Hasil untuk "Applied mathematics. Quantitative methods"

Yuqi Si, Jingcheng Du, Zhao Li et al.

OBJECTIVES Patient representation learning refers to learning a dense mathematical representation of a patient that encodes meaningful information from Electronic Health Records (EHRs). This is generally performed using advanced deep learning methods. This study presents a systematic review of this field and provides both qualitative and quantitative analyses from a methodological perspective. METHODS We identified studies developing patient representations from EHRs with deep learning methods from MEDLINE, EMBASE, Scopus, the Association for Computing Machinery (ACM) Digital Library, and the Institute of Electrical and Electronics Engineers (IEEE) Xplore Digital Library. After screening 363 articles, 49 papers were included for a comprehensive data collection. RESULTS Publications developing patient representations almost doubled each year from 2015 until 2019. We noticed a typical workflow starting with feeding raw data, applying deep learning models, and ending with clinical outcome predictions as evaluations of the learned representations. Specifically, learning representations from structured EHR data was dominant (37 out of 49 studies). Recurrent Neural Networks were widely applied as the deep learning architecture (Long short-term memory: 13 studies, Gated recurrent unit: 11 studies). Learning was mainly performed in a supervised manner (30 studies) optimized with cross-entropy loss. Disease prediction was the most common application and evaluation (31 studies). Benchmark datasets were mostly unavailable (28 studies) due to privacy concerns of EHR data, and code availability was assured in 20 studies. DISCUSSION & CONCLUSION The existing predictive models mainly focus on the prediction of single diseases, rather than considering the complex mechanisms of patients from a holistic review. We show the importance and feasibility of learning comprehensive representations of patient EHR data through a systematic review. Advances in patient representation learning techniques will be essential for powering patient-level EHR analyses. Future work will still be devoted to leveraging the richness and potential of available EHR data. Reproducibility and transparency of reported results will hopefully improve. Knowledge distillation and advanced learning techniques will be exploited to assist the capability of learning patient representation further.

I. Kovacic, R. Rand, S. Sah

Linh Thi Hoai Nguyen, Ton Viet Ta, Atsushi Yagi

This note reviews our mathematical models for fish schooling, considered in free space, and in space with obstacle and food resource. These models are performed by stochastic differential equations or stochastic partial differential equations. We then present an example for the model in the last case.

Sahil Arora

In this paper, first, we investigate the existence and uniqueness of common fixed point for two pairs of weakly compatible maps which form a new type of integral-type condition via CLR property in the context of intuitionistic fuzzy metric space. The given results not only associate but also establish various existing results in the literature. Second, we present application of common fixed point theorem for the existence and uniqueness of solutions for functional equations occurring in dynamic programming of multistage decision processes. We also give an illustrative example which yields the main result.

Amr Ismaiel

Wind turbine blade structural dynamics are crucial in the turbine structural design phase. Blade deflections and loads can affect the weight of the rotor as well as the power performance of a wind turbine if the deflections are extremely high. Predictions of the turbine’s blade deflections and loads can lead to informative decisions on optimizing the design of the blade. In this work, a multivariate machine learning (ML) approach is used to predict the blade’s dynamics based on the wind flow conditions and control actions of the turbine. Three different datasets were generated using the OpenFAST software tool for three different wind turbulence classes. Various ML algorithms were trained to predict the blade deflections at the tip and blade loads at the root in the edgewise and flapwise directions. The ML models were tested for generalization of the model to different flow conditions. A model is trained for one dataset with one of the turbulence classes and then used to predict the outputs of the other two datasets. The random forest ML algorithm gave the best accuracy for predicting the outputs for the dataset it was trained for, as well as the other two datasets. The accuracy of predictions was found to be higher in the edgewise direction for both load and deflection outputs. In the flapwise direction, the model could predict the outputs of the data it was trained for with an accuracy of around 99% and for the other two datasets with an accuracy of over 75%. While in the edgewise direction, the model trained on only one dataset gave a prediction accuracy above 95% for all three datasets.

