|
|
 |
|
Jeudi 3 Décembre
| Heure: |
10:00 - 13:00 |
| Lieu: |
Salle B107, bâtiment B, Université de Villetaneuse |
| Résumé: |
Long-range order in random 3-colorings of Z^d [10h-12h] |
| Description: |
Yinon Spinka Consider a random coloring of a bounded domain in Zd with the probability of each coloring F proportional to exp(-?*N(F)), where ?>0 is a parameter (representing the inverse temperature) and N(F) is the number of nea rest neighboring pairs colored by the same color. This is the anti-ferromagnetic 3-state Potts model of statistical physics, used to describe magnetic interactions in a spin system. The Kotecký conjecture is that in such a model, for d?3 and high enough ?, a sampled coloring will typically exhibit long-range order, placing the same color at most of either the even or odd vertices of the domain. We give the first rigorous proof of this fact for large d. This extends previous works of Peled and of Galvin, Kahn, Randall and Sorkin, who treated the case ?=infinity.No background in statistical physics will be assumed and all terms will be explained thoroughly.Joint work with Ohad Feldheim. |
| Heure: |
12:15 - 13:30 |
| Lieu: |
Salle B107, bâtiment B, Université de Villetaneuse |
| Résumé: |
Distributed nearest neighbour mean shift clustering |
| Description: |
Tarn Duong Data clustering is an important tool for extracting meaningful information from large data sets. Despite the popularity of k-means clustering, it possesses two important limitations as it (a) requires a prior choice of the number of clusters and (b) produces only ellipsoidal clusters. Mean shift clustering is a generalisation of k-means which overcomes these limitations by defining clusters via a gradient ascent search of the data density. Nearest neighbour approaches are well-suited to computing the gradient ascent for multivariate data as they adapt to the local data density. On the other hand, the data adaptivity of nearest neighbour mean shift (NNMS) involves a higher computational burden, in terms of execution time and memory than k-means, which has hindered the more widespread use of NN MS. Its computational burden can be reduced with approximate nearest neighbours via random scalar projections (Locality Sensitive Hashing, LSH). To illustrate the feasibility of Big Data Clustering beyond k-means, we implement NNMS-LSH on a distributed Spark Scala ecosystem for multivariate clustering and image segmentation. |
| Heure: |
14:00 - 17:00 |
| Lieu: |
Salle B107, bâtiment B, Université de Villetaneuse |
| Résumé: |
Long-range order in random 3-colorings of Z^d [10h-12h] |
| Description: |
Yinon Spinka Consider a random coloring of a bounded domain in Zd with the probability of each coloring F proportional to exp(-?*N(F)), where ?>0 is a parameter (representing the inverse temperature) and N(F) is the number of nea rest neighboring pairs colored by the same color. This is the anti-ferromagnetic 3-state Potts model of statistical physics, used to describe magnetic interactions in a spin system. The Kotecký conjecture is that in such a model, for d?3 and high enough ?, a sampled coloring will typically exhibit long-range order, placing the same color at most of either the even or odd vertices of the domain. We give the first rigorous proof of this fact for large d. This extends previous works of Peled and of Galvin, Kahn, Randall and Sorkin, who treated the case ?=infinity.No background in statistical physics will be assumed and all terms will be explained thoroughly.Joint work with Ohad Feldheim. |
|
|
