3D environments provide new possibilities for musical interaction. They allow musicians to manipulate and visualize large sets of sound processes associated to 3D objects by connecting graphical parameters to sound parameters. Several of these audiovisual mappings can be combined on a single 3D object. However, this brings up the issues of the choice of these mappings and of their combinations....

Music is one of the strongest triggers of emotions. Recent studies have shown strong emotional predispositions for musical instrument timbres. They have also shown significant correlations between spectral centroid and many emotions. Our recent study on spectral centroid-equalized tones further suggested that the even/odd harmonic ratio is a salient timbral feature after attack time and brightn...

We present a controlled experiment that measures the effect, on retrieval effectiveness and efficiency, of varying the maximum keyword number used to represent documents in Web search engines. We defined a general methodology to quantitatively evaluate the impact of a given design option on the retrieval effectiveness-efficiency trad-offs, and apply to this particular case of centroid size. The...

ranking fuzzy numbers plays a very important role in decision making and some other fuzzy application systems. many different methods have been proposed to deal with ranking fuzzy numbers. constructing ranking indexes based on the centroid of fuzzy numbers is an important case. but some weaknesses are found in these indexes. the purpose of this paper is to give a new ranking index to rank vario...

We introduce a novel parametric family of symmetric information-theoretic distances based on Jensen’s inequality for a convex functional generator. In particular, this family unifies the celebrated Jeffreys divergence with the Jensen-Shannon divergence when the Shannon entropy generator is chosen. We then design a generic algorithm to compute the unique centroid defined as the minimum average d...

Ah&act-If a point is picked at random inside a regular simplex, octahedron, 600-cell, or other polytope, what is its average squared distance from the centroid? In n-dimensional space, what is the average squared distance of a random point from the closest point of the lattice A, (or D,, , En, A: or D,*)? The answers are given here, together with a description of the Voronoi (or nearest neighbo...

Consider convex plane domains D(t) = (1− t)D0 + tD1, 0 ≤ t ≤ 1. We first prove that the 1/4-power of the polar moment of inertia about the centroid of D(t) is concave in t. From this we deduce some isoperimetric inequalities.