A new DBN model predicts inventory levels in retail, accounting for lost items.
problem Stock freezing due to lost, stolen, or broken items.
method Dynamic Bayesian Network (DBN) with EM algorithm to estimate sales and loss distributions.
result The DBN model accurately predicts inventory levels, improving upon traditional methods.
The paper identifies redundant columns in matrices for feature selection and clustering.
problem Identifying redundant columns in matrices for feature selection and clustering.
method Proves that after re-ordering columns, a matrix can be block-diagonalized revealing linearly dependent columns.
result Identifies redundant columns in matrices, aiding in feature selection and clustering.
Ethereum block builders can earn up to $14M/month by reordering transactions, harming users.
problem Block builders can exploit transaction reordering to earn significant profits, harming users.
method Estimation of MEV payments and analysis of reordering effects.
result Block builders can earn up to $14M/month by reordering transactions, skewing the distribution.
A new approach uses circuit topology to study complex polymer interactions.
problem Understanding structural phase transitions in entangled polymer systems.
method Braided circuit topology framework for multiple-chain systems.
result Circuit topological motif fractions are effective order parameters for structural transitions.
Wavelet scattering predicts material properties beyond training data.
problem Predict material properties beyond training data.
method Atomic orbital wavelet scattering transform.
result Extrapolation of material properties achieved.
Attention forcing improves sequence-to-sequence model training stability.
problem Training auto-regressive sequence-to-sequence models with attention mechanism is challenging.
method Attention forcing guides the model with generated output history and reference attention.
result Attention forcing trains models to recover from mistakes without requiring a schedule or classifier.
E-LTH finds winning tickets scalable across different network architectures.
problem Finding winning tickets in different network architectures efficiently.
method Tweaking winning tickets from one network to another.
result Winning tickets from one network can be stretched or squeezed into another network's subnetwork.
New manifolds found without interior conjugate points.
problem Existence of interior conjugate points in hyperbolic manifolds.
method Construction of non-trapping asymptotically hyperbolic manifolds.
result Found manifolds without interior conjugate points.
Example shows not all conjugate points are bifurcation points in semi-Riemannian geodesics.
problem Determining which conjugate points in semi-Riemannian geodesics are bifurcation points.
method Revisiting and correcting an example by Musso, Pejsachowicz, and Portaluri.
result Every conjugate point on the improved example is a bifurcation point.
Proposes model-based approach for MI learning using point process theory.
problem Lack of statistical point pattern models in MI learning.
method Develops framework using point process theory for principled extensions of MI learning tasks.
result Tractable point pattern models and solutions for MI learning and decision making.
Estimator calculates surface curvature from point cloud samples.
problem Accurately estimating curvature from limited point cloud data.
method Algorithm using probability distribution and nearby points control.
result Controlled number of points ensures accurate curvature estimation.
This paper analyzes saddle points and minimax points in non-convex smooth games.
problem Understanding local optimal points in non-convex smooth games.
method Comprehensive analysis of local minimax points, including their optimality conditions and stability.
result Local saddle points are uniformly local minimax points under mild continuity assumptions.
New tools for constructing fixed point sets in digital topology.
problem Constructing fixed point sets in digital topology.
method Defining excludable points and articulation points, and showing their exclusion from freezing sets.
result Excludable points and articulation points can be excluded from all freezing sets.
Study on connection points on double regular polygons, providing coordinates and proving non-connection points.
problem Identifying connection points on double regular polygons.
method Examined coordinates in trace field, provided constructive proof for prime n. result For n=7, conjectured all remaining points are connection points; for n≥7 prime, provided explicit separatrix. New families of translation surfaces with multiple oblivious points discovered.
problem Identifying points on translation surfaces without nearby closed geodesics.
method Constructing new families of translation surfaces and proving existence in higher genera.
result Translation surfaces in every genus ≥3 have at least one oblivious point.
PoPPy simplifies point process modeling and analysis.
problem Efficient modeling and analysis of sequential data.
method Flexible design and efficient learning of point process models.
result PoPPy enables large-scale point process analysis, simulation, and prediction.
This paper reverses a construction by merging boundary critical points into an interior one.
problem Pushing interior critical points to the boundary and splitting them into two boundary points.
method Specific assumptions allow merging two boundary critical points into one interior critical point.
result Merging two boundary critical points into a single interior critical point.
