Relevant bibliographies by topics / Chain graph models

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Chain graph models'

Author: Grafiati
Published: 9 March 2023
Last updated: 31 July 2025

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Journal articles on the topic "Chain graph models"

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Drton, Mathias. "Discrete chain graph models." Bernoulli 15, no. 3 (2009): 736–53. http://dx.doi.org/10.3150/08-bej172.

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Skornyakov, Vladimir, Maria Skornyakova, Antonina Shurygina, and Pavel Skornyakov. "Finite-state discrete-time Markov chain models of gene regulatory networks." F1000Research 3 (September 12, 2014): 220. http://dx.doi.org/10.12688/f1000research.4669.1.

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In this study, Markov chain models of gene regulatory networks (GRN) are developed. These models make it possible to apply the well-known theory and tools of Markov chains to GRN analysis. A new kind of finite interaction graph called a combinatorial net is introduced to represent formally a GRN and its transition graphs constructed from interaction graphs. The system dynamics are defined as a random walk on the transition graph, which is a Markov chain. A novel concurrent updating scheme (evolution rule) is developed to determine transitions in a transition graph. The proposed scheme is based
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Ferrándiz, Juan, Enrique F. Castillo, and Pilar Sanmartín. "Temporal aggregation in chain graph models." Journal of Statistical Planning and Inference 133, no. 1 (2005): 69–93. http://dx.doi.org/10.1016/j.jspi.2004.03.012.

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Wang, Yuhao, and Arnab Bhattacharyya. "Identifiability of Linear AMP Chain Graph Models." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 9 (2022): 10080–89. http://dx.doi.org/10.1609/aaai.v36i9.21247.

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We study identifiability of linear Andersson-Madigan-Perlman (AMP) chain graph models, which are a common generalization of linear structural equation models and Gaussian graphical models. AMP models are described by DAGs on chain components which themselves are undirected graphs. For a known chain component decomposition, we show that the DAG on the chain components is identifiable if the determinants of the residual covariance matrices of the chain components are equal (or more generally, monotone non-decreasing in topological order). This condition extends the equal variance identifiability
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Oluwatumininu Anne Ajayi. "Anticipating supply chain disruptions with graph AI models." World Journal of Advanced Engineering Technology and Sciences 7, no. 1 (2022): 241–44. https://doi.org/10.30574/wjaets.2022.7.1.0095.

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Supply chain networks are increasingly complex and interconnected, making them vulnerable to disruptions caused by natural disasters, geopolitical tensions, cyberattacks, and market volatility. Traditional forecasting and risk management techniques often fall short in dynamically capturing the multi-relational and non-linear dependencies within these networks. This paper explores the role of Graph AI models—particularly Graph Neural Networks (GNNs)—in modeling, predicting, and mitigating supply chain disruptions. We propose a framework for integrating Graph AI into supply chain operations, emp
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Knudsen, Michael, and Carsten Wiuf. "A Markov Chain Approach to Randomly Grown Graphs." Journal of Applied Mathematics 2008 (2008): 1–14. http://dx.doi.org/10.1155/2008/190836.

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A Markov chain approach to the study of randomly grown graphs is proposed and applied to some popular models that have found use in biology and elsewhere. For most randomly grown graphs used in biology, it is not known whether the graph or properties of the graph converge (in some sense) as the number of vertices becomes large. Particularly, we study the behaviour of the degree sequence, that is, the number of vertices with degree0,1,…,in large graphs, and apply our results to the partial duplication model. We further illustrate the results by application to real data.
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Vo, Thi Phuong Thuy. "Chain-referral sampling on stochastic block models." ESAIM: Probability and Statistics 24 (2020): 718–38. http://dx.doi.org/10.1051/ps/2020025.

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The discovery of the “hidden population”, whose size and membership are unknown, is made possible by assuming that its members are connected in a social network by their relationships. We explore these groups by a chain-referral sampling (CRS) method, where participants recommend the people they know. This leads to the study of a Markov chain on a random graph where vertices represent individuals and edges connecting any two nodes describe the relationships between corresponding people. We are interested in the study of CRS process on the stochastic block model (SBM), which extends the well-kn
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Lauritzen, Steffen L., and Thomas S. Richardson. "Chain graph models and their causal interpretations." Journal of the Royal Statistical Society: Series B (Statistical Methodology) 64, no. 3 (2002): 321–48. http://dx.doi.org/10.1111/1467-9868.00340.

