Hasil untuk "Mathematics"

Claudia Scheimbauer

This lecture covers several basic methods for standard tasks in data analysis and image processing. A non-exclusive and non-exhaustive list of meth-ods: histograms, dimension reduction, clustering, filters, frequency analysis, morphological methods. . . We will develop the mathematical theory that underlies these methods which is the basis for thorough understanding and proper execution of the method. Moreover, we will deal with the practical implementation of the methods and apply them to solve problems such as image denoising, image deblurring, or music identification. This lecture should enable you to take a deeper dive into image and data analysis and prepares you to follow recent developments in the field. If you want to understand the inner working of image compression with JPEG or music recognition with tools like Shazam, come to this lecture!

A. Broder, M. Mitzenmacher

A. Kaufmann, R. Faure, Henry C. Sneyd

Martin D. Davis, H. Putnam

R. Moore

M. Stein, B. Grover, M. Henningsen

H. Weitzner, Julian D. Cole

A. M. Mutawa, Khalid Sabti, Bibin Shalini Sundaram Thankaleela et al.

Diabetic macular edema (DME) is a primary contributor to visual impairment in diabetic patients, necessitating precise and prompt analysis for optimal treatment. Recent breakthroughs in deep learning (DL) and machine learning (ML) have yielded promising outcomes in ophthalmic image analysis. However, researchers often overlook the significance of optimization algorithms in enhancing the efficacy of their models for DME-related tasks. This review aims to consolidate, seek, discover, assess, and integrate existing work on the application of DL and ML, with emphasis on the integration and impact of optimization algorithms in enhancing their efficacy, robustness, and performance for DME in the fields of computer science and engineering. The population, intervention, comparison, and outcome framework was employed in this study to facilitate a clear and comprehensive analysis. The procedural superiority of the included investigations was evaluated using the Joanna Briggs Institute Critical Appraisal Tools for assessing methodological quality. The Auto-Metric Graph Neural Network achieved the greatest accuracy of 99.57% for combined diabetic retinopathy-DME grading, illustrating the higher efficacy of hybrid architectures augmented by meta-heuristic optimizers, such as Jaya and ant colony optimization. Successful deployment, however, depends on overcoming hurdles, such as the low mean average precision in lesion identification (0.1540) in YOLO-based models in the test set performance, and improved clinical interpretability to foster clinician trust. A Sankey diagram visually analyzes the flow of quantities between different entities of the survey.Systematic review registrationB. (2025, November 2). A Review of Optimization Strategies for Deep and Machine Learning in DME. Retrieved from osf.io/qsh4j.

Ming Han, Ge Sun, Paul F. Nealey et al.

Abstract Machine learning (ML) offers considerable promise for the design of new molecules and materials. In real-world applications, the design problem is often domain-specific, and suffers from insufficient data, particularly labeled data, for ML training. In this study, we report a data-efficient, deep-learning framework for molecular discovery that integrates a coarse-grained functional-group representation with a self-attention mechanism to capture intricate chemical interactions. Our approach exploits group-contribution concepts to create a graph-based intermediate representation of molecules, serving as a low-dimensional embedding that substantially reduces the data demands typically required for training. Using a self-attention mechanism to learn the subtle but highly relevant chemical context of functional groups, the method proposed here consistently outperforms existing approaches for predictions of multiple thermophysical properties. In a case study focused on adhesive polymer monomers, we train on a limited dataset comprising only 6,000 unlabeled and 600 labeled monomers. The resulting chemistry prediction model achieves over 92% accuracy in forecasting properties directly from SMILES strings, exceeding the performance of current state-of-the-art techniques. Furthermore, the latent molecular embedding is invertible, enabling the design pipeline to automatically generate new monomers from the learned chemical subspace. We illustrate this functionality by targeting several properties, including high and low glass transition temperatures (Tg), and demonstrate that our model can identify new candidates with values that surpass those in the training set. The ease with which the proposed framework navigates both chemical diversity and data scarcity offers a promising route to accelerate and broaden the search for functional materials.

Maria J. Esteban

The fundamental role of mathematics as an inspiration for artists, but also as a tool for art creation, is presented in this paper following different art fields, like architecture, sculpture, painting, photography, literature and poetry, movie making and music. The historical viewpoint is completed with recent applications of mathematics to create art in the digital era. Finally, the article contains a discussion about the possibility of the mathematical creation being considered artistic.

