Related papers: Simple t-designs: A recursive construction for arb…

Let M be an oriented compact 3-manifold and let T be a (loose) triangulation of M, with ideal vertices at the components of the boundary of M and possibly internal vertices. We show that any spin structure s on M can be encoded by extra…

Structured recursion schemes have been widely used in constructing, optimising, and reasoning about programs over inductive and coinductive datatypes. Their plain forms, catamorphisms and anamorphisms, are restricted in expressiveness. Thus…

Many random combinatorial objects have a component structure whose joint distribution is equal to that of a process of mutually independent random variables, conditioned on the value of a weighted sum of the variables. It is interesting to…

We propose here to look at how abstract a model of a usable system can be, but still say something useful and interesting, so this paper is an exercise in abstraction and formalisation, with usability-of-design as an example target use. We…

Some iterative techniques are defined to solve reversible inverse problems and a common formulation is explained. Numerical improvements are suggested and tests validate the methods.

We propose a recursive algorithm for identifying all finite sequences of positive integers whose product equals their sum. Our method uses solutions of strictly shorter length that are iteratively extended in pursuit of a valid solution.…

This article presents a methodology that automatically derives a combinatorial specification for a permutation class C, given its basis B of excluded patterns and the set of simple permutations in C, when these sets are both finite. This is…

In this paper, we study the possibility of designing non-trivial random CSP models by exploiting the intrinsic connection between structures and typical-case hardness. We show that constraint consistency, a notion that has been developed to…

We introduce the notion of a Tits arrangement on a convex open cone as a special case of (infinite) simplicial arrangements. Such an object carries a simplicial structure similar to the geometric representation of Coxeter groups. The…

We apply a new approach to the reverse protein folding problem. Our method uses a minimization function in the design process which is different from the energy function used for folding. For a lattice model, we show that this new approach…

We are presenting an algorithm capable of simplifying tensor polynomials with indices when the building tensors have index symmetry properties. These properties include simple symmetry, cyclicity and those due to the presence of covariant…

Various specifiable combinatorial structures, with d extensive parameters, can be exactly sampled both by the recursive method, with linear arithmetic complexity if a heavy preprocessing is performed, or by the Boltzmann method, with…

Self-assembly materials are traditionally designed so that molecular or meso-scale components form a single kind of large structure. Here, we propose a scheme to create "multifarious assembly mixtures", which self-assemble many different…

Response surface designs are usually described as being run under complete randomization of the treatment combinations to the experimental units. In practice, however, it is often necessary or beneficial to run them under some kind of…

We show that every small model category that satisfies certain size conditions can be completed to yield a combinatorial model category, and conversely, every combinatorial model category arises in this way. We will also see that these…

We conjecture that for a strongly minimal theory T in a finite signature satisfying the Zilber Trichotomy, there are only three possibilities for the recursive spectrum of T: all countable models of T are recursively presentable; none of…

The obvious way to construct a GDD (group-divisible design) recursively is to use Wilson's Fundamental Construction for GDDs (WFC). Then a PBD (pairwise balanced design) is often obtained by adding a new point to each group of the GDD.…

Generally, combinatorial design concerns with the arrangement of a finite set of elements into patterns (subsets, words, arrays) according to specified rules. The usefulness of this design method is that the number of input combination can…

The field of complex self-assembly is moving toward the design of multi-particle structures consisting of thousands of distinct building blocks. To exploit the potential benefits of structures with such `addressable complexity,' we need to…

In this paper we generalize notions of iterated integral with regard to an unpredictable process. We establish a formula of integration by parts, the existence of a continuous modification and give an expression of the increasing process.