The study classifies complex parallelisable nilmanifolds with unobstructed deformations.
problem Characterizing complex parallelisable nilmanifolds with unobstructed deformations.
method Analyzing Lie algebras associated with nilmanifolds and their verbal ideals.
result There are finitely many complex homotopy types of unobstructed complex parallelisable nilmanifolds up to dimension 19, and infinitely many in dimension 20.
We show that the verbal width is infinite for acylindrically hyperbolic groups, which include hyperbolic groups, mapping class groups and Out(Fn).
Paper develops a method for valid inference using language model predictions from verbal autopsy narratives.
problem Valid inference from verbal autopsy narratives for public health decision-making.
method Develops multiPPI++ method for valid inference using NLP techniques for COD prediction.
result Demonstrates the effectiveness of multiPPI++ in handling transportability issues and recovering ground truth estimates.
VTA combines verbal and latent reasoning for accurate stock time-series forecasts.
problem Challenges in combining textual analysis with time-series data for financial forecasting.
method Converts stock price data into textual annotations, optimizes reasoning trace using inverse MSE, conditions time-series model outputs on reasoning attributes.
result VTA achieves state-of-the-art forecasting accuracy and interpretable reasoning traces.
We address the problem of bootstrapping language acquisition for an artificial system similarly to what is observed in experiments with human infants. Our method works by associating meanings to words in manipulation tasks, as a robot interacts with objects and listens to verbal descriptions of the interactions. The mo…
New framework assesses LM uncertainty without thresholding.
problem Uncertainty quantification for LMs, especially comparing different measures.
method Rank-Calibration framework to assess uncertainty and confidence measures.
result Higher uncertainty correlates with lower generation quality.
Paper introduces a method for generating interlocutor-aware facial gestures in dyadic settings.
problem Generating appropriate non-verbal behavior for conversational agents in dyadic settings.
method Probabilistic method using multi-modal cues from the interlocutor to synthesize facial gestures.
result The model successfully leverages multi-modal input from the interlocutor to generate more appropriate behavior.
A Python tool generates synthetic data for cluster analysis from high-level descriptions.
problem Creating synthetic data for cluster analysis is laborious and requires detailed geometric parameters.
method Proposes natural language-based synthetic data generation and implements it in a Python package.
result Makes it easy to set up interpretable and reproducible benchmarks for cluster analysis.
A new framework evaluates LLM calibration in open-ended QA.
problem Evaluating LLM calibration in open-ended QA settings.
method Sem-ECE framework: sampling answers, grouping by semantic classes, and using frequencies as confidence.
result Sem-ECE estimators are unbiased and Sem2 achieves smaller calibration error. The rich set of sensors in smartphones and wearable devices provides the possibility to passively collect streams of data in the wild. The raw data streams, however, can rarely be directly used in the modeling pipeline. We provide a generic framework that can process raw data streams and extract useful features related…
A trading system uses LLMs to adapt to volatile crypto markets.
problem Volatility and market sentiment in cryptocurrencies make traditional models ineffective.
method Specialized LLM agents for technical analysis, sentiment evaluation, and decision-making; verbal feedback for continuous improvement.
result Agents outperform buy-and-hold strategy with consistent gains across market phases.
Functional Magnetic Resonance Imaging (fMRI) provides dynamical access into the complex functioning of the human brain, detailing the hemodynamic activity of thousands of voxels during hundreds of sequential time points. One approach towards illuminating the connection between fMRI and cognitive function is through dec…
The semantic map calibrates uncertainty from language model probabilities.
problem Uncertainty in language model probabilities for professional decisions.
method Prespecified semantic map linking probabilities of verbal responses to probabilities of declared states.
result Language-derived probabilities outperform printed numerical probabilities and recover valid uncertainty coverage.
For every group genetic code with finite number of generating and at most with one defining relation we introduce the braid group of this genetic code. This construction includes the braid group of Euclidean plane, the braid groups of closed orientable surfaces, B type groups of Artin-Brieskorn, and allow us to study a…
Study aims to develop a humanoid robot dialogue system.
problem Current dialogue systems lack attention to non-verbal cues.
method Participated in a competition to develop a system with facial expressions and gaze control.
result Developed a humanoid robot dialogue system.
The study proves poor ideal three-edge triangulations are minimal for certain 3-manifolds.
problem Finding minimal ideal triangulations for specific 3-manifolds.
method Analyzing properties of poor ideal three-edge triangulations and applying them to construct minimal triangulations.
result Poor ideal three-edge triangulations are proven to be minimal for certain 3-manifolds.
We give a simple method to find ideal points of the character variety of a 3-manifold from an ideal triangulation.
