The conformal Laplacian's algebraic structure is explored in 2D, revealing a central charge.
problem Exploring the algebraic structure of the conformal Laplacian in 2D.
method Using prefactorization algebras and Green functions.
result In 2D, the conformal Laplacian's algebraic structure is revealed through a central charge.
This paper investigates the relationship between algebraic quantum field theories and factorization algebras on globally hyperbolic Lorentzian manifolds. Functorial constructions that map between these two types of theories in both directions are developed under certain natural hypotheses, including suitable variants o…
The paper uses machine learning to compute rare event probabilities in stochastic systems.
problem Characterizing rare events in stochastic dynamical systems with weak noise.
method Developed a neural network framework for computing quasipotential, most probable paths, and prefactors.
result Demonstrated higher effectiveness and accuracy of the algorithm in calculating mean exit times.
This study generalizes an econophysics model to account for trader heterogeneity, finding robust power-law exponents but sensitive prefactors.
problem The original Lillo-Mike-Farmer model assumed homogeneity in traders' order-splitting strategies, which this study generalizes.
method The study proposes a generalised Lillo-Mike-Farmer model and solves it exactly without heuristic assumptions.
result The power-law exponent in the order-sign ACF is robust for arbitrary heterogeneous intensity distributions, but the prefactor is sensitive to heterogeneity.
Paper derives closed-form solutions for CEV model using semiclassical approximation.
problem Analyzing the constant elasticity variance (CEV) option pricing model.
method Utilizes semiclassical (WKB) approximation and Van Vleck-Morette determinant.
result Derives an exponential factor not previously considered in the kernel.
Sharp large deviations and Gibbs conditioning for portfolio credit risk models.
problem Analyzing the risk of default in financial portfolios with dependent factors.
method Sharp large deviation estimates and conditional Bahadur-Rao estimates for threshold models with diverging latent factors.
result Conditioned on a large exceedance event, default indicators become asymptotically i.i.d., and loss-given-default is exponentially tilted.
We confirm the square-root law of market impact on Apple Inc. using a large dataset.
problem Testing the square-root law of market impact on a single U.S. large-cap equity.
method Using a full market-by-order feed, we reconstruct metaorders and calibrate impact using the square-root formula.
result The square-root law is confirmed with a prefactor of 0.34, consistent with worldwide data.
This work studies the smooth 1-Wasserstein distance and its limit distribution in high dimensions.
problem Addressing the curse of dimensionality in empirical approximation.
method Conducts a statistical study including limit distribution, bootstrap consistency, and concentration inequalities.
result Derives a nondegenerate limit distribution for empirical SWD, contrasting with classic W1. Study measures volume of foliations on surfaces, finding integrability range.
problem Volume of combinatorial unit ball of measured foliations on bordered surfaces.
method Analyzes combinatorial moduli spaces and Kontsevich measure.
result Determines range of integrability for (BΣmcomb)s. Derives continuum model from discrete ε-graphs with connectivity functional.
problem Modeling diffusion in networks with varying connectivity.
method Energy-based continuum limit derivation, neural-network reconstruction of connectivity.
result Error between discrete and continuum energies is O(ε), valid even with fluctuations. Paper improves SDR estimation speed and conditions.
problem Improving sufficient dimension reduction for multi-index models.
method Estimating expected smoothed gradient outer product.
result Achieves fast parametric convergence rate of Cd⋅n−1/2. Proposes a new sampling policy for ranking and selection problems.
problem Improving ranking and selection in adaptive sampling policies.
method Annealed entropic allocation, using soft-min weights and saddlepoint corrections.
result Consistently competitive performance in various settings.
Analyzes tunneling effects for Schrödinger operators on vector bundles.
problem Tunneling effects in quantum systems with multiple potential wells.
method Quasimodes and WKB analysis near potential wells, interaction matrix for coupling between wells.
result Polynomial prefactor for exponentially small eigenvalue splitting determined by dimension of minimal geodesics.
Proposes a non-crossing deep neural network quantile regression method.
problem Quantile crossing in nonparametric quantile regression.
method Non-crossing constraints via rectified linear unit penalty function.
result Established non-asymptotic upper bounds for excess risk.
We characterize the communication complexity of the following distributed estimation problem. Alice and Bob observe infinitely many iid copies of ρ-correlated unit-variance (Gaussian or ±1 binary) random variables, with unknown ρ∈[−1,1]. By interactively exchanging k bits, Bob wants to produce an estimate $…
Nonparametric Thompson Sampling achieves optimal regret for risk-averse bandits with sub-Gaussian rewards.
problem Optimizing risk-averse bandit problems with sub-Gaussian rewards.
method Anchor-free nonparametric Thompson Sampling algorithm ρext−NPTSSG. result Achieves regret matching the instance-dependent lower bound to leading order in logn. One-pass SGD dynamics in overparameterized quadratic networks show slow escape from poor solutions.
problem Slow escape from poor generalization solutions in overparameterized neural networks.
method Analysis of one-pass SGD dynamics using ordinary differential equations for overlap matrices.
result Overparameterization only modestly accelerates escape from poor solutions.
