From Isomorphism-Based Security for Graphs to Semantics-Preserving Security for the Resource Description Framework (RDF)

Resource Description Framework (RDF) is a graph-like data model designed for the web. One of its compelling features is a precise, model-theoretic semantics. We address security in the context of the RDF. We first observe that the problem of securing RDF is related closely to the more traditional problem of securing graphs. Consequently, before we address security for RDF, we make broader contributions to security in the context of graphs. Specifically, we reconcile four different notions of security that have been proposed in prior work, and compare them from the standpoint of strength of security --- whether satisfaction of one implies satisfaction of another. We then ask whether strength of security is correlated to computational complexity. We make the somewhat surprising observation that the answer to this question is, "no.'' We then extend the two strongest notions of security in a natural way for RDF. We establish results on RDF's semantics that then gives us a way of meaningfully quantifying the loss of information from security. Thus, for RDF, we are able to pose the natural trade-off between information-quality and security in a precise way. We show that a corresponding decision problem is NP-Complete, and with a reduction to CNF-SAT that we have designed and implemented, present empirical results on realistic data. Our empirical results show interesting relationships between the various parameters, such as the size of the graph versus the information-loss, to achieve a particular level of security

Dynamic Privacy Management In Services Based Interactions

Technology advancements have enabled the distribution and sharing of users personal data over several data sources. Each data source is potentially managed by a different organization, which may expose its data as a Web service. Using such Web services, dynamic composition of atomic data items coupled with the context in which the data is accessed may breach sensitive data that may not comply with the users preference at the time of data collection. Thus, providing uniform access policies to such data can lead to privacy problems. Some fairly recent research has focused on providing solutions for dynamic privacy management. This thesis advances these techniques, and fills some gaps in the existing works. In particular, dynamically incorporating user access context into the privacy policy decision, and its enforcement

Power network and smart grids analysis from a graph theoretic perspective

The growing size and complexity of power systems has given raise to the use of complex network theory in their modelling, analysis, and synthesis. Though most of the previous studies in this area have focused on distributed control through well established protocols like synchronization and consensus, recently, a few fundamental concepts from graph theory have also been applied, for example in symmetry-based cluster synchronization. Among the existing notions of graph theory, graph symmetry is the focus of this proposal. However, there are other development around some concepts from complex network theory such as graph clustering in the study. In spite of the widespread applications of symmetry concepts in many real world complex networks, one can rarely find an article exploiting the symmetry in power systems. In addition, no study has been conducted in analysing controllability and robustness for a power network employing graph symmetry. It has been verified that graph symmetry promotes robustness but impedes controllability. A largely absent work, even in other fields outside power systems, is the simultaneous investigation of the symmetry effect on controllability and robustness. The thesis can be divided into two section. The first section, including Chapters 2-3, establishes the major theoretical development around the applications of graph symmetry in power networks. A few important topics in power systems and smart grids such as controllability and robustness are addressed using the symmetry concept. These topics are directed toward solving specific problems in complex power networks. The controllability analysis will lead to new algorithms elaborating current controllability benchmarks such as the maximum matching and the minimum dominant set. The resulting algorithms will optimize the number of required driver nodes indicated as FACTS devices in power networks. The second topic, robustness, will be tackled by the symmetry analysis of the network to investigate three aspects of network robustness: robustness of controllability, disturbance decoupling, and fault tolerance against failure in a network element. In the second section, including Chapters 4-8, in addition to theoretical development, a few novel applications are proposed for the theoretical development proposed in both sections one and two. In Chapter 4, an application for the proposed approaches is introduced and developed. The placement of flexible AC transmission systems (FACTS) is investigated where the cybersecurity of the associated data exchange under the wide area power networks is also considered. A new notion of security, i.e. moderated-k-symmetry, is introduced to leverage on the symmetry characteristics of the network to obscure the network data from the adversary perspective. In chapters 5-8, the use of graph theory, and in particular, graph symmetry and centrality, are adapted for the complex network of charging stations. In Chapter 5, the placement and sizing of charging stations (CSs) of the network of electric vehicles are addressed by proposing a novel complex network model of the charging stations. The problems of placement and sizing are then reformulated in a control framework and the impact of symmetry on the number and locations of charging stations is also investigated. These results are developed in Chapters 6-7 to robust placement and sizing of charging stations for the Tesla network of Sydney where the problem of extending the capacity having a set of pre-existing CSs are addressed. The role of centrality in placement of CSs is investigated in Chapter 8. Finally, concluding remarks and future works are presented in Chapter 9