Short proof for ideal polygons with near optimal orthogeodesic decomposition.
problem Decomposing ideal polygons into orthogeodesics.
method Short proof with orthogeodesic decomposition of length at most 2log(n). result Optimal orthogeodesic decomposition of ideal polygons with length 2log(n). A method uses CG to create efficient channels for ideal observers.
problem Computational intractability of ideal observers for high-dimensional image data.
method Conjugate gradient (CG) method for constructing efficient channels.
result CG-based channels approximate IO and HO performance efficiently.
The goal of this work is to study the ideals of the Goldman Lie algebra S. To do so, we construct an algebra homomorphism from S to a simpler algebraic structure, and focus on finding ideals of this new structure instead. The structure S can be regarded as either a Q-module or a Q-module gen…
We investigate the rigidity of hyperbolic cone metrics on 3-manifolds which are isometric gluing of ideal and hyper-ideal tetrahedra in hyperbolic spaces. These metrics will be called ideal and hyper-ideal hyperbolic polyhedral metrics. It is shown that a hyper-ideal hyperbolic polyhedral metric is determined up to i…
Defines timelike ideal boundary for non-positively curved Lorentzian spaces.
problem Understanding the geometry of non-positively curved Lorentzian spaces.
method Introduces timelike ideal boundary as asymptotic classes of geodesic rays, endows with topology and metric, and studies upper curvature bounds.
result Established upper curvature bounds for the resulting metric space.
A taut ideal triangulation of a 3-manifold is a topological ideal triangulation with extra combinatorial structure: a choice of transverse orientation on each ideal 2-simplex, satisfying two simple conditions. The aim of this paper is to demonstrate that taut ideal triangulations are very common, and that their behavio…
The paper studies dynamical properties in semigroups modulo ideals.
problem Analyzing shadowing, expansivity, and stability in semigroups with ideals.
method Investigates shadowing, expansivity, and stability properties in uniform transformation semigroups modulo an ideal.
result Establishes that if a semigroup exhibits shadowing and expansivity modulo an ideal, it is also topologically stable modulo that ideal.
We define the ideal simplicial volume for compact manifolds with boundary. Roughly speaking, the ideal simplicial volume of a manifold M measures the minimal size of possibly ideal triangulations of M "with real coefficients", thus providing a variation of the ordinary simplicial volume defined by Gromov in 1982, t…
The notion of ideal immersions was introduced by the author in 1990s. Roughly speaking, an ideal immersion of a Riemannian manifold into a real space form is a nice isometric immersion which produces the least possible amount of tension from the ambient space at each point. In this paper, we classify all ideal hypersur…
New formula calculates volumes of ideal hyperbolic drums.
problem Computing volumes of ideal hyperbolic drums.
method Proved a volume formula for arbitrary ideal hyperbolic antiprisms (drums).
result Volume formula for ideal hyperbolic drums.
Study of combinatorial Calabi flow on ideal circle patterns.
problem Finding ideal circle patterns with prescribed curvatures.
method Combinatorial Calabi flow in hyperbolic and Euclidean geometry.
result Flow converges exponentially to ideal circle patterns.
A biconservative submanifold of a Riemannian manifold is a sub- manifold with divergence free stress-energy tensor with respect to bienergy. These are generalizations of biharamonic submanifolds. In 2013, B. Y. Chen and M.I. Munteanu proved that δ(2)-ideal and δ(3)-ideal biharmonic hypersurfaces in Euclidean space …
The paper studies deformations of Lie ideals in Lie algebras.
problem Understanding deformations of Lie ideals in Lie algebras.
method Develops deformation theory, compares cohomologies, enriches deformation complex.
result Deformation cohomology classes differentiate smooth deformations of ideals.
This work creates a system for understanding human movement in spaces.
problem Simplify communication and interaction between robots and humans in spatial tasks.
method Uses unsupervised learning with neural autoencoding to learn continuous representations of spatio-temporal trajectory data.
result Proposes a method to form prototypical representations of movement based on spatial context.
Paper solves long-standing problem of infinite ideal polyhedra in hyperbolic space.
problem Characterize infinite ideal polyhedra in hyperbolic 3-space.
method Introduced combinatorial Ricci flow for infinite ideal circle patterns.
result Proved characterization of infinite ideal circle patterns under specific conditions.
