Explicit computation of Kontsevich weights for symplectic Poisson structures.
problem Computing weights of Kontsevich graphs in symplectic Poisson structures.
method Detailed explicit computation using hypergeometric functions and simpler formulas.
result Explicit expressions for curvature weights and their simplification in cotangent bundles.
Formula found for neural network error with fixed weights.
problem Understanding error in neural networks with fixed weights.
method Provided an explicit formula for approximation error.
result Explicit formula for neural network error with fixed weights.
Explicitly constructs moduli spaces of stable parabolic bundles.
problem Understanding moduli spaces of stable parabolic bundles over the Riemann sphere.
method Explicit construction and quotient of stable parabolic structures by bundle automorphisms.
result Explicit models of moduli spaces as smooth, compact complex manifolds.
Enhances mixture models with classifier-defined weights.
problem Density evaluation and sampling in mixture models.
method Introduces Classifier Weighted Mixtures (CWM) with functional weights.
result Improves expressivity in variational estimation without increasing complexity.
New method for training deep neural networks with regularization, converging to better generalization.
problem Improving generalization of deep neural networks through explicit regularization.
method Regularizer Mirror Descent (RMD) method, inspired by convergence properties of stochastic mirror descent (SMD).
result RMD converges to a point close to the minimizer of the cost function, leading to better generalization performance.
Adaptive learning of sample weights for better model performance.
problem Overfitting to biased training data with corrupted labels or class imbalance.
method Adaptive learning of an explicit weighting function using a meta-weight-net.
result Improves model accuracy in class imbalance and noisy label cases.
We construct new explicit toric scalar-flat K{ä}hler ALE metrics on weighted projective spaces of non-compact type, which we use to obtain smooth extremal K{ä}hler metrics on appropriate resolutions of orbifolds. In particular, we obtain new extremal metrics certain resolutions of weighted projective spaces of compact …
No regularization needed for InLDL, achieving efficient and effective model.
problem InLDL struggles with performance degradation due to missing degrees.
method Proposes a model that uses label distribution as a prior, implicitly regularizing the learning process.
result Achieves competitive performance without explicit regularization.
Develops a new method for benchmark portfolios and market outperformance strategies.
problem Creating effective benchmark portfolios for market outperformance.
method Explicit formulaic algorithm and multifactor risk model tailored for long-only portfolios.
result Explicit positive weights for benchmarks without principal components or iterations.
Deep equilibrium models converge globally without explicit computation.
problem Global convergence of deep learning models with implicit layers.
method Analysis of gradient dynamics and proof of convergence rate.
result Deep equilibrium models converge to global optimum at a linear rate.
We extend the Bismut-Elworthy-Li formula to non-degenerate jump diffusions and "payoff" functions depending on the process at multiple future times. In the spirit of Fournie et al [13] and Davis and Johansson [9] this can improve Monte Carlo numerics for stochastic volatility models with jumps. To this end one needs so…
Researchers extend asymptotic analysis to Bergman projections with Gevrey weights.
problem Analyzing Bergman projections with Gevrey weights.
method Extending direct approach to semiclassical asymptotics to Gevrey weights using Fourier integral operators.
result Gevrey symbol amplitude of asymptotic Bergman projection with Gevrey weights and Gevrey-type growth rate.
Study of g-vector cones in cluster algebras from weighted orbifolds.
problem Determine the closure of g-vector cones in cluster algebras. method Analyzing g-vector cones in a cluster algebra defined from a weighted orbifold. result Closure of the union of g-vector cones is Rn except for specific weighted orbifolds. We give an explicit algorithm and source code for combining alpha streams via bounded regression. In practical applications typically there is insufficient history to compute a sample covariance matrix (SCM) for a large number of alphas. To compute alpha allocation weights, one then resorts to (weighted) regression ove…
Counting HCMU sphere components using weighted trees.
problem Counting components of moduli space of HCMU spheres.
method Using weighted plane trees to characterize HCMU spheres with a single integral conical angle, and an explicit counting formula is derived.
result An explicit counting formula for the components of the moduli space of HCMU spheres.