Optimized concentric helices minimize the ropelength of non-alternating torus knots.
problem Optimizing the ropelength of non-alternating torus knots.
method Optimized geometry and combinatorics of concentric helices.
result Optimized ropelength of concentric helices is approximately 7.83Q^(3/2).
This paper contains a phenomenological description of the whole U.S. forward rate curve (FRC), based on an data in the period 1990-1996. We find that the average FRC (measured from the spot rate) grows as the square-root of the maturity, with a prefactor which is comparable to the spot rate volatility. This suggests th…
Quantitative analysis of order-splitting behavior in Japanese stock market.
problem Understanding and quantifying the order-splitting behavior of traders in the Japanese stock market.
method Analysis of a large dataset of trading accounts over nine years, clustering traders into order-splitting and random traders, and applying statistical methods to analyze metaorder length and sign correlation.
result The metaorder length distribution follows power laws with exponent α, and the sign correlation exponent γ is approximately α-1, supporting the LMF model.
New algebraic structure derived from Hopf algebra and Drinfel'd twist.
problem Developing a new algebraic structure from existing mathematical concepts.
method Extending L∞-algebra to a Hopf algebra, twisting with Drinfel'd twist, and identifying Hopf morphisms and braided morphisms. result Braided L∞-algebra is derived from the process. Study of cluster and skein algebras for surfaces, showing their connection.
problem Understanding algebraic structures of curve algebras on surfaces.
method Generalization and explicit definition of maps between cluster and skein algebras.
result Explicit maps between cluster and skein algebras, showing their close relationship.
Study on pseudo-Riemannian algebraic Ricci solitons in 4D Lie groups.
problem Investigating conditions for pseudo-Riemannian algebraic Ricci solitons on 4D Lie algebras.
method Analyzing the algebraic Ricci soliton equation for each 4D Lie algebra.
result Complete description of pseudo-Riemannian algebraic Ricci solitons in dimension four.
Characterizes Lie groups with specific structures and finds a correspondence between carrollian and galilean Lie algebras.
problem Understanding Lie groups with specific structures.
method Using structure theory of metric Lie algebras and defining new Lie algebras with skew-symmetric derivations.
result A canonical correspondence between carrollian and galilean Lie algebras mediated by bargmannian Lie algebras.
We extend the classical characterization of a finite-dimensional Lie algebra g in terms of its Maurer-Cartan algebra-the familiar differential graded algebra of alternating forms on g with values in the ground field, endowed with the standard Lie algebra cohomology operator-to sh Lie-Rinehart algebras. To this end, we …
New tools for studying Hsiang algebras discovered, linking them to known algebraic structures.
problem Classifying Hsiang algebras and understanding their properties.
method Introducing quasicomposition and tripling constructions to study Hsiang algebras.
result The triple of a quasicomposition algebra is an exceptional Hsiang algebra.
A Lie-admissible algebra gives by anticommutativity a Lie algebra. In this work we study remarkable classes of Lie-admissible algebras such as Vinberg, PreLie algebras. We compute the corresponding binary quadratic operads and study their Koszul duality. Considering Lie algebras as Lie-admissible algebras we can define…
Study biderivations in complete Leibniz algebras, extending Lie algebra results.
problem Defining and studying biderivations in complete Leibniz algebras.
method Analyze biderivations according to two definitions, provide conditions for biderivations, and compare symmetric and skew-symmetric biderivations.
result Necessary and sufficient conditions for biderivations in Leibniz algebras are provided.
The paper extends a theorem to Lie-Rinehart algebras and provides new decompositions of universal enveloping algebras.
problem Understanding universal enveloping algebras of Lie-Rinehart algebras.
method Extending a theorem to left Hopf algebroids and applying it to universal enveloping algebras of Lie-Rinehart algebras.
result Provides a crossed product decomposition of universal enveloping algebras for curved and flat connections.
The paper classifies Lie algebras with special operators.
problem Classifying 3D Lie algebras with regular semisimple algebraic Nijenhuis operators.
method Described all Nijenhuis eigenbases for each 3D Lie algebra.
result Different answers in real and complex cases, some Lie algebras admit operators, others do not.
Symmetric spaces' connections form Lie admissible triple algebras.
problem Understanding the algebraic structure of symmetric spaces' connections.
method Analyzing the connection as a binary operator on tangent bundle sections, identifying Lie admissibility constraints.
result Connection algebra of symmetric spaces is a Lie admissible triple algebra.
The paper generalizes para-Kähler Lie algebras to k-para-Kähler Lie algebras and explores their structures.
problem Characterizing and understanding k-para-Kähler Lie algebras.
method Generalization of para-Kähler Lie algebras to k-para-Kähler Lie algebras, introduction of new structures, determination of Lie algebras.
result Determination of all k-symplectic Lie algebras of dimension (k+1) and six-dimensional 2-para-Kähler Lie algebras.
