http://popups.lib.uliege.be/1373-5411/index.php?id=1936 Index terms fr 0 http://popups.lib.uliege.be/1373-5411/index.php?id=1934 The problem of recognition of geometrical objects in different types of data and signals is considered. The main tool in the proposed methodology is a new definition of a cluster based on the invariants of some transformations of space. The invariant properties are closely connected to the symmetry groups of objects. As an illustration, the classical symmetries of space such as continuous groups (Lie transformations) are considered. The particular case of spike recognition in neurophysiology is described in details. Preliminary investigations show the high potential power of method. The further prospects of the proposed method are discussed including the problem of perception and models of mentality. Wed, 17 Jul 2024 15:05:56 +0200 Thu, 10 Oct 2024 10:49:15 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=1934 http://popups.lib.uliege.be/1373-5411/index.php?id=1388 This conference highlights a compositional approach recovering and developping the hypothesis of an organic principle of the melody. Unlike the usual methods, which differentiates the organization of notes and rhythm, this principle is characterized by a strong structuration binding the notes and their respective locations in time. Its application reveals a representation of melodic objects in a geometrical space, objects called solid melodies, by analogy to the visual space. Thus, melodic objects can be observed and manipulated by mathematical transformation tools which respect their internal structures or, on the contrary, break them. One of the most interesting function taking advantage of this musical material, preventing any damage to it, is rotation. Its interest is multiple in composition: first, it generalizes the four symmetrical forms used in traditional counterpoint, second, it allows a meticulous understanding of melodic objects, facilitated by the simplicity of the processes used. Finally, this function allows a musical kinematics with succession of images obtained by rotations of an unique basic object. The comparison between visual space and sound space becomes a fertile source for the construction and the manipulation of new sound buildings. Thu, 11 Jul 2024 16:15:14 +0200 Mon, 07 Oct 2024 15:45:28 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=1388 http://popups.lib.uliege.be/1373-5411/index.php?id=3964 The antique study of geometric properties of symmetries continued by algebra with the group theory, and then with matrix calculus. The present paper illustrates new trends in the study of symmetry concept and its implication in explanation of the matter structure and of the evolutionary phenomena from nature. It is well known that in 2008 the Nobel Prize in Physics was awarded for the discovery of the mechanism of spontaneous broken symmetry in subatomic physics. As an introduction to the necessity to study symmetryn ot for static states only, but also for dynamic systems, the paper presents the philosophical concept of the symmetry of senses in the profound matter. For the dynamical systems, the definition of the symmetry by anticipation and retardation belong to the author. Certain cases when the symmetrical evolution of two conjugate systems is broken are indicated in a mathematical model. Tue, 01 Oct 2024 16:54:19 +0200 Tue, 01 Oct 2024 16:54:32 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=3964