Moerdijk’s site description for equivariant sheaf toposes on open topological groupoids is used to give a proof for the (known, but apparently unpublished) proposition that if H is a subgroupoid of an open topological groupoid G , then the topos of equivariant sheaves on H is a subtopos of the topos of equivariant sheaves on G . This proposition is then applied to the study of quotient geometri...

We discuss when a generic subspace of some fixed proportional dimension of a finite-dimensional normed space can be isomorphic to a generic quotient of some proportional dimension of another space. We show (in Theorem 4.1) that if this happens (for some natural random structures) then for any proportion arbitrarily close to 1, the first space has a lot of Euclidean subspaces and the second spac...

Glottal volume velocity waveform characteristics of 224 subjects, categorized in four groups according to gender and vocal training, were determined, and their relations to sound-pressure level, fundamental frequency, intra-oral pressure, and age were analyzed. Subjects phonated at three intensity conditions. The glottal volume velocity waveforms were obtained by inverse filtering the oral flow...

Let R be a non empty poset. One can verify that there exists an order sorted set of R which is binary relation yielding. Let R be a non empty poset, let A, B be many sorted sets indexed by the carrier of R, and let I1 be a many sorted relation between A and B. We say that I1 is os-compatible if and only if the condition (Def. 1) is satisfied. (Def. 1) Let s1, s2 be elements of the carrier of R....

In this paper we propose a method for blind signal decomposition that does not require the independence or stationarity of the sources. We define suitable quotients of linear combinations of the images of the mixtures in a given frame and we show experimentally that such quotients can be used to recursively extract three sources from only two measurements. A general strategy to extract more tha...

The formulation of trace quotient is shared by many computer vision problems; however, it was conventionally approximated by an essentially different formulation of quotient trace, which can be solved with the generalized eigenvalue decomposition approach. In this paper, we present a direct solution to the former formulation. First, considering that the feasible solutions are constrained on a G...

Given a normed cone (X , p) and a subcone Y, we construct and study the quotient normed cone (X/Y, p̃) generated by Y . In particular we characterize the bicompleteness of (X/Y, p̃) in terms of the bicompleteness of (X , p), and prove that the dual quotient cone ((X/Y )∗,‖ · ‖p̃,u) can be identified as a distinguished subcone of the dual cone (X∗,‖ · ‖p,u). Furthermore, some parts of the theory ar...

Higher inductive types (HITs) in Homotopy Type Theory (HoTT) allow the definition of datatypes which have constructors for equalities over the defined type. HITs generalise quotient types, and allow to define types which are not sets in the sense of HoTT (i.e. do not satisfy uniqueness of equality proofs) such as spheres, suspensions and the torus. However, there are also interesting uses of HI...

In this paper, we present that genotype-phenotype mapping can be theoretically interpreted using the concept of quotient space in mathematics. Quotient space can be considered as mathematically-defined phenotype space in the evolutionary computation theory. The quotient geometric crossover has the effect of reducing the search space actually searched by geometric crossover, and it introduces pr...