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KhudaBukhsh, Wasiur R., Arnab Auddy, Yann Disser, and Heinz Koeppl. "Approximate lumpability for Markovian agent-based models using local symmetries." Journal of Applied Probability 56, no. 3 (2019): 647–71. http://dx.doi.org/10.1017/jpr.2019.44.

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AbstractWe study a Markovian agent-based model (MABM) in this paper. Each agent is endowed with a local state that changes over time as the agent interacts with its neighbours. The neighbourhood structure is given by a graph. Recently, Simon, Taylor, and Kiss [40] used the automorphisms of the underlying graph to generate a lumpable partition of the joint state space, ensuring Markovianness of the lumped process for binary dynamics. However, many large random graphs tend to become asymmetric, rendering the automorphism-based lumping approach ineffective as a tool of model reduction. In order t
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Wang, Mingjie, Yifan Huo, Junhong Zheng, and Lili He. "SC-TKGR: Temporal Knowledge Graph-Based GNN for Recommendations in Supply Chains." Electronics 14, no. 2 (2025): 222. https://doi.org/10.3390/electronics14020222.

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Graph neural networks (GNNs) are widely used in recommendation systems to improve prediction performance, especially in scenarios with diverse behaviors and complex user interactions within supply chains. However, while existing models have achieved certain success in capturing the temporal and dynamic aspects of supply chain behaviors, challenges remain in effectively addressing the time-sensitive fluctuations of market demands and user preferences. Motivated by these challenges, we propose SC-TKGR, a supply chain recommendation framework based on temporal knowledge graphs. It employs enhance
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Dissertations / Theses on the topic "Chain graph models"

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Drton, Mathias. "Maximum likelihood estimation in Gaussian AMP chain graph models and Gaussian ancestral graph models /." Thesis, Connect to this title online; UW restricted, 2004. http://hdl.handle.net/1773/8952.

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Levitz, Michael. "Separation, completeness, and Markov properties for AMP chain graph models /." Thesis, Connect to this title online; UW restricted, 2000. http://hdl.handle.net/1773/9564.

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Gastaldello, Mattia. "Enumeration Algorithms and Graph Theoretical Models to Address Biological Problems Related To Symbiosis." Thesis, Lyon, 2018. http://www.theses.fr/2018LYSE1019/document.

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Dans cette thèse, nous abordons deux problèmes de théorie des graphes liés à deux problèmes biologiques de symbiose (deux organismes vivent en symbiose s'ils ont une interaction étroite et à long terme). Le premier problème est lié au phénomène de l'Incompatibilité cytoplasmique (IC) induit par certaines bactéries parasites chez leurs hôtes. L'IC se traduit par l'impossibilité de donner naissance à une progéniture saine lorsqu'un mâle infecté s'accouple avec une femelle non infectée. En termes de graphe ce problème peut s'interpréter comme la recherche d'une couverture minimum par des "sous-g
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NICOLUSSI, FEDERICA. "Marginal parametrizations for conditional independence models and graphical models for categorical data." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2013. http://hdl.handle.net/10281/43679.

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The graphical models (GM) for categorical data are models useful to representing conditional independencies through graphs. The parametric marginal models for categorical data have useful properties for the asymptotic theory. This work is focused on nding which GMs can be represented by marginal parametrizations. Following theorem 1 of Bergsma, Rudas and Németh [9], we have proposed a method to identify when a GM is parametrizable according to a marginal model. We have applied this method to the four types of GMs for chain graphs, summarized by Drton [22]. In particular, with regard to
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Sonntag, Dag. "Chain Graphs : Interpretations, Expressiveness and Learning Algorithms." Doctoral thesis, Linköpings universitet, Databas och informationsteknik, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-125921.

