This paper summarizes work on a parallel algorithm for an interacting particle model, derived from the model by Czirok, Vicsek, et. al. [13] [3] [14] [4] [5]. Our model is particularly geared toward simulating the behavior of sh in large shoals. In this paper, the back- ground and motivation for the problem are given, as well as an introduction to the mathematical model. A discussion of implementing this model in MATLAB and C++ follows. The parallel implementation is discussed with challenges particular to this mathematical model and how the authors addressed these challenges. Both static and dynamic load balancing were performed and are discussed. Finally, a performance analysis follows, using a performance metric to compare the MATLAB, C++, and parallelized code.

The analysis of graphs has become increasingly important to a wide range of applications. Graph analysis presents a number of unique challenges in the areas of (1) software complexity, (2) data complexity, (3) security, (4) mathematical complexity, (5) theoretical analysis, (6) serial performance, and (7) parallel performance. Implementing graph algorithms using matrix-based approaches provides a number of promising solutions to these challenges. The GraphBLAS standard (istcbigdata.org/GraphBlas) is being developed to bring the potential of matrix based graph algorithms to the broadest possible audience. The GraphBLAS mathematically defines a core set of matrix-based graph operations that can be used to implement a wide class of graph algorithms in a wide range of programming environments. This paper provides an introduction to the GraphBLAS and describes how the GraphBLAS can be used to address many of the challenges associated with analysis of graphs.

The GraphBLAS standard (GraphBlas.org) is being developed to bring the potential of matrix-based graph algorithms to the broadest possible audience. Mathematically, the GraphBLAS defines a core set of matrix-based graph operations that can be used to implement a wide class of graph algorithms in a wide range of programming environments. This paper provides an introduction to the mathematics of the GraphBLAS. Graphs represent connections between vertices with edges. Matrices can represent a wide range of graphs using adjacency matrices or incidence matrices. Adjacency matrices are often easier to analyze while incidence matrices are often better for representing data. Fortunately, the two are easily connected by matrix multiplication. A key feature of matrix mathematics is that a very small number of matrix operations can be used to manipulate a very wide range of graphs. This composability of a small number of operations is the foundation of the GraphBLAS. A standard such as the GraphBLAS can only be effective if it has low performance overhead. Performance measurements of prototype GraphBLAS implementations indicate that the overhead is low.

A germline mutation in the 3'-untranslated region of KRAS (rs61764370, KRAS-variant: TG/GG) has previously been associated with altered patient outcome and drug resistance/sensitivity in various cancers. We examined the prognostic and predictive significance of this variant in recurrent/metastatic (R/M) head and neck squamous cell carcinoma (HNSCC).

Patients and methods

We conducted a retrospective study of 103 HNSCCs collected from three completed clinical trials. KRAS-variant genotyping was conducted for these samples and 8 HNSCC cell lines. p16 expression was determined in a subset of 26 oropharynx tumors by immunohistochemistry. Microarray analysis was also utilized to elucidate differentially expressed genes between KRAS-variant and non-variant tumors. Drug sensitivity in cell lines was evaluated to confirm clinical findings.

Results

KRAS-variant status was determined in 95/103 (92%) of the HNSCC tumor samples and the allelic frequency of TG/GG was 32% (30/95). Three of the HNSCC cell lines (3/8) studied had the KRAS-variant. No association between KRAS-variant status and p16 expression was observed in the oropharynx subset (Fisher's exact test, P = 1.0). With respect to patient outcome, patients with the KRAS-variant had poor progression-free survival when treated with cisplatin (log-rank P = 0.002). Conversely, KRAS-variant patients appeared to experience some improvement in disease control when cetuximab was added to their platinum-based regimen (log-rank P = 0.04).

Conclusions

The TG/GG rs61764370 KRAS-variant is a potential predictive biomarker for poor platinum response in R/M HNSCC patients.