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…
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,291 papers · 148 categories
Trend · papers per month
48 results for “Lehmer's question”
Reformulates Lehmer and Schinzel-Zassenhaus questions on polynomial measures.
problem Understanding the difference between reciprocal and skew-reciprocal polynomials.
method Comparing Mahler measures and houses of polynomials.
result The complexity of orientation-preserving and orientation-reversing mapping classes.
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.
Complexity of periodic graphs linked to Mahler measure.
problem Understanding growth rates of graph complexity.
method Defining graph complexity and linking it to Mahler measure.
result Lehmer's question about polynomial roots is equivalent to complexity growth of certain graphs.
New Lehmer Transform for analyzing non-stationary signals.
problem Analyzing non-stationary signals like brain waves.
method Proposes a new Lehmer Transform to decompose statistical moments.
result Theoretical properties of the Lehmer Transform are presented.
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.
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…
Study on instanton homology of pretzel knots and pillowcase Floer homology.
problem Investigating instanton knot homology and Floer homology for a family of pretzel knots.
method Analyzes the reduced singular instanton knot homology and computes bounding cochains in the pillowcase.
result Computed bounding cochains in the pillowcase, revealing a sharp experimental law and rigidity asymmetry.
Crowdsourced science questions improve exam accuracy.
problem Generating high-quality, domain-specific multiple choice questions is challenging.
method Leveraging a corpus and existing questions, the method suggests document selection and answer distractors.
result Crowdsourced questions are indistinguishable from original questions and improve exam accuracy.
Hybrid QC system for Bengali questions using smart data balancing.
problem Classifying factoid questions in Bengali.
method Two-stage approach with 1D CNN for coarse classification and SGD for fine classification.
result Effectiveness of smart data balancing technique in improving classification accuracy.
Paper tackles medical question similarity using domain-relevant embeddings.
problem Identifying same-question pairs in medical contexts.
method Semi-supervised pre-training of a neural network on medical question-answer pairs.
result Our model achieves 82.6% accuracy on medical question similarity task.
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.
Paper evaluates Arabic question similarity, 9 teams participated.
problem Predicting semantic similarity between Arabic questions.
method 9 teams participated in a shared task to predict semantic similarity.
result 9 teams participated in the task, results made publicly available.
Paper proposes a neural network for generating better questions from text.
problem Automatic generation of relevant questions from sentences and paragraphs.
method Adaptive copying recurrent neural network model with a copying mechanism added to a bidirectional LSTM architecture.
result The model outperforms state-of-the-art methods in question generation metrics.
Paper tackles Arabic question similarity, outperforming state-of-the-art.
problem Detecting semantically similar questions in Arabic is challenging.
method Utilizes contextualized word representations (ELMo embeddings) trained on MSA and dialectic sentences, combined with a pairwise similarity layer.
result Achieves 93% F1-score on Modern Standard Arabic benchmark and 82% on dialectical benchmark.
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 …
MAC Net improves natural language question answering with data-driven reasoning.
problem Natural Language Question Answering requires complex reasoning.
method MAC Net architecture separates memory and control for iterative reasoning.
result MAC Net achieves high efficiency and interpretability in NLP tasks.
R2DE assesses new exam questions quickly and accurately.
problem Assessing newly generated exam questions efficiently and accurately.
method R2DE uses NLP to estimate difficulty and discrimination of questions based on their text.
result R2DE can estimate question difficulty and discrimination quickly and accurately.
Unified QuesNet learns comprehensive representations for diverse test questions.
problem Lack of labeled data for test questions in online learning systems.
method Unified framework and two-level hierarchical pre-training algorithm for unsupervised learning of heterogeneous question representations.
result QuesNet effectively learns comprehensive question representations and outperforms existing methods.
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.
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.
Proposes CNN Inception + Gate model for visual question answering.
problem Deep understanding of images and texts for visual question answering.
method Proposes a CNN Inception + Gate model for learning textual representations.
result Improves question representations and overall accuracy in visual question answering.
DiffQue estimates relative difficulty of questions in CQA services.
problem Estimating relative difficulty of questions in community Q&A services.
method Network-aided edge directionality prediction.
result DiffQue outperforms state-of-the-art methods by significant margins.
Algorithm transfers visual concepts to answer out-of-vocabulary questions.
problem Leveraging off-the-shelf visual and linguistic data for out-of-vocabulary answers in visual question answering.
method Unsupervised task discovery for learning task conditional visual classifier, then transferring to visual question answering models.
result Algorithm generalizes to out-of-vocabulary answers successfully.
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.
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.
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.
We are raising questions on discrete and dense subgroups of Diff(I). Most of the questions are around the problems discussed in [A1]-[A4].
Predicts programming languages from Stack Overflow questions and snippets.
problem Incorrectly tagging programming languages in Stack Overflow questions.
method Combines NLP features from titles, bodies, and code snippets for prediction.
result Combined features classifier achieves 91.1% accuracy.
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.
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.
New task AQA tackles acoustic reasoning from sound scenes.
problem Promote research in acoustic reasoning.
method Generate acoustic scenes from elementary sounds and formulate questions.
result Preliminary results with models FiLM and MAC show promise.
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…
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.
The paper justifies two questions on special maps on subgroup of reals.
problem Justifying two questions on special maps on subgroup of reals.
method Different points of view and discussion of two versions of Anderson's Involution Conjecture.
result Discussion of two versions of Anderson's Involution Conjecture.
Paper tackles natural science exam questions, improving over previous systems.
problem Hard natural science exam questions requiring advanced logic reasoning.
method Constructs contextual knowledge graphs for questions and supporting sentences, learns to reason with neural embeddings.
result Model outperforms previous state-of-the-art QA systems on the ARC Challenge Set.