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Probabilistic graphical models are currently one of the most commonly used architectures for modelling and reasoning with uncertainty. The most widely used subclass of these models is directed acyclic graphs, also known as Bayesian networks, which are used in a wide range of applications both in research and industry. Directed acyclic graphs do, however, have a major limitation, which is that only asymmetric relationships, namely cause and effect relationships, can be modelled between their variables. A class of probabilistic graphical models that tries to address this shortcoming is chain gra
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Di, Natale Anna. "Stochastic models and graph theory for Zipf's law." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2018. http://amslaurea.unibo.it/17065/.

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In questo elaborato ci siamo occupati della legge di Zipf sia da un punto di vista applicativo che teorico. Tale legge empirica afferma che il rango in frequenza (RF) delle parole di un testo seguono una legge a potenza con esponente -1. Per quanto riguarda l'approccio teorico abbiamo trattato due classi di modelli in grado di ricreare leggi a potenza nella loro distribuzione di probabilità. In particolare, abbiamo considerato delle generalizzazioni delle urne di Polya e i processi SSR (Sample Space Reducing). Di questi ultimi abbiamo dato una formalizzazione in termini di catene di Markov. I
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Moghadasin, Babak. "An Approach on Learning Multivariate Regression Chain Graphs from Data." Thesis, Linköpings universitet, Databas och informationsteknik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-94019.

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The necessity of modeling is vital for the purpose of reasoning and diagnosing in complex systems, since the human mind might sometimes have a limited capacity and an inability to be objective. The chain graph (CG) class is a powerful and robust tool for modeling real-world applications. It is a type of probabilistic graphical models (PGM) and has multiple interpretations. Each of these interpretations has a distinct Markov property. This thesis deals with the multivariate regression chain graph (MVR-CG) interpretation. The main goal of this thesis is to implement and evaluate the results of t
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PENNONI, FULVIA. "Metodi statistici multivariati applicati all'analisi del comportamento dei titolari di carta di credito di tipo revolving." Bachelor's thesis, Universita' degli studi di Perugia, 2000. http://hdl.handle.net/10281/50024.

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Il presente lavoro di tesi illustra un'applicazione dei modelli grafici per il l’analisi del credit scoring comportamentale o behavioural scoring. Quest'ultimo e' definito come: ‘the systems and models that allow lenders to make better decisions in managing existing clients by forcasting their future performance’, secondo Thomas (1999). La classe di modelli grafici presa in considerazione e’ quella dei modelli garfici a catena. Sono dei modelli statistici multivariati che consetono di modellizzare in modo appropriato le relazioni tra le variabili che descrivono il comporatemento dei ti
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Weng, Huibin. "A Social Interaction Model with Endogenous Network Formation." University of Cincinnati / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=ucin159317152899108.

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Wang, Yan-Jiang, and yanjiang_wang@tmmu edu cn. "Clearance of amyloid-beta in Alzheimer's disease: To understand the pathogenesis and develop potential therapies in animal models." Flinders University. School of Medicine, 2010. http://catalogue.flinders.edu.au./local/adt/public/adt-SFU20100419.124325.

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Alzheimer's disease (AD) is the most common cause of dementia. No strong disease-modifying treatments are currently available. Amyloid-beta peptide (Abeta) appears to play a pivotal role in the pathogenesis of AD. We focused our interest on revealing the pathogenesis of the disease and developing novel therapeutic modalities. The thesis consists of three projects: 1. Prevention of AD by intramuscular delivery of an anti-Abeta single chain antibody (scFv) gene: Immunotherapy is effective in removing brain Abetaƒzbut was associated with detrimental effects. In the present study, the gene of an
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Books on the topic "Chain graph models"

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Yücesan, Enver. Analysis of Markov chains using simulation graph models. INSEAD, 1990.

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O, Seppäläinen Timo, ed. A course on large deviations with an introduction to Gibbs measures. American Mathematical Society, 2015.

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Coolen, A. C. C., A. Annibale, and E. S. Roberts. Graphs with hard constraints: further applications and extensions. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198709893.003.0007.

