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The method of exhaustion is generalized to a simple formula that can be used to integrate functions under very general conditions, provided that the integral exists. Both a geometric proof (following the usual procedure for the method of…
Evaluation of counterfactual queries (e.g., "If A were true, would C have been true?") is important to fault diagnosis, planning, determination of liability, and policy analysis. We present a method of revaluating counterfactuals when the…
There is a useful counterpart of conformal prediction for e-values, called conformal e-prediction. Conformal prediction can serve as basis for testing the assumption of exchangeability, leading to conformal testing. Similarly, conformal…
To begin with, it is pointed out that the form of the quantum probabil- ity formula originates in the very initial state of the object system as seen when the state is expanded with the eigen-projectors of the measured ob- servable. Making…
Quantum backflow is usually understood as a quantum interference phenomenon where probability current of a quantum particle points in the opposite direction to particle's momentum. Here, we quantify the amount of quantum backflow for…
Inspired by the early Wittgenstein's concept of nonsense (meaning that which lies beyond the limits of language), we investigate two different types of nonsense: formal nonsense and pragmatic nonsense. The simpler notion of formal nonsense…
In reinforcement learning, we can learn a model of future observations and rewards, and use it to plan the agent's next actions. However, jointly modeling future observations can be computationally expensive or even intractable if the…
There is an error in the main result. We provide an easy generalization to the irreducibility criterion in the title.
We consider the quantified constraint satisfaction problem (QCSP) which is to decide, given a structure and a first-order sentence (not assumed here to be in prenex form) built from conjunction and quantification, whether or not the…
In this paper, besides a counterexample to Bloch's principle, normality criteria leading to counterexamples to the converse of Bloch's principle in several complex variables are proved. Some Picard-type theorems and their corresponding…
Formulae for the line-of-sight and transverse comoving distances, proper motion distance, angular diameter distance, luminosity distance, k-correction, distance modulus, comoving volume, lookback time, age, and object intersection…
This is the third and last of three papers introducing generalised Cesaro convergence and is split into two parts. In part 1 we introduce the notion of a "Cesaro-adapted scale" and use it to prove the key generalised Cesaro…
When combining apparently inconsistent experimental results, one often implements errors on errors. The Particle Data Group's phenomenological prescription offers a practical solution but lacks a firm theoretical foundation. To address…
It is widely claimed that the quantile function is equivariant under increasing transformations. We show by a counterexample that this is not true (even for strictly increasing transformations). However, we show that the quantile function…
Application of the uncertainty principle to conditional measurements is investigated, and found to be valid for measurements on separated sub-systems. In light of this, an apparent violation of the uncertainty principle obtained by Kim and…
We present a new variant of the Faa di Bruno formula with a simpler summation order.
Conformal predictors provide set or functional predictions that are valid under the assumption of randomness, i.e., under the assumption of independent and identically distributed data. The question asked in this paper is whether there are…
Formal explainability guarantees the rigor of computed explanations, and so it is paramount in domains where rigor is critical, including those deemed high-risk. Unfortunately, since its inception formal explainability has been hampered by…
We show that in the context of classification the property of source and target distributions to be related by covariate shift may be lost if the information content captured in the covariates is reduced, for instance by dropping components…
A highly accurate but overconfident model is ill-suited for deployment in critical applications such as healthcare and autonomous driving. The classification outcome should reflect a high uncertainty on ambiguous in-distribution samples…