相关论文: Higher-Order Neyman Orthogonality in Moment-Condit…
Many developmental processes in biology utilize Notch-Delta signaling to construct an ordered pattern of cellular differentiation. This signaling modality is based on nearest-neighbor contact, as opposed to the more familiar mechanism…
We consider a simple model of higher order, functional computation over the booleans. Then, we enrich the model in order to encompass non-termination and unrecoverable errors, taken separately or jointly. We show that the models so defined…
Higher order moment estimates for solutions to nonlinear SPDEs governed by locally-monotone operators are obtained under appropriate coercivity condition. These are then used to extend known existence and uniqueness results for nonlinear…
We study oracle complexity of gradient based methods for stochastic approximation problems. Though in many settings optimal algorithms and tight lower bounds are known for such problems, these optimal algorithms do not achieve the best…
The Hermite-Taylor method evolves all the variables and their derivatives through order $m$ in time to achieve a $2m+1$ order rate of convergence. The data required at each node of the staggered Cartesian meshes used by this method makes…
In this paper, we introduce a higher-order multiscale method for time-dependent problems with highly oscillatory coefficients. Building on the localized orthogonal decomposition (LOD) framework, we construct enriched correction operators to…
We study the effect of curvature on the Parabolic Anderson model by posing it over a Cartan-Hadamard manifold. We first construct a family of noises white in time and colored in space parameterized by a regularity parameter $\alpha$, which…
In this article we study a class of parameters with the so-called `mixed bias property'. For parameters with this property, the bias of the semiparametric efficient one step estimator is equal to the mean of the product of the estimation…
A model of phase transitions with coupling between the order parameter and its gradient is proposed. It is shown, that this nonlinear model is suitable for the description of phase transitions accompanied by the formation of spatially…
The unrivaled robustness of topologically ordered states of matter against perturbations has immediate applications in quantum computing and quantum metrology, yet their very existence poses a challenge to our understanding of phase…
The study of first-order optimization is sensitive to the assumptions made on the objective functions. These assumptions induce complexity classes which play a key role in worst-case analysis, including the fundamental concept of algorithm…
Higher order conformal perturbation theory is studied for theories with and without boundaries. We identify systematically the universal quantities in the beta function equations, and we give explicit formulae for the universal coefficients…
We extend the close interplay between continued fractions, orthogonal polynomials, and Gaussian quadrature rules to several variables in a special but natural setting which we characterize in terms of moment sequences. The crucial condition…
We calculate reduced moments $\overline \xi_q$ of the matter density fluctuations, up to order $q=5$, from counts in cells produced by Particle--Mesh numerical simulations with scale--free Gaussian initial conditions. We use power--law…
Features in machine learning problems are often time-varying and may be related to outputs in an algebraic or dynamical manner. The dynamic nature of these machine learning problems renders current higher order accelerated gradient descent…
Statistical inference in the presence of nuisance functionals with complex survey data is an important topic in social and economic studies. The Gini index, Lorenz curves and quantile shares are among the commonly encountered examples. The…
Arising in semi-parametric statistics, control applications, and as sub-problems in global optimization methods, certain optimization problems can have objective functions requiring numerical integration to evaluate, yet gradient function…
Functional factor analysis is an important dimension reduction method for functional and longitudinal data. Factor loadings give insight into patterns of variability of the observations, while latent factors provide a low-dimensional…
A topology optimization problem in a phase field setting is considered to obtain rigid structures, which are resilient to external forces and constructable with additive manufacturing. Hence, large deformations of overhangs due to gravity…
In this paper, we focus on model reduction of biomolecular systems with multiple time-scales, modeled using the Linear Noise Approximation. Considering systems where the Linear Noise Approximation can be written in singular perturbation…