Smooth Component Research Articles

Automated tight Lyapunov analysis for first-order methods

AbstractWe present a methodology for establishing the existence of quadratic Lyapunov inequalities for a wide range of first-order methods used to solve convex optimization problems. In particular, we consider (i) classes of optimization problems of finite-sum form with (possibly strongly) convex and possibly smooth functional components, (ii) first-order methods that can be written as a linear system on state-space form in feedback interconnection with the subdifferentials of the functional components of the objective function, and (iii) quadratic Lyapunov inequalities that can be used to draw convergence conclusions. We present a necessary and sufficient condition for the existence of a quadratic Lyapunov inequality within a predefined class of Lyapunov inequalities, which amounts to solving a small-sized semidefinite program. We showcase our methodology on several first-order methods that fit the framework. Most notably, our methodology allows us to significantly extend the region of parameter choices that allow for duality gap convergence in the Chambolle–Pock method when the linear operator is the identity mapping.

Solar and Wind Data Recognition: Fourier Regression for Robust Recovery

Accurate prediction of renewable energy output is essential for integrating sustainable energy sources into the grid, facilitating a transition towards a more resilient energy infrastructure. Novel applications of machine learning and artificial intelligence are being leveraged to enhance forecasting methodologies, enabling more accurate predictions and optimized decision-making capabilities. Integrating these novel paradigms improves forecasting accuracy, fostering a more efficient and reliable energy grid. These advancements allow better demand management, optimize resource allocation, and improve robustness to potential disruptions. The data collected from solar intensity and wind speed is often recorded through sensor-equipped instruments, which may encounter intermittent or permanent faults. Hence, this paper proposes a novel Fourier network regression model to process solar irradiance and wind speed data. The proposed approach enables accurate prediction of the underlying smooth components, facilitating effective reconstruction of missing data and enhancing the overall forecasting performance. The present study focuses on Midland, Texas, as a case study to assess direct normal irradiance (DNI), diffuse horizontal irradiance (DHI), and wind speed. Remarkably, the model exhibits a correlation of 1 with a minimal RMSE (root mean square error) of 0.0007555. This study leverages Fourier analysis for renewable energy applications, with the aim of establishing a methodology that can be applied to a novel geographic context.

Повышение адекватности моделей электромеханотронных систем

Development of electromechanotronic systems is connected with modeling and calculation of processes of various kinds. Electromagnetic, mechanical and thermal processes are analyzed, control, regulation, protection, monitoring and diagnostics problems are solved. Systems may contain a large number of power semiconductor elements. Short-term and multi-hour processes are calculated. Taking into account mutual connections of processes of various kinds in calculations of complex systems requires inadmissibly large expenditures of machine time. The problems are solved under more or less significant assumptions, which leads to a decrease in the adequacy of the results. The methods of systems calculation are proposed, which allow to reduce machine time consumption and to use more detailed description of installations and more accurate computer models. Possibilities of calculation of processes by «smooth components» of variables, and also application of dual models, in which speed and accuracy are combined, are considered. As an example, a system with an active cascade frequency converter containing 780 transistors and diodes, parasitic inductances and snubber circuits, and a vector-controlled induction motor with ladder circuits accounting for current displacement is analyzed. The model takes into account energy losses in the converter and in the motor, as well as the distribution of losses by components. It also takes into account emergency operation modes associated with disconnection of a part of low-voltage units of the cascade converter and maintenance of power quality at its input and output by symmetrization of the main current components and suppression of parasitic components.

