Regularization Scheme Research Articles

Modular Hamiltonian in the semi infinite line. Part II. Dimensional reduction of Dirac fermions in spherically symmetric regions

In this article, we extend our study on a new class of modular Hamiltonians on an interval attached to the origin on the semi-infinite line, introduced in a recent work dedicated to scalar fields. Here, we shift our attention to fermions and similarly to the scalar case, we investigate the modular Hamiltonians of theories which are obtained through dimensional reduction, this time, of a free massless Dirac field in d dimensions. By following the same methodology, we perform dimensional reduction on both the physical and modular Hamiltonians. This process enables us to establish a correspondence: we identify the modular Hamiltonian in an interval connected to the origin to the one obtained from the reduction of the modular Hamiltonian pertaining to the conformal parent theory on a sphere. Intriguingly, although the resulting one-dimensional theories lack conformal symmetry due to the presence of a term proportional to 1/r, the corresponding modular Hamiltonians are local functions in the energy density. This phenomenon mirrors the well known behaviour observed in the conformal case and indicates the existence of a residual symmetry, characterized by a subset of the original conformal group.Furthermore, through an analysis of the spectrum of the modular Hamiltonians, we derive an analytic expression for the associated entanglement entropy. Our findings also enable us to successfully recover the conformal anomaly coefficient from the universal piece of the entropy in even dimensions, as well as the universal constant F term in d = 3, by extending the radial regularization scheme originally introduced by Srednicki to perform the sum over angular modes.

Renormalization scheme factorization of one-loop Fierz identities

We present a proof of the factorization of renormalization scheme in one-loop-corrected Fierz identities. This scheme factorization facilitates the simultaneous transformation of operator basis and renormalization scheme using only relations between physical operators; the evanescent operators in the respective bases may be chosen entirely independently of each other. The relations between evanescent operators in the two bases is automatically accounted for by the corrected Fierz identities. We illustrate the utility of this result with a two-loop anomalous dimension matrix computation using the Naive-Dimensional Regularization scheme, which is then transformed via one-loop Fierz identities to the known result in the literature given in a different basis and calculated in the Larin scheme. Additionally, we reproduce results from the literature of basis transformations involving the rotation of evanescent operators into the physical basis using our method, without the need to explicitly compute one-loop matrix elements of evanescent operators.

Artificial first-order phase transition in a magnetized Nambu–Jona-Lasinio model with a quark anomalous magnetic moment

Recently, first-order phase transitions have been predicted as an effect of the inclusion of quark anomalous magnetic moment (AMM) in the hot and magnetized Nambu–Jona-Lasinio model (NJL). These transitions appear in the chiral condensate for different combinations of AMM and magnetic fields and could lead to inverse magnetic catalysis. However, in this work, we show that the predicted first-order phase transitions are related to regularization-dependent issues. To show this, we explore, in the context of the vacuum magnetic regularization (VMR) scheme, two different scenarios: when mass-dependent (MD) and mass-independent (MI) terms are present in the subtraction of the divergences. In the MD case, as we increase the AMM value, it is observed the appearance of a nonmassive minimum in the thermodynamical potential, which induces a first-order phase transition from the massive minimum. We argue that the MD terms must be avoided in order to satisfy the predictions of Lattice QCD, and we propose a MI solution that is valid in the limit which the magnetic fields are smaller than the squared of vacuum effective quark mass. Published by the American Physical Society 2024

Nonlinear Tikhonov regularization in Hilbert scales for inverse learning

In this paper, we study Tikhonov regularization scheme in Hilbert scales for a nonlinear statistical inverse problem with general noise. The regularizing norm in this scheme is stronger than the norm in the Hilbert space. We focus on developing a theoretical analysis for this scheme based on conditional stability estimates. We utilize the concept of the distance function to establish high probability estimates of the direct and reconstruction errors in the Reproducing Kernel Hilbert space setting. Furthermore, explicit rates of convergence in terms of sample size are established for the oversmoothing case and the regular case over the regularity class defined through an appropriate source condition. Our results improve upon and generalize previous results obtained in related settings.

Robust fiber orientation distribution function estimation using deep constrained spherical deconvolution for diffusion-weighted magnetic resonance imaging.

