Complex nilmanifolds have limited algebraic dimension based on holomorphic differentials.
problem Determining the algebraic dimension of complex nilmanifolds.
method Analyzing holomorphic differentials and meromorphic maps on complex nilmanifolds.
result The algebraic dimension a(M) is bounded by the dimension of the space of holomorphic differentials. Study algebraic varieties using Galois groups.
problem Understanding rational parallelisms of algebraic varieties.
method Using Galois groups from Picard-Vessiot theory.
result Measure the transcendence of symmetries.
Study transcendence of abelian differential periods from bi-algebraic perspective.
problem Arithmetic and functional transcendence of periods of abelian differentials.
method Bi-algebraic structure on strata of abelian differentials.
result Characterization of arithmetic points and proof of linear bi-algebraic curves.
This paper revisits Differential Galois Theory using Hopf algebras for Lie pseudogroups.
problem Understanding the structure of algebraic Lie pseudogroups using differential algebra and geometry.
method Mixing differential algebra, differential geometry, and algebraic geometry; using Hopf algebras.
result Reveals confusion between prime differential ideals and maximal ideals in Vessiot's work.
Paper connects Painlevé VI equation to irregular systems, solving monodromy data.
problem Solving monodromy data for irregular systems related to Painlevé VI.
method Expressed Frobenius integrability in terms of PVI, computed monodromy data for coalescing eigenvalues.
result Computed monodromy data for transcendentals holomorphic at critical points of PVI.
We finish the proof of the conjecture of F. Bogomolov and F. Pop: Let F1 and F2 be fields finitely-generated and of transcendence degree ≥2 over k1 and k2, respectively, where k1 is either Qˉ or Fˉp, and k2 is algebraically closed. We denote by $G_{…
Paper tackles CC generation for metrics in GR.
problem Finding CC for metrics in GR.
method Homological snake lemma approach.
result Link between CC, formal exactness, and FI.
This paper is the next installment of our analysis of length-commensurable locally symmetric spaces begun in Publ. math. IHES 109(2009), 113-184. For a Riemannian manifold M, we let L(M) be the weak length spectrum of M, i.e. the set of lengths of all closed geodesics in M, and let F(M) denote the s…
We give a gauge invariant characterisation of the elliptic affine sphere equation and the closely related Tzitzéica equation as reductions of real forms of $SL(3, \C)$ anti--self--dual Yang--Mills equations by two translations, or equivalently as a special case of the Hitchin equation. We use the Loftin--Yau--Zaslow co…
New optimal trading strategies found for risk-averse and cumulative prospect theory traders in illiquid markets.
problem Optimal trading strategies for risk-averse and cumulative prospect theory traders in illiquid markets.
method An extension of Skorohod's representation theorem for tight sequences of probability measures.
result Existence of optimal strategies for agents with cumulative prospect theory preferences in continuous-time illiquid markets.
We present two constructions of new solutions to the dispersionless KP (dKP) equation arising from the first two Painlevé transcendents. The first construction is a hodograph transformation based on Einstein--Weyl geometry, the generalised Nahm's equation and the isomonodromy problem. The second construction, motivated…
An ordinary differential field (F,d) of characteristic zero, a subgroup H of affine group GL(n,C)∝Cn with respect to its identical representation in Fn and the following two fields of differential rational functions in x=(x1,x2,...,xn)-column vector, $$C< x, d>^H=\{f^d< x> \in C< x, d> : f^d< hx+…
In this paper we address the following questions: (i) Let C⊂C2 be an orbit of a polynomial vector field which has finite total Gaussian curvature. Is C contained in an algebraic curve? (ii) What can be said of a polynomial vector field which has a finitely curved transcendent orbit? We give a positi…
It is shown that both the sinh--Gordon equation and the elliptic Tzitzeica equation can be interpreted as the Taubes equation for Abelian vortices on a CMC surface embedded in R2,1, or on a surface conformally related to a hyperbolic affine sphere in R3. In both cases the Higgs field and the U(1) vortex conn…
Deep learning improves evolutionary algorithms' adaptability.
problem Improving evolutionary algorithms' adaptability to various circumstances.
method Using deep reinforcement learning to dynamically adjust evolutionary algorithms' strategies.
result Deep learning enhances evolutionary algorithms' fitness increase and attainable fitness.
