Lehmer's question is equivalent to one about generalized growth rates of Lefschetz numbers of iterated pseudo-Anosov surface homeomorphisms. One need consider only homeomorphisms that arise as monodromies of fibered knots in lens spaces L(n,1), n>0. Lehmer's question for Perron polynomials is equivalent to one about ge…
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48 results for “Lehmer's Question”
This paper addresses a long standing open problem due to Lehmer in which the triple 2,3,7 plays a notable role. Lehmer's problem asks whether there is a gap between 1 and the next smallest algebraic integer with respect to Mahler measure. The question has been studied in a wide range of contexts including number theory…
Complexity of signed graphs linked to Alexander polynomials and Lehmer's question.
problem Complexity of signed graphs and its relation to Alexander polynomials.
method Definition of graph complexity using Laplacian matrix and Mahler measure, linking to Alexander polynomials and Lehmer's question.
result Complexity growth of signed graphs is related to the growth rate of Alexander polynomials.
New Lehmer constants computed for free groups, improving bounds.
problem Tackles Lehmer's problem on Mahler measures and Fuglede-Kadison determinants.
method Uses relations between Fuglede-Kadison determinants and random walks on Cayley graphs, and gluing formula for -torsions.
result Computes new upper bound of for Lehmer's constants of torsion-free groups with non-cyclic free subgroups.
We reformulate Lehmer's question from 1933 and a question due to Schinzel and Zassenhaus from 1965 in terms of a comparison of the Mahler measures and the houses, respectively, of monic integer reciprocal and skew-reciprocal polynomials of the same degree. This entails that understanding the difference between orientat…
We propose a new class of transforms that we call {\it Lehmer Transform} which is motivated by the {\it Lehmer mean function}. The proposed {\it Lehmer transform} decomposes a function of a sample into their constituting statistical moments. Theoretical properties of the proposed transform are presented. This transform…
In this report I discuss the relations between systoles and volumes of hyperbolic manifolds and a conjecture of Lehmer about the Mahler measure of non-cyclotomic polynomials.
The (torsion) complexity of a finite edge-weighted graph is defined to be the order of the torsion subgroup of the abelian group presented by its Laplacian matrix. When G is d-periodic (i.e., G has a free action of the rank-d free abelian group by graph automorphisms, with finite quotient) the Mahler measure of its Lap…
Study Veech groups in fibered 3-manifolds, proving no parabolics for fibers.
problem Characterizing Veech groups in fibered 3-manifolds.
method Analyzing pseudo-Anosov monodromies and foliations, proving properties of Veech groups.
result Veech groups in fibers typically contain no parabolic elements.
Estimates the degree of trace fields of hyperbolic Dehn fillings.
problem Estimating the complexity of hyperbolic 3-manifolds.
method Using Lehmer's conjecture, bounds the degree of trace fields.
result Estimates the degree of trace fields of hyperbolic Dehn fillings.
The study computes trace fields and minimal polynomials for specific knots and links.
problem Computing trace fields and minimal polynomials for specific knots and links.
method Using factorization theorems for sparse polynomials.
result Results depend on the degrees of the trace fields over Q being sufficiently large.
Study on mapping classes of real rational surface automorphisms, focusing on reducible maps and pseudo-Anosov maps.
problem Investigating the mapping classes of real rational surface automorphisms and their restrictions.
method Analysis of reducible maps, determination of pseudo-Anosov mapping classes, and comparison with Penner's construction.
result Realized Lehmer's number as the stretch factor of a pseudo-Anosov map on a specific surface.
A new neural network model using weighted Lehmer means and multiplets.
problem Creating a neural network that can emulate different generalized mean cases.
method Replacing dot product with weighted Lehmer mean and using multiplets of neurons.
result The network can emulate the exclusive-or problem and approximate functions.
From a simple observation about a construction of Thurston, we derive several interesting facts about subgroups of the mapping class group generated by two positive multi-twists. In particular, we identify all configurations of curves for which the corresponding groups fail to be free, and show that a subset of these d…
SmartDCA superiorityq-fin.PM
SmartDCA improves investment returns by adjusting purchases based on prices.
problem Inefficiency of Dollar-Cost Averaging (DCA) in volatile markets.
method Developed SmartDCA, a more efficient investment strategy that adjusts purchases based on price levels, and analyzed its performance using mathematical inequalities and mean definitions.
result SmartDCA outperforms DCA in long-term investments, with higher performance gains for higher power values of .
