Four conditions ensure low-rank projection costs using random matrix tricks.
problem Preserving projection costs in low-rank approximations.
method Four structural conditions using randomized matrix techniques.
result Conditions guarantee cost preservation in rank-k projections. FI-GRL learns graph node representations efficiently and generalizes to unseen nodes.
problem Transductive graph representation learning requires all nodes to be known, limiting generalization.
method FI-GRL uses random projection to preserve graph structure and feature extraction via SVD.
result FI-GRL achieves accurate representations for seen nodes and generalizes to unseen nodes.
Paper proposes a method to estimate project cost contingency reserves considering various types of uncertainty.
problem Inaccurate estimation of project cost contingency reserves due to ignoring different types of uncertainty.
method Quantitative determination of project cost contingency reserves using Monte Carlo Simulation considering aleatoric, stochastic, and epistemic uncertainties.
result The proposed method provides more accurate contingency reserves that align with actual project risks.
Empirical study finds IT project costs follow a power-law distribution, exposing risk underestimation.
problem IT project cost overruns are underestimated due to normal distribution assumptions.
method Analyzed 5,392 IT projects to examine cost overruns following a power-law distribution.
result IT project cost overruns follow a power-law distribution with a fat tail of extreme overruns.
The study examines how individual ability and project benefit influence cooperation in public goods games.
problem Maximizing cooperation in public goods games with varying individual contributions and benefits.
method A generalized public goods game model incorporating individual ability and project benefit.
result The upper limit of individual benefit promotes cooperation, while the upper limit of individual contribution inhibits it.
Deterministic column sampling using ridge leverage scores provides accurate matrix sketches for ridge regression.
problem Regularizing ill-posed linear least-squares problems with small but non-zero coefficients.
method Deterministic column sampling using ridge leverage scores.
result Deterministic algorithm provides (1 + ε) error column subset selection and projection-cost preservation.
A major source of risk in project management is inaccurate forecasts of project costs, demand, and other impacts. The paper presents a promising new approach to mitigating such risk, based on theories of decision making under uncertainty which won the 2002 Nobel prize in economics. First, the paper documents inaccuracy…
Cover trees speed up MRI fingerprint recovery by reducing computation.
problem Efficiently reconstructing MRI fingerprint signals from compressed sensing data.
method Use cover trees for fast approximate nearest neighbor searches in IPG algorithm.
result Achieves 2-3 orders of magnitude reduction in computations.
Cost overruns in transport infrastructure projects know no geographical limits, overruns are a global phenomenon. Nevertheless, the size of cost overruns varies with location. In the Netherlands, cost overruns appear to be smaller compared to the rest of the world. This paper tests whether Dutch projects perform signif…
Hong Kong uses reference class forecasting to improve roadwork project cost and duration estimates.
problem Optimism bias and strategic misrepresentation in infrastructure project forecasts.
method Reference class forecasting applied to 25 roadwork projects in Hong Kong.
result Forecast accuracy distribution and project benchmarking established.
Firefly algorithm improves software effort estimation models.
problem Improving accuracy of software effort estimation models.
method Using Firefly Algorithm to optimize COCOMO-based models.
result High accuracy and significant error minimization of Firefly Algorithm.
Paper analyzes LPSA algorithm for constrained optimization, revealing phase transitions and bias-variance trade-offs.
problem Optimization problems with linear constraints.
method Loopless projection stochastic approximation (LPSA) with jump diffusion approximation.
result LPSA trajectories converge to SDEs, revealing asymptotic behaviors and phase transitions.
PCA adapted for curved spaces improves data analysis.
problem PCA's limitations in curved spaces.
method Space Form PCA (SFPCA) for Riemannian manifolds.
result SFPCA provides faster and more accurate subspaces estimation.
A new method prioritizes project risks using Monte Carlo Simulation.
problem Determining the relative importance of project risks.
method Monte Carlo Simulation (MCS) for quantitative prioritization.
result Differentiates critical risks based on their impact on project duration and cost.
Proposes a Carbon Equivalence Principle for financial products to align incentives and drive sustainability.
problem Align financial market incentives with carbon emissions to limit global warming.
method Introduces a Carbon Equivalence Principle requiring financial products to describe equivalent carbon flows alongside cash flows.
result Transparency of carbon flows in financial products can align incentives and reduce future costs, necessitating project re-structuring and financial net-zero designs.
Research proposes an ensemble learning model for efficient software defect prediction.
problem Efficient and cost-effective software testing to minimize project resources.
method Machine learning analysis on different datasets using KNN, Decision Tree, SVM, and Naïve Bayes.
result Ensemble learning model outperforms other techniques in accuracy, precision, recall, and F1-score.
