New upper bounds for the connective constant of self-avoiding walks in a hypercubic lattice are obtained by automatic generation of finite automata for counting walks with finite memory. The upper bound in dimension two is 2.679192495.

The knotting probability is defined by the probability with which an N -step self-avoiding polygon (SAP) with a fixed type of knot appears in the configuration space. We evaluate these probabilities for some knot types on a simple cubic lattice. For the trivial knot, we find that the knotting probability decays much slower for the SAP on the cubic lattice than for continuum models of the SAP as...

The equilibrium properties of isolated ring molecules were investigated using an off-lattice model with no excluded volume but with dynamics that preserve the topological class. Using an efficient set of long range moves, chains of more than 2000 monomers were studied. Despite the lack of any excluded volume interaction, the radius of gyration scaled like that of a self avoiding walk, as had be...

A comprehensive numerical study of self-avoiding walks (SAW’s) on randomly diluted lattices in two and three dimensions is carried out. The critical exponents ν and χ are calculated for various different occupation probabilities, disorder configuration ensembles, and walk weighting schemes. These results are analyzed and compared with those previously available. Various subtleties in the calcul...

We introduce and study the uniform infinite planar quadrangulation (UIPQ) with a boundary via an extension of the construction of [14]. We then relate this object to its simple boundary analog using a pruning procedure. This enables us to study the aperture of these maps, that is, the maximal distance between two points on the boundary, which in turn sheds new light on the geometry of the UIPQ....

Although the “tragedy of the commons” is common currency in popular accounts of problems arising in human–environment relations, empirical research has shown that common-property systems do not always lead to tragic outcomes. Moreover, systems of private property or public property, often proposed as solutions to the tragedy of the commons, can generate tragedies of their own that are equally s...

Property disputes are frequent occurrences in rapidly urbanizing regions. Among the legal issues concerning building property rights, solar rights prevalent because text clauses on rely diverse measurements or calculations. Moreover, previous studies measuring addressed only sunlight duration and neglected daylight factor (daylighting coefficient), which is an integral component of rights. Ther...

A matching in a group G is a bijection φ from a subset A to a subset B in G such that aφ(a) / ∈ A for all a ∈ A. The group G is said to have the matching property if, for any finite subsets A,B in G of same cardinality with 1 / ∈ B, there is a matching from A to B. Using tools from additive number theory, Losonczy proved a few years ago that the only abelian groups satisfying the matching prope...

It is common to use invariant assertions to analyze functional properties of loops (such as partial correctness) and to use variant functions to analyze operational properties of loops (such as termination). In this paper, we explore an orthogonal approach, based on invariant relations, which enables us to reason about functional properties as well as termination in a uniform manner; also, our ...

Nonlinear L2-gain is a generalization of the wellknown finite L2-gain robust stability property for nonlinear systems. Computation of tight performance bounds associated with this nonlinear L2-gain property is key to avoiding conservatism in its application, for example in small-gain based design. In previous work, a number of max-plus eigenvector methods have been proposed to facilitate this c...