We show that the generalized Kähler-Ricci soliton equation on 4-dimensional toric Kähler orbifolds reduces to ODEs assuming there is a Hamiltonian 2-form. This leads to an explicit resolution of this equation on labeled triangles and convex labeled quadrilaterals. In particular, we give the explicit expression of the K…
The paper calculates sensitivities for financial derivatives using path weighting methods.
problem Computing sensitivities for path-dependent financial derivatives with high variance and degeneracy issues.
method Proposes explicit path weighting formula, variance reduction adjustment, and covariance inflation technique.
result Effective methods to address high variance and degeneracy in sensitivities computation.
Research disproves the extension of a weight system to a 4-invariant for graphs.
problem Whether the sl(2)-weight system extends to a unique 4-invariant of graphs.
method Analyzing the sl(2)-weight system and constructing recurrence relations for extensions.
result The sl(2)-weight system does not extend to a 4-invariant for graphs in full generality.
Paper offers a new approach to locally weighted regression and classification.
problem Optimal number of neighbors and weights in k-nearest neighbors.
method Locally weighted regression with explicit bias-variance tradeoff.
result Efficiently finds optimal weights and number of neighbors for each data point.
Pruned neural networks learn digital circuits with 99% weight reduction.
problem Efficiently train deep neural networks with minimal weights.
method Constrained binarized networks to zero or one weights.
result Pruned networks achieve similar performance to standard networks with 99% weight reduction.
A new method estimates uncertainty without explicit prediction models.
problem Costly data acquisition in machine learning.
method Distance-weighted Class Impurity method for uncertainty estimation.
result Distance-weighted Class Impurity effectively estimates uncertainty without prediction models.
We propose an explicit recursive method to approximate a power-law with a finite sum of weighted exponentials. Applications to moving averages with long memory are discussed in relationship with stochastic volatility models.
The paper derives a formula for Chow weights of toric blow-ups.
problem Chow weights of toric blow-ups.
method Combinatorial formula derived from toric manifold and Delzant polytope.
result Explicit formula for Chow weights of blow-ups.
This paper provides an explicit form for symmetric differentials and their corresponding holomorphic functions.
problem Understanding the correspondence between symmetric differentials and L2 holomorphic functions on quotient spaces. method Explicit description of the correspondence between symmetric differentials and weighted L2-holomorphic functions. result Derivation of several applications based on the explicit form of the correspondence.
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.
New method finds minimal neural networks without weights.
problem Importance of weight parameters in neural networks.
method Search for minimal neural network architectures without explicit weight training.
result Minimal neural networks can perform tasks without weight training.
The paper proves lower bounds for Gaussian-weighted curvature integrals of self-shrinkers.
problem Proving lower bounds for Gaussian-weighted \(L^2\)-curvature integrals of self-shrinkers.
method Combining normal coordinate functions with weighted Poincaré inequalities and first-eigenvalue estimates.
result Explicit lower bounds in terms of entropy for closed self-shrinkers, leading to curvature gaps.
Proposes a new K-means method for efficient clustering of nonlinear data.
problem Challenges of kernel K-means, including high memory usage and computational inefficiency.
method Combines linear and nonlinear approaches using explicit feature maps based on spectral analysis.
result Demonstrates Explicit Kernel Minkowski Weighted K-means (Explicit KMWK-means) reduces memory usage and improves efficiency.
Paper introduces a new test for conditional independence using weighted partial copulas.
problem Testing conditional independence between variables.
method The approach uses a weighted partial copula function and a bootstrap procedure to compute regions of rejection.
result The proposed test has competitive power compared to existing methods.
Exact method found for estimating ILP weights from data.
problem Estimating objective-function parameters for integer linear programs.
method Projected subgradient descent applied to suboptimality loss.
result Explicit iteration complexity as a function of problem size.
The Cartan-Hartogs domains are defined as a class of Hartogs type domains over irreducible bounded symmetric domains. The purpose of this paper is twofold. Firstly, for a Cartan-Hartogs domain ΩBd0(μ) endowed with the canonical metric g(μ), we obtain an explicit formula for the Bergman kernel of the weighted…
TQFT used to study symplectic group modules.
problem Calculating dimensions and characters of specific modules.
method Applied Topological Quantum Field Theory (TQFT).
result Explicit formulae for dimensions and characters.
Optimizes option portfolios for skewed-t returns using VaR and variance measures.
problem Optimizing portfolios for skewed-t returns with heavy tails and skewness.
method Uses variance and VaR measures, departing from normal returns, and provides explicit portfolio weights.
result Optimal portfolio weights differ significantly from variance optimal weights due to skewness.
