New projection techniques reduce the frequency of projections in solving LCPs.
problem Solving linearly constrained problems efficiently with reduced projection frequency.
method Delayed projection technique to call a projection less frequently.
result Theoretical and practical improvements in convergence rates and efficiency.
Study on Gauduchon manifolds finds metrics for projectively flat bundles.
problem Existence of Hermitian-Poisson metrics on projectively flat bundles.
method Heat flow techniques and continuity methods.
result Established a correspondence between Hermitian-Poisson metrics and semi-simplicity.
In Finsler geometry, there are infinitely many models of constant curvature. The Funk metrics, the Hilbert-Klein metrics and the Bryant metrics are projectively flat with non-zero constant curvature. A recent example constructed by the author is projectively flat with zero curvature. In this paper, we introduce a techn…
Random projections simplify complex data for classification.
problem Handling high-dimensional data in classification problems.
method Two techniques: ensemble of random projections and hashing/sketching.
result Approximate statistical efficiency with reduced complexity.
The paper studies knots in projective space using virtual link theory.
problem Understanding knots in three-dimensional projective space.
method Associate virtual links to projective links and apply virtual knot theory techniques.
result Equivalent projective links correspond to equivalent virtual links modulo a flype move.
A new technique segments customers from diverse data, improving recommendation accuracy.
problem Segmenting customers with diverse, incomplete preference data.
method Model-based projection technique to transform and cluster data.
result Asymptotic recovery of true customer segments with theoretical guarantees.
Extends techniques to show existence of all cusp types in convex projective manifolds.
problem Existence of all cusp types in convex projective manifolds.
method Extension of techniques by Ballas-Marquis.
result Existence of all cusp types in all dimensions except diagonalizable.
Paper constructs positive Ricci metrics on various connected sums of projective spaces.
problem No universal bound on Betti numbers for manifolds with positive Ricci curvature.
method Revisits and extends Perelman's techniques to construct metrics.
result Positive Ricci metrics constructed on arbitrary connected sums of complex, quaternionic, and octonionic projective spaces.
The study improves bounds on space waists using advanced geometry techniques.
problem Understanding the waist of different geometric spaces.
method Advanced geometric techniques, including Borsuk-Ulam-Crofton method, Hausdorff measure.
result Established new waist bounds for various spaces.
The study proves rationality of complex projective varieties with holomorphic vector fields.
problem Rationality of complex projective varieties with holomorphic vector fields.
method Key technique by Harvey-Lawson on finite volume flows.
result Uniform upper bound on Betti numbers for varieties with holomorphic vector fields.
As a typical dimensionality reduction technique, random projection can be simply implemented with linear projection, while maintaining the pairwise distances of high-dimensional data with high probability. Considering this technique is mainly exploited for the task of classification, this paper is developed to study th…
Geometric techniques reveal new insights into Gromov-Witten invariants.
problem Formulating Gromov-Witten invariants for complete intersections in projective space.
method Combining geometric group theory and geometric topology, focusing on geodesic laminations.
result Primitive cohomologies unify mathematical formulations of Gromov-Witten invariants.
The paper presents a practical method for evaluating investment projects using real options.
problem Evaluating investment projects under uncertainty and strategic risk management.
method Binomial trees and real options techniques for evaluating investment projects.
result The method can be used for most real options and introduces Project Value at Risk for feasibility.
Recent theoretical work has identified random projection as a promising dimensionality reduction technique for learning mixtures of Gausians. Here we summarize these results and illustrate them by a wide variety of experiments on synthetic and real data.
The paper classifies vector fields on 5D nilpotent Lie groups.
problem Classifying left-invariant affine and projective vector fields on 5D nilpotent Lie groups.
method Algebraic characterization and case-by-case analysis of vector fields.
result All projective vector fields are affine, extending classical results.
New method uses data characteristics for better random projections.
problem Improving random projections for better data reduction.
method Data-dependent random projections for superior performance.
result Proves superior performance in matrix multiplication, regression, and classification.
Sinh-acceleration speeds up B-spline option pricing.
problem Improving efficiency in option pricing calculations.
method Using sinh-acceleration on B-spline probability density projection.
result SINH acceleration technique improves error control and reduces CPU time.
