Exponential Weights Research Articles

Um caso de hipotiroidismo auto-imune como origem de atraso de crescimento e de desenvolvimento neuropsicomotor na primeira infância

A previously healthy 4 and a half year old boy presented to primary health care consultation. Due to red flags in the neurodevelopment evaluation, autism spectrum disorder is suspected and the child was oriented to child psychiatry. Seven months later, he is evaluated once again and, in addition to worsening neurodevelopmental delay and poor school performance, growth retardation is noted, as well as exponential weight gain. Prader Willi syndrome is suspected and the patient was referred to the pediatricians consultation. An analytical study was performed showing an exponentially elevated TSH (>750 mUI/L) associated with a decreased free T4 (0.24 ng/dL). A radiograph of the hand and fist revealed mineral bone age around two years and eight months. The autoimmune study revealed positive antithyroid peroxidase antibodies and antithyroglobulin antibodies and the diagnosis of autoimmune hypothyroidism was established. Levothyroxine was initiated with clinical improvement and return to linear growth. However, cognitive impairment was still present. Autoimmune thyroiditis is the most common cause of acquired hypothyroidism in pediatric age, although it is rare under the age of three. This condition, if not treated in a timely manner, can cause adult height loss and delayed neurodevelopment. The presented case illustrates the importance of including thyroid function in the study of children with growth retardation and unexplained weight gain. Changes in behavior and school performance should also alert to this diagnosis.

Poverty Level Forecasting in Maluku Province Using the Exponential Smoothing Method

The purpose of this study is to predict the poverty rate in Maluku Province in 2021-2025 using the Exponential Smoothing method. The Exponential Smoothing method is a moving average forecasting method that gives exponential or multilevel weight to the latest data so that the latest data will get greater weight. The data in this study were sourced from the Central Bureau of Statistics for Maluku Province. In this study, the results obtained were a comparison of several Exponential Smoothing methods, namely Simple Exponential Smoothing, Brown Linear Trend, and Holt Linear Trend. The best method for forecasting poverty levels in Maluku Province was obtained, namely the Holt Linear Trend Exponential Smoothing method with MAPE (3.251), RMSE (1.057), and MAE (0.722) values. Therefore, the poverty rate in Maluku Province is estimated at 18.14 in 2021, 18.29 in 2022, 18.44 in 2023, 18.59 in 2024, and 18.74 in 2025 with intervals between 4.46 and 33.02.

An artificial neural network-based model for roping prediction in aluminum alloy sheet

Roping is a common macroscopic surface defect in AA6XXX aluminum alloy sheets resulting from the three-dimensional (3-D) spatial distribution of specific textures. The crystal plasticity finite element model (CPFEM) has been applied to study roping behavior and achieves good agreement with experimental observations but suffers from expensive computational consumption due to large-area and multi-layer characteristics of the roping phenomenon. In the present work, an artificial neural network-based (ANN) model is developed to predict thickness strain and corresponding surface roping under tensile deformation. A 3-D artificial orientation map generation algorithm is proposed and combined with CPFEM to produce reliable datasets to train, test, and validate the ANN model. The layer-by-layer random texture replacement strategy is adopted for dataset generation and facilitates the ANN model to capture the effects of individual layer textures on the thickness strain. A novel exponential weight loss function is also introduced to solve the imbalance problem of texture components. The ANN-based model demonstrates good prediction capability and generalizability in multiple validation cases with various artificial and experimental textures. The proposed ANN-based model provides an efficient and accurate alternative to the conventional physics-based method for roping analysis in aluminum alloy and can be also applied to similar microstructure-related deformation prediction in other materials.

A generalised proportional-derivative type scheme with multiple saturating structure for the finite-time and exponential tracking continuous control of Euler–Lagrange systems with bounded inputs

A generalised proportional-derivative type scheme for the finite-time and exponential tracking continuous control of Euler–Lagrange systems with input constraints is developed. Its generalised design permits the choice among multiple saturating structures. Suitable functions are involved for the appropriate shaping of every error correction term, and complementarily of their addition, to achieve the concerned type of convergence (in addition to the input saturation avoidance). Such a shaping is carried out through control parameters that act as exponential weights on the gained configuration and generalised velocity errors and on their joint action. Compared to previous finite-time approaches, such exponential weights are required to satisfy generalised comparative conditions, avoiding a fixed equivalence relation among any of them. This permits to give rise to a wider spectrum of finite-time convergent closed-loop trajectories and gives an optional type of (unconventional) exponential convergence (in addition to the conventional one). The resulting extended conditions on the exponential weights and the generalised saturating structure enlarge the controller potential for performance improvement or adjustment. The generalised design is supported through a more general analysis based on more general strict Lyapunov functions, stating more solid analytical bases for possible design extensions on the accomplishment of other control objectives. The study is further supported through experimental tests on a 3-degree-of-freedom robot manipulator.

