Clinical guidelines underscore the importance of regularly monitoring and surveilling arteriovenous fistula (AVF) access in hemodialysis patients to promptly detect any dysfunction. Although phono-angiography/sound analysis overcomes the limitations of standardized AVF stenosis diagnosis tool, prior studies have depended on conventional feature extraction methods, restricting their applicability in diverse contexts. In contrast, representation learning captures fundamental underlying factors that can be readily transferred across different contexts. We propose an approach based on deep denoising autoencoders (DAEs) that perform dimensionality reduction and reconstruction tasks using the waveform obtained through one-level discrete wavelet transform, utilizing representation learning. Our results demonstrate that the latent representation generated by the DAE surpasses expectations with an accuracy of 0.93. The incorporation of noise-mixing and the utilization of a noise-to-clean scheme effectively enhance the discriminative capabilities of the latent representation. Moreover, when employed to identify patient-specific characteristics, the latent representation exhibited performance by surpassing an accuracy of 0.92. Appropriate light-weighted methods can restore the detection performance of the excessively reduced dimensionality version and enable operation on less computational devices. Our findings suggest that representation learning is a more feasible approach for extracting auscultation features in AVF, leading to improved generalization and applicability across multiple tasks. The manipulation of latent representations holds immense potential for future advancements. Further investigations in this area are promising and warrant continued exploration.
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We investigate error of the Euler scheme in the case when the right-hand side function of the underlying ODE satisfies nonstandard assumptions such as local one-sided Lipschitz condition and local H\"older continuity. Moreover, we assume two cases in regards to information availability: exact and noisy with respect to the right-hand side function. Optimality analysis of the Euler scheme is also provided. Finally, we present the results of some numerical experiments.
We discuss applications of exact structures and relative homological algebra to the study of invariants of multiparameter persistence modules. This paper is mostly expository, but does contain a pair of novel results. Over finite posets, classical arguments about the relative projective modules of an exact structure make use of Auslander-Reiten theory. One of our results establishes a new adjunction which allows us to "lift" these arguments to certain infinite posets over which Auslander-Reiten theory is not available. We give several examples of this lifting, in particular highlighting the non-existence and existence of resolutions by upsets when working with finitely presentable representations of the plane and of the closure of the positive quadrant, respectively. We then restrict our attention to finite posets. In this setting, we discuss the relationship between the global dimension of an exact structure and the representation dimension of the incidence algebra of the poset. We conclude with our second novel contribution. This is an explicit description of the irreducible morphisms between relative projective modules for several exact structures which have appeared previously in the literature.
We propose an automated nonlinear model reduction and mesh adaptation framework for rapid and reliable solution of parameterized advection-dominated problems, with emphasis on compressible flows. The key features of our approach are threefold: (i) a metric-based mesh adaptation technique to generate an accurate mesh for a range of parameters, (ii) a general (i.e., independent of the underlying equations) registration procedure for the computation of a mapping $\Phi$ that tracks moving features of the solution field, and (iii) an hyper-reduced least-square Petrov-Galerkin reduced-order model for the rapid and reliable estimation of the mapped solution. We discuss a general paradigm -- which mimics the refinement loop considered in mesh adaptation -- to simultaneously construct the high-fidelity and the reduced-order approximations, and we discuss actionable strategies to accelerate the offline phase. We present extensive numerical investigations for a quasi-1D nozzle problem and for a two-dimensional inviscid flow past a Gaussian bump to display the many features of the methodology and to assess the performance for problems with discontinuous solutions.
We study the numerical solution of a Cahn-Hilliard/Allen-Cahn system with strong coupling through state and gradient dependent non-diagonal mobility matrices. A fully discrete approximation scheme in space and time is proposed which preserves the underlying gradient flow structure and leads to dissipation of the free-energy on the discrete level. Existence and uniqueness of the discrete solution is established and relative energy estimates are used to prove optimal convergence rates in space and time under minimal smoothness assumptions. Numerical tests are presented for illustration of the theoretical results and to demonstrate the viability of the proposed methods.