Adenomatoid tumor with extensive reactive smooth muscle: a diagnostic dilemma

Abstract Introduction/Objective Adenomatoid tumors are slow-growing benign tumors of mesothelial origin. They comprise 30% of all tumors of the paratesticular area. In this location, they commonly involve the epididymis, spermatic cord, ejaculatory duct and rarely testicular parenchyma. Histologically, a spectrum of growth patterns can be seen, such as adenoid, tubular, glandular, solid, or cystic. In some cases, a smooth muscle component can also be present. The purpose of this report is to describe a case of adenomatoid tumor with exuberant smooth muscle component, mimicking leiomyoma. Methods/Case Report A 28-year-old male presented with painless left inguinal bulge. He noticed it five years prior, and it had been slowly growing since then. Examination revealed a paratesticular mass which was subsequently excised. Grossly, the tumor was firm with smooth, white-tan cut surfaces. Microscopically, the tumor was well- circumscribed, showing predominance of smooth muscle bundles and rare cuboidal to ovoid cells in tubular growth pattern. In the background there was little intervening stroma. Immunohistochemical stains showed the cuboidal cells to be positive for WT1 and calretinin, confirming the mesothelial origin. Diagnosis of adenomatoid tumor was rendered. In contrast to adenomatoid tumors, leiomyomas are whiter and firmer on gross examination and lack the characteristic tubules or cystic spaces lined by mesothelial cells. Results (if a Case Study enter NA) N/A Conclusion Exuberant smooth muscle differentiation in adenomatoid tumor can mislead to diagnosis of leiomyoma. Careful inspection for tubules of mesothelial origin and appropriate immunohistochemical stains are key to accurate diagnosis. Pathologists need to be aware of this potential pitfall.

CTDNet: cartoon-texture decomposition-based gray image super-resolution network with multiple degradations

In the case of multiple degradations, current deep-learning-based gray image super-resolution (SR) methods equally process all components in an image, resulting in missing subtle details. To address this issue, we elaborate a cartoon-texture decomposition-based (CTD) module that can automatically decompose an image into a smooth cartoon component and an oscillatory texture component. The CTD module is a plug-and-play prior module that can be applied in solving imaging inverse problems. Specifically, for the SR task under multiple degradations, we apply CTD as a prior module to build an unfolding SR network termed CTDNet. For the SR task of real terahertz images, the boundary (i.e., the boundary between the object of interest and the carrier table) recovered by CTDNet has artifacts, which limits its realistic applications. To reduce these boundary artifacts, we post-process the SR terahertz images by using a boundary artifact reduction method. Experimental results on the synthetic dataset and real terahertz images demonstrate that the proposed algorithms can maintain subtle details and achieve comparable visual results. The code can be found at https://github.com/shibaoshun/CTDNet.

Malignant female genital tract smooth muscle tumors with adipocytic differentiation: A morphologic, immunohistochemical, MDM2 fluorescence in situ hybridization and molecular genetic study of 6 lipoleiomyosarcomas

Leiomyosarcoma with adipocytic differentiation or lipoleiomyosarcoma is an uncommon sarcoma of the female genital tract with only a few individual reports in the literature. We therefore performed a morphologic, immunohistochemical, MDM2 gene amplification and RNA and DNA sequencing analysis of a series of gynecologic lipoleiomyosarcoma to better define the clinicopathologic spectrum. Six tumors from 6 patients were identified and classified as spindled lipoleiomyosarcoma (n = 2), mixed spindled and myxoid lipoleiomyosarcoma (n = 1), epithelioid lipoleiomyosarcoma with focal myxoid features (n = 1) and mixed spindled and epithelioid lipoleiomyosarcoma (n = 2). Patient age ranged from 41 to 64 years (mean: 49; median: 50). Primary location included uterine corpus (3), uterine corpus/cervix (2) and broad ligament (1). Tumor size ranged from 4.5 to 22 cm (mean: 11.2; median: 9.8). Four patients had metastasis at presentation or subsequently developed recurrent or distant disease. Patient status was known for 5: 2 dead of disease, 2 alive with disease and 1 alive without evidence of disease. Immunohistochemical expression of smooth muscle markers, ER, PR and WT-1 showed patterns similar to non-adipocytic gynecologic leiomyosarcomas. MDM2 amplification fluorescence in situ hybridization performed on 2 tumors was negative in 1 and equivocal in 1. Sequencing studies performed on 3 tumors found TP53 mutations in 3, with 1 tumor also having an ATRX alteration. No gene fusions were identified. Although lipoleiomyosarcomas have a diverse morphologic spectrum, our findings suggest the smooth muscle component shares morphologic and immunohistochemical features with female genital tract non-adipocytic leiomyosarcomas. Lipoleiomyosarcomas also have genetic alterations associated with non-adipocytic gynecologic leiomyosarcomas.