Diffusion-weighted magnetic resonance imaging (DW-MRI) is a critical imaging method for capturing and modeling tissue microarchitecture at a millimeter scale. A common practice to model the measured DW-MRI signal is via fiber orientation distribution function (fODF). This function is the essential first step for the downstream tractography and connectivity analyses. With recent advantages in data sharing, large-scale multisite DW-MRI datasets are being made available for multisite studies. However, measurement variabilities (e.g., inter- and intrasite variability, hardware performance, and sequence design) are inevitable during the acquisition of DW-MRI. Most existing model-based methods [e.g., constrained spherical deconvolution (CSD)] and learning-based methods (e.g., deep learning) do not explicitly consider such variabilities in fODF modeling, which consequently leads to inferior performance on multisite and/or longitudinal diffusion studies. In this paper, we propose a data-driven deep CSD method to explicitly constrain the scan-rescan variabilities for a more reproducible and robust estimation of brain microstructure from repeated DW-MRI scans. Specifically, the proposed method introduces a three-dimensional volumetric scanner-invariant regularization scheme during the fODF estimation. We study the Human Connectome Project (HCP) young adults test-retest group as well as the MASiVar dataset (with inter- and intrasite scan/rescan data). The Baltimore Longitudinal Study of Aging dataset is employed for external validation. From the experimental results, the proposed data-driven framework outperforms the existing benchmarks in repeated fODF estimation. By introducing the contrastive loss with scan/rescan data, the proposed method achieved a higher consistency while maintaining higher angular correlation coefficients with the CSD modeling. The proposed method is assessing the downstream connectivity analysis and shows increased performance in distinguishing subjects with different biomarkers. We propose a deep CSD method to explicitly reduce the scan-rescan variabilities, so as to model a more reproducible and robust brain microstructure from repeated DW-MRI scans. The plug-and-play design of the proposed approach is potentially applicable to a wider range of data harmonization problems in neuroimaging.

Regularized Finite Impulse Response Models versus Laguerre Models: A Comparison

While in recent years, the estimation of finite impulse response (FIR) models has been improved by introducing new regularization schemes, also other orthonormal basis function (OBF) models are now becoming more prominent again. Although Laguerre models show very similar properties to the regularized FIR models, they are only rarely used for system identification. Therefore, in this paper, regularized FIR models and Laguerre models will be compared. This work focuses on the model structure and its similarities and differences, as well as the hyperparameter optimization utilizing the generalized cross-validation (GCV) error. Finally, the two model types are investigated using three different processes and the model performance is evaluated. Both model types show significant improvements compared to standard (unregularized) FIR models.

Regularized Iterative Weighted Total Least Squares for Vehicle Mass Estimation

This work addresses the challenge of vehicle mass estimation using a longitudinal vehicle dynamics model, which adopts an errors-in-variables formulation due to the presence of noise-contaminated measurements in both input and output variables. The reduced vehicle dynamics model is ill-conditioned by nature of correlated input variables and a lack of persistent excitation in the measured data. A regularized iterative weighted total least squares (RIWTLS) method is therefore developed and has the advantage of producing parameter uncertainty quantification and measurement bias estimation alongside the estimated system parameters. A complementary adaptive regularization scheme is developed and serves to control the numerical stability of the RIWTLS algorithm based on the conditioning of incoming data. Experimental tests using electric vehicle data and a batch estimation scheme highlight the performance of the proposed RIWTLS algorithm, estimating vehicle mass to within ±1% accuracy.

Modeling Hierarchical Uncertainty for Multimodal Emotion Recognition in Conversation.

Approximating the uncertainty of an emotional AI agent is crucial for improving the reliability of such agents and facilitating human-in-the-loop solutions, especially in critical scenarios. However, none of the existing systems for emotion recognition in conversation (ERC) has attempted to estimate the uncertainty of their predictions. In this article, we present HU-Dialogue, which models hierarchical uncertainty for the ERC task. We perturb contextual attention weight values with source-adaptive noises within each modality, as a regularization scheme to model context-level uncertainty and adapt the Bayesian deep learning method to the capsule-based prediction layer to model modality-level uncertainty. Furthermore, a weight-sharing triplet structure with conditional layer normalization is introduced to detect both invariance and equivariance among modalities for ERC. We provide a detailed empirical analysis for extensive experiments, which shows that our model outperforms previous state-of-the-art methods on three popular multimodal ERC datasets.

Improved Diversity-Promoting Collaborative Metric Learning for Recommendation.

