Paper proves ratios of Chern numbers differ for complex hyperbolic branched covers.
problem Proving differences in Chern number ratios for complex hyperbolic branched covers.
method Analyzes Chern numbers of complex hyperbolic branched covers and compares them to those of complex hyperbolic manifolds.
result Ratio of Chern numbers for branched covers are not all equal to those of complex hyperbolic manifolds.
We introduce a model-independent approximation for the branching ratio of Hawkes self-exciting point processes. Our estimator requires knowing only the mean and variance of the event count in a sufficiently large time window, statistics that are readily obtained from empirical data. The method we propose greatly simpli…
The Blum medial axis rigidity is studied in terms of cross ratios and differential geometry.
problem Examining rigidity properties of the Blum medial axis under diffeomorphisms.
method Using cross ratios from projective geometry and differential geometry.
result Cross ratios and differential geometry uniquely determine the angles between smooth sheets.
Computes constants for cyclic covers of translation surfaces.
problem Asymptotic number of cylinders on translation surfaces.
method Topological invariants and number-theoretic properties of degree.
result Ratio of Siegel-Veech constants is independent of degree.
New method estimates order book dynamics efficiently.
problem Understanding complex order book dynamics in financial markets.
method Nonparametric estimation of branching ratio matrix for multivariate Hawkes process.
result Reveals relationships between order book events.
Study measures subcritical branching in crypto liquidation cascades.
problem Understanding the mechanism of crypto liquidation cascades.
method Analyzed seven major crypto liquidation events, measured branching ratio, and compared with theoretical models.
result Found the cascades to be subcritical, with branching ratio around 0.1-0.2.
Model captures both slow and fast time variations in financial data.
problem Analyzing high-frequency financial data with varying background rates.
method Developed a Hawkes process with a time-varying background rate using Bayesian estimation.
result Model significantly improves goodness-of-fit to financial data, especially during fluctuating background rates.
We define an activity dependent branching ratio that allows comparison of different time series Xt. The branching ratio bx is defined as bx=E[ξx/x]. The random variable ξx is the value of the next signal given that the previous one is equal to x, so ξx={Xt+1∣Xt=x}. If bx>1, the process is …
New method for ancestral inference in branching processes with random environments.
problem Determining ancestor distribution parameters in branching processes with random environments.
method Generalized method of moments for ancestral inference.
result Limiting distribution of ancestor and offspring estimators decouple and converge to independent Gaussian variables under certain conditions.
The study connects triangulated surfaces to complex projective structures and circle patterns.
problem Understanding circle patterns on complex projective tori.
method Using discrete holomorphic quadratic differentials, the approach involves cross ratio systems and Delaunay angles.
result For any triangulated torus, the projection map is a covering map with at most one branch point.
Lipschitz equivalence of self-similar sets is an important area in the study of fractal geometry. It is known that two dust-like self-similar sets with the same contraction ratios are always Lipschitz equivalent. However, when self-similar sets have touching structures the problem of Lipschitz equivalence becomes much …
We first describe the local and global moduli spaces of germs of foliations defined by analytic functions in two variables with p transverse smooth branches, and with integral multiplicities (in the univalued holomorphic case) or complex multiplicities (in the multivalued ''Darboux'' case). We specify normal forms in e…
New GAN model deblends galaxy images with high accuracy and speed.
problem Deblending blended galaxy images in dense regions of the universe.
method Branched generative adversarial network (GAN) to produce images of deblended galaxies.
result High peak signal-to-noise ratio and structural similarity scores compared to ground truth images.
Improved machine learning with reduced tensor rank constraints and dropout.
problem Efficiently approximating large tensors in machine learning.
method Tree tensor networks with CP rank constraints and tensor dropout.
result Low-rank TTN classifier achieves 90.3% accuracy in Fashion-MNIST.
Hard phase in inference problems is glassy and hard to reconstruct.
problem Hard phase in inference problems that are hard to solve algorithmically.
method Study of metastable states and their entropy in low-rank matrix factorization.
result AMP algorithm performance is not improved by considering glassy states.
