Rewriting for Monoidal Closed Categories

This paper develops a formal string diagram language for monoidal closed categories. Previous work has shown that string diagrams for freely generated symmetric monoidal categories can be viewed as hypergraphs with interfaces, and the axioms of these categories can be realized by rewriting systems. This work proposes hierarchical hypergraphs as a suitable formalization of string diagrams for monoidal closed categories. We then show double pushout rewriting captures the axioms of these closed categories

Parsing of Hyperedge Replacement Grammars with Graph Parser Combinators

Graph parsing is known to be computationally expensive. For this reason the construction of special-purpose parsers may be beneficial for particular graph languages. In the domain of string languages so-called parser combinators are very popular for writing efficient parsers. Inspired by this approach, we have proposed graph parser combinators in a recent paper, a framework for the rapid development of special-purpose graph parsers. Our basic idea has been to define primitive graph parsers for elementary graph components and a set of combinators for the flexible construction of more advanced graph parsers. Following this approach, a declarative, but also more operational description of a graph language can be given that is a parser at the same time. In this paper we address the question how the process of writing correct parsers on top of our framework can be simplified by demonstrating the translation of hyperedge replacement grammars into graph parsers. The result are recursive descent parsers as known from string parsing with some additional nondeterminism

Analysis and Optimization of Scientific Applications through Set and Relation Abstractions

Writing high performance code has steadily become more challenging since the design of computing systems has moved toward parallel processors in forms of multi and many-core architectures. This trend has resulted in exceedingly more heterogeneous architectures and programming models. Moreover, the prevalence of distributed systems, especially in fields relying on supercomputers, has caused the programming of such diverse environment more difficulties. To mitigate such challenges, an assortment of tools and programming models have been introduced in the past decade or so. Some efforts focused on the characteristics of the code, such as polyhedral compilers (e.g. Pluto, PPCG, etc.) while others took in consideration the aspects of the application domain and proposed domain specific languages (DSLs). DSLs are developed either in the form of a stand-alone language, like Halide for image processing, or as a part of a general purpose language (e.g., Firedrake- a DSL embedded in Python for solving PDEs using FEM.) called embedded. All these approaches attempt to provide the best input to the underlying common programming models like MPI and OpenMP for distributed and shared memory systems respectively. This dissertation introduces Kaashi, a high-level run-time system, embedded in C++ language, designed to manage memory and execution order of programs with large input data and complex dependencies. Kaashi provides a uniform front-end to multiple back-ends focusing on distributed systems. Kaashi abstractions allows the programmer to define the problem’s data domain as a collection of sets and relations between pairs of such sets. The aforesaid level of abstraction could enable series of optimizations which, otherwise, are very expensive to detect or not feasible at all. Furthermore, Kaashi’s API helps novice programmers to write their code more structurally without getting involved in details of data management and communication

Hypergraph Partitioning in the Cloud

The thesis investigates the partitioning and load balancing problem which has many applications in High Performance Computing (HPC). The application to be partitioned is described with a graph or hypergraph. The latter is of greater interest as hypergraphs, compared to graphs, have a more general structure and can be used to model more complex relationships between groups of objects such as non-symmetric dependencies. Optimal graph and hypergraph partitioning is known to be NP-Hard but good polynomial time heuristic algorithms have been proposed. In this thesis, we propose two multi-level hypergraph partitioning algorithms. The algorithms are based on rough set clustering techniques. The first algorithm, which is a serial algorithm, obtains high quality partitionings and improves the partitioning cut by up to 71\% compared to the state-of-the-art serial hypergraph partitioning algorithms. Furthermore, the capacity of serial algorithms is limited due to the rapid growth of problem sizes of distributed applications. Consequently, we also propose a parallel hypergraph partitioning algorithm. Considering the generality of the hypergraph model, designing a parallel algorithm is difficult and the available parallel hypergraph algorithms offer less scalability compared to their graph counterparts. The issue is twofold: the parallel algorithm and the complexity of the hypergraph structure. Our parallel algorithm provides a trade-off between global and local vertex clustering decisions. By employing novel techniques and approaches, our algorithm achieves better scalability than the state-of-the-art parallel hypergraph partitioner in the Zoltan tool on a set of benchmarks, especially ones with irregular structure. Furthermore, recent advances in cloud computing and the services they provide have led to a trend in moving HPC and large scale distributed applications into the cloud. Despite its advantages, some aspects of the cloud, such as limited network resources, present a challenge to running communication-intensive applications and make them non-scalable in the cloud. While hypergraph partitioning is proposed as a solution for decreasing the communication overhead within parallel distributed applications, it can also offer advantages for running these applications in the cloud. The partitioning is usually done as a pre-processing step before running the parallel application. As parallel hypergraph partitioning itself is a communication-intensive operation, running it in the cloud is hard and suffers from poor scalability. The thesis also investigates the scalability of parallel hypergraph partitioning algorithms in the cloud, the challenges they present, and proposes solutions to improve the cost/performance ratio for running the partitioning problem in the cloud. Our algorithms are implemented as a new hypergraph partitioning package within Zoltan. It is an open source Linux-based toolkit for parallel partitioning, load balancing and data-management designed at Sandia National Labs. The algorithms are known as FEHG and PFEHG algorithms