Collaborative Metric Learning (CML) has recently emerged as a popular method in recommendation systems (RS), closing the gap between metric learning and collaborative filtering. Following the convention of RS, existing practices exploit unique user representation in their model design. This paper focuses on a challenging scenario where a user has multiple categories of interests. Under this setting, the unique user representation might induce preference bias, especially when the item category distribution is imbalanced. To address this issue, we propose a novel method called Diversity-Promoting Collaborative Metric Learning (DPCML), with the hope of considering the commonly ignored minority interest of the user. The key idea behind DPCML is to introduce a set of multiple representations for each user in the system where users' preference toward an item is aggregated by taking the minimum item-user distance among their embedding set. Specifically, we instantiate two effective assignment strategies to explore a proper quantity of vectors for each user. Meanwhile, a Diversity Control Regularization Scheme (DCRS) is developed to accommodate the multi-vector representation strategy better. Theoretically, we show that DPCML could induce a smaller generalization error than traditional CML. Furthermore, we notice that CML-based approaches usually require negative sampling to reduce the heavy computational burden caused by the pairwise objective therein. In this paper, we reveal the fundamental limitation of the widely adopted hard-aware sampling from the One-Way Partial AUC (OPAUC) perspective and then develop an effective sampling alternative for the CML-based paradigm. Finally, comprehensive experiments over a range of benchmark datasets speak to the efficacy of DPCML.

A Fine-Grained Regularization Scheme for Nonnegative Latent Factorization of High-Dimensional and Incomplete Tensors

A Fine-Grained Regularization Scheme for Nonnegative Latent Factorization of High-Dimensional and Incomplete Tensors

Sparse additive support vector machines in bounded variation space

Abstract We propose the total variation penalized sparse additive support vector machine (TVSAM) for performing classification in the high-dimensional settings, using a mixed $l_{1}$-type functional regularization scheme to induce sparsity and smoothness simultaneously. We establish a representer theorem for TVSAM, which turns the infinite-dimensional problem into a finite-dimensional one, thereby providing computational feasibility. Even for the least squares loss, our result fills a gap in the literature when compared with the existing representer theorem. Theoretically, we derive some risk bounds for TVSAM under both exact sparsity and near sparsity, and with arbitrarily specified internal knots. In this process, we develop an important interpolation inequality for the space of functions of bounded variation, relying on analytic techniques such as mollification and partition of unity. An efficient implementation based on the alternating direction method of multipliers is employed.

Consistency-guided Differential Decoding for Enhancing Semi-supervised Medical Image Segmentation.

Semi-supervised learning (SSL) has been proven beneficial for mitigating the issue of limited labeled data, especially on volumetric medical image segmentation. Unlike previous SSL methods which focus on exploring highly confident pseudo-labels or developing consistency regularization schemes, our empirical findings suggest that differential decoder features emerge naturally when two decoders strive to generate consistent predictions. Based on the observation, we first analyze the treasure of discrepancy in learning towards consistency, under both pseudo-labeling and consistency regularization settings, and subsequently propose a novel SSL method called LeFeD, which learns the feature-level discrepancies obtained from two decoders, by feeding such information as feedback signals to the encoder. The core design of LeFeD is to enlarge the discrepancies by training differential decoders, and then learn from the differential features iteratively. We evaluate LeFeD against eight state-of-the-art (SOTA) methods on three public datasets. Experiments show LeFeD surpasses competitors without any bells and whistles, such as uncertainty estimation and strong constraints, as well as setting a new state of the art for semi-supervised medical image segmentation. Code has been released at https://github.com/maxwell0027/LeFeD.

Fuzzy Levenberg-Marquardt damping factor update strategy and Tikhonov regularization applied to a coupled conduction-radiation inverse heat transfer problem

The recently proposed Fuzzy Levenberg-Marquardt Damping Factor Updating Strategy (FLM) is used along with Tikhonov Regularization (TR) in order to solve a coupled conduction-radiation function estimation inverse problem. FLM consists of updating the Levenberg-Marquardt (LM) damping factor with the assist of Fuzzy Logic. To test the FLM algorithm combined with TR, a conduction-radiation problem is addressed, and it serves as test bed to the numerical experiments, where the objective is to obtain estimatives of parameters, such as the spatially variable scattering albedo, the thermal conductivity and the optical thickness, simultaneously, which is often performed separately. Two main test cases are presented, one considering only the radiation problem, used as benchmark, in order to investigate noise levels and hyperparameters. The second main test case deals with the coupled conduction-radiation heat transfer problem for different functional forms of the spatially variable scattering albedo. For all presented numerical experiments, good estimates were achieved for the sought functions and parameters. These results demonstrate that the methodology presented in this work, through the combination of the Fuzzy LM dampting factor updating strategy and the Tikhonov regularization scheme, may provide valuable tools for inverse heat transfer problems.