Echo state networks with random weights can approximate any continuous system.
problem Approximating continuous dynamical systems using echo state networks.
method Randomly generated internal weights and a sampling procedure for activation functions.
result Echo state networks with random weights can approximate any continuous casual time-invariant operators with high probability.
Deep ReLU networks can be simplified to a three-layer model.
problem Understanding the behavior of deep neural networks.
method Constructive proof and algorithm to transform deep networks into shallow ones.
result Deep ReLU networks can be represented by a simpler three-layer structure.
Sharp inequalities for weighted log canonical thresholds derived.
problem Understanding weighted log canonical thresholds in complex analysis.
method Combining integrability estimates, complex line restrictions, and pluripotential theory.
result Uniform control of difference quotients and explicit lower bounds derived.
Study of n-ary differential operators on weighted densities with canonical symbol and quantization maps.
problem Analysis of n-ary differential operators acting on weighted densities. method Existence and uniqueness of conformally equivariant symbol maps and quantization maps.
result Existence and explicit expression of conformally equivariant symbol and quantization maps.
Improved generalization bounds for multi-class CNNs without explicit class dependence.
problem Generalization error bounds for deep learning with multi-class CNNs.
method Adapted Rademacher analysis to incorporate weight sharing, reducing dependence on the number of classes.
result Bounds have no explicit dependence on the number of classes, scaling with the norm of weight matrices.
The paper proves instability of translating λ-solitons and provides bounds on their length.
problem Stability of translating λ-solitons in cylindrical geometry.
method Analytical proof of instability and explicit length bounds.
result Explicit bounds on the length of unstable translating λ-solitons.
Random variables of the generalized Pareto distribution, can be transformed to that of the Pareto distribution. Explicit expressions exist for the maximum likelihood estimators of the parameters of the Pareto distribution. The performance of the estimation of the shape parameter of generalized Pareto distributed using …
Study on tropical moduli spaces of weighted stable curves, proving homotopy and connectivity properties.
problem Understanding the topology of weighted stable curves and their moduli spaces.
method Identification of moduli space with dual complex, homotopy proofs, Betti number calculations, and structural results.
result Explicit formulas for Betti numbers and structural relations between genus 0 and 1 spaces.
The paper explores weight systems and their applications to graph and embedded graph invariants.
problem Developing weight systems for graphs and embedded graphs.
method Construction of weight systems from graph invariants and metrized Lie algebras, and extending to arbitrary embedded graphs.
result Explicit forms of generating functions and recurrence relations for weight systems on chord diagrams and embedded graphs.
We expand volatility models for rough stochastic volatility.
problem Modeling rough stochastic volatility.
method Vol-of-vol expansion for potentially infinite dimensional models.
result Explicit representations of push-down Malliavin weights.
New invariants for RNA foldings and stuck links defined.
problem Defining invariants for RNA foldings and stuck links.
method Assigning Boltzmann weights at classical and stuck crossings.
result Explicit computations of new invariants provided.
Hypertoric varieties are hyperkähler analogues of toric varieties, and are constructed as abelian hyperkähler quotients of a quaternionic affine space. Just as symplectic toric orbifolds are determined by labelled polytopes, orbifold hypertoric varieties are intimately related to the combinatorics of hyperplane arrange…
Paper presents a method to summarize HMC samples for neural networks, providing meaningful uncertainty estimates.
problem Lack of interpretable summary statistics for HMC samples in neural networks due to permutation symmetry.
method Introducing a transpositions metric to quantify permutations and using rebasin method to summarize HMC samples.
result Compact representation of HMC samples provides meaningful uncertainty estimates for each weight in a neural network.
The paper studies the curvature behavior near the boundary of certain domains.
problem Investigating the asymptotic behavior of bisectional curvature for weighted Bergman metrics.
method Characterizing extremal functions via L2-orthogonal projections and using the squeezing function. result The bisectional curvature at strongly pseudoconvex boundary points asymptotically matches that of the unit ball.
We identify the difference between the CM polarisation and the Chow polarisation on the ``Hilbert scheme''. As a consequence, we give a numerical criterion for the CM stability as in Mumfords' G.I.T.. Also, we write down an explicit formula for the generalised futaki invariant interms of weights and multiplicities of t…