Study properties of balanced hyperbolic compact complex manifolds.
problem Understanding cohomology and harmonic spaces of balanced hyperbolic manifolds.
method Proved vanishing theorems and Hard Lefschetz-type theorems for balanced hyperbolic compact complex manifolds.
result Non-existence of certain L1 currents on the universal covering space of a balanced hyperbolic manifold. Finite presentation for a specific group in 3D handlebody topology.
problem Finding a finite presentation for a specific group in 3D handlebody topology.
method Constructed a finite presentation for the liftable Hilden group to derive the presentation for the balanced superelliptic handlebody group.
result A finite presentation was given for the balanced superelliptic handlebody group.
Finite presentations for mapping class groups of surfaces and surfaces with points/boundaries.
problem Finding finite presentations for balanced superelliptic mapping class groups.
method Construct finite presentations for corresponding liftable mapping class groups in a different generating set.
result Finite presentations for balanced superelliptic mapping class groups of various surfaces.
Generalized Thurston's characterization for branched coverings of the 2-sphere.
problem Characterize branched coverings of the 2-sphere.
method Introduced local balance and operations against balanced graphs.
result New proof of a theorem by Eremenko-Gabrielov-Mukhin-Tarasov-Varchenko.
We construct a generalization of twistor spaces of hypercomplex manifolds and hyper-Kahler manifolds M, by generalizing the twistor P1 to a more general complex manifold Q. The resulting manifold X is complex if and only if Q admits a holomorphic map to P1. We make branched double cove…
Three elements generate balanced superelliptic mapping class groups.
problem Generating balanced superelliptic mapping class groups.
method Proving groups are generated by three elements through normalizers and liftable mapping class groups.
result Balanced superelliptic mapping class groups are generated by three elements.
Study of fundamental groups of 3D small covers using Morse theory.
problem Understanding the fundamental groups of 3D small covers.
method Morse-theoretic approach to get explicit, balanced presentations of fundamental groups.
result Explicit, balanced presentations of fundamental groups with minimal generators and minimal Heegaard splittings.
Proves a minimal generating set for a specific group of mapping classes.
problem Finding a minimal generating set for a specific group of mapping classes.
method Proved the group is generated by four elements, with minimal exceptions.
result Minimal generating set for the balanced superelliptic mapping class group.
The hyperelliptic mapping class group has been studied in various contexts within topology and algebraic geometry. What makes this study tractable is that there is a surjective map from the hyperelliptic mapping class group to a mapping class group of a punctured sphere. The more general family of superelliptic mapping…
JRFs improve semi-supervised learning by balancing generation and classification.
problem Mode missing and mode covering issues in GANs and VAEs, and conflict between good classification and generation.
method Joint-stochastic-approximation random fields (JRFs) for deep undirected generative models.
result JRFs achieve good classification and generation results in SSL.
Extends Thurston's combinatorial characterization to all branched coverings of the 2-sphere.
problem Characterizing branched coverings of the 2-sphere.
method Generalizing Thurston's local balancing to all branched coverings.
result Provides a new proof for a theorem concerning real rational functions.
Let p be a prime number. We develop a theory of p-adic Mahler measure of polynomials and apply it to the study of Z-covers of rational homology 3-spheres branched over links. We obtain a p-adic analogue of the asymptotic formula of the torsion homology growth and a balance formula among the leading coe…
Let f:S2→S2 be an orientation-preserving branched covering map of degree d≥2, and let Σ be an oriented Jordan curve passing through the critical values of f. Then Γ:=f−1(Σ) is an oriented graph on the sphere. In a group email discussion in Fall 2010, W. Thurston introduced balanced planar graphs a…
The paper studies liftable mapping class groups of cyclic covers of spheres.
problem Understanding liftable mapping class groups of cyclic covers of spheres.
method Derived finite generating sets, provided algorithms, determined isomorphism classes, derived presentations, and calculated normalizers and centralizers.
result Presentations and isomorphism classes of liftable mapping class groups for various covers.
Analyzes Indian commercial dynamism using time series data.
problem Understanding commercial dynamism in India.
method Time series analysis of various economic indicators.
result Detailed insights into growth rate, trade balance, etc.
PC-PG balances exploration and exploitation in reinforcement learning.
problem Local policy gradient methods struggle with exploration.
method PC-PG uses an ensemble of learned policies (policy cover) to balance exploration and exploitation.
result PC-PG provides strong theoretical guarantees and empirical validation.