Radosław Wolniak, Katarzyna Turoń

Bike-sharing initiatives play a crucial role in sustainable urban transportation, addressing vehicular congestion, air quality issues, and sedentary lifestyles. However, the connection between bike-sharing facilities and the advantages perceived by users remains insufficiently explored particular in post-industrial regions, such as Silesia, Poland. This study develops a multidimensional framework linking infrastructure elements—such as station density, bicycle accessibility, maintenance standards, and technological integration—to perceived benefits. Using a mixed-methods approach, a survey conducted in key Silesian cities combines quantitative analysis (descriptive statistics, factor analysis, and regression modelling) with qualitative insights from user feedback. The results indicate that the most valuable benefits are health improvements (e.g., improved physical fitness and mobility) and environmental sustainability. However, infrastructural deficiencies—disjointed bike path systems, uneven station placements, and irregular maintenance—substantially hinder system efficiency and accessibility. Inadequate bike maintenance adversely affects efficiency, safety, and sustainability, highlighting the necessity for predictive upkeep and optimised services. This research underscores innovation as a crucial factor for enhancing systems, promoting seamless integration across multiple modes, diversification of fleets (including e-bikes and cargo bikes), and the use of sophisticated digital solutions like real-time tracking, contactless payment systems, and IoT-based monitoring. Furthermore, the transformation of post-industrial areas into cycling-supportive environments presents strategic opportunities for sustainable regional revitalisation. These findings extend beyond the context of Silesia, offering actionable insights for policymakers, urban mobility planners, and Smart City stakeholders worldwide, aiming to foster inclusive, efficient, and technology-enabled bike-sharing systems.

Houmem Slimi, Ala Balti, Mounir Sayadi et al.

We propose a novel hybrid deep learning framework that synergistically integrates Convolutional Neural Networks (CNNs), Spiking Neural Networks (SNNs), and Generative Adversarial Networks (GANs) for robust and accurate classification of high-resolution frontal and sagittal human gait video sequences—capturing both lower-limb kinematics and upper-body posture—from subjects with Knee Osteoarthritis (KOA), Parkinson’s Disease (PD), and healthy Normal (NM) controls, classified into three disease-type categories. Our approach first employs a tailored CNN backbone to extract rich spatial features from fixed-length clips (e.g., 16 frames resized to 128 × 128 px), which are then temporally encoded and processed by an SNN layer to capture dynamic gait patterns. To address class imbalance and enhance generalization, a conditional GAN augments rare severity classes with realistic synthetic gait sequences. Evaluated on the controlled, marker-based KOA-PD-NM laboratory public dataset, our model achieves an overall accuracy of 99.47%, a sensitivity of 98.4%, a specificity of 99.0%, and an F1-score of 98.6%, outperforming baseline CNN, SNN, and CNN–SNN configurations by over 2.5% in accuracy and 3.1% in F1-score. Ablation studies confirm that GAN-based augmentation yields a 1.9% accuracy gain, while the SNN layer provides critical temporal robustness. Our findings demonstrate that this CNN–SNN–GAN paradigm offers a powerful, computationally efficient solution for high-precision, gait-based disease classification, achieving a 48.4% reduction in FLOPs (1.82 GFLOPs to 0.94 GFLOPs) and 9.2% lower average power consumption (68.4 W to 62.1 W) on Kaggle P100 GPU compared to CNN-only baselines. The hybrid model demonstrates significant potential for energy savings on neuromorphic hardware, with an estimated 13.2% reduction in energy per inference based on FLOP-based analysis, positioning it favorably for deployment in resource-constrained clinical environments and edge computing scenarios.

Jae Choon Cha, Geunho Lim

We obtain a solution to a bordism version of Gromov's linearity problem over a large family of acyclic groups, for manifolds with arbitrary dimension. Every group embeds into some acyclic group in this family. Thus, the linear bordism problem has an affirmative solution over a possibly enlarged acyclic group. Our result holds in both PL and smooth categories, and for both oriented and unoriented cases. In the PL case, our results hold without assuming bounded local geometry. As an application, we prove that there is a universal linear bound for the Cheeger-Gromov $L^2$ $ρ$-invariants of PL $(4k-1)$-manifolds associated with arbitrary regular covers. We also show that the minimum number of simplices in a PL triangulation of $(4k-1)$-manifolds with a fixed simple homotopy type is unbounded if the fundamental group has nontrivial torsion. The proof of our main results builds on quantitative algebraic and geometric techniques over the simplicial classifying spaces of groups.

Bela Bajnok, Evan Chen

We present the problems and solutions to the 61st Annual International Mathematical Olympiad

Hsuan-Wei Lee, Colin Cleveland, Attila Szolnoki

In a social dilemma situation, where individual and collective interests are in conflict, it sounds a reasonable assumption that the presence of super or smart players, who simultaneously punish defection and reward cooperation without allowing exploitation, could solve the basic problem. The behavior of such a multi-strategy system, however, is more subtle than it is firstly anticipated. When exploring the complete parameter space, we find that the emergence of cyclic dominance among strategies is rather common, which results in several counter-intuitive phenomena. For example, the defection level can be lowered at higher temptation, or weaker punishment provides better conditions for smart players. Our study indicates that smart cooperators can unexpectedly thrive under high temptation, emphasizing the complexity of strategic interactions. This study suggests that the principles governing these interactions can be applied to other moral behaviors, such as truth-telling and honesty, providing valuable insights for future research in multi-agent systems.