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This chapter looks at further topics pertaining to the effective use of Markov Chain Monte Carlo to sample from hard- and soft-constrained exponential random graph models. The chapter considers the question of how moves can be sampled efficiently without introducing unintended bias. It is shown mathematically and numerically that apparently very similar methods of picking out moves can give rise to significant differences in the average topology of the networks generated by the MCMC process. The general discussion in complemented with pseudocode in the relevant section of the Algorithms chapte
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Brémaud, Pierre. Discrete Probability Models and Methods: Probability on Graphs and Trees, Markov Chains and Random Fields, Entropy and Coding. Springer International Publishing AG, 2017.

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Brémaud, Pierre. Discrete Probability Models and Methods: Probability on Graphs and Trees, Markov Chains and Random Fields, Entropy and Coding. Springer, 2018.

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Bremaud, Pierre. Discrete Probability - Models and Methods: Probability on Graphs and Trees, Markov Chains and Random Fields, Entropy and Coding. Springer, 2017.

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Book chapters on the topic "Chain graph models"

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Sonntag, Dag. "On Expressiveness of the AMP Chain Graph Interpretation." In Probabilistic Graphical Models. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-11433-0_30.

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Nicolussi, Federica, and Manuela Cazzaro. "Context-Specific Independencies Embedded in Chain Graph Models of Type I." In Statistical Learning of Complex Data. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-21140-0_18.

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Peña, Jose M. "Every LWF and AMP Chain Graph Originates from a Set of Causal Models." In Lecture Notes in Computer Science. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-20807-7_29.

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Larsen, Casper Abild, Simon Meldahl Schmidt, Jesper Steensgaard, Anna Blume Jakobsen, Jaco van de Pol, and Andreas Pavlogiannis. "A Truly Symbolic Linear-Time Algorithm for SCC Decomposition." In Tools and Algorithms for the Construction and Analysis of Systems. Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-30820-8_22.

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AbstractDecomposing a directed graph to its strongly connected components (SCCs) is a fundamental task in model checking. To deal with the state-space explosion problem, graphs are often represented symbolically using binary decision diagrams (BDDs), which have exponential compression capabilities. The theoretically-best symbolic algorithm for SCC decomposition is Gentilini et al’s $$\textsc {Skeleton}$$ S K E L E T O N algorithm, that uses O(n) symbolic steps on a graph of n nodes. However, $$\textsc {Skeleton}$$ S K E L E T O N uses $$\Theta (n)$$ Θ ( n ) symbolic objects, as opposed to (pol
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Richardson, Thomas S. "Chain Graphs and Symmetric Associations." In Learning in Graphical Models. Springer Netherlands, 1998. http://dx.doi.org/10.1007/978-94-011-5014-9_9.

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Peña, Jose M. "Learning Marginal AMP Chain Graphs under Faithfulness." In Probabilistic Graphical Models. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-11433-0_25.

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Dai, Qionghai, and Yue Gao. "Mathematical Foundations of Hypergraph." In Artificial Intelligence: Foundations, Theory, and Algorithms. Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-99-0185-2_2.

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AbstractIn this chapter, we introduce the mathematical foundations of hypergraph and present the mathematical notations that are used to facilitate deep understanding and analysis of hypergraph structure. A hypergraph is composed of a set of vertices and hyperedges, and it is a generalization of a graph, where a weighted hypergraph quantifies the relative importance of hyperedges or vertices. Hypergraph can also be divided into two main categories, i.e., the undirected hypergraph representation and the directed hypergraph representation. The latter one further divides the vertices in one hyper
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Ding, Huafeng, Wenjian Yang, and Andrés Kecskeméthy. "Unified Graph Model of Planar Kinematic Chains." In Springer Tracts in Mechanical Engineering. Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-1508-6_3.

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Gelgfren, Jan M., Hélène Arvis, Simon Hagemann, and Sigrid Wenzel. "Mixed-Integer Programming Model for Scheduling of Modular Automotive Body-In-White Production Systems." In Advances in Automotive Production Technology – Towards Software-Defined Manufacturing and Resilient Supply Chains. Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-27933-1_7.

