Related papers: Unified Approach to Crossover Phenomena
In this paper, we investigate the identifiability of average controlled direct effects and average natural direct effects in causal systems represented by summary causal graphs, which are abstractions of full causal graphs, often used in…
We present an asymptotic evaluation unitary formula for large argument values existing for defined class of functions. The asymptotic evaluation is obtained using only power series expansion coefficients of a function, what is a new result…
Uniform asymptotic expansions are derived for the zeros of the reverse generalized Bessel polynomials of large degree $n$ and real parameter $a$. It is assumed that $-\Delta_{1} n+\frac{3}{2} \leq a \leq \Delta_{2} n$ for fixed arbitrary…
In recent years, the asymptotic normality of some famous combinatorial sequences has been the subject of extensive study. However, the methods used to prove the asymptotic normality of various combinatorial sequences differ significantly.…
Cross-validation is a popular non-parametric method for evaluating the accuracy of a predictive rule. The usefulness of cross-validation depends on the task we want to employ it for. In this note, I discuss a simple non-parametric setting,…
We develop a unified framework for a broad class of nonlocal elliptic problems, encompassing a wide spectrum of nonlocal terms, including the classical Kirchhoff and Carrier-type equations as particular cases, and nonlinearities having…
The universal typical-signal estimators of entropy and cross entropy based on the asymptotics of recurrence and waiting times play an important role in information theory. Building on their construction, we introduce and study universal…
Real physical systems are only understood, experimentally or theoretically, to a finite resolution so in their analysis there is generally an ignorance of possible short-range phenomena. It is also well-known that the boundary conditions of…
The asymptotics of a singularly perturbed problem is constructed. describing the transport of a polydisperse impurity in the atmosphere, taking into account the processes of precipitation and wind pick-up, as well as the processes of…
Randomized clinical trials are the gold standard when estimating the average treatment effect. However, they are usually not a random sample from the real-world population because of the inclusion/exclusion rules. Meanwhile, observational…
The core challenge in unsupervised anomaly detection is identifying abnormal patterns without prior knowledge of their characteristics. While existing methods have addressed aspects of this problem, they often struggle to learn a robust…
Bifurcation analysis collects techniques for characterizing the dependence of certain classes of solutions of a dynamical system on variations in problem parameters. Common solution classes of interest include equilibria and periodic…
We enumerate the connected graphs that contain a linear number of edges with respect to the number of vertices. So far, only the first term of the asymptotics was known. Using analytic combinatorics, i.e. generating function manipulations,…
Form a pure mathematical point of view, common functional forms representing different physical phenomena can be defined. For example, rates of chemical reactions, diffusion and heat transfer are all governed by exponential-type…
Despite a growing literature on explaining neural networks, no consensus has been reached on how to explain a neural network decision or how to evaluate an explanation. Our contributions in this paper are twofold. First, we investigate…
Higher criticism is a large-scale testing procedure that can attain the optimal detection boundary for sparse and faint signals. However, there has been a lack of knowledge in most existing works about its asymptotic distribution for more…
Intersection types have been originally developed as an extension of simple types, but they can also be used for refining simple types. In this survey we concentrate on the latter option; more precisely, on the use of intersection types for…
Unsupervised anomaly detection of multivariate time series is a challenging task, given the requirements of deriving a compact detection criterion without accessing the anomaly points. The existing methods are mainly based on reconstruction…
Complicated physical problems usually are solved by resorting to perturbation theory leading to solutions in the form of asymptotic series in powers of small parameters. However, finite, and even large values of the parameters often are of…
We analyze the conditions on the Taylor coefficients of an analytic function to admit global analytic continuation, complementing a recent paper of Breuer and Simon on general conditions for natural boundaries to form. A new summation…