Study of Ricci flow on trees, focusing on edge weights and curvatures.
problem Understanding the evolution of metrics on trees under Ricci flow.
method Continuous-time Ricci flow based on Lin-Lu-Yau Ollivier Ricci curvature.
result Ricci flow converges to zero curvature on edge weights of positive normalized values in caterpillar trees.
The paper connects two clustering methods by showing gradient ascent flow can move up the cluster tree.
problem Establishing a strong correspondence between clustering methods.
method Moving up the cluster tree by following the gradient ascent flow.
result Gradient ascent flow can be used to move up the cluster tree.
Paper proves equivalence of two Floer theories using pearly trees and Hamiltonian flows.
problem Proving equivalence between two Floer theories.
method Using pearly tree discs and local Hamiltonian flows.
result Equivalence relation between immersed Lagrangian Floer theory and Hamiltonian immersed Lagrangian Floer theory.
New method for Lagrangian Floer homology groups using flow trees.
problem Computing equivariant Lagrangian Floer homology.
method Constructing and exploiting an A-infinity module structure on the Floer complex.
result Established constructions of equivariant Lagrangian Floer homology groups.
The paper introduces a new type of Ricci flow on graphs to study their curvature.
problem Understanding the curvature of graphs and their convergence properties.
method Proposes a weighted Forman and Lin-Lu-Yau Ricci flow on graphs and proves the existence and uniqueness of solutions.
result The normalized curvature flow on trees converges to a constant curvature metric.
Gromov-Wasserstein (GW) is a powerful tool to compare probability measures whose supports are in different metric spaces. GW suffers however from a computational drawback since it requires to solve a complex non-convex quadratic program. We consider in this work a specific family of cost metrics, namely \textit{tree me…
Non-ergodic geodesic flow on Cantor tree surfaces found.
problem Determining when geodesic flow on Cantor tree surfaces is non-ergodic.
method Interpolating between two rates of convergence of cuff lengths to zero to prove non-ergodicity.
result Cantor tree surfaces with certain rates of cuff length convergence are non-parabolic.
New insights into pseudo-Anosov flows with special periodic orbits.
problem Understanding pseudo-Anosov flows with periodic orbits in 3-manifolds.
method Analyzing the topological features corresponding to trees of scalloped regions and classifying flows with the same free homotopy data.
result Explicit examples of flows with the same free homotopy data but not orbit equivalent.
Study evaluates Tree-Ring Watermarking in rectified flow-based models, revealing detection and separability limitations.
problem Detecting and separating Tree-Ring Watermarks in rectified flow-based models.
method Extensive experimentation comparing SD 2.1 and FLUX.1-dev models with various text guidance configurations and augmentation attacks.
result Inversion limitations affect watermark recovery and statistical separation.
We propose a faster and more accurate method for learning classification trees.
problem Learning optimal binary classification trees is challenging and slow.
method We introduce a stronger MIP formulation and Benders' decomposition method.
result Our method is 50 times faster and improves out-of-sample performance.
Generative model for tabular data density regression.
problem Estimating conditional distribution of outcomes given covariates.
method Tree-based flow model for efficient sampling and likelihood evaluation.
result Our method achieves comparable or superior performance with reduced training and sampling costs.
New method solves tree-structured Schrödinger Bridge problems.
problem Computing Schrödinger Bridge between tree-structured distributions.
method Iterative Markovian Fitting (IMF) procedure for tree-structured costs.
result Extends IMF to tree-structured Schrödinger Bridge problems.
Study on network flow singularities, focusing on Type-0 singularities.
problem Understanding singularities in network flow evolution.
method Analysis of curvature evolution and junction behavior.
result Bounded curvature for Type-0 singularities in network flow.
We empirically investigated the effects of market factors on the information flow created from N(N-1)/2 linkage relationships among stocks. We also examined the possibility of employing the minimal spanning tree (MST) method, which is capable of reducing the number of links to N-1. We determined that market factors car…
Branching Flows generates sequences of varying lengths using binary trees.
problem Generating sequences of unknown lengths or fixed elements.
method A generative modeling framework that evolves states over binary trees, controlling sequence length.
result Branching Flows can generate sequences of varying lengths and mix different types of state spaces.