A new model for point processes without intensity function trade-offs.
problem Inefficiency and trade-offs in existing point process models.
method Point Set Diffusion, a diffusion-based latent variable model.
result Achieves state-of-the-art performance in point process generation.
Develops a method for mapping 3D point clouds with uniform conformal distortions.
problem Challenges in mapping 3D point clouds, especially feature-endowed ones.
method Proposes TEMPO, a novel method based on discrete Teichmüller extremal mappings.
result Introduces TEMPO for accurate recognition and classification of point clouds.
PINNACLE optimizes point selection for PINNs, improving accuracy.
problem Challenges in selecting points for training Physics-Informed Neural Networks (PINNs).
method Introduces PINNACLE, an algorithm that jointly optimizes collocation and experimental points selection, adjusting point proportions dynamically.
result PINNACLE outperforms existing methods in forward, inverse, and transfer learning problems.
The minimal number of critical points is studied for smooth functions on closed manifolds.
problem Determining the minimal number of critical points for smooth functions on closed manifolds.
method Investigates cylindrical ball neighborhoods and exotic critical points, proving the conjecture for certain types of critical points.
result The minimal number of critical points is the same for smooth functions without exotic critical points on closed manifolds of dimension at least 6.
Gradient-based methods struggle with saddle points; curvature exploitation helps.
problem Gradient-based methods struggle with saddle points, leading to undesired stable stationary points.
method Exploits curvature information to escape undesired stationary points.
result Different optimization methods, including gradient and Adagrad, can escape non-optimal stationary points when curvature exploitation is used.
Unified analysis of EG and OGDA for saddle point problems using proximal point method.
problem Solving saddle point problems in bilinear and strongly convex-strongly concave settings.
method Unified analysis as approximations of the proximal point method.
result Unified analysis of EG and OGDA for saddle point problems.
Proposes a method to explain deep neural networks by identifying representer points in the training set.
problem Explaining the predictions of deep neural networks.
method Identifying representer points in the training set to decompose neural network predictions.
result Provides a deeper understanding of neural network predictions through positive and negative representer values.
Investigates point spectra of vector fields and their properties.
problem Understanding the point spectra of vector fields.
method Define and study point spectra, prove properties under isometries, and analyze compactly supported fields.
result Point spectra are well-behaved under isometries and trivial for compactly supported fields.
Adding a point to configurations in closed balls depends on the number of points and their ordering.
problem When can a new point be added to configurations of n distinct points in a closed ball?
method Analyzes the conditions for adding a point based on the number of points and their ordering.
result The possibility of adding a point depends on the number of points and their ordering.
Hard to approximate critical points for simple nonconvex functions.
problem Approximating critical points of nonconvex functions.
method Proving hardness results for polynomial-time approximation of critical points.
result Proving that approximating critical points is intractable for simple nonconvex functions.
Algorithm finds periodic points on Veech surfaces.
problem Finding periodic points on non-square-tiled Veech surfaces.
method Developed an algorithm to compute periodic points.
result Proved that in low discriminant, non-square-tiled Veech surfaces have no periodic points, except for fixed points of the Prym involution.
Estimating boundaries from point clouds with improved accuracy and rigorous error estimates.
problem Identifying the boundary of a domain from point cloud samples.
method Developed new estimators for normal vectors, distances, and boundary tests; provided error estimates.
result Efficient and accurate estimators for boundary properties on point clouds.
The paper classifies circle actions on 6D manifolds with isolated fixed points.
problem Classifying circle actions on 6D manifolds with isolated fixed points.
method Performing equivariant connected sums at fixed points with specific manifolds.
result A sequence of operations can reduce the fixed point data to the empty collection.
The paper models user-advertiser interactions using point processes.
problem Causal inference problems in user-advertiser interaction.
method Temporal marked point processes and neural point processes.
result Neural point processes as practical solutions.
A limit point p of a discrete group of Mobius transformations acting on S^n is called a concentration point if for any sufficiently small connected open neighborhood U of p, the set of translates of U contains a local basis for the topology of S^n at p. For the case of Fuchsian groups (n = 1), every concentration point…
Study fixed points in digital images, introducing new invariants.
problem Understanding properties of digital images through fixed points.
method Introduce new invariants and freezing/cold sets to analyze fixed point sets.
result Existence of fixed point sets restricts maps on their complements.
