More Like this

1. Overview of ARQMath 2020 (Updated Working Notes Version): CLEF Lab on Answer Retrieval for Questions on Math

   Zanibbi, Richard; Oard, Douglas W.; Agarwal, Anurag; Mansouri, Behrooz (January 2020, Working Notes of CLEF 2020 - Conference and Labs of the Evaluation Forum)

   The ARQMath Lab at CLEF considers finding answers to new mathematical questions among posted answers on a community question answering site (Math Stack Exchange). Queries are question posts held out from the searched collection, each containing both text and at least one formula. This is a challenging task, as both math and text may be needed to find relevant answer posts. ARQMath also includes a formula retrieval sub-task: individual formulas from question posts are used to locate formulae in earlier question and answer posts, with rele- vance determined considering the context of the post from which a query formula is taken, and the posts in which retrieved formulae appear. 

   more » « less
2. Finding Old Answers to New Math Questions: The ARQMath Lab at CLEF 2020

   https://doi.org/10.1007/978-3-030-45442-5_73  

   Mansouri, Behrooz; Agarwal, Anurag; Oard, Douglas W.; Zanibbi, Richard (January 2020, Proc. European Conference on Information Retrieval)

   The ARQMath Lab at CLEF 2020 considers the problem of finding answers to new mathematical questions among posted answers on a community question answering site (Math Stack Exchange). Queries are question postings held out from the test collection, each containing both text and at least one formula. We expect this to be a challenging task, as both math and text may be needed to find relevant answer posts. While several models have been proposed for text question answering, math question answering is in an earlier stage of development. To advance math-aware search and mathematical question answering systems, we will create a standard test collection for researchers to use for benchmarking. ARQMath will also include a formula retrieval sub-task: individual formulas from question posts are used to locate formulas in earlier answer posts, with relevance determined by narrative fields created based on the original question. We will use these narrative fields to explore diverse information needs for formula search (e.g., alternative notation, applications in specific fields or definition). 

   more » « less
3. On blowup of secant varieties of curves

   https://doi.org/10.3934/era.2021055  

   Ein, Lawrence; Niu, Wenbo; Park, Jinhyung (January 2021, Electronic Research Archive)

   In this paper, we show that for a nonsingular projective curve and a positive integer $ k $$, the $ k $$-th secant bundle is the blowup of the $ k $$-th secant variety along the $ (k-1) $$-th secant variety. This answers a question raised in the recent paper of the authors on secant varieties of curves. 

   more » « less
4. Misiurewicz polynomials and dynamical units, part I

   https://doi.org/10.1142/S1793042123500616  

   Benedetto, Robert L; Goksel, Vefa (July 2023, International Journal of Number Theory)

   We study the dynamics of the unicritical polynomial family [Formula: see text]. The [Formula: see text]-values for which [Formula: see text] has a strictly preperiodic postcritical orbit are called Misiurewicz parameters, and they are the roots of Misiurewicz polynomials. The arithmetic properties of these special parameters have found applications in both arithmetic and complex dynamics. In this paper, we investigate some new such properties. In particular, when [Formula: see text] is a prime power and [Formula: see text] is a Misiurewicz parameter, we prove certain arithmetic relations between the points in the postcritical orbit of [Formula: see text]. We also consider the algebraic integers obtained by evaluating a Misiurewicz polynomial at a different Misiurewicz parameter, and we ask when these algebraic integers are algebraic units. This question naturally arises from some results recently proven by Buff, Epstein, and Koch and by the second author. We propose a conjectural answer to this question, which we prove in many cases. 

   more » « less
5. Temporal Attention and Consistency Measuring for Video Question Answering

   https://doi.org/10.1145/3382507.3418886  

   Zhang, Lingyu; Radke, Richard J. (October 2020, Publication: ICMI '20: Proceedings of the 2020 International Conference on Multimodal Interaction)

   Social signal processing algorithms have become increasingly better at solving well-defined prediction and estimation problems in audiovisual recordings of group discussion. However, much human behavior and communication is less structured and more subtle. In this paper, we address the problem of generic question answering from diverse audiovisual recordings of human interaction. The goal is to select the correct free-text answer to a free-text question about human interaction in a video. We propose an RNN-based model with two novel ideas: a temporal attention module that highlights key words and phrases in the question and candidate answers, and a consistency measurement module that scores the similarity between the multimodal data, the question, and the candidate answers. This small set of consistency scores forms the input to the final question-answering stage, resulting in a lightweight model. We demonstrate that our model achieves state of the art accuracy on the Social-IQ dataset containing hundreds of videos and question/answer pairs. 

   more » « less