Proves positive mass theorem for non-spin weighted manifolds.
problem Proving the positive mass theorem for non-spin weighted manifolds.
method Establishing density theorem and generalizing Geroch conjecture.
result Proves positive weighted mass theorem for non-spin weighted manifolds.
Paper extends positive energy theorem to anti-de Sitter spacetimes.
problem Proving positive energy theorem for weighted anti-de Sitter spacetimes.
method Generalized positive energy theorem for 3D anti-de Sitter initial data sets.
result Positive energy theorem proved for weighted anti-de Sitter spacetimes.
In this paper, we give a new generalization of positive sectional curvature called positive weighted sectional curvature. It depends on a choice of Riemannian metric and a smooth vector field. We give several simple examples of Riemannian metrics which do not have positive sectional curvature but support a vector field…
Unified positive mass theorem and Dirac operator study on weighted manifolds.
problem Establishing a unified positive mass theorem for weighted manifolds and smooth metric measure spaces.
method Analyzing Dirac operators on warped product manifolds and applying results to the positive mass theorem.
result Equivalence of weighted positive mass theorem to usual positive mass theorem.
Positive weights improve kernel quadrature's accuracy.
problem Improving kernel quadrature weights to be positive and stable.
method Using convex geometry to approximate the kernel mean embedding with positive weights.
result Positive weights lead to improved kernel quadrature bounds with Monte-Carlo-beating rates.
The paper studies Finsler manifolds with a new curvature concept.
problem Understanding Finsler manifolds with positive weighted flag curvature.
method Introducing a new curvature concept based on the flag curvature and a non-Riemannian quantity, T-curvature.
result Positive weighted flag curvature implies the manifold is diffeomorphic to Euclidean space.
Paper solves CR positive mass and Yamabe problems on weighted spaces.
problem CR positive mass and Yamabe problems on weighted spaces.
method Analyzes sub-Laplacian on Folland-Stein spaces.
result CR positive mass and Yamabe problems resolved.
Study preserves metrics with positive Bakry-Émry Ricci curvature via surgery.
problem Preserving metrics with positive Bakry-Émry Ricci curvature after surgery.
method Established theorems for connected sums and surgeries along higher-dimensional spheres.
result Local surgery results for positive Bakry-Émry Ricci curvature.
Study semilinear equations on weighted manifolds to prove rigidity.
problem Prove rigidity of weighted manifolds via classification of semilinear equations.
method Classify positive solutions at the Sobolev-critical exponent, proving rigidity and weight triviality.
result Existence of positive solutions implies rigidity and weight triviality under certain curvature conditions.
Extends double linear policy with time-varying weights and proves robust positive expectation.
problem Ensuring robustness in policy optimization with time-varying parameters.
method Employed a novel elementary symmetric polynomials characterization approach to prove robust positive expectation (RPE). Derived explicit expressions for expected cumulative gain-loss and variance.
result Proved the robust positive expectation property holds for the extended double linear policy.
We propose an iterative scheme for feature-based positioning using a new weighted dissimilarity measure with the goal of reducing the impact of large errors among the measured or modeled features. The weights are computed from the location-dependent standard deviations of the features and stored as part of the referenc…
Fundamental weight systems identified as quantum states.
problem Identifying which weight systems are quantum states.
method Analyzing the Cayley distance kernel on the symmetric group and its positivity.
result All fundamental gl(n)-weight systems are quantum states.
Estimates for harmonic functions in curved spaces.
problem Quantifying harmonic functions in curved spaces.
method Quantitative Sobolev estimates for p-harmonic functions in manifolds with curvature conditions. result Established a quantitative second order Sobolev estimate for p-harmonic functions. Paper proves optimal systolic inequality for manifolds with positive triRic curvature.
problem Optimal systolic inequality for manifolds with positive triRic curvature.
method Stable weighted k-slicing, volume comparison theorem, and metric deformation. result Proves an optimal systolic inequality and characterizes the equality case.
This paper tackles negative transfer in multi-task learning by introducing class-wise weights.
problem Negative transfer hampers function from achieving optimality in multi-task learning.
method Introduces class-wise weights to drive positive transfer and suppress negative transfer.
result Demonstrates improved performance in multi-task learning by reducing negative transfer.
The paper proves a Harnack inequality for heat equations on Finsler metric measure manifolds.
problem Proving a Harnack inequality for positive solutions to heat equations on Finsler metric measure manifolds.
method Volume comparison theorem, weighted Poincaré inequality, local uniform Sobolev inequality, mean value inequalities.
result Derives a Harnack inequality for positive solutions to heat equations.
