Smoothness Properties Research Articles

A new dietary low-fat custard formulation made by waxy corn starch and xylitol: Rheological, sensory and in vitro digestibility investigation

Custard is a dairy starch-based dessert, in which presence of milk increases its nutritional value and sensitivity to freezing, pH, and storage. Producing a custard with less phase separation during storage and improving its functionality is challenging. The present study has investigated the effect of starch type (native corn starch and waxy corn starch), fat content (2.67% & 0.1%) and sucrose-xylitol ratio (1:0, 1:1, 0:1) on rheological, textural, enzyme digestibility and sensory properties of custard desserts. The back extrusion test showed a significant increase in consistency (40.60 mJ) by using xylitol and decreasing fat content compared to the control sample (2.16 mJ). Also, applying waxy corn starch diminished hardness (1.66 N) compared to the control (13.55 N), which was accompanied by a decrease of syneresis after five days of storage from 10.29% to 0.02% and improvement of sensory properties of creaminess, smoothness and taste intensity. Accordingly, low-fat custard formulation containing waxy corn starch and xylitol indicated high creaming stability (98.08%), adhesiveness (9.45 mJ), viscosity at a constant shear rate of 50 s−1 (3.58 Pa s), and water holding capacity after five days of storage at 4 °C (99.99%) and thickness (9.53). Also, xylitol reduced custards’ glucose release after amylase objection.

Advancing Supervised Learning with the Wave Loss Function: A Robust and Smooth Approach

Loss function plays a vital role in supervised learning frameworks. The selection of the appropriate loss function holds the potential to have a substantial impact on the proficiency attained by the acquired model. The training of supervised learning algorithms inherently adheres to predetermined loss functions during the optimization process. In this paper, we present a novel contribution to the realm of supervised machine learning: an asymmetric loss function named wave loss. It exhibits robustness against outliers, insensitivity to noise, boundedness, and a crucial smoothness property. Theoretically, we establish that the proposed wave loss function manifests the essential characteristic of being classification-calibrated. Leveraging this breakthrough, we incorporate the proposed wave loss function into the least squares setting of support vector machines (SVM) and twin support vector machines (TSVM), resulting in two robust and smooth models termed as Wave-SVM and Wave-TSVM, respectively. To address the optimization problem inherent in Wave-SVM, we utilize the adaptive moment estimation (Adam) algorithm, which confers multiple benefits, including the incorporation of adaptive learning rates, efficient memory utilization, and faster convergence during training. It is noteworthy that this paper marks the first instance of Adam’s application to solve an SVM model. Further, we devise an iterative algorithm to solve the optimization problems of Wave-TSVM. To empirically showcase the effectiveness of the proposed Wave-SVM and Wave-TSVM, we evaluate them on benchmark UCI and KEEL datasets (with and without feature noise) from diverse domains. Moreover, to exemplify the applicability of Wave-SVM in the biomedical domain, we evaluate it on the Alzheimer’s Disease Neuroimaging Initiative (ADNI) dataset. The experimental outcomes unequivocally reveal the prowess of Wave-SVM and Wave-TSVM in achieving superior prediction accuracy against the baseline models. The source codes of the proposed models are publicly available at https://github.com/mtanveer1/Wave-SVM.

An Introduction to Extended Gevrey Regularity

Gevrey classes are the most common choice when considering the regularities of smooth functions that are not analytic. However, in various situations, it is important to consider smoothness properties that go beyond Gevrey regularity, for example, when initial value problems are ill-posed in Gevrey settings. In this paper, we consider a convenient framework for studying smooth functions that possess weaker regularity than any Gevrey function. Since the available literature on this topic is scattered, our aim is to provide an overview of extended Gevrey regularity, highlighting its most important features. Additionally, we consider related dual spaces of ultra distributions and review some results on micro-local analysis in the context of extended Gevrey regularity. We conclude the paper with a few selected applications that may motivate further study of the topic.

Sobolev spaces on arbitrary domains and semigroups generated by the fractional Laplacian

We describe a procedure to introduce on an arbitrary domain of Rd Sobolev spaces of arbitrary order s∈R and with an intrinsic characterization via fractional powers of the Dirichlet Laplacian. In particular, the well-definedness of the spaces of both non-homogeneous and homogeneous type together with their duality properties, embeddings, and Gagliardo-Nirenberg inequalities will be discussed. We also show the continuity and the smoothing property of the semigroup generated by the fractional Dirichlet Laplacian.

