General Problem Research Articles

The time-dependent harmonic oscillator revisited

Abstract We point out a rather effective approach for solving the time-dependent harmonic oscillator q ¨ = − ω 2 q under various regularity assumptions. Where ω ( t ) is C 1 this is reduced to Hamilton equation for the angle variable ψ alone (the action variable I is obtained by quadrature). The fixed point theorem for the integral equation equivalent to the generic Cauchy problem for ψ ( t ) yields a sequence { ψ ( h ) } h ∈ N 0 converging to ψ rather fast; if ω varies slowly or little, already ψ ( 0 ) approximates ψ well for rather long time lapses. The discontinuities of ω, if any, determine those of ψ , I . The zeros of q , q ˙ are investigated via Riccati equations. Our approach may simplify the study of: upper and lower bounds on the solutions; the stability of the trivial one; parametric resonance when ω ( t ) is periodic; the adiabatic invariance of I ; asymptotic expansions in a slow time parameter ɛ; time-dependent driven and damped parametric oscillators; etc.

Improving the Solving of Optimization Problems: A Comprehensive Review of Quantum Approaches

Optimization is a crucial challenge across various domains, including finance, resource allocation, and mobility. Quantum computing has the potential to redefine the way we handle complex problems by reducing computational complexity and enhancing solution quality. Optimization, particularly of objective functions, stands to benefit significantly from quantum solvers, which leverage principles of quantum mechanics like superposition, entanglement, and tunneling. The Ising and Quadratic Unconstrained Binary Optimization (QUBO) models are the most suitable formulations for these solvers, involving binary variables and constraints treated as penalties within the overall objective function. To harness quantum approaches for optimization, two primary strategies are employed: exploiting quantum annealers—special-purpose optimization devices—and designing algorithms based on quantum circuits. This review provides a comprehensive overview of quantum optimization methods, examining their advantages, challenges, and limitations. It demonstrates their application to real-world scenarios and outlines the steps to convert generic optimization problems into quantum-compliant models. Lastly, it discusses available tools and frameworks that facilitate the exploration of quantum solutions for optimization tasks.

A stochastic primal-dual splitting algorithm with variance reduction for composite optimization problems

This paper revisits the generic structured primal-dual problem involving the infimal convolution in real Hilbert spaces. For this purpose, we develop a stochastic primal-dual splitting with variance reduced for solving this generic problem. Weak almost sure convergence of the iterates is proved. The linear convergence rate of the primal-dual gap is obtained under an additional condition like the strong convexity.

Enhanced detection of tomato leaf diseases using ensemble deep learning: INCVX-NET model

<p align="justify"><span lang="EN-US">Automated leaf disease detection quickly identifies early symptoms, and saves time on large farms. Traditional methods like visual inspection and laboratory detection are prevalent despite being labor-intensive, time-consuming, and susceptible to human error. Recently, deep learning (DL) has emerged as a promising alternative for crop disease recognition. However, these models usually demand extensive training data and face problems in generalization due to the diverse features among different crop diseases. This complexity makes it difficult to achieve optimal recognition performance across all scenarios. To solve this issue, a novel ensemble approach INCVX-Net is proposed to integrate the three DL models, ‘Inception, visual geometry group (VGG)-16, and Xception’ using weighted averaging ensemble for tomato crop leaf disease detection. This approach utilizes the strengths of three DL models to recognize a wide range of disease patterns and captures even slight changes in leaf characteristics. INCVX-Net achieves an impressive 99.5% accuracy in disease detection, outperforming base models such as InceptionV2 (93.4%), VGG-16 Net (92.7%), and Xception (95.2%). This significant leap in accuracy demonstrates the growing power of ensemble DL models in disease detection compared to standalone DL models. The research paves the groundwork for future advancements in disease detection, enhancing precision agriculture through ensemble models.</span></p>

Identification of subwavelength microstructural information from macroscopic boundary measurements in elastodynamics

We present a method to obtain microstructural information from macroscopic boundary measurements exploiting scattering governed by the wave equation in a bounded linearly elastic domain in the long-wavelength regime. Applying a force to the outer boundary of the body on the macroscopic scale while measuring the resulting boundary displacement, we solve the inverse problem of identifying the geometry of the microstructure in the context of periodic homogenization minimizing a tracking-type objective functional as long as the geometry of the microstructure is parameterized by a finite set of parameters. Shape calculus is used to characterize the Gâteaux derivative of the objective function facilitating the use of gradient-based algorithms, and we present numerical experiments for a generic non-destructive testing problem for ellipsoidal microstructures showcasing the functioning of the identification method.

