's principle. Here this principle is applied in a full Eulerian form to derive the complete system of equations with the color function. This method proves to be particularly suitable for this type of development and as an illustration it is also applied to recover another model proposed by Lallement et al. [39, 73]. Finally, both models are compared from a theoretical point of view and the advantages of the new color function based model are discussed.

A finite time discrete distributed learning algorithm using stochastic configuration network

In this paper, we propose a finite-time discrete distributed learning algorithm, denoted as the FTDDL algorithm, using the Stochastic Configuration Network (SCN) and Zero Gradient Sum (ZGS) strategy. In distributed scenarios, the communication networks that store data are modeled as algebraic graphs and the learning problems are formulated as distributed optimization problems. The FTDDL algorithm persists the universal approximation of the SCN learner. The process of the FTDDL algorithm is divided into two phases, namely “distributed hidden parameters configuration” and “distributed output weights determination”. It has been theoretically proved that the FTDDL algorithm works in distributed manner and achieves the same efficiency as the centralized SCN. According to the FTDDL algorithm, each node over the communication network transmits the updated output weights of the SCN with its direct neighbors. Thus, the FTDDL algorithm preserves data privacy and saves network bandwidth. The FTDDL algorithm is theoretically proved to converge to the global optimal output weights of the SCN within finite time. Compared with the other distributed learning algorithms using SCNs, the FTDDL algorithm can significantly reduce the iteration times. At last, some experiments are shown in Simulations part to verify the effectiveness of the FTDDL algorithm.

Self-Sparse Generative Adversarial Networks

Generative Adversarial Networks (GANs) are an unsupervised generative model that learns data distribution through adversarial training. However, recent experiments indicated that GANs are difficult to train due to the requirement of optimization in the high dimensional parameter space and the zero gradient problem. In this work, we propose a Self Sparse Generative Adversarial Network (Self-Sparse GAN) that reduces the parameter space and alleviates the zero gradient problem. In the Self-Sparse GAN, we design a Self-Adaptive Sparse Transform Module (SASTM) comprising the sparsity decomposition and feature-map recombination, which can be applied on multi-channel feature maps to obtain sparse feature maps. The key idea of Self-Sparse GAN is to add the SASTM following every deconvolution layer in the generator, which can adaptively reduce the parameter space by utilizing the sparsity in multi-channel feature maps. We theoretically prove that the SASTM can not only reduce the search space of the convolution kernel weight of the generator but also alleviate the zero gradient problem by maintaining meaningful features in the Batch Normalization layer and driving the weight of deconvolution layers away from being negative. The experimental results show that our method achieves the best FID scores for image generation compared with WGAN-GP on MNIST, Fashion-MNIST, CIFAR-10, STL-10, mini-ImageNet, CELEBA-HQ, and LSUN bedrooms, and the relative decrease of FID is 4.76% ~ 21.84%.

Numerical analysis of complex heat storage unit during freezing of phase change material enhanced withTiO2 nanoparticles

Improvement of discharging process of system with inclusion of nanoparticles (TiO2) and install of new style of fins have been illustrated in this investigation. The scrutinized paraffin (n-eicosane) become solidify at 309 K and fraction of nanoparticles is less than 0.03 for all cases which is permission of using homogeneous model for estimating properties. Although the efficacy of gravity force can be neglected in freezing, in current modeling, the related term has been applied and contours for velocity have been reported. The outer wall of tank has square shape and zero gradient condition was applied for that wall. The circular wall which the fins attached to this has cold wall (296 K). Thus, appearance of fins makes the freezing faster. Number of fins (n = 1, 3, 7) and fraction of TiO2 (ϕ = 0, 0.03) were the variables of simulations. With adding nano-powders, the required time declines about 3.33 %, 2.69 % and 2.015 % when n = 1, 3 and 7, respectively. Increasing number of fins from 1 to 3 and 7, makes freezing time to decline around 23.24 % and 28.41 %.