Bela Bajnok

We present the problems and solutions to the 50th Annual USA Mathematical Olympiad.

Alejandro Ortiz Fernández

In this walk we are going to walk through some domains of harmonic analysis and partial differential equations (PDE). The objective of this article is to motivate students and colleagues to study these beautiful areas of analysis and therefore we emphasize the ideas, some mathematical results and some historical data. In this “ tourist” tour we will see a panorama of such areas in the 19th and 20 th centuries, a panorama of the Fourier series; we give a vision of the theory of distributions, of the theory of linear partial differential operators and we culminate by given a vision of harmonic analysis and its relationship we the PDE.

C. Cattani, R. Spigler

Modelling, simulation, and applications of Fractional Calculus have recently become increasingly popular subjects, with impressive growth concerning applications. The founding and limited ideas on fractional derivatives have achieved an incredibly valuable status. The variety of applications in mathematics, physics, engineering, economics, biology, and medicine, have opened new, challenging fields of research. For instance, in soil mechanics, a suitable definition of the fractional operator has shed some light on viscoelasticity, explaining memory effects on materials. Needless to say, these applications require the development of practical mathematical tools in order to extract quantitative information from models, newly reformulated in terms of fractional differential equations. Even confining ourselves to the field of ordinary differential equations, the well-known Bagley-Torvik model showed that fractional derivatives may actually arise naturally within certain physical models, and are not merely fanciful mathematical generalizations. This Special Issue focuses on the most recent advances in fractional calculus, applied to dynamic problems, linear and nonlinear fractional ordinary and partial differential equations, integral fractional differential equations, and stochastic integral problems arising in all fields of science, engineering, and other applied fields. In this issue, we have collected several significant papers devoted to applications of fractional methods with a focus on dynamical aspects. The applications range from theoretical mathematical-numerical aspects [1,2] to bio-medical subjects [3–7]. Applications to complex materials are investigated in [8], aiming at proposing a generalized definition of fractional operators. Special diffusion models are studied in [9–11].

Wei Gong, Peng Sun, C. Zhai et al.

Background Brucellosis is a chronic zoonotic disease, and Ningxia is one of the high prevalence regions in China. To mitigate the spread of brucellosis, the government of Ningxia has implemented a comprehensive prevention and control plan (2022-2024). It is meaningful to quantitatively evaluate the accessibility of this strategy. Methods Based on the transmission characteristics of brucellosis in Ningxia, we propose a dynamical model of sheep-human-environment, which coupling with the stage structure of sheep and indirect environmental transmission. We first calculate the basic reproduction number $$R_0$$ R 0 and use the model to fit the data of human brucellosis. Then, three widely applied control strategies of brucellosis in Ningxia, that is, slaughtering of sicked sheep, health education to high risk practitioners, and immunization of adult sheep, are evaluated. Results The basic reproduction number is calculated as $$R_{0}=1.47$$ R 0 = 1.47 , indicating that human brucellosis will persist. The model has a good alignment with the human brucellosis data. The quantitative accessibility evaluation results show that current brucellosis control strategy may not reach the goal on time. “Ningxia Brucellosis Prevention and Control Special Three-Year Action Implementation Plan (2022-2024)” will be achieved in 2024 when increasing slaughtering rate  $$\gamma$$ γ  by 30 $$\%$$ % , increasing health education to reduce $$\beta _{h}$$ β h  to 50 $$\%$$ % , and an increase of immunization rate of adult sheep $$\theta$$ θ by 40 $$\%$$ % . Conclusion The results demonstrate that the comprehensive control measures are the most effective for brucellosis control, and it is necessary to further strengthen the multi-sectoral joint mechanism and adopt integrated measures to prevention and control brucellosis. These results can provide a reliable quantitative basis for further optimizing the prevention and control strategy of brucellosis in Ningxia.

Pin Wang, Xianling Hu, Yong-min Li et al.

Aamod Shanker, Johannes Froech, Saswata Mukherjee et al.

