Current Issue : July-September Volume : 2026 Issue Number : 3 Articles : 5 Articles
Quantum machine learning (QML) is an emerging field combining quantum computing and artificial intelligence, with promising applications in medicine and healthcare. This survey reviews more than 60 studies published between 2018 and 2025, highlighting a sharp increase in research activity, especially in the last three years. We address seven core research questions related to publication trends, the use of real quantum hardware versus simulators, quantum architectures overview, dataset types, medical domains, algorithmic frameworks, and reported results. Our analysis shows that mostQMLresearch in healthcare is conducted on simulators due to limited hardware access, and it relies on small datasets. Quantum convolutional neural network (QCNN) architectures dominate image-based medical tasks such as tumor detection, pneumonia diagnosis, and ECG interpretation, while feature-based datasets are mainly analyzed with variational quantum classifiers and quantum support vector machines. Despite hardware constraints, QML models often match or surpass classical machine learning approaches in accuracy, frequently reaching 95–99%. However, these performance statements should be qualified to recognize experimental limitations and avoid excessive optimism and should not be interpreted as definitive proof of quantum superiority at this stage. Additionally, issues with reproducibility and reporting of hardware details persist, which is a significant research gap. This review emphasizes the need for standardized benchmarks, more real hardware testing, and architectureaware algorithm design. With the potential for accelerated diagnostics and personalized healthcare, QML represents a strategic direction for future medical research....
Let ΦN(X,Y) be the N-th classical modular polynomial and let Z0(N) = {(X,Y) ∈ C2 | ΦN(X,Y) = 0} be the plane model of the modular curve X0(N). We present an explicit procedure that, for a prime ℓ, enumerates all non-cuspidal singular points of Z0(ℓ) over C and outputs the corresponding pairs of distinct points on X0(ℓ) mapping to each node. The method relies on the arithmetic (CM) classification of self-intersections of the map X0(ℓ) → Z0(ℓ) and on effective computations of proper ideal classes in imaginary quadratic orders. We also provide a complete and self-contained exposition of Kara’s proof of the automorphism-group equality Aut(E) = Aut(E′) in the self-intersection setting, making explicit where Kolyvagin’s conductor lemma is used essentially. Finally, we discuss termination, correctness, and practical complexity issues, and we report computational evidence for larger primes using a parallel implementation; in particular, for ℓ = 389, we obtained 151,288 output pairs in 151,017 seconds on a 56-core machine....
The interdisciplinary study of volcanic processes, which extend across all timescales and lengths, requires a multitude of approaches, ranging from analogue and numerical modelling to observations and fieldwork and extending to mathematics. A conference was held at the East African Institute for Fundamental Research, affiliated with the University of Rwanda, a country which, along with the Democratic Republic of Congo, presents a unique geodynamic context. Located along the East African Rift, an active seismic region, Rwanda is close to two of Africa's most active volcanoes, including Nyiragongo, which overlooks Lake Kivu, a deep volcanic lake rich in dissolved carbon dioxide and methane, the latter of which is used for electricity generation. In this context, the conference addressed many “classic” volcanological topics and their modern advances, such as multiphase lava flows, subsurface magma propagation, seismic and deformation signals from a volcano, modelling of volcanic emission dispersion, and volcanic lakes. Yet, it broadened the discussion to the volcanic particle-water interface and its impact on soils, volcanoes and climate change, and volcanoes and health. This article aims to highlight and share the richness of the integration and interconnectedness of the various questions related to a volcanic environment, as well as their impact on society. Ultimately, this conference also demonstrated the importance of promoting science in Africa and developing countries so that the next generation of African researchers is equipped to address the challenges facing their nations....
We consider the mathematical properties of economic models concerned with value maximisation, including integrated assessment models. We illustrate how the outcomes that result from maximising value subject to convergence to a steady state in the long run may be very different from the outcomes that arise from maximising value without requiring such convergence. We contend that many economicmodels include an assumption (sometimes hidden) that the economy converges to a steady state in the long run, so the outcome if such an assumption does not hold true may be very different from the model predictions. We reflect on the intergenerational injustice relating to this and other ethical and mathematical considerations in economic models, in the context of environmental and social issues. We hope to encourage improved communication and awareness of modelling assumptions, and a more fundamental rethink of economic models, values and policies, given the magnitude of the risks currently faced by humanity....
This research-oriented report analyzes the impact of a class of time-independent forces and their time-dependent counterparts on the characteristics of solutions to the wave equation on a one-dimensional string. The solution of these equations, subject to Initial and Boundary Value (IBV) conditions, is investigated, yielding modified standing waves. Analyses are heavily Computer Algebra oriented. The popular Computer Algebra System (CAS), specifically Mathematica , has been pivotal in uncovering the numerical, algebraic, and graphical aspects of the investigation. The time-dependent force functions not only generalize the scope of the analysis but also possess 1) a character that their functionality by transitioning to the coordinate-dependent only is conducive to expected output, and 2) the absence of these forces frees the imposed IBV, conducive to the characteristics of the standard standing waves. This comprehensive report embodies an atlas of graphs for both mentioned forces. It is shown that the proposed one-dimensional time-independent forces give rise to previously unseen standing waves with a peculiar character. The report includes the essential Mathematica code for most calculations and all the graphs depicted. The report allows reproduction by individuals familiar with Mathematica . It is crafted and developed so that modification and generalization of the applied IBVs are readily possible. The Conclusion segment embodies a suggestion to expand the scope of future investigations....
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