Defines conformal reference frames for Lorentzian manifolds.
problem Understanding causal relations in cosmology.
method Projection of six-dimensional sky bundle to three-dimensional manifold, celestial transform, contact structure.
result Explicit expression of a 1-form generating contact structure and equation for flow of time.
Machine learning models classify celestial objects like pulsars and black holes.
problem Classifying high-energy celestial objects using photometric data.
method Applied tree-based models and RNN to classify pulsars and black holes.
result RNN showed potential for real-time object discrimination and classification.
Study periodic orbits in Stark-Zeeman systems using Arnold's J+-invariant.
problem Understanding periodic orbits in Stark-Zeeman systems.
method Apply Arnold's theory of generic smooth plane curves to Stark-Zeeman systems and introduce invariants of periodic orbits based on Arnold's J+-invariant. result Study the behavior of invariants of periodic orbits in planar Stark-Zeeman systems.
Investigates the rotating Kepler problem for energy values ≤ -3/2.
problem Understanding periodic orbits and symplectic structures in rotating celestial mechanics.
method Ligon-Schaaf and Levi-Civita symplectic regularizations, special concave toric domain construction.
result Identification of a special concave toric domain (SCTD) for the RKP phase space.
A reconstruction theorem in terms of the topology and geometrical structures on the spaces of light rays and skies of a given space-time is discussed. This result can be seen as part of Penrose and Low's programme intending to describe the causal structure of a space-time M in terms of the topological and geometrical…
New spaces at infinity identified for Minkowski spacetime.
problem Characterizing asymptotic infinities of Minkowski spacetime.
method Embedding and describing homogeneous spaces of the Poincaré group.
result Determined new structures on asymptotic infinities.
Survey on finding global surfaces of section for Reeb flows.
problem Finding global surfaces of section for Reeb flows.
method Symplectic Topology methods.
result Existence of closed geodesics and sharp systolic inequalities.
We present a new, fully generative model of optical telescope image sets, along with a variational procedure for inference. Each pixel intensity is treated as a Poisson random variable, with a rate parameter dependent on latent properties of stars and galaxies. Key latent properties are themselves random, with scientif…
The study of Reeb dynamics on contact manifolds without periodic orbits.
problem Existence of periodic Reeb orbits on bm-contact manifolds. method Generalization of the Weinstein conjecture, proof of periodic orbits, existence of traps.
result In dimension 3, there are infinitely many periodic orbits on the critical set.
The paper examines how the topology of level sets changes with critical points in Morse theory.
problem Understanding how the topology of level sets changes with critical points in Morse theory.
method Study of sublevel sets and level sets of Morse functions, analysis of critical points and their indices.
result For a general class of functions, the topology of a regular level set changes when passing a single critical point, unless the index is half the dimension of the manifold.
Sturm theory applied to symplectic geometry and mechanics.
problem Detecting geometric properties of solutions in symplectic geometry and mechanics.
method Generalization of symplectic Sturm theory to Hamiltonians and application to semi-Riemannian manifolds and singular Lagrangian systems.
result Detection of conjugate and focal points on semi-Riemannian manifolds and geometrical properties of solutions space.
Novel method transfers orometric measures to metric data sets, identifying key items.
problem Identifying key items in metric data sets like knowledge graphs.
method Transfers orometric measures to bounded metric spaces, using 'isolation' and 'prominence' functions.
result Identifies structurally relevant items in geographic data sets of Germany and France.
The paper models star dynamics using Ricci flow and Perelman entropy, revealing chaotic behavior.
problem Modeling chaotic positional dynamics of stars in celestial systems.
method Discrete dynamical systems, Ricci flow, Perelman entropy, Lyapunov exponents, bifurcation analysis.
result Entropy increases exponentially, indicating challenging long-term star position prediction.
It is shown that if M is a strongly causal free of naked singularities space-time, then its causal structure is completely characterized by a partial order in the space of skies defined by means of a class non-negative Legendrian isotopies. It is also proved that such partial order is determined by the class of futur…
Robot science discovers new materials faster.
problem Discovering advanced materials in complex synthesis landscapes.
method Closed-loop, active learning-driven autonomous system.
result Discovery of a novel epitaxial nanocomposite phase-change memory material.