Weighted Composition Operators between Bergman Spaces with Exponential Weights

Weighted Composition Operators between Bergman Spaces with Exponential Weights

Spectral Gap Formation to Kinetic Equations with Soft Potentials in Bounded Domain

It has been unknown in kinetic theory whether the linearized Boltzmann or Landau equation with soft potentials admits a spectral gap in the spatially inhomogeneous setting. Most of existing works indicate a negative answer because the spectrum of two linearized self-adjoint collision operators is accumulated to the origin in case of soft interactions. In the paper we rather prove it in an affirmative way when the space domain is bounded with an inflow boundary condition. The key strategy is to introduce a new Hilbert space with an exponential weight function that involves the inner product of space and velocity variables and also has the strictly positive upper and lower bounds. The action of the transport operator on such space-velocity dependent weight function induces an extra non-degenerate relaxation dissipation in large velocity that can be employed to compensate the degenerate spectral gap and hence give the exponential decay for solutions in contrast with the sub-exponential decay in either the spatially homogeneous case or the case of torus domain. The result reveals a new insight of hypocoercivity for kinetic equations with soft potentials in the specified situation.

Numerical solution of Korteweg–de Vries equation using discrete least squares meshless method

In this study, a meshless approach called Discrete Least Squares Meshless is used to solve the third-order nonlinear Korteweg–de Vries equation numerically. In shallow water, the Korteweg–de Vries equation illustrates the unidirectional propagation of waves. For function approximation, the suggested technique uses moving least squares shape functions. Furthermore, the least squares functional constructed on certain auxiliary points known as sampling points is minimized in order to generate the system of algebraic equations. This approach may be considered meshless since it does not need a mesh for field variable approximation or system of equations creation; it also gives a symmetric and positive definite matrix even for non-self adjoint differential operators. To demonstrate the applicability of the current meshless approach, the propagation of a single soliton and multi-solitons is explored. The approach may be applied directly to the Korteweg–de Vries equation because to the high degrees of continuity of the moving least squares shape function when an exponential weight function is utilized. Several benchmark numerical instances are explored and the resulting results are compared to earlier research to test the capabilities of the suggested approach for the solution of Korteweg–de Vries equation.

A Wearable Capsule Endoscope Electromagnetic Localization System Based on a Novel WCL Algorithm.

The wearable localization system for wireless capsule endoscopy (WCE) is a potential technology to realize rapid diagnosis and treatment of the gastrointestinal (GI). However, the electromagnetic localization accuracy of WCE still needs to be improved. In this paper, based on RSSI electromagnetic fading model, the accurate fitting parameter values are obtained by Kalman filter and the least square method. A novel weighted centroid localization (WCL) algorithm based on exponential weights is proposed, which can achieve high-accuracy localization by using only sparse reception matrix. The simulation results show that when the standard deviation of the localization data is 7.85, the localization root mean square error (RMSE) is 25.4 mm; when the standard deviation of the localization data is 5.475, the localization RMSE is 2.5 mm. These two localization RMSEs are 38% and 79% less than those of the conventional centroid localization algorithm, respectively. An experimental platform of wearable wireless communication and localization system using 24 array receiving antennas is developed in human phantom environment. The experimental results show that the wearable WCE electromagnetic localization system based on the proposed algorithm achieves a localization RMSE of 36.3 mm, which is 17% lower than that of the conventional centroid localization algorithm and meets the needs of clinical diagnosis.

Stability of Traveling Oscillating Fronts in Complex Ginzburg Landau Equations

Traveling oscillating fronts (TOFs) are specific waves of the form $U_\star (x,t) = e^{-i \omega t} V_\star(x - ct)$ with a profile $V_{\star}$ which decays at $- \infty$ but approaches a nonzero limit at $+\infty$. TOFs usually appear in complex Ginzburg Landau equations of the type $U_t = \alpha U_{xx} + G(|U|^2)U$. In this paper we prove a theorem on the asymptotic stability of TOFs, where we allow the initial perturbation to be the sum of an exponentially localized part and a front-like part which approaches a small but nonzero limit at $+ \infty$. The underlying assumptions guarantee that the operator, obtained from linearizing about the TOF in a co-moving and co-rotating frame, has essential spectrum touching the imaginary axis in a quadratic fashion and that further isolated eigenvalues are bounded away from the imaginary axis. The basic idea of the proof is to consider the problem in an extended phase space which couples the wave dynamics on the real line to the ODE dynamics at $+ \infty$. Using slowly decaying exponential weights, the framework allows to derive appropriate resolvent estimates, semigroup techniques, and Gronwall estimates.

