The Movement of Dance

These series of paintings displays a way skeletons can be shown and not just associated with death but in a fun and whimsical way shown through dance. I am making are about full body portraits of skeletons that are in costumes while in dancing poses. This is similar to the pictures in dance institution of the dancer. The influence comes from my own childhood with dancing is shared by using the colors of the costumes as very bright colors. The usage of the skeletons is the purest form of the body which can represent anyone and can feel more related towards the work. I like to play with the anatomy of the still figure and use movement in the figure much like Cezanne’s paintings were with color movement. Degas is another influence for my series because he works with dancers and their environment they’re in. The brush strokes of Cezanne and colors he used will he bought in through my background and figure with neutrals will balance out the costumes.The colors of the background is supposed to show movement more than the skeletons itself but isn’t the most important movement of the painting. The costumes that are vibrant also shows movement happening as well. The different dances I will be showing in the series is ballet, tap and jazz. The dances poses that are picked resonances with me because those were the very first dance styles I’ve learned. Conclusion: The body of work focuses on movement of the form and background. With the background the form compliment each other to show a tonality through action

Phase transition in a sequential assignment problem on graphs

We study the following sequential assignment problem on a finite graph G = (V ,E). Each edge e ∈ E starts with an integer value n e ≥ 0, and we write n =∑ e∈En e. At time t, 1 ≤ t ≤ n, a uniformly random vertex v ∈ V is generated, and one of the edges f incident with v must be selected. The value of f is then decreased by 1. There is a unit final reward if the configuration (0, . . . , 0) is reached. Our main result is that there is a phase transition: as n←∞, the expected reward under the optimal policy approaches a constant c G &gt; 0 when (n e/n : e ∈ E) converges to a point in the interior of a certain convex set R G, and goes to 0 exponentially when (n e/n : e ∈ E) is bounded away from R G. We also obtain estimates in the near-critical region, that is when (n e/n : e ∈ E) lies close to ∂R G. We supply quantitative error bounds in our arguments. </p

Sandpile models

This survey is an extended version of lectures given at the Cornell Probability Summer School 2013. The fundamental facts about the Abelian sandpile model on a finite graph and its connections to related models are presented. We discuss exactly computable results via Majumdar and Dhar's method. The main ideas of Priezzhev's computation of the height probabilities in 2D are also presented, including explicit error estimates involved in passing to the limit of the infinite lattice. We also discuss various questions arising on infinite graphs, such as convergence to a sandpile measure, and stabilizability of infinite configurations

Toppling and height probabilities in sandpiles

We study Abelian sandpiles numerically, using exact sampling. Our method uses a combination of Wilson's algorithm to generate uniformly distributed spanning trees, and Majumdar and Dhar's bijection with sandpiles. We study the probability of topplings of individual vertices in avalanches initiated at the centre of large cubic lattices in dimensions d = 2, 3 and 5. Based on these, we estimate the values of the toppling probability exponent in the infinite volume limit in dimensions d = 2, 3, and find good agreement with theoretical results on the mean-field value of the exponent in d ≥ 5. We also study the distribution of the number of waves in 2D avalanches. Our simulation method, combined with a variance reduction idea, lends itself well to studying some problems even in very high dimensions. We illustrate this with an estimation of the single site height probability distribution in d = 32, and compare this to the asymptotic behaviour as d → ∞

The lowest crossing in 2D critical percolation

We study the following problem for critical site percolation on the triangular lattice. Let A and B be sites on a horizontal line e separated by distance n. Consider, in the half-plane above e, the lowest occupied crossing R from the half-line left of A to the half-line right of B. We show that the probability that R has a site at distance smaller than m from AB is of order (log (n/m))^{-1}, uniformly in 1 <= m < n/2. Much of our analysis can be carried out for other two-dimensional lattices as well.Comment: 16 pages, Latex, 2 eps figures, special macros: percmac.tex. Submitted to Annals of Probabilit

Geometry of uniform spanning forest components in high dimensions

We study the geometry of the component of the origin in the uniform spanning forest of Z^d and give bounds on the size of balls in the intrinsic metric.<br/