Wintgen ideal surfaces in E^4 form an important family of surfaces, namely surfaces with circular ellipse of curvature. Obviously, Wintgen ideal surfaces satisfy the pointwise equality K+K_N=H^2. In the present study we consider the Wintgen ideal surfaces in n-dimensional Euclidean space E^4. We have shown that Wintgen…
We discuss two different in general natural approaches to the ideal closure and ideal boundary of Busemann nonpositively curved metric space. It is shown that the identity map of the space admits surjective continuation from its coarse ideal closure to the weak one. We consider some situations when these closures coinc…
In this paper we provide a new obstruction to 0-concordance of knotted surfaces in S4 in terms of Alexander ideals. We use this to prove the existence of infinitely many linearly independent 0-concordance classes and to provide the first proof that the submonoid of 2-knots is not a group. The main result is that the…
Combinatorial description of 3-manifolds using ordered triangulations.
problem Understanding closed 3-manifolds through ideal triangulations.
method Combining ordered ideal triangulations and Pachner moves.
result Closed 3-manifolds can be described via ordered triangulations and moves.
Proof of existence for ideal triangulations that normalize fibers in certain 3-manifolds.
problem Existence of ideal triangulations that normalize fibers in specific 3-manifolds.
method Proof and algorithm construction for ideal triangulations.
result Existence of ideal triangulations that normalize fibers in certain 3-manifolds.
Paper connects fair machine learning to political philosophy, highlighting flaws in ideal approaches.
problem Lack of natural formulation for social desiderata in machine learning.
method Proposes metrics and algorithms to satisfy subsets of fairness parities, trading off against utility.
result Misguided fair machine learning algorithms reflect broader flaws in ideal methodological approaches.
Every biharmonic Wintgen ideal submanifold in a Riemannian manifold of constant sectional curvature is either minimal or has constant mean curvature.
problem Biharmonic Wintgen ideal submanifolds in Riemannian manifolds of constant sectional curvature
method Show that every biharmonic Wintgen ideal submanifold in a Riemannian manifold of nonpositive constant sectional curvature is minimal and that every biharmonic Wintgen ideal submanifold in a Riemannian manifold of positive constant sectional curvature has constant mean curvature.
result Partial affirmative answers to Chen's conjecture, generalized Chen's conjecture in hyperbolic spaces, and Balmuş-Montaldo-Oniciuc conjecture in spheres within the class of Wintgen ideal submanifolds.
Study on Hermitian metrics on Lie algebras with specific ideals.
problem Classifying Hermitian metrics on Lie algebras with abelian ideals.
method Examined unimodular Lie algebras with abelian ideals of codimension two, classified metrics.
result Classification of Bismut Kähler-like and Bismut torsion-parallel metrics.
TBIP uses texts to quantify lawmakers' political positions.
problem Quantifying lawmakers' political positions from speeches, tweets, etc.
method Unsupervised probabilistic topic model analyzing texts.
result TBIP separates lawmakers by party and infers ideal points close to vote-based.
The notion of ideal embeddings was introduced in [B.-Y. Chen, {Strings of Riemannian invariants, inequalities, ideal immersions and their applications.} The Third Pacific Rim Geometry Conference (Seoul, 1996), 7-60, Int. Press, Cambridge, MA, 1998]. Roughly speaking, an ideal embedding (or a best of living) is an isome…
We generalise work of Young-Eun Choi to the setting of ideal triangulations with vertex links of arbitrary genus, showing that the set of all (possibly incomplete) hyperbolic cone-manifold structures realised by positively oriented hyperbolic ideal tetrahedra on a given topological ideal triangulation and with prescrib…
Study laws of cosines and sines for hyperbolic shapes with ideal vertices.
problem Formulating trigonometric laws for shapes with ideal vertices in hyperbolic geometry.
method Using hyperboloid model and Lorentzian geometry, establishing laws for quadrilaterals, pentagons, and partially truncated tetrahedra.
result Transversal lengths of partially truncated tetrahedra depend only on internal edge lengths at ideal vertices.
Improved bounds on ideal vertices in right-angled hyperbolic polyhedra.
problem Finding bounds on ideal vertices in hyperbolic polyhedra.
method Improved Nikulin's inequality and Nonaka's lower bound.
result Shorter proofs and improved bounds on ideal vertices.
Verifies a conjecture for the figure eight knot.
problem Relates A-ideal and recurrence ideal of knots.
method Uses quantum A-ideals, q-holonomicity, and AJ conjecture.
result Strong AJ conjecture verified for figure eight knot.
Ideal attribution mechanisms track model interactions for faithful watermarks.
problem Ensuring models provide transparent and fair attribution decisions.
method Introducing ideal attribution mechanisms and a ledger for tracking model interactions.
result A unified framework for evaluating watermarking schemes, clarifying attainable guarantees.
A dynamical analog of the prime ideals for simple non-commutative rings is introduced. We prove a factorization theorem for the dynamical ideals. The result is used to classify the surface knots and links in the smooth 4-dimensional manifolds.