The Fisher-KPP equation over simple graphs: Varied persistence states in river networks

In this article, we study the growth and spread of a new species in a river network with two or three branches via the Fisher-KPP advection-diffusion equation over some simple graphs with every edge a half infinite line. We obtain a rather complete description of the long-time dynamical behavior for every case under consideration, which can be loosely described by a trichotomy (see Remark 1.7), including two different kinds of persistence states as parameters vary. The phenomenon of "persistence below carrying capacity" revealed here appears new, which does not occur in related models of the existing literature where the river network is represented by graphs with finite-lengthed edges, or the river network is simplified to a single infinite line

Reshaping limit diagrams and cofinality in higher category theory

We present some results on (co)limits of diagrams in $\infty$-categories, as well as those in $(n, 1)$-categories. In particular, we deduce a way to reshape colimit diagrams into simplicial ones, and a characterizations of $n$-cofinality for functor between $\infty$-categories. Some basics on $n$-siftedness are also briefly treated.Comment: 15 pages, with small correction and addition. Comments are welcom

Hard and Soft Error Resilience for One-sided Dense Linear Algebra Algorithms

Dense matrix factorizations, such as LU, Cholesky and QR, are widely used by scientific applications that require solving systems of linear equations, eigenvalues and linear least squares problems. Such computations are normally carried out on supercomputers, whose ever-growing scale induces a fast decline of the Mean Time To Failure (MTTF). This dissertation develops fault tolerance algorithms for one-sided dense matrix factorizations, which handles Both hard and soft errors. For hard errors, we propose methods based on diskless checkpointing and Algorithm Based Fault Tolerance (ABFT) to provide full matrix protection, including the left and right factor that are normally seen in dense matrix factorizations. A horizontal parallel diskless checkpointing scheme is devised to maintain the checkpoint data with scalable performance and low space overhead, while the ABFT checksum that is generated before the factorization constantly updates itself by the factorization operations to protect the right factor. In addition, without an available fault tolerant MPI supporting environment, we have also integrated the Checkpoint-on-Failure(CoF) mechanism into one-sided dense linear operations such as QR factorization to recover the running stack of the failed MPI process. Soft error is more challenging because of the silent data corruption, which leads to a large area of erroneous data due to error propagation. Full matrix protection is developed where the left factor is protected by column-wise local diskless checkpointing, and the right factor is protected by a combination of a floating point weighted checksum scheme and soft error modeling technique. To allow practical use on large scale system, we have also developed a complexity reduction scheme such that correct computing results can be recovered with low performance overhead. Experiment results on large scale cluster system and multicore+GPGPU hybrid system have confirmed that our hard and soft error fault tolerance algorithms exhibit the expected error correcting capability, low space and performance overhead and compatibility with double precision floating point operation

JVM-based Techniques for Improving Java Observability

Observability measures the support of computer systems to accurately capture, analyze, and present (collectively observe) the internal information about the systems. Observability frameworks play important roles for program understanding, troubleshooting, performance diagnosis, and optimizations. However, traditional solutions are either expensive or coarse-grained, consequently compromising their utility in accommodating today’s increasingly complex software systems. New solutions are emerging for VM-based languages due to the full control language VMs have over program executions. Existing such solutions, nonetheless, still lack flexibility, have high overhead, or provide limited context information for developing powerful dynamic analyses. In this thesis, we present a VM-based infrastructure, called marker tracing framework (MTF), to address the deficiencies in the existing solutions for providing better observability for VM-based languages. MTF serves as a solid foundation for implementing fine-grained low-overhead program instrumentation. Specifically, MTF allows analysis clients to: 1) define custom events with rich semantics ; 2) specify precisely the program locations where the events should trigger; and 3) adaptively enable/disable the instrumentation at runtime. In addition, MTF-based analysis clients are more powerful by having access to all information available to the VM. To demonstrate the utility and effectiveness of MTF, we present two analysis clients: 1) dynamic typestate analysis with adaptive online program analysis (AOPA); and 2) selective probabilistic calling context analysis (SPCC). In addition, we evaluate the runtime performance of MTF and the typestate client with the DaCapo benchmarks. The results show that: 1) MTF has acceptable runtime overhead when tracing moderate numbers of marker events; and 2) AOPA is highly effective in reducing the event frequency for the dynamic typestate analysis; and 3) language VMs can be exploited to offer greater observability