Quantitative phase imaging (QPI) recovers the exact wavefront of light from the intensity measured by a camera. Topographical maps of translucent microscopic bodies can be extracted from these quantified phase shifts. We demonstrate quantitative phase imaging at the tip of an optical fiber endoscope with a chromatic silicon nitride metalens. Our method leverages spectral multiplexing to recover phase from multiple defocus planes in a single capture. The half millimeter wide metalens shows phase imaging capability with a 280 field of view and 0.1λ sensitivity in experiments with an endoscopic fiber bundle. Since the spectral functionality is encoded directly in the imaging lens, no additional filters are needed. Key limitations in the scaling of a phase imaging system, such as multiple acquisition, interferometric alignment or mechanical scanning are completely mitigated in the proposed scheme

Kazumasa Oida

Abstract Bipolarization is a phenomenon in which either a large or very small information cascade appears randomly when the retweet rate is high. This phenomenon, which has been observed only in simulations, has the potential to significantly advance the prediction of final cascade sizes because forecasters need only focus on the two peaks in the final cascade size distribution rather than considering the effects of various details, such as network structure and user behavioral patterns. The phenomenon also suggests the difficulty of identifying factors that lead to the emergence of large-scale cascades. To verify the existence of bipolarization, this paper theoretically derives mathematical expressions of the cascade final size distribution using urn models, which simplify the diffusion behavior of actual online social networks. Under the assumption of infinite network size, the distribution exhibits power-law behavior, consistent with the results of existing diffusion models and previous Twitter analytical outcomes. Under the assumption of finite network size, bipolarization is observed.

Wanlin Wang, Jinxiong Chen, Zhenkun Huang

An innovative cascade predictor is presented in this study to forecast the state of recurrent neural networks (RNNs) with delayed output. This cascade predictor is a chain-structured observer, as opposed to the conventional single observer, and is made up of several sub-observers that individually estimate the state of the neurons at various periods. This new cascade predictor is more useful than the conventional single observer in predicting neural network states when the output delay is arbitrarily large but known. In contrast to examining the stability of error systems solely employing the Lyapunov–Krasovskii functional (LKF), several new global asymptotic stability standards are obtained by combining the application of the Linear Parameter Varying (LPV) approach, LKF and convex principle. Finally, a series of numerical simulations verify the efficacy of the obtained results.

Lifang Zhou, P. Xue, Yixin Zhang et al.

Background Over the decades, many assessment methods have been developed around the world and used for occupational health risk assessment (OHRA). This scoping review integrated the literature on methodological studies of OHRA in China and aimed to identifies the research hot-spots and methodological research perspectives on OHRA in China. Methods A scoping review of literature was undertaken to explore the research progress on OHRA methods in China. Focusing on OHRA methods, the authors systematically searched Chinese and English databases and relevant guideline websites from the date of establishment to June 30, 2022. Databases included Web of Science, PubMed, Scopus, the China National Knowledge Internet, WanFang Database. Some other websites were also searched to obtain gray literature. The extracted information included the author, year, region of first author, the target industry, risk assessment model, study type, the main results and conclusions. Results Finally, 145 of 9,081 studies were included in this review. There were 108 applied studies, 30 comparative studies and 7 optimization studies on OHRA in China. The OHRA methods studied included: (1) qualitative methods such as Romanian model, Australian model, International Council on Mining and Metals model, and Control of Substances Hazardous to Health Essentials; (2) quantitative methods such as the U. S. Environmental Protection Agency inhalation risk assessment model, Physiologically Based Pharmacokinetic, and Monte Carlo simulation; (3) semi-quantitative methods such as Singapore model, Fuzzy mathematical risk assessment model, Likelihood Exposure Consequence method and Occupational Hazard Risk Index assessment method; (4) comprehensive method (Chinese OHRA standard GBZ/T 298-2017). Each of the OHRA methods had its own strengths and limitations. In order to improve the applicability of OHRA methods, some of them have been optimized by researchers. Conclusions There is a wide range of OHRA methods studied in China, including applied, comparative, and optimization studies. Their applicability needs to be further tested through further application in different industries. Furthermore, quantitative comparative studies, optimization studies, and modeling studies are also needed.

S. Benzekry, S. Benzekry

The amount of 'big' data generated in clinical oncology, whether from molecular, imaging, pharmacological or biological origin, brings novel challenges. To mine efficiently this source of information, mathematical models able to produce predictive algorithms and simulations are required, with applications for diagnosis, prognosis, drug development or prediction of the response to therapy. Such mathematical and computational constructs can be subdivided into two broad classes: biologically agnostic, statistical models using artificial intelligence techniques, and physiologically-based, mechanistic models. In this review, recent advances in the applications of such methods in clinical oncology are outlined. These include machine learning applied to big data (omics, imaging or electronic health records), pharmacometrics, quantitative systems pharmacology, tumor size kinetics, and metastasis modeling. Focus is set on studies with high potential of clinical translation, as well as applied to cancer immunotherapy. Perspectives are given in terms of combinations of the two approaches: 'mechanistic learning'.