Navigating automated driving systems (ADSs) through complex driving environments is difficult. Predicting the driving behavior of surrounding human-driven vehicles (HDVs) is a critical component of an ADS. This paper proposes an enhanced motion-planning approach for an ADS in a highway-merging scenario. The proposed enhanced approach utilizes the results of two aspects: the driving behavior and long-term trajectory of surrounding HDVs, which are coupled using a hierarchical model that is used for the motion planning of an ADS to improve driving safety.
Lung cancer and covid-19 have one of the highest morbidity and mortality rates in the world. For physicians, the identification of lesions is difficult in the early stages of the disease and time-consuming. Therefore, multi-task learning is an approach to extracting important features, such as lesions, from small amounts of medical data because it learns to generalize better. We propose a novel multi-task framework for classification, segmentation, reconstruction, and detection. To the best of our knowledge, we are the first ones who added detection to the multi-task solution. Additionally, we checked the possibility of using two different backbones and different loss functions in the segmentation task.
While macroscopic traffic flow models consider traffic as a fluid, microscopic traffic flow models describe the dynamics of individual vehicles. Capturing macroscopic traffic phenomena remains a challenge for microscopic models, especially in complex road sections such as on-ramps. In this paper, we propose a microscopic model for on-ramps derived from a macroscopic network flow model calibrated to real traffic data. The microscopic flow-based model requires additional assumptions regarding the acceleration and the merging behavior on the on-ramp to maintain consistency with the mean speeds, traffic flow and density predicted by the macroscopic model. To evaluate the model's performance, we conduct traffic simulations assessing speeds, accelerations, lane change positions, and risky behavior. Our results show that, although the proposed model may not fully capture all traffic phenomena of on-ramps accurately, it performs better than the Intelligent Driver Model (IDM) in most evaluated aspects. While the IDM is almost completely free of conflicts, the proposed model evokes a realistic amount and severity of conflicts and can therefore be used for safety analysis.
We consider the information fiber optical channel modeled by the nonlinear Schrodinger equation with additive Gaussian noise. Using path-integral approach and perturbation theory for the small dimensionless parameter of the second dispersion, we calculate the conditional probability density functional in the leading and next-to-leading order in the dimensionless second dispersion parameter associated with the input signal bandwidth. Taking into account specific filtering of the output signal by the output signal receiver, we calculate the mutual information in the leading and next-to-leading order in the dispersion parameter and in the leading order in the parameter signal-to-noise ratio (SNR). Further, we find the explicit expression for the mutual information in case of the modified Gaussian input signal distribution taking into account the limited frequency bandwidth of the input signal.
We examine the last-iterate convergence rate of Bregman proximal methods - from mirror descent to mirror-prox and its optimistic variants - as a function of the local geometry induced by the prox-mapping defining the method. For generality, we focus on local solutions of constrained, non-monotone variational inequalities, and we show that the convergence rate of a given method depends sharply on its associated Legendre exponent, a notion that measures the growth rate of the underlying Bregman function (Euclidean, entropic, or other) near a solution. In particular, we show that boundary solutions exhibit a stark separation of regimes between methods with a zero and non-zero Legendre exponent: the former converge at a linear rate, while the latter converge, in general, sublinearly. This dichotomy becomes even more pronounced in linearly constrained problems where methods with entropic regularization achieve a linear convergence rate along sharp directions, compared to convergence in a finite number of steps under Euclidean regularization.
Nonlinear extensions to the active subspaces method have brought remarkable results for dimension reduction in the parameter space and response surface design. We further develop a kernel-based nonlinear method. In particular we introduce it in a broader mathematical framework that contemplates also the reduction in parameter space of multivariate objective functions. The implementation is thoroughly discussed and tested on more challenging benchmarks than the ones already present in the literature, for which dimension reduction with active subspaces produces already good results. Finally, we show a whole pipeline for the design of response surfaces with the new methodology in the context of a parametric CFD application solved with the Discontinuous Galerkin method.
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