Abstract Animals can efficiently process sensory stimuli whose attributes vary over orders of magnitude by devoting specific neural pathways to process specific features in parallel. Weakly electric fish offer an attractive model system as electrosensory pyramidal neurons responding to amplitude modulations of their self-generated electric field are organized into three parallel maps of the bod...

Most existing crowd counting methods require object location-level annotation which is labor-intensive and time-consuming to obtain. In contrast, weaker annotations that only label the total count of objects can be easy obtain in many practical scenarios. This paper focuses on problem weakly-supervised learns a model from small amount (fully-supervised) large count-level (weakly-supervised). Ou...

The paper is aimed at studying the topological dimension for sets definable in weakly o-minimal structures in order to prepare background for further investigation of groups, group actions and fields definable in the weakly o-minimal context. We prove that the topological dimension of a set definable in a weakly o-minimal structure is invariant under definable injective maps, strengthening an a...

We argue that combinatorial maps theory is mathematical challenge that is not sufficiently developed but rather is some unreasonably unattended or weakly supported by interest of researchers area of mathematics.

We study Dirac-harmonic maps from a Riemann surface to a sphere Sn. We show that a weakly Dirac-harmonic map is in fact smooth, and prove that the energy identity holds during the blow-up process.

The purpose of this paper is to establish a common fixed point theorem for pairs of weakly compatible maps in dislocated metric space which generalizes and improves similar fixed point results. 2000 Mathematics Subject Classification: 47H10, 54H25.

The purpose of this paper is to obtain some common fixed point theorems under weaker conditions such as sub compatible mappings and weakly commuting with respect g in the setting of non normal cone metric space.

Harmonic maps between Riemannian manifolds are maps which extremize a certain natural energy functional; they appear in particle physics as nonlinear sigma models. Their infinitesimal deformations are called Jacobi fields. It is important to know whether the Jacobi fields along the harmonic maps between given Riemannian manifolds are integrable, i.e., arise from genuine variations through harmo...