Real Sample Consistency Regularization for GANs.

Mode collapse has always been a fundamental problem in generative adversarial networks. The recently proposed Zero Gradient Penalty (0GP) regularization can alleviate the mode collapse, but it will exacerbate a discriminator’s misjudgment problem, that is the discriminator judges that some generated samples are more real than real samples. In actual training, the discriminator will direct the generated samples to point to samples with higher discriminator outputs. The serious misjudgment problem of the discriminator will cause the generator to generate unnatural images and reduce the quality of the generation. This paper proposes Real Sample Consistency (RSC) regularization. In the training process, we randomly divided the samples into two parts and minimized the loss of the discriminator’s outputs corresponding to these two parts, forcing the discriminator to output the same value for all real samples. We analyzed the effectiveness of our method. The experimental results showed that our method can alleviate the discriminator’s misjudgment and perform better with a more stable training process than 0GP regularization. Our real sample consistency regularization improved the FID score for the conditional generation of Fake-As-Real GAN (FARGAN) from 14.28 to 9.8 on CIFAR-10. Our RSC regularization improved the FID score from 23.42 to 17.14 on CIFAR-100 and from 53.79 to 46.92 on ImageNet2012. Our RSC regularization improved the average distance between the generated and real samples from 0.028 to 0.025 on synthetic data. The loss of the generator and discriminator in standard GAN with our regularization was close to the theoretical loss and kept stable during the training process.

Active Learning for Enumerating Local Minima Based on Gaussian Process Derivatives.

We study active learning (AL) based on gaussian processes (GPs) for efficiently enumerating all of the local minimum solutions of a black-box function. This problem is challenging because local solutions are characterized by their zero gradient and positive-definite Hessian properties, but those derivatives cannot be directly observed. We propose a new AL method in which the input points are sequentially selected such that the confidence intervals of the GP derivatives are effectively updated for enumerating local minimum solutions. We theoretically analyze the proposed method and demonstrate its usefulness through numerical experiments.

Simulation of Combustion Flowfield in Porous Media with Lattice Boltzmann Method

In this paper, two-dimensional numerical modeling of a premixed porous combustion is presented by a Lattice Boltzmann approach. In this solution, the flow distribution is replaced by a pressure distribution equation using the Darcy and Forchheimer model as the multiple-relaxation-time code. The laminar propane-air mixture with Reynolds number of 100 and Prandtl number of 0.75 is put through a silicon carbide porous medium channel. The boundary conditions are included as the uniform inlet temperature and velocity, atmospheric output pressure, periodic wall temperature, and nonslip walls with initial zero gradient for products and reactants. For validation of this model, the presented data of temperature, molar concentration, and velocity comprised published data where the existence of acceptable agreements confirms the accuracy of this solution. The results show that, in the porous medium, the flame position is located at closer distance from the entrance of channel rather than the nonporous medium. Furthermore, the maximum temperature is reduced up to 5.8% when Darcy number is decreasing from 0.1 to 0.001, and with the reduction of Darcy number, the size of vortices is decreased. Moreover, when the porosity coefficient decreases, the size of high-temperature region decreases, and with increasing equivalence ratio from 0.6 to 1, the maximum temperature is significantly augmented with a value of 24.3%.

Distributed semi-supervised learning algorithm based on extreme learning machine over networks using event-triggered communication scheme

In this paper, we propose a distributed semi-supervised learning (DSSL) algorithm based on the extreme learning machine (ELM) algorithm over communication network using the event-triggered (ET) communication scheme. In DSSL problems, training data consisting of labeled and unlabeled samples are distributed over a communication network. Traditional semi-supervised learning (SSL) algorithms cannot be used to solve DSSL problems. The proposed algorithm, denoted as ET-DSS-ELM, is based on the semi-supervised ELM (SS-ELM) algorithm, the zero gradient sum (ZGS) distributed optimization strategy and the ET communication scheme. Correspondingly, the SS-ELM algorithm is used to calculate the local initial value, the ZGS strategy is used to calculate the globally optimal value and the ET scheme is used to reduce communication times during the learning process. According to the ET scheme, each node over the communication network broadcasts its updated information only when the event occurs. Therefore, the proposed ET-DSS-ELM algorithm not only takes the advantages of traditional DSSL algorithms, but also saves network resources by reducing communication times. The convergence of the proposed ET-DSS-ELM algorithm is guaranteed by using the Lyapunov method. Finally, some simulations are given to show the efficiency of the proposed algorithm.

