State Complexity of Reversals of Deterministic Finite Automata with Output

We investigate the worst-case state complexity of reversals of deterministic finite automata with output (DFAOs). In these automata, each state is assigned some output value, rather than simply being labelled final or non-final. This directly generalizes the well-studied problem of determining the worst-case state complexity of reversals of ordinary deterministic finite automata. If a DFAO has $n$ states and $k$ possible output values, there is a known upper bound of $k^n$ for the state complexity of reversal. We show this bound can be reached with a ternary input alphabet. We conjecture it cannot be reached with a binary input alphabet except when $k = 2$, and give a lower bound for the case $3 \le k < n$. We prove that the state complexity of reversal depends solely on the transition monoid of the DFAO and the mapping that assigns output values to states.Comment: 18 pages, 3 tables. Added missing affiliation/funding informatio

Palindromic complexity of trees

We consider finite trees with edges labeled by letters on a finite alphabet $\varSigma$. Each pair of nodes defines a unique labeled path whose trace is a word of the free monoid $\varSigma^*$. The set of all such words defines the language of the tree. In this paper, we investigate the palindromic complexity of trees and provide hints for an upper bound on the number of distinct palindromes in the language of a tree.Comment: Submitted to the conference DLT201

Classifying Non-periodic Sequences by Permutation Transducers

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Back from a Predicted Climatic Extinction of an Island Endemic: A Future for the Corsican Nuthatch

The Corsican Nuthatch (Sitta whiteheadi) is red-listed as vulnerable to extinction by the IUCN because of its endemism, reduced population size, and recent decline. A further cause is the fragmentation and loss of its spatially-restricted favourite habitat, the Corsican pine (Pinus nigra laricio) forest. In this study, we aimed at estimating the potential impact of climate change on the distribution of the Corsican Nuthatch using species distribution models. Because this species has a strong trophic association with the Corsican and Maritime pines (P. nigra laricio and P. pinaster), we first modelled the current and future potential distribution of both pine species in order to use them as habitat variables when modelling the nuthatch distribution. However, the Corsican pine has suffered large distribution losses in the past centuries due to the development of anthropogenic activities, and is now restricted to mountainous woodland. As a consequence, its realized niche is likely significantly smaller than its fundamental niche, so that a projection of the current distribution under future climatic conditions would produce misleading results. To obtain a predicted pine distribution at closest to the geographic projection of the fundamental niche, we used available information on the current pine distribution associated to information on the persistence of isolated natural pine coppices. While common thresholds (maximizing the sum of sensitivity and specificity) predicted a potential large loss of the Corsican Nuthatch distribution by 2100, the use of more appropriate thresholds aiming at getting closer to the fundamental distribution of the Corsican pine predicted that 98% of the current presence points should remain potentially suitable for the nuthatch and its range could be 10% larger in the future. The habitat of the endemic Corsican Nuthatch is therefore more likely threatened by an increasing frequency and intensity of wildfires or anthropogenic activities than by climate change

A niche remedy for the dynamical problems of neutral theory

We demonstrate how niche theory and Hubbell's original formulation of neutral theory can be blended together into a general framework modeling the combined effects of selection, drift, speciation, and dispersal on community dynamics. This framework connects many seemingly unrelated ecological population models, and allows for quantitative predictions to be made about the impact of niche stabilizing and destabilizing forces on population extinction times and abundance distributions. In particular, the existence of niche stabilizing forces in our blended framework can simultaneously resolve two major problems with the dynamics of neutral theory, namely predictions of species lifetimes that are too short and species ages that are too long.Comment: 47 pages, 4 figures, Accepted to Theoretical Ecolog

New effective potentials extraction method for the interaction between cations and water

A very simple method for the extraction of effective interaction potentials from ab initio calculations was proposed (Periole et al. J. Phys. Chem. 1997, 101, 5018), and simple two-body cation-water interaction potentials were derived for several cations, Li+, Na+, K+, Be2+, Mg2+, and Ca2+, using two facts: first, water molecules in the close vicinity of cations are strongly structured and present a constrained orientation towards the io