Partial Smoothing of the Stochastic Wave Equation and Regularization by Noise Phenomena

We establish partial smoothing properties of the transition semigroup (Pt)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(P_t)$$\\end{document} associated to the linear stochastic wave equation driven by a cylindrical Wiener noise on a separable Hilbert space. These new results allow the study of related vector-valued infinite-dimensional PDEs in spaces of functions which are Hölder continuous along special directions. As an application we prove strong uniqueness for semilinear stochastic wave equations involving nonlinearities of Hölder type. We stress that we are able to prove well-posedness although the Markov semigroup (Pt)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(P_t)$$\\end{document} is not strong Feller.

Data-based adaptive refinement of finite element thin plate spline

The thin plate spline, as introduced by Duchon, interpolates a smooth surface through scattered data. It is computationally expensive when there are many data points. The finite element thin plate spline (TPSFEM) possesses similar smoothing properties and is efficient for large data sets. Its efficiency is further improved by adaptive refinement that adapts the precision of the finite element grid. Adaptive refinement processes and error indicators developed for partial differential equations may not apply to the TPSFEM as it incorporates information about the scattered data. This additional information results in features not evident in partial differential equations. An iterative adaptive refinement process and five error indicators were adapted for the TPSFEM. We give comprehensive depictions of the process in this article and evaluate the error indicators through a numerical experiment with a model problem and two bathymetric surveys in square and L-shaped domains.

Alternating block linearized Bregman iterations for regularized nonnegative matrix factorization

In this paper, we propose an alternating block variant of the linearized Bregman iterations for a class of regularized nonnegative matrix factorization (NMF) problems. The proposed method exploits the block structure of NMF, utilizes the smooth adaptable property of the loss function based on the Bregman distance, and at the same time follows the iterative regularization idea of the linearized Bregman iterations method. Theoretically, we show that the proposed method is a descent method by adjusting the involved parameters. Finally, we end with several illustrative numerical experiments.

Finite-time consensus control of second-order multi-agent systems with input saturation constraint

A novel finite-time consensus technique is derived for second-order linear multi-agent systems with input saturation constraints. The hyperbolic tangent–based saturation function is presented for achieving input saturation while reducing the chattering issue of classical saturation functions. The leader-following consensus controller with a single saturation function is constructed to address the issue of saturation level partition between position feedback and velocity feedback. Theoretically, the property of finite-time consensus, bounded input, and smoothness of a closed-form system are proved by the Lyapunov theory in detail. Numerical simulations are conducted to exhibit the effectiveness of the proposed method fully.

Effect of nifedipine administration before embryo transfer on reproductive outcome in ICSI cycles, a double-blind control trial study.

Nifedipine is a calcium channel blocker with smooth muscle relaxing properties. This study set out to investigate the efficacy of nifedipine administered orally before embryo transfer (ET) on the improvement of theintracytoplasmic sperm injection (ICSI) outcome. This randomized, double-blind, comparator-controlled, was carried out between 2019 and 2020 in the infertility center of Babol, Iran. 200 women candidates for ICSI and recipients of frozen-thawed ET aged 18-40years were randomly assigned in the ratio 1:1 to an intervention group that received nifedipine 20mg tablets orally 30min before ET (n = 100) or to a group of placebo (n = 100). A randomization center in Babol University of Medical Science used computer-generated numbers to allocate treatments. The allocation treatment was blind to the participants, the sonographer of endometer monitoring, the staff of the ICSI laboratory, and the outcome assessor. The primary analysis was based on the intention-to-treat principle done on 200 participants, (n = 100), comparing chemical pregnancy rates in the two comparing groups at 14days' follow-up after ET. Implantation rate and clinical pregnancy were considered secondary outcomes. 200 participants were analyzed. There is no significant difference in the number of oocytes and the quality of embryos in the nifedipine and placebo groups. Despite a numerical increase in the rate of chemical pregnancy, there were no statistical differences in the study group versus the comparison group (24% vs 14%, P = 0.1, rate ratio 0.88, 95% CI 0.77 to 1.01), respectively. Also, no significant increase in clinical pregnancy was found compared with the placebo (17% vs 8%, P = 0.26, rate ratio 0.90, 0.81 to 1.00). Nifedipine administered orally 30min before embryo transfer did not improve the chemical pregnancy rate, and clinical pregnancy rate in infertile women undergoing ICSI. This trial has been registered on the Iranian Clinical Trials Registration Site (IRCT) with the number IRCT20180417039338N3.

Gevrey and Gelfand–Shilov smoothing effect for the spatially inhomogeneous Landau equation with hard potentials

In this work, we study the Cauchy problem of the spatially inhomogeneous Landau equation with hard potential in torus. It is showed that the smooth mild solution near Maxwellians to the Cauchy problem enjoys a Gelfand–Shilov regularizing effect in velocity variable and Gevrey smoothness property in space variable.

