Hasil untuk "Mathematics"

Dan Hendrycks, Collin Burns, Saurav Kadavath et al.

Many intellectual endeavors require mathematical problem solving, but this skill remains beyond the capabilities of computers. To measure this ability in machine learning models, we introduce MATH, a new dataset of 12,500 challenging competition mathematics problems. Each problem in MATH has a full step-by-step solution which can be used to teach models to generate answer derivations and explanations. To facilitate future research and increase accuracy on MATH, we also contribute a large auxiliary pretraining dataset which helps teach models the fundamentals of mathematics. Even though we are able to increase accuracy on MATH, our results show that accuracy remains relatively low, even with enormous Transformer models. Moreover, we find that simply increasing budgets and model parameter counts will be impractical for achieving strong mathematical reasoning if scaling trends continue. While scaling Transformers is automatically solving most other text-based tasks, scaling is not currently solving MATH. To have more traction on mathematical problem solving we will likely need new algorithmic advancements from the broader research community.

M. Newman

N. Keyfitz

G. Marchuk

P. Elliott

Mohey Eldeen H. H. Ali, Ahmed F. Tayel, Hossam M. Ezzat et al.

Energy plays a crucial role in national development, influencing critical sectors such as industry, agriculture, healthcare, and education. Accurate energy consumption prediction is essential for efficient energy management, helping prevent imbalances between supply and demand and potential energy shortages. This study aims to forecast the total primary energy supply (TPES), using Egypt as a case study for the first time in literature and utilizing several models (ordinary differential equations (ODEs), regression, and ANN models). Although ordinary differential equations (ODEs) offer flexibility and convenience, their application in energy forecasting remains limited. One of the main objectives of this research is to evaluate the effectiveness of ODEs in predicting energy consumption. Various ODE and regression models are employed to identify the most suitable model amongst each category for forecasting energy demand. Additionally, an artificial neural network (ANN) is developed, trained, validated, and tested for the same forecasting task. The study compares the performance of the selected ODE model (Mendelsohn), with the selected regression model (Polynomial), and an ANN model predicting Egypt’s TPES until 2035. By assessing multiple forecasting methods, this work improves the accuracy and reliability of energy consumption predictions, which is crucial for sustainable energy planning and policy development.

Alejandro Espinosa, Xavier Samos, Daniel Ulied et al.

Abstract As the usage of the edge-cloud continuum increases, Kubernetes presents itself as a solution that allows easy control and deployment of applications in these highly-distributed and heterogeneous environments. In this context, Artificial Intelligence methods have been proposed to aid in the task allocation process to optimize different aspects of the system, such as application execution time, load balancing or energy consumption. In this paper, we present a comparative study focused on optimizing energy consumption through dynamic task allocation in a realistic V2X application scenario. We evaluate and compare two methods representing the most common algorithmic families for resource allocation: Particle Swarm Optimization (PSO) and Proximal Policy Optimization (PPO). Our methodology includes the design of a custom Kubernetes Operator to enforce the models’ node recommendations, allowing for rigorous, real-world validation against the base Kubernetes scheduler. Experiments demonstrate that while both PSO and PPO models successfully reduce energy consumption, PSO delivers the highest savings, reducing energy use by up to 20%. Crucially, our study highlights a key trade-off: although PSO is performance-superior for energy, the PPO model remains a faster and more computationally lightweight option that can be used widely on any kind of device, even with limited resources.

G. Howson

Jingsi Hou, Guangyan Huang, Sammy Suliman et al.

In 20th century mathematics, the field of topology, which concerns the properties of geometric objects under continuous transformation, has proved surprisingly useful in application to the study of discrete mathematics, such as combinatorics, graph theory, and theoretical computer science. In this paper, we seek to provide an introduction to the relevant topological concepts to non-specialists, as well as a selection of some existing applications to theorems in discrete mathematics.