We present a careful analysis of possible issues on the application of the self-excited Hawkes process to high-frequency financial data. We carefully analyze a set of effects leading to significant biases in the estimation of the "criticality index" n that quantifies the degree of endogeneity of how much past events tr…
In order to disentangle the internal dynamics from exogenous factors within the Autoregressive Conditional Duration (ACD) model, we present an effective measure of endogeneity. Inspired from the Hawkes model, this measure is defined as the average fraction of events that are triggered due to internal feedback mechanism…
New formulas for knot polynomial evaluations from covering spaces.
problem Evaluating knot polynomials uniquely from covering spaces.
method Using singular determinants and linking pairings.
result Explicit formulae for Jones and Q-polynomial evaluations. Closed and broken electromagnetic orbits in Kerr-Newman spacetime
problem Constructing closed and broken electromagnetic orbits in the Kerr-Newman spacetime
method Constructing smooth closed electromagnetic orbits tangent to the axial Killing field and proving the existence of spherical electromagnetic orbits
result Proving the existence of spherical electromagnetic orbits and constructing closed broken electromagnetic orbits
Study on moduli spaces of branched projective structures on surfaces.
problem Characterizing and understanding moduli spaces of branched projective structures.
method Analytic and geometric methods to study the moduli spaces of branched projective structures.
result The moduli space of marked branched projective structures is a complex analytic space with specific dimensions and singular points.
We define a laminar branched surface to be a branched surface satisfying the following conditions: (1) Its horizontal boundary is incompressible; (2) there is no monogon; (3) there is no Reeb component; (4) there is no sink disk (after eliminating trivial bubbles in the branched surface). The first three conditions are…
Proper branched coverings are homeomorphisms on 3D balls or when branch set is empty.
problem Global injectivity of proper branched coverings on Euclidean balls.
method Analyzing the global injectivity of proper branched coverings defined on the Euclidean n-ball. result Proper branched coverings are homeomorphisms on 3D balls or when branch set is empty.
New criterion for branched covers between 2-spheres.
problem Existence of specific types of branched covers between 2-spheres.
method Combining complex analysis and topology techniques.
result Established a complete criterion for the existence of branched covers.
A study on the depth of graph neural networks on sparse graphs, revealing a dichotomy based on the Kesten-Stigum ratio.
problem Determining the optimal depth of graph neural networks for sparse graphs.
method Analyzing the sparse contextual stochastic block model with a message-passing classifier.
result The value of depth is governed by the Kesten-Stigum ratio, with thresholds dividing performance into geometric and branching processes.
Given a branched covering of degree d between closed surfaces, it determines a collection of partitions of d, the branch data. In this work we show that any branch data are realized by an indecomposable primitive branched covering on a connected close surface N with Euler's characteristic less than or equal to 0. This …
For surface-knots, branched covers with degree 3 have simplifying numbers <3.
problem Understanding numerical invariants of branched covering surface-knots.
method Analyzing numerical invariant (simplifying number) of branched covering surface-knots with degree 3.
result Branched covering surface-knots with degree 3 have simplifying numbers less than 3.
Ideal triangulations of 3-manifolds are shown equivalent up to certain moves.
problem Equivalence of ideal triangulations in 3-manifolds.
method Using branched triangulations and transit equivalences, the paper shows that ideal triangulations are equivalent up to certain moves.
result Ideal triangulations of 3-manifolds are equivalent up to certain moves.
New framework optimizes portfolio diversification beyond mean-variance.
problem Optimizing portfolio diversification beyond classical methods.
method Introduces portfolio dimensionality, connects diversification to non-Gaussian returns, and develops global optimization algorithms.
result Maximizing portfolio dimensionality leads to highly non-trivial optimization problems with multiple local optima.
Open and discrete maps with specific branch set images are equivalent to PL branched covers.
problem Understanding the equivalence of open and discrete maps and PL branched covers.
method Demonstrated that an open and discrete map f:SnoSn with a specific branch set image is equivalent to a PL branched cover up to homeomorphism. result Open and discrete maps with a specific branch set image are equivalent to PL branched covers.
Criteria found for knots not determined by their double branched covers.
problem Determining knots from their double branched covers.
method Criteria based on tunnel number one knots and their double branched covers.
result Provided criteria for knots not determined by their double branched covers.