Eigenvalues of Toeplitz matrices emerging from finite differences for certain ordinary differential operators

Eigenvalues of Toeplitz matrices emerging from finite differences for certain ordinary differential operators

Unsupervised Domain-Adaptive Object Detection via Localization Regression Alignment.

Unsupervised domain-adaptive object detection uses labeled source domain data and unlabeled target domain data to alleviate the domain shift and reduce the dependence on the target domain data labels. For object detection, the features responsible for classification and localization are different. However, the existing methods basically only consider classification alignment, which is not conducive to cross-domain localization. To address this issue, in this article, we focus on the alignment of localization regression in domain-adaptive object detection and propose a novel localization regression alignment (LRA) method. The idea is that the domain-adaptive localization regression problem can be transformed into a general domain-adaptive classification problem first, and then adversarial learning is applied to the converted classification problem. Specifically, LRA first discretizes the continuous regression space, and the discrete regression intervals are treated as bins. Then, a novel binwise alignment (BA) strategy is proposed through adversarial learning. BA can further contribute to the overall cross-domain feature alignment for object detection. Extensive experiments are conducted on different detectors in various scenarios, and the state-of-the-art performance is achieved; these results demonstrate the effectiveness of our method. The code will be available at: https://github.com/zqpiao/LRA.

Analyzing Robustness of Automatic Scientific Claim Verification Tools against Adversarial Rephrasing Attacks

The coronavirus pandemic has fostered an explosion of misinformation about the disease, including the risk and effectiveness of vaccination. AI tools for automatic Scientific Claim Verification (SCV) can be crucial to defeat misinformation campaigns spreading through social media channels. However, over the past years, many concerns have been raised about the robustness of AI to adversarial attacks, and the field of automatic SCV is not exempt. The risk is that such SCV tools may reinforce and legitimize the spread of fake scientific claims rather than refute them. This article investigates the problem of generating adversarial attacks for SCV tools and shows that it is far more difficult than the generic NLP adversarial attack problem. The current NLP adversarial attack generators, when applied to SCV, often generate modified claims with entirely different meaning from the original. Even when the meaning is preserved, the modification of the generated claim is too simplistic (only a single word is changed), leaving many weaknesses of the SCV tools undiscovered. We propose T5-ParEvo, an iterative evolutionary attack generator, that is able to generate more complex and creative attacks while better preserving the semantics of the original claim. Using detailed quantitative and qualitative analyses, we demonstrate the efficacy of T5-ParEvo in comparison with existing attack generators.

Slab assignment to non-identical reheat furnaces running in parallel mode

This article analyses a slab assignment problem for non-identical reheat furnaces in the steelmaking industry. We tackle the problem of assigning slabs to different types of reheat furnaces, a walking beam and a pusher type furnace. Furthermore, we need to determine the feed-in as well as the residence time for each slab. The aim is to (i) reduce the energy consumption, (ii) increase the production rate and (iii) the heating quality of the slabs which depends on the assigned furnace and to what extent the slabs are overheated. Moreover, the subsequent production stage (Hot Rolling Mill), needs to be synchronized with the furnaces which is essential for a smooth production. We specify the problem as a mixed integer optimization formulation that is solved with iterative parameter adjustment. Rapid convergence leads to a novel two-phase solution method that yields furnace schedules that are optimal for the adjusted parameter values in reasonable time. The results show that our proposed method performs better than an industry benchmark by increasing the production rate and increasing the reheating quality. Furthermore, the new generic problem formulation allows using standard software and can be applied to identical or non-identical furnaces highlighting its broad applicability across steel-making companies.

Dynamic and modal analysis of nearly incompressible structures with stabilised displacement-volumetric strain formulations

Dynamic and modal analysis of nearly incompressible structures with stabilised displacement-volumetric strain formulations

Multi-core interference over-estimation reduction by static scheduling of multi-phase tasks

Interference between tasks running on separate cores in multi-core processors is a major challenge to predictability for real-time systems, and a source of over-estimation of worst-case execution duration bounds. This paper investigates how the multi-phase task model can be used together with static scheduling algorithms to improve the precision of the interference analysis. The paper focuses on single-period task systems (or multi-periodic systems that can be expanded over an hyperperiod). In particular, we propose an Integer Linear Programming (ILP) formulation of a generic scheduling problem as well as 3 heuristics that we evaluate on synthetic benchmarks and on 2 realistic applications. We observe that, compared to the classical 1-phase model, the multi-phase model allows to reduce the effect of interference on the worst-case makespan of the system by around 9% on average using the ILP on small systems, and up to 24% on our larger case studies. These results pave the way for future heuristics and for the adoption of the multi-phase model in multi-core context.