Orthogonal systems based stable estimator for non parametric regression problems

. In this work, we study a univariate as well as a multivariate Jacobi polynomial-based estimator for solving the fundamental problem of non parametric (NP) regression. The proposed NP regression estimator aims to approximate a possibly very low regular regression function from the knowledge of its noised values given at some n random sampling points. We first study the univariate version of the proposed estimator, then extend this study to the general multivariate case with random sampling vectors drawn according to an unknown distribution. Our proposed estimator has the advantage of being stable with reasonable time complexity. Moreover, it has an optimal convergence rate under the weak condition that the regression function has a certain low Sobolev smoothness property. Although the proposed estimators are studied under the hypothesis that the random sampling vectors are supported on the d dimensional unit hypercube, by applying trivial transformations, the results of this work are still valid in the more general setting of any d dimensional hyperrectangle. Finally, the theoretical results of this work are illustrated by some numerical simulations on synthetic as well as real datasets.

Synthesis and application of silicone-modified polyurethane as a slip-elastic finishing agent for polyamide fabrics

Despite the wide application of polyamide in clothing and home textiles, its inherent stiffness hardly meets consumers' preference for a smooth and elastic hand feel. In this study, a new hydroxyl silane coupling agent (KHS), 1-(4-(4-(4-(trimethoxysilyl)butyl)piperazin-1-yl)-3-(3-(trimethoxysilyl)propoxy) propan-2-ol, was synthesized and used to prepare a series of silicone-modified polyurethane (KHS-PU). KHS-PU then was finished onto the polyamide fabric via a pad-dry-cure procedure. The finishing process was optimized using the Minitab software. The morphology and elemental distribution of KHS-PU finished polyamide fabric were characterized using scanning electron microscopy (SEM) and energy dispersive spectrometry (EDS), respectively. The hand evaluation tests demonstrated that KHS-PU not only significantly enhanced the fabric's smooth and elastic properties, specifically evidenced by a 23 % reduction in surface friction coefficient, a 13 % decrease in bending average stiffness, a 10 % reduction in compression work, and a 40 % increase in compression recovery rate, but also exhibited good wash durability. In addition, the thermal and mechanical properties of KHS-PU finished fabric were further investigated. This work provides a valuable contribution to the field of surface science and textile engineering, offering insights into advanced fabric finishing techniques.

Embeddings of a Multi-Weighted Anisotropic Sobolev Type Space

Parameters such as various integral and differential characteristics of functions, smoothness properties of regions and their boundaries, as well as many classes of weight functions cause complex relationships and embedding conditions for multi-weighted anisotropic Sobolev type spaces. The desire not to restrict these parameters leads to the development of new approaches based on the introduction of alternative definitions of spaces and norms in them or on special localization methods. This article examines the embeddings of multi-weighted anisotropic Sobolev type spaces with anisotropy in all the defining characteristics of the norm of space, including differential indices, summability indices, as well as weight coefficients. The applied localization method made it possible to obtain an embedding for the case of an arbitrary domain and weights of a general type, which is important in applications in differential operators’ theory, numerical analysis.

Federated X-armed Bandit

This work establishes the first framework of federated X-armed bandit, where different clients face heterogeneous local objective functions defined on the same domain and are required to collaboratively figure out the global optimum. We propose the first federated algorithm for such problems, named Fed-PNE. By utilizing the topological structure of the global objective inside the hierarchical partitioning and the weak smoothness property, our algorithm achieves sublinear cumulative regret with respect to both the number of clients and the evaluation budget. Meanwhile, it only requires logarithmic communications between the central server and clients, protecting the client privacy. Experimental results on synthetic functions and real datasets validate the advantages of Fed-PNE over various centralized and federated baseline algorithms.

Tensor recovery from binary measurements fused low-rankness and smoothness

Tensor compressed sensing (TCS) from binary measurements aims to recover a tensor with low-rankness from the binary quantization of its degraded linear measurements, which inherits the advantages of low equipment cost and high sampling efficiency of coarse quantization. Recently, numerous studies have demonstrated that incorporating the properties of low-rankness and local smoothness, which are commonly observed in practical tensor data, can significantly enhance conventional tensor recovery tasks. This motivates us to utilize the low-rank and smooth properties in solving TCS problems from binary measurements. Equipped with the recently proposed tensor correlated total variation (TCTV) that simultaneously regularizes low-rankness and smoothness, we present a regularized model for this problem in this paper. We rigorously prove the recovery guarantee for the proposed model and provide an explicit selection rule for the regularization parameter. Moreover, the theoretical results demonstrate the robustness of the proposed method against both bit flips and pre-quantization noises. An algorithm based on alternating direction multiplier method (ADMM) is presented for solving the proposed model, with its global convergence been proven. Finally, a series of experiments demonstrate the superior performance of our method compared to many other competing approaches.