We explicitly compute the diffeomorphism group of several types of linear foliations (with dense leaves) on the torus Tn, n≥2, namely codimension one foliations, flows, and the so-called non-quadratic foliations. We show in particular that non-quadratic foliations are rigid, in the sense that they do not admit…
China integrates ESG into corporate strategy for sustainable growth.
problem Corporate focus on short-term financial metrics.
method Deep integration of ESG principles into corporate culture and strategy.
result Companies are expected to fulfill social responsibilities and create long-term value.
NeuroPaint infers missing brain area dynamics from multi-animal datasets.
problem Leveraging multi-animal datasets to understand interactions between brain areas.
method Masked autoencoding approach trained across animals with partial observations.
result Models can successfully reconstruct dynamics of unrecorded brain areas.
RL framework optimizes trading costs in noisy markets.
problem Optimal execution and placement in noisy markets.
method Dual-window Denoise PPO RL network, imitation learning, comprehensive market features, flexible action formulation.
result RL agents outperformed TWAP strategy in execution cost.
Introduces generalized hyperpolygons and their geometric and algebraic properties.
problem Understanding moduli spaces of generalized hyperpolygons.
method Representation of a comet-shaped quiver, associated meromorphic Higgs bundles, Hitchin systems, and integrable Hamiltonian systems.
result Generalized hyperpolygons admit the structure of a completely integrable Hamiltonian system.
R-PCA extends PCA to Riemannian manifolds for structured data.
problem Applying PCA to data on Riemannian manifolds without vector space operations.
method Adapting PCA to Riemannian manifolds by equipping data with local metrics.
result Unified approach for dimensionality reduction and statistical analysis on manifolds.
Unified framework for complex financial networks using lattice theory.
problem Complex financial networks with multiple currencies and dependencies.
method Recast classical financial clearing model into lattice liability networks.
result Lattice-valued clearing sections form a complete lattice, enabling tractable analysis.
Introduces a network-based framework to analyze swarm intelligence.
problem Lack of a common framework to compare swarm-based algorithms.
method Introduces an interaction network to examine swarm-based systems.
result Shows how swarm-based algorithms can be studied as systems.
This paper explores crypto, blockchain, and Metaverse risks and opportunities.
problem Understanding crypto crashes and blockchain technologies.
method Interdisciplinary approach combining fintech, machine learning, and risk assessment.
result Blockchain technologies will continue to dominate, but discerning genuine projects is crucial.
Unique hyperbolic affine spheres associated with convex cones in 3D.
problem Characterizing and classifying self-associated convex cones in 3D.
method Using affine spheres, hyperbolic geometry, and differential equations.
result Complete classification of self-associated convex cones and their associated affine spheres.
Study shows not all ML models are uniquely identifiable from data.
problem Identifiability issues in machine learning models.
method Investigated through a case study on gait dynamics using a bipedal-spring mass model.
result Some parameters can be identified, but others remain unidentifiable.
FairACE improves fairness in GNNs by balancing node performance across degree groups.
problem Degree biases in GNNs lead to unequal prediction performance among nodes with varying degrees.
method Integrates asymmetric contrastive learning with adversarial training to balance performance between high-degree and low-degree nodes.
result Significantly improves degree fairness metrics while maintaining competitive accuracy.
Develops degree theory for orbifolds, a generalization of differential topology.
problem No suitable problem statement as the abstract focuses on the development of theory.
method Defined a mapping degree for proper maps between orbifolds, satisfying invariance properties.
result The mapping degree counts preimages of regular values with appropriate weights.
The paper uses AI to analyze ECG data, revealing age-related changes and identifying key features.
problem Investigating age-related changes in ECG data to distinguish healthy from disease-related changes.
method Employed deep-learning and tree-based models on raw ECG signals and features from a diverse age group.
result Identified age-related declines in breathing rates and high SDANN values in elderly individuals.
Extends graph degree theorem to simplicial closure of Auter space.
problem Connectivity of graphs in Auter space.
method Defines degree for simplicial closure, extends Hatcher-Vogtmann theorem.
result Simplicial closure of Auter space is (d-1)-connected for degree d.
This paper finds all prime alternating knots with minimal warping degree two.
problem Finding knots with minimal warping degree.
method Examined all prime alternating knots and determined those with minimal warping degree two.
result All prime alternating knots with minimal warping degree two were identified.
Paper shows how to identify and reconstruct degree-d PTFs robustly from their Fourier coefficients.
problem Identifying and reconstructing degree-d polynomial threshold functions (PTFs) from their Fourier coefficients.
method Proves a robust version of the theorem that degree-d Chow parameters uniquely characterize degree-d PTFs, and uses this to develop efficient algorithms.
result Boolean degree-d PTFs are robustly identifiable from their degree-d Chow parameters.
