Here we investigate the correlations between coding sequence substitutions as a function of their separation along the protein sequence. We consider both substitutions between the reference genomes of several Drosophilids as well as polymorphisms in a population sample of Zimbabwean Drosophila melanogaster. We find that amino acid substitutions are "clustered" along the protein sequence, that i...

The amino acid sequence of a polypeptide defines both the folding pathway and the final three-dimensional structure of a protein. Eighteen amino acid substitutions have been identified in bacteriophage P22 coat protein that are defective in folding and cause their folding intermediates to be substrates for GroEL and GroES. These temperature-sensitive folding (tsf) substitutions identify amino a...

Backbone modifications via insertions and deletions (InDels) may exert dramatic effects, for better (mediating new functions) and for worse (causing loss of structure and/or function). However, contrary to point mutations (substitutions), our knowledge of the evolution and structural-functional effects of InDels is limited and so is our capability to engineer them. We sought to assess how delet...

In this note we compare propositional logics for closed substitutions and propositional logics for open substitutions in constructive arithmetical theories. We provide a strong example where these logics diverge in an essential way. We prove that for Markov’s Arithmetic, i.e. Heyting’s Arithmetic plus Markov’s principle plus Extended Church’s Thesis, the logic of closed and the logic of open su...

We consider dynamical systems arising from substitutions over a finite alphabet. We prove that such a system is linearly repetitive if and only if it is minimal. Based on this characterization we extend various results from primitive substitutions to minimal substitutions. This includes applications to random Schrödinger operators and to number theory.

In this paper we consider a widely attested process: sonority substitutions whereby sounds of a certain sonority class change into sounds of another sonority class. These sonority substitutions concern, for example, liquids (/l,r/) changing into glides (/j,w/). The target word groen ‘green’ may be realized by an aphasic speaker as [xjUn] or [xwUn]. We will discuss these sonority substitutions i...

We refine the simulation technique introduced in (Di Cosmo and Kesner 1997) to show strong normalization of λ-calculi with explicit substitutions via termination of cut elimination in proof nets (Girard 1987). We first propose a notion of equivalence relation for proof nets that extends the one in (Di Cosmo and Guerrini 1999), and we show that cut elimination modulo this equivalence relation is...

While the priority argument has been one of the main techniques of recursion theory, it has seen only a few applications to other areas of mathematics [Mar75, Sol84]. One possibility for another such application was pointed out by Kreisel: Hilbert’s ǫsubstitution method, a technique for proving the 1-consistency of theories. Kreisel’s observation was that the proof that the method works [Ack40]...

For first-order classical logic a new notion of admissible substitution is defined. This notion allows optimizing the procedure of the application of quantifier rules when logical inference search is made in sequent calculi. Our objective is to show that such a computer-oriented sequent technique may be created that does not require a preliminary skolemization of initial formulas and that is ef...

Codon-and amino acid-substitution models are widely used for the evolutionary analysis of protein-coding DNA sequences. Using codon models, the amounts of both nonsynonymous and synonymous DNA substitutions can be estimated. The ratio of these amounts represents the strength of selective pressure. Using amino acid models, the amount of nonsynonymous substitutions is estimated, but that of synon...