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November 27, 2014 (v1)PublicationUploaded on: December 4, 2022
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May 19, 2017 (v1)Publication
We study the application of the continuous wavelet transform to perform signal 1ltering processes. We 1rst show that the convolution and correlation of two wavelet functions satisfy the required admissibility and regularity conditions. By using these new wavelet functions to analyze both convolutions and correlations, respectively, we derive...
Uploaded on: March 27, 2023 -
May 30, 2018 (v1)Publication
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Uploaded on: March 27, 2023 -
September 14, 2021 (v1)Publication
In this work we present the notion of greyscale of a graph as a colouring of its vertices that uses colours from the real interval [0,1]. Any greyscale induces another colouring by assigning to each edge the non-negative dif- ference between the colours of its vertices. These edge colours are ordered in lexicographical decreasing ordering and...
Uploaded on: March 25, 2023 -
September 21, 2023 (v1)Publication
In this paper we present the notion of greyscale of a graph as a colouring of its vertices that uses colours from the real interval [0,1]. Any greyscale induces another colouring by assigning to each edge the non-negative difference between the colours of its vertices. These edge colours are ordered in lexicographical decreasing ordering and...
Uploaded on: October 11, 2023 -
September 14, 2021 (v1)Publication
In this paper,we present the notion of greyscale of a graph, as a colouring of its vertices that uses colours from the continuous spectrum [0, 1]. Any greyscale induces another colouring by assigning to each edge the non-negative difference between the colours of its vertices. These edge colours are ordered in lexicographical increasing order...
Uploaded on: March 25, 2023 -
February 2, 2016 (v1)Publication
A graph G is said to be grid locatable if it admits a representation such that vertices are mapped to grid points and edges to line segments that avoid grid points but the extremes. Additionally G is said to be properly embeddable in the grid if it is grid locatable and the segments representing edges do not cross each other. We study the area...
Uploaded on: December 5, 2022 -
March 18, 2016 (v1)Publication
Given a bicolored point set S, it is not always possible to construct a monochromatic geometric planar k-factor of S. We consider the problem of finding such a k-factor of S by using auxiliary points. Two types are considered: white points whose position is fixed, and Steiner points which have no fixed position. Our approach provides algorithms...
Uploaded on: December 4, 2022 -
February 12, 2016 (v1)Publication
We study the existence of monochromatic planar geometric k-factors on sets of red and blue points. When it is not possible to find a k-factor we make use of auxiliary points: white points, whose position is given as a datum and which color is free; and Steiner points whose position and color is free. We present bounds on the number of white...
Uploaded on: December 5, 2022 -
May 20, 2021 (v1)Publication
Apico-basal cell intercalations (scutoids) optimize packing and energy expenditure in curved epithelia. Further consequences of this new paradigm of tissue packing remain uncharacterized. In particular, how scutoids modify the 3D cellular connectivity is an open question. This property is crucial for understanding epithelial architecture and is...
Uploaded on: March 25, 2023