A physics-embedded dual-learning imaging framework for electrical impedance tomography.

This paper presents two complementary classes of analytical benchmark problems for the one-dimensional wave equation governing longitudinal vibration of a prismatic rod with mixed (clamped–free) boundary conditions. The first benchmark class consists of classical initial-value problems and includes both compatible and incompatible initial data at the space–time corners, highlighting their influence on convergence, regularity, and termwise differentiation of displacement, velocity, and axial force series representations. The second benchmark class prescribes the displacement at two time instants (initial and final time), leading to a fundamentally different modal structure and revealing spectral conditioning effects governed by the ratio L/(cte). The derived closed-form solutions provide reference configurations for verification of transient numerical solvers, particularly in scenarios where classical smooth compatibility assumptions are not satisfied.

General inertial proximal stochastic mirror descent algorithm beyond Lipschitz smoothness assumption

In recent work by the author it was found that there is an absence of diffeomorphism symmetry for black hole horizons constrained by the causal structure of spacetime. This absence puts stringent constraints on the black hole spacetime manifold, topology, and smoothness. In particular, it suggests that such manifolds may have only continuity of data but no differentiability. In mathematics, this is described as a spacetime manifold with a C<sup>0</sup> structure, and the assumption of smoothness as a C<sup>∞</sup> structure might not hold. Previously, we supposed that the spacetime manifold may have a Finsler structure and might not be a homogeneous manifold, thus requiring new insights to study black hole spacetime. Investigating the spacetime manifold picture, we presume a mathematical concept called stratification of spacetime with smooth gluing of manifold data as an essential criterion for understanding the topology of black hole spacetime. In basic terms, stratification is a way of gluing spacetime into a collection of disjoint regions called strata such that the strata themselves are smooth, but the whole manifold may or may not have a differentiable structure. The topology of the spacetime manifold then depends on the criteria used for the process called stratification of spacetime. We investigate these and relatable ideas further in this paper. For smooth readability, we have referenced relevant literature grouped by topics or subtopics throughout the text.

We study Maximum Entropy density estimation on continuous domains under finitely many moment constraints, formulated as the minimization of the Kullback–Leibler divergence with respect to a reference measure. To model uncertainty in empirical moments, constraints are relaxed through convex penalty functions, leading to an infinite-dimensional convex optimization problem over probability densities. The main contribution of this work is a rigorous convex-analytic treatment of such relaxed Maximum Entropy problems in a functional setting, without discretization or smoothness assumptions on the density. Using convex integral functionals and an extension of Fenchel duality, we show that, under mild and explicit qualification conditions, the infinite-dimensional primal problem admits a dual formulation involving only finitely many variables. This reduction can be interpreted as a continuous-domain instance of partially finite convex programming. The resulting dual problem yields explicit primal–dual optimality conditions and characterizes Maximum Entropy solutions in exponential form. The proposed framework unifies exact and relaxed moment constraints, including box and quadratic relaxations, within a single variational formulation, and provides a mathematically sound foundation for relaxed Maximum Entropy methods previously studied mainly in finite or discrete settings. A brief numerical illustration demonstrates the practical tractability of the approach.

Large language models (LLMs) are increasingly deployed as information systems that evolve over time, where managing internal knowledge—acquisition, retention, and removal—becomes essential. In practice, these processes are primarily realized through continual learning and machine unlearning mechanisms. Despite this, these two mechanisms are often studied in isolation, limiting both interpretability and controllability. In this work, we present a parameter-efficient knowledge management framework where continual learning and machine unlearning—despite employing distinct task-specific objectives—are integrated through a shared retention-controlled parameter evolution mechanism. We ground these structural constraints in a drift-aware design principle: under a model smoothness assumption, we establish a formal upper bound showing that Kullback–Leibler (KL) divergence on retained knowledge is controlled by the magnitude and direction of parameter updates, providing a principled rationale for combining Low-Rank Adaptation (LoRA) freezing, sparse masking, and orthogonal gradient projection into a unified constraint system. Experiments on the Task of Fictitious Unlearning (TOFU) benchmark and real-world benchmarks demonstrate effective knowledge acquisition, selective removal, and robust retention across sequential tasks with strong overall performance and stability. This work provides a practical parameter-efficient recipe and a drift-aware design principle validated on controlled interleaved benchmarks, offering insights toward reliable knowledge management in evolving deployment scenarios.