The influence of quark anomalous magnetic moment in the Nambu–Jona‐Lasinio model with different regularizations

AbstractThe Nambu–Jona‐Lasinio model is known for its simplicity and capacity to reproduce some of the basic characteristics of the quantum chromodynamics phase diagram. However, since it is a nonrenormalizable model, there are regularization issues that should be treated conveniently. This is the case when considering the quark anomalous magnetic moment (AMM) when external constant magnetic fields are present. Regularization procedures based on entangled functions between the magnetic field and the cutoff of the model can predict first‐order phase transitions for chiral symmetry restoration at finite values of magnetic fields and inverse magnetic catalysis. The strengths of magnetic fields explored in NJL model and lattice QCD do not show first‐order phase transition. In the present work, we show that some of the previous results are regularization‐dependent effects and how to handle the divergences using the vacuum magnetic regularization scheme.

Homogeneous-heterogeneous reactions on Darcy-Forchheimer nanofluid flow system

The use of artificial neural networks (ANNs) to solve complex fluid dynamics problems has revolutionized computational approaches. This article explores novel ANN solutions for fluid problems. ANNs have demonstrated unmatched effectiveness in comprehending and forecasting fluidic behaviors, from mimicking complex fluid flow trends to optimizing structures for dynamics. This study emphasizes the significance of neural networks in revolutionizing our understanding and control of fluidic systems by using ANNs and Bayesian Regularization. This study examined the 3D Darcy-Forchheimer stretching flow (TDDFSF) of nanofluid under convective conditions along with homogeneous and heterogeneous reactions by employing the scheme of Bayesian Regularization with the procedure of backpropagation in neural networks (SBR-BNNs). The flow is influenced by Brownian diffusion, thermophoresis and zero nanoparticles mass flux condition. The PDEs given in this model are converted into nonlinear ODEs. Results from MSE, regression analysis, and error histogram are used to verify the performance of SBR-BNNs. The absolute errors lie in the ranges up to 10−9, which depict the worth of the solver SBR-BNNs. The absolute error measures the discrepancy between the values actually observed and those predicted by the SBR-BNNs model. SBR-BNNs' high precision in TDDFSF models can lead to more effective and reliable solutions.

Double-parameter regularization for solving the backward diffusion problem with parallel-in-time algorithm

We propose a double-parameter regularization scheme for dealing with the backward diffusion process. Considering the smoothing effect of Yosida approximation for PDE, we propose to regularize this ill-posed problem by modifying original governed system in terms of a pseudoparabolic equation together with a quasi-boundary condition simultaneously, which consequently contains two regularizing parameters. Theoretically, we establish the optimal error estimates between the regularizing solution and the exact one in terms of suitable choice strategy for the regularizing parameters, under a-priori regularity assumptions on the exact solution. The a-posteriori choice strategy for the regularizing parameters based on the discrepancy principle is also studied. To weaken the heavy computational cost for solving the discrete nonsymmetric linear regularizing system by finite difference scheme, especially in higher spatial dimensional cases, the block divide-and-conquer method together with the properties of the Schur complement is applied to decompose the linear system into two half-size linear systems, one of which can be solved by the diagonalization technique, and consequently an efficient parallel-in-time algorithm originally developed for direct problem is applicable. Our proposed method is of much lower complexity than the standard solver for the corresponding linear system. Finally, some numerical examples are presented to verify the efficiency of our proposed method.

