Directed Acyclic Graph Representation Research Articles

Hunting for protective drugs at the break of a pandemic: Causal inference from hospital data.

At the break of a pandemic, the protective efficacy of therapeutic interventions needs rapid evaluation. An experimental approach to the problem will not always be appropriate. An alternative route are observational studies, whether based on regional health service data or hospital records. In this paper, we discuss the use of methods of causal inference for the analysis of such data, with special reference to causal questions that may arise in a pandemic. We apply the methods by using the aid of a directed acyclic graph (DAG) representation of the problem, to encode our causal assumptions and to logically connect the scientific questions. We illustrate the usefulness of DAGs in the context of a controversy over the effects of renin aldosterone system inhibitors (RASIs) in hypertensive individuals at risk of (or affected by) severe acute respiratory syndrome coronavirus 2 disease. We consider questions concerning the existence and the directions of those effects, their underlying mechanisms, and the possible dependence of the effects on context variables. This paper describes the cognitive steps that led to a DAG representation of the problem, based on background knowledge and evidence from past studies, and the use of the DAG to analyze our hospital data and assess the interpretive limits of the results. Our study contributed to subverting early opinions about RASIs, by suggesting that these drugs may indeed protect the older hypertensive Covid-19 patients from the consequences of the disease. Mechanistic interaction methods revealed that the benefit may be greater (in a sense to be made clear) in the older stratum of the population.

Cryptanalytic time–memory trade-off for password hashing schemes

Increasing threat of password leakage from compromised password hashes demands a resource consuming password-hashing algorithm to prevent the precomputation of the password hashes. A class of password-hashing schemes (PHS) provides such a defense by making the design Memory hard. This ensures that any reduction in the memory consumed by the algorithm leads to an exponential increase in its runtime. The security offered by a memory-hard PHS design is measured in terms of its time–memory trade-off (TMTO) defense. Another important measure for a good PHS is its efficiency in utilizing all the available memory as quickly as possible, and fast running time when more than the required memory is available. In this work, we present a simple technique to analyze TMTO for a password-hashing scheme which can be represented as a directed acyclic graph (DAG). The nodes of the DAG correspond to the storage required by the algorithm and the edges correspond to the flow of the execution. Our proposed technique provides expected runtimes at varied levels of available storage utilizing the DAG representation of the algorithm. We show the effectiveness of our proposed technique by applying it on three designs from the “Password Hashing Competition" (PHC)—Argon2-Version 1.2.1 (the PHC winner), Catena-Version 3.2 and Rig-Version 2. Our analysis shows that Argon2i is not providing expected memory hardness which is also highlighted in a recent work by Corrigan-Gibbs et al. We analyze these PHS for performance under various settings of time and memory complexities. Our experimental results show (i) simple DAGs for PHS are efficient but not memory hard, (ii) complex DAGs for PHS are memory hard but less efficient, and (iii) combination of two simple graphs in the representation of a DAG for PHS achieves both memory hardness and efficiency.

I/O efficient: computing SCCs in massive graphs

A strongly connected component ($$\mathsf {SCC}$$SCC) is a maximal subgraph of a directed graph $$G$$G in which every pair of nodes is reachable from each other in the $$\mathsf {SCC}$$SCC. With such a property, a general directed graph can be represented by a directed acyclic graph (DAG) by contracting every $$\mathsf {SCC}$$SCC of $$G$$G to a node in DAG. In many real applications that need graph pattern matching, topological sorting, or reachability query processing, the best way to deal with a general directed graph is to deal with its DAG representation. Therefore, finding all $$\mathsf {SCC}$$SCCs in a directed graph $$G$$G is a critical operation. The existing in-memory algorithms based on depth first search (DFS) can find all $$\mathsf {SCC}$$SCCs in linear time with respect to the size of a graph. However, when a graph cannot reside entirely in the main memory, the existing external or semi-external algorithms to find all $$\mathsf {SCC}$$SCCs have limitation to achieve high I/O efficiency. In this paper, we study new I/O-efficient semi-external algorithms to find all $$\mathsf {SCC}$$SCCs for a massive directed graph $$G$$G that cannot reside in main memory entirely. To overcome the deficiency of the existing DFS-based semi-external algorithm that heavily relies on a total order, we explore a weak order based on which we investigate new algorithms. We propose a new two-phase algorithm, namely, tree construction and tree search. In the tree construction phase, a spanning tree of $$G$$G can be constructed in bounded number of sequential scans of $$G$$G. In the tree search phase, it needs to sequentially scan the graph once to find all $$\mathsf {SCC}$$SCCs. In addition, we propose a new single-phase algorithm, which combines the tree construction and tree search phases into a single phase, with three new optimization techniques. They are early acceptance, early rejection, and batch processing. By the single-phase algorithm with the new optimization techniques, we can significantly reduce the number of I/Os and the CPU cost. We prove the correctness of the algorithms. We conduct extensive experimental studies using 4 real datasets including a massive real dataset and several synthetic datasets to confirm the I/O efficiency of our approaches.