Purpose This study aims to develop a new three-parameter Jarratt-type iterative method for solving systems of nonlinear equations with higher order convergence, increased flexibility, and improved numerical performance compared to well-known existing iterative schemes. Design/methodology/approach The theoretical properties of the proposed iterative scheme are analysed using Taylor series expansions and a Lipschitz-type framework in Banach spaces, and an analytical expression for the radius of convergence is established. Stability and dynamic behaviour are investigated via basins of attraction in the cartesian plane and compared with some well-known existing methods. Findings The proposed method attains fourth-order convergence and exhibits superior efficiency and accuracy in numerical experiments. The radius of convergence is computed for several test problems. Comparative numerical results demonstrate faster convergence and enhanced robustness over existing methods, while basin-of-attraction analysis indicates a wider convergence region with fewer divergent points. Research limitations/implications The analysis is restricted to problems satisfying standard smoothness and Lipschitz continuity assumptions. Practical implications Due to its high convergence order, flexibility, and stability, the proposed iterative method is well suited for efficiently solving systems of nonlinear equations arising in applied mathematics, engineering, and scientific computing, including boundary value problems and nonlinear integral equations. Originality/value The originality of this work lies in the construction of a three-parameter Jarratt-type iterative method achieving fourth-order convergence, together with a rigorous convergence and radius analysis in Banach spaces. Furthermore, basin-of-attraction analysis offers new insights into the stability and robustness of the proposed scheme.

Abstract Performative prediction refers to scenarios where model predictions influence the underlying data distribution they aim to predict. A desirable property in this context is performative stability , where model predictions are already optimal for the distribution they induce, indicating converged model parameters and no need for further retraining. Achieving performative stability requires characterizing the data distribution map $$\mathcal {D}(\theta )$$ , i.e., the relationship between predictions and the resulting distribution shifts. Current studies typically quantify distribution differences using metrics like $$\mathcal {W}_1$$ distance or $$\chi ^2$$ divergence, which may not provide isometric embeddings or maintain metric equivalence in practical scenarios, limiting their applicability across various data distribution maps. Moreover, the crucial smoothness parameter $$\beta $$ in existing work is often unobtainable in performative scenarios, constraining the real-world utility of current theoretical results and methods. To address these challenges, we develop an algorithm that learns a performatively stable model for arbitrary data distribution maps without requiring the joint smoothness parameter $$\beta $$ . Specifically, we introduce a new $$\hat{\varepsilon }$$ -sensitivity measure for $$\mathcal {D}(\theta )$$ , quantified by the gradient of the loss function, which naturally and directly characterizes how distribution shifts affect the optimization of the objective function. Based on this sensitivity, we formulate a $$\gamma $$ -strongly convex loss function and optimize the deployed model accordingly, where $$\gamma $$ is derived from the defined $$\hat{\varepsilon }$$ , eliminating the need for the $$\beta $$ -joint smoothness assumption. Our theoretical results guarantee the convergence of the deployed model to performative stability. Extensive experiments on synthetic and real-world datasets with diverse data distribution maps demonstrate the superiority of our method over state-of-the-art techniques in two key aspects: prediction accuracy and performative stability.

Expected values weighted by the inverse of a multivariate density or, equivalently, Lebesgue integrals of regression functions with multivariate regressors occur in various areas of applications, including estimating average treatment effects, nonparametric estimators in random coefficient regression models or deconvolution estimators in Berkson errors-in-variables models. The frequently used nearest-neighbor and matching estimators suffer from bias problems in multiple dimensions. By using polynomial least squares fits on each cell of the Kth-order Voronoi tessellation for sufficiently large K, we develop novel modifications of nearest-neighbor and matching estimators, which again converge at the parametric n-rate under mild smoothness assumptions on the unknown regression function and without any smoothness conditions on the unknown density of the covariates. We stress that in contrast to competing methods for correcting for the bias of matching estimators, our estimators do not involve nonparametric function estimators and in particular do not rely on sample-size dependent smoothing parameters. We complement the upper bounds with appropriate lower bounds derived from information-theoretic arguments, which show that some smoothness of the regression function is indeed required to achieve the parametric rate. Simulations illustrate the practical feasibility of the proposed methods.