Uniformly branching trees are equivalent to certain metric spaces.
problem Characterizing metric spaces equivalent to uniformly branching trees.
method Proving equivalence between trivalent quasiconformal trees and uniformly branching trees.
result Any two uniformly branching trees are quasisymmetrically equivalent.
Study of geodesic branching in 2D sub-Riemannian manifolds.
problem Branching of geodesics in sub-Riemannian manifolds of rank two.
method Analysis of geodesic behavior in sub-Riemannian geometry.
result Continuous families of strictly abnormal branching geodesics and accumulation of branching points.
The paper studies which branched covers can be lifted to braided embeddings.
problem Which branched covers lift to braided embeddings?
method Analyzes conditions for liftability using Hansen's criterion and examples in different dimensions.
result Not all branched covers lift to braided embeddings; examples are provided in various dimensions.
New method finds unrealizable branched cover data.
problem Existence of branched covers between Riemann surfaces.
method Connecting spherical conic metrics to combinatorial constraints.
result New infinite sets of exceptional branching data found.
The paper details folding of branched covers of the 3-sphere over knots.
problem Understanding folding of branched covers of the 3-sphere over knots.
method Presenting detailed foldings of dihedral covers of the 3-sphere branched over torus knots.
result Detailed foldings of dihedral covers of the 3-sphere branched over torus knots are presented.
New method learns better branching policies for MILP problems.
problem Improving branch and bound search for solving MILP problems.
method Imitates strong branching rule with parameterized state of B&B search tree.
result Generalized policies outperform current state-of-the-art.
Simplifies surface-knots using chart moves involving black vertices.
problem Simplifying branched covering surface-knots.
method Chart moves involving black vertices to simplify surface-knots.
result Properties of simplified branched covering surface-knots with branch points.
Course on knots using branched coverings.
problem Determining knots using cyclic branched coverings.
method Cyclic branched coverings of knots.
result New insights into knot classification.
In this work we characterize branch data of branched coverings of even degree over the projective plane which are realizable by indecomposable branched coverings.
Techniques for constructing codimension 2 embeddings and immersions of the 2 and 3-fold branched covers of the 3 and 4-dimensional spheres are presented. These covers are in braided form, and it is in this sense that they are folded. More precisely the composition of the embedding (or immersion) and the canonical proje…
Formula compares metrics on branched coverings of line bundles.
problem Comparing metrics on branched coverings of line bundles.
method Formula to compare Quillen metrics on branched coverings.
result Formula for comparing Quillen metrics on branched coverings.
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.
Proofs for decomposing branched affine surfaces into triangles and cylinders.
problem Decomposing branched affine surfaces into simpler geometric shapes.
method Proof of Veech's theorem and introduction of invariant α.
result Any pair of decompositions can be connected by flips.
New examples show transverse knots are determined by their branched covers.
problem Transverse knots and their isotopy classes.
method Constructing and analyzing non-isotopic transverse knots with contactomorphic cyclic branched covers.
result Transverse isotopy classes of many transverse knots are determined by the contactomorphism type of their cyclic branched covers.
Finite distortion maps cannot have compact branch sets under growth conditions.
problem Understanding the structure of branch sets in mappings of finite distortion.
method Analyzing the asymptotic growth of distortion and constructing specific examples.
result The bound on the size of branch sets is strict and achievable.
We establish a calculus for branched spines of 3-manifolds by means of branched Matveev-Piergallini moves and branched bubble-moves. We briefly indicate some of its possible applications in the study and definition of State-Sum Quantum Invariants.
Quantized Coulomb branches linked to skein algebras.
problem Understanding the relationship between quantized Coulomb branches and skein algebras.
method Association of quantized Coulomb branches to surfaces, description of relationship for specific surfaces, formulation of a conjecture.
result A conjecture linking quantized Coulomb branches and skein algebras.
We prove that if S is a closed compact surface of negative Euler characteristic, and if R is a quasi-Fuchsian representation in PSL(2,C), then the deformation space M(k,R) of branched projective structures on S with total branching order k and holonomy R is connected, as soon as k>0. Equivalently, two branched projecti…