LSTM-CNN: An efficient diagnostic network for Parkinson's disease utilizing dynamic handwriting analysis.

BACKGROUND AND OBJECTIVES: Dynamic handwriting analysis, due to its noninvasive and readily accessible nature, has emerged as a vital adjunctive method for the early diagnosis of Parkinson's disease (PD). An essential step involves analysing subtle variations in signals to quantify PD dysgraphia. Although previous studies have explored extracting features from the overall signal, they may ignore the potential importance of local signal segments. In this study, we propose a lightweight network architecture to analyse dynamic handwriting signal segments of patients and present visual diagnostic results, providing an efficient diagnostic method. METHODS: To analyse subtle variations in handwriting, we investigate time-dependent patterns in local representation of handwriting signals. Specifically, we segment the handwriting signal into fixed-length sequential segments and design a compact one-dimensional (1D) hybrid network to extract discriminative temporal features for classifying each local segment. Finally, the category of the handwriting signal is fully diagnosed through a majority voting scheme. RESULTS: The proposed method achieves impressive diagnostic performance on the new DraWritePD dataset (with an accuracy of 96.2%, sensitivity of 94.5% and specificity of 97.3%) and the well-established PaHaW dataset (with an accuracy of 90.7%, sensitivity of 94.3% and specificity of 87.5%). Moreover, the network architecture stands out for its excellent lightweight design, occupying a mere 0.084M parameters, with only 0.59M floating-point operations. It also exhibits nearly real-time CPU inference performance, with the inference time for a single handwriting signal ranging from 0.106 to 0.220 s. CONCLUSIONS: We present a series of experiments with extensive analysis, which systematically demonstrate the effectiveness and efficiency of the proposed method in quantifying dysgraphia for a precise diagnosis of PD.

Semi-Sparsity for Smoothing Filters.

In this paper, we propose a semi-sparsity smoothing method based on a new sparsity-induced minimization scheme. The model is derived from the observations that semi-sparsity prior knowledge is universally applicable in situations where sparsity is not fully admitted such as in the polynomial-smoothing surfaces. We illustrate that such priors can be identified into a generalized L0-norm minimization problem in higher-order gradient domains, giving rise to a new "feature-aware" filter with a powerful simultaneous-fitting ability in both sparse singularities (corners and salient edges) and polynomial-smoothing surfaces. Notice that a direct solver to the proposed model is not available due to the non-convexity and combinatorial nature of L0-norm minimization. Instead, we propose to solve it approximately based on an efficient half-quadratic splitting technique. We demonstrate its versatility and many benefits to a series of signal/image processing and computer vision applications.

Intrinsic Image Transfer for Illumination Manipulation.

This article presents a novel intrinsic image transfer (IIT) algorithm for image illumination manipulation, which creates a local image translation between two illumination surfaces. This model is built on an optimization-based framework composed of illumination, reflectance and content photo-realistic losses, respectively. Each loss is first defined on the corresponding sub-layers factorized by an intrinsic image decomposition and then reduced under the well-known spatial-varying illumination illumination-invariant reflectance prior knowledge. We illustrate that all losses, with the aid of an "exemplar" image, can be directly defined on images without the necessity of taking an intrinsic image decomposition, thereby giving a closed-form solution to image illumination manipulation. We also demonstrate its versatility and benefits to several illumination-related tasks: illumination compensation, image enhancement and tone mapping, and high dynamic range (HDR) image compression, and show their high-quality results on natural image datasets.

Hardy inequalities on metric measure spaces, II: the case p > q.

In this paper, we continue our investigations giving the characterization of weights for two-weight Hardy inequalities to hold on general metric measure spaces possessing polar decompositions. Since there may be no differentiable structure on such spaces, the inequalities are given in the integral form in the spirit of Hardy's original inequality. This is a continuation of our paper (Ruzhansky & Verma 2018. Proc. R. Soc. A 475, 20180310 (doi:10.1098/rspa.2018.0310)) where we treated the case p ≤ q. Here the remaining range p > q is considered, namely, 0 < q < p, 1 < p < ∞. We give several examples of the obtained results, finding conditions on the weights for integral Hardy inequalities on homogeneous groups, as well as on hyperbolic spaces and on more general Cartan-Hadamard manifolds. As in the first part of this paper, we do not need to impose doubling conditions on the metric.

Hardy inequalities on metric measure spaces.

In this note, we give several characterizations of weights for two-weight Hardy inequalities to hold on general metric measure spaces possessing polar decompositions. Since there may be no differentiable structure on such spaces, the inequalities are given in the integral form in the spirit of Hardy's original inequality. We give examples obtaining new weighted Hardy inequalities on R n , on homogeneous groups, on hyperbolic spaces and on Cartan-Hadamard manifolds. We note that doubling conditions are not required for our analysis.

Hyperbolic systems with non-diagonalisable principal part and variable multiplicities, I: well-posedness.

In this paper we analyse the well-posedness of the Cauchy problem for a rather general class of hyperbolic systems with space-time dependent coefficients and with multiple characteristics of variable multiplicity. First, we establish a well-posedness result in anisotropic Sobolev spaces for systems with upper triangular principal part under interesting natural conditions on the orders of lower order terms below the diagonal. Namely, the terms below the diagonal at a distance k to it must be of order - k . This setting also allows for the Jordan block structure in the system. Second, we give conditions for the Schur type triangularisation of general systems with variable coefficients for reducing them to the form with an upper triangular principal part for which the first result can be applied. We give explicit details for the appearing conditions and constructions for 2 × 2 and 3 × 3 systems, complemented by several examples.

Uncertainty relations on nilpotent Lie groups.

We give relations between main operators of quantum mechanics on one of most general classes of nilpotent Lie groups. Namely, we show relations between momentum and position operators as well as Euler and Coulomb potential operators on homogeneous groups. Homogeneous group analogues of some well-known inequalities such as Hardy's inequality, Heisenberg-Kennard type and Heisenberg-Pauli-Weyl type uncertainty inequalities, as well as Caffarelli-Kohn-Nirenberg inequality are derived, with best constants. The obtained relations yield new results already in the setting of both isotropic and anisotropic [Formula: see text], and of the Heisenberg group. The proof demonstrates that the method of establishing equalities in sharper versions of such inequalities works well in both isotropic and anisotropic settings.