The paper defines projections for Wasserstein distances to preserve convex order in probability measures.
problem Designing sampling techniques to preserve convex order in probability measures.
method Defining projections for Wasserstein distances and solving optimization problems.
result The projections do not depend on ρ in dimension 1 and their quantile functions are explicit.
Entropy rigidity proven for 3D and higher convex projective manifolds.
problem Entropy rigidity for strictly convex projective manifolds.
method Uses techniques from Besson, Courtois, and Gallot's entropy rigidity theorem.
result Uniform lower bounds on volume for finite volume strictly convex projective manifolds in dimensions ≥ 3.
In this note, we present a new averaging technique for the projected stochastic subgradient method. By using a weighted average with a weight of t+1 for each iterate w_t at iteration t, we obtain the convergence rate of O(1/t) with both an easy proof and an easy implementation. The new scheme is compared empirically to…
Construct special Lagrangian submanifolds in complex projective space.
problem Finding special Lagrangian submanifolds in complex projective space.
method Moment map technique and classification of cohomogeneity one actions.
result Examples of special Lagrangian submanifolds constructed.
Develops an oblique projection technique to approximate a foliation for non-normal dynamics.
problem Modeling dynamics far from a primary Spectral Submanifold (SSM) in non-normal systems.
method Oblique projection technique based on experimental data.
result Approximates a stable invariant foliation for non-normal dynamics efficiently.
Model projection transfers convolutional network properties to feedforward networks.
problem Transferring properties between feedforward and convolutional networks.
method Unified node-level framework with tensor-valued activations, model projection.
result Projected CNN nodes inherit GFFN-style trainable structure.
The paper compares PCA and PP for scRNA sequencing data.
problem Limitations of PCA in scRNA sequencing data.
method Applied PCA and PP (using negative Shannon's entropy) on scRNA sequencing data.
result PP outperforms PCA in scRNA sequencing data.
The paper updates SVD of evolving matrices using projection techniques.
problem Updating the rank-k truncated SVD of evolving matrices.
method Projection viewpoint, building subspaces to approximate singular vectors.
result The proposed algorithm leads to higher accuracy, especially for large singular values.
This paper classifies superintegrable systems on 2D geometries with projective symmetries.
problem Classifying superintegrable systems on 2D geometries with projective symmetries.
method Combining metric projective differential geometry and superintegrability, defining projective equivalence, and applying transformation rules.
result Potentials of projectively equivalent Hamiltonians follow a linear superimposition rule.
A new method sorts projects using Quicksort and Bradley-Terry model for uncertain long-term benefits.
problem Selecting projects with uncertain long-term benefits.
method Combining Quicksort and Bradley-Terry model for ranking projects based on uncertain long-term benefits.
result Proposed methods outperform existing aggregation methods and can be combined with sampling techniques.
We determine that the deformation space of convex real projective structures, that is, projectively flat torsion-free connections with the geodesic convexity property on a compact 2-orbifold of negative Euler characteristic is homeomorphic to a cell of certain dimension. The basic techniques are from Thurston's lecture…
The study improves bounds on non-secant defectivity of projective varieties.
problem Bounding non-secant defectivity of projective varieties.
method Using osculating projections and bounds on linear projections.
result Asymptotic non-defectivity of Grassmannians for h≤(r+1n+1)⌊log2(r)floor. Classifies curves up to symplectic isotopy.
problem Classifying rational cuspidal curves up to symplectic isotopy.
method Topological tools, pseudoholomorphic techniques, and birational transformations.
result Classifies rational cuspidal curves of degrees 6 and 7 up to symplectic isotopy.
In this paper we construct a parametrization-free embedding technique for numerically evolving reaction-diffusion PDEs defined on algebraic curves that possess an isolated singularity. In our approach, we first desingularize the curve by appealing to techniques from algebraic geometry. We create a family of smooth curv…
Paper improves multi-objective optimization using machine learning and KSA.
problem Improving performance of multi-objective optimization solutions.
method Employed machine learning to identify the best projected space for KSA.
result Up to 12% improvement in time achieved through learning method.
