We propose a new and general method for discovering novel ordered phases of block copolymer melts. The method involves minimizing a free energy functional in an arbitrary unit cell with respect to the composition profile and the dimensions of the unit cell, without any prior assumption of the microphase symmetry. Varying the initial conditions allows to search for different stable and metastabl...

We show that it is decidable in exponential time whether the lexicographic ordering of a context-free language is scattered, or a wellordering.

We consider avoiding squares and overlaps over the natural numbers, using a greedy algorithm that chooses the least possible integer at each step; the word generated is lexicographically least among all such infinite words. In the case of avoiding squares, the word is 01020103 · · · , the familiar ruler function, and is generated by iterating a uniform morphism. The case of overlaps is more cha...

Based on thermodynamic principles, we derive expressions quantifying the non-harmonic vibrational behavior of materials, which are rigorous yet easily evaluated from experimentally available data for the thermal expansion coefficient and the phonon density of states. These experimentally-derived quantities are valuable to benchmark first-principles theoretical predictions of harmonic and non-ha...

In this paper we prove decidability of two kinds of branching time temporal logics. First we show that the non-local version of propositional PCTL∗, in which truth values of atoms may depend on the branch of evaluation, is decidable. Then we use this result to establish decidability of various fragments of quantified PCTL∗, where the next-time operator can be applied only to formulas with at mo...

Let L be a first-order language and let M = 〈M, I〉 be a model for L. Then every formula φ(x1, . . . , xn) of L determines a unique n-place predicate: φ = {〈a1, . . . , an〉 ∈M n : M |= φ[a1, . . . , an]} Here, of course, the notation φ(x1, . . . , xn) is used to indicate that the free variables of φ constitute a subset of {x1, . . . , xn} (see [1] p. 24). A n-placed relation R ⊆M is said to be d...

We solve a problem of Petrova, finalizing the classification of letter patterns avoidable by ternary square-free words; we show that there is a ternary square-free word avoiding letter pattern xyzxzyx. In fact, we • characterize all the (two-way) infinite ternary square-free words avoiding letter pattern xyzxzyx • characterize the lexicographically least (one-way) infinite ternary square-free w...

Second-order uniication is undecidable in general. Miller showed that uniication of so-called higher-order patterns is decidable and unitary. We show that the uniication of a linear higher-order pattern s with an arbitrary second-order term that shares no variables with s is decidable and nitary. A few extensions of this uniication problem are still decidable: unifying two second-order terms, w...

We present several characterisations of the class of prefix-recognisable graphs including representations via graph-grammars and MSO-interpretations. The former implies that prefix-recognisable graphs have bounded clique-width; the latter is used to extend this class to arbitrary relational structures. We prove that the prefix-recognisable groups are exactly the context-free groups. Finally, we...

The plactic monoid is the quotient of the free monoid by the congruence generated by Knuth’s well-celebrated rules. It is well-known that the set of Young tableaux is a cross-section of this congruence which happens to be regular. The main result of this work shows that the set of alphabetically minimal elements in the congruence classes is also regular. We give a full combinatorial characteriz...