Energy consumption, carbon emissions, and economic growth in India: Evidence from directed acyclic graphs

This study investigates the temporal linkages among economic growth, energy consumption, and carbon emissions for India during the period 1970–2008 using recently developed methods of out-of-sample Granger causality tests and directed acyclic graphs (DAG). Building on the data-driven DAG representation, we uncover the contemporaneous causal patterns between economic activities and environmental pollutants, which is first documented in the literature and could further improve the investigation of the dynamic linkage pattern. The results show that energy consumption uni-directionally Granger causes carbon emissions and economic growth, while there is a bidirectional causality between carbon emissions and economic growth. We also find that trade openness is one of the important determinants of energy consumption and carbon emissions. Some important policy implications are also discussed.

Conjugate and conditional conjugate Bayesian analysis of discrete graphical models of marginal independence

A conjugate and conditional conjugate Bayesian analysis is presented for bi-directed discrete graphical models, which are used to describe and estimate marginal associations between categorical variables. To achieve this, each bi-directed graph is re-expressed by a Markov equivalent, over the observed margin, directed acyclic graph (DAG). This DAG equivalent model is obtained using the same vertex set or with the addition of some latent variables when required. It is characterised by a minimal set of marginal and conditional probability parameters. Hence compatible priors based on products of Dirichlet distributions can be applied. For models with DAG representation on the same vertex set, the posterior distribution and the marginal likelihood is analytically available, while for the remaining ones a data augmentation scheme introducing additional latent variables is required. For the latter, the marginal likelihood is estimated using Chib’s estimator. Additional implementation details including identifiability of such models are discussed. Moreover, analytic details concerning the computation of the posterior distributions of the marginal log-linear parameters are provided. The computation is achieved via a simple transformation of the simulated values of the probability parameters of the bi-directed model under study. The marginal log-linear parameterisation provides a straightforward interpretation in terms of log-odds ratios on specific marginals quantifying the associations between variables involved in the corresponding marginal. The proposed methodology is illustrated using a popular 4-way dataset.

Measuring financial contagion: a directed acyclic graphs and error correction model

Vector autoregressions (VARs) are economically interpretable only when identified by being transformed into a structural form the (SVAR) in which the contemporaneous variables stand in a well-defined causal order. These identifying transformations are not unique. It is widely believed that practitioners must choose between them using a priori theory or other criteria not rooted in the data under analysis. We show how to apply graph-theoretical approach of searching for causal structure based on relations of conditional independence to select the possible causal orders – or at least to reduce the admissible them to a narrow equivalence class. This study investigates the dynamic structure of four major stock markets using an error correction model and directed acyclic graphs (DAG). The DAG representation provides a structure of causality among these markets in a contemporaneous time. Building this contemporaneous structure and the estimated error correction model, innovation accounting techniques are applied.