The paper develops methods to create private synthetic spatial point patterns.
problem Generating private synthetic spatial point patterns.
method Developed differentially private Poisson and Cox point synthesizers.
result The synthesizers effectively maintain privacy and utility of synthetic data.
Self-focal points on ellipsoids of dimension 3 or higher are rare.
problem Existence of self-focal points on Riemannian manifolds of dimension 3 or higher.
method Analyzing geodesics and umbilic points on ellipsoids of various dimensions.
result Ellipsoids of dimension 3 or higher with at least 4 distinct axes have no self-focal points.
Classifies markings on translation surfaces from covering constructions.
problem Understanding point markings on translation surfaces.
method Branched covering constructions and periodic points.
result Complete classification of point markings over strata of quadratic differentials.
Proves new fixed point formulae for complex manifolds with boundary.
problem Fixed points on complex manifolds with boundary conditions.
method Logarithmic Lefschetz fixed point formulae, normal rescaling, relative duality.
result Resonant boundary terms record normal contact and tangential multiplicity.
The paper introduces a method to probabilistically select inducing points in sparse Gaussian processes.
problem The challenge is selecting the optimal number of inducing points in sparse Gaussian processes.
method A point process prior is applied to the inducing points, and the posterior is approximated using stochastic variational inference.
result The model learns which and how many inducing points to use, leading to fewer inducing points being preferred as they become less informative.
Groups with special properties always have fixed points.
problem Groups acting on finite CW-complexes without fixed points.
method Exhibited specific groups with strong fixed-point properties.
result Groups with finite generation and torsion-freeness have global fixed points.
Heavy-ball algorithms can always avoid saddle points with random initialization.
problem Optimizing nonconvex functions with saddle points.
method Developed a new mapping to interpret heavy-ball algorithms as iterations, proving they can escape saddle points.
result Heavy-ball algorithms can escape saddle points with random initialization.
Hybrid BFP-FP improves DNN training accuracy with 8.5x higher throughput.
problem Limited dynamic range of fixed-point arithmetic for DNN training convergence.
method Introducing HBFP, a hybrid BFP-FP approach.
result HBFP matches floating point's accuracy while delivering up to 8.5x higher throughput.
The paper proves Γ-convergence of discrete tangent-point energies to continuous energies and ropelength, with applications to biarc curves.
problem Proving convergence of discrete tangent-point energies to continuous energies and ropelength.
method Using biarc curves and interpolation, the paper proves Γ-convergence of discretized tangent-point energies to the continuous tangent-point energies and ropelength functional. result Discrete almost minimizing biarc curves converge to ropelength minimizers and minimizers of continuous tangent-point energies.
Characterizes extreme points in polygon limit sets.
problem Identifying boundary points in polygon limit sets.
method Characterization through affine dilations and polygon vertices.
result Characterizes which points lie on the boundary of convex hull.
The study confirms a conjecture about critical points of smooth functions.
problem Understanding isolated critical points of smooth functions.
method Investigated cone-like, reasonable, and Rothe H hypothesis critical points.
result The conjecture holds true for certain critical points.
Study circle actions on manifolds with discrete fixed points, focusing on 4D.
problem Characterize circle actions on oriented manifolds with discrete fixed points.
method Use fixed point data and multigraphs to classify actions in dimension 4.
result Classify fixed point data in 4D and prove existence of corresponding manifolds.
New method upsamples sparse, non-uniform point clouds more accurately.
problem Suboptimal results from existing point cloud upsampling methods.
method Imposes manifold distribution constraints using Gaussian functions.
result Generates higher-quality, more uniformly distributed dense point clouds.
Characterizes Lebesgue points using nearest neighbor methods.
problem Consistency of classification algorithms based on nearest neighbors.
method Characterization of Lebesgue points via 1-Nearest Neighbor regression.
result Proves convergence of 1-Nearest Neighbor classification algorithms in metric spaces.
Fixed-point techniques compute semifree geometric circle-equivariant complex cobordism.
problem Computing the coefficient ring of semifree geometric circle-equivariant complex cobordism.
method Fixed-point techniques applied to 19th-century methods.
result Recover a 2004 result of Sinha.