Abstract We consider an Euler–Bernoulli plate equation with Kelvin–Voigt damping in a bounded domain. The damping is localized in an appropriate open strict subset $$\omega $$ ω of the domain $$\Omega $$ Ω . While it is known that the solutions of this model with a full damping $$\omega = \Omega $$ ω = Ω generate an analytic semigroup, this property is no longer valid for locally distributed damping. In view of this, we study regularity of the equation as expressed by a membership in an appropriate Gevrey’s class. It turns out that the final result depends on both “geometric” and analytical properties of the support function defining the dissipation. First, assuming that the damping coefficient d is $$C^2$$ C 2 and satisfies some structural conditions, we prove that the underlying semigroup is of Gevrey class s : for every $$s>7/2$$ s > 7 / 2 , when the damping region is a collar around the whole boundary, for every $$s>4$$ s > 4 , when the damping region is more general, for every $$s>7/2$$ s > 7 / 2 , when the damping region is more general, and the function d is $$C^3$$ C 3 and satisfies one more structural condition than in the two cases above. In all cases, the semigroup is infinitely differentiable on $$(0,\infty )$$ ( 0 , ∞ ) and also exponentially stable. Next, we drop the smoothness assumption on the damping coefficient and show that the corresponding semigroup decays at a rational rate $$O(t^{-1})$$ O ( t - 1 ) . Our proofs are based on the frequency domain method combined with an adequate smoothing procedure, interpolation inequalities, and multipliers technique. The main features of our proof of the Gevrey regularity are: (i) the introduction of suitable auxiliary functions, (ii) an appropriate estimate of the localized kinetic energy and exploitation of structural constraints on the damping coefficient to prove localized regularity, and, (iii) the use of Hahn–Banach theorem to derive a sharp estimate of a negative norm of the velocity nonsmooth component, (iv) the use of commutators to simplify our presentation. Our rational stability and Gevrey regularity results are the first for the plate equation with localized Kelvin–Voigt damping in higher space dimensions.

Anomaly detection is an important task in many domains, and involves the identification of observations that deviate from normal data. Recent work has established theoretical results for deep ReLU neural networks under smoothness and noise assumptions, yet these results rely on extreme sparsity constraints that limit their practical use. In this work, we introduce shallow ReLU neural networks for unsupervised anomaly detection that retain the same theoretical guarantees. Under the Tsybakov noise condition and Hölder smoothness of the underlying density, we prove that the empirical hinge risk minimiser consistently estimates the optimal Bayes classifier with an excess risk that vanishes as the sample size increases. These findings indicate that shallow ReLU neural network architectures can be a theoretically justified and computationally efficient alternative to deep neural network models for density level set based anomaly detection.

Nonconvex optimization presents significant challenges in many fields, particularly in training deep neural networks (DNNs), where poor local minima can degrade generalization-especially with limited data. High-dimensional nonconvex optimization presents two central challenges: 1) effectively balancing global exploration with rapid local exploitation and 2) establishing convergence guarantees, particularly with sparse individuals under nonsmooth regularizations. To address these limitations, we propose adaptive niching-based gradient-accelerated DE (AdaptiveGDE), an AdaptiveGDE differential evolution (DE) algorithm. It introduces a novel two-step mutation operator that decouples differential mutation and gradient descent, allowing independent control of exploration and exploitation. An adaptive niching strategy dynamically adjusts the number of subpopulations based on population similarity and iteration progress, enabling diverse early exploration and refined late-stage convergence. Under relaxed smoothness assumptions and approximate $\ell _{1}$ regularization, we provide convergence guarantees in expectation to a near-optimal solution within $\mathcal {O}(1/\epsilon ^{4})$ iterations. Extensive experiments show that AdaptiveGDE achieves robust global exploration on complex multimodal functions, strong local exploitation on convex problems, and significantly improves test accuracy and loss in DNN training, especially under limited data scenarios.

