Efficient Identification of Equivalences in Dynamic Graphs and Pedigree Structures

We propose a new framework for designing test and query functions for complex structures that vary across a given parameter such as genetic marker position. The operations we are interested in include equality testing, set operations, isolating unique states, duplication counting, or finding equivalence classes under identifiability constraints. A motivating application is locating equivalence classes in identity-by-descent (IBD) graphs, graph structures in pedigree analysis that change over genetic marker location. The nodes of these graphs are unlabeled and identified only by their connecting edges, a constraint easily handled by our approach. The general framework introduced is powerful enough to build a range of testing functions for IBD graphs, dynamic populations, and other structures using a minimal set of operations. The theoretical and algorithmic properties of our approach are analyzed and proved. Computational results on several simulations demonstrate the effectiveness of our approach.Comment: Code for paper available at http://www.stat.washington.edu/~hoytak/code/hashreduc

Identity-by-descent estimation with population- and pedigree-based imputation in admixed family data

BACKGROUND: In the past few years, imputation approaches have been mainly used in population-based designs of genome-wide association studies, although both family- and population-based imputation methods have been proposed. With the recent surge of family-based designs, family-based imputation has become more important. Imputation methods for both designs are based on identity-by-descent (IBD) information. Apart from imputation, the use of IBD information is also common for several types of genetic analysis, including pedigree-based linkage analysis. METHODS: We compared the performance of several family- and population-based imputation methods in large pedigrees provided by Genetic Analysis Workshop 19 (GAW19). We also evaluated the performance of a new IBD mapping approach that we propose, which combines IBD information from known pedigrees with information from unrelated individuals. RESULTS: Different combinations of the imputation methods have varied imputation accuracies. Moreover, we showed gains from the use of both known pedigrees and unrelated individuals with our IBD mapping approach over the use of known pedigrees only. CONCLUSIONS: Our results represent accuracies of different combinations of imputation methods that may be useful for data sets similar to the GAW19 pedigree data. Our IBD mapping approach, which uses both known pedigree and unrelated individuals, performed better than classical linkage analysis

Identity-by-descent estimation with population- and pedigree-based imputation in admixed family data

Background: In the past few years, imputation approaches have been mainly used in population-based designs of genome-wide association studies, although both family- and population-based imputation methods have been proposed. With the recent surge of family-based designs, family-based imputation has become more important. Imputation methods for both designs are based on identity-by-descent (IBD) information. Apart from imputation, the use of IBD information is also common for several types of genetic analysis, including pedigree-based linkage analysis. Methods: We compared the performance of several family- and population-based imputation methods in large pedigrees provided by Genetic Analysis Workshop 19 (GAW19). We also evaluated the performance of a new IBD mapping approach that we propose, which combines IBD information from known pedigrees with information from unrelated individuals. Results: Different combinations of the imputation methods have varied imputation accuracies. Moreover, we showed gains from the use of both known pedigrees and unrelated individuals with our IBD mapping approach over the use of known pedigrees only. Conclusions: Our results represent accuracies of different combinations of imputation methods that may be useful for data sets similar to the GAW19 pedigree data. Our IBD mapping approach, which uses both known pedigree and unrelated individuals, performed better than classical linkage analysis

Algorithms and the mathematical foundations of computer science

The goal of this chapter is to bring to the attention of philosophers of mathematics the concept of algorithm as it is studied incontemporary theoretical computer science, and at the same time address several foundational questions about the role this notion plays in our practices. A view known as algorithmic realism will be described which maintains that individual algorithms are identical to mathematical objects. Upon considering several ways in which the details of algorithmic realism might be formulated, it will be argued (pace Moschovakis and Gurevich) that there are principled reasons to think that this view cannot be systematically developed in a manner which is compatible with the practice of computational complexity theory and algorithmic analysis

The Philosophical Foundations of PLEN: A Protocol-theoretic Logic of Epistemic Norms

