Local Perturbation Method Research Articles

Local perturbation of critical subgraph based social network structural privacy protection

In social networks, the direct exposure of structural data containing numerous authentic relationships significantly risks user privacy leakage. Thus, safeguarding the privacy of such data has emerged as a pressing concern. Existing methodologies commonly employ global perturbation, randomly altering the network structure and resulting in diminished data availability upon publication. Notably, these methods often overlook the privacy implications associated with critical nodes and diverse structural features within subgraphs, thereby exacerbating the risk of privacy breaches. In response to these challenges, we present a novel privacy protection approach, termed CGLP, tailored for social network structures and centered on the concept of local perturbation of critical subgraphs. Specifically, CGLP meticulously identifies critical nodes, factoring in local structural complexity and positional features, and subsequently identifies subcritical nodes exhibiting structural similarity through graph embedding and clustering. The method further constructs critical node subgraph and core critical node subgraphs. Crucially, diverse local perturbation methods are strategically designed for subgraphs with varying structural features, mitigating the potential issues of under-protection and over-protection. Evaluation results on real datasets demonstrate that CGLP effectively balances the availability and privacy of the published network structure, concurrently addressing the privacy concerns associated with critical nodes.

LDPORR: A localized location privacy protection method based on optimized random response

The broad use of mobile intelligent terminals with locating functions encourages the rapid development of location-based services (LBS), which are widely used in a variety of industries such as social networking, transportation, finance, and entertainment. While enjoying the convenience brought by LBS, the threat of location privacy leakage should not be overlooked. In view of the complex encoding mechanism and low availability of the current location privacy protection methods, a local differential privacy location protection method based on optimized random response is proposed in this paper. A spatial decomposition and Hilbert encoding mechanism are designed based on the Hilbert curve, which can reduce the two-dimensional location data into one-dimensional Hilbert encoding results. A local differential privacy location perturbation method based on optimized random response is proposed to improve the availability of perturbed locations and the accuracy of data aggregation. Experiments on actual location datasets prove that the proposed method can provide better location data availability and operational efficiency based on realizing local differential privacy protection of users’ location.

Stability of a mean field game of production adjustment

AbstractWe propose a mean field game model to study the stability of production adjustment by extending a kind of linear quadratic Gaussian game in large population systems. First, we present the model's equilibrium solutions by a backward HJB equation and a forward FPK equation. Second, we employ the local perturbation method to transform the nonlinear problem into a linear one to study the solutions' stability. Third, we use the spectrum and contraction analyses to study the stationary solutions' linear stability. At last, we validate the results by the numerical simulation. The results show that the additional cost coefficient and noise intensity affect the system's stability. If the additional cost coefficient and the noise intensity are large enough for firms to change their outputs, then firms will try to reduce their production adjustment and remain stable long‐term.

Exact solution for local fractional Diffusion and Wave Equations on Cantor Sets

In this paper, the local fractional homotopy perturbation method and the local fractional Sumudu transform are used to study diffusion and wave equations defined on Cantor sets with the fractal conditions with local fractional derivatives. The LFSHPM analytical method minimizes the computational size and may be applied directly to fractional differential equations without any linearization, discretization of variables, transformation, or restrictive assumptions. It provides series solutions that converge quickly in a few iterations. The proposed analytical method is successfully applied to diffusion and wave equations defined on cantor sets with fractal conditions, and proved to be highly efficient and computational accurate.
 Abstract: To solve the diffusion and wave equations on the Cantor set, the local fractional Sumudu homotopy perturbation method (LFSHPM) is used. In the local sense, the operators are used. The local fractional Sumudu homotopy perturbation method, which is the coupling method of the local fractional homotopy perturbation method and the Sumudu transform, is used to obtain non-differentiable approximate solutions. Illustrative examples are provided to show the new algorithm's excellent accuracy and fast convergence.

Online Appendix for “Macro-Finance Models with Nonlinear Dynamics”

Section 1 describes the model in greater details. Section 2 displays a benchmark model without intermediary frictions and compare the decentralized frictionless model with the social planner’s problem. Section 3 briefly introduces the various numerical solution methods we use to solve the model. Section 4 provides additional results of quantitative analysis. Section 5 compare two cases with high and low investment rates, and we show that the local perturbation method can fail in the case of low investment rate.

