A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
New connection found between complex polynomials and surface homeomorphisms.
We give a simple algorithm that determines whether a given post-critically finite topological polynomial is Thurston equivalent to a polynomial. If it is, the algorithm produces the Hubbard tree; otherwise, the algorithm produces the canonical obstruction. Our approach is rooted in geometric group theory, using iterati…
We describe the space of measured foliations induced on a compact Riemann surface by meromorphic quadratic differentials. We prove that any such foliation is realized by a unique such differential if we prescribe, in addition, the principal parts of at the poles. This generalizes a theorem of Hubbard and …
The paper finds a pervasive and severe bias in accounting semi-identity models.
We show that Thurston's skinning maps of Teichmuller space have finite fibers. The proof centers around a study of two subvarieties of the SL_2(C) character variety of a surface, one associated to complex projective structures and the other associated to a 3-manifold. Using the Morgan-Shalen compactification of the cha…
A meromorphic quadratic differential with poles of order two, on a compact Riemann surface, induces a measured foliation on the surface, with a spiralling structure at any pole that is determined by the complex residue of the differential at the pole. We introduce the space of such measured foliations, and prove that f…
New knot found with unique property.
Solves infinite family of cubic polynomial problems.
We introduce a topological object, called hairy Cantor set, which in many ways enjoys the universal features of objects like Jordan curve, Cantor set, Cantor bouquet, hairy Jordan curve, etc. We give an axiomatic characterisation of hairy Cantor sets, and prove that any two such objects in the plane are ambiently homeo…
New algorithm samples from Ising models efficiently, even with outliers.
Machine learning methods for solving the equations of dynamical mean-field theory are developed. The method is demonstrated on the three dimensional Hubbard model. The key technical issues are defining a mapping of an input function to an output function, and distinguishing metallic from insulating solutions. Both meta…
The Chabauty space of a topological group is the set of its closed subgroups, endowed with a natural topology. As soon as , the Chabauty space of has a rather intricate topology and is not a manifold. By an investigation of its local structure, we fit it into a wider, but too wild, class of topological space…
The study characterizes infinite Riemann surfaces and their foliations using quadratic differentials.
We prove that the knot Floer homology of a fibered knot is nontrivial in its next-to-top Alexander grading. Immediate applications include new proofs of Krcatovich's result that knots with -space surgeries are prime and Hedden and Watson's result that the rank of knot Floer homology detects the trefoil among knots i…
Solves generalized twisted rabbit problems for higher degree polynomials.
We reconsider the problem of calculating a general spectral correlation function containing an arbitrary number of products and ratios of characteristic polynomials for a N x N random matrix taken from the Gaussian Unitary Ensemble (GUE). Deviating from the standard "supersymmetry" approach, we integrate out Grassmann …
A meromorphic quadratic differential on a punctured Riemann surface induces horizontal and vertical measured foliations with pole-singularities. In a neighborhood of a pole such a foliation comprises foliated strips and half-planes, and its leaf-space determines a metric graph. We introduce the notion of an asymptotic …
Learning from data has led to a paradigm shift in computational materials science. In particular, it has been shown that neural networks can learn the potential energy surface and interatomic forces through examples, thus bypassing the computationally expensive density functional theory calculations. Combining many-bod…
An analytic approach and description are presented for the moduli cotangent sheaf for suitable stable curve families including noded fibers. For sections of the square of the relative dualizing sheaf, the residue map at a node gives rise to an exact sequence. The residue kernel defines the vanishing residue subsheaf. F…
Boosting meta-trees improve decision tree performance.
The paper studies geometric properties of quasi-trees and tree approximations.
Efficiently updates posterior tree distributions over meta-trees.
This paper describes experiments, on two domains, to investigate the effect of averaging over predictions of multiple decision trees, instead of using a single tree. Other authors have pointed out theoretical and commonsense reasons for preferring the multiple tree approach. Ideally, we would like to consider predictio…
We introduce a novel incremental decision tree learning algorithm, Hoeffding Anytime Tree, that is statistically more efficient than the current state-of-the-art, Hoeffding Tree. We demonstrate that an implementation of Hoeffding Anytime Tree---"Extremely Fast Decision Tree", a minor modification to the MOA implementat…
We introduce block-tree graphs as a framework for deriving efficient algorithms on graphical models. We define block-tree graphs as a tree-structured graph where each node is a cluster of nodes such that the clusters in the graph are disjoint. This differs from junction-trees, where two clusters connected by an edge al…
This paper introduces TNTK to study infinite soft tree ensembles.
Paper analyzes soft tree ensembles using NTK, finding only leaf count matters.
Researchers improve tree model recovery from noisy data.
Optimal survival trees ensemble reduces tree count and improves predictive performance.
Width trees link link invariants and bridge number.
Paper studies ensemble probabilistic regression trees for smooth approximations.
The task of translating between programming languages differs from the challenge of translating natural languages in that programming languages are designed with a far more rigid set of structural and grammatical rules. Previous work has used a tree-to-tree encoder/decoder model to take advantage of the inherent tree s…
Recently proposed budding tree is a decision tree algorithm in which every node is part internal node and part leaf. This allows representing every decision tree in a continuous parameter space, and therefore a budding tree can be jointly trained with backpropagation, like a neural network. Even though this continuity …
Characterizes fundamental groups of disjointly tree-graded spaces.
SBT model uses randomized sharding and sub-models to improve Bayesian Additive Regression Trees.
Decision Machines embeds decision trees into vector spaces for improved optimization.
Trees and their products compared to octahedron.
Tree Index evaluates cluster quality by creating decision trees from data.
TES-AE uses tree grammars to speed up autoencoding for tree data.
Flexible tree ensemble learning framework supports arbitrary loss functions and multi-task learning.
Kauri is a novel unsupervised binary tree for clustering that outperforms existing methods.
HATT improves online decision tree ensembles by using a more eager splitting strategy.
We introduce the concept of community trees that summarizes topological structures within a network. A community tree is a tree structure representing clique communities from the clique percolation method (CPM). The community tree also generates a persistent diagram. Community trees and persistent diagrams reveal topol…
Optimal Survival Trees improve accuracy in medical data analysis.
A novel tree algorithm improves time series forecasting accuracy.
Tree ensembles such as random forests and boosted trees are accurate but difficult to understand, debug and deploy. In this work, we provide the inTrees (interpretable trees) framework that extracts, measures, prunes and selects rules from a tree ensemble, and calculates frequent variable interactions. An rule-based le…
We introduce a method for creating a special type of tree, called a tree position, from a weighted graph. Leaves of the tree correspond to vertices of the original graph, and the tree edges contain information which can be used to partition these vertices. By repeatedly applying reducing operations to the tree position…
dtControl uses decision trees to represent controllers efficiently and explainably.