Nataliya M. Ivanova

This study examines the potential of using math-themed postage stamps in mathematics lessons as a tool to engage students and integrate the subject with history, art, and culture. Since the first mathematical stamps appeared in the early 20th century, featuring prominent scholars like Carl Friedrich Gauss and Isaac Newton, they serve not only as philatelic artifacts but also as historical carriers of knowledge. The paper presents several practical projects to interest students, such as creating their own math stamps, investigating the price trends of math-themed stamps, and developing a timeline of mathematical discoveries depicted in philatelic issues. The proposed projects develop students' mathematical skills in areas such as percentage calculations, general arithmetic, working with time intervals, and statistical analysis. Students can analyze shapes, symmetry, and patterns on stamps, study principles of proportion, and explore geometric figures. Using stamps broadens students' horizons, providing an opportunity to become familiar with renowned mathematicians from different eras, countries, and cultures. This also offers students a new perspective on the subject, presenting mathematical discoveries as part of the world's cultural heritage. Postage stamps dedicated to mathematics can become a powerful tool for visualizing theoretical knowledge, stimulating interest in mathematics, and encouraging independent research among students.

Nurezayana Zainal, Mohanavali Sithambranathan, Umar Farooq Khattak et al.

Because of its versatility and ability to work with difficult materials, Electrical Discharge Machining (EDM) has become an essential tool in many different industries. It can produce precise shapes and intricate details. EDM has transformed fabrication processes in a variety of industries, including aerospace and electronics, medical implants and surgical instruments, and the shaping of small components. Its capacity to machine undercuts and deep cavities with little material removal makes it ideal for producing complex geometries that would be challenging or impossible to accomplish with conventional machining techniques. Several attempts have been carried out to solve the optimization problem involved in the EDM process. This paper emphasizes optimizing the EDM process using three metaheuristic algorithms: Glowworm Swarm Optimization (GSO), Grey Wolf Optimizer (GWO), and Whale Optimization Algorithm (WOA). The study's outcome showed that the GWO algorithm outperformed the GSO and WOA algorithms in solving the EDM optimization problem and achieved the minimum surface roughness value of 1.7593µm.

M.K. Sharma, Nitesh Dhiman, Ajendra Sharma et al.

Accurate disease monitoring is an extremely time-consuming task for medical experts and technocrats involved, requiring technical support for diagnostic systems. To overcome this situation, we developed an Internet of Medical Things (IoMT) based on Tsukamoto Type 2 Fuzzy Inference System (TT2FIS) that can easily handle diagnostic and predictive aspects in the medical field. In the proposed system, we developed a Tsukamoto type 2 fuzzy inference system that takes the patient’s symptoms as input factors and the medical device as the output factor of the result. The aim of this work is to demonstrate the usefulness of type 2 fuzzy sets in Tuberculosis and Alzheimer’s disease diagnostic system. Numerical calculations are also performed to illustrate the applicability of the proposed method. A validation of the proposed derivation of the proposed IoMT model is also discussed in the results and conclusions section.

Mohammad Souri, Sohail Elahi, Farshad Moradi Kashkooli et al.

Abstract Intratumoral delivery and localized chemotherapy have demonstrated promise in tumor treatment; however, the rapid drainage of therapeutic agents from well-vascularized tumors limits their ability to achieve maximum therapeutic efficacy. Therefore, innovative approaches are needed to enhance treatment efficacy in such tumors. This study utilizes a mathematical modeling platform to assess the efficacy of combination therapy using anti-angiogenic drugs and drug-loaded nanoparticles. Anti-angiogenic drugs are included to reduce blood microvascular density and facilitate drug retention in the extracellular space. In addition, incorporating negatively charged nanoparticles aims to enhance diffusion and distribution of therapeutic agents within well-vascularized tumors. The findings indicate that, in the case of direct injection of free drugs, using compounds with lower drainage rates and higher diffusion coefficients is beneficial for achieving broader diffusion. Otherwise, drugs tend to accumulate primarily around the injection site. For instance, the drug doxorubicin, known for its rapid drainage, requires the prior direct injection of an anti-angiogenic drug with a high diffusion rate to reduce microvascular density and facilitate broader distribution, enhancing penetration depth by 200%. Moreover, the results demonstrate that negatively charged nanoparticles effectively disperse throughout the tissue due to their high diffusion coefficient. In addition, a faster drug release rate from nanoparticles further enhance treatment efficacy, achieving the necessary concentration for complete eradication of tumor compared to slower drug release rates. This study demonstrates the potential of utilizing negatively charged nanoparticles loaded with chemotherapy drugs exhibiting high release rates for localized chemotherapy through intratumoral injection in well-vascularized tumors.

