Related papers: A New Approach to the Hofstadter $Q$-Recurrence

The problem of large order behaviour of perturbation theory for quantum mechanical systems is considered. A new approach to it is developed. An explicit mechanism showing the connection between large order recursive relations and classical…

We provide evidence of an extreme form of sensitivity to initial conditions in a family of one-dimensional self-ruling dynamical systems. We prove that some hyperchaotic sequences are closed-form expressions of the orbits of these…

First-order factoid question answering assumes that the question can be answered by a single fact in a knowledge base (KB). While this does not seem like a challenging task, many recent attempts that apply either complex linguistic…

The identification of causal relations is a cornerstone of the scientific method. Traditional approaches to this task are based on classical statistics. However, such classical approaches do not apply in the quantum domain, where a broader…

We present the first example of a phase transition in a nonequilibrium steady-state that can be argued analytically to be first order. The system of interest is a two-species reaction-diffusion problem whose control parameter is the total…

Stochastic processes that are randomly reset to an initial condition serve as a showcase to investigate non-equilibrium steady states. However, all existing results have been restricted to the special case of memoryless resetting protocols.…

Many systems that exhibit nonmonotonic behavior have been described and studied already in the literature. The general notion of nonmonotonic reasoning, though, has almost always been described only negatively, by the property it does not…

This work proposes a novel approach based on sequence-to-sequence (seq2seq) models for context-aware conversational systems. Exist- ing seq2seq models have been shown to be good for generating natural responses in a data-driven…

We investigate form factors of local operators in the multi-component Quantum Non-linear Schr\"odinger model, a prototype theory solvable by the so-called nested Bethe Ansatz. We determine the analytic properties of the infinite volume form…

Nestedness is a common property of communication, finance, trade, and ecological networks. In networks with high levels of nestedness, the link positions of low-degree nodes (those with few links) form nested subsets of the link positions…

A nondecreasing sequence of positive integers is $(\alpha,\beta)$-Conolly, or Conolly-like for short, if for every positive integer $m$ the number of times that $m$ occurs in the sequence is $\alpha + \beta r_m$, where $r_m$ is $1$ plus the…

A number of writers have been attracted to the idea that some of the peculiarities of quantum theory might be manifestations of 'backward' or 'retro' causality, underlying the quantum description. This idea has been explored in the…

Dialogue participants often refer to entities or situations repeatedly within a conversation, which contributes to its cohesiveness. Subsequent references exploit the common ground accumulated by the interlocutors and hence have several…

We consider arithmetic sequences, here defined as ordered lists of positive integers. Any such a sequence can be cast onto a quantum state, enabling the quantification of its `surprise' through von Neumann entropy. We identify typical…

First Passage (FP) processes are utilized widely to model phenomena in many areas of mathematical applications, from biology to computer science. Introducing a mechanism to restart the parent process can alter the first passage…

Second order recurrence relations of real numbers arise form various applications in discrete time dynamical systems as well as in the context on Markov chains. Solutions to the recurrence relations are fully defined by the first two…

Multi-sentence questions (MSQs) are sequences of questions connected by relations which, unlike sequences of standalone questions, need to be answered as a unit. Following Rhetorical Structure Theory (RST), we recognise that different…

We investigate recurrence phenomena in coupled two degrees of freedom systems. It is shown that an initial well localized wave packet displays recurrences even in the presence of coupling in these systems. We discuss the interdependence of…

For rotationally invariant first passage percolation (FPP) on the plane, we use a multi-scale argument to prove stretched exponential concentration of the first passage times at the scale of the standard deviation. Our results are proved…

Quantum superposition, a cornerstone of quantum mechanics, enables systems to exist in multiple states simultaneously, giving rise to probabilistic outcomes. In quantum information science, conditional entropy has become a key metric for…