Torsion divisors of plane curves and Zariski pairs

This paper is devoted to the study of the embedded topology of reducible plane curves having a smooth irreducible component. In previous studies, the relationship between the topology and certain torsion classes in the Picard group of degree zero of the smooth component was implicitly considered. Here this relationship is formulated clearly and a criterion is given for distinguishing the embedded topology in terms of torsion classes. Furthermore, a method is presented for systematically constructing examples of curves where this criterion is applicable, and new examples of Zariski N N -tuples are produced.

Anatomically compliant modes of variations: New tools for brain connectivity.

Anatomical complexity and data dimensionality present major issues when analysing brain connectivity data. The functional and anatomical aspects of the connections taking place in the brain are in fact equally relevant and strongly intertwined. However, due to theoretical challenges and computational issues, their relationship is often overlooked in neuroscience and clinical research. In this work, we propose to tackle this problem through Smooth Functional Principal Component Analysis, which enables to perform dimensional reduction and exploration of the variability in functional connectivity maps, complying with the formidably complicated anatomy of the grey matter volume. In particular, we analyse a population that includes controls and subjects affected by schizophrenia, starting from fMRI data acquired at rest and during a task-switching paradigm. For both sessions, we first identify the common modes of variation in the entire population. We hence explore whether the subjects' expressions along these common modes of variation differ between controls and pathological subjects. In each session, we find principal components that are significantly differently expressed in the healthy vs pathological subjects (with p-values < 0.001), highlighting clearly interpretable differences in the connectivity in the two subpopulations. For instance, the second and third principal components for the rest session capture the imbalance between the Default Mode and Executive Networks characterizing schizophrenia patients.

Load forecasting for regional integrated energy system based on complementary ensemble empirical mode decomposition and multi-model fusion

The multiple loads of the Regional Integrated Energy System (RIES) possess characteristics of randomness and relatively higher complexity. The current forecasting methods struggle to effectively handle the non-stationary sequence of these multiple loads, leading to less accurate load forecasting. To address this problem, this paper proposes a multi-model fusion prediction method based on Complementary Ensemble Empirical Mode Decomposition (CEEMD), Genetic Algorithm-Long Short Term Memory (GA-LSTM), Radial Basis Fusion-Autoencoder (RBF-AE), and Particle Swarm Optimization-Support Vector Machine (PSO-SVM). First, the load sequence is decomposed into different frequency Intrinsic Mode Functions (IMFs) components using CEEMD. The IMFs components are then grouped based on their zero-crossing rate and Sample Entropy (SE), resulting in three distinct groups: high-, medium-, and low-frequency components. Next, the high-frequency load component, which exhibit strong randomness, are predicted using GA-LSTM. The medium-frequency load component, which have weaker randomness, are predicted using RBF-AE. The smooth and periodic low-frequency load component are predicted using PSO-SVM. The prediction results from these three models are reconstructed to obtain the final predictive value. Finally, experimental results confirm that the forecasting model can effectively handle non-stationary load sequences and demonstrate the highest level of forecasting accuracy.