Improved bounds for algebraic degeneracy and hyperbolicity of hypersurfaces.
problem Improving bounds for algebraic degeneracy and hyperbolicity of hypersurfaces in complex projective space.
method Combining techniques from Diverio-Merker-Rousseau, Bérczi, and Darondeau with computer explorations.
result New degree bounds for algebraic degeneracy and hyperbolicity, improving previous results.
The paper uses remote sensing to validate global economic growth patterns.
problem Lack of reliable data on economic growth and wealth distribution.
method Introduces a novel economic observatory using remote sensing of Earth's surface.
result Observed sigma-convergence in post-Cold War period, but failed after financial crisis.
Gaussian processes model sparse data in astrophysics and chemistry.
problem Scarcity of data in high-energy astrophysics and synthetic chemistry.
method Gaussian processes for uncertainty-aware predictions and inferences.
result GPs enable predictions and model latent emission from black holes and molecules.
Study extends geodesic ray transform results to orientable surfaces.
problem Characterize and stabilize mixed and transverse ray transforms on surfaces.
method Algebraic arguments applied to various geometries and ray transforms.
result Characterization of kernel and stability for mixed and transverse ray transforms on orientable surfaces.
Classifies different types of Darboux transformations for multidimensional operators.
problem Classifying Darboux transformations for multidimensional operators.
method Analyzes all known types of Darboux transformations and introduces new types.
result Full classification of first-order Darboux transformations and a description of higher-order transformations.
The paper introduces models to learn generalized transformation equivariant representations.
problem Capturing intrinsic visual structures equivariant to various transformations.
method Deterministic and probabilistic AutoEncoding Transformations (AET and AVT) models trained to learn visual representations from generic groups of transformations.
result Generalized TERs (GTERs) that are equivariant to transformations in a more general fashion.
New filter bank sparsifying transforms outperform patch-based methods for image denoising.
problem Improving image denoising performance using data-adaptive sparsifying transforms.
method Proposes a new transform learning framework using undecimated perfect reconstruction filter banks, allowing independent filter length choice.
result Filter bank sparsifying transforms outperform existing patch-based methods for image denoising.
Integration procedure for Lie groupoid natural transformations.
problem Infinitesimal counterpart of natural transformations in Lie groupoids.
method Integration procedure for Lie groupoid morphisms.
result Provides smooth natural transformations between Lie groupoid morphisms.
Proposes differential and integral invariants under Mobius transformation.
problem Handling non-rigid deformation in 2-D and 3-D shapes.
method Focuses on Mobius transformation, proposes differential and integral invariants.
result Proposes differential and integral invariants under Mobius transformation.
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.
Introduces pseudo-codecomposition of transformation groups.
problem Understanding and categorizing transformation groups.
method Introduces pseudo-codecomposition and analyzes properties of transformation groups.
result The class of pseudo-codecomposable transformation groups is a proper intermediate class.
This paper investigates efficient Transformers and finds they scale with problem size.
problem Finding suitable replacements for standard Transformers in large-scale tasks.
method Modeling efficient Transformers (Sparse and Linear) as Dynamic Programming problems and analyzing their reasoning capabilities.
result Efficient Transformers scale with problem size, but can be more efficient for certain DP problems.
The conformal geometry of spacelike surfaces in 4-dimensional Lorentzian space forms has been studied by the authors in a previous paper, where the so-called polar transform was introduced. Here it is shown that this transform preserves spacelike conformal isothermic surfaces. We relate this new transform with the know…
Paper improves tensor completion using unitary transforms.
problem Robust tensor completion for various datasets.
method Transformed tensor SVD with unitary matrices.
result Recovered images have better PSNR than traditional methods.
Transforms classical connections using pushforwards and gauge transformations.
problem Transforming classical connections in categorical settings.
method Constructing pushforwards and applying gauge transformations to decorated path spaces.
result Combines traditional gauge transformation with affine translation.
Paper introduces graph-based transforms for video compression.
problem Efficiently represent video signals for compression.
method Develops two techniques for designing graph-based transforms (GL-GBTs and EA-GBTs).
result Graph-based transforms outperform traditional KLT in video compression.
Transformers interpret as probabilistic mixtures, offering new insights.
problem Understanding Transformers from a probabilistic perspective.
method Modeling Transformers as mixtures of Gaussian models.
result Transformers can be seen as maximum posterior probability estimators.