This paper analyzes and improves active learning techniques for real-world projects.
problem Reducing labelling effort in machine learning models with real-world constraints.
method Systematic study of active learning issues, proposing techniques to address model convergence, annotation error, and dataset imbalance.
result Presentation of two techniques to speed up active learning: partial uncertainty sampling and larger query size.
We consider an important class of signal processing problems where the signal of interest is known to be sparse, and can be recovered from data given auxiliary information about how the data was generated. For example, a sparse Green's function may be recovered from seismic experimental data using sparsity optimization…
The paper introduces DP algorithms using random projections and sign random projections for improved privacy in machine learning.
problem Improving differential privacy in machine learning applications.
method Developed algorithms based on random projections and sign random projections, focusing on individual differential privacy (iDP) and standard differential privacy (DP).
result DP-SignOPORP and iDP-SignRP achieve superior performance in differential privacy, especially for small epsilon values.
Quantum cohomology gives a finite dimensional integrable system via the Dubrovin connection. Motivated by Givental's work on mirror symmetry, we use gauge theory techniques and the Frobenius Integrability Theorem to find flat sections for the Dubrovin connection. An explicit calculation is given for projective space.
The paper proves a conjecture about the positivity of the Euler characteristic for complex projective manifolds.
problem Proving the positivity of the Euler characteristic for complex projective manifolds with large fundamental groups.
method Introducing a vanishing cycle functor of multivalued one-forms and applying non-abelian Hodge theory techniques.
result The paper proves a stronger statement about the positivity of the Euler characteristic for complex projective manifolds with large fundamental groups and almost faithful linear representations.
Develops precise expressions for random projections for better machine learning tasks.
problem Improving the accuracy of dimensionality reduction in machine learning tasks.
method Exploits recent developments in spectral analysis of random matrices to derive accurate expressions for random projection matrices.
result Provides precise expressions that reflect the practical performance of sketching methods, including Gaussian and Rademacher sketches.
Weil-Petersson volumes vary continuously with weighted points on a projective line.
problem Continuity of Weil-Petersson volumes in moduli space with weighted points.
method Localization and geometric computation methods.
result CM volume converges to geometric volume as weights approach Calabi-Yau geometry.
Paper solves robust multi-dimensional scaling with accelerated projections.
problem Localize point locations from noisy pairwise distances.
method Alternating projections with tangent space acceleration.
result Linear convergence of reconstructed points to original points.
This work is the first part of a project dealing with an in-depth study of effective techniques used in econometrics in order to make accurate forecasts in the concrete framework of one of the major economies of the most productive Italian area, namely the province of Verona. In particular, we develop an approach mainl…
We extend GAN latent space projection for Gaussian priors.
problem Non-trivial latent space projection for GANs with Gaussian priors.
method Extend previous techniques to Gaussian priors.
result Demonstrated effectiveness of extended technique.
Proves methods for creating convex projective 3-manifolds with cusps.
problem Creating convex projective 3-manifolds with generalized cusps.
method Properly convex deformations of hyperbolic structures, controlling cusp types.
result First known example of a 1-cusped hyperbolic 3-manifold with a type 2 cusp.
Fixed points of Minkowski valuations are found in specific ball neighborhoods.
problem Finding fixed points of Minkowski valuations.
method Lutwak-Schneider class reduction technique and Petty's conjectured projection inequality.
result Balls are the only solutions to the fixed-point problem for certain Minkowski valuations.
In this paper, we propose a new algorithm for exploratory projection pursuit. The basis of the algorithm is the insight that previous approaches used fairly narrow definitions of interestingness / non interestingness. We argue that allowing these definitions to depend on the problem / data at hand is a more natural app…
Paper introduces a new project control method using Monte Carlo and statistical learning.
problem Project control under uncertainty.
method Integrates Earned Value Methodology with Monte Carlo simulation and statistical learning.
result Estimates probabilities of project success and duration.
UMAP simplifies data visualization while preserving global structure.
problem Data visualization and dimension reduction challenges
method UMAP combines geometric and topological principles for efficient data embedding
result UMAP outperforms t-SNE in run time and global structure preservation
New algorithm reduces adaptive regret without projections.
problem Computational expense of projections in online convex optimization.
method Lazy gradient-based algorithm with set-membership computations.
result Near-optimal adaptive regret bounds for general convex functions.