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.
Introduces representations of surface groups into Lie groups preserving order.
problem Representations of surface groups into Lie groups that preserve the group order.
method Relates order preserving representations to weakly maximal representations and uses geometric and causal structure.
result Order preserving representations into Lie groups of Hermitian type are faithful with discrete image and form a closed set.
A scalable framework preserves personalized higher-order network proximities.
problem Lack of expressive methods to preserve personalized higher-order network proximities.
method Incorporates random walk into a sound objective to preserve arbitrary higher-order proximities and introduces random walk with restart for personalized-weighted preservation.
result Consistently and substantially outperforms state-of-the-art methods on real-world networks.
Paper solves equivalence problems for fifth-order differential operators using Cartan's method.
problem Equivalence problem for fifth-order differential operators under fiber-preserving transformations.
method Cartan's method of equivalence applied to solve two versions of the equivalence problem.
result Sufficient and necessary conditions for fiber-preserving transformations between fifth-order differential operators.
New method calibrates deep networks by preserving top-k predictions.
problem Calibrated confidence scores for multi-class deep networks to avoid rare mistakes.
method Intra order-preserving functions combined with neural network architecture.
result Outperforms state-of-the-art methods in evaluation metrics.
Method preserves order in hierarchical clustering of ordered data.
problem Order preserving hierarchical clustering of directed acyclic graphs.
method Combination of classical hierarchical clustering and ultrametric fitting.
result Optimal clustering preserves both cluster quality and order.
It is well known that a countable group admits a left-invariant total order if and only if it acts faithfully on R by orientation preserving homeomorphisms. Such group actions are special cases of group actions on simply connected 1-manifolds, or equivalently, actions on oriented order trees. We characterize a class of…
Method studies equivalence of second order ODEs under specific transformations.
problem Classifying second order ODEs modulo fibre-preserving transformations.
method Using Moser's method of normal forms and Lie algebra computations.
result Normal forms can be used to prove fibre-preserving equivalence.
A new curve flow preserves area and converges to a circle.
problem Preserving area in centro-equiaffine geometry.
method Fourth-order centro-equiaffine invariant curve flow via affine Minkowski formula.
result The flow preserves area and converges to a round circle.
We review the fundamentals of coupling constant metamorphosis (CCM) and the Stäckel transform, and apply them to map integrable and superintegrable systems of all orders into other such systems on different manifolds. In general, CCM does not preserve the order of constants of the motion or even take polynomials in the…
OP-GFNs sample candidates in order-preserving proportion to a learned reward function.
problem Sampling diverse candidates with varying rewards in multi-objective optimization.
method Order-Preserving GFlowNets (OP-GFNs) use a learned reward function consistent with a provided order on candidates.
result Training OP-GFNs sparsifies the reward landscape, focusing on higher-ranked candidates.
In present paper, the equivalence problem for fourth order differential operators with one variable under general fiber-preserving transformation using the Cartan method of equivalence is applied. Two versions of equivalence problems are considered. First, the direct equivalence problem and second equivalence problem i…
Develops high-order geometric integrators for nonholonomic systems.
problem Simulating nonholonomic mechanical systems with preserved geometric properties.
method High-order geometric (pseudo-variational) integrators for nonholonomic systems.
result Preserves the geometry and constraints of nonholonomic systems.
We apply the Cartan equivalence method to the study of real analytic second order ODEs under the local real analytic diffeomorphism of $\C^2$ which are area-preserving. This enables us to give a characterization of the second order ODEs which are equivalent to y′′=0 under such transformations. Moreover w…
In this note we review some results regarding higher order elliptic differential operators on manifolds without boundary.
New set class preserves Fourier series terms for planar ovals, leading to isoperimetric inequalities.
problem Investigate geometric properties of kth Order Preserving Sets and ovals. method Introduce and analyze kth Order Preserving Sets and Midpoint Sets; study geometric properties and isoperimetric inequalities. result Established an isoperimetric-type inequality relating perimeter and area of ovals and their associated sets.
