Colorful Strips

Given a planar point set and an integer $k$, we wish to color the points with $k$ colors so that any axis-aligned strip containing enough points contains all colors. The goal is to bound the necessary size of such a strip, as a function of $k$. We show that if the strip size is at least $2k{-}1$, such a coloring can always be found. We prove that the size of the strip is also bounded in any fixed number of dimensions. In contrast to the planar case, we show that deciding whether a 3D point set can be 2-colored so that any strip containing at least three points contains both colors is NP-complete. We also consider the problem of coloring a given set of axis-aligned strips, so that any sufficiently covered point in the plane is covered by $k$ colors. We show that in $d$ dimensions the required coverage is at most $d(k{-}1)+1$. Lower bounds are given for the two problems. This complements recent impossibility results on decomposition of strip coverings with arbitrary orientations. Finally, we study a variant where strips are replaced by wedges

Coloring Hypergraphs Induced by Dynamic Point Sets and Bottomless Rectangles

We consider a coloring problem on dynamic, one-dimensional point sets: points appearing and disappearing on a line at given times. We wish to color them with k colors so that at any time, any sequence of p(k) consecutive points, for some function p, contains at least one point of each color. We prove that no such function p(k) exists in general. However, in the restricted case in which points appear gradually, but never disappear, we give a coloring algorithm guaranteeing the property at any time with p(k)=3k-2. This can be interpreted as coloring point sets in R^2 with k colors such that any bottomless rectangle containing at least 3k-2 points contains at least one point of each color. Here a bottomless rectangle is an axis-aligned rectangle whose bottom edge is below the lowest point of the set. For this problem, we also prove a lower bound p(k)>ck, where c>1.67. Hence for every k there exists a point set, every k-coloring of which is such that there exists a bottomless rectangle containing ck points and missing at least one of the k colors. Chen et al. (2009) proved that no such function $p(k)$ exists in the case of general axis-aligned rectangles. Our result also complements recent results from Keszegh and Palvolgyi on cover-decomposability of octants (2011, 2012).Comment: A preliminary version was presented by a subset of the authors to the European Workshop on Computational Geometry, held in Assisi (Italy) on March 19-21, 201

Polychromatic Coloring for Half-Planes

We prove that for every integer $k$, every finite set of points in the plane can be $k$-colored so that every half-plane that contains at least $2k-1$ points, also contains at least one point from every color class. We also show that the bound $2k-1$ is best possible. This improves the best previously known lower and upper bounds of $\frac{4}{3}k$ and $4k-1$ respectively. We also show that every finite set of half-planes can be $k$ colored so that if a point $p$ belongs to a subset $H_p$ of at least $3k-2$ of the half-planes then $H_p$ contains a half-plane from every color class. This improves the best previously known upper bound of $8k-3$. Another corollary of our first result is a new proof of the existence of small size \eps-nets for points in the plane with respect to half-planes.Comment: 11 pages, 5 figure

A Promenade Through Paris

I have written and illustrated a short story that takes place during one day in Paris, France. The story is drawn from my own experience living in another culture. I have created a main character that brings the reader through the story. Along the way the reader visits wonderful places in the city of Paris and learns snippets about Parisian culture and lifestyle. The text and artwork themselves appear in a book that I have made by hand. I began by inventing a unique paper of a cotton base, lilies, cattails, and other starchy plants. At the end of the process I made over one hundred 5.5” by 8.5” sheets of beige textured paper with fun edges and traces of lilies laced throughout. Then I sewed each page onto colorful strips of cloth and then sewed the cloth together to serve as the binding. The book covers are a hard surface covered with a different and elaborately colorful cloth that is attached to the binding with ribbon. The illustrations are done in various different styles and mediums. Some are shrunken paintings adhered to the paper of the book while others are done directly on the handmade paper. They illustrate many of the scenes, people, places, and events that occur in the story. The text has been adhered into the book on a plain paper that compliments the color of the handmade paper. The story, illustrations, and book combined serve as a creative thesis that reflect more of what my project is and means to me than would a series of paintings

Locked Doors

“No one should die near Eid days,” I climbed up on the charpoy to sit near her while taking the bowl of hot halwa out of my mother’s hands, who, with her stare, told me that I had, yet again, uttered words that I should not have. But ignoring that long and discontented stare, I continued to deliver my thoughts on the funeral announcement just made through the mosque loudspeaker. “It ruins Eid for their loved ones forever. Every year twice, near Eid, their happiness would be overshadowed by the loss.

The LaGuardia - Red Hook Caregiver

Vol. II, No. 3; This document was produced as a result of a training and development project for staff in the social services system through a contractual agreement between the New York State Department of Social Services and the Research Foundation of the City University of New York on behalf of La Guardia Community College. No date, library receipt, 13 September 1979

Modernized Tradition: Transformation of Public Transport

Due to incrementing environmental issues, the Philippine government has aimed solutions for sustainable development by pursuing the Public Utility Vehicle Modernization Program (PUVMP), which was launched in 2017 and took effect in 2020. The program included the modernization of jeepneys, which is a historical icon in the country. The modernization of jeepneys affected jeepney drivers, operators, and commuters alike; thus it is crucial to take their opinions into consideration. In this study, the researchers ought to know the thoughts and opinions of jeepney drivers and commuters concerning the PUVMP in Baguio City. The study that was executed embraced a phenomenological approach. Due to the pandemic the world is facing at present, the responses were gathered using an online survey as it was seen to be fit for the current situation. The results exhibited divided opinions towards the program as drivers and operators were against it, while commuters supported the program. The jeepney drivers and operators used their financial status as a basis for their opinion, while commuters prioritized their safety and comfort. When asked how will they cope with the PUVMP, jeepney drivers showcased a negative array of choices. Their answers varied from complying just because it is what the government wants, opting for illegal schemes to earn money, to losing their jobs completely. The results acquired can be used as a basis for adjustments and changes to produce an ameliorated program which satisfies the needs and wants of the affected groups

Aesthetic aspects for the Mosque of Ibn Tulun and patchwork techniques on contemporary fashion

Islamic art is one of the greatest achievements of the Islamic culture in Egypt. This research concerns the Islamic Geometrical Patterns in the mosque of Ibn Tulun in Cairo, Egypt and summarizes techniques of patchwork in order to demonstrate the significance of patchwork on contemporary fashion. The design project of this research includes 14 contemporary fashion designs for women of the age group (25-35 years). The statistic analysis shows that the designs express the geometrical patterns in the Mosque of Ibn Tulun and patchwork techniques by 96%. It also shows that the designs are suitable for women of the age group (25-35 years) by 95%. Analysis shows that "Design 4" has the lowest mean while “Design 1" has the highest mean