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PRIMUS 2023年第8期33卷 901-915页

作者： Ritchey, Katherine Patterson, Sarah Patterson, Blain Ritchey, Nathan University of Mount Union Mathematics and Computer Science Department United States Virginia Military Institute in the Applied Mathematics Department United States Applied Mathematics at Virginia Military Institute United States Kent State University in the Department of Mathematical Sciences United States

Wordle, a game in which a player has six chances to find a five-letter word, has become quite popular. In this paper, we present four activities that are based on Wordle and are designed to help students advance their knowledge and skill of a particular concept. Some of the activities could be used for beginning students and some activities could be used for more advanced students. The activities are designed to promote mathematical engagement and interest and can be used individually, or collectively, to fit the specific needs of the intended audience. The first two activities enhance students' knowledge of combinatorics and probability when letter words are chosen at random. In another activity, individual and pairs of letter counts from the list of possible Wordle words are presented in graphical format. More advanced students can replicate these graphs using a computer program, while other students can simply use the graphs that are included. In the fourth activity, students have the opportunity to play Wordle and develop strategies to minimize the number of steps required to solve a particular puzzle. Classroom experience is included and student responses to the activities are presented. © 2023 Taylor & Francis Group, LLC.

关键词： combinatorics decision making mathematical modeling probability statistics Wordle

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Constant-Loop Dominators for Single-Path Code Optimization 21

Constant-Loop Dominators for Single-Path Code Optimization

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21st International Workshop on Worst-Case Execution Time Analysis, WCET 2023

作者： Maroun, Emad Jacob Schoeberl, Martin Puschner, Peter Institute of Computer Engineering TU Wien Vienna Austria Department of Applied Mathematics and Computer Science Technical University of Denmark Lyngby Denmark

ISBN: (纸本)9783959772938

Single-path code is a code generation technique specifically designed for real-time systems. It guarantees that programs execute the same instruction sequence regardless of runtime conditions. Single-path code uses loop bounds to ensure all loops iterate a fixed number of times equal to their upper loop bound. When the lower and upper bounds are equal, the loop must iterate the same number of times, which we call a constant loop. In this paper, we present the constant-loop dominance relation on control-flow graphs. It is a variation of the traditional dominance relation that considers constant loops to find basic blocks that are always executed the same number of times. Using this relation, we present an optimization that reduces the code needed to manage single-path code. Our evaluation shows significant performance improvements, with one example of up to 90%, with mostly minor effects on code size. © Emad Jacob Maroun, Martin Schoeberl, and Peter Puschner.

关键词： Real time systems

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Keep That Card in Mind: Card Guessing with Limited Memory 13

Keep That Card in Mind: Card Guessing with Limited Memory

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13th Innovations in Theoretical computer science Conference, ITCS 2022

作者： Menuhin, Boaz Naor, Moni Department of Computer Science and Applied Mathematics Weizmann Institute of Science Rehovot Israel

ISBN: (纸本)9783959772174

A card guessing game is played between two players, Guesser and Dealer. At the beginning of the game, the Dealer holds a deck of n cards (labeled 1,..., n). For n turns, the Dealer draws a card from the deck, the Guesser guesses which card was drawn, and then the card is discarded from the deck. The Guesser receives a point for each correctly guessed card. With perfect memory, a Guesser can keep track of all cards that were played so far and pick at random a card that has not appeared so far, yielding in expectation ln n correct guesses, regardless of how the Dealer arranges the deck. With no memory, the best a Guesser can do will result in a single guess in expectation. We consider the case of a memory bounded Guesser that has m 2 n) memory bits that scores a near optimal result against any static Dealer. 2. We show that no Guesser with m bits of memory can score better than O(√m) correct guesses against a random Dealer, thus, no Guesser can score better than min{√m, ln n}, i.e., the above Guesser is optimal. 3. We show an efficient adaptive Dealer against which no Guesser with m memory bits can make more than ln m + 2 ln log n + O(1) correct guesses in expectation. These results are (almost) tight, and we prove them using compression arguments that harness the guessing strategy for encoding. © Boaz Menuhin and Moni Naor;licensed under Creative Commons License CC-BY 4.0

关键词： Information theory

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Automated Text-based Depression Detection using Hybrid ConvLSTM and Bi-LSTM Model 3

Automated Text-based Depression Detection using Hybrid ConvL...