The influence of subhaloes on host halo properties

ABSTRACT Within the ΛCDM cosmology, dark matter haloes are composed of both a smooth component and a population of smaller gravitationally bound subhaloes. These components are often treated as a single halo when properties, such as density profiles, are extracted from simulations. Recent work has shown that density profiles change substantially when subhalo mass is excluded. In this paper, we expand on this result by analysing three specific host halo properties – concentration (cNFW), spin (λB), and shape (c/a) – when calculated only from the smooth component of the halo. This analysis is performed on both Milky Way-mass haloes and cluster-mass haloes in high-resolution zoom-in N-body simulations. We find that when subhaloes are excluded, the median value of (1) cNFW is enhanced by $\approx 30\pm 11$ and $\approx 77\pm 8.1~{{\ \rm per\ cent}}$ for Milky Way-mass ($10^{12.1}\, \text{M}_\odot$) and cluster-mass ($10^{14.8}\, \text{M}_\odot$) haloes, respectively, (2) λB is reduced for Milky Way-mass by $\approx 11\pm 4.9~{{\ \rm per\ cent}}$ and cluster-mass haloes by $\approx 27\pm 3.5~{{\ \rm per\ cent}}$. Additionally, with the removal of subhaloes, cluster-mass haloes tend to become more spherical as the ratio of minor-to-major axis, c/a, increases by $\approx 11\pm 3.6~{{\ \rm per\ cent}}$, whereas Milky Way-mass haloes remain approximately the same shape with c/a changed by $\approx 1.0\pm 5.8~{{\ \rm per\ cent}}$. Fractional changes of each of these properties depend primarily on the amount of mass in subhaloes and, to a lesser extent, mass accretion history. Our findings demonstrate that the properties of the smooth components of dark matter haloes are biased relative to the total halo mass.

Detecting low-mass perturbers in cluster lenses using curved arc bases

ABSTRACT Strong gravitationally lensed arcs produced by galaxy clusters have been observationally detected for several decades now. These strong lensing constraints provided high-fidelity mass models for cluster lenses that include substructure down to $10^{9{-}10}\, \mathrm{M}_\odot$. Optimizing lens models, where the cluster mass distribution is modelled by a smooth component and subhaloes associated with the locations of individual cluster galaxies, has enabled deriving the subhalo mass function, providing important constraints on the nature and granularity of dark matter. In this work, we explore and present a novel method to detect and measure individual perturbers (subhaloes, line-of-sight haloes, and wandering supermassive black holes) by exploiting their proximity to highly distorted lensed arcs in galaxy clusters, and by modelling the local lensing distortions with curved arc bases. This method offers the possibility of detecting individual low-mass perturber subhaloes in clusters and haloes along the line of sight down to a mass resolution of $10^8\, \mathrm{M}_\odot$. We quantify our sensitivity to low-mass perturbers ($M\sim 10^{7{-}9}\, \mathrm{M}_\odot$) in clusters (M ∼ 1014–15 M⊙), by creating realistic mock data. Using three lensed images of a background galaxy in the cluster SMACS J0723, taken by JWST, we study the retrieval of the properties of potential perturbers with masses $M=10^{7{-}9}\, \mathrm{M}_\odot$. From the derived posterior probability distributions for the perturber, we constrain its concentration, redshift, and ellipticity. By allowing us to probe lower mass substructures, the use of curved arc bases can lead to powerful constraints on the nature of dark matter as discrimination between dark matter models appears on smaller scales.

Evaluation of the influence of mean stress on the fatigue behavior of notched and smooth medium carbon steel components through an energetic local approach

AbstractIn the present paper, the influence of the mean stress on the fatigue behavior of smooth and notched medium carbon steel components (C45 grade) is investigated through conventional and more advanced design methodologies. Original experimental data are provided for two notched specimen geometries and three different high load ratios (R = {0.7, 0.8, 0.9}). To assess the effect of the mean stress in a larger range, the bulk of fatigue data has been widened through more than 150 tests on C45 steel drawn from literature. The considered experimental data ranged between a load ratio of −2 and 0.9. The mean stress effect has been assessed in a first attempt through well‐established literature models resulting in a data correlation characterized by a large scatter. Finally, an attempt to uniquely consider both geometrical and load ratio effects has been performed through a numerical application of the strain energy density (SED) method. Elevated load ratios (R ≥ 0.7) prove to be highly detrimental for C45 steel with a fatigue life reduction of up to 3 orders of magnitude; however, this effect can be considered with a sufficient degree of accuracy through the SED method.

