Related papers: Costello's pushforward formula: errata and general…
On [3, p. 199] one says "We mention parenthetically that the proof of [99, Lemma 41.3] is incorrect, and we do not know whether it, [99, Theorem 41.5] and [99, Theorem 41.6] are true". The previously cited reference [99] is our reference…
Quasi-Monte Carlo sampling can attain far better accuracy than plain Monte Carlo sampling. However, with plain Monte Carlo sampling it is much easier to estimate the attained accuracy. This article describes methods old and new to quantify…
The asymptotically optimal hypothesis testing problem with the general sources as the null and alternative hypotheses is studied under exponential-type error constraints on the first kind of error probability. Our fundamental philosophy in…
This paper is devoted to the complexity of the quantified boolean formula problem. We describe a simple deterministic algorithm that, for a given quantified boolean formula $F$, stops in time bounded by $O(|F|^4)$ and answers yes if $F$ is…
Abductive forgetting is removing variables from a logical formula while maintaining its abductive explanations. It is carried in two alternative ways depending on its intended application. Both differ from the usual forgetting, which…
Positivity, the assumption that every unique combination of confounding variables that occurs in a population has a non-zero probability of an action, can be further delineated as deterministic positivity and stochastic positivity. Here, we…
The generally accepted wisdom in computational circles is that pure proof verification is a solved problem and that the computationally hard elements and fertile areas of study lie in proof discovery. This wisdom presumably does hold for…
We give an endorsement for Cornacchia's famous algorithm. Thus we do not claim anything new but an approach which is supposed to be simpler than those of previous works written with the same aim.
We consider a modal logic that can formalise statements about uncertainty and beliefs such as `I think that my wallet is in the drawer rather than elsewhere' or `I am confused whether my appointment is on Monday or Tuesday'. To do that, we…
A test of quantum mechanics proposed by K. Popper and dealing with two-particle entangled states emitted from a fixed source has been criticized by several authors. Some of them claim that the test becomes inconclusive once all the quantum…
Three recent arguments seek to show that the universal applicability of unitary quantum theory is inconsistent with the assumption that a well-conducted measurement always has a definite physical outcome. In this paper I restate and analyze…
This contribution to the debate on confidence limits focuses mostly on the case of measurements with `open likelihood', in the sense that it is defined in the text. I will show that, though a prior-free assessment of {\it confidence} is, in…
In this paper, we give corrected and improved definitions of the sets $S$ and $\Delta$ compared to [1]. By using these new definitions, we go throughout the proof of the main result in [1], and we correct it.
The first version of this paper gave another proof of the Kropholler Conjecture, which gives a relative version of Stallings Ends Theorem, following an earlier incorrect proof. It has been pointed out by Sam Shepherd that the the second…
Pluralistic alignment requires systems to adapt to diverse user values, communication styles, and contextual assumptions. We believe that a foundational prerequisite for such alignment enabling accurate preference elicitation from people…
This is an erratum to an earlier paper, "Generalizations of the Poincar\'e-Birkhoff theorem." An error in the statement of one of the theorems is corrected.
Let $(\Omega, \mathcal{A}, \mu)$ be a probability space. The classical Borel-Cantelli Lemma states that for any sequence of $\mu$-measurable sets $E_i$ ($i=1,2,3,\dots$), if the sum of their measures converges then the corresponding…
Properness for supervised losses stipulates that the loss function shapes the learning algorithm towards the true posterior of the data generating distribution. Unfortunately, data in modern machine learning can be corrupted or twisted in…
We investigate explainability via short Boolean formulas in the data model based on unary relations. As an explanation of length k, we take a Boolean formula of length k that minimizes the error with respect to the target attribute to be…
Khabibullin's conjecture for integral inequalities has two numeric parameters $n$ and $\alpha$ in its statement, $n$ being a positive integer and $\alpha$ being a positive real number. This conjecture is already proved in the case where…