The conormal lift of a link K in R3 is a Legendrian submanifold ΛK in the unit cotangent bundle U∗R3 of R3 with contact structure equal to the kernel of the Liouville form. Knot contact homology, a topological link invariant of K, is defined as the Legendrian homology of ΛK, the homology of a di…
Analysis of flow cytometry data is an essential tool for clinical diagnosis of hematological and immunological conditions. Current clinical workflows rely on a manual process called gating to classify cells into their canonical types. This dependence on human annotation limits the rate, reproducibility, and complexity …
PhyloGFN uses GFlowNets to infer phylogenetic trees from sequence data.
problem Challenging phylogenetic tree inference from sequence data due to high complexity.
method Adopting GFlowNets for parsimony-based and Bayesian phylogenetic inference.
result PhyloGFN produces diverse and high-quality evolutionary hypotheses.
Local existence and uniqueness of Bakry-Émery Ricci flow solutions on finite graphs.
problem Analyzing the behavior of Ricci flow on finite graphs.
method Local existence and uniqueness proof for solutions of the Bakry-Émery Ricci flow.
result Local existence and uniqueness of solutions to the Ricci flow on finite graphs.
Study of flows with a single singular point on a 2D disk.
problem Classifying flows with a unique singular point on a 2D disk.
method Used a two-colored rooted tree (destingueshed graph) to classify flows and constructed a flow code.
result Found all possible structures of flows with up to 7 separatrices.
Using transfer entropy, we observed the strength and direction of information flow between stock indices. We uncovered that the biggest source of information flow is America. In contrast, the Asia/Pacific region the biggest is receives the most information. According to the minimum spanning tree, the GSPC is located at…
Ensemble method for fast portfolio valuation and risk management.
problem Dynamic portfolio valuation and risk management from cash flow data.
method Regression trees for dynamic value process learning.
result Fast and accurate estimator with closed-form solution.
A new approach to Morse theory using folded ribbon trees.
problem Applying Morse theory on symmetric products of surfaces.
method Introducing an A-infinity category with objects as κ-tuples of Morse functions, and showing conditions for the endomorphism to be a Hecke algebra.
result The endomorphism of a specific type of κ-tuple of Morse functions on T*R^2 is the Hecke algebra associated to the symmetric group.
Let L⊂J1(M) be a Legendrian submanifold of the 1-jet space of a Riemannian n-manifold M. A correspondence is established between rigid flow trees in M determined by L and boundary punctured rigid pseudo-holomorphic disks in T∗M, with boundary on the projection of L and asymptotic to the doubl…
New method estimates root-directed tree from extreme data.
problem Discovering causality in river networks from extreme flow data.
method Qualitative max-linear Bayesian network approach to estimate bivariate scores and root-directed spanning tree.
result The new estimator is consistent under max-linear Bayesian network model with noise.
We analyse the existence question for essential laminations in 3-manifolds. The purpose is to prove that there are infinitely many closed hyperbolic 3-manifolds which do not admit essential laminations. This answers in the negative a question posed by Gabai and Oertel. The proof is obtained by analysing certain group a…
Harmonic map flow's singularity properties proven with Lojasiewicz inequalities.
problem Finite-time singularities of harmonic map flow in critical dimensions.
method Proving a weighted Lojasiewicz inequality.
result Continuity of body map and no-neck property for bubble-tree decompositions.
Functional central limit theorem for kernel gradient flow and infinitesimal gradient boosting
problem Fluctuations of boosting processes around their deterministic limit
method Stochastic perturbation analysis of ODEs in Banach spaces
result Rescaled deviations converge to a Gaussian process
Study proves Lojasiewicz inequalities for harmonic maps near simple bubble trees.
problem Analyzing harmonic maps near simple bubble trees.
method Proves Lojasiewicz inequalities for harmonic maps close to simple bubble trees.
result Obtains new results on the convergence of harmonic map flow and energy spectrum.
A new metric for comparing measures on tree systems reduces computational burden.
problem Heavy computation in Optimal Transport problems.
method Introducing tree systems and a novel metric (Tree-Sliced Wasserstein distance on Systems of Lines, TSW-SL).
result TSW-SL performs favorably compared to Sliced Wasserstein and its variants.
Classifies pseudo-Anosov flows on 3-manifolds up to orbit equivalence.
problem Classifying pseudo-Anosov flows on 3-manifolds up to orbit equivalence.
method Generalized Anosov-like actions on bifoliated planes, ideal boundary analysis.
result Pseudo-Anosov flows on 3-manifolds are determined up to orbit equivalence by their ideal boundary actions.
