Related papers: On the Lambek-Moser Theorem

We give a counterexample to a recently conjectured variant of the Penrose inequality.

We extend de Finetti's [Ann. Inst. H. Poincar\'{e} 7 (1937) 1--68] notion of exchangeability to finite and countable sequences of variables, when a subject's beliefs about them are modelled using coherent lower previsions rather than…

We give a probabilistic proof of the orbit-counting lemma.

Our paper is the first study of what one might call "reverse mathematics of explicit fixpoints". We study two methods of constructing such fixpoints for formulas whose principal connective is the intuitionistic Lewis arrow. Our main…

We prove a conjecture by W. Bergweiler and A. Eremenko on the traces of elements of modular group in this paper

Model interpretability methods are often used to explain NLP model decisions on tasks such as text classification, where the output space is relatively small. However, when applied to language generation, where the output space often…

We apply simple linear programming methods and an LP solver to refute a number of open conjectures in extremal combinatorics.

In the paper it is demonstrated that Bells theorem is an unprovable theorem.

An equivalent but useful version on the Homological Nerve Theorem is proved.

One way of proving theorems in modal logics is translating them into the predicate calculus and then using conventional resolution-style theorem provers. This approach has been regarded as inappropriate in practice, because the resulting…

We consider the task of distinguishing between two different alternative models that can roughly equally explain observed time series data, mainly focusing on the period ambiguity case (aliasing). We propose a test for checking whether the…

Working from definitions and an elementarily obtained integral formula for the Euler-Mascheroni constant, we give an alternative proof of the classical Puiseux representation of the exponential integral.

We give an alternative proof of Madsen-Weiss' generalized Mumford conjecture. Our proof is based on ideas similar to Madsen-Weiss' original proof, but it is more geometrical and less homotopy theoretical in nature. At the heart of the…

As language models (LMs) deliver increasing performance on a range of NLP tasks, probing classifiers have become an indispensable technique in the effort to better understand their inner workings. A typical setup involves (1) defining an…

In this paper, we give a bijective proof of the reduced lecture hall partition theorem. It is possible to extend this bijection in lecture hall partition theorem. And refined versions of each theorems are also presented.

A very short proof of Kneser's theorem via transversal is given.

Distributed representations (such as those based on embeddings) and discrete representations (such as those based on logic) have complementary strengths. We explore one possible approach to combining these two kinds of representations. We…

Lov\'asz Local Lemma (LLL) is a probabilistic tool that allows us to prove the existence of combinatorial objects in the cases when standard probabilistic argument does not work (there are many partly independent conditions). LLL can be…

A version of Bohm's model incorporating retrocausality is presented, the aim being to explain the nonlocality of Bell's theorem while maintaining Lorentz invariance in the underlying ontology. The strengths and weaknesses of this…

A salient approach to interpretable machine learning is to restrict modeling to simple models. In the Bayesian framework, this can be pursued by restricting the model structure and prior to favor interpretable models. Fundamentally,…