Lueck expressed the Gromov norm of a knot complement in terms of an infinite series that can be computed from a presentation of the fundamental group of the knot complement. In this note we show that Lueck's formula, applied to torus knots, yields surprising power series expansions for the logarithm function. This gene…
This paper presents a construction of fibered links out of chord diagrams $\sL$. Let be the incidence graph of $\sL$. Under certain conditions on $\sL$ the symmetrized Seifert matrix of equals the bilinear form of the simply-laced Coxeter system associated to ; and the monodromy of $(K,Σ)…
In this paper we prove that there is a direct relationship between Salem numbers and translation lengths of hyperbolic elements of arithmetic hyperbolic groups that are determined by a quadratic form over a totally real number field. As an application we determine a sharp lower bound for the length of a closed geodesic…
We present a novel method for obtaining high-quality, domain-targeted multiple choice questions from crowd workers. Generating these questions can be difficult without trading away originality, relevance or diversity in the answer options. Our method addresses these problems by leveraging a large corpus of domain-speci…
Question classification (QC) is the primary step of the Question Answering (QA) system. Question Classification (QC) system classifies the questions in particular classes so that Question Answering (QA) System can provide correct answers for the questions. Our system categorizes the factoid type questions asked in natu…
Paper analyzes biases in video QA datasets, showing models can answer 37-48% questions correctly without multimodal context.
problem Question answering biases in video QA datasets can lead to model overfitting and poor generalization.
method Analyzed popular video question answering datasets, conducted ablation studies on biases from annotators and question types.
result Pretrained language models can answer 37-48% questions correctly without multimodal context, far exceeding random guess baseline.
Online surveys have the potential to support adaptive questions, where later questions depend on earlier responses. Past work has taken a rule-based approach, uniformly across all respondents. We envision a richer interpretation of adaptive questions, which we call dynamic question ordering (DQO), where question order …
On two questions of Jamesmath.DG
James's octonionic Stiefel spaces questions answered partially.
problem Two fundamental questions about octonionic Stiefel spaces.
method Partial answers to James's questions about octonionic Stiefel spaces.
result Partial answers to James's questions about octonionic Stiefel spaces.
First Proofcs.AI
AI tested on 10 math questions from research.
problem Assessing AI's ability to solve research-level math problems.
method Shared 10 math questions not previously publicly available.
result Answers to questions are known to authors but encrypted.
Question semantic similarity is a challenging and active research problem that is very useful in many NLP applications, such as detecting duplicate questions in community question answering platforms such as Quora. Arabic is considered to be an under-resourced language, has many dialects, and rich in morphology. Combin…
The rate at which medical questions are asked online far exceeds the capacity of qualified people to answer them, and many of these questions are not unique. Identifying same-question pairs could enable questions to be answered more effectively. While many research efforts have focused on the problem of general questio…
Predicts student performance in interactive online question pools using GNNs.
problem Predicting student performance in interactive online question pools with evolving knowledge.
method Proposes R^2GCN, a GNN model for heterogeneous networks to predict student performance.
result Achieves higher accuracy in student performance prediction than traditional methods.
EduQG generates better educational questions by pre-training on scientific text.
problem Improving the quality of educational questions for scalable self-assessment.
method Adapting a large language model for educational question generation, pre-trained on scientific text.
result EduQG produces superior educational questions compared to baseline models.
Understanding learning materials (e.g. test questions) is a crucial issue in online learning systems, which can promote many applications in education domain. Unfortunately, many supervised approaches suffer from the problem of scarce human labeled data, whereas abundant unlabeled resources are highly underutilized. To…
Solved a specific case of Salter's question on Burau representation.
problem Under what conditions are matrices in the image of the Burau representation of .
method Algorithmically constructed a counterexample to Salter's specific question.
result The central quotient of the Burau image group is not the central quotient of a certain subgroup of the unitary group.
