Statistics on Partitions Arising from Seaweed Algebras

Using the index theory of seaweed algebras, we explore various new partition statistics. We find relations to some well-known families of partitions as well as a surprising periodicity result.

On the largest part size and its multiplicity of a random integer partition

Let λ be a partition of the positive integer n chosen uniformly at random among all such partitions. Let Ln = Ln(λ) and Mn = Mn(λ) be the largest part size and its multiplicity, respectively. For large n, we focus on a comparison between the partition statistics Ln and LnMn. In terms of convergence in distribution, we show that they behave in the same way. However, it turns out that the expectation of LnMn – Ln grows as fast as {1 \over 2}\log n . We obtain a precise asymptotic expansion for this expectation and conclude with an open problem arising from this study.

Extracting Flooded Roads by Fusing GPS Trajectories and Road Network

Urban roads are the lifeline of urban transportation and satisfy the commuting and travel needs of citizens. Following the acceleration of urbanization and the frequent extreme weather in recent years, urban waterlogging is occurring more than usual in summer and has negative effects on the urban traffic networks. Extracting flooded roads is a critical procedure for improving the resistance ability of roads after urban waterlogging occurs. This paper proposes a flooded road extraction method to extract the flooding degree and the time at which roads become flooded in large urban areas by using global positioning system (GPS) trajectory points with driving status information and the high position accuracy of vector road data with semantic information. This method uses partition statistics to create density grids (grid layer) and uses map matching to construct a time-series of GPS trajectory point density for each road (vector layer). Finally, the fusion of grids and vector layers obtains a more accurate result. The experiment uses a dataset of GPS trajectory points and vector road data in the Wuchang district, which proves that the extraction result has a high similarity with respect to the flooded roads reported in the news. Additionally, extracted flooded roads that were not reported in the news were also found. Compared with the traditional methods for extracting flooded roads and areas, such as rainfall simulation and SAR image-based classification in urban areas, the proposed method discovers hidden flooding information from geospatial big data, uploaded at no cost by urban taxis and remaining stable for a long period of time.

OLAPS: Online load-balancing in range-partitioned main memory database with approximate partition statistics

Modern database systems can achieve high throughput main-memory query execution by being aware of the dynamics of highly parallel hardware. In such systems, data is partitioned into smaller pieces to reach a better parallelism. Unfortunately, data skew is one of the main problems faced during parallel processing in a parallel main memory database. In some data-intensive applications, parallel range queries over a dynamic range partitioned system are important. Continuous insertions/deletions can lead to a very high degree of data skew and consequently a poor performance of parallel range queries. In this paper, we propose an approach for maintaining balanced loads over a set of nodes as in a system of communicating vessels, by migrating tuples between neighboring nodes. These frequent (or even continuous) data transfers inevitably involve dynamic changes in the partition statistics. To avoid the performance degradation typically associated with this dynamism, we provide a solution based on an approximate Partition Statistics Table. The basic idea behind this table is that both clients and nodes may have an imperfect knowledge about the effective load distribution. They can nevertheless locate any data with almost the same efficiency as using exact partition statistics. Furthermore, maintaining load distribution statistics do not require exchanging additional messages as opposed to the cost of efficient solutions from the state-of-art (which requires at least O(logn) messages). We show through intensive experiments that our proposal supports efficient range queries, while simultaneously guaranteeing storage balance even in the presence of numerous concurrent insertions/deletions generating a heavy skewed data distribution.

A General Asymptotic Scheme for the Analysis of Partition Statistics

We consider statistical properties of random integer partitions. In order to compute means, variances and higher moments of various partition statistics, one often has to study generating functions of the form P(x)F(x), where P(x) is the generating function for the number of partitions. In this paper, we show how asymptotic expansions can be obtained in a quasi-automatic way from expansions of F(x) around x = 1, which parallels the classical singularity analysis of Flajolet and Odlyzko in many ways. Numerous examples from the literature, as well as some new statistics, are treated via this methodology. In addition, we show how to compute further terms in the asymptotic expansions of previously studied partition statistics.