We present a novel factor analysis method that can be applied to the discovery of common factors shared among trajectories in multivariate time series data. These factors satisfy a precedence-ordering property: certain factors are recruited only after some other factors are activated. Precedence-ordering arise in appli…
In this paper we further investigate the geometry of monads of order-preserving functionals and of positively homogeneous functionals. We prove that for any compactum X with w(X)=τ the map μFX, where F∈{O,OH}, is homeomorphic to trivial Iτ-fibration if and only if X is openly generated χ-homogeneou…
Polytopes A(P) for posets P compactify spaces of order-preserving maps.
problem Compactifying spaces of order-preserving maps for posets.
method Constructing polytopes A(P) and compactifying spaces of order-preserving maps. result Polytopes A(P) correspond to nested collections of subsets of posets. Study on braids and their impact on hyperbolic 3-manifolds' orderability.
problem Investigating the relationship between braids and the orderability of hyperbolic 3-manifolds.
method Examined faithful representations of braid groups on automorphism groups of free groups, focusing on bi-orderability.
result Found that the bi-orderability of hyperbolic 3-manifolds' fundamental groups is linked to the braids used.
This article is dedicated to solve the equivalence problem for two third order differential operators on the line under general fiber--preserving transformation using the Cartan method of equivalence. We will do three versions of the equivalence problems: first via the direct equivalence problem, second equivalence pro…
We address the problem of local geometry of third order ODEs modulo contact, point and fibre-preserving transformations of variables. Several new and already known geometries are described in a uniform manner by the Cartan method of equivalence. This includes conformal, Weyl and metric geometries in three and six dimen…
Study curves evolving on hypersurfaces with free boundaries, preserving length.
problem Evolution of curves on hypersurfaces with free boundaries.
method Nonlocal evolution equation with nonlinear boundary conditions, short-time existence, uniqueness, and parabolic energy estimates.
result Global existence and convergence to critical points proved.
We construct a family of split signature Einstein metrics in four dimensions, corresponding to particular classes of third order ODEs considered modulo fiber preserving transformations of variables.
New criterion for bi-ordering free groups under automorphisms.
problem Bi-ordering free groups under automorphisms.
method New criterion for bi-ordering free groups.
result Fundamental group of the magic manifold is bi-orderable.
Study proposes BFEL framework for privacy-preserving FL in personalized healthcare.
problem Privacy and security concerns in traditional cloud-centric ML, especially in wearable devices.
method Develops a blockchain-enhanced federated edge learning (BFEL) framework based on FedCurv, incorporating fisher information matrix and public key encryption.
result Significant reduction in communication cost and high efficiency for federated training on non-iid and heterogeneous data.
This paper is devoted to apply the equivariant moving frame method to study the local equivalence problem of third order ordinarily differential equation under the pseudo-group of fiber preserving transformations.
The study shows finite measure-preserving isometry groups for certain metric measure spaces.
problem Understanding the structure of isometry groups in metric measure spaces.
method Analyzing synthetic negative Ricci curvature and Bakry-Émery Ricci curvature.
result The measure-preserving isometry group is finite for compact metric measure spaces with specific curvature conditions.
Privacy-preserving crypto exchanges adjust prices based on Gaussian noise.
problem Ensuring fair pricing in privacy-preserving cryptocurrency exchanges.
method Derive Kyle equilibrium with Gaussian noise perturbation, rescaling price-impact and strategy factors.
result Identify a privacy subsidy as a transfer from LP pool to traders, invariant to noise.
A new index rebalancing strategy reduces large constituent weights without undesirable effects.
problem Undesirable effects of current Nasdaq-100 index rebalancing.
method A simple rebalancing strategy that avoids undesirable effects.
result Preserves the order of index weights and prevents maximum weight increase.
We consider the orientation-preserving actions of finite groups G on pairs (S3,Γ), where Γ is a connected graph of genus g>1, embedded in S3. For each g we give the maximum order mg of such G acting on (S3,Γ) for all such Γ⊂S3. Indeed we will classify all graphs Γ⊂S3 which re…
Privacy-preserving deep learning for medical data across distributed platforms.
problem Data leakage in medical platforms.
method Separates hidden layers; first layer local, others centralized for training.
result Improved learning performance with all data used during training.