We provide three 3-dimensional characterizations of the Z-slice genus of a knot, the minimal genus of a locally-flat surface in 4-space cobounding the knot whose complement has cyclic fundamental group: in terms of balanced algebraic unknotting, in terms of Seifert surfaces, and in terms of presentation matrices of the…
A modern version of Monetary Circuit Theory with a particular emphasis on stochastic underpinning mechanisms is developed. It is explained how money is created by the banking system as a whole and by individual banks. The role of central banks as system stabilizers and liquidity providers is elucidated. It is shown how…
We introduce a notion of Gieseker stability for a filtered holomorphic vector bundle F over a projective manifold. We relate it to an analytic condition in terms of hermitian metrics on F coming from a construction of the Geometric Invariant Theory (G.I.T). These metrics are balanced in the sense of S.K. Donaldson.…
An increase in energy production from renewable energy sources is viewed as a crucial achievement in most industrialized countries. The higher variability of power production via renewables leads to a rise in ancillary service costs over the power system, in particular costs within the electricity balancing markets, ma…
A 3-manifold is Haken if it contains a topologically essential surface. The Virtual Haken Conjecture posits that every irreducible 3-manifold with infinite fundamental group has a finite cover which is Haken. In this paper, we study random 3-manifolds and their finite covers in an attempt to shed light on this difficul…
These notes give an introduction to the Strominger system of partial differential equations, and are based on lectures given in September 2015 at the GEOQUANT School, held at the Institute of Mathematical Sciences (ICMAT) in Madrid. We describe the links with the theory of balanced metrics in hermitian geometry, the He…
Kernel-UCBVI algorithm balances exploration and exploitation in metric state-action spaces.
problem Exploration-exploitation dilemma in finite-horizon reinforcement learning with metric state-action spaces.
method Kernel-UCBVI, leveraging smoothness and kernel estimators of rewards and transitions.
result First regret bound for kernel-based RL using smoothing kernels, O(H3K2d/(2d+1)). Motivated by social balance theory, we develop a theory of link classification in signed networks using the correlation clustering index as measure of label regularity. We derive learning bounds in terms of correlation clustering within three fundamental transductive learning settings: online, batch and active. Our mai…
Algorithm balances learning and coverage for multi-robots over unknown fields.
problem Balancing learning and coverage for multi-robots over unknown, nonuniform sensory fields.
method DSLC algorithm that schedules learning and coverage epochs, using Gaussian Process modeling and coverage regret analysis.
result Upper bound on expected cumulative coverage regret provided for DSLC.
Balances and eliminates base algorithms in bandits and RL to bound total regret.
problem Model selection in bandits and reinforcement learning with unknown optimal regret.
method Balances and eliminates base algorithms based on candidate regret bounds.
result Total regret bound is the best valid candidate regret bound times a small multiplicative factor.
The paper calculates heat kernel and closed geodesic asymptotics for nilpotent coverings.
problem Heat kernel and closed geodesic asymptotics for nilpotent coverings.
method Finite-dimensional rational Floquet-Bloch theory, Pytlik functional, and spectral sums.
result Genuinely local, pointwise higher-order heat-kernel expansions.
Study of special Kato manifolds derived from toric geometry.
problem Characterize and study properties of Kato manifolds.
method Construction from toric geometry, topological and analytical properties, combinatorial data, flat degenerations, Hermitian geometry.
result No Kato manifold supports balanced or pluriclosed metrics.
The paper defines two types of hyperbolicity for complex manifolds and proves related results.
problem Defining and studying hyperbolicity for a broader class of complex manifolds.
method Introducing SKT hyperbolicity and Gauduchon hyperbolicity, proving results using SKT and Gauduchon metrics.
result Every SKT hyperbolic manifold is also Kobayashi/Brody hyperbolic and every Gauduchon hyperbolic manifold is divisorially hyperbolic.
This paper surveys gradient-based multi-objective deep learning methods.
problem Balancing multiple conflicting objectives in deep learning models.
method Gradient-based techniques adapted from Multi-Objective Optimization.
result Comprehensive survey of gradient-based multi-objective deep learning algorithms.
Study on balanced Hermitian structures on Lie algebras twisted by representations.
problem Conditions for balanced and locally conformally balanced Hermitian structures on Lie algebras.
method Analysis of Hermitian structures on twisted cartesian products of Lie algebras.
result Classification of six-dimensional balanced Hermitian twisted cartesian products Lie algebras.
