An automatic method for edge detection on biological images (otolith images) using a multi-agent system is presented. One of the major problems encountered during an automatic contour detection is the lack of structure continuity perception. In this paper we present a new approach to perceive continuity based on a 2D reconstruction of closed contours using a multi-agent system. Each agent is pr...

We prove that arbitrary homomorphisms from one of the groups Homeo(2), Homeo(2), Aut(Q, <), Homeo(R) or Homeo(S) into a separable group are automatically continuous. This has consequences for the representations of these groups as discrete groups. For example, it follows, in combination with a result of V. G. Pestov, that any action of the discrete group Homeo+(R) by homeomorphisms on a compact...

In this paper we present an algorithm for the detection of fish otolith growth rings based on a graph construction method. The identification of growth rings, for age estimation, is routinely achieved in fishery laboratories by human readers. One of the major problem encountered during an automatic image processing is the lack of ring continuity perception. We present an approach to this contin...

As part of a project on automatic generation of proofs involving both logic and computation, we have automated the production of some proofs involving epsilon-delta arguments. These proofs involve two or three quantifiers on the logical side, and on the computational side, they involve algebra, trigonometry, and some calculus. At the border of logic and computation, they involve several types o...

We show that any homomorphism from the homeomorphism group of a compact 2-manifold, with the compact-open topology, or equivalently, with the topology of uniform convergence, into a separable topological group is automatically continuous.

Let A be a C-algebra acting on a Hilbert space H, σ : A → B(H) be a linear mapping and d : A → B(H) be a σ-derivation. Generalizing the celebrated theorem of Sakai, we prove that if σ is a continuous ∗-mapping then d is automatically continuous. In addition, we show the converse is true in the sense that if d is a continuous ∗-σ-derivation then there exists a continuous linear mapping Σ : A → B...