Accelerated stochastic symmetric ADMM for nonconvex optimization problems without Lipschitz smoothness assumption

Financial time series are heterogeneous, nonstationary, and dispersed across institutions that cannot share raw data. While federated learning enables collaborative modeling under privacy constraints, fixed architectures struggle to accommodate cross-market drift and device-resource diversity; conversely, existing neural architecture search techniques presume centralized data and typically ignore communication, latency, and privacy budgets. This paper introduces FedRegNAS, a regime-aware federated NAS framework that jointly optimizes forecasting accuracy, communication cost, and on-device latency under user-level (ε,δ)-differential privacy. FedRegNAS trains a shared temporal supernet composed of candidate operators (dilated temporal convolutions, gated recurrent units, and attention blocks) with regime-conditioned gating and lightweight market-aware personalization. Clients perform differentiable architecture updates locally via Gumbel-Softmax and mirror descent; the server aggregates architecture distributions through Dirichlet barycenters with participation-weighted trust, while model weights are combined by adaptive, staleness-robust federated averaging. A risk-sensitive objective emphasizes downside errors and integrates transaction-cost-aware profit terms. We further inject calibrated noise into architecture gradients to decouple privacy leakage from weight updates and schedule search-to-train phases to reduce communication. Across three real-world equity datasets, FedRegNAS improves directional accuracy by 3–7 percentage points and Sharpe ratio by 18–32%. Ablations highlight the importance of regime gating and barycentric aggregation, and analyses outline convergence of the architecture mirror-descent under standard smoothness assumptions. FedRegNAS yields adaptive, privacy-aware architectures that translate into materially better trading-relevant forecasts without centralizing data.

We revisit moment-based refinements of Jensen's inequality for convex functions and provide a rigorous framework that explicitly states all smoothness, integrability, and remainder assumptions. Our contribution is twofold: (i) a fourth-order expansion equipped with computable remainder bounds that formally justify the inclusion of skewness and kurtosis under verifiable moment conditions; and (ii) a transparent derivation bridging pointwise Taylor expansions with their expected-value counterparts, thus avoiding common conflations between local and integral approximations. Beyond the theoretical analysis, we demonstrate the practical value of these results through validated approximations of exponential moments and utility-based insurance premiums. Numerical experiments highlight the regions of parameter space where the remainder control ensures accuracy, and identify regimes in which higher-order corrections become essential.

Purpose Propose an approximation procedure to efficiently represent aggregate supply and demand curves in the electricity market. Design/methodology/approach Two approximation procedures based on one-step functions are designed using the L1 and L2 metrics as error measures. For the metric L2 a closed-form solution is obtained to reduce the global error over the entire domain. For the metric L1, which lacks a closed-form solution, a linear programming problem is solved to improve the local approximation within intervals defined by the nodes. The dependence on the node locations is addressed by different node selection strategies. In particular, a heuristic strategy is proposed that combines descriptive information from the offers with a dyadic search procedure to minimize the approximation error. Findings The performance of our proposals is evaluated and compared using curves from the day-ahead Spanish electricity market. Our procedure achieves a promising approximation performance compared with existing approaches. Practical implications The proposed procedures will allow the development of efficient methods for forecasting supply and demand curves and, consequently, market clearing prices. Having these forecasts is of interest to both producers and consumers. Originality/value Existing procedures for representing step supply and demand curves often involve high computational costs or, alternatively, make assumptions of smoothness and differentiability of the curves that contradict the nature of these step curves. Our proposals address these challenges, obtaining approximations that resemble real curves in a parsimonious and practical way.