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AbstractThe turbulent transition in the automotive industry towards electric vehicles is highly challenging, both in product development and in production. Conventional, linear assembly lines struggle to meet the flexibility requirements imposed by this market development. Thispaper presents the first mixed-integer programming (MIP) model which is tailor-made for the scheduling of modular body-in-white (BIW)production systems. The main novelty of the presented approach lies in using precedence graphs for modelling the joining steps of the BIW production and allowing for different capabilities
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Causo, Maria Serena, Erika Cerasti, Fabrizio De Fausti, and Monica Scannapieco. "Exploring Globalization with Cosmopolitics." In Proceedings e report. Firenze University Press and Genova University Press, 2023. http://dx.doi.org/10.36253/979-12-215-0106-3.30.

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Cosmopolitics, an open-source dashboard designed by an Istat team to perform exploratory data analysis using Eurostat statistical open data on international trade, offers several tools for investigating globalization phenomena such as the dynamics of global value chains (GVC). The advantage of this widely spread economic organization is well known: companies obtain economic advantages by direct foreign investments or by production outsourcing, i.e. relocating some production phases to countries where high specialization or an advantageous labor market create greater opportunities. However, by
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Conference papers on the topic "Chain graph models"

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Jin, Bowen, Chulin Xie, Jiawei Zhang, et al. "Graph Chain-of-Thought: Augmenting Large Language Models by Reasoning on Graphs." In Findings of the Association for Computational Linguistics ACL 2024. Association for Computational Linguistics, 2024. http://dx.doi.org/10.18653/v1/2024.findings-acl.11.

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Huang, Jia-Xuan, and En-Liang Yan. "COTKEG: A Chain-of-Thought and Knowledge Graph Enhanced Method for Medical Large Language Models." In 2025 4th International Symposium on Computer Applications and Information Technology (ISCAIT). IEEE, 2025. https://doi.org/10.1109/iscait64916.2025.11010691.

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Ge, Xing, Yafei Liu, Pei Yang, et al. "Research and Application of Electronic Data Retrieval in Material Supply Chain Enhanced by Large Language Models and Knowledge Graph." In 2024 International Conference on Information Technology, Communication Ecosystem and Management (ITCEM). IEEE, 2024. https://doi.org/10.1109/itcem65710.2024.00037.

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Chong, Daniel J. S., Timothy G. Walmsley, Martin J. Atkins, Botond Bertok, and Michael RW Walmsley. "Aotearoa-New Zealand�s Energy Future: A Model for Industrial Electrification through Renewable Integration." In The 35th European Symposium on Computer Aided Process Engineering. PSE Press, 2025. https://doi.org/10.69997/sct.189578.

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This work explores Aotearoa-New Zealand�s potential to fully electrify and source industrial process heat demands from renewable energy for 286 industrial sites while exploring the feasibility of green methanol production using excess electricity. Most energy models rely on spatially aggregated supply and demand, which limits the accurate representation of energy value chains. To address this limitation, the model incorporates industrial sites with varied temperature profiles, enabling the use of diverse heating technologies such as heat pumps, electrode boilers, bubbling fluidised bed reactor
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Loevenich, Johannes F., Erik Adler, Tobias Hürten, Florian Spelter, Damian Roncevic, and Roberto Rigolin F. Lopes. "Automating Cyber Threat Intelligence and Attack Chain Generation using Cyber Security Knowledge Graphs and Large Language Models." In 2025 International Conference on Military Communication and Information Systems (ICMCIS). IEEE, 2025. https://doi.org/10.1109/icmcis64378.2025.11047951.

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Dabrowski, Christopher, and Fern Hunt. "Identifying Failure Scenarios in Complex Systems by Perturbing Markov Chain Models." In ASME 2011 Pressure Vessels and Piping Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/pvp2011-57683.

