The presence of characteristic fine folds is important for modeling realistic looking virtual garments. While recent garment capture techniques are quite successful at capturing the low-frequency garment shape and motion over time, they often fail to capture the numerous high-frequency folds, reducing the realism of the reconstructed spacetime models. In our work we propose a method for reintro...

We present an extension to the quantifier-free theory of integer arrays which allows us to express counting. The properties expressible in Array Folds Logic (AFL) include statements such as “the first array cell contains the array length,” and “the array contains equally many minimal and maximal elements.” These properties cannot be expressed in quantified fragments of the theory of arrays, nor...

This paper is devoted to the proof and applications of a theorem giving conditions under which the inverse of a partial function can be expressed as a relational hylomorphism. The theorem is a generalisation of a previous result, due to Bird and de Moor, that gave conditions under which a total function can be expressed a relational fold. The theorem is illustrated with three problems, all deal...

BACKGROUND The recent rapid increase in the number of available three-dimensional protein structures has further highlighted the necessity to understand the relationship between biological function and structure. Using structural classification schemes such as SCOP, CATH and DALI, it is now possible to explore global relationships between protein fold and function, something which was previousl...

Fold functions are a general mechanism for computing over recursive data structures. First-order folds compute results bottom-up. With higher-order folds, computations that inherit attributes from above can also be expressed. In this paper, we explore folds over a form of recursive higher-order function, called hyperfunctions, and show that hyperfunctions allow fold computations to coroutine ac...

As more and more protein structures are determined, there is increasing interest in the question of how many different folds have been used in biology. The history of the rate of discovery of new folds and the distribution of sequence families among known folds provide a means of estimating the underlying distribution of fold use. Previous models exploiting these data have led to rather differe...

Protein structures are a very special class among all possible structures. It has been suggested that a "designability principle" plays a crucial role in nature's selection of protein sequences and structures. Here, we provide a theoretical base for such a selection principle, using a simple model of protein folding based on hydrophobic interactions. A structure is reduced to a string of 0s and...

The familiar division of compact Riemann surfaces into 3 cases g = 0, g = 1 and g ≥ 2 corresponds to the well known trichotomy of spherical, Euclidean and hyperbolic non-Euclidean plane geometry. Classification aims to treat all projective algebraic varieties in terms of this trichotomy; the model is Castelnuovo and Enriques’ treatment of surfaces around 1900 (reworked by Kodaira in the 1960s)....

Only about 1,000 qualitatively different protein folds are believed to exist in nature. Here, we review theoretical studies which suggest that some folds are intrinsically more designable than others, i.e. are lowest energy states of an unusually large number of sequences. The sequences associated with these folds are also found to be unusually thermally stable. The connection between highly de...

Designing curved folds of a developable surface remains an open problem. No analytical method for the design of curved folds has been reported. Although optimization methods exist, it is difficult to interactively design valid curved folds of a single developable surface using such methods. In the present paper, we propose an interactive system for designing a surface with planar curved folds b...