Zero Gradient Control for R-744 refrigeration cycles

This paper proposes a method called Zero Gradient Control, which is used to control the heat rejection pressure and the rotational speed of the fans of the gascooler of R-744 refrigeration cycles nearly energy optimal. The basic concept is to develop algebraic terms for the partial derivatives of the COP with respect to the heat rejection pressure and the speed of the fans. These equations are evaluated online with measurement signals and directly fed to decentralized controllers with setpoint zero. The control structure is the same for both sub- and transcritical operation, requires little parameterization and can be applied to a wide range of systems. Using Zero Gradient Control, there is no need to calculate setpoints, which simplifies the mathematical effort in the implementation. Measurements for various scenarios validate the method even in the case of atypical system behavior or gascooler fouling.

Some Results of the Clinical Use of the Proton Therapy Complex “Prometheus”

In November 2015, the proton therapy complex “Prometheus”, developed at PTC LPI RAS, started being used for the clinical treatment of patients with head and neck cancer. This complex consists of a compact zero gradient synchrotron, which is able to accelerate protons to energies of 330 MeV. In this paper, there are some key parameters of the extracted beam, the working process of the complex and the results of treatment received during the first year of using the accelerator in therapeutic purposes (treatment was carried out on 82 patients).

Seasonal variability of ice temperature upon the results of measuring at “North Pole-38” drifting station

Vertical profiles of ice temperature were measured in November 2010 – September 2011 at “North Pole-38” drifting station. These observations were made at five locations, including young ice, residual first-year ice, second-year ice, multi-year ice. Methods of measurements are considered. Time-temperature profiles for all types of ice as well as time profile for the gradient of temperature of ice, as an example, are shown. A snow cover gives substantial thermal resistance, reducing a heat flux between atmosphere and ocean. The periods of warming-up and cooling of ice in the annual cycle alternate with periods, when vertical distribution of ice temperature close to linear: with a maximal gradient in winter and zero gradient in summer. A general pattern of the seasonal evolution of ice temperature is discussed. A cold front is propagating down through the ice from October to June. Ice growth lasts, on the average, to a middle of May. Warming of ice to the freezing point occurs mainly in August.

Improving the FLORIS wind plant model for compatibility with gradient-based optimization

The FLORIS (FLOw Redirection and Induction in Steady-state) model, a parametric wind turbine wake model that predicts steady-state wake characteristics based on wind turbine position and yaw angle, was developed for optimization of control settings and turbine locations. This article provides details on changes made to the FLORIS model to make the model more suitable for gradient-based optimization. Changes to the FLORIS model were made to remove discontinuities and add curvature to regions of non-physical zero gradient. Exact gradients for the FLORIS model were obtained using algorithmic differentiation. A set of three case studies demonstrate that using exact gradients with gradient-based optimization reduces the number of function calls by several orders of magnitude. The case studies also show that adding curvature improves convergence behavior, allowing gradient-based optimization algorithms used with the FLORIS model to more reliably find better solutions to wind farm optimization problems.