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3rd International Conference on Artificial Intelligence and Smart Energy, ICAIS 2023

作者： Firoz, Neda Beresteneva, Olga Grigorievna Vladimirovich, Aksyonov Sergey Tahsin, Mohammad Sadman Tafannum, Faiza Tomsk State University Institute of Applied Mathematics and Computer Science Tomsk Russia Tomsk Polytechnic University Department of I.T Institute of Applied Mathematics and Computer Sciences Tomsk Russia Brac University Department of Computer Sciences and Engineering Dhaka Bangladesh

ISBN: (纸本)9781665462167

Depression and its symptoms are very common disorders of mental health. They affect the day-to-day activity of the person and degrade the quality of life. The article presents the comparative study of different deep learning models on natural language processing data for detection of depression using textual data. Several studies have been performed for depression detection using artificial intelligence and deep learning state of the art methods. This article investigates the state-of-the-art models and perform hyperparameter tuning for best accuracy results and develop our own hybrid model for detection of depression with improved accuracy scores. The aim of our study is to research and compare the existing findings in deep learning and machine learning models for depression detection and build a precise hybrid model for depression detection with higher accuracy and scores. © 2023 IEEE.

关键词： Long short-term memory

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Consensus learning with deep sets for essential matrix estimation 24

Consensus learning with deep sets for essential matrix estim...

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Proceedings of the 38th International Conference on Neural Information Processing Systems

作者： Dror Moran Yuval Margalit Guy Trostianetsky Fadi Khatib Meirav Galun Ronen Basri Department of Computer Science and Applied Mathematics Weizmann Institute of Science

ISBN: (纸本)9798331314385

Robust estimation of the essential matrix, which encodes the relative position and orientation of two cameras, is a fundamental step in structure from motion pipelines. Recent deep-based methods achieved accurate estimation by using complex network architectures that involve graphs, attention layers, and hard pruning steps. Here, we propose a simpler network architecture based on Deep Sets. Given a collection of point matches extracted from two images, our method identifies outlier point matches and models the displacement noise in inlier matches. A weighted DLT module uses these predictions to regress the essential matrix. Our network achieves accurate recovery that is superior to existing networks with significantly more complex architectures.

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From Infants to AI: Incorporating Infant-like Learning in Models Boosts Efficiency and Generalization in Learning Social Prediction Tasks

arXiv

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arXiv 2025年

作者： Treger, Shify Ullman, Shimon Department of Computer Science and Applied Mathematics Weizmann Institute of Science

Early in development, infants learn a range of useful concepts, which can be challenging from a computational standpoint. This early learning comes together with an initial understanding of aspects of the meaning of concepts, e.g., their implications, causality, and using them to predict likely future events. All this is accomplished in many cases with little or no supervision, and from relatively few examples, compared with current network models. In learning about objects and human-object interactions, early acquired and possibly innate concepts are often used in the process of learning additional, more complex concepts. In the current work, we model how early-acquired concepts are used in the learning of subsequent concepts, and compare the results with standard deep network modeling. We focused in particular on the use of the concepts of animacy and goal attribution in learning to predict future events. We show that the use of early concepts in the learning of new concepts leads to better learning (higher accuracy) and more efficient learning (requiring less data). We further show that this integration of early and new concepts shapes the representation of the concepts acquired by the model. The results show that when the concepts were learned in a human-like manner, the emerging representation was more useful, as measured in terms of generalization to novel data and tasks. On a more general level, the results suggest that there are likely to be basic differences in the conceptual structures acquired by current network models compared to human learning. © 2025, CC BY.

关键词： Contrastive Learning

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A Neuro-Fuzzy Approach to MOPP Open Time Prediction for Chemical Threats in Low-Intensity Conflicts

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International Journal of Fuzzy System Applications 2022年第1期11卷 1-17页

作者： Kumar, Vijay Tyagi, Lakshya Department of Applied Mathematics Amity Institute of Applied Sciences Amity University Noida India Department of Computer Science and Engineering ASET Amity University Noida India

CBRN (chemical, biological, radiological, and nuclear) weapons systems hold the potential to cause great damage to a fighting unit. Chemical warfare agents are cheaper and easier to produce and deploy. Mission-oriented protective posture (MOPP) equipment is used to isolate soldiers from the toxic environment in case of a chemical attack. Sustained wearing of MOPP overgarments can put soldiers at the risk of dehydration and heat stress, while reducing their capability to carry out labour-intensive tasks efficiently. A hierarchal adaptive neuro-fuzzy inference system (HANFIS) model is proposed to predict worst case MOPP open times for surfaces covered with chemical agent resistant coating (CARC). The model can provide decision support for commanders when determining MOPP open or unmasking time. From the HANFIS simulation results, it was concluded that the model can accurately predict MOPP open times according to data present in military field manuals in a manner that is computationally efficient and easy to interpret based on linguistic rules, and most importantly, easy to customize according to the needs of in-theatre commander based on intelligence on the enemy's arsenal of CW agents and weather conditions of their unit's location. This work adds to the body of evidence that soft computing techniques can be effectively applied to the design of decision support systems for defence sciences. Copyright © 2022, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited.