In the present paper we study interval identification systems of order three. We prove that the Rauzy induction preserves symmetry: for any symmetric interval identification system of order three after finitely many iterations of the Rauzy induction we always obtain a symmetric system. We also provide an example of sym…
Curves become nearly circular over time without initial assumptions.
problem Understanding the asymptotic behavior of area-preserving flows.
method Proving asymptotic circularity without additional assumptions.
result Immortal solutions become asymptotically circular without initial assumptions.
Rational homology ribbon cobordism defines a partial order on 3-manifolds.
problem Classifying 3-manifolds based on their homology
method Proving a partial order on homeomorphism classes of 3-manifolds
result Closed, connected, oriented 3-manifolds are partially ordered by rational homology ribbon cobordism.
We study groups of C^1 orientation-preserving homeomorphisms of the plane, and pursue analogies between such groups and circularly-orderable groups. We show that every such group with a bounded orbit is circularly-orderable, and show that certain generalized braid groups are circularly-orderable. We also show that the …
The study explores large group actions on 3-manifolds and their Heegaard splittings.
problem Understanding finite group actions on 3-manifolds and their properties.
method Investigates maximal group orders and presents specific examples of 3-manifolds with large actions.
result The existence of a unique hyperbolic 3-manifold with a specific large group action.
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.
It is of interest to study supergravity solutions preserving a non-minimal fraction of supersymmetries. A necessary condition for supersymmetry to be preserved is that the spacetime admits a Killing spinor and hence a null or timelike Killing vector field. Any spacetime admitting a covariantly constant null vector fiel…
New variational model preserves image contrasts and features using Weingarten map minimization.
problem Image reconstruction with preservation of contrasts and features.
method Variational model with L1 norm of Weingarten map, ADMM algorithm, gradient descent. result The proposed models preserve image contrasts and features efficiently.
RotEqNet preserves rotation symmetry in fluid systems using high-order tensors.
problem Lack of rotational symmetry in machine learning models for fluid systems.
method Introduces RotEqNet, a network that guarantees rotation-equivariance for high-order tensors.
result RotEqNet reduces errors and maintains rotation-equivariance in fluid systems.
RP-GFRFT unifies fractional order and rotation control for graph signals.
problem Lack of rotation-based spectral control in GFRFT and zero-angle degeneracy in AGFT.
method Rotation-parameterized graph fractional Fourier transform (RP-GFRFT) with degeneracy preserving rotation matrix.
result RP-GFRFT improves spectral filtering performance over existing methods.
Paper proves higher-order flow matching preserves optimality in generative modeling.
problem Theoretical guarantees for higher-order flow matching in generative modeling.
method Neural network approximations with controlled depth, width, and sparsity.
result Proves worst case optimality for second-order flow matching.
FraudTransformer detects payment fraud by preserving event order and time gaps.
problem Detecting payment fraud in real-world banking streams with irregular time gaps.
method Augments a GPT-style architecture with a dedicated time encoder and a learned positional encoder.
result FraudTransformer outperforms classical and transformer baselines, achieving highest AUROC and PRAUC on held-out test set.
The paper classifies surfaces in a 3-torus with maximal symmetry.
problem Classifying surfaces with maximal symmetry in a 3-torus.
method Analyzing group actions and their effects on surfaces.
result All group actions and surfaces achieving maximal symmetry are identified.
Efficient algorithm for clustering and classification using MBO scheme.
problem Data clustering and classification tasks.
method Introduces constraints on cluster size leading to a linear integer problem, proving it's induced by a novel order statistic. Develops exact and efficient algorithms based on variational viewpoint connecting to volume-preserving mean curvature flow.
result Estimates computational complexity better than state-of-the-art, proving rigorous analysis.
This method infers models from data with physical insights, minimizing model order.
problem Learning models from data while preserving physical insights.
method Structure preservation and rank minimization via Sylvester equations.
result Models of low order are obtained with fewer degrees of freedom.
Study continuous deformations of branched projective structures on surfaces, preserving holonomy and branch points.
problem Continuous deformations of branched projective structures on closed surfaces of genus g≥2. method Schiffer variations and analysis of canonical divisors.
result Branch points are necessarily arranged on a canonical divisor when the underlying complex structure is infinitesimally preserved.