We propose a novel causal estimand that elucidates how response to an earlier treatment (e.g., treatment initiation) modifies the effect of a later treatment (e.g., treatment discontinuation), thus learning if there are effects among the (un)affected. Specifically, we consider a working marginal structural model summarizing how the average effect of a later treatment varies as a function of the (estimated) conditional average effect of an earlier treatment. We define the estimand to be a data-adaptive causal parameter, allowing for estimation of the conditional average treatment effect using machine learning without making strong smoothness assumptions. We show how a sequentially randomized design can be used to identify this causal estimand, and we describe a targeted maximum likelihood estimator for the resulting statistical estimand, with influence curve-based inference. We present simulation studies that evaluate the performance of this estimator under various finite-sample scenarios. Throughout, we use the "Adaptive Strategies for Preventing and Treating Lapses of Retention in HIV Care" trial (NCT02338739) as an illustrative example, showing that discontinuation of conditional cash transfers for HIV care adherence was most harmful among those who had an increase in benefit from them initially.

Abstract It has been shown that in one dimension the environment viewed by the particle process (EVP process) in quasi periodic random environment is uniquely ergodic and mixing under mild additional assumptions. Here we construct an analytic quasi periodic environment on higher dimensional torus such that the EVP process is not uniquely ergodic. The stationary measures in this counterexample are necessarily atomless. We show also that the EVP process is mixing with respect to any ergodic stationary measure under some smoothness assumption.

Susan Howe, recognized as one of the most innovative American poets of our day, Susan Howe is noted for her radically experimental and fragmented poetic structures that disallow any smooth assumptions regarding the text, meaning, and history. Combining fragments of historical documents with memories and typographic experiments, Howe's works offer rich opportunities for multidisciplinary inquiry. Titled “From Fragment to Form: Multidisciplinary Insights in Susan Howe’s Poetry,” this paper proposes to read Howe's poetry by way of literary theory, Derridean grammatology, history, and cultural studies, as an act that illustrates how her recursive fragmentation of text peaks multiple layers of meaning. Howe with special attention to the interaction of form and content, the use of historical material, and the breakdown of linear narrative. Under the domain of Derrida's grammatology, the paper conceives Howe's deconstruction of language. Through a qualitative and interpretive study, the paper attempts the analysis of selected works of age as writing itself being the site for the creation of meaning. Besides, from a multidisciplinary standpoint, this paper illuminates how insights from literature, philosophy, and history intermesh, revealing the depth and complexity of her texts. This research argues that Howe’s poetry is not merely a literary experiment but a cultural and historical exploration; fragments become tools for reconstructing memory and interrogating the past. Further on, the study describes how the innovative use of typography, spatial configurations, and non-linear narratives demands that the reader actively participate in creating meaning. Bridging disciplinary boundaries, this paper argues that contemporary literary studies indeed are open to incorporating a variety of analytical lenses, thus supporting a truly holistic approach in the reading of a poetic text. The findings highlight the importance of multidisciplinary approaches in literary research and promote the adoption of philosophical, historical, and cultural approaches to experimental poetry. This study offers new insight for the rising debate in contemporary poetics, Derridean theory, and interdisciplinary literary criticism, reinforcing the ongoing importance of Howe's work for understanding the link of text to form and meaning.

Abstract Motivated by the broad applications of wave propagation in non-uniform and time-varying environments, such as in acoustics, elasticity, and seismology, we investigate the controllability of degenerate wave equations with time-dependent wave speeds. In this work, we examine non-autonomous degenerate wave equations in a one-dimensional spatial domain, addressing both divergence and non-divergence forms. A control function is applied at the non-degeneracy boundary point, while Dirichlet or Neumann conditions are imposed at the degeneracy one. Using the generalized energy conservation law, we first establish boundary observability for the homogeneous problem, a key step in our analysis. Building on this, we prove the null-controllability of the non-autonomous degenerate wave systems. To achieve this, we construct solutions using the transposition method, which accommodates low regularity requirements, enabling us to handle weaker smoothness assumptions while maintaining rigorous control over the system’s behavior. We conclude by presenting some insightful observations and potential avenues for future work, which could further advance the understanding of this problem.