Algorithm confirms non-order-preserving braids, proving infinite family not order-preserving.
problem Determining if a braid is non-order-preserving.
method Algorithm that checks non-order-preserving property of braids.
result Infinite family of simple 3-braids are not order-preserving.
The paper studies area-preserving and length-preserving inverse curvature flow for planar curves with singularities.
problem Investigating the evolution of planar curves with singularities under area-preserving and length-preserving inverse curvature flow.
method Area-preserving and length-preserving inverse curvature flow for ℓ-convex Legendre curves. result The flow results in a circle for ℓ-convex Legendre curves, providing geometric inequalities. Preserves metric space properties under certain function constraints.
problem Understanding functions that preserve specific geometric properties in metric spaces.
method Formulating and proving conjectures about isometries and level sets in complete Riemannian manifolds.
result Functions preserving at least one level set of a metric space are isometries under certain conditions.
Study fiber-preserving, orientation-reversing involutions on Seifert fibered 3-manifolds.
problem Characterize fiber-preserving, orientation-reversing involutions on Seifert fibered 3-manifolds.
method Construct a class of involutions, extend product involutions, and use double covering.
result Any fiber-preserving, orientation-reversing involution factors as a product of an orientation-preserving and a specific class of involutions.
Study on group cocycles for volume-preserving diffeomorphisms.
problem Understanding group cocycles on volume-preserving diffeomorphisms.
method Constructed two types of group cocycles on the volume-preserving diffeomorphism group.
result One cocycle yields the Euler class of flat sphere bundles for the sphere.
Classifies geodesic-preserving bijections in Thurston geometries.
problem Identifying bijections that preserve geodesics in different geometries.
method Comprehensive classification and proof for various geometries.
result Complete classification of geodesic-preserving bijections in Thurston geometries.
The paper studies quasimorphisms on density-preserving diffeomorphisms of the Möbius band.
problem Exploring quasimorphisms on groups of diffeomorphisms of non-orientable manifolds.
method Investigates the group of density-preserving diffeomorphisms on the Möbius band and shows the existence of unbounded quasimorphisms.
result The group of density-preserving diffeomorphisms on the Möbius band admits countably many unbounded quasimorphisms.
The paper examines flows that preserve area and length in hyperbolic geometry.
problem Preserving area and length in hyperbolic geometry.
method Inverse curvature flows for convex curves in hyperbolic plane.
result The flows converge to geodesic circles under certain conditions.
Proposes a method to preserve information in heterogeneous domain adaptation.
problem Preserving information in different feature spaces between domains.
method Joint information preservation method integrating paired and structural information.
result Superior performance compared to state-of-the-art HDA algorithms.
We investigate which jump-diffusion models are convexity preserving. The study of convexity preserving models is motivated by monotonicity results for such models in the volatility and in the jump parameters. We give a necessary condition for convexity to be preserved in several-dimensional jump-diffusion models. This …
Preserves sensitive data distribution for privacy while maintaining utility.
problem Protecting individual privacy while preserving data utility for specific analyses.
method Combines distribution-preserving quantization and k-member clustering.
result Demonstrates improved privacy and utility in real-world applications.
Counterexample shows level-preserving map from isotopy is not always an embedding.
problem Level-preserving maps from isotopies not always embeddings.
method Simple counterexample.
result Level-preserving map from isotopy is not always an embedding.
This work preserves linear invariants in ensemble filters for non-Gaussian data assimilation.
problem Maintaining critical invariants like mass, stoichiometric balance, and charge in non-Gaussian data assimilation.
method Introducing a novel class of nonlinear ensemble filters using measure transport theory.
result Recovery of a constrained Kalman filter for Gaussian settings and combination with regularization techniques.
Volume-preserving neural networks prevent gradient issues.
problem Vanishing and exploding gradients in deep neural networks.
method A new neural network architecture with volume-preserving sublayers.
result Volume-preserving neural networks maintain gradient stability.
BiLipschitz mappings can be extended to preserve area.
problem Extending biLipschitz mappings to preserve area.
method Proving biLipschitz mappings can be extended to biLipschitz mappings preserving area.
result BiLipschitz mappings can be extended to preserve area.
For any α>0, we study kα-type length-preserving and area-preserving nonlocal flow of convex closed plane curves and show that these two types of flow evolve such curves into round circles in C∞-norm. Other relevant kα-type nonlocal flow is also discussed when α≥1.
