The Monge-Ampere equation: various forms and numerical methods

We present three novel forms of the Monge-Ampere equation, which is used, e.g., in image processing and in reconstruction of mass transportation in the primordial Universe. The central role in this paper is played by our Fourier integral form, for which we establish positivity and sharp bound properties of the kernels. This is the basis for the development of a new method for solving numerically the space-periodic Monge-Ampere problem in an odd-dimensional space. Convergence is illustrated for a test problem of cosmological type, in which a Gaussian distribution of matter is assumed in each localised object, and the right-hand side of the Monge-Ampere equation is a sum of such distributions.Comment: 24 pages, 2 tables, 5 figures, 32 references. Submitted to J. Computational Physics. Times of runs added, multiple improvements of the manuscript implemented

Writing Russia's future: paradigms, drivers, and scenarios

The development of prediction and forecasting in the social sciences over the past century and more is closely linked with developments in Russia. The Soviet collapse undermined confidence in predictive capabilities, and scenario planning emerged as the dominant future-oriented methodology in area studies, including the study of Russia. Scenarists anticipate multiple futures rather than predicting one. The approach is too rarely critiqued. Building on an account of Russia-related forecasting in the twentieth century, analysis of two decades of scenarios reveals uniform accounts which downplay the insights of experts and of social science theory alike

Parallel string graph construction and transitive reduction for de novo genome assembly

One of the most computationally intensive tasks in computational biology is de novo genome assembly, the decoding of the sequence of an unknown genome from redundant and erroneous short sequences. A common assembly paradigm identifies overlapping sequences, simplifies their layout, and creates consensus. Despite many algorithms developed in the literature, the efficient assembly of large genomes is still an open problem. In this work, we introduce new distributed-memory parallel algorithms for overlap detection and layout simplification steps of de novo genome assembly, and implement them in the diBELLA 2D pipeline. Our distributed memory algorithms for both overlap detection and layout simplification are based on linear-algebra operations over semirings using 2D distributed sparse matrices. Our layout step consists of performing a transitive reduction from the overlap graph to a string graph. We provide a detailed communication analysis of the main stages of our new algorithms. diBELLA 2D achieves near linear scaling with over 80% parallel efficiency for the human genome, reducing the runtime for overlap detection by 1.2 - 1.3 × for the human genome and 1.5 - 1.9 × for C.elegans compared to the state-of-the-art. Our transitive reduction algorithm outperforms an existing distributed-memory implementation by 10.5 - 13.3 × for the human genome and 18- 29 × for the C. elegans. Our work paves the way for efficient de novo assembly of large genomes using long reads in distributed memory

High-Productivity and High-Performance Analysis of Filtered Semantic Graphs

Abstract—High performance is a crucial consideration when executing a complex analytic query on a massive semantic graph. In a semantic graph, vertices and edges carry attributes of various types. Analytic queries on semantic graphs typically depend on the values of these attributes; thus, the computation must view the graph through a filter that passes only those individual vertices and edges of interest. Knowledge Discovery Toolbox (KDT), a Python library for parallel graph computations, is customizable in two ways. First, the user can write custom graph algorithms by specifying operations between edges and vertices. These programmer-specified operations are called semiring operations due to KDT’s underlying linear-algebraic abstractions. Second, the user can customize existing graph algorithms by writing filters that return true for those vertices and edges the user wants to retain during algorith