Counter-ion transport number and membrane potential in working membrane systems

In this work we use the general space-charge (SC) theory for a combined transport model of fluid and ion through cylindrical nanopores to derive equations for the membrane potential and counter-ion transport numbers. We discuss this approach for ion exchange membranes assuming aqueous domains as interconnected network of cylindrical pores. The transport number calculations from the SC theory are compared with the corresponding ones from the uniform potential (UP) and Teorell-Meyer-Sievers (TMS) models in the case of both zero and non-zero concentration gradient across the membrane and with an applied current density. By using this approach we suggest the optimal conditions for performing membrane potential experiments (i.e. choice of electrolyte and concentration difference) depending on an easily accessible membrane property, namely the volumetric charge density. We also theoretically describe a novel dynamic method to determine in a single experiment the membrane potential and membrane conductivity. To exemplify the use of the dynamic method we report the calculations based on typical operating conditions of the reverse electrodialysis process. The numerical results are presented in terms of the electrical potential difference versus the average pore radius and charge density. The resulting map is a useful tool for a rational design of an effective membrane morphology for a specific electrochemical application.

Simultaneous orthogonal plane imaging.

Intrafraction motion can result in a smearing of planned external beam radiation therapy dose distributions, resulting in an uncertainty in dose actually deposited in tissue. The purpose of this paper is to present a pulse sequence that is capable of imaging a moving target at a high frame rate in two orthogonal planes simultaneously for MR-guided radiotherapy. By balancing the zero gradient moment on all axes, slices in two orthogonal planes may be spatially encoded simultaneously. The orthogonal slice groups may be acquired with equal or nonequal echo times. A Cartesian spoiled gradient echo simultaneous orthogonal plane imaging (SOPI) sequence was tested in phantom and in vivo. Multiplexed SOPI acquisitions were performed in which two parallel slices were imaged along two orthogonal axes simultaneously. An autocalibrating phase-constrained 2D-SENSE-GRAPPA (generalized autocalibrating partially parallel acquisition) algorithm was implemented to reconstruct the multiplexed data. SOPI images without intraslice motion artifacts were reconstructed at a maximum frame rate of 8.16 Hz. The 2D-SENSE-GRAPPA reconstruction separated the parallel slices aliased along each orthogonal axis. The high spatiotemporal resolution provided by SOPI has the potential to be beneficial for intrafraction motion management during MR-guided radiation therapy or other MRI-guided interventions. Magn Reson Med 78:1700-1710, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

THE EFFECTS OF ADMINISTRATION OF VALPROIC ACID ON BRAIN DERIVED NEUROTROPHIC FACTOR (BDNF) AND DEPRESSION OF ANIMAL ALZHEIMER’S DISEASE DURING EIGHT WEEK LONG ENDURANCE EXERCISES

Abstract. The objective of the present study is to analyze the effects of administration of valproic acid on Brain Derived Neurotrophic Factor (BDNF) and depression of alzheimer’s disease of desert rat during eight week long endurance exercises. In order to administer the study, 140 Sprague Dawley desert rats (70 of which are male and the other half, female) are categorized randomly into seven research groups, which includes 1) control group 2) sham group and testing groups 3) long distance training group 4) valproic acid 100 group 5) valproic acid 200 group 6) training group of valproic acid 100 7) training group of valproic acid 200. During the eight week period, research desert rats of groups 3, 6 and 7 run for 15 minutes and 30 seconds on zero gradient laboratory treadmill, with the speed of 15 to 20 meters per minute in each training lapse. The lapses are frequented five times a week. Furthermore, for a 14 day period, groups 4 and 6 are daily administered with 100 milligrams valproic acid on kilogram and groups 5 and 7 are daily administered with 200 milligrams valproic acid. Research Methodology For research data analysis, one-way variance test and post hoc Tukey’s test are utilized. The findings indicate that the level of BDNF in all the research groups is significantly higher than the sham group (p<0.05) and Tumor Necrosis Factor Alpha (TNF) and depression level of all the research groups are significantly lower than the sham group (p<0.05). Research Findings According to the research findings, it is indicated that endurance exercises, valproic acid and their synthetic administration increase the level of BDNF and decrease the levels of TNF and depression in desert rats with alzheimer’s disease.