A discrete method for the initialization of semi-discrete optimal transport problem

Semi-discrete optimal transport setting is a very important formulation in the computation of Wasserstein distance, as it is an approximation form of the continuous setting of optimal transport. However, initialization process of dual weight vector for the dual problem in this setting is required for the computation of the first and second order methods, since the Laguerre cells associated to the dual weight vector ought to have positive mass during the calculation. Although there are approaches to initialize the weight vector, systematic computing procedure has not been available. To resolve this problem, we discretize the domain of source distribution of this problem, approximate the Laguerre cells with respect to the weight vector, and finally employ the local perturbation method (Jocelyn, 2019) combined with boundary method to force all measures of the Laguerre cells great than zero. In addition, we study the corresponding theoretical results of the computation process and provide the algorithm, ensuring that the problem can indeed be efficiently computed.

Why are countries’ asset portfolios exposed to nominal exchange rates?

Most countries hold large gross asset positions, lending in their domestic currency and borrowing in foreign currency. As a result, their balance sheets are exposed to nominal exchange rate movements. We argue that when asset markets are incomplete, this exposure provides partial insurance against shocks that move exchange rates. We demonstrate that this insurance motive can simultaneously generate realistic gross asset positions and resolve the Backus-Smith puzzle: that countries’ relative consumption and real exchange rates are negatively correlated. Local perturbation methods are inaccurate in this setting as they approximate around the wrong interest rate, even when they correctly characterize the average portfolio holdings. So to accurately solve the equilibrium portfolio problem, we extend Maliar and Maliar (2015)’s global projection method.

Local Fractional Natural Homotopy Perturbation Method for Solving Partial Differential Equations with Local Fractional Derivative

Local Fractional Natural Homotopy Perturbation Method for Solving Partial Differential Equations with Local Fractional Derivative

Why are Countries' Asset Portfolios Exposed to Nominal Exchange Rates?

Most countries hold large gross asset positions, lending in domestic currency and borrowingin foreign. Thus, their balance sheets are exposed to nominal exchange rates. We argue thatwhen asset markets are incomplete, nominal exchange rate exposure allows countries topartially insure against shocks that move real exchange rates. We demonstrate that assetmarket incompleteness can simultaneously generate realistic gross asset positions and resolvethe Backus-Smith puzzle: that relative consumptions and real exchange rates correlatenegatively. We also show that local perturbation methods that use stabilizing endogenousdiscount factors are inaccurate when average and steady state interest rates differ. To addressthis, we develop a novel global solution method to accurately solve the model.

Why are Countries' Asset Portfolios Exposed to Nominal Exchange Rates?

Most countries hold large gross asset positions, lending in domestic currency and borrowing in foreign. Thus, their balance sheets are exposed to nominal exchange rates. We argue that when asset markets are incomplete, nominal exchange rate exposure allows countries to partially insure against shocks that move real exchange rates. We demonstrate that asset market incompleteness can simultaneously generate realistic gross asset positions and resolve the Backus-Smith puzzle: that relative consumptions and real exchange rates correlate negatively. We also show that local perturbation methods that use stabilizing endogenous discount factors are inaccurate when average and steady state interest rates differ. To address this, we develop a novel global solution method to accurately solve the model.

A local perturbation method for the approximate calculation of the acoustic wave diffraction with impedance interface conditions

The problem of incidence of an acoustic wave on the interface between media with impedance interface conditions is considered. An approximate method is proposed for calculating the result of diffraction under such conditions. The method is implemented as a computer program, and the result is compared with the analytical solution for the impedance conditions and with the calculations by a program for the contact boundary conditions. Good accuracy of the method and high computation speed are demonstrated, which allow one to apply the proposed approximate method to solving both direct and inverse problems of acoustics.

Light Amplification and Scattering by Clusters Made of Small Active Particles: The Local Perturbation Approach

The light amplification by finite active media is used extensively in modern optics applications. In this paper the light amplification and scattering by cluster of small particles is studied analytically and numerically with the help of the local perturbation method and phenomenological laser theory. It is shown that light amplification is possible even for one small particle, and that the amplification is more profound when the light frequency nears the frequency of the cluster's morphological resonance. Theoretical discussions are supplemented by numerical results for scattering by clusters which particles positioned at ordered and at slightly disordered positions.

Improvement research on the one-step algorithm for bus rollover collision based on the improved gradient method

The generalised imbalanced forces of each node of the initial solution of the one-step algorithm for bus rollover collision are iterated to balance based on the improved gradient method. Meanwhile, the local perturbation method is introduced into the equilibrium iteration process of the generalised imbalanced forces of the nodes of the improved algorithm, and the final deformation of rollover collision is quickly obtained. Comparing with the original Newton–Raphson iteration method, the computational efficiency is greatly promoted, and the simulation precision of the one-step collision algorithm is guaranteed at the same time. A case study on rollover collision for a typical 12 meter bus body section is carried out using the improved one-step collision algorithm. The practical effectiveness of the proposed method of this paper is verified by comparing the simulation results with that of the original algorithm and rollover test.

