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The space of topological decompositions into triangulations of a surface has a natural graph structure where two triangulations share an edge if they are related by a so-called flip. This space is a sort of combinatorial Teichm\"uller space…
We present a preference learning framework for multiple criteria sorting. We consider sorting procedures applying an additive value model with diverse types of marginal value functions (including linear, piecewise-linear, splined, and…
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 present a new and simple randomized algorithm for constructing the Delaunay triangulation using nearest neighbor graphs for point location. Under suitable assumptions, it runs in linear expected time for points in the plane with…
Neural networks have seen an explosion of usage and research in the past decade, particularly within the domains of computer vision and natural language processing. However, only recently have advancements in neural networks yielded…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
The truss, a relaxation of the clique based on triangles, serves to identify clusters of actors in a way that is easy to interpret and is computationally attractive. This paper introduces the 4-cycle-based relative to the truss, called the…
Real time application of deep learning algorithms is often hindered by high computational complexity and frequent memory accesses. Network pruning is a promising technique to solve this problem. However, pruning usually results in irregular…
Problem definition: To mitigate excessive crowding in public transit networks, network expansion is often not feasible due to financial and time constraints. Instead, operators are required to make use of existing infrastructure more…
We illustrate the relationship between spin networks and their dual representation by labelled triangulations of space in 2+1 and 3+1 dimensions. We apply this to the recent proposal for causal evolution of spin networks. The result is…
The new concept of multilevel network is introduced in order to embody some topological properties of complex systems with structures in the mesoscale which are not completely captured by the classical models. This new model, which…
In order to represent the preferences of a group of individuals, we introduce Probabilistic CP-nets (PCP-nets). PCP-nets provide a compact language for representing probability distributions over preference orderings. We argue that they are…
In spatial networks vertices are arranged in some space and edges may cross. When arranging vertices in a 1-dimensional lattice edges may cross when drawn above the vertex sequence as it happens in linguistic and biological networks. Here…
We consider 3-dimensional pseudo-manifolds M with a given set of marked point V such that M-V is the interior of a compact 3-manifold with boundary. An ideal triangulation T of (M, V ) has V as its set of vertices. A branching (T, b)…
In the framework of coupled cell systems, a coupled cell network describes graphically the dynamical dependencies between individual dynamical systems, the cells. The fundamental network of a network reveals the hidden symmetries of that…
Mechanistic interpretability aims to explain what a neural network has learned at a nuts-and-bolts level. What are the fundamental primitives of neural network representations? Previous mechanistic descriptions have used individual neurons…
In a previous paper, the sup-interpretation method was proposed as a new tool to control memory resources of first order functional programs with pattern matching by static analysis. Basically, a sup-interpretation provides an upper bound…
The study of complexity and optimization in decision theory involves both partial and complete characterizations of preferences over decision spaces in terms of real-valued monotones. With this motivation, and following the recent…
Complex systems are characterized by many interacting units that give rise to emergent behavior. A particularly advantageous way to study these systems is through the analysis of the networks that encode the interactions among the system's…
When analyzing complex networks a key target is to uncover their modular structure, which means searching for a family of modules, namely node subsets spanning each a subnetwork more densely connected than the average. This work proposes a…