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In recent years, substantial research has been devoted to monitoring and predicting performance degradations in real-world complex systems within large entities such as nuclear power plants, electrical grids, and distributed computing systems. Special challenges are posed by the fact that such systems operate in uncertain environments, are highly dynamic, and exhibit emergent behaviors that can lead to catastrophic failure. Discrete Time Markov chains (DTMCs) provide important tools for analysis of such systems, because they represent dynamic behavior succinctly, provide a means to measure unc
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Zhao, Ruilin, Feng Zhao, Long Wang, Xianzhi Wang, and Guandong Xu. "KG-CoT: Chain-of-Thought Prompting of Large Language Models over Knowledge Graphs for Knowledge-Aware Question Answering." In Thirty-Third International Joint Conference on Artificial Intelligence {IJCAI-24}. International Joint Conferences on Artificial Intelligence Organization, 2024. http://dx.doi.org/10.24963/ijcai.2024/734.

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Large language models (LLMs) encounter challenges such as hallucination and factual errors in knowledge-intensive tasks. One the one hand, LLMs sometimes struggle to generate reliable answers based on the black-box parametric knowledge, due to the lack of responsible knowledge. Moreover, fragmented knowledge facts extracted by knowledge retrievers fail to provide explicit and coherent reasoning paths for improving LLM reasoning. To address these challenges, we propose KG-CoT, a novel knowledge-augmented paradigm that leverages a small-scale step-by-step graph reasoning model to reason over kno
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Malhomme, Olivier, Luigui Salazar, Xianyun Zhuang, Robert Plana, and Nicolas Bureau. "Enhancing the management of nuclear information systems through graph theory-based methods and human-centered modeling." In Human Interaction and Emerging Technologies (IHIET 2025). AHFE International, 2025. https://doi.org/10.54941/ahfe1006746.

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The integration of digital technologies is crucial for enhancing the efficiency and performance of nuclear facilities throughout their entire lifecycle. However, the nuclear industry faces significant challenges due to its intricate supply chain, resulting in fragmented data exchanges and inefficiencies. The expansion of complex information systems has introduced considerable challenges to data management, leading to inconsistencies and inaccuracies that adversely affect operational performance.To address these challenges, this study proposes an integrated analytical approach that combines gra
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Mohan, Prashant, Payam Haghighi, Jami J. Shah, and Joseph K. Davidson. "Automatic Detection of Directions of Dimensional Control in Mechanical Parts." In ASME 2014 International Manufacturing Science and Engineering Conference collocated with the JSME 2014 International Conference on Materials and Processing and the 42nd North American Manufacturing Research Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/msec2014-4143.

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This research is part of a larger project which aims at developing a tool to help designers create effective GD&T schemas. The first step towards this goal is to determine the particular directions in which dimensions and tolerances need to be controlled. These directions we label here as “Directions of (Dimensional) Control” or DoC for short. Regardless of whether one uses chain dimensioning, reference dimensioning or geometric tolerancing, all size and basic dimensions of position line up in a finite number of directions or Directions of Control. This paper presents an approach for autom
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Ding, Huafeng, Jing Zhao, and Zhen Huang. "The Establishment of Novel Structure Representation Models for Several Kinds of Mechanisms." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-86074.

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This paper attempts to establish the unified topological models and corresponding mathematical representations for planar simple joint, multiple joint and geared (cam) kinematic chains. First, the conventional topological representation models of kinematic chains are introduced. Then new topological models of multiple joint and geared (cam) kinematic chains, which are derived from the topological graph of simple joint kinematic chains, are presented. The characteristics of the new topological graphs and their associations with the topological graph of simple joint kinematic chains are also add
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Reports on the topic "Chain graph models"

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Oron, Gideon, Raphi Mandelbaum, Carlos E. Enriquez, et al. Optimization of Secondary Wastewater Reuse to Minimize Environmental Risks. United States Department of Agriculture, 1999. http://dx.doi.org/10.32747/1999.7573077.bard.

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The main purpose of the research was to examine approaches and to evaluate methods for minimizing the risks during applying treated domestic wastewater for agricultural irrigation. This general purpose consisted of examining under field conditions the possibilities when implementing different application technologies for minimizing health and environmental risks. It was assumed that Subsurface Drip Irrigation (SDI) will provide adequate conditions for safe effluent reuse. Controlled field experiments where conducted in commercial fields to evaluate the alternatives. Main efforts where conducte
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