Smooth metrics can hide thin shells

In this note, I consider a class of metric tensors with smooth components that naively appear to describe dynamical wormholes with vanishing spacetime curvature. I point out that the smoothness of the metric tensor components is deceptive, and that in general relativity, such metrics must be sourced by exotic thin shells.

Constraints on the Abundance of Primordial Black Holes from X-Ray Quasar Microlensing Observations: Substellar to Planetary Mass Range

We use X-ray observations of quasar microlensing (sensitive to smaller compact objects than in the optical) to study the possible presence of a population of low mass black holes (BHs; from ∼10−3 M ⊙ to 10−1 M ⊙) in lens galaxies. We compare these observations with microlensing magnification simulations of a mixed population of stars and BHs plus a smooth matter component. We estimate the individual mass fractions of both stars and BHs for three different BH masses in the range of substellar to planetary masses. Our Bayesian analysis indicates that the contribution of BHs is negligible in the substellar mass range but that a population of BHs of planetary mass (M ≲ 10−3 M ⊙) could pass unnoticed to X-ray microlensing. We provide new upper limits to the contribution of BHs to the fraction of dark matter based on both, the quasar microlensing data in the X-ray band, and our previous estimates in the optical of intermediate-mass BHs with an additional upper limit at M = 3M ⊙.

The Temporal Symmetrical and Translational Structure in Gamma-Ray Burst Light Curves

Tremendous information is hidden in the light curve of a gamma-ray burst (GRB). Based on Compton Gamma Ray Observatory/Burst And Transient Source Experiment (BATSE) data, Hakkila found a majority of GRBs can be characterized by a smooth, single-peaked component superposed with a temporally symmetrical residual structure, i.e., a mirror feature for the fast-varying component. In this study, we conduct a similar analysis on the same data, as well as on Fermi/Gamma-Ray Burst Monitor data. We obtained a similar conclusion, which is that most GRBs have this symmetrical fast-varying component. Furthermore, we chose an alternative model to characterize the smooth component and used a three-parameter model to identify the residual, i.e., the fast component. By choosing 226 BATSE GRBs based on a few criteria, we checked the time-symmetrical feature and time-translational feature for the fast components and found the ratio is roughly 1:1. We propose that both features could come from the structure of the ejected shells. In the future, the Square Kilometre Array might be able to observe the early radio emission from the collision of the shells.

Torsion free instanton sheaves on the blow-up of [formula omitted] at a point

We define the analogue of instanton sheaves on the blow-up Pn˜ of the n-dimensional projective space at a point. We choose an appropriate polarisation on Pn˜ and construct rank 2 examples of locally free and non locally free (but torsion free) type. In general, the defined instantons also turn out to be the cohomology of monads, although non-linear ones. Moreover, in the five dimensional case, we show that there are continuous families of them that fill, at least, a smooth component in the moduli of semi-stable sheaves.

Integrable Multi-Hamiltonian Systems from Reduction of an Extended Quasi-Poisson Double of {text {U}}(n)

We construct a master dynamical system on a {text {U}}(n) quasi-Poisson manifold, {mathcal {M}}_d, built from the double {text {U}}(n) times {text {U}}(n) and dge 2 open balls in mathbb {C}^n, whose quasi-Poisson structures are obtained from T^* mathbb {R}^n by exponentiation. A pencil of quasi-Poisson bivectors P_{underline{z}} is defined on {mathcal {M}}_d that depends on d(d-1)/2 arbitrary real parameters and gives rise to pairwise compatible Poisson brackets on the {text {U}}(n)-invariant functions. The master system on {mathcal {M}}_d is a quasi-Poisson analogue of the degenerate integrable system of free motion on the extended cotangent bundle T^*!{text {U}}(n) times mathbb {C}^{ntimes d}. Its commuting Hamiltonians are pullbacks of the class functions on one of the {text {U}}(n) factors. We prove that the master system descends to a degenerate integrable system on a dense open subset of the smooth component of the quotient space {mathcal {M}}_d/{text {U}}(n) associated with the principal orbit type. Any reduced Hamiltonian arising from a class function generates the same flow via any of the compatible Poisson structures stemming from the bivectors P_{underline{z}}. The restrictions of the reduced system on minimal symplectic leaves parameterized by generic elements of the center of {text {U}}(n) provide a new real form of the complex, trigonometric spin Ruijsenaars–Schneider model of Krichever and Zabrodin. This generalizes the derivation of the compactified trigonometric RS model found previously in the d=1 case.