Another look at polynomials orthogonal relative to exponential integral weight functions

Another look at polynomials orthogonal relative to exponential integral weight functions

An Analytic and Numerical Analysis of Weighted Singular Cauchy Integrals with Exponential Weights on ℝ

This article concerns an analytic and numerical analysis of a class of weighted singular Cauchy integrals with exponential weights with finite moments and with smooth external fields with varying smooth convex rate of increase for large argument. Our analysis relies in part on weighted polynomial interpolation at the zeros of orthonormal polynomials with respect to w 2. We also study bounds for the first derivatives of a class of functions of the second kind for w 2.

A more exhaustive study on the finite‐time and exponential tracking continuous control for constrained‐input mechanical systems: Improved design and experiments

AbstractA more exhaustive study on the finite‐time/exponential tracking continuous control for mechanical systems with input constraints is developed. The resulting control scheme is characterized by the inclusion of position‐error and velocity‐error correction terms which are suitably shaped to achieve the concerned types of convergence. Such a shaping is carried out through control parameters that act as exponential weights on the gained position and velocity errors. As an innovative aspect of the proposal, such exponential weights are not restricted to satisfy a fixed equivalence relation among them but rather a wider comparative one. This gives rise to a wider spectrum of finite‐time convergent closed‐loop trajectories and gives an optional type of (unconventional) exponential convergence (in addition to the conventional one), which enlarges the controller potential for performance adjustment. This is further potentiated through a more generalized saturating structure on the error correction terms, that includes the usual saturating‐proportional saturating‐derivative type one as a particular case. The improved design is supported through a more general analysis based on more general strict Lyapunov functions, stating more solid analytical bases for possible design extensions on the accomplishment of other (more complex) control objectives. The study is further supported through experimental tests on a 3‐degree‐of‐freedom robot manipulator.

Asymptotics for Bergman projections with smooth weights: a direct approach

We extend the direct approach to the semiclassical Bergman kernel asymptotics, developed recently in Deleporte et al. (Ann Fac Sci Toulouse Math, 2020) for real analytic exponential weights, to the smooth case. Similar to Deleporte et al. (2020), our approach avoids the use of the Kuranishi trick and it allows us to construct the amplitude of the asymptotic Bergman projection by means of an asymptotic inversion of an explicit Fourier integral operator.

Fourier Representations for Black-Box Optimization over Categorical Variables

Optimization of real-world black-box functions defined over purely categorical variables is an active area of research. In particular, optimization and design of biological sequences with specific functional or structural properties have a profound impact in medicine, materials science, and biotechnology. Standalone search algorithms, such as simulated annealing (SA) and Monte Carlo tree search (MCTS), are typically used for such optimization problems. In order to improve the performance and sample efficiency of such algorithms, we propose to use existing methods in conjunction with a surrogate model for the black-box evaluations over purely categorical variables. To this end, we present two different representations, a group-theoretic Fourier expansion and an abridged one-hot encoded Boolean Fourier expansion. To learn such representations, we consider two different settings to update our surrogate model. First, we utilize an adversarial online regression setting where Fourier characters of each representation are considered as experts and their respective coefficients are updated via an exponential weight update rule each time the black box is evaluated. Second, we consider a Bayesian setting where queries are selected via Thompson sampling and the posterior is updated via a sparse Bayesian regression model (over our proposed representation) with a regularized horseshoe prior. Numerical experiments over synthetic benchmarks as well as real-world RNA sequence optimization and design problems demonstrate the representational power of the proposed methods, which achieve competitive or superior performance compared to state-of-the-art counterparts, while improving the computation cost and/or sample efficiency, substantially.

A robust Poisson multi-Bernoulli filter for multi-target tracking based on arithmetic average fusion

The coalescence and missed detection are two key challenges in Multi-Target Tracking (MTT). To balance the tracking accuracy and real-time performance, the existing Random Finite Set (RFS) based filters are generally difficult to handle the above problems simultaneously, such as the Track-Oriented marginal Multi-Bernoulli/Poisson (TOMB/P) and Measurement-Oriented marginal Multi-Bernoulli/Poisson (MOMB/P) filters. Based on the Arithmetic Average (AA) fusion rule, this paper proposes a novel fusion framework for the Poisson Multi-Bernoulli (PMB) filter, which integrates both the advantages of the TOMB/P filter in dealing with missed detection and the advantages of the MOMB/P filter in dealing with coalescence. In order to fuse the different PMB distributions, the Bernoulli components in different Multi-Bernoulli (MB) distributions are associated with each other by Kullback-Leibler Divergence (KLD) minimization. Moreover, an adaptive AA fusion rule is designed on the basis of the exponential fusion weights, which utilizes the TOMB/P and MOMB/P updates to solve these difficulties in MTT. Finally, by comparing with the TOMB/P and MOMB/P filters, the performance of the proposed filter in terms of accuracy and efficiency is demonstrated in three challenging scenarios.