Franziska Böhnlein, Benjamin Bruske, Sven-Ake Wegner

In their 2022 lecture notes on condensed sets, Clausen and Scholze mentioned in a remark that the important subclass of quasiseparated condensed sets is equivalent to the category of so-called compactological spaces defined by Waelbroeck in the 1960s. In this paper we survey the latter category in detail, we give a rigorous proof of Clausen and Scholze's claim, and we establish that condensed sets are a formal categorical completion of Waelbroeck's compactological spaces. The latter answers a question asked by Hanson in 2023 and permits the interpretation of compactological sets as an 'elementary' approach to condensed mathematics.

H. M. Roberts, D. Stockton

Gabriel Nicolae Popa, Corina Maria Diniș

Among many other applications, electronic converters can be used with sensors with analogue outputs (DC voltage). This article presents an analogue computation converter with two DC voltages at the inputs (one input changes the frequency of the output signal, another input changes the amplitude of the output signal) that provide a periodic sinusoidal signal (with variable frequency and amplitude) at the output. On the basis of the analogue computation converter is a nonhomogeneous second-order linear ordinary differential equation which is solved analogically. The analogue computation converter consists of analogue multipliers and operational amplifiers, composed of seven function circuits: two analogue multiplication circuits, two analogue addition circuits, one non-inverting amplifier, and two integration circuits (with RC time constants). At the output of an oscillator is a sinusoidal signal which depends on the DC voltages applied on two inputs (0 ÷ 10 V): at one input, a DC voltage is applied to linearly change the sinusoidal frequency output (up to tens of kHz, according to two time constants), and at the other input, a DC voltage is applied to linearly change the amplitude of the oscillator output signal (up to 10 V). It can be used with sensors which have a DC output voltage and must be converted to a sine wave signal with variable frequency and amplitude with the aim of transmitting information over longer distances through wires. This article presents the detailed theory of the functioning, simulations, and experiments of the analogue computation converter.

Pablo Sala, Sara Murciano, Yue Liu et al.

Entanglement, measurement, and classical communication together enable teleportation of quantum states between distant parties, in principle, with perfect fidelity. To what extent do correlations and entanglement of a many-body wave function transfer under imperfect teleportation protocols? We address this question for the case of an imperfectly teleported quantum critical wave function, focusing on the ground state of a critical Ising chain. We demonstrate that imperfections, e.g., in the entangling gate adopted for a given protocol, effectively manifest as weak measurements acting on the otherwise pristinely teleported critical state. Armed with this perspective, we leverage and further develop the theory of measurement-altered quantum criticality to quantify the resilience of critical-state teleportation. We identify classes of teleportation protocols for which imperfection (i) preserves both the universal long-range entanglement and correlations of the original quantum critical state, (ii) weakly modifies these quantities away from their universal values, and (iii) obliterates long-range entanglement altogether while preserving power-law correlations, albeit with a new set of exponents. We also show that mixed states describing the average over a series of sequential imperfect teleportation events retain pristine power-law correlations due to a “built-in” decoding algorithm, though their entanglement structure measured by the negativity depends on errors similarly to individual protocol runs. These results may allow one to design teleportation protocols that optimize against errors—highlighting a potential practical application of measurement-altered criticality.

Roberta Coletti, Mónica Leiria de Mendonça, Susana Vinga et al.

Tumor heterogeneity is a challenge to designing effective and targeted therapies. Glioma-type identification depends on specific molecular and histological features, which are defined by the official World Health Organization (WHO) classification of the central nervous system (CNS). These guidelines are constantly updated to support the diagnosis process, which affects all the successive clinical decisions. In this context, the search for new potential diagnostic and prognostic targets, characteristic of each glioma type, is crucial to support the development of novel therapies. Based on The Cancer Genome Atlas (TCGA) glioma RNA-sequencing data set updated according to the 2016 and 2021 WHO guidelines, we proposed a 2-step variable selection approach for biomarker discovery. Our framework encompasses the graphical lasso algorithm to estimate sparse networks of genes carrying diagnostic information. These networks are then used as input for regularized Cox survival regression model, allowing the identification of a smaller subset of genes with prognostic value. In each step, the results derived from the 2016 and 2021 classes were discussed and compared. For both WHO glioma classifications, our analysis identifies potential biomarkers, characteristic of each glioma type. Yet, better results were obtained for the WHO CNS classification in 2021, thereby supporting recent efforts to include molecular data on glioma classification.