Phase-field description of fracture in NiTi single crystals

A phase-field model for thermomechanically-induced fracture in NiTi at the single crystal level, i.e., fracture under loading paths that may take advantage of either of the functional properties of NiTi–superelasticity or shape memory effect–, is presented, formulated within the kinematically linear regime. The model accounts for reversible phase transformation from austenite to martensite habit plane variants and plastic deformation in the austenite phase. Transformation-induced plastic deformation is viewed as a mechanism for accommodation of the local deformation incompatibility at the austenite–martensite interfaces and is accounted for by introducing an interaction term in the free energy derived based on the Mori–Tanaka and Kröner micromechanical assumptions and the hypothesis of martensite instantaneous growth within austenite. Based on experimental observations suggesting that NiTi fractures in a stress-controlled manner, damage is assumed to be driven by the elastic energy, i.e., phase transformation and plastic deformation are assumed to contribute in crack formation and growth indirectly through stress redistribution. The model is restricted to quasistatic mechanical loading (no latent heat effects), thermal loading sufficiently slow with respect to the time rate of heat transfer by conduction (no thermal gradients), and a temperature range below Md, which is the temperature above which the austenite phase is stable, i.e., stress-induced martensitic transformation is suppressed. The numerical implementation of the model is based on an efficient scheme of viscous regularization in both phase transformation and plastic deformation, an explicit numerical integration via a tangent modulus method, and a staggered scheme for the coupling of the unknown fields. The model is shown able to capture transformation-induced toughening, i.e., stable crack advance attributed to the shielding effect of inelastic deformation left in the wake of the growing crack under nominal isothermal loading, actuation-induced fracture under a constant bias load, and crystallographic dependence on crack pattern.

Stability and guaranteed error control of approximations to the Monge–Ampère equation

This paper analyzes a regularization scheme of the Monge–Ampère equation by uniformly elliptic Hamilton–Jacobi–Bellman equations. The main tools are stability estimates in the L∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^\\infty $$\\end{document} norm from the theory of viscosity solutions which are independent of the regularization parameter ε\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varepsilon $$\\end{document}. They allow for the uniform convergence of the solution uε\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$u_\\varepsilon $$\\end{document} to the regularized problem towards the Alexandrov solution u to the Monge–Ampère equation for any nonnegative Ln\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^n$$\\end{document} right-hand side and continuous Dirichlet data. The main application are guaranteed a posteriori error bounds in the L∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^\\infty $$\\end{document} norm for continuously differentiable finite element approximations of u or uε\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$u_\\varepsilon $$\\end{document}.

Working Conditions and Self-Reported Health Among Undocumented and Newly Regularized Migrants in Geneva: A Cross-Sectional Study.

Objectives: Most undocumented migrants are employed in so-called "dirty jobs" or "3D jobs" (dangerous, dirty and degrading) due to their lack of legal status. This study aimed to describe the self-reported health of undocumented and newly regularized migrants in relation to their working conditions. Methods: A cross-sectional study was conducted using data collected during the first phase of the Parchemins study (2017-18), a survey that monitors the socioeconomic and health impact of a regularization scheme for undocumented workers in Geneva, Switzerland. The sample consists of 395 undocumented and newly regularized migrants. Results: Overall, 147 (37.2%) rated their health as very good or excellent. Multivariable regression analysis indicated that work-related factors associated with better self-reported health included higher satisfaction with working conditions, while legal status regularization showed only a borderline association. By contrast, workers performing very demanding tasks and having more difficulties finding a new job were less likely to report very good or excellent health. Conclusion: Findings show that work-related factors had a stronger influence on self-reported health compared to legal status change. Further research is needed to evaluate the long-term impact of regularization on working conditions and self-rated health.

Intermediate mass black hole feedback in dwarf galaxy simulations with a resolved ISM and accurate nuclear stellar dynamics

AbstractRecent observations have established that dwarf galaxies can host black holes of intermediate mass (IMBH, 100Mȯ < MIMBH ≲ 105 Mȯ). With modern numerical models, we can test the growth of IMBHs as well as their evolutionary impact on the host galaxy. Our novel subsolar-mass (0.8 solar mass) resolution simulations of dwarf galaxies (M* = 2 × 107 Mȯ) have a resolved three-phase interstellar medium and account for non-equilibrium heating, cooling, and chemistry processes. The stellar initial mass function is fully sampled between 0.08–150 Mȯ while massive stars can form HII regions and explode as resolved supernovae. The stellar dynamics around the IMBH is integrated accurately with a regularization scheme. We present a viscous accretion disk model for the IMBH with momentum, energy, and mass conserving wind feedback. We demonstrate how the IMBH can grow from accretion of the cold and warm gas phase and how the presence of the IMBH and its feedback impacts the gas phase structure.