Study normal operators of double fibration transforms with conjugate points.
problem Normal operators of double fibration transforms with conjugate points.
method Stable conditions on the distribution of conjugate points, splitting into elliptic and Fourier integral operators.
result Normal operator splits into an elliptic pseudodifferential operator and Fourier integral operators.
Transformer-MGK replaces redundant heads with Gaussian key mixtures, improving efficiency and performance.
problem Redundant attention heads in transformers degrade performance and efficiency.
method Transformer-MGK replaces redundant heads with a mixture of Gaussian keys.
result Transformer-MGK accelerates training and inference, reduces parameters and FLOPs, and achieves comparable or better accuracy.
Adversarial learning improves image augmentation for neural networks.
problem Improving data augmentation for neural networks with limited data.
method Adversarial learning using an encoder-decoder architecture with a spatial transformer network.
result Our approach outperforms previous generative data augmentation methods.
B-cos transformers explain Vision Transformers' decisions.
problem Lack of holistic explanations for transformer outputs.
method Formulate each component as dynamic linear, allowing a single linear transform for summarization.
result Bcos-ViTs are highly interpretable and competitive on ImageNet.
The paper examines how polarized curves behave near singular points.
problem Analyzing the behavior of polarized curves near singular points.
method Investigates the limiting behavior of Darboux and Calapso transforms of polarized curves in the conformal n-dimensional sphere.
result For a pole of first order, all transforms converge to the original curve. For a pole of second order, a generic Darboux transform converges, but a Calapso transform has a limit point or circle.
The paper analyzes transformation models in high-dimensional settings.
problem Analyzing transformation models in high-dimensional data.
method Proposed an estimator for transformation parameter and showed asymptotic normality.
result The proposed estimator works well in small samples and tests the log-wage transformation.
XR-Transformer accelerates XMC by recursively fine-tuning on multi-resolution objectives.
problem Efficiently classifying texts with large label sets.
method Recursive multi-resolution fine-tuning of transformers.
result XR-Transformer achieves 20x faster training time and 54% Precision@1 on Amazon-3M.
Novel power transform unifies various mathematical functions.
problem Normalizing and standardizing datasets.
method Presented a novel power transform.
result Unified various mathematical functions.
Algorithm finds optimal affine transformation to minimize overall distortion.
problem Minimizing distortion in affine transformations.
method Riemannian geometry approach to define and minimize distortion.
result Mean distorting transformation found for minimizing overall distortion.
We study the dynamics of the discrete bicycle (Darboux, Backlund) transformation of polygons in n-dimensional Euclidean space. This transformation is a discretization of the continuous bicycle transformation, recently studied by Foote, Levi, and Tabachnikov. We prove that the respective monodromy is a Moebius transform…
Transformers struggle to approximate smooth functions, relying on piecewise constant approximations.
problem Understanding the expressivity of Transformers for function approximation.
method Theoretical analysis and experimental validation of Transformer's ability to approximate smooth functions.
result Transformers cannot reliably approximate smooth functions, relying on piecewise constant approximations.
The Weyl transform is introduced as a rich framework for data representation. Transform coefficients are connected to the Walsh-Hadamard transform of multiscale autocorrelations, and different forms of dyadic periodicity in a signal are shown to appear as different features in its Weyl coefficients. The Weyl transform …
Defines gauge transformations for Jacobi structures and their effects on contact groupoids.
problem Understanding transformations of Jacobi structures and their implications.
method Definition and discussion of gauge transformations for Jacobi structures and their impact on contact groupoids.
result Gauge transformations affect the contact structure of contact groupoids.
Gaussian process quadrature improves moment transformation accuracy.
problem Computing moments of transformed Gaussian variables with error accounting.
method Bayesian quadrature (Gaussian process quadrature) for numerically estimating integrals.
result Proposed method outperforms classical quadrature methods in accuracy.
We define a transformation on harmonic maps from a Riemann surface into the 2-sphere which depends on a complex parameter, the so-called mu-Darboux transformation. In the case when the harmonic map N is the Gauss map of a constant mean curvature surface f and the parameter is real, the mu-Darboux transformation of -N i…
Transforms surfaces into spheres using mean curvature.
problem Transforming surfaces into spheres.
method Transformation based on mean curvature.
result Surfaces morphed into round spheres.