关键词： Chemical warfare

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Lie algebra and conservation laws for the time-fractional heat equation

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Transactions of the Royal Society of South Africa 2023年第3期78卷 227-240页

作者： Halder, Amlan K. Duba, C.T. Leach, P.G.L. Department of Mathematics Pondicherry University Puducherry India School of Computer Science and Applied Mathematics University of the Witwatersrand Johannesburg South Africa Institute for Systems Science Durban University of Technology Durban South Africa School of Mathematics Statistics and Computer Science University of KwaZulu-Natal Durban South Africa

The Lie symmetry method is applied to derive the point symmetries for the N-dimensional fractional heat equation. We find that the numbers of symmetries and Lie brackets are reduced significantly as compared to the integer order for all dimensions. In fact for integer order linear heat equation the number of solution symmetries is equal to the product of the order and space dimension, whereas for the fractional case, it is half of the product on the order and space dimension. The Lie algebras for the integer and fractional order equations are mentioned using the subsequent computations of Lie brackets and by inspection. Interestingly, it is observed that for the one-dimensional fractional heat equation, the Lie algebra obtained by inspection of symmetries is similar to the result obtained by computation of Lie brackets, which is (Formula presented.). The Lie algebra using the symmetries of the two-dimensional heat equation is observed to be (Formula presented.), whereas using the Lie brackets the algebra is deduced to be (Formula presented.). Hence, it can be concluded that the Lie algebra obtained from the nonzero Lie brackets can be conflated to the algebra which is obtained by inspection. Further, the subsequent Lie algebras are mentioned for the three and four-dimensional integer and fractional equations and the conservation laws are explicitly stated. © 2023 Royal Society of South Africa.

关键词： conservation laws fractional partial differential equations lie symmetries solutions

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Optimal Lot Size and Backordered Quantity Under Carbon Tax

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International Journal of applied and Computational mathematics 2024年第4期10卷 1-16页

作者： Raiya, Geetanjali Mittal, Mandeep Department of Mathematics Amity Institute of Applied Sciences Amity University Uttar Pradesh Noida 201313 India Department of Mathematics School of Computer Science Engineering and Technology Bennett University Uttar Pradesh Greater Noida India

Researchers and industry are working together to develop low carbon inventory models that comply with carbon pricing regulations while maintaining company profits. However, this task becomes more challenging when companies also face issues related to product quality imperfections. To address this issue, a new study has developed an economic order quantity (EOQ) model that takes into account carbon emission tax, defective rates, selling prices, imperfect items, scrap items and backordering. The objective of this mathematical model is reduce overall expenses, encompassing emissions-related costs. A numerical example is come up to adorn the model, based on previous data. Sensitivity analysis has also been performed to validate the model and understand system characteristics, identifying the factors that affect total emissions. © The Author(s), under exclusive licence to Springer Nature India Private Limited 2024.

关键词： Carbon tax Defective items EOQ Optimization Shortages

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Sensorless Unmanned Bicycle Robot

Sensorless Unmanned Bicycle Robot

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2022 International Conference on Electrical, computer, Communications and Mechatronics Engineering, ICECCME 2022

作者： Efraim, Hanoch Basri, Ronen Weizmann Institute of Science Dept. of Computer Science and Applied Mathematics Rehovot Israel

ISBN: (数字)9781665470957

ISBN: (纸本)9781665470957

In this work, we present a new approach for designing an autonomous bicycle robot. It is well known that bicycles can be laterally stable at certain velocities. This means that if the steering bar remains free to rotate, a bicycle can be designed so that it naturally steers in a way that corrects for deviations, keeping the bicycle upright. However, to the best of our knowledge this desirable property is not taken advantage of in previous works, since connecting a standard actuator to the steering bar, which is required in order to guide the bicycle to a desired direction, does not allow the steerer to be free to rotate. In this work we propose a unique actuation mechanism that allows guidance while keeping the steerer free to rotate, thus preserving the natural stability of the bicycle. Since the bicycle is mechanically stable there is no need for a low level controller, and thus, no need for sensors and sensor fusion algorithms. We demonstrate the concept with experiments performed on a 3D printed bicycle powered by a small electric motor and guided remotely. We provide all the CAD files and software in hope that it will be used by additional researchers in the field, and advance the frontiers of autonomous systems. © 2022 IEEE.

关键词： Bicycles

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