On the Hausdorff dimension of radial slices

Let \(t \in (1,2)\), and let \(B \subset \mathbb{R}^{2}\) be a Borel set with \(\dim_{\mathrm{H}} B > t\). I show that \(\mathcal{H}^{1}(\{e \in S^{1} \colon \dim_{\mathrm{H}} (B \cap \ell_{x,e}) \geq t - 1\}) > 0\) for all \(x \in \mathbb{R}^{2} \setminus E\), where \(\dim_{\mathrm{H}} E \leq 2 - t\). This is the sharp bound for \(\dim_{\mathrm{H}} E\). The main technical tool is an incidence inequality of the form \(\mathcal{I}_{\delta}(\mu,\nu) \lesssim_{t} \delta \cdot \sqrt{I_{t}(\mu)I_{3 - t}(\nu)}\), \(t \in (1,2)\), where \(\mu\) is a Borel measure on \(\mathbb{R}^{2}\), and \(\nu\) is a Borel measure on the set of lines in \(\mathbb{R}^{2}\), and \(\mathcal{I}_{\delta}(\mu,\nu)\) measures the \(\delta\)-incidences between \(\mu\) and the lines parametrised by \(\nu\). This inequality can be viewed as a \(\delta^{-\epsilon}\)-free version of a recent incidence theorem due to Fu and Ren. The proof in this paper avoids the high-low method, and the induction-on-scales scheme responsible for the \(\delta^{-\epsilon}\)-factor in Fu and Ren's work. Instead, the inequality is deduced from the classical smoothing properties of the \(X\)-ray transform.

Characterization of Heat Kernel Lower Bounds for Symmetric Jump Processes

This paper is devoted to symmetric mixture stable-like processes on metric measure space.Assume that the process enjoys upper bounds of heat kernel,characterization of near diagonal lower bounds of heat kernel is given.different from previous work which is usually based on regularity of elliptic harmonic functions,here we make full use of smooth properties of functions space associated with the generator of the process.

Certified Distributional Robustness on Smoothed Classifiers

The robustness of deep neural networks (DNNs) against adversarial example attacks has raised wide attention. For smoothed classifiers, we propose the worst-case adversarial loss over input distributions as a robustness certificate. Compared with previous certificates, our certificate better describes the empirical performance of the smoothed classifiers. By exploiting duality and the smoothness property, we provide an easy-to-compute upper bound as a surrogate for the certificate. We adopt a noisy adversarial learning procedure to minimize the surrogate loss to improve model robustness. We show that our training method provides a theoretically tighter bound over the distributional robust base classifiers. Experiments on a variety of datasets further demonstrate superior robustness performance of our method over the state-of-the-art certified or heuristic methods.

Piecewise polynomial numerical method for Volterra integral equations of the fourth-kind with constant delay

This work studies the fourth-kind integral equation as a mixed system of first and second-kind Volterra integral equations (VIEs) with constant delay. Regularity, smoothing properties and uniqueness of the solution of this mixed system are obtained by using theorems which give the relevant conditions related to first and second-kind VIEs with delays. A numerical collocation algorithm making use of piecewise polynomials is designed and the global convergence of the proposed numerical method is established. Some typical numerical experiments are also performed which confirm our theoretical result.

Periodic solutions for Boussinesq systems in weak-Morrey spaces

We prove the existence and polynomial stability of periodic mild solutions for Boussinesq systems in critical weak-Morrey spaces for dimension n⩾3. Those systems are derived via the Boussinesq approximation and describe the movement of an incompressible viscous fluid under natural convection filling the whole space Rn. Using certain dispersive and smoothing properties of heat semigroups on Morrey-Lorentz spaces as well as Yamazaki-type estimate on block spaces, we prove the existence of bounded mild solutions for the linear systems corresponding to the Boussinesq systems. Then, we establish a Massera-type theorem to obtain the existence and uniqueness of periodic solutions to corresponding linear systems on the half line time-axis by using a mean-ergodic method. Next, using fixed point arguments, we can pass from linear systems to prove the existence uniqueness and polynomial stability of such solutions for Boussinesq systems. Finally, we apply the results to Navier-Stokes equations.