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We study the properties of a simple lattice model of repulsive particles diffusing in a pinning landscape. The behaviour of the model is very similar to the observed physics of vortices in superconductors. We compare and discuss the…
We study reflection-symmetric realisations of symmetric graphs in the plane that allow a continuous symmetry and edge-length preserving deformation. To do so, we identify a necessary combinatorial condition on graphs with…
A discretisation scheme that preserves topological features of a physical problem is extended so that differential geometric structures can be approximated in a consistent way thus giving access to the study of physical systems which are…
Using a lattice-gas model with pairwise interactions, we study the ordered structures, coverage dependence of the heat of adsorption, and other experimentally observable behavior of adsorbed CO overlayers on Pd(100) single crystal surfaces.…
The topologies permitted in joint ocular dominance (OD), orientation preference (OP), and direction preference (DP) maps in the primary visual cortex (V1) are considered, with the aim of finding a maximally symmetric periodic case that can…
We describe the mathematical properties of pairwise comparisons matrices with coefficients in an arbitrary group. We provide a vocabulary adapted for the description of main algebraic properties of inconsistency maps, describe an example…
We study multigranulation spaces of two equivalences. The lattice-theoretical properties of so-called "optimistic" and "pessimistic" multigranular approximation systems are given. We also consider the ordered sets of rough sets determined…
We extend a result proved in \cite{Col} for mirror symmetries of planar systems to measure-preserving non-linear reversibilities of $n$-dimensional systems, dropping the analyticity and nondegeneracy conditions.
The Weil pairing on elliptic curves has deep links with discrete logarithm problems. In practice, to better suit the functionalities of cryptosystems, one often needs to modify the original Weil pairing via what is called a distortion map.…
Hartle's model provides the most widely used analytic framework to describe isolated compact bodies rotating slowly in equilibrium up to second order in perturbations in the context of General Relativity. Apart from some explicit…
A study of harmonic maps into Lie groups as a generalisation of the study of other well-known integrable systems, particularly the Toda and self-dual Chern Simons theories.
This thesis deals with the enumerative study of combinatorial maps, and its application to the enumeration of other combinatorial objects. Combinatorial maps, or simply maps, form a rich combinatorial model. They have an intuitive and…
This article is devoted to the study of mappings defined in the region on the plane. Under certain conditions, the upper estimate of the distortion of the modulus of families of paths is obtained. Similarly, the upper estimate of the…
We discuss several approaches to motivic complexes and explicit constructions of the regulator maps from the motivic complexes to Deligne complexes.
For an arbitrary partially ordered set $P$ its {\em dual} $P^*$ is built as the collection of all monotone mappings $P\to\2$ where $\2=\{0,1\}$ with $0<1$. The set of mappings $P^*$ is proved to be a complete lattice with respect to the…
We consider a graph called a lattice diagram, which is a graph in the $xy$-plane such that each edge is parallel to the $x$-axis or the $y$-axis. In [4], we investigated transformations of certain lattice diagrams, and we considered the…
We study a class of minimal geometric partial differential equations that serves as a framework to understand the evolution of boundaries between states in different pattern forming systems. The framework combines normal growth, curvature…
We study learning of indexed families from positive data where a learner can freely choose a hypothesis space (with uniformly decidable membership) comprising at least the languages to be learned. This abstracts a very universal learning…
We study the dynamics of fronts in parametrically forced oscillating lattices. Using as a prototypical example the discrete Ginzburg-Landau equation, we show that much information about front bifurcations can be extracted by projecting onto…
We study linear relations among correlation functions on a lattice obtained from integration-by-parts identities. We use the framework of twisted cocycles and determine for a scalar theory a basis of correlation functions, in which all…