A novel fire danger rating model based on time fading precipitation model — A case study of Northeast China

With the increase of extreme climate and global warming, forest fires have become more frequent. Therefore, it is important to accurately predict whether fires will occur in forest in the future. Precipitation is an important factor that affects the probability of the occurrence of forest fires in the future. Previous models selected annual average precipitation, monthly average precipitation or drought days as the precipitation value, which the attenuation of precipitation is not considered. In this study, a time fading model is used to calculate the comprehensive precipitation index, which is an exponential weight decay model. The earlier the precipitation time, the smaller the weight. This method can better represent the effect of precipitation in predicting the occurrence of forest fires. Moreover, in this study, discrete fire points are converted into a continuous fire-point density. The structure of the prediction model is more reasonable, which is conducive to obtaining higher-precision prediction results. Besides, the SVM regression model was used to construct a forest fire danger rating model. In the same area, considering the comprehensive precipitation index compared with the average precipitation value, the accuracy of the three forest areas in northeastern China in the test set has been improved by about 5%. The accuracy rates of 90.13%, 93.04% and 87.5% can be achieved respectively.

Relating random matrix map enumeration to a universal symbol calculus for recurrence operators in terms of Bessel–Appell polynomials

Maps are polygonal cellular networks on Riemann surfaces. This paper analyzes the construction of closed form general representations for the enumerative generating functions associated to maps of fixed but arbitrary genus. The method of construction developed here involves a novel asymptotic symbol calculus for difference operators based on the relation between spectral asymptotics for Hermitian random matrices and asymptotics of orthogonal polynomials with exponential weights. These closed form expressions have a universal character in the sense that they are independent of the explicit valence distribution of the cellular networks within a broad class. Nevertheless the valence distributions may be recovered from the closed form generating functions by a remarkable unwinding identity in terms of Appell polynomials generated by Bessel functions. Our treatment reveals the generating functions to be solutions of nonlinear conservation laws and their prolongations. This characterization enables one to gain insights that go beyond more traditional methods that are purely combinatorial. Universality results are connected to stability results for characteristic singularities of conservation laws that were studied by Caflisch, Ercolani, Hou and Landis, Multi-valued solutions and branch point singularities for nonlinear hyperbolic or elliptic systems, Commun. Pure Appl. Math. 46 (1993) 453–499, as well as directly related to universality results for random matrix spectra.

Initial-boundary value problems on a half-strip for the generalized Kawahara–Zakharov–Kuznetsov equation

Initial-boundary value problems on a half-strip with different types of boundary conditions for the generalized Kawahara-Zakharov-Kuznetsov equation with nonlinearity of higher order are considered. In particular, nonlinearity can be quadratic and cubic. Results on global existence and uniqueness in classes of weak and strong solutions and large-time decay of small solutions are established. The solutions are considered in weighted at infinity Sobolev spaces. The use of weighted spaces is crucial for the study. To this end new interpolating inequalities in weighted anisotropic Sobolev spaces are established. Both exponential and power weights are admissible.

Exponential Weight Moving Average (EWMA) Control Chart for Quality Control of Crude Palm Oil Product

In several cases of product quality control in manufactur industries, data that has a small average shift is found due to autocorrelated data, which is a state where the data currently taken is influenced by previous data. The commonly used control chart - the Shewhart control chart, does not show the real situation in the company. The Exponential Moving Weight Average (EMWA) control map is used as an alternative control map to detect small average shifts. In measurement of quality of Crude Palm Oil Product, such as Free Fatty Acid content and level of Colour, where the sampling points are the same, or the samples used are the same, but are collected at different times, this situation could happen. As a result, predictions based on control charts are sometimes not in accordance with real conditions. This study aims to compare the EMWA control chart with the Shewart control chart in analizing the quality of a product. The product used was crude palm oil (CPO) with a case study data from PT X laboratories, a palm oil processing company in Dumai, Riau. We compared the performance of EWMA Control Chart with basic Shewart Control Chart and found that EWMA Control Chart give best performance and much shorter of out of control data.

Semiclassical Gevrey operators and magnetic translations

We study semiclassical Gevrey pseudodifferential operators acting on the Bargmann space of entire functions with quadratic exponential weights. Using some ideas from time frequency analysis, we show that such operators are uniformly bounded on a natural scale of exponentially weighted spaces of holomorphic functions, provided that the Gevrey index is greater than or equal to 2.