Machine learning methods for classifying novel fentanyl analogs from Raman spectra of pure compounds

In previous research, we demonstrated the promise of detecting novel fentanyl analogs from mass spectra using machine learning models. This approach complements existing library matching methods and provides a key capability amid the recent sharp increase in abuse of fentanyl and its analogs. However, many applications rely upon portable devices such as Raman spectrometers, rather than mass spectrometers that are generally located in laboratories. In response, we adapted our models to Raman-based sensing, devising a machine learning approach for detecting novel fentanyl analogs from Raman spectra. Whereas mass spectra consist of well-defined discrete peaks, Raman spectra are continuous. To aid model development, we extracted features from each spectrum using smoothing, background subtraction, and principal component analysis (PCA). Additionally, we extracted features related to spectral peaks and similarity to spectra of known compounds; these features were guided by subject-matter expertise. We also used a third feature set that combined the features from PCA and from spectral peaks. With these three feature sets as inputs, we developed fentanyl analog classification models using various machine learning techniques. These techniques included multi-layer perceptron, neural network, partial least squares, penalized multinomial regression, random forest, regularized logistic regression, support vector machines, and extreme gradient boosting. We developed and tested our models using 320 Raman spectra of pure compounds, assessing performance via cross-validation. Models with PCA-based features performed better than those using expert-based features, achieving more than 90% probability of detection alongside less than 1% probability of false alarm. Although fentanyl compounds are often found with other components (e.g., cutting agents), some applications such as mail screening may encounter relatively pure fentanyl analogs. The results within this study suggest that our machine learning models are particularly promising for such applications.

A Two-stage Signal Decomposition into Jump, Oscillation and Trend using ADMM

We present a thorough implementation of the two-stage framework proposed in [A. Cicone, M. Huska, S.H. Kang and S. Morigi, JOT: a Variational Signal Decomposition into Jump, Oscillation and Trend, IEEE Transactions on Signal Processing, 2022]. The method assumes as input a 1D signal represented by a finite-dimensional vector in R^N. In the first stage the signal is decomposed into Jump (piece-wise constant), Oscillation, and Trend (smooth) components, and in the second stage the results are refined using residuals of other components. We propose an efficient numerical solution for the first stage based on alternating direction method of multipliers, and a solid algorithm for the solution of the second stage.

Building energy consumption prediction based on VMD-CNN-BILSTM-Attention

Accurate building energy consumption prediction can help buildings optimize energy allocation and save energy. To achieve accurate and reliable building energy consumption prediction, this paper proposes a building energy consumption prediction method based on VMD decomposition and noise reduction, i.e., CNN-BILSTM-Attention hybrid prediction. In this paper, we first use the VMD method to decompose the historical energy consumption series to obtain relatively smooth multiple components, which lays the foundation for accurate prediction. Then we combine Convolutional Neural Network (CNN) and Bi-directional Long and Short Term Memory (BILSTM) network to fully extract the Spatio-temporal characteristics of energy consumption data and then introduce the Attention mechanism to automatically assign corresponding weights to the BILSTM hidden layer states to distinguish the importance of different influencing factors on energy consumption and improve the prediction accuracy. To verify the effectiveness of the model, the most later analyzed with real building energy consumption data of a region, and the prediction results were shown by python, and the prediction results were improved by 40% compared with the traditional machine learning algorithm.