Related papers: Partial Derivatives on Causal Sets
The Adomian decomposition method is a semi-analytical method for solving ordinary and partial nonlinear differential equations. The aim of this paper is to apply Adomian decomposition method to obtain approximate solutions of nonlinear…
When considering fractional diffusion equation as model equation in analyzing anomalous diffusion processes, some important parameters in the model related to orders of the fractional derivatives, are often unknown and difficult to be…
Inversive meadows are commutative rings with a multiplicative identity element and a total multiplicative inverse operation whose value at 0 is 0. Divisive meadows are inversive meadows with the multiplicative inverse operation replaced by…
The theory of matrix splitting is a useful tool for finding solution of rectangular linear system of equations, iteratively. The purpose of this paper is two-fold. Firstly, we revisit theory of weak regular splittings for rectangular…
Statistical methods for causal inference with continuous treatments mainly focus on estimating the mean potential outcome function, commonly known as the dose-response curve. However, it is often not the dose-response curve but its…
The application of the approximation-operational approach to solving linear differential equations of fractional order with variable coefficients is considered. It is shown that the method can also be applied to solving differential…
This paper addresses the problem of measurement errors in causal inference and highlights several algebraic and graphical methods for eliminating systematic bias induced by such errors. In particulars, the paper discusses the control of…
The objective of this contribution is to compare two methods proposed recently in order to build efficient reduced-order models for geometrically nonlinear structures. The first method relies on the normal form theory that allows one to…
We introduce and extend the outer product and contractive product of tensors and matrices, and present some identities in terms of these products. We offer tensor expressions of derivatives of tensors, focus on the tensor forms of…
This paper explores the use of unstructured, multimodal data, namely text and images, in causal inference and treatment effect estimation. We propose a neural network architecture that is adapted to the double machine learning (DML)…
The predominant method for evaluating the quality of causal models is to measure the graphical accuracy of the learned model structure. We present an alternative method for evaluating causal models that directly measures the accuracy of…
We present a non-parametric method to estimate the discount curve from market quotes based on the Moore-Penrose pseudoinverse. The discount curve reproduces the market quotes perfectly, has maximal smoothness, and is given in closed-form.…
This Element offers a practical guide to estimating conditional marginal effects-how treatment effects vary with a moderating variable-using modern statistical methods. Commonly used approaches, such as linear interaction models, often…
A new method for approximating fractional derivatives of the Gaussian function and Dawson's integral are presented. Unlike previous approaches, which are dominantly based on some discretization of Riemann-Liouville integral using polynomial…
We study inertial versions of primal-dual proximal splitting, also known as the Chambolle--Pock method. Our starting point is the preconditioned proximal point formulation of this method. By adding correctors corresponding to the…
This paper is concerned with the estimation of the partial derivatives of a probability density function of directional data on the $d$-dimensional torus within the local thresholding framework. The estimators here introduced are built by…
A causal set is a partially ordered set on a countably infinite ground-set such that each element is above finitely many others. A natural extension of a causal set is an enumeration of its elements which respects the order. We bring…
The accurate numerical solution of partial differential equations is a central task in numerical analysis allowing to model a wide range of natural phenomena by employing specialized solvers depending on the scenario of application. Here,…
The main objective of this article is to study several generalizations of the reverse order law for the Moore-Penrose inverse in ring with involution.
In this brief note we critically examine the process of partial and of total differentiation, showing some of the problems that arise when we relate both concepts. A way to solve all the problems is proposed.