In this dissertation, I defend the protocol-theoretic account of epistemic norms. The protocol-theoretic account amounts to three theses: (i) There are norms of epistemic rationality that are procedural; epistemic rationality is at least partially defined by rules that restrict the possible ways in which epistemic actions and processes can be sequenced, combined, or chosen among under varying conditions. (ii) Epistemic rationality is ineliminably defined by procedural norms; procedural restrictions provide an irreducible unifying structure for even apparently non-procedural prescriptions and normative expressions, and they are practically indispensable in our cognitive lives. (iii) These procedural epistemic norms are best analyzed in terms of the protocol (or program) constructions of dynamic logic. I defend (i) and (ii) at length and in multi-faceted ways, and I argue that they entail a set of criteria of adequacy for models of epistemic dynamics and abstract accounts of epistemic norms. I then define PLEN, the protocol-theoretic logic of epistemic norms. PLEN is a dynamic logic that analyzes epistemic rationality norms with protocol constructions interpreted over multi-graph based models of epistemic dynamics. The kernel of the overall argument of the dissertation is showing that PLEN uniquely satisfies the criteria defended; none of the familiar, rival frameworks for modeling epistemic dynamics or normative concepts are capable of satisfying these criteria to the same degree as PLEN. The overarching argument of the dissertation is thus a theory-preference argument for PLEN

Tools and Algorithms for the Construction and Analysis of Systems

This open access book constitutes the proceedings of the 28th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2022, which was held during April 2-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 46 full papers and 4 short papers presented in this volume were carefully reviewed and selected from 159 submissions. The proceedings also contain 16 tool papers of the affiliated competition SV-Comp and 1 paper consisting of the competition report. TACAS is a forum for researchers, developers, and users interested in rigorously based tools and algorithms for the construction and analysis of systems. The conference aims to bridge the gaps between different communities with this common interest and to support them in their quest to improve the utility, reliability, exibility, and efficiency of tools and algorithms for building computer-controlled systems

Spatial spread of farm animal diseases

Data on cattle movements within the United Kingdom have recently become available. As part of the conditions for lifting an export ban on British beef following the bovine spongiform encephalopathy epidemic, the European Union required that the UK should have "An effective animal identification and movement recording system". The Cattle Tracing System (CTS) was introduced in September 1998, and the scheme was extended to include all cattle by the beginning of 2001. Contact networks have proved valuable in studying the epidemiology of diseases in man, such as human immunodeficiency virus; the availability of CTS cattle movement data has enabled contact network analysis to be applied to diseases of farm livestock. The CTS data may be represented as a large network; cattle holdings are represented as nodes, with a movement of cattle between holdings being an edge. To address concerns about the quality of this cattle movement data, a field study was conducted on Lewis, one of the Western Isles of Scotland. Farmers were recruited with the assistance of the local veterinary surgeon, and asked to record a range of potential risk behaviours relating to the transmission of infectious diseases (moving livestock, sharing pasture, etc.) for a one-month period. For the study area in question, movements of cattle not reported to CTS (especially to or from common grazing land) were a substantial contribution to the contact network during the study period. A wide range of measures of network structure exist, but their relevance to the dynamics of infectious diseases on networks is unclear. To address this, a discrete-time stochastic SIR simulation model of disease on a network was designed and implemented in software. Using this simulation model, a network model with the key structural features of the CTS contact network was constructed, by considering a range of measures of network structure, and testing resulting model networks against CTS-derived networks. The resulting model was shown to predict the dynamics of a simulated disease model on that contact network more closely than existing models of global network structure. Much work on the contact structure of the UK cattle herd has relied on relatively simple static network representations of movement data. By using simulated diseases, the serious shortcomings of static network representations compared to more complex dynamic network representations were demonstrated. A substantial library of software for the generation and analysis of large networks, and the simulation of disease thereupon, has been produced, and has been made generally available. The design and implementation of this software is discussed, including the algorithms and data structures deployed, as well as validation of the software, and its portability to different computing platforms.This work was funded by BBSRC and the Tetra-Laval Research Fund; its revision was funded by the Wellcome Trust

Tools and Algorithms for the Construction and Analysis of Systems

This open access book constitutes the proceedings of the 28th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2022, which was held during April 2-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 46 full papers and 4 short papers presented in this volume were carefully reviewed and selected from 159 submissions. The proceedings also contain 16 tool papers of the affiliated competition SV-Comp and 1 paper consisting of the competition report. TACAS is a forum for researchers, developers, and users interested in rigorously based tools and algorithms for the construction and analysis of systems. The conference aims to bridge the gaps between different communities with this common interest and to support them in their quest to improve the utility, reliability, exibility, and efficiency of tools and algorithms for building computer-controlled systems