Study G-degree for singular 3D manifolds, classifying up to G-degree 6.
problem Classifying singular 3D manifolds using G-degree.
method Analyzes properties of G-degree for graphs representing singular manifolds, focusing on 3D closed PL manifolds.
result Complete topological classification up to G-degree 6 in 3D.
The stochastic block model is a powerful tool for inferring community structure from network topology. However, it predicts a Poisson degree distribution within each community, while most real-world networks have a heavy-tailed degree distribution. The degree-corrected block model can accommodate arbitrary degree distr…
For harmonic maps of degree 2, a similar quantitative stability estimate does not hold uniformly.
problem Investigate the quantitative stability of harmonic maps of degree 2.
method Prove a local quantitative stability result for harmonic maps of degree 2, showing dependence on the given harmonic map.
result A uniformly quantitative stability estimate does not hold for degree 2 harmonic maps.
Study Kazdan-Warner equations on graphs using Brouwer degree theory.
problem Proving existence of solutions to Kazdan-Warner equations on finite graphs.
method Degree theory approach to uniformly bound and compute Brouwer degree.
result New proofs of existence results for Kazdan-Warner equations.
Proposes a method to infer networks using node-specific degree priors.
problem Network inference from partially observed edges.
method Formulates network inference as a matrix completion problem regularized by a node-specific degree prior derived from observed edges.
result Improves network recovery error bound compared to previous methods.
In Stochastic blockmodels, which are among the most prominent statistical models for cluster analysis of complex networks, clusters are defined as groups of nodes with statistically similar link probabilities within and between groups. A recent extension by Karrer and Newman incorporates a node degree correction to mod…
The study finds lower bounds for the warping degree of a knot projection.
problem Determining the warping degree of a knot projection.
method Examining the maximal number of regions sharing no crossings for a fixed crossing in a knot projection.
result Lower bounds for the warping degree of a knot projection are provided.
Social media enhances or diminishes scientific status, depending on usage.
problem Impact of social media on scientific stratification and mobility.
method Logistic Attribution Analysis combining statistical and machine learning methods.
result Social media promotes stratification and mobility, but beyond a threshold, it negatively impacts status.
Christoffel function characterizes the corruption a bounded-degree certificate cannot remove in robust halfspace learning.
problem Robust halfspace learning under malicious noise
method Sum-of-Squares degree of outlier-removal certificate
result Christoffel function bounds the corruption a bounded-degree certificate cannot remove
New formula recovers degree of colored Jones polynomials for pretzel knots.
problem Determining the degree of colored Jones polynomials for specific knots.
method Alternate expansion of the colored Jones polynomial for pretzel links, focusing on 3-tangle knots.
result Determined the degrees of the colored Jones polynomials for a new family of 3-tangle pretzel knots.
Research examines curves of degree 8 with specific singularities.
problem Existence of curves with prescribed singularities.
method Algebraic and symplectic approaches.
result Characterization of curves with specific singularities.
The paper reveals that deep neural networks have fewer degrees of freedom than parameters, impacting model performance.
problem Understanding the relationship between degrees of freedom and model performance in deep neural networks.
method Developed an efficient Monte-Carlo method to estimate degrees of freedom for multi-class classification methods.
result Degrees of freedom in deep networks are dramatically smaller than the number of parameters, often by several orders of magnitude.
Low-degree method fails to predict robust subspace recovery problem.
problem Predicting computational tractability of robust subspace recovery problem.
method Low-degree polynomial framework, anti-concentration properties.
result Low-degree method fails to predict computational tractability of robust subspace recovery problem even up to high degree.
The study classifies graphs with specific curvature and maximum degree.
problem Graphs with nonnegative Ricci curvature and maximum degree constraints.
method Classification of graphs with Lin-Lu-Yau-Ollivier Ricci curvature, maximum degree ≤ 3, and diameter ≥ 6.
result Classification of graphs meeting the specified criteria.
The paper corrects for node degree in spectral clustering using random walk Laplacian.
problem Node degree heterogeneity in spectral clustering.
method Graph spectral embedding using the random walk Laplacian.
result The embedding provides uniformly consistent estimates of degree-corrected latent positions.
GCNs favor high-degree nodes, leading to biased performance; a new method mitigates this.
problem Degree-related biases in GCNs, especially for low-degree nodes.
method Developed a novel SL-DSGC that reduces model and data biases.
result SL-DSGC improves GCN accuracy significantly for low-degree nodes.