Question semantic similarity (Q2Q) is a challenging task that is very useful in many NLP applications, such as detecting duplicate questions and question answering systems. In this paper, we present the results and findings of the shared task (Semantic Question Similarity in Arabic). The task was organized as part of t…
Automatic question generation is an important problem in natural language processing. In this paper we propose a novel adaptive copying recurrent neural network model to tackle the problem of question generation from sentences and paragraphs. The proposed model adds a copying mechanism component onto a bidirectional LS…
We are raising questions on discrete and dense subgroups of Diff(I). Most of the questions are around the problems discussed in [A1]-[A4].
This study analyzes financial equity research reports to identify frequently asked questions and automates 80% of them.
problem Insufficient empirical analysis of questions answered in financial equity research reports.
method Analyzed 72 financial equity research reports, classifying sentences into 169 unique question archetypes. Used public corporate reports to classify questions' potential for automation.
result Approximately 80% of financial equity research reports can be automated, with 78.7% of questions automatable.
Abstract reviews known and open questions on spaces with lower Ricci bounds.
problem Understanding the structure and regularity of spaces with lower Ricci curvature bounds.
method Review of known results and presentation of open questions.
result Presentation of new open questions in the field.
Automatic estimation of relative difficulty of a pair of questions is an important and challenging problem in community question answering (CQA) services. There are limited studies which addressed this problem. Past studies mostly leveraged expertise of users answering the questions and barely considered other properti…
Visual question answering is a recently proposed artificial intelligence task that requires a deep understanding of both images and texts. In deep learning, images are typically modeled through convolutional neural networks, and texts are typically modeled through recurrent neural networks. While the requirement for mo…
Paper proposes a fair grading method for randomized exams.
problem Ensuring fairness in grading for randomized exams.
method Maximum-likelihood estimator for Bradley-Terry-Luce model on student-question graph.
result Maximum-likelihood estimator is consistent and outperforms simple averaging in fairness and accuracy.
Stack Overflow is the most popular Q&A website among software developers. As a platform for knowledge sharing and acquisition, the questions posted in Stack Overflow usually contain a code snippet. Stack Overflow relies on users to properly tag the programming language of a question and it simply assumes that the progr…
Paper answers Gromov's compactness question on noncompact manifolds.
problem Gromov's compactness question on positive scalar curvature metrics.
method Construct examples and prove vanishing of certain index theoretic invariants.
result Positive answer for a class of 1-tame manifolds.
Community-based Question Answering (CQA) sites play an important role in addressing health information needs. However, a significant number of posted questions remain unanswered. Automatically answering the posted questions can provide a useful source of information for online health communities. In this study, we deve…
The main objective of exams consists in performing an assessment of students' expertise on a specific subject. Such expertise, also referred to as skill or knowledge level, can then be leveraged in different ways (e.g., to assign a grade to the students, to understand whether a student might need some support, etc.). S…
We study how to leverage off-the-shelf visual and linguistic data to cope with out-of-vocabulary answers in visual question answering task. Existing large-scale visual datasets with annotations such as image class labels, bounding boxes and region descriptions are good sources for learning rich and diverse visual conce…
qDKT improves KT models by considering individual question outcomes.
problem Ignoring question-specific outcomes leads to inaccurate learner skill tracking.
method qDKT incorporates graph Laplacian regularization and uses a fastText-inspired initialization scheme.
result qDKT achieves state-of-the-art performance in predicting learner outcomes.
The paper tackles adaptive questioning to classify candidate ability.
problem Designing an optimal sequence of adaptive questions to classify candidate ability.
method Develops lower bounds and geometrical insights for sequential questioning strategies, and arrives at algorithms that match these bounds.
result Asymptotically, any candidate needs to be asked questions at most at two levels, facilitating endogenous exploration.
New model improves diversity in question generation over text.
problem Inadequate evaluation metrics for diverse questions.
method Proposed a variational encoder-decoder model and evaluation scheme.
result Improved diversity in generated questions without loss of quality.
A new model answers questions about medical images.
problem Lack of transparency in deep learning models for medical imaging.
method A question-centric model that queries image models directly.
result The model achieves equal or higher accuracy than existing methods.
Quriosity: Analyzing Human Questioning Behavior and Causal Inquiry through Curiosity-Driven Queriescs.CL
Quriosity analyzes curiosity-driven questions from diverse sources.
problem Understanding and analyzing human curiosity-driven questions.
method Collection of 13.5K questions from various sources, development of an iterative prompt improvement framework.
result 42% of questions are causal, revealing unique linguistic properties.