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Boyer and Moore have discussed a recursive function that puts conditional expressions into normal form [1]. It is difficult to prove that this function terminates on all inputs. Three termination proofs are compared: (1) using a measure…

We prove an asymptotic for the number of additive triples of bijections $\{1,\dots,n\}\to\mathbb{Z}/n\mathbb{Z}$, that is, the number of pairs of bijections $\pi_1,\pi_2\colon \{1,\dots,n\}\to\mathbb{Z}/n\mathbb{Z}$ such that the pointwise…

Nonlinear modifications of quantum theory are considered potential candidates for the theory of quantum gravity, with the intuitive argument that since Einstein field equations are nonlinear, quantum gravity should be nonlinear as well.…

Citations are increasingly used for research evaluations. It is therefore important to identify factors affecting citation scores that are unrelated to scholarly quality or usefulness so that these can be taken into account. Regression is…

In a recent Letter, Bennett and coworkers [1] argue that proofs of exotic quantum effects using closed timelike curves (CTC's) based on the work of Deutsch [2], or other nonlinear quantum dynamics, suffer from a fallacy that they call the…

Academic citations are widely used for evaluating research and tracing knowledge flows. Such uses typically rely on raw citation counts and neglect variability in citation types. In particular, citations can vary in their fidelity as…

We propose finite difference methods for degenerate fully nonlinear elliptic equations and prove the convergence of the schemes. Our focus is on the pure equation and a related free boundary problem of transmission type. The cornerstone of…

This paper investigates the expected number of complex roots of nonlinear equations. Those equations are assumed to be analytic, and to belong to certain inner product spaces. Those spaces are then endowed with the Gaussian probability…

References, the mechanism scientists rely on to signal previous knowledge, lately have turned into widely used and misused measures of scientific impact. Yet, when a discovery becomes common knowledge, citations suffer from obliteration by…

The lack of predictability of citation-based measures frequently used to gauge impact, from impact factors to short-term citations, raises a fundamental question: Is there long-term predictability in citation patterns? Here, we derive a…

In applied probability, the normal approximation is often used for the distribution of data with assumed additive structure. This tradition is based on the central limit theorem for sums of (independent) random variables. However, it is…

The theory of regular cost functions is a quantitative extension to the classical notion of regularity. A cost function associates to each input a non-negative integer value (or infinity), as opposed to languages which only associate to…

Contextuality - the obstruction to describing quantum mechanics in a classical statistical way - has been proposed as a resource that powers quantum computing. The measurement-based model provides a concrete manifestation of contextuality…

Citation texts are sometimes not very informative or in some cases inaccurate by themselves; they need the appropriate context from the referenced paper to reflect its exact contributions. To address this problem, we propose an unsupervised…

Motivated by the problem of finding finite versions of classical incompleteness theorems, we present some conjectures that go beyond ${\bf NP\neq co NP}$. These conjectures formally connect computational complexity with the difficulty of…

In proof theory the notion of canonical proof is rather basic, and it is usually taken for granted that a canonical proof of a sentence must be unique up to certain minor syntactical details (such as, e.g., change of bound variables). When…

Singularities appear in numerous important mathematical models used in Physics. And in most of such cases singularities are involved in essentially nonlinear contexts. For more than four decades, general enough nonlinear theories of…

Although classical mechanics and quantum mechanics are separate disciplines, we live in a world where Planck's constant \hbar>0, meaning that the classical and quantum world views must actually {\it coexist}. Traditionally, canonical…

We introduce here a new axiomatisation of the rational fragment of the ZX-calculus, a diagrammatic language for quantum mechanics. Compared to the previous axiomatisation introduced in [8], our axiomatisation does not use any metarule , but…

Citation analysis is one of the most frequently used methods in research evaluation. We are seeing significant growth in citation analysis through bibliometric metadata, primarily due to the availability of citation databases such as the…