We study the intrinsic geometrical structure of hypersurfaces in 6-manifolds carrying a balanced Hermitian SU(3)-structure, which we call {\em balanced} SU(2)-{\em structures}. We provide conditions which imply that such a 5-manifold can be isometrically embedded as a hypersurface in a manifold with a balanced SU(3)-st…
The study identifies assets with local balance deviating from global balance to mitigate financial risk.
problem Selecting outperforming assets during financial crises.
method Investigates deviations of local balance from global balance as a criterion for asset selection.
result Assets with local balance deviating from global balance can mitigate financial risk.
Proposes φ-balancing for more balanced expert utilization in MoE models.
problem Balanced expert utilization in MoE models to avoid bias.
method Directly targets population-level balance by minimizing a convex potential function.
result Consistently outperforms prior methods in stability and effectiveness.
Estimates causal effects using neural networks for balancing covariates.
problem Estimating causal effects from observational data.
method Neural Balancing Weights (NBW) using α-divergence for density ratio estimation. result Generalized approach for balancing multidimensional data.
Blowing up flat metrics yields balanced ones with constant curvature.
problem Constructing balanced metrics with constant curvature on orbifolds.
method Blowing up a compact orbifold with balanced Chern-Ricci flat metrics.
result Blown-up orbifolds admit balanced metrics with constant Chern scalar curvature.
We will consider locally conformally balanced manifolds. We prove that a locally conformally balanced condition is not stable under a small deformation. We prove that locally conformally balanced condition is stable under any proper modification. We prove that symmetric products of the Kodaira surface can be resolve to…
In this paper, the concept of balanced manifolds is generalized to reduced complex spaces: the class B and balanced spaces. Compared with the case of Kahlerian, the class B is similar to the Fujiki class C and the balanced space is similar to the Kahler space. Some properties about these complex spaces are obtained, an…
Study balanced Hermitian structures on almost abelian Lie algebras, classifying six-dimensional cases.
problem Classify balanced Hermitian structures on almost abelian Lie algebras.
method Classify six-dimensional almost abelian Lie algebras with balanced structures, investigate flow of balanced metrics and anomaly flow.
result Prove conjecture for compact almost abelian solvmanifolds with left-invariant complex structures.
CT compares two distributions using Bayes' theorem and chain rule.
problem Measuring the difference between two probability distributions.
method Conditional transport (CT) using chain rule and Bayes' theorem.
result CT strikes a good balance between mode-covering and mode-seeking behaviors.
Study examines how balancing methods affect model behavior in imbalanced classification problems.
problem Impact of balancing methods on model behavior in imbalanced classification problems.
method Used Explainable Artificial Intelligence tools (variable importance method, partial dependence profile, accumulated local effects) to compare model behavior before and after balancing.
result Significant changes in model behavior due to balancing methods, leading to biased models.
Determined the balanced cone of a specific geometric space.
problem Determining the balanced cone of the small resolution of the quintic conifold.
method Intersection number method to explicitly determine the cone.
result Explicitly determined the balanced cone of the small resolution of the quintic conifold.
The paper argues for using Neyman orthogonal score for balancing in debiased machine learning.
problem Debiased machine learning requires a proper approach to balance covariates.
method The paper advocates for using Riesz regression with basis functions of X for balancing.
result Covariate balancing is only valid when the score-relevant regression error is a function of covariates alone.
Paper proves Chow stability implies balanced embedding.
problem Chow stability and balanced embeddings in projective varieties.
method Continuity method conditional on technical hypothesis.
result Chow stability implies balanced embedding.
Study on balanced Hermitian threefolds with parallel Bismut torsion.
problem Characterizing compact, balanced BTP threefolds.
method Detailed description of all compact, balanced BTP threefolds.
result Characterization of all compact, balanced BTP threefolds.
Improves causal inference with observational data by balancing features and weights.
problem Achieving balance in predictive features for causal inference with observational data.
method Integrates balancing weights into representation learning for causal learning.
result Developed an algorithm for accurate estimation of causal effects.
Paper proves non-existence of certain balanced metrics on six-manifolds.
problem Existence of balanced metrics on six-manifolds with specific properties.
method Analysis of cohomogeneity one actions and properties of balanced structures.
result Non-existence of balanced non-Kähler SU(3)-structures on six-manifolds.
Positive factorization found for a specific map on surfaces.
problem Balanced superelliptic rotation on surfaces.
method Positive factorization approach.
result Positive factorization for balanced superelliptic rotation.