Towards Understanding Convergence and Generalization of AdamW.

AdamW modifies Adam by adding a decoupled weight decay to decay network weights per training iteration. For adaptive algorithms, this decoupled weight decay does not affect specific optimization steps, and differs from the widely used l2-regularizer which changes optimization steps via changing the first- and second-order gradient moments. Despite its great practical success, for AdamW, its convergence behavior and generalization improvement over Adam and l2-regularized Adam ( l2-Adam) remain absent yet. To solve this issue, we prove the convergence of AdamW and justify its generalization advantages over Adam and l2-Adam. Specifically, AdamW provably converges but minimizes a dynamically regularized loss that combines vanilla loss and a dynamical regularization induced by decoupled weight decay, thus yielding different behaviors with Adam and l2-Adam. Moreover, on both general nonconvex problems and PŁ-conditioned problems, we establish stochastic gradient complexity of AdamW to find a stationary point. Such complexity is also applicable to Adam and l2-Adam, and improves their previously known complexity, especially for over-parametrized networks. Besides, we prove that AdamW enjoys smaller generalization errors than Adam and l2-Adam from the Bayesian posterior aspect. This result, for the first time, explicitly reveals the benefits of decoupled weight decay in AdamW. Experimental results validate our theory.

Can items derived from international literature be used in national quality of life instruments? A qualitative study conceptualising the EQ-HWB in China

IntroductionThe EQ Health and Wellbeing (EQ-HWB) is a new questionnaire for measuring quality of life (QoL) from a broad perspective. The items of the EQ-HWB were derived based on a ‘qualitative review’ of literature, which reported primarily on Western studies. It can be argued that the QoL is a cultural-related concept and therefore people from China have a different understanding of the QoL. This study aimed to explore whether Chinese citizens could understand the EQ-HWB’s candidate items and what they thought of those items. In doing so, we wanted to examine the face validity of the candidate items and explore if further cultural adaptation is necessary.MethodsThis research was part of the E-QALY project, in which 36 candidate items were selected for the EQ-HWB from a 97-item pool. In China, three interviewers investigated the face validity of these EQ-HWB candidate items in semi-structured qualitative face-to-face interviews. Respondents were invited to report ‘problems’ with regard to the interpretation of the items and these problems were grouped into themes. We explored to what extent those themes related to specific cultural aspects in China. We also classified the rates of reported problems for each item into three groups: 1) less than 20%, 2) from 20–50%, and 3) over 50%.ResultsFor 17 items the rate of reported problems was less than 20%, 15 items fell into the second group (with 20 − 50%) and for 4 items the rate of problems reported was more than 50%. The thematic analysis revealed eight themes: ambiguous problems in the interpretation of 16 items; difficult to understand (11); contained a complex negative expression (10); examples used seemed inappropriate (7); misleading connotation in Chinese (2); long and complex (2); complex response options (1); and use of non-colloquial language (1).DiscussionOur research shows that EQ-HWB candidate items require careful examination to make them more comprehensible. Most of the reported problem themes were generic problems related to the items, and only a few face validity issues appeared to relate to specific cultural aspects in China, even though most of the items were based on Western studies. Our findings are reassuring for the instrument’s international application, especially in China.

Source-Free Domain Adaptation With Domain Generalized Pretraining for Face Anti-Spoofing.

Source-free domain adaptation (SFDA) shows the potential to improve the generalizability of deep learning-based face anti-spoofing (FAS) while preserving the privacy and security of sensitive human faces. However, existing SFDA methods are significantly degraded without accessing source data due to the inability to mitigate domain and identity bias in FAS. In this paper, we propose a novel Source-free Domain Adaptation framework for FAS (SDA-FAS) that systematically addresses the challenges of source model pre-training, source knowledge adaptation, and target data exploration under the source-free setting. Specifically, we develop a generalized method for source model pre-training that leverages a causality-inspired PatchMix data augmentation to diminish domain bias and designs the patch-wise contrastive loss to alleviate identity bias. For source knowledge adaptation, we propose a contrastive domain alignment module to align conditional distribution across domains with a theoretical equivalence to adaptation based on source data. Furthermore, target data exploration is achieved via self-supervised learning with patch shuffle augmentation to identify unseen attack types, which is ignored in existing SFDA methods. To our best knowledge, this paper provides the first full-stack privacy-preserving framework to address the generalization problem in FAS. Extensive experiments on nineteen cross-dataset scenarios show our framework considerably outperforms state-of-the-art methods.