The paper investigates gradings of complex simple Lie algebras, focusing on ∣3∣-gradings and their algebraic structures.
problem Investigating the algebraic structure of ∣3∣-gradings of complex simple Lie algebras. method Completely determining the possible reductive algebras n0 and proving the uniqueness of a specific free nilpotent Lie algebra. result The only free nilpotent Lie algebra of step 3 that appears as the negative part of a ∣3∣-grading is the usual ∣3∣-grading of the exceptional Lie algebra g2. New algebra pong algebra computed for knot Floer homology.
problem Computing A-infinity structure on knot Floer homology.
method Introduced differential graded algebra, pong algebra.
result Computed A-infinity structure on pong algebra's homology.
Study resolves conjecture linking two algebraic structures on surfaces.
problem Compatibility of skein and cluster algebra structures on surfaces.
method Established compatibility between skein and cluster algebras of surfaces.
result Cluster algebra of positive genus surfaces is not finitely generated.
Study on pre-Lie structures for semisimple Lie algebras over C.
problem Admissibility of pre-Lie structures in semisimple Lie algebras.
method Examined properties of anti-flexible algebras (AFAs), computed Lie-admissibility criteria, and provided examples.
result Explicit counterexample of an AFA admissible by sl(2, C).
Develops a bialgebra theory for post-Lie algebras using geometric interpretations and bilinear forms.
problem Characterizing and understanding post-Lie algebras and their associated structures.
method Utilizes Manin triples and generalized Hessian Lie groups to define and characterize post-Lie algebras with nondegenerate symmetric invariant bilinear forms.
result Establishes a bialgebra theory for post-Lie algebras via the Manin triple approach, including new algebraic structures like pp-post-Lie algebras.
Characterizes G2-structures on Lie algebras with non-trivial center.
problem Classifying Lie algebras with G2-structures.
method Analyzing Lie algebras with non-trivial center, using contactization and symplectic properties.
result Six unimodular Lie algebras with non-trivial center admit closed G2-structures.
This paper presents results on the framization of some knot algebras, defined by the authors. We explain the motivations of the concept of framization, coming from the Yokonuma--Hecke algebras, as well as recent results on the framization of the Temperley--Lieb algebra. Finally, we propose framizations for other knot a…
For finite dimensional real Lie algebras, we investigate the existence of an inner product having a basis comprised of geodesic elements. We give several existence and non-existence results in certain cases: unimodular solvable Lie algebras having an abelian nilradical, algebras having an abelian derived algebra, algeb…
Twilled L(ie-)R(inehart)-algebras generalize, in the Lie-Rinehart context, complex structures on smooth manifolds. An almost complex manifold determines an "almost twilled pre-LR algebra", which is a true twilled LR-algebra iff the almost complex structure is integrable. We characterize twilled LR structures in terms o…
Similarity algebra extends algebraic structures with quantitative bounds.
problem Exact algebraic structures with strict axioms.
method Framework for approximate algebraic and Lie structures with ε-estimates. result Similarity structures converge to classical algebraic objects as εightarrow0. Extends Loday-Quillen-Tsygan theorem to bornological Lie algebra homology.
problem Calculating Lie algebra homology of gauge algebras using cyclic homology.
method Extends proof to bornological Lie algebra homology of Fréchet and LF-algebras, prepares statements about homological algebra of topological vector spaces.
result Constructs a spectral sequence to calculate stable part of bornological Lie algebra homology of gauge algebras.
New algebra for twice-punctured torus curves.
problem Constructing a new algebra for skein theory.
method Using Heegaard dual of Iwahori--Hecke operator, Dehn twists are represented.
result Automorphisms correspond to Dehn twists on the twice-punctured torus.
We define a Poisson Algebra called the {\em swapping algebra} using the intersection of curves in the disk. We interpret a subalgebra of the fraction algebra of the swapping algebra -- called the {\em algebra of multifractions} -- as an algebra of functions on the space of cross ratios and thus as an algebra of functio…
New braided Frobenius algebras created from specific Hopf algebras.
problem Creating new algebraic structures from Hopf algebras.
method Heap operation and Yang-Baxter operator on tensor product.
result Heap operation induces a braiding compatible with Frobenius operations.
Poisson algebra is usually defined to be a commutative algebra together with a Lie bracket, and these operations are required to satisfy the Leibniz rule. We describe Poisson structures in terms of a single bilinear operation. This enables us to explore Poisson algebras in the realm of non-associative algebras. We stud…
The paper examines differential smoothness in specific algebra types.
problem Differential smoothness in 3D skew polynomial algebras and diffusion algebras.
method Analyzes the properties of 3D skew polynomial algebras and diffusion algebras.
result Provides insights into the differential smoothness of these algebra types.