John Harris, H. Stöcker

F. Thomas Bruss

{\bf Abstract.} The present article is an essay about mathematical intuition and Artificial intelligence (A.I.), followed by a guided excursion to a well-known open problem. It has two objectives. The first is to reconcile the way of thinking of a computer program as a sequence of mathematically defined instructions with what we face nowadays with newer developments. The second and major goal is to guide interested readers through the probabilistic intuition behind Robbins' problem and to show why A.I., and in particular Deep Learning, may contribute an essential part in its solution. This article contains no new mathematical results, and no implementation of deep learning either. Nevertheless, we hope to find through its semi-historic narrative style, with well-known examples and an easily accessible terminology, the interest of mathematicians of different inclinations.

Klaas Landsman, Kirti Singh

We re-examine the old question to what extent mathematics may be compared with a game. Mainly inspired by Hilbert and Wittgenstein, our answer is that mathematics is something like a rhododendron of language games, where the rules are inferential. The pure side of mathematics is essentially formalist, where we propose that truth is not carried by theorems corresponding to whatever independent reality and arrived at through proof, but is defined by correctness of rule-following (and as such is objective given these rules). Goedel's theorems, which are often seen as a threat to formalist philosophies of mathematics, actually strengthen our concept of truth. The applied side of mathematics arises from two practices: first, the dual nature of axiomatization as taking from heuristic practices like physics and informal mathematics whilst giving proofs and logical analysis; and second, the ability of using the inferential role of theorems to make surrogative inferences about natural phenomena. Our framework is pluralist, combining various (non-referential) philosophies of mathematics.

Vito Antonio Cimmelli

We propose a thermodynamic model describing the thermoelastic behavior of composition graded materials. The compatibility of the model with the second law of thermodynamics is explored by applying a generalized Coleman–Noll procedure. For the material at hand, the specific entropy and the stress tensor may depend on the gradient of the unknown fields, resulting in a very general theory. We calculate the speeds of coupled first- and second-sound pulses, propagating either trough nonequilibrium or equilibrium states. We characterize several different types of perturbations depending on the value of the material coefficients. Under the assumption that the deformation of the body can produce changes in its stoichiometry, altering locally the material composition, the possibility of propagation of pure stoichiometric waves is pointed out. Thermoelastic perturbations generated by the coupling of stoichiometric and thermal effects are analyzed as well.

Wenqi Zhang, Dan Jin, Ruizhi Yang

In this paper, a diffusive predator–prey model with a memory effect in predator and anti-predator behaviour in prey is studied. The stability of the coexisting equilibrium and the existence of Hopf bifurcation are analysed by analysing the distribution of characteristic roots. The property of Hopf bifurcation is investigated by the theory of the centre manifold and normal form method. Through the numerical simulations, it is observed that the anti-predator behaviour parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula>, the memory-based diffusion coefficient parameter <i>d</i>, and memory delay <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>τ</mi></semantics></math></inline-formula> can affect the stability of the coexisting equilibrium under some parameters and cause the spatially inhomogeneous oscillation of prey and predator’s densities.

G. Cobb, D. Moore