Study extends Huygens' principle to Finsler spaces, with applications in gravity.
problem Validating Huygens' principle in Finsler spaces for wavefronts.
method Extending a theorem to n-dimensional Finsler spaces and applying to analogue gravity.
result Finsler geometry reveals directional spacetime structures like horizons and ergospheres.
Note establishes a local maximum principle for Ricci flow under curvature conditions.
problem Preserving nonnegativity of curvature along Ricci flow with unbounded curvature.
method Combining scaling invariant curvature condition with Dirichlet heat kernel estimates.
result Unified and more direct proof of localized maximum principle.
New geometric approach to optimal control theory using Stokes Theorem.
problem Optimal control theory, specifically the Mayer problem.
method Geometric unfolding based on the Stokes Theorem.
result Derives a new necessary and sufficient condition for optimal solutions.
Paper develops techniques to create 3-manifold invariants.
problem Constructing non-trivial invariants of 3-manifolds.
method Photography principle and Ptolemy relation techniques.
result Direct implementation leads to a trivial invariant, highlighting difficulties.
The concept of an objective spatial direction in special relativity is investigated and theories assuming light-speed isotropy while accepting the existence of a privileged spatial direction are classified. A natural generalization of the proper time principle is introduced which makes it possible to devise experimenta…
Gradients help find global optima in complex functions.
problem Finding global optima in functions with many local minima.
method A principle for generating search directions from non-local quadratic approximants based on gradients.
result The proposed algorithm and CMA-ES perform better than random reinitialized BFGS.
We embed KKT points in neural networks of different sizes.
problem Classifying data using homogeneous neural networks.
method Introducing KKT point embedding principle and proving it for different network types.
result KKT points of a smaller network can be mapped to those of a larger network via linear transformations.
A new principle minimizes residual and introduces momentum to improve PDE solution dynamics.
problem Ill-conditioning in Dirac-Frenkel residual minimization leads to non-unique parameter dynamics.
method Introduces a history variable (momentum) to select better-conditioned parameter velocities, preserving residual minimization while promoting smooth parameter evolutions.
result The approach leads to increased robustness in singular and near-singular PDE solution regimes.
We establish the proportionality principle between the Riemannian volume and locally finite simplicial volume for Q-rank 1 locally symmetric spaces covered by products of hyperbolic spaces, giving the first examples for manifolds whose cusp groups are not necessarily amenable. Also, we give a simple direct proof of the…
Study of GCR hypersurfaces in Minkowski spaces, including classification and examples.
problem Classifying and understanding GCR hypersurfaces in Minkowski spaces.
method Geometrical analysis and classification of GCR hypersurfaces in Minkowski spaces.
result Complete classification of GCR surfaces in the Minkowski 3-space.
The paper explores the freedom of h(2)-variationality in sprays.
problem Investigating the number of variational principles for sprays.
method Analyzing h(2)-variationality and using the holonomy distribution to calculate freedom.
result The holonomy distribution can be used to calculate the freedom of h(2)-variationality of a spray.
Paper addresses identifiability for directed cyclic graphical models with feedback.
problem Identify causal relationships in multivariate data with feedback.
method Introduces new identifiability assumptions and develops search algorithms.
result New identifiability assumptions outperform the faithfulness assumption in selecting true skeletons.
The study reveals non-homotopy equivalent subspaces of curves with curvature constraints.
problem Understanding the homotopy type of subspaces of curves with curvature constraints.
method Used a version of the h-principle to prove results.
result Explicit construction of exotic generators for some homotopy and cohomology groups.
The paper examines how distortion principles affect insurance pricing under risk aversion and ambiguity.
problem Understanding how risk aversion and ambiguity impact insurance pricing.
method Investigates sensitivity of distortion functionals to risk aversion and ambiguity, using Wasserstein distance.
result Identifies worst-case distributions and methods to identify distortion densities.
We study the Lipschitz simplicial volume, which is a metric version of the simplicial volume. We introduce the piecewise straightening procedure for singular chains, which allows us to generalize the proportionality principle and the product inequality to the case of complete Riemannian manifolds of finite volume with …
Framework identifies causal direction from single data setting.
problem Identify causal direction from single observational data.
method VCEI framework based on ICM principle and artificial variation.
result VCEI is competitive to other frameworks in identifying causal direction.
