Related papers: On avoidability of formulas with reversal
We give the avoidance indices (morphic and antimorphic) for all unary patterns with involution.
Associated to a random walk on $\mathbb{Z}$ and a positive integer $n$, there is a return probability of the random walk returning to the origin after $n$ steps. An interesting question is when the set of return probabilities uniquely…
It has been proved several times in the literature that a polynomial map from $C^2$ to $C$ with irreducible rational fibers cannot be a component of a counterexample to the Jacobian Conjecture. This note points out that this result is…
Turing's famous 'machine' framework provides an intuitively clear conception of 'computing with real numbers'. A recursive counterexample to a theorem shows that the theorem does not hold when restricted to computable objects. These…
Investigation of the reversibility of the directional hierarchy in the interdependency among the notions of conditional independence, conditional mean independence, and zero conditional covariance, for two random variables X and Y given a…
In many cases, the values of some model parameters are determined by maximising the likelihood of a set of data points given the parameter values. The presence of outliers in the data and correlations between data points complicate this…
This article addresses the question of when physical laws and their consequences can be computed. If a physical system is capable of universal computation, then its energy gap can't be computed. At an even more fundamental level, the most…
It is recalled that closed (isolated) systems are essentially reversible whilst open systems like the Earth, or living beings on it, are irreversible because they are not isolated. Earth and life irreversibility derives from the evolution…
In causal models, a given mechanism is assumed to be invariant to changes of other mechanisms. While this principle has been utilized for inference in settings where the causal variables are observed, theoretical insights when the variables…
We establish a close connection between a reversible programming language based on type isomorphisms and a formally presented univalent universe. The correspondence relates combinators witnessing type isomorphisms in the programming…
This paper considers (partial) identification of a variety of counterfactual parameters in binary response models with possibly endogenous regressors. Our framework allows for nonseparable index functions with multi-dimensional latent…
It is shown that the phenomenon of irreversibility in many-body and few-body systems can be explained and described within the framework of the concept of direct (not instantaneous) interaction of particles without using probabilistic…
We study the notion of irreducibility of semigroup morphisms. Given an alphabet $\Sigma$, a morphism $\varphi:\Sigma^+\rightarrow\Sigma^+$ is irreducible if any factorisation $\varphi=\psi_2\circ\psi_1$ can only be satisfied if $\psi_1$ or…
If an infinite non-periodic word is uniformly recurrent or is of bounded repetition, then the limit of its periodicity complexity is infinity. Moreover, there are uniformly recurrent words with the periodicity complexity arbitrarily high at…
We discuss on very general grounds possible lineshapes of composite particles with one unstable constituent. Expressions are derived in a coupled-channel formalism for constituents interacting in an S-wave with no assumption made on the…
This paper concerns the probabilistic evaluation of the effects of actions in the presence of unmeasured variables. We show that the identification of causal effect between a singleton variable X and a set of variables Y can be accomplished…
A new integral identity for functions with continuous second partial derivatives is derived. It is shown that the value of any function f(r,t) at position r and time t is completely determined by its previous values at all other locations…
We discuss a field transformation from fields $\psi_a$ to other fields $\phi_i$ that involves derivatives, $\phi_i = \bar \phi_i(\psi_a, \partial_\alpha \psi_a, \ldots ;x^\mu)$, and derive conditions for this transformation to be…
In this paper, we prove some invariant curve theorems for the planar almost periodic reversible mappings. As an application, we will discuss the existence of almost periodic solutions and the boundedness of all solutions for the nonlinear…
There have been controversies among statisticians on (i) what to model and (ii) how to make inferences from models with unobservables. One such controversy concerns the difference between estimation methods for the marginal means not…