Family Of Nonlinear Functions Research Articles

SA-LuT-Nets: Learning Sample-Adaptive Intensity Lookup Tables for Brain Tumor Segmentation.

In clinics, the information about the appearance and location of brain tumors is essential to assist doctors in diagnosis and treatment. Automatic brain tumor segmentation on the images acquired by magnetic resonance imaging (MRI) is a common way to attain this information. However, MR images are not quantitative and can exhibit significant variation in signal depending on a range of factors, which increases the difficulty of training an automatic segmentation network and applying it to new MR images. To deal with this issue, this paper proposes to learn a sample-adaptive intensity lookup table (LuT) that dynamically transforms the intensity contrast of each input MR image to adapt to the following segmentation task. Specifically, the proposed deep SA-LuT-Net framework consists of a LuT module and a segmentation module, trained in an end-to-end manner: the LuT module learns a sample-specific nonlinear intensity mapping function through communication with the segmentation module, aiming at improving the final segmentation performance. In order to make the LuT learning sample-adaptive, we parameterize the intensity mapping function by exploring two families of non-linear functions (i.e., piece-wise linear and power functions) and predict the function parameters for each given sample. These sample-specific parameters make the intensity mapping adaptive to samples. We develop our SA-LuT-Nets separately based on two backbone networks for segmentation, i.e., DMFNet and the modified 3D Unet, and validate them on BRATS2018 and BRATS2019 datasets for brain tumor segmentation. Our experimental results clearly demonstrate the superior performance of the proposed SA-LuT-Nets using either single or multiple MR modalities. It not only significantly improves the two baselines (DMFNet and the modified 3D Unet), but also wins a set of state-of-the-art segmentation methods. Moreover, we show that, the LuTs learnt using one segmentation model could also be applied to improving the performance of another segmentation model, indicating the general segmentation information captured by LuTs.

Exact Controllability of Semilinear Third Order Dispersion Equation

In this paper, a family of nonlinear functions is given for the exact controllability of semilinear third order dispersion equation. The obtained result has been illustrated by applying it on nonlinear Korteweg-de Vries (KdV) equation.

AUTOMATED BIFURCATION ANALYSIS FOR NONLINEAR ELLIPTIC PARTIAL DIFFERENCE EQUATIONS ON GRAPHS

We seek solutions u ∈ ℝn to the semilinear elliptic partial difference equation -Lu + fs(u) = 0, where L is the matrix corresponding to the Laplacian operator on a graph G and fs is a one-parameter family of nonlinear functions. This article combines the ideas introduced by the authors in two papers: (a) Nonlinear elliptic partial difference equations on graphs (J. Experimental Mathematics, 2006), which introduces analytical and numerical techniques for solving such equations, and (b) Symmetry and automated branch following for a semilinear elliptic PDE on a fractal region (SIAM J. Dynamical Systems, 2006), wherein we present some of our recent advances concerning symmetry, bifurcation and automation for PDE. We apply the symmetry analysis found in the SIAM paper to arbitrary graphs in order to obtain better initial guesses for Newton's method, create informative graphics, and better understand the role of symmetry in the underlying variational structure. We use two modified implementations of the gradient Newton–Galerkin algorithm (GNGA, Neuberger and Swift) to follow bifurcation branches in a robust way. By handling difficulties that arise when encountering accidental degeneracies and higher-dimensional critical eigenspaces, we can find many solutions of many symmetry types to the discrete nonlinear system. We present a selection of experimental results which demonstrate our algorithm's capability to automatically generate bifurcation diagrams and solution graphics starting with only an edgelist of a graph. We highlight interesting symmetry and variational phenomena.

Online Signature Verification Based on User-Generic Fusion Model with Markov Chain Monte Carlo, Taking into Account User Individuality

Personal authentication is becoming an increasingly important problem. Online signature verification is one promising form of biometric authentication. However, the verification accuracy of online signature verification is not high enough and still needs to be improved. To do so, we previously proposed a user-generic fusion model. Although the verification accuracy was reasonably good, the proposed method cannot adequately take into account users’ individuality. In this paper, to further improve the verification accuracy, we propose a method that can take such individuality into account. First, in a training phase, we divide a training dataset into several groups. Then, several fusion models are generated using a parameterized family of nonlinear functions by a Markov chain Monte Carlo method. In an enrollment phase, in order to take into account users’ individuality, we introduce model reliability. The model reliability for each user and each model is different, enabling us to take users’ individuality into account. In a verification phase, a marginal likelihood is calculated for each group. Then, a verification score is calculated by a weighted sum of the marginal likelihoods from the groups, using the model reliability. To evaluate the performance of the proposed algorithm, we conducted experiments using the SVC2004 database. The verification accuracy was improved over the previous algorithm.

A new family of blind adaptive equalization algorithms

New blind adaptive channel equalization techniques based on a deterministic optimization criterion are presented. A family of nonlinear functions is proposed which constitutes a generic class of blind algorithms. They have been shown to have better performance than the conventional constant modulus algorithm (CMA)-like approaches. The advantages include the relaxed stability range on the step size and that an automatic gain control unit which estimates the gain of the channel, is no longer of crucial importance.