In this paper will be applied some principles and methods from econophysics in the case of the direct foreign investitions (D.F.I.), particularised for the Greenfield type, and mixed firms of trade and industrial production (Joint Ventures). To this aim will be used some similarities and parallelisms between the mentio…
Study semiclassical measures on complex hyperbolic quotients, identifying measure supports.
problem Understanding Laplacian eigenfunctions on complex hyperbolic quotients.
method Combining fractal uncertainty principle and Ratner theory to analyze measure supports.
result Semiclassical measures support is either cosphere bundle or a compact submanifold.
Discussing AI's difficulty and physics' simplicity, suggesting AI benefits from physics principles.
problem AI difficulty compared to physics simplicity.
method Drawing on physical intuition and theoretical physics to improve AI.
result AI and physics principles are strongly coupled through sparsity.
A new BMF algorithm outperforms existing methods using MDL.
problem Developing a BMF algorithm that performs well across multiple metrics.
method From-below Boolean matrix factorization algorithm based on MDL principle.
result The proposed algorithm outperforms existing methods in various experiments.
Study large deviations in random walks on Lie groups.
problem Large deviations in sub-Riemannian random walks.
method Prove large deviation principle for random walks on stratified Lie groups.
result Proved a large deviation principle with a rate function adapted to sub-Riemannian geometry.
Unified algorithm for efficient pure exploration using dual variables.
problem Efficiently achieving a specific goal through adaptive experimentation.
method Introducing dual variables to derive optimal allocation conditions, leading to Information-Directed Selection.
result Top-two Thompson sampling attains asymptotic optimality for Gaussian best-arm identification.
A new flow-based framework improves graph-based semi-supervised learning while enhancing interpretability.
problem Improving interpretability of semi-supervised learning on graphs.
method Introduces a flow-based learning framework that subsumes and enhances Laplacian-based approaches.
result The flow-based framework improves prediction accuracy without sacrificing interpretability.
The Frenet frame is generally known an orthonormal vector frame for curves. But, it does not always meet the needs of curve characterizations. In this study, with the help of associated curves of any spatial curve we obtained a new orthonormal frame which has the property that the second vector makes a constant angle w…
Study geometric properties of spacelike foliations on Lorentz manifolds.
problem Investigate conditions for spacelike foliations to be totally umbilical or geodesic.
method Develop an equation relating foliation to ambient manifold, apply Maximum principle.
result Obtain an obstruction for totally geodesic foliations in spacetimes with positive Ricci curvature.
A principle for specialized decision-making divides complex problems into manageable parts.
problem Complex decision-making problems beyond individual capabilities.
method An on-line learning rule that learns a partitioning of the problem space for specialized linear policies.
result The approach solves problems that exceed individual decision-makers' capabilities.
New method shows almost complex structures can be approximated smoothly.
problem Approximating almost complex structures on manifolds.
method Combining h-principle techniques with directed immersion relation.
result Smooth approximation of almost complex structures with controlled error.
New approach to Lagrangian systems using intrinsic geometry.
problem Developing a new framework for Lagrangian systems.
method Direct reformulation of Hamiltonian formalism, introduction of spatial equation and spatial-gauge symmetry.
result Covariant and non-covariant canonical variational principles demonstrated for Maxwell equations.
Generalizes Fermat's principle for wave propagation in cone structures.
problem Wave propagation in complex media with discontinuities and anisotropy.
method Generalizes Fermat's principle to smooth interfaces separating two cone structures representing wave propagation in various media.
result Conditions for critical points of arrival time functional, generalizing Snell's law and reflection.
We establish a parametric extension h-principle for overtwisted contact structures on manifolds of all dimensions, which is the direct generalization of the 3-dimensional result from \cite{Eli89}. It implies, in particular, that any closed manifold admits a contact structure in any given homotopy class of almost co…
The maximum principle is one of the most important tools in the analysis of geometric partial differential equations. Traditionally, the maximum principle is applied to a scalar function defined on a manifold, but in recent years more sophisticated versions have emerged. One particularly interesting direction involves …
Study Loday algebroids, prove splitting theorem, and linearize problems.
problem Splitting and linearization of Loday algebroids.
method Local splitting-type results, Euler-like derivations.
result Established a general linearization principle.
A new method identifies causal direction using dense functional classes.
problem Determining causal direction between two univariate, continuous-valued variables.
method Minimum Description Length (MDL) principle applied to cubic regression splines.
result LCUBE method achieves superior precision in identifying causal direction.