Modeling biochemical transformation processes and information processing with Narrator

BACKGROUND: Software tools that model and simulate the dynamics of biological processes and systems are becoming increasingly important. Some of these tools offer sophisticated graphical user interfaces (GUIs), which greatly enhance their acceptance by users. Such GUIs are based on symbolic or graphical notations used to describe, interact and communicate the developed models. Typically, these graphical notations are geared towards conventional biochemical pathway diagrams. They permit the user to represent the transport and transformation of chemical species and to define inhibitory and stimulatory dependencies. A critical weakness of existing tools is their lack of supporting an integrative representation of transport, transformation as well as biological information processing. RESULTS: Narrator is a software tool facilitating the development and simulation of biological systems as Co-dependence models. The Co-dependence Methodology complements the representation of species transport and transformation together with an explicit mechanism to express biological information processing. Thus, Co-dependence models explicitly capture, for instance, signal processing structures and the influence of exogenous factors or events affecting certain parts of a biological system or process. This combined set of features provides the system biologist with a powerful tool to describe and explore the dynamics of life phenomena. Narrator's GUI is based on an expressive graphical notation which forms an integral part of the Co-dependence Methodology. Behind the user-friendly GUI, Narrator hides a flexible feature which makes it relatively easy to map models defined via the graphical notation to mathematical formalisms and languages such as ordinary differential equations, the Systems Biology Markup Language or Gillespie's direct method. This powerful feature facilitates reuse, interoperability and conceptual model development. CONCLUSION: Narrator is a flexible and intuitive systems biology tool. It is specifically intended for users aiming to construct and simulate dynamic models of biology without recourse to extensive mathematical detail. Its design facilitates mappings to different formal languages and frameworks. The combined set of features makes Narrator unique among tools of its kind. Narrator is implemented as Java software program and available as open-source from

Functorial String Diagrams for Reverse-Mode Automatic Differentiation

We formulate a reverse-mode automatic differentiation (RAD) algorithm for (applied) simply typed lambda calculus in the style of Pearlmutter and Siskind [Barak A. Pearlmutter and Jeffrey Mark Siskind, 2008], using the graphical formalism of string diagrams. Thanks to string diagram rewriting, we are able to formally prove for the first time the soundness of such an algorithm. Our approach requires developing a calculus of string diagrams with hierarchical features in the spirit of functorial boxes, in order to model closed monoidal (and cartesian closed) structure. To give an efficient yet principled implementation of the RAD algorithm, we use foliations of our hierarchical string diagrams

Prioritized Repairing and Consistent Query Answering in Relational Databases

A consistent query answer in an inconsistent database is an answer obtained in every (minimal) repair. The repairs are obtained by resolving all conflicts in all possible ways. Often, however, the user is able to provide a preference on how conflicts should be resolved. We investigate here the framework of preferred consistent query answers, in which user preferences are used to narrow down the set of repairs to a set of preferred repairs. We axiomatize desirable properties of preferred repairs. We present three different families of preferred repairs and study their mutual relationships. Finally, we investigate the complexity of preferred repairing and computing preferred consistent query answers.Comment: Accepted to the special SUM'08 issue of AMA

Uncovering the structure of hypergraphs through tensor decomposition: an application to folksonomy analysis

Folksonomies - shared vocabularies generated by users through collective annotation (tagging) of web-based content, which are formally hypergraphs connecting users, tags and objects, are beginning to play an increasingly important role in social media. Effective use of folksonomies for organizing and locating web content, discovering and organizing user communities in order to facilitate the contact and collaboration between users who share parts of their interests and attitudes calls for effective methods for discovering coherent groupings of users, objects, and tags. We empirically compare the results of several folksonomy clustering methods using tensor decompositions such as PARAFAC, Tucker3 and HOSVD which are generalizations of principal component analysis and singular value decomposition with standard methods that use 2-dimensional projections of the original 3-way relationships. Our results suggest that the proposed methods overcome some of the limitations of 2-way decomposition methods in clustering folksonomies