MingHui Zhong, YePing Zhou

Abstract With the rapid development of information technology, new educational models using virtual reality technology have received widespread attention from relevant researchers. In the field of vocational education, vocational colleges and training institutions can effectively mobilize students' learning initiative and improve their learning efficiency by using virtual reality technology. This study details the development process and system evaluation of a bespoke virtual reality system that offers a solution to the issues of uncertainty regarding hazards, high teaching expenses, and spatial constraints inherent in the practical training of elevator maintenance. By establishing a virtual environment that is highly reproducible and designing abundant interaction methods, this system facilitates students in attaining mastery over the structural make‐up of elevators, the principles of their operation, and the techniques involved in calibrating elevator governors. The system underwent testing by multiple users, and the satisfaction level of the system was ascertained through a questionnaire study, while the effectiveness of the system was evaluated using independent samples t test for data statistics concerning students' performance. The results of the study indicate that the system gained widespread praise among users, and it notably enhanced the students' learning drive, practical abilities, and on‐site adaptability.

Michel Caffarel, Pierre del Moral, Luc de Montella

The Diffusion Monte Carlo method with constant number of walkers, also called Stochastic Reconfiguration as well as Sequential Monte Carlo, is a widely used Monte Carlo methodology for computing the ground-state energy and wave function of quantum systems. In this study, we present the first mathematically rigorous analysis of this class of stochastic methods on non necessarily compact state spaces, including linear diffusions evolving in quadratic absorbing potentials, yielding what seems to be the first result of this type for this class of models. We present a novel and general mathematical framework with easily checked Lyapunov stability conditions that ensure the uniform-in-time convergence of Diffusion Monte Carlo estimates towards the top of the spectrum of Schrödinger operators. For transient free evolutions, we also present a divergence blow up of the estimates w.r.t. the time horizon even when the asymptotic fluctuation variances are uniformly bounded. We also illustrate the impact of these results in the context of generalized coupled quantum harmonic oscillators with non necessarily reversible nor stable diffusive particle and a quadratic energy absorbing well associated with a semi-definite positive matrix force.

D. Touretzky

Rattanakorn Wattanataweekul, Kobkoon Janngam

Abstract In this paper, we define a new concept of left and right coordinate affine of a directed graph and then employ it to introduce a new accelerated common fixed point algorithm for a countable family of G-nonexpansive mappings in a real Hilbert space with a graph. We prove, under certain conditions, weak convergence theorems for the proposed algorithm. As applications, we also apply our results to solve convex minimization and image restoration problems. Moreover, we show that our algorithm provides better convergence behavior than other methods in the literature.

Nikolay Chepachenko, Marina Yudenko, Anna Gospodinova et al.

The current trend of globalization of the world economy necessitates the use of high-tech developments and innovations that allow achieving strategic goals at the national, regional, and sectoral levels. The prerequisites of the study are determined by the urgency of finding solutions to problematic issues of formation and implementation of priority strategic guidelines for the development of enterprises of the construction sector, designed to ensure an adequate contribution to the strategic vector of advanced industrial, technological and socio-economic development of the construction industry and the national economy. This determines the need to find a solution to the problem of forming and implementing priority strategic guidelines for the development of enterprises mainly by increasing technological and innovative potentials that form the economic potential of the development of enterprises by the type of activity "Construction". The purpose of the study is to identify strategic guidelines for the development of enterprises of the construction sector that meet the targets of the fourth scientific and technological revolution and the achievement of strategic goals for the development of national economies. The findings of the paper outline the key signs of development, inherent in the nature of the development of material objects and economic entities of the economy are revealed. This allowed us to propose a systematization of the formation of priority strategic guidelines for the economic development of construction enterprises, reflecting the relationship with the targets for achieving national goals and strategic objectives for the development of economies of various countries and meeting the targets of the fourth scientific and technological revolution Industry 4.0. The practical implications refer to enterprises of the construction sector.