We introduce SADs to reveal how network architecture shapes score-based generative models.
problem Understanding and predicting the inductive biases of score-based generative models.
method Introducing Score Anisotropy Directions (SADs) to analyze network architecture.
result SADs reliably capture model behavior and correlate with performance.
This paper presents a method to summarize directed graphs while preserving edge information.
problem Summarizing directed graphs while maintaining edge directionality.
method A model based on minimizing reconstruction error with non-negative constraints, related to Max-Cut criterion, using multiplicative update algorithms.
result The proposed method identifies compressed nodes and directed compressed relations, providing a more accurate representation of directed graphs.
Blockchain aims to improve trust in AI systems, but lacks systematic studies.
problem Lack of systematic studies on blockchain design principles for AI trust.
method Hybrid qualitative and quantitative studies.
result Vast opportunities for future research and practice in blockchain design.
This paper uses PCA for stock price prediction, reducing complexity and improving accuracy.
problem Predicting stock prices from past data using PCA.
method Dimensionality reduction through PCA to project noisy data onto a principle subspace.
result The method improves prediction accuracy and reduces risk.
New method clusters directed and undirected graphs without losing directional information.
problem Clustering directed graphs due to asymmetry in edge connectivity.
method Generalized Dirichlet Energy (GDE) and generalized spectral clustering (GSC).
result GSC outperforms existing methods in clustering accuracy and robustness.
New framework optimizes multi-asset portfolio choice for high dimensions.
problem Optimizing high-dimensional continuous-time portfolio choice.
method Combines Pontryagin's Maximum Principle with BPTT for neural network policy learning.
result Achieves near-optimal policies with improved efficiency and precision.
We show that the ``classical'' Harder-Narasimhan filtration associated to a non semistable vector bundle E can be viewed as a limit object for the action of the gauge group in the direction of an optimal destabilizing vector. This vector appears as an extremal value of the so called "maximal weight function". We give…
Unified approach to Merton's portfolio problem using Pontryagin's principles.
problem Optimizing consumption and investment strategies in financial portfolios.
method PG-DPO framework combining neural networks with Pontryagin's maximum principle.
result Locally optimal policies closely tied to classical stochastic control.
BICompFL tackles bi-directional compression challenges in stochastic FL, reducing communication costs by an order of magnitude.
problem Communication bottleneck in federated learning, especially with stochastic updates.
method Introduces BICompFL, a bi-directional compression approach for stochastic federated learning.
result Significantly reduces communication costs (by an order of magnitude) while maintaining accuracy.
A novel framework infers causal direction from symbolic sequences using pattern entropy.
problem Challenges in discovering causal direction from temporal symbolic data.
method Dictionary Based Pattern Entropy (DPE) framework integrating AIT and Shannon Information Theory. result Minimizing pattern level uncertainty yields a robust framework for causal discovery.
New method identifies common cause in causal insufficiency, revealing complex phase transitions.
problem Identifying common cause in causal insufficiency with observed joint probability.
method Generalized maximum likelihood method, closely related to maximum entropy principle.
result Identifies consistent common cause that aligns with the common cause principle.
Novel approach for SEM in small samples with p>n.
problem Small sample size and p>n issues in factor-based SEM. method Reformulates covariance structure into self-covariance and cross-covariance, defines a feasible set with relative error constraint.
result Improved stability and directional information in small-sample settings.
Direct and indirect RL methods classified and compared.
problem Classifying RL methods for sequential decision making.
method Direct RL solves optimal policy directly, indirect RL solves Bellman equation.
result Direct and indirect RL methods are equivalent and can be unified.
DPERC efficiently estimates covariance matrices for mixed data with missing values.
problem Estimating covariance matrices for datasets with missing values and mixed features.
method Direct Parameter Estimation for Randomly Missing Data with Categorical Features (DPERC).
result DPERC outperforms other methods in estimating covariance matrices for mixed data with missing values.
Two environments are enough to infer causal graphs and counterfactuals.
problem Inferring causal relations from multiple environments, especially for nonlinear mechanisms.
method Using structural causal models and the invariance principle, the study shows that only two auxiliary environments are sufficient for causal graph inference and counterfactual inference.
result Two auxiliary environments are sufficient for identifying causal graphs and counterfactuals.