Viral B. Shah

USING CIRCUIT THEORY TO MODEL CONNECTIVITY IN ECOLOGY, EVOLUTION, AND CONSERVATION

Connectivity among populations and habitats is important for a wide range of ecological processes. Understanding, preserving, and restoring connectivity in complex landscapes requires connectivity models and metrics that are reliable, efficient, and process based. We introduce a new class of ecological connectivity models based in electrical circuit theory. Although they have been applied in other disciplines, circuit-theoretic connectivity models are new to ecology. They offer distinct advantages over common analytic connectivity models, including a theoretical basis in random walk theory and an ability to evaluate contributions of multiple dispersal pathways. Resistance, current, and voltage calculated across graphs or raster grids can be related to ecological processes (such as individual movement and gene flow) that occur across large population networks or landscapes. Efficient algorithms can quickly solve networks with millions of nodes, or landscapes with millions of raster cells. Here we review basic circuit theory, discuss relationships between circuit and random walk theories, and describe applications in ecology, evolution, and conservation. We provide examples of how circuit models can be used to predict movement patterns and fates of random walkers in complex landscapes and to identify important habitat patches and movement corridors for conservation planning.

High-performance graph algorithms from parallel sparse matrices

Large-scale computation on graphs and other discrete structures is becoming increasingly important in many applications, including computational biology, web search, and knowledge discovery. High-performance combinatorial computing is an infant field, in sharp contrast with numerical scientific computing. We argue that many of the tools of high-performance numerical computing - in particular, parallel algorithms and data structures for computation with sparse matrices - can form the nucleus of a robust infrastructure for parallel computing on graphs. We demonstrate this with an implementation of a graph analysis benchmark using the sparse matrix infrastructure in Star-P, our parallel dialect of the MATLAB programming language.

Sparse matrices in Matlab*P: design and implementation

Matlab*P is a flexible interactive system that enables computational scientists and engineers to use a high-level language to program cluster computers The Matlab*P user writes code in the Matlab language Parallelism is available via data-parallel operations on distributed objects and via task-parallel operations on multiple objects Matlab*P can store distributed matrices in either full or sparse format As in Matlab, most matrix operations apply equally to full or sparse operands Here, we describe the design and implementation of Matlab*Ps sparse matrix support, and an application to a problem in computational fluid dynamics.

A Unified Framework for Numerical and Combinatorial Computing

A rich variety of tools help researchers with high-performance numerical computing, but few tools exist for large-scale combinatorial computing. The authors describe their efforts to build a common infrastructure for numerical and combinatorial computing by using parallel sparse matrices to implement parallel graph algorithms.

13. Implementing Sparse Matrices for Graph Algorithms

Sparse matrices are a key data structure for implementing graph algorithms using linear algebra. This chapter reviews and evaluates storage formats for sparse matrices and their impact on primitive operations. We present complexity results of these operations on different sparse storage formats both in the random access memory (RAM) model and in the input/output (I/O) model. RAM complexity results were known except for the analysis of sparse matrix indexing. On the other hand, most of the I/O complexity results presented are new. The chapter focuses on different variations of the triples (coordinates) format and the widely used compressed sparse row (CSR) and compressed sparse column (CSC) formats. For most primitives, we provide detailed pseudocodes for implementing them on triples and CSR/CSC.

gflow: software for modelling circuit theory‐based connectivity at any scale

Summary Increasing habitat connectivity is important for mitigating the effects of climate change, landscape fragmentation and habitat loss for biodiversity conservation. However, modelling connectivity at the relevant scales over which these threats occur has been limited by computational requirements. Here, we introduce the open-source software gflow, which massively parallelizes the computation of circuit theory-based connectivity. The software is developed for high-performance computing, but scales to consumer-grade desktop computers running modern Linux or Mac OS X operating systems. We report high computational efficiency representing a 173× speedup over existing software using high-performance computing and a 8·4× speedup using a desktop computer while drastically reducing memory requirements. gflow allows large-extent and high-resolution connectivity problems to be calculated over many iterations and at multiple scales. We envision gflow being immediately useful for large-landscape efforts, including climate-driven animal range shifts, multitaxa connectivity, and for the many developing use-cases of circuit theory-based connectivity.

An Interactive Environment to Manipulate Large Graphs

Interactive environments such as Matlab and Star-P have made numerical computing tremendously accessible to engineers and scientists. They allow people who are not well-versed in the art of numerical computing to nonetheless reap the benefits of numerical computing. The same is not true in general for combinatorial computing. Often, many interesting problems require a mix of numerical and combinatorial computing. Tools developed for numerical computing - such as sparse matrix algorithms - can also be used to develop a comprehensive infrastructure for graph algorithms. We describe the current status of our effort to build a comprehensive infrastructure for operations on large graphs in an interactive parallel environment such as Star-P.

Asset Pricing in an Exchange Economy with Bayesian Agents

This paper extends the standard Mehra-Prescott one-good, pure exchange economy to the case where agents are assumed to be in ignorance of the true transition probabilities of the growth rate of output and to learn them using bayes rule. The main conclusion is that the proposed bayes model yields asset prices and equity premium that are nearly identical to the one in the standard model when the expected transition probabilities of the former equals the transition probabilities of the latter.

Julia: dynamism and performance reconciled by design

Julia is a programming language for the scientific community that combines features of productivity languages, such as Python or MATLAB, with characteristics of performance-oriented languages, such as C++ or Fortran. Julias productivity features include: dynamic typing, automatic memory management, rich type annotations, and multiple dispatch. At the same time, Julia allows programmers to control memory layout and leverages a specializing just-in-time compiler to eliminate much of the overhead of those features. This paper details the design choices made by the creators of Julia and reflects on the implications of those choices for performance and usability.

Circuit-theory applications to connectivity science and conservation

Conservation practitioners have long recognized ecological connectivity as a global priority for preserving biodiversity and ecosystem function. In the early years of conservation science, ecologists extended principles of island biogeography to assess connectivity based on source patch proximity and other metrics derived from binary maps of habitat. From 2006 to 2008, the late Brad McRae introduced circuit theory as an alternative approach to model gene flow and the dispersal or movement routes of organisms. He posited concepts and metrics from electrical circuit theory as a robust way to quantify movement across multiple possible paths in a landscape, not just a single least-cost path or corridor. Circuit theory offers many theoretical, conceptual, and practical linkages to conservation science. We reviewed 459 recent studies citing circuit theory or the open-source software Circuitscape. We focused on applications of circuit theory to the science and practice of connectivity conservation, including topics in landscape and population genetics, movement and dispersal paths of organisms, anthropogenic barriers to connectivity, fire behavior, water flow, and ecosystem services. Circuit theory is likely to have an effect on conservation science and practitioners through improved insights into landscape dynamics, animal movement, and habitat-use studies and through the development of new software tools for data analysis and visualization. The influence of circuit theory on conservation comes from the theoretical basis and elegance of the approach and the powerful collaborations and active user community that have emerged. Circuit theory provides a springboard for ecological understanding and will remain an important conservation tool for researchers and practitioners around the globe.