We propose weighted inner product similarity (WIPS) for neural network-based graph embedding. In addition to the parameters of neural networks, we optimize the weights of the inner product by allowing positive and negative values. Despite its simplicity, WIPS can approximate arbitrary general similarities in…
We prove a maximum principle for mild solutions to stochastic evolution equations with (locally) Lipschitz coefficients and Wiener noise on weighted L2 spaces. As an application, we provide sufficient conditions for the positivity of forward rates in the Heath-Jarrow-Morton model, considering the associated Musiela …
It is well known that Expected Shortfall (also called Average Value-at-Risk) is a convex risk measure, i. e. Expected Shortfall of a convex linear combination of arbitrary risk positions is not greater than a convex linear combination with the same weights of Expected Shortfalls of the same risk positions. In this shor…
A new approach optimizes weights in DLP for better risk-adjusted performance.
problem Optimizing time-varying weights in Double Linear Policy (DLP) for better risk-adjusted performance.
method Stochastic Model Predictive Control (SMPC) framework to maximize risk-adjusted returns while enforcing constraints.
result Empirical results show improved risk-adjusted performance and drawdown control.
The study characterizes hypersurfaces in weighted cylinders and generalizes confinement properties.
problem Characterizing hypersurfaces in weighted Riemannian products.
method Analyzing parabolic hypersurfaces with boundary in weighted cylinders.
result Generalized confinement properties of hypersurfaces in weighted cylinders.
Study of metrics on positive-definite matrices from power potential, linking to power means.
problem Understanding metrics on positive-definite matrices derived from power potential.
method Explicit expressions for geodesics and distance function derived from Hessian of power potential.
result Geodesics and distance function converge to weighted matrix geometric mean as β tends to zero.
The paper studies heat kernels on weighted Riemannian manifolds with curvature bounds.
problem Estimating heat kernels on weighted Riemannian manifolds with lower Ricci curvature bounds.
method Establishing parabolic Harnack inequalities, proving Gaussian bounds for heat kernels, and constructing Li-Yau-type gradient estimates.
result Gaussian upper and lower bounds for the heat kernel, Liouville theorem, uniqueness property, and eigenvalue bounds.
New lower bounds of the first nonzero eigenvalue of the weighted p-Laplacian are established on compact smooth metric measure spaces with or without boundaries. Under the assumption of positive lower bound for the m-Bakry--Émery Ricci curvature, the Escober--Lichnerowicz--Reilly type estimates are proved; under the…
We introduce a principled method for the signed clustering problem, where the goal is to partition a graph whose edge weights take both positive and negative values, such that edges within the same cluster are mostly positive, while edges spanning across clusters are mostly negative. Our method relies on a graph-based …
The paper extends RDPG model to handle weighted graphs, enabling better analysis of network data.
problem Modeling networks with weighted edges to capture heterogeneous weight distributions.
method Proposes a nonparametric W-RDPG model with latent positions and moment-generating functions.
result Establishes statistical guarantees for estimating nodal latent positions and sampling graphs.
Let (MN,g,e−fdv) be a complete smooth metric measure space with ∞-Bakry-Émery Ricci tensor bounded from below. We derive elliptic gradient estimates for positive solutions of a weighted nonlinear parabolic equation \begin{align*} \displaystyle \Big(Δ_f - \frac{\partial}{\partial t}\Big) u(x,t) +q(x,t)u^α…
We prove structure theorems for complete manifolds satisfying both the Ricci curvature lower bound and the weighted Poincaré inequality. In the process, a sharp decay estimate for the minimal positive Green's function is obtained. This estimate only depends on the weight function of the Poincaré inequality, and yields …
Symmetry proven for positive solutions of a weighted p-Laplace operator inequality.
problem Proving symmetry of positive solutions to a specific type of inequality.
method Analyzing positive critical points of Caffarelli-Kohn-Nirenberg inequalities with a weighted p-Laplace operator.
result Complete classification and symmetry result for positive solutions in a range of parameters.
We prove that square integrable holomorphic functions (with respect to a plurisubharmonic weight) can be extended in a square integrable manner from certain singular hypersurfaces (which include uniformly flat, normal crossing divisors) to entire functions in affine space. This provides evidence for a conjecture regard…
We present a method of rank-optimal weighting which can be used to explore the best possible position of a subject in a ranking based on a composite indicator by means of a mathematical optimization problem. As an example, we explore the dataset of the OECD Better Life Index and compute for each country a weight vector…
Prove top wedge power of Ricci form has finite integral for Kähler manifolds with positive sectional curvature
problem Prove top wedge power of Ricci form has finite integral for Kähler manifolds with positive sectional curvature
method Use Bézout estimates and a Lipschitz weight with finite Monge-Ampère mass
result Prove top wedge power of Ricci form has finite integral for Kähler manifolds with positive sectional curvature
Proves non-positivity of Hirzebruch form on stable weights and connects to flat logarithmic connections.
problem Non-positivity of Hirzebruch form on stable weights
method Kempf--Ness and frame-potential inequality
result Zero locus of Hirzebruch form on stable weights corresponds to flat logarithmic connections
Uniformises Kähler surfaces with positive curvature to complex plane.
problem Uniformisation of complete Kähler surfaces with positive sectional curvature.
method New approach using uniformly Lipschitz plurisubharmonic weight functions and weighted holomorphic functions.
result Proves any complete non-compact Kähler surface with positive sectional curvature is biholomorphic to C^2.