Convexity properties are preserved under radial transformations in hyperbolic and spherical geometries.
problem Preserving convexity in hyperbolic and spherical geometries under radial transformations.
method Used Poincaré disk model for hyperbolic geometry and stereographic projection for spherical geometry to prove preservation of convexity under radial expansion and contraction.
result Radial expansion and contraction preserve hyperbolic and spherical convexity, respectively.
Turing complete flow on 4-sphere preserves volume.
problem Creating a Turing complete flow on a 4-sphere.
method Smooth, conservative flow on the 4-sphere.
result Achieved a Turing complete, volume-preserving flow.
Study proves stability and uniqueness for a specific type of flow.
problem Volume-preserving mean curvature flow stability and uniqueness.
method New gradient flow calibrations for volume preservation, stability estimate in distributional solutions.
result Strong solutions are calibrated and stable under certain conditions.
Study of area preserving Willmore flow on Schwarzschild-like manifolds.
problem Stability of Willmore spheres in Schwarzschild-like ends.
method Area preserving Willmore flow analysis in C3−close Schwarzschild ends. result Leaves of the Willmore foliation are strict local area preserving maximizers of Hawking mass.
In this article we introduce order preserving representations of fundamental groups of surfaces into Lie groups with bi-invariant orders. By relating order preserving representations to weakly maximal representations, introduced in arXiv:1305.2620, we show that order preserving representations into Lie groups of Hermit…
Every homeomorphism of Euclidean space is a commutator of two homeomorphisms.
problem Understanding the structure of homeomorphisms in Euclidean space.
method Proving every orientation-preserving homeomorphism can be written as a commutator of two such homeomorphisms.
result Every orientation-preserving homeomorphism of Euclidean space is a commutator of two homeomorphisms.
Maps preserving edges on curve graphs and Hatcher-Thurston graphs are induced by homeomorphisms of surfaces.
problem Characterizing maps preserving edges on curve graphs and Hatcher-Thurston graphs.
method Proving edge-preserving maps on curve graphs and Hatcher-Thurston graphs are induced by homeomorphisms of surfaces.
result Edge-preserving maps on curve graphs and Hatcher-Thurston graphs are unique up to isotopy when (g,n)eq(2,0). New saddle network architectures preserve convex-concave geometry in optimization problems.
problem Optimization models with convex x and concave y components.
method Structured separable decomposition and saddle network architectures.
result Proven one-dimensional approximation theorem and high accuracy on various test functions.
Preserves content while changing style in text.
problem Text style transfer often fails to preserve content.
method Leverages linguistic information in structured supervisions.
result Significant improvement in content preservation and style transfer.
Sharp 3D Alexandrov inequality applied to volume-preserving flows.
problem Volume-preserving geometric flows in 3D space.
method Sharp quantitative Alexandrov inequality for C2-regular sets. result Established a 3D sharp quantitative version of the Alexandrov inequality.
Exponential map proof for area-preserving diffeomorphisms on surfaces.
problem Proving the properties of the exponential map for a specific group of diffeomorphisms.
method Analyzing the Riemannian exponential map of the right-invariant L2 metric. result The exponential map is a nonlinear Fredholm map of index zero.
The paper extends a measure preserving property to bi-Lipschitz maps between Moran sets.
problem Extending the measure preserving property to Moran sets.
method Analyzing bi-Lipschitz maps between Moran sets.
result Bi-Lipschitz maps between Moran sets preserve measure locally.
The paper preserves positivity along a flow over projective bundles.
problem Preserving positivity in geometric flows over projective bundles.
method Introducing a flow over projective bundles and proving semipositivity preservation under certain conditions.
result Semipositivity of curvature is preserved along the flow under specific conditions.
Paper proves conjecture about star-shaped curves evolving under GAPF, but not always preserves star shape.
problem What conditions guarantee global existence of Gage's area-preserving flow for nonconvex initial curves?
method Using Dittberner's singularity analysis theory, constructed a ``flying wing'' curve to show limitations.
result Gage's area-preserving flow does not always preserve star-shapedness of evolving curves.
Hausdorff reflection keeps space shape intact.
problem Preserving shape type in spaces.
method Hausdorff reflection method.
result Hausdorff reflection preserves shape type.
Extends Arnold's linking theory to higher dimensions and submanifolds.
problem Volume-preserving actions in higher dimensions and submanifolds.
method Generalization of V. Arnold's theory to Rk and Rℓ. result Extension of asymptotic linking to higher dimensions and submanifolds.