Related papers: $\epsilon'/\epsilon$: three years later
In this paper we show that the lengths of the approximating processes in epsilon substitution method are calculable by ordinal recursions in an optimal way.
We consider the classical sequential binary hypothesis testing problem in which there are two hypotheses governed respectively by distributions $P_0$ and $P_1$ and we would like to decide which hypothesis is true using a sequential test. It…
The predicate complementary to the well-known Godel's provability predicate is defined. From its recursiveness new consequences concerning the incompleteness argumentation are drawn and extended to new results of consistency, completeness…
A simple procedure to estimate O(alpha_s^3) and O(alpha_s^4) corrections to mass-dependent observables is conjectured. The method is tested in a number of cases where the O(alpha_s^3) contribution is exactly known, and reasonable agreement…
As a baseball game progresses, batters appear to perform better the more times they face a particular pitcher. The apparent drop-off in pitcher performance from one time through the order to the next, known as the Time Through the Order…
Iterative numerical algorithms are typically equipped with a stopping criterion, where the iteration process is terminated when some error or misfit measure is deemed to be below a given tolerance. This is a useful setting for comparing…
Bayesian, classical, and extended maximum likelihood approaches to estimation of upper limits in experiments with small numbers of signal events are surveyed. The discussion covers only experiments whose outcomes are well described by a…
The distance between the true and numerical solutions in some metric is considered as the discretization error magnitude. If error magnitude ranging is known, the triangle inequality enables the estimation of the vicinity of the approximate…
I discuss recent developments in the determination of parton distributions from global fits. I concentrate on the errors associated with these parton distributions and with the physical quantities which are determined in terms of them. I…
We correct erroneous conclusions from Ref.[1] regarding the values of various critical exponents, calculated to the two-loop order, and argue that $\epsilon$-expansion near two spatial dimension, with $\epsilon=d-2$ may not be reliable to…
The convergence of the Q expansion in the ^3S_1-^3D_1 mixing angle is investigated through the renormalization condition used to fit the free paramteter encountered at NNLO. Although the NNLO calculation describes the data well at momenta…
Original paper: We revisit the probability that any two consecutive events in a Poisson process N on [0,t] are separated by a time interval which is greater than s(<t) (a particular scan statistic probability), and the closely related…
The production of the three jets in hadron-hardon collision is the first more complex process which allow us to define a branch of variables in order to do more precise measurement of the strong coupling and the parton distribution function…
The triton point charge radius is calculated to next-to-next-to-leading order (NNLO) in pionless effective field theory ($\mathrm{EFT}(\not{\!\pi})$), yielding a prediction of $1.14\pm0.19$ fm (leading order), $1.59\pm0.08$ fm (next-to…
Performance of text classification models tends to drop over time due to changes in data, which limits the lifetime of a pretrained model. Therefore an ability to predict a model's ability to persist over time can help design models that…
In the field of large language model (LLM)-based proof generation, despite extensive training on large datasets such as ArXiv, LLMs still exhibit only modest performance on proving tasks of moderate difficulty. We believe that this is…
We use machine learning to provide a tractable measure of the amount of predictable variation in the data that a theory captures, which we call its "completeness." We apply this measure to three problems: assigning certain equivalents to…
The advance of the pericenter of the orbit of a test body around a massive body in general relativity can be calculated in a number of ways. In one method, one studies the geodesic equation in the exact Schwarzschild geometry and finds the…
Large Language Models (LLMs) that can express interpretable and calibrated uncertainty are crucial in high-stakes domains. While methods to compute uncertainty post-hoc exist, they are often sampling-based and therefore computationally…
The past century has seen a steady increase in the need of estimating and predicting complex systems and making (possibly critical) decisions with limited information. Although computers have made possible the numerical evaluation of…