Babette\u27s Feast: The Persistence of Love

In lieu of an abstract, below is the essay\u27s first paragraph. After one\u27s first viewing of Babette\u27s Feast, a film by Gabriel Axel, one may easily think that the main point of the film revolves around interpretation of religion and food. Although these certainly are two major aspects, I personally found that in many ways, love and the way it persists through time is a major feature of the movie as well. Thanks to Axel, the movie can be viewed through the lends of love, and as the plot unfolds, it becomes more obvious that the persistence of love is a point Axel wanted to send to his audience

On the complexity of optimal homotopies

In this article, we provide new structural results and algorithms for the Homotopy Height problem. In broad terms, this problem quantifies how much a curve on a surface needs to be stretched to sweep continuously between two positions. More precisely, given two homotopic curves $\gamma_1$ and $\gamma_2$ on a combinatorial (say, triangulated) surface, we investigate the problem of computing a homotopy between $\gamma_1$ and $\gamma_2$ where the length of the longest intermediate curve is minimized. Such optimal homotopies are relevant for a wide range of purposes, from very theoretical questions in quantitative homotopy theory to more practical applications such as similarity measures on meshes and graph searching problems. We prove that Homotopy Height is in the complexity class NP, and the corresponding exponential algorithm is the best one known for this problem. This result builds on a structural theorem on monotonicity of optimal homotopies, which is proved in a companion paper. Then we show that this problem encompasses the Homotopic Fr\'echet distance problem which we therefore also establish to be in NP, answering a question which has previously been considered in several different settings. We also provide an O(log n)-approximation algorithm for Homotopy Height on surfaces by adapting an earlier algorithm of Har-Peled, Nayyeri, Salvatipour and Sidiropoulos in the planar setting

Minimum cycle and homology bases of surface embedded graphs

We study the problems of finding a minimum cycle basis (a minimum weight set of cycles that form a basis for the cycle space) and a minimum homology basis (a minimum weight set of cycles that generates the $1$-dimensional ($\mathbb{Z}_2$)-homology classes) of an undirected graph embedded on a surface. The problems are closely related, because the minimum cycle basis of a graph contains its minimum homology basis, and the minimum homology basis of the $1$-skeleton of any graph is exactly its minimum cycle basis. For the minimum cycle basis problem, we give a deterministic $O(n^\omega+2^{2g}n^2+m)$-time algorithm for graphs embedded on an orientable surface of genus $g$. The best known existing algorithms for surface embedded graphs are those for general graphs: an $O(m^\omega)$ time Monte Carlo algorithm and a deterministic $O(nm^2/\log n + n^2 m)$ time algorithm. For the minimum homology basis problem, we give a deterministic $O((g+b)^3 n \log n + m)$-time algorithm for graphs embedded on an orientable or non-orientable surface of genus $g$ with $b$ boundary components, assuming shortest paths are unique, improving on existing algorithms for many values of $g$ and $n$. The assumption of unique shortest paths can be avoided with high probability using randomization or deterministically by increasing the running time of the homology basis algorithm by a factor of $O(\log n)$.Comment: A preliminary version of this work was presented at the 32nd Annual International Symposium on Computational Geometr

A Thesis is Not a Diary and Other Myths

How do you write about a feeling you do not understand? How do you organize what is purposefully messy? How can you name a ghost of something that you push into the world with your hands? In this thesis, I will explain my practice, form, and material as a way to illuminate my art, along with various readings and philosophies that I use to guide the work

Recruitment, Preparation, Retention: A case study of computing culture at the University of Illinois at Urbana-Champaign

Computer science is seeing a decline in enrollment at all levels of education, including undergraduate and graduate study. This paper reports on the results of a study conducted at the University of Illinois at Urbana-Champaign which evaluated students attitudes regarding three areas which can contribute to improved enrollment in the Department of Computer Science: Recruitment, preparation and retention. The results of our study saw two themes. First, the department's tight research focus appears to draw significant attention from other activities -- such as teaching, service, and other community-building activities -- that are necessary for a department's excellence. Yet, as demonstrated by our second theme, one partial solution is to better promote such activities already employed by the department to its students and faculty. Based on our results, we make recommendations for improvements and enhancements based on the current state of practice at peer institutions.Comment: 37 pages, 13 figures. For better quality figures, please download the .pdf from http://www.cs.uiuc.edu/research/techreports.php?report=UIUCDCS-R-2007-281

Regulation of UV-Protective Pathways Downstream of the Melanocortin 1 Receptor in Melanocytes

Malignant cutaneous melanoma is the deadliest form of skin cancer, and a majority of melanoma diagnoses are a result of exposure to ultraviolet (UV) radiation. UV radiation causes DNA damage, which if not repaired correctly via nucleotide excision repair (NER) can result in mutations and melanomagenesis. The melanocortin 1 receptor (MC1R) is a Gs protein coupled receptor located on melanocyte plasma membranes and is involved in protecting the skin from UV induced damage. MC1R signaling results in the activation of two protective pathways: 1) induction of eumelanin synthesis downstream of micropthalmia-associated transcription factor (MITF) and 2) acceleration of NER downstream of ataxia telangiectaseia mutated and Rad3 related (ATR). MC1R signaling, however, also promotes melanocyte proliferation, therefore, the activation of the MC1R pathway must be regulated. The overall hypothesis of this dissertation is that the pathways downstream of MC1R can be manipulated to protect against UV induced damage. Chapter 2 investigates the regulation of the MC1R neutral antagonist human β-defensin 3 (βD3). UV damage did not induce βD3 mRNA expression in ex vivo human skin explants. The induction of βD3 expression instead correlated with inflammatory cytokines including TNF. Chapter 3 investigates the interdependence and cross talk between the two protective pathways downstream of MC1R. We directly tested the effect of MITF on the acceleration of NER and the effect of ATR on the induction of eumelanin synthesis following MC1R activation. MITF was not required for the acceleration of NER as mediated by ATR, however, the induction of transcription of enzymes involved in eumelanin synthesis was dependent upon ATR kinase activity. Finally, Chapter 4 investigates the mechanism by which MC1R promoted proliferation and whether the two UV protective pathways downstream of MC1R could be selectively activated without the risk of melanocyte proliferation. MC1R signaling resulted in activation of the mechanistic target of rapamycin complex 1 (mTORC1), a major regulator of cell growth and proliferation. Inhibition of mTORC1 signaling via rapamycin prevented MC1R induced proliferation in vitro. Rapamycin, however, did not prevent MC1R induced eumelanin synthesis or the acceleration of NER in vitro or in vivo suggesting it is possible to selectively activate the beneficial signaling pathways without the risk of melanocyte proliferation. The results of this dissertation suggest that MC1R signaling could be augmented in individuals to prevent UV induced damage

Constructing monotone homotopies and sweepouts

This article investigates when homotopies can be converted to monotone homotopies without increasing the lengths of curves. A monotone homotopy is one which consists of curves which are simple or constant, and in which curves are pairwise disjoint. We show that, if the boundary of a Riemannian disc can be contracted through curves of length less than $L$, then it can also be contracted monotonously through curves of length less than $L$. This proves a conjecture of Chambers and Rotman. Additionally, any sweepout of a Riemannian $2$-sphere through curves of length less than $L$ can be replaced with a monotone sweepout through curves of length less than $L$. Applications of these results are also discussed.Comment: 16 pages, 6 figure