PPSO and Bayesian game for intrusion detection in WSN from a macro perspective

The security of wireless sensor networks is a hot topic in current research. Game theory can provide the optimal selection strategy for attackers and defenders in the attack-defense confrontation. Aiming at the problem of poor generality of previous game models, we propose a generalized Bayesian game model to analyze the intrusion detection of nodes in wireless sensor networks. Because it is difficult to solve the Nash equilibrium of the Bayesian game by the traditional method, a parallel particle swarm optimization is proposed to solve the Nash equilibrium of the Bayesian game and analyze the optimal action of the defender. The simulation results show the superiority of the parallel particle swarm optimization compared with other heuristic algorithms. This algorithm is proved to be effective in finding optimal defense strategy. The influence of the detection rate and false alarm rate of nodes on the profit of defender is analyzed by simulation experiments. Simulation experiments show that the profit of defender decreases as false alarm rate increases and decreases as detection rate decreases. Using heuristic algorithm to solve Nash equilibrium of Bayesian game provides a new method for the research of attack-defense confrontation. Predicting the actions of attacker and defender through the game model can provide ideas for the defender to take active defense.

A general solution to the quasi linear screening problem

A general solution to the quasi linear screening problem

On the accuracy of Prony's method for recovery of exponential sums with closely spaced exponents

On the accuracy of Prony's method for recovery of exponential sums with closely spaced exponents

Insights and future research directions from a bibliometric mapping of studies in stope layout optimisation

ABSTRACT Stope layout optimisation is an important sub-problem of the generic underground mining optimisation problem that contributes towards optimal ore extraction. It is a growing research area as some surface mines transition from open-pit to underground mining. Several researchers acknowledge the complexity of optimising underground mine layouts because exact methods are limited in generating three-dimensional optimal solutions, hence the growing use of metaheuristic approaches to solve the problem in three dimensions. This paper presents a PRISMA-based bibliometric mapping of stope layout optimisation approaches using R-Biblioshiny and VOSviewer software, their concomitant limitations, and suggests potential future research directions in stope layout optimisation.

Physicist's view on the unbalanced k-cardinality assignment problem.

The k-cardinality unbalanced assignment problem asks for assigning k "agents" to k "tasks" on a one-to-one basis, while minimizing the total cost associated with the assignment, with the total number of agents N and the total number of tasks M possibly different and larger than k. While many exact algorithms have been proposed to find such an optimal assignment, these methods are computationally prohibitive when the problem is large. We propose an approach to solving the k-cardinality assignment problem using techniques adapted from statistical physics. This paper provides a full description of this formalism, including all the proofs of its main claims. We derive a strongly concave free-energy function that captures the constraints of the k-assignment problem at a finite temperature. We prove that this free energy decreases monotonically as a function of β, the inverse of temperature, to the optimal assignment cost, providing a robust framework for temperature annealing. We also prove that for large enough β values the exact solution to the k-assignment problem can be derived using simple round-off to the nearest integer of the elements of the computed assignment matrix. We show that this framework can be adapted to handle degenerate k-assignment problems. We describe a computer implementation of our framework that is optimized for the GPU parallel architecture, using the library CUDA. This implementation is found to be as efficient as state-of-the-art implementations of parallel Hungarian algorithms on generic assignment problems, and orders of magnitude faster than those algorithms for pathological assignment cases.

Learnable Graph Matching: A Practical Paradigm for Data Association.

Data association is at the core of many computer vision tasks, e.g., multiple object tracking, image matching, and point cloud registration. however, current data association solutions have some defects: they mostly ignore the intra-view context information; besides, they either train deep association models in an end-to-end way and hardly utilize the advantage of optimization-based assignment methods, or only use an off-the-shelf neural network to extract features. In this paper, we propose a general learnable graph matching method to address these issues. Especially, we model the intra-view relationships as an undirected graph. Then data association turns into a general graph matching problem between graphs. Furthermore, to make optimization end-to-end differentiable, we relax the original graph matching problem into continuous quadratic programming and then incorporate training into a deep graph neural network with KKT conditions and implicit function theorem. In MOT task, our method achieves state-of-the-art performance on several MOT datasets. For image matching, our method outperforms state-of-the-art methods on a popular indoor dataset, ScanNet. For point cloud registration, we also achieve competitive results.