scholarly journals Visualisation of Collage Grammar to CellWorks: ET0L Mode and Part Sensitive Mode

2017 ◽  
Vol 16 (3) ◽  
pp. 47-56
Author(s):  
Ann Susa Thomas
Keyword(s):  
Computer Science ◽  
Human Life ◽  
Three Dimensional ◽  
Theoretical Computer Science ◽  
Two Dimensional ◽  
Theoretical Computer ◽  
Finite Set ◽  
A Cell ◽  
Hyperedge Replacement ◽  
Better Than

Images are an important aspect of human life as one remembers pictures better than words. Informally, a twodimensional string is called a picture. A two-dimensional language (or picture language) is a set of pictures. Picture generation and analysis has become a widely investigated field in Theoretical Computer Science and in Mathematics. Collage grammars are studied as devices that generate pictures by rewriting based on hyperedge replacement. A cell-work is a finite set of cells where each cell (being a three dimensional entity) is surrounded by one or more faces. This paper focuses on how cell work languages can be captured by collage grammar in ET0L and Part Sensitive modes.

scholarly journals On the Prefix–Suffix Duplication Reduction

2020 ◽  
Vol 31 (01) ◽  
pp. 91-102
Author(s):  
Szilárd Zsolt Fazekas ◽  
Robert Mercaş ◽  
Daniel Reidenbach
Keyword(s):  
Computer Science ◽  
Theoretical Computer Science ◽  
Theoretical Computer ◽  
Square Roots ◽  
Context Free Language ◽  
Finite Set ◽  
Context Free ◽  
Free Language

This work answers some questions proposed by Bottoni, Labella, and Mitrana (Theoretical Computer Science 682, 2017) regarding the prefix–suffix reduction on words. The operation is defined as a reduction by one half of every square that is present as either a prefix or a suffix of a word, leading thus to a finite set of words associated to the starting one. The iterated case considers consecutive applications of the operations, on all the resulting words. We show that the classes of linear and context-free language are closed under iterated bounded prefix–suffix square reduction, and that for a given word we can determine in [Formula: see text] time all of its primitive prefix–suffix square roots.

scholarly journals Do 3D Face Images Capture Cues of Strength, Weight, and Height Better than 2D Face Images do?

2021 ◽  
Vol 7 (3) ◽  
pp. 209-219
Author(s):  
Iris J Holzleitner ◽  
Alex L Jones ◽  
Kieran J O’Shea ◽  
Rachel Cassar ◽  
Vanessa Fasolt ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Physical Characteristics ◽  
Two Dimensional ◽  
3D Images ◽  
3D Face ◽  
Face Images ◽  
Similar Accuracy ◽  
2D And 3D ◽  
2D Images ◽  
Better Than

Abstract Objectives A large literature exists investigating the extent to which physical characteristics (e.g., strength, weight, and height) can be accurately assessed from face images. While most of these studies have employed two-dimensional (2D) face images as stimuli, some recent studies have used three-dimensional (3D) face images because they may contain cues not visible in 2D face images. As equipment required for 3D face images is considerably more expensive than that required for 2D face images, we here investigated how perceptual ratings of physical characteristics from 2D and 3D face images compare. Methods We tested whether 3D face images capture cues of strength, weight, and height better than 2D face images do by directly comparing the accuracy of strength, weight, and height ratings of 182 2D and 3D face images taken simultaneously. Strength, height and weight were rated by 66, 59 and 52 raters respectively, who viewed both 2D and 3D images. Results In line with previous studies, we found that weight and height can be judged somewhat accurately from faces; contrary to previous research, we found that people were relatively inaccurate at assessing strength. We found no evidence that physical characteristics could be judged more accurately from 3D than 2D images. Conclusion Our results suggest physical characteristics are perceived with similar accuracy from 2D and 3D face images. They also suggest that the substantial costs associated with collecting 3D face scans may not be justified for research on the accuracy of facial judgments of physical characteristics.

scholarly journals Optimization Over the Boolean Hypercube Via Sums of Nonnegative Circuit Polynomials

2021 ◽  
Author(s):  
Mareike Dressler ◽  
Adam Kurpisz ◽  
Timo de Wolff
Keyword(s):  
Computer Science ◽  
Affine Transformation ◽  
Optimization Problems ◽  
Polynomial Optimization ◽  
Theoretical Computer Science ◽  
Sums Of Squares ◽  
Theoretical Computer ◽  
Complexity Bounds ◽  
Polynomial Optimization Problems ◽  
Transformation Of Variables

AbstractVarious key problems from theoretical computer science can be expressed as polynomial optimization problems over the boolean hypercube. One particularly successful way to prove complexity bounds for these types of problems is based on sums of squares (SOS) as nonnegativity certificates. In this article, we initiate optimization problems over the boolean hypercube via a recent, alternative certificate called sums of nonnegative circuit polynomials (SONC). We show that key results for SOS-based certificates remain valid: First, for polynomials, which are nonnegative over the n-variate boolean hypercube with constraints of degree d there exists a SONC certificate of degree at most $$n+d$$ n + d . Second, if there exists a degree d SONC certificate for nonnegativity of a polynomial over the boolean hypercube, then there also exists a short degree d SONC certificate that includes at most $$n^{O(d)}$$ n O ( d ) nonnegative circuit polynomials. Moreover, we prove that, in opposite to SOS, the SONC cone is not closed under taking affine transformation of variables and that for SONC there does not exist an equivalent to Putinar’s Positivstellensatz for SOS. We discuss these results from both the algebraic and the optimization perspective.

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