A self-contained account of the theory of structure trees for edge cuts in networks is given. Applications include a generalisation of the Max-Flow Min-Cut Theorem to infinite networks and a short proof of a conjecture of Kropholler. This gives a relative version of Stallings' Theorem on the structure of groups with mo…
Improved phylogenetic inference using VBPI-Mixtures for tree topology and branch length.
problem Multimodality of tree-topology posterior distributions in phylogenetic inference.
method VBPI-Mixtures algorithm that uses mixture learning within the BBVI framework.
result VBPI-Mixtures captures tree-topology distributions better than VBPI.
Revises derivative pricing post financial crisis by defining a discount rate.
problem Derivative pricing became complex with XVA adjustments.
method Developed a binomial tree model for pricing with counterparty and funding risks.
result Coherent XVAs naturally result from decomposing the discount rate.
Protein Thoughts interprets protein interactions with clear reasoning, improving prediction accuracy.
problem Lack of mechanistic justification in protein-protein interaction predictions.
method Interpretable search problem reformulation, hypothesis-guided entropy-regularized Tree-of-Thoughts search, embedding-space flow matching.
result Improves mean best-binder rank from 47.7 to 11.2 on SHS148k benchmark.
While normalizing flows have led to significant advances in modeling high-dimensional continuous distributions, their applicability to discrete distributions remains unknown. In this paper, we show that flows can in fact be extended to discrete events---and under a simple change-of-variables formula not requiring log-d…
The paper proves a Lojasiewicz inequality for maps from the 2-sphere to itself.
problem Analyzing maps from the 2-sphere to itself using Lojasiewicz inequalities.
method Using Lojasiewicz-Simon inequalities and Topping's repulsion estimates, along with a bubble-tree induction argument.
result Polynomial convergence of weak solutions of harmonic map flow on compact domains.
The paper uses regression trees/random forests to price Bermudan options more efficiently.
problem Pricing Bermudan options with conditional expectation estimation.
method Estimates conditional expectations using regression trees or random forests instead of traditional regression methods.
result Regression trees/random forests provide better results in high dimensions.
We consider the inference of the structure of an undirected graphical model in an exact Bayesian framework. More specifically we aim at achieving the inference with close-form posteriors, avoiding any sampling step. This task would be intractable without any restriction on the considered graphs, so we limit our explora…
Program comprehension is a fundamental task in software development and maintenance processes. Software developers often need to understand a large amount of existing code before they can develop new features or fix bugs in existing programs. Being able to process programming language code automatically and provide sum…
In this paper it is shown that for any network there is a uniquely determined network based on a structure tree that provides a convenient way of determining a minimal cut separating a pair s,t where each of s,t is either a vertex or an end in the original network. A Max-Flow Min-Cut Theorem is proved for any net…
Develops RKHS framework for analyzing tree ensembles.
problem Analyzing the theoretical properties of tree ensembles.
method Reproducing Kernel Hilbert Spaces (RKHS) for tree ensembles.
result Characterizes Random Forest predictor as minimizer of a penalized empirical risk functional in RKHS.
Predicting traffic incident duration is a major challenge for many traffic centres around the world. Most research studies focus on predicting the incident duration on motorways rather than arterial roads, due to a high network complexity and lack of data. In this paper we propose a bi-level framework for predicting th…
Since the machine learning techniques are improving rapidly, it has been shown that the image recognition techniques in deep neural networks can be used to detect jet substructure. And it turns out that deep neural networks can match or outperform traditional approach of expert features. However, there are disadvantage…
Geodesics in curved spaces spread evenly over time.
problem Equidistribution of geodesics in negatively curved spaces.
method Proving equidistribution of geodesic flow orbits towards measures of maximal entropy and Bowen-Margulis measure.
result Equidistribution of divergent geodesics in negative curvature as their complexity increases.
This paper shows neural networks can solve complex graph problems efficiently.
problem Solving exact maximum flow computation and minimum spanning tree problems.
method Introduces Max-Affine Arithmetic Programs and shows equivalence to neural networks.
result Two combinatorial optimization problems can be solved with polynomial-size neural networks.
While market is a social field where information flows over the interacting agents, there have been not so many methods to observe the spreading information in the prices comprising the market. By incorporating the entropy transfer in information theory in its relation to the Granger causality, the paper proposes a tre…
Distribution grid is the medium and low voltage part of a large power system. Structurally, the majority of distribution networks operate radially, such that energized lines form a collection of trees, i.e. forest, with a substation being at the root of any tree. The operational topology/forest may change from time to …