Related papers: \delta-expansion and self-consistent calculation
Sensitivity analysis informs causal inference by assessing the sensitivity of conclusions to departures from assumptions. The consistency assumption states that there are no hidden versions of treatment and that the outcome arising…
In mathematical logic there are two seemingly distinct kinds of principles called "reflection principles." Semantic reflection principles assert that if a formula holds in the whole universe, then it holds in a set-sized model. Syntactic…
In this work we consider a possibility to use the conception of $(\delta, L)$-model of a function for optimization tasks, whereby solving a primal problem there is a necessity to recover a solution of a dual problem. The conception of…
The parametric complexity is the key quantity in the minimum description length (MDL) approach to statistical model selection. Rissanen and others have shown that the parametric complexity of a statistical model approaches a simple function…
This paper extends the literature on the strict-tolerant logical approach by applying its methods to intuitionistic and minimal logic. In short, the strict-tolerant approach modifies the usual notion of logical consequence by stipulating…
We introduce and discuss the method of Linear Delta Expansion for the calculation of effective potentials in superspace, by adopting the improved version of the super-Feynman rules. Calculations are carried out up to two-loops and an…
For many nonlinear physical systems, approximate solutions are pursued by conventional perturbation theory in powers of the non-linear terms. Unfortunately, this often produces divergent asymptotic series, collectively dismissed by Abel as…
We study an expansion method for high-dimensional parabolic PDEs which constructs accurate approximate solutions by decomposition into solutions to lower-dimensional PDEs, and which is particularly effective if there are a low number of…
Describing complex phenomena by means of cellular automata (CA) has shown to be a very effective approach in pure and applied sciences. In fact, the number of published papers concerning this topic has tremendously increased over the last…
We show that high-accuracy guarantees for log-concave sampling -- that is, iteration and query complexities which scale as $\mathrm{poly}\log(1/\delta)$, where $\delta$ is the desired target accuracy -- are achievable using stochastic…
We develop new sub-optimality bounds for gradient descent (GD) that depend on the conditioning of the objective along the path of optimization rather than on global, worst-case constants. Key to our proofs is directional smoothness, a…
In this note we give a short and self-contained proof that, for any $\delta > 0$, $\sum_{x \leq n \leq x+x^\delta} \lambda(n) = o(x^\delta)$ for almost all $x \in [X, 2X]$. We also sketch a proof of a generalization of such a result to…
We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…
We derive the first exact, rigorous but practical, globally valid remainder terms for asymptotic expansions about saddles and contour endpoints of arbitrary order degeneracy derived from the method of steepest descents. The exact remainder…
We continue the study of properties related to monotone countable paracompactness, investigating various monotone versions of $\delta$-normality. We factorize monotone normality and stratifiability in terms of these weaker properties.
This paper studies the regularity of the minimum time function, $T(\cdot)$, for a control system with a general closed target, taking the state equation in the form of a differential inclusion. Our first result is a sensitivity relation…
We study lower and upper bounds for the density of a diffusion process in ${\mathbb{R}}^n$ in a small (but not asymptotic) time, say $\delta$. We assume that the diffusion coefficients $\sigma_1,\ldots,\sigma_d$ may degenerate at the…
Building on insights of Jovanovic (1982) and subsequent authors, we develop a comprehensive theory of optimal timing of decisions based around continuation value functions and operators that act on them. Optimality results are provided…
The results of training a neural network are heavily dependent on the architecture chosen; and even a modification of only its size, however small, typically involves restarting the training process. In contrast to this, we begin training…
We prove a strong approximation result for the empirical process associated to a stationary sequence of real-valued random variables, under dependence conditions involving only indicators of half lines. This strong approximation result also…