The structure of interdependence in international stock markets

This study investigates the dynamic structure of nine major stock markets using an error correction model and directed acyclic graphs (DAG). The DAG representation provides a structure of causality among these markets in contemporaneous time. Building on this contemporaneous structure and the estimated error correction model, innovation accounting techniques are applied. The results show that the Japanese market is among the most highly exogenous and the Canadian and French markets among the least exogenous in our nine-market study. The US market is highly influenced by its own historical innovations, but it is also influenced by market innovations from the UK, Switzerland, Hong Kong, France and Germany. The US market is the only market that has a consistently strong impact on price movements in other major stock markets in the longer-run.

The Structure of Interdependence in International Stock Markets

This study investigates the dynamic structure of nine major stock markets using an error correction model and directed acyclic graphs (DAG). The DAG representation provides a structure of causality among these markets in contemporaneous time. Building on this contemporaneous structure and the estimated error correction model, innovation accounting techniques are applied. The results show that the Japanese market is among the most highly exogenous and the Canadian and French markets among the least exogenous in our nine-market study. The U.S. market is highly influenced by its own historical innovations, but it is also influenced by market innovations from the U.K., Switzerland, Hong Kong, France and Germany. The U.S. market is the only market that has a consistently strong impact on price movements in other major stock markets in the longer-run.

Efficient methodology for hand-coding video algorithms for VLIW-type processors

Digital signal processors (DSP) based on very large instruction word (VLIW) architectures are potentially well suited for software-based implementation of video codecs. In order to achieve real-time performance, the implementation has to be efficiently mapped to the target architecture. Although sophisticated compilers are available for VLIW-type processors, time-critical video coding algorithms can often be more efficiently coded by hand. This is because compilers are still not intelligent enough to fine-tune the organization of data structures or make trade-offs on an abstract algorithmic level. However, hand-coding typically is a very demanding, error-prone and time-consuming task. Exploring as many scheduling opportunities as possible and making the right scheduling decisions is a complex task but is essential for achieving an efficient implementation. In order to address these problems, we have developed a systematic hand-coding methodology which is based on a framework of scheduling heuristics and a directed acyclic graph (DAG) representation with incorporated processor resources. The methodology helps to produce more efficient code in a shorter time compared to ad-hoc hand-coding approaches. Another benefit is that the implementation is well documented through the DAG representation which allows possible modifications to be easily accommodated. The methodology is explained on the examples of two video algorithms, the discrete cosine transform (DCT) and sum of absolute differences (SAD) which have been implemented on the Texas Instruments TMS320C6201 DSP. The performance results confirm the effectiveness of our methodology. The presented methodology may also provide a basis for a visual, semi-automated, interactive developing tool which gives the programmer more control over the implementation of critical algorithms or procedures.

STATIC SCHEDULING OF HIERARCHICAL PROGRAM GRAPHS

Many parallel compilation systems represent programs internally as Directed Acyclic Graphs (DAGs). However, the storage of these DAGs becomes prohibitive when the program being compiled is large. In this paper we describe a compile-time scheduling methodology for hierarchical DAG programs represented in the IFX intermediate form. The method we present is itself hierarchical reducing the storage that would otherwise be required by a single flat DAG representation. We describe the scheduling model and demonstrate the method using the Optimizing Sisal Compiler and two scientific applications.

Term matching on parallel computers

Term matching is an important problem that arises very often in term rewriting and in functional and equational programming. We present a new parallel algorithm for the term-matching problem on the EREW (exclusive read, exclusive write) model of parallel computation. Our algorithm assumes a string representation of the two terms as its input. The string representation is first transformed into two labeled ordered trees, and term matching is then performed on these two trees. If n is the length of the input terms, then for any constant ϵ (0 < ϵ ≤ 1) our algorithm uses O( n 1-ϵ) processors and takes O( n ϵlog n) time. If ϵ = 0, the same algorithm will run in O(log 2 n) time. The only other known parallel algorithm for this problem, due to Dwork, Kanellakis, and Stockmeyer, requires O( n 2) processors and takes either O(log n) or O(log 2 n) time. However, their algorithm uses the stronger CREW (concurrent read, exclusive write) model of parallel computation and assumes a DAG (directed acyclic graph) representation of the two terms as its input. On the CRCW (concurrent read, concurrent write) model our algorithm requires n processors and O(log n) time.