Study improves Bayesian optimisation with ensemble transfer learning.
problem Improving sample efficiency in Bayesian optimisation of expensive functions.
method Empirical analysis of ensemble-based transfer learning methods and pipeline components.
result Two components (warm start initialisation and positive weight constraint) improve transfer learning Bayesian optimisation performance.
We introduce a new normalization technique that exhibits the fast convergence properties of batch normalization using a transformation of layer weights instead of layer outputs. The proposed technique keeps the contribution of positive and negative weights to the layer output balanced. We validate our method on a set o…
Smooth superspace with special weights has a Fubini-Study form.
problem Describing a new smooth superspace with a special structure.
method Construction of weighted projective superspace and description of its structure.
result Smooth superspace with weights +1,−1 has an analog of the Fubini-Study form. The paper validates Stokes' theorem for differential subcomplexes in positively graded Lie groups.
problem Validating Stokes' theorem for differential subcomplexes in positively graded Lie groups.
method Introducing geometric conditions and spectral complexes to recover Stokes' theorem on locally smooth intrinsic graphs.
result Stokes' theorem holds for Rumin complex and new spectral complexes on Carnot groups.
This paper addresses the problem of prediction with expert advice for outcomes in a geodesic space with non-positive curvature in the sense of Alexandrov. Via geometric considerations, and in particular the notion of barycenters, we extend to this setting the definition and analysis of the classical exponentially weigh…
The Penrose theorem and Hawking's topology theorem are extended to weighted spacetimes.
problem Extending Penrose's singularity theorem and Hawking's topology theorem to weighted spacetimes.
method Using weighted null energy condition and synthetic dimension to generalize the theorems.
result Generalized versions of the Penrose and Hawking theorems hold under a weighted null energy condition.
The paper extends spin geometry to weighted manifolds and defines a new mass for Ricci flow.
problem Generalizing spin geometry to weighted manifolds and defining a new mass.
method Investigates spectral properties of the weighted Dirac operator and defines a new mass.
result Defines a new mass for weighted asymptotically Euclidean manifolds and shows its monotonicity under Ricci flow.
We prove in this paper that the weighted volume of the set of integral transportation matrices between two integral histograms r and c of equal sum is a positive definite kernel of r and c when the set of considered weights forms a positive definite matrix. The computation of this quantity, despite being the subject of…
Defines diversification as a binary relationship between financial portfolios.
problem Defines diversification in a new binary relationship for financial portfolios.
method Proposes a new definition of diversification based on convex linear combinations and second order stochastic dominance.
result The proposed definition coincides with second order stochastic dominance.
The paper studies Harnack inequalities on Finsler metric measure spaces.
problem Analyzing Harnack inequalities on Finsler metric measure spaces.
method Using weighted Ricci curvature and distortion conditions, the authors derive an elliptic p-Harnack inequality.
result The paper establishes an elliptic p-Harnack inequality and derives Hölder continuity and gradient estimates for positive harmonic functions.
Positive representations of surface groups in PO(p,q) form connected components of character varieties.
problem Characterizing representations of surface groups in special orthogonal groups PO(p,q).
method Using Anosov representations and root versus weight collar lemmas.
result Connected components of character varieties are formed by Θ-positive Anosov representations. In this paper we study sectional curvature bounds for Riemannian manifolds with density from the perspective of a weighted torsion free connection introduced recently by the last two authors. We develop two new tools for studying weighted sectional curvature bounds: a new weighted Rauch comparison theorem and a modifie…
We show that the limiting unicolored sl(N) Khovanov-Rozansky chain complex of any infinite positive braid categorifies a highest-weight projector. This result extends an earlier result of Cautis categorifying highest-weight projectors using the limiting complex of infinite torus braids. Additionally, we sh…
This paper extends liquidity returns in geometric mean markets to time-varying weights.
problem Understanding returns and no-arbitrage prices in geometric mean markets with time-varying weights.
method Extending known results for constant-weight G3Ms to the general case of G3Ms with time-varying and potentially stochastic weights.
result LP shares can replicate the payoffs of financial derivatives and various trading strategies.