Article
Mathematics
Enrico Leuzinger, Robert Young
Summary: The paper proves sharp filling inequalities for (arithmetic) lattices in higher rank semisimple Lie groups, showing that the n-dimensional filling volume function grows at the same rate as that of the associated symmetric space when n is less than the rank, and exponentially when n is equal to the rank. This generalizes previous theorems on length distortion in lattices and confirms conjectures of various mathematicians.
ANNALS OF MATHEMATICS
(2021)
Article
Mathematics
Chao Li, Yifeng Liu
Summary: This article examines the relationship between the Chow group and L-functions under certain conditions, proving a portion of the Beilinson-Bloch conjecture and constructing elements while calculating their heights.
ANNALS OF MATHEMATICS
(2021)
Article
Mathematics
Sergey Mikhailovich Dudakov
Summary: In this paper, the theory of finite subsets of a commutative cancellative monoid M is considered. It has been previously proven that elementary arithmetic can be interpreted in the theory of finite subsets of M. The paper extends this result to Abelian torsion groups with elements of unbounded order.
Article
Multidisciplinary Sciences
Tessa E. S. Charlesworth, Aylin Caliskan, Mahzarin R. Banaji
Summary: This study analyzes the historical change and stability of social group representations using word embeddings from 850 billion words in English-language Google Books. The results show that while the top-associated words and traits changed over time, the average valence of these stereotypes remained generally persistent.
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
(2022)
Article
Computer Science, Artificial Intelligence
Klim Zaporojets, Giannis Bekoulis, Johannes Deleu, Thomas Demeester, Chris Develder
Summary: This study proposes a method for solving arithmetic word problems in natural language processing systems, using Tree-RNN to score candidate solution equations. Experimental results show that this method outperforms previous algorithms in terms of accuracy.
EXPERT SYSTEMS WITH APPLICATIONS
(2021)
Article
Computer Science, Software Engineering
Jean-Michel Muller, Laurence Rideau
Summary: This study analyzes a complete set of algorithms for manipulating double-word numbers and provides formal proofs for all the theorems given in the original article. The formal proof work helps identify mistakes in the original paper proofs, improves error bounds, and generalizes some results by changing the rounding mode. The formal proofs make the algorithms presented in the article more reliable and even more accurate than previously believed.
ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
(2022)
Article
Mathematics
Nir Avni, Chen Meiri
Summary: The study proves that for a higher rank arithmetic lattice F, which is a centerless irreducible group in characteristic zero, if F is either nonuniform or is uniform of orthogonal type and dimension at least 9, then F has a bi-interpretation with the ring of integers 7L. This implies that the first-order theory of F is undecidable, all finitely generated subgroups of F are definable, and F can be characterized by a single first-order sentence among all finitely generated groups.
DUKE MATHEMATICAL JOURNAL
(2023)
Article
Mathematics
Michael Magee, Doron Puder
Summary: This article investigates the expected value of the trace of a word in the free group and shows that it has a convergent Laurent expansion at n = infinity involving maps on surfaces and L2-Euler characteristics of mapping class groups. The results obtained generalize previous theorems and provide important corollaries and estimates.
MATHEMATISCHE ANNALEN
(2022)
Article
Psychology, Multidisciplinary
Marian Hickendorff
Summary: The study found that students' performance in solving arithmetic word problems did not significantly differ across grades, even when problems contained irrelevant numerical information. Non-verbal reasoning was more important in standard word problems in one-step arithmetic, while reading comprehension was more important in solving two-step arithmetic word problems.
FRONTIERS IN PSYCHOLOGY
(2021)
Article
Mathematics
Cristina Ayala-Altamirano, Eder Pinto, Marta Molina, Maria C. Canadas
Summary: This study examines how 9-10-year-old pupils work with equations and their understanding of indeterminate quantities. The findings suggest that arithmetic word problems can help students engage with indeterminate quantities and represent them using equations.
Article
Mathematics, Applied
Beibei Liu, Shi Wang
Summary: We study the Eisenstein series associated with full rank cusps in complete hyperbolic manifolds. It is shown that each full rank cusp corresponds to a cohomology class in H-n (Gamma, V), where V can be either the trivial coefficient or the adjoint representation, for a given Kleinian group Gamma < Isom(+)(Hn+1). Furthermore, by computing the intertwining operator, it is shown that different cusps give rise to linearly independent classes.
FORUM OF MATHEMATICS SIGMA
(2023)
Article
Computer Science, Theory & Methods
Andrey Chusov
Summary: The article presents parallel and vectorized algorithms for full-word addition of big unsigned integers with efficient carry propagation. The algorithms detect carry origins within vector operands, mask corresponding bits, and perform scalar addition to compute the sum. Experimental results demonstrate that the proposed parallel and vectorized implementations outperform sequential methods and adders based on redundant number systems.
IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS
(2022)
Article
Mathematics, Applied
G. Conant, A. Pillay, C. Terry
Summary: The paper investigates the structural characteristics of subsets A in a finite group with VC-dimension less than k, using algebraically well-structured sets to describe the structure of A and considering normal subgroups with bounded index in terms of k, r, and ε for groups with a uniformly fixed finite exponent r. For nonabelian groups, the introduction of Bohr neighborhoods involves model-theoretic methods and structural analysis of compactifications of pseudofinite groups, as well as results related to approximate homomorphisms.
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY
(2022)
Article
Mathematics, Applied
James Rickards
Summary: This article presents a practical algorithm for computing the fundamental domain of an arithmetic Fuchsian group. The algorithm combines and improves upon methods proposed by Voight and Page, resulting in enhanced efficiency.
MATHEMATICS OF COMPUTATION
(2022)
Article
Physics, Mathematical
Michael Magee
Summary: This paper studies random representations of fundamental groups of surfaces into special unitary groups, establishing the existence of a large n asymptotic expansion for the expected value of the trace of any fixed element of the fundamental group under a random representation. The main technical contribution lies in effectively analyzing and controlling the entire contribution from irreducible representations outside certain carefully chosen rational families.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2022)
