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(ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image).In this paper we study general ... regularized unconstrained minimization problems. In particular, we derive lower bounds for nonzero entries of the first- and second-order stationary points and hence also of local minimizers of the ... minimization problems. We extend some existing iterative reweighted ... (...) and ... (...) minimization methods to solve these problems and propose new variants for them in which each subproblem has a closed-form solution. Also, we provide a unified convergence analysis for these methods. In addition, we propose a novel Lipschitz continuous ...-approximation to ... Using this result, we develop new ... methods for the ... minimization problems and show that any accumulation point of the sequence generated by these methods is a first-order stationary point, provided that the approximation parameter ... is below a computable threshold value. This is a remarkable result since all existing iterative reweighted minimization methods require that ... be dynamically updated and approach zero. Our computational results demonstrate that the new ... method and the new variants generally outperform the existing ... methods (Chen and Zhou in 2012; Foucart and Lai in Appl Comput Harmon Anal 26:395-407, 2009).

With the advent and advancement of machine learning and deep learning techniques, machine-based recognition systems for mathematical text have captivated the attention of the research community for the last four decades. Mathematical Expression Recognition systems have been identified based on terms of their techniques, approach, dataset, and accuracies. This study majorly targets a rigorous review of both the published form of literature and the least attended literature, i.e., grey literature. Apart from the digital libraries, the papers and other instances of information have been gathered from the grey sources like google patents, archives, technical reports, app stores, etc., culminating in 262 instances. After the heedful filtration imposed on both white and grey literature, the final pool of studies has been investigated for eight formulated research questions. The answers extracted have been analyzed, providing both quantitative and qualitative insights. The analysis and surveys have systematically summed up the potentials of both white and grey shades of literature present on MER and brought exciting extractions out of 155 formal white literature and 107 grey sources. The survey extracts and brings out the highlighting observations after analysis, which sublimates the fact that 52% of grey literature is composed of mobile applications and user interfaces, whereas the published 63% of white data is presently concentrated in 39 different conferences, and the prominent conference is ICDAR (#30). A list of challenges and open issues has been extracted for directing future research dimensions.

Tools based on machine learning (ML) have seen widespread application in the prediction and categorization of mathematical symbols and phrases. The purpose of this work is to conduct a comprehensive analysis of the machine learning and non-machine learning strategies that are currently in use for the recognition of mathematical expressions. (MEs). The authors collected and analyzed research studies on the recognition of MEs (and closely related models and issues as well), which are published from January 2000 to December 2022 in the SLR. The review has nominated 98 primary studies out of the extracted 202 studies after heedful filtering using inclusion/exclusion criteria and quality assessment. The pertinent data is derived from IEEE explore, Science Direct, Wiley, Scopus, ACM Digital Library, etc. For assiduously reviewing and synthesizing the data, the authors used grounded theory and other qualitative and quantitative techniques. The analysis reveals that the support vector machine as an ML model with CROHME as the dataset and expression recognition rate as an accuracy metric is frequently used in the chosen studies. Recognition is typically fragmented down into three stages—segmenting symbols, recognizing symbols, and analyzing structures—in non-ML studies. In conclusion, this work aims to synthesize the results of existing research to provide a summary of the state-of-the-art in recognizing handwritten MEs.

In this paper, we extend the notions of ( Φ , ρ ) -invexity and generalized ( Φ , ρ ) -invexity to the continuous case and we use these concepts to establish sufficient optimality conditions for the considered class of nonconvex multiobjective variational control problems. Further, multiobjective variational control mixed dual problem is given for the considered multiobjective variational control problem and several mixed duality results are established under ( Φ , ρ ) -invexity.

General high-order rogue waves in the nonlinear Schrödinger equation are derived by the bilinear method. These rogue waves are given in terms of determinants whose matrix elements have simple algebraic expressions. It is shown that the general N-th order rogue waves contain N−1 free irreducible complex parameters. In addition, the specific rogue waves obtained by Akhmediev et al. (Akhmediev et al. 2009 Phys. Rev. E 80, 026601 (doi:10.1103/PhysRevE.80.026601)) correspond to special choices of these free parameters, and they have the highest peak amplitudes among all rogue waves of the same order. If other values of these free parameters are taken, however, these general rogue waves can exhibit other solution dynamics such as arrays of fundamental rogue waves arising at different times and spatial positions and forming interesting patterns.

The closed-cycle dilution refrigerator for space applications is an on-going development to improve the performance of the open-cycle dilution refrigerator successfully used on the Planck mission. This solution has been considered in various projects in X-ray and far-infrared space instruments for astrophysics (ATHENA, SPICA) and in advanced studies for future CMB polarization surveys (COrE). It is shown that for sub-Kelvin applications, this refrigerator is fully competitive with some ADR-based solutions. Compared to ADR, the main advantages are (1) a stable cooling power adapted to long uninterrupted sky surveys (2) a low mass of the coldest stages (3) the absence of magnetic field. We present the current status of the development and discuss the options for the 3 He compressor.

For centuries, scientists have attempted to identify and document analytical laws that underlie physical phenomena in nature. Despite the prevalence of computing power, the process of finding natural laws and their corresponding equations has resisted automation. A key challenge to finding analytic relations automatically is defining algorithmically what makes a correlation in observed data important and insightful. We propose a principle for the identification of nontriviality. We demonstrated this approach by automatically searching motion-tracking data captured from various physical systems, ranging from simple harmonic oscillators to chaotic double-pendula. Without any prior knowledge about physics, kinematics, or geometry, the algorithm discovered Hamiltonians, Lagrangians, and other laws of geometric and momentum conservation. The discovery rate accelerated as laws found for simpler systems were used to bootstrap explanations for more complex systems, gradually uncovering the \"alphabet\" used to describe those systems.

The modal view in the cognitive and neural sciences holds that consciousness is necessary for abstract, symbolic, and rule-following computations. Hence, semantic processing of multiple-word expressions, and performing of abstract mathematical computations, are widely believed to require consciousness. We report a series of experiments in which we show that multiple-word verbal expressions can be processed outside conscious awareness and that multistep, effortful arithmetic equations can be solved unconsciously. All experiments used Continuous Flash Suppression to render stimuli invisible for relatively long durations (up to 2,000 ms). Where appropriate, unawareness was verified using both objective and subjective measures. The results show that novel word combinations, in the form of expressions that contain semantic violations, become conscious before expressions that do not contain semantic violations, that the more negative a verbal expression is, the more quickly it becomes conscious, and that subliminal arithmetic equations prime their results. These findings call for a significant update of our view of conscious and unconscious processes.

Large models have recently played a dominant role in natural language processing and multimodal vision-language learning. However, their effectiveness in text-related visual tasks remains relatively unexplored. In this paper, we conducted a comprehensive evaluation of large multimodal models, such as GPT4V and Gemini, in various text-related visual tasks including text recognition, scene text-centric visual question answering (VQA), document-oriented VQA, key information extraction (KIE), and handwritten mathematical expression recognition (HMER). To facilitate the assessment of optical character recognition (OCR) capabilities in large multimodal models, we propose OCRBench, a comprehensive evaluation benchmark. OCRBench contains 29 datasets, making it the most comprehensive OCR evaluation benchmark available. Furthermore, our study reveals both the strengths and weaknesses of these models, particularly in handling multilingual text, handwritten text, non-semantic text, and mathematical expression recognition. Most importantly, the baseline results presented in this study could provide a foundational framework for the conception and assessment of innovative strategies targeted at enhancing zero-shot multimodal techniques. The evaluation pipeline and benchmark are available at https://github.com/Yuliang-Liu/MultimodalOCR .