Mathematical analysis on a multidimensional model of morphogen transport with receptor synthesis

In biological development, morphogens are locally produced and spread to other regions in organs, forming gradients that control the inter-related pattern and growth of developing organs. Mechanisms of morphogen transport were built and investigated by numerical simulations in [A. D. Lander, Q. Nie and F. Y. M. Wan, Do morphogen gradients arise by diffusion? Developmental Cell2 (2002) 785–796]. In that paper, model C, which considers endocytosis, exocytosis and receptor synthesis and degradation, is in a one-dimensional spatial region and couples a partial differential equation with ordinary differential equations. Here, this model is promoted to an arbitrary dimension bounded region. We prove existence, uniqueness and non-negativity of a global solution for this advanced model, of its steady-state solution and linear stability of steady state by operator semigroup, the Schauder theorem and local perturbation method. Our results improve previous results for this model in a one dimension region.

Spatial sensitivity and penetration depth of three cerebral oxygenation monitors.

The spatial sensitivities of NIRO-100, ISS Oximeter and TRS-20 cerebral oxygenation monitors are mapped using the local perturbation method to inform on their penetration depths and susceptibilities to superficial contaminations. The results show that TRS-20 has the deepest mean penetration depth and is less sensitive than the other monitors to a localized absorption change in the superficial layer. However, an integration time of more than five seconds is required by the TRS-20 to achieve an acceptable level of signal-to-noise ratio, which is the poorest amongst the monitors. With the exception of NIRO-100 continuous wave method, the monitors are not significantly responsive to layer-wide absorption change that occurs in the superficial layer.

Dynamic scattering by cluster of small particles: local perturbation approach

The wave scattering by moving particles (dynamic scattering) is a well known physical problem routinely occurring in practice. For the particles which are much smaller than the incident wavelength, the static scattering problem can be solved by using the local perturbation method. In this paper we apply the local perturbation approach to the problem of the dynamic scattering by the cluster of small particles. We calculate the fields scattered by the cluster of moving particles. As an example, the scattered light field and its resonance frequency are calculated for moving sphere in scalar approximation and in vector case.

Optical contrast analysis and reflectance optimization of photonic clusters: an analytical approach

The reflectance of photonic clusters is an important characteristic for nanophotonic applications, especially when it is needed to hide the cluster or to make it extremely visible. Currently, there are a lack of methods clearly describing how to design a photonic cluster with a predefined reflectance. In this paper two analytical methods are proposed for designing clusters with predefined scattering. The first method is used for the optical contrast analysis of the cluster and for reflectance optimization by modifying the optical contrast of the cluster. This method combines linear sampling and local perturbation methods. The second method is used to modify the incident field for the optimization of the cluster’s scattering and is based on the local perturbation method. The proposed methods are suitable for the clusters which can be considered as composed of particles smaller than the incident wavelength.

Taking Perturbation to the Accuracy Frontier: A Hybrid of Local and Global Solutions

Local (perturbation) methods compute solutions in one point and tend to deliver far lower accuracy levels than global solution methods. We develop a hybrid method that solves for some policy functions locally (using a perturbation method) and that solves for the other policy functions globally (using closed-form expressions and a numerical solver). We applied our hybrid method to solve large-scale RBC models used in the comparison analysis of Kollmann et al. (J Econ Dyn Control 35:186–202, 2011b). We obtain more accurate solutions than those produced by any other (either local or global) solution method participating in that comparison. Our running time is a few seconds.

On the analysis of a plate with a local shape perturbation

The asymptotic behavior of the solution of the bending problem of plates with local shape perturbations (connections, ribs, holes comparable in size with the plate thickness) is studied in a three-dimensional formulation using the local perturbation method. The problem is completely decomposed into a two-dimensional problem of plate theory and local problems describing the threedimensional stress-strain state in the perturbation region. The local problems are solved using numerical methods.

Scattering Optimization of Photonic Cluster: From Minimal to Maximal Reflectance

Scattering optimization is a challenging engineering problem with an extensive list of potential applications. For some practical applications, the reflectance of the photonic cluster should be variable from minimal to maximal values. The theoretical investigation of such problem is extremely difficult due to multiple interactions between particles in the cluster. In this paper, the optimization of the light scattered by the photonic cluster made of small particles is studied with the help of the special optimization algorithm and the local perturbation method. It was shown that the photonic cluster can be transformed in such a way that its reflectance will be increased or decreased by several orders of magnitude for selected wavelength and direction.