Related papers: Biologically Unavoidable Sequences
We show that essentially the Fibonacci sequence is the unique binary recurrence which contains infinitely many three-term arithmetic progressions. A criterion for general linear recurrences having infinitely many three-term arithmetic…
We introduce a new family of meta-Fibonacci sequences $(f(n))_{n\in\mathbb{N}}$, governed by the recurrence relation $$f(n)=af(n-u_{n}-1)+bf(n-u_{n}-2),$$ where $\mathbf{u}=(u_{n})_{n\in \mathbb{N}}$ is a sequence with values $0,1$. Our…
Selection, the tendency of some traits to become more frequent than others in a population under the influence of some (natural or artificial) agency, is a key component of Darwinian evolution and countless other natural and social…
Algorithmic theories of randomness can be related to theories of probabilistic sequence prediction through the notion of a predictor, defined as a function which supplies lower bounds on initial-segment probabilities of infinite sequences.…
In this work, we show that very natural, apparently simple problems in quantum measurement theory can be undecidable even if their classical analogues are decidable. Undecidability hence appears as a genuine quantum property here. Formally,…
Mortality is an instrument of natural selection. Evolutionary motivated theories imply its irreversibility and life history dependence. This is inconsistent with mortality data for protected populations. Accurate analysis yields mortality…
The chase procedure is a fundamental algorithmic tool in databases that allows us to reason with constraints, such as existential rules, with a plethora of applications. It takes as input a database and a set of constraints, and iteratively…
In a previous paper we addressed the question "Does the Rapid Appearance of Life on Earth Suggest that Life is Common in the Universe?" The non-observability of recent biogenesis is a self-selection effect that needs to be considered if…
In this work we present a model for computation of random processes in digital computers which solves the problem of periodic sequences and hidden errors produced by correlations. We show that systems with non-invertible non-linearities can…
Open-ended evolution (OEE) is relevant to a variety of biological, artificial and technological systems, but has been challenging to reproduce in silico. Most theoretical efforts focus on key aspects of open-ended evolution as it appears in…
Existential rules, long known as tuple-generating dependencies in database theory, have been intensively studied in the last decade as a powerful formalism to represent ontological knowledge in the context of ontology-based query answering.…
It is a well-known fact that genetic sequences may contain sections with repeated units, called repeats, that differ in length over a population, with a length distribution of geometric type. A simple class of recombination models with…
Background: A metabolic genotype comprises all chemical reactions an organism can catalyze via enzymes encoded in its genome. A genotype is viable in a given environment if it is capable of producing all biomass components the organism…
Sweepstakes reproduction may be generated by chance matching of reproduction with favorable environmental conditions. Gene genealogies generated by sweepstakes reproduction are in the domain of attraction of multiple-merger coalescents…
We consider a nonlinear model for electrical conduction in biological tissues. The nonlinearity appears in the interface condition prescribed on the cell membrane. The purpose of this paper is proving asymptotic convergence for large times…
Existential rules are a very popular ontology-mediated query language for which the chase represents a generic computational approach for query answering. It is straightforward that existential rule queries exhibiting chase termination are…
The lefthanded Lov\'asz local lemma (LLLL) is a generalization of the Lov\'asz local lemma (LLL), a powerful technique from the probabilistic method. We prove a computable version of the LLLL and use it to effectivize a collection of…
Diagnosing an inherited disease often requires identifying the pattern of inheritance in a patient's family. We represent family trees with genetic patterns of inheritance using hypergraphs and latent state space models to provide…
Completely antipersistent binary time series are sequences in which every time that an $N$-bit string $\mu$ appears, the sequence is continued with a different bit than at the last occurrence of $\mu$. This dynamics is phrased in terms of a…
Sequential sampling occurs when the entire population is not known in advance and data are obtained one at a time or in groups of units. This manuscript proposes a new algorithm to sequentially select a balanced sample. The algorithm…