GRAPE: Parallel Graph Query Engine

The need for graph computations is evident in a multitude of use cases. To support computations on large-scale graphs, several parallel systems have been developed. However, existing graph systems require users to recast algorithms into new models, which makes parallel graph computations as a privilege to experienced users only. Moreover, real world applications often require much more complex graph processing workflows than previously evaluated. In response to these challenges, the thesis presents GRAPE, a distributed graph computation system, shipped with various applications for social network analysis, social media marketing and functional dependencies on graphs. Firstly, the thesis presents the foundation of GRAPE. The principled approach of GRAPE is based on partial evaluation and incremental computation. Sequential graph algorithms can be plugged into GRAPE with minor changes, and get parallelized as a whole. The termination and correctness are guaranteed under a monotonic condition. Secondly, as an application on GRAPE, the thesis proposes graph-pattern association rules (GPARs) for social media marketing. GPARs help users discover regularities between entities in social graphs and identify potential customers by exploring social influence. The thesis studies the problem of discovering top-k diversified GPARs and the problem of identifying potential customers with GPARs. Although both are NP- hard, parallel scalable algorithms on GRAPE are developed, which guarantee a polynomial speedup over sequential algorithms with the increase of processors. Thirdly, the thesis proposes quantified graph patterns (QGPs), an extension of graph patterns by supporting simple counting quantifiers on edges. QGPs naturally express universal and existential quantification, numeric and ratio aggregates, as well as negation. The thesis proves that the matching problem of QGPs remains NP-complete in the absence of negation, and is DP-complete for general QGPs. In addition, the thesis introduces quantified graph association rules defined with QGPs, to identify potential customers in social media marketing. Finally, to address the issue of data consistency, the thesis proposes a class of functional dependencies for graphs, referred to as GFDs. GFDs capture both attribute-value dependencies and topological structures of entities. The satisfiability and implication problems for GFDs are studied and proved to be coNP-complete and NP-complete, respectively. The thesis also proves that the validation problem for GFDs is coNP- complete. The parallel algorithms developed on GRAPE verify that GFDs provide an effective approach to detecting inconsistencies in knowledge and social graphs

Q(sqrt(-3))-Integral Points on a Mordell Curve

We use an extension of quadratic Chabauty to number fields,recently developed by the author with Balakrishnan, Besser and M ̈uller,combined with a sieving technique, to determine the integral points overQ(√−3) on the Mordell curve y2 = x3 − 4

Proceedings of the 1st International Conference on Algebras, Graphs and Ordered Sets (ALGOS 2020)

International audienceOriginating in arithmetics and logic, the theory of ordered sets is now a field of combinatorics that is intimately linked to graph theory, universal algebra and multiple-valued logic, and that has a wide range of classical applications such as formal calculus, classification, decision aid and social choice.This international conference “Algebras, graphs and ordered set” (ALGOS) brings together specialists in the theory of graphs, relational structures and ordered sets, topics that are omnipresent in artificial intelligence and in knowledge discovery, and with concrete applications in biomedical sciences, security, social networks and e-learning systems. One of the goals of this event is to provide a common ground for mathematicians and computer scientists to meet, to present their latest results, and to discuss original applications in related scientific fields. On this basis, we hope for fruitful exchanges that can motivate multidisciplinary projects.The first edition of ALgebras, Graphs and Ordered Sets (ALGOS 2020) has a particular motivation, namely, an opportunity to honour Maurice Pouzet on his 75th birthday! For this reason, we have particularly welcomed submissions in areas related to Maurice’s many scientific interests:• Lattices and ordered sets• Combinatorics and graph theory• Set theory and theory of relations• Universal algebra and multiple valued logic• Applications: formal calculus, knowledge discovery, biomedical sciences, decision aid and social choice, security, social networks, web semantics..

Category theory for scientists (Old version)

There are many books designed to introduce category theory to either a mathematical audience or a computer science audience. In this book, our audience is the broader scientific community. We attempt to show that category theory can be applied throughout the sciences as a framework for modeling phenomena and communicating results. In order to target the scientific audience, this book is example-based rather than proof-based. For example, monoids are framed in terms of agents acting on objects, sheaves are introduced with primary examples coming from geography, and colored operads are discussed in terms of their ability to model self-similarity. A new version with solutions to exercises will be available through MIT Press.Comment: 267 pages, 5 chapters, 280 exercises, an index. This book was written as course notes for a special subjects Math class at MIT called "18-S996: Category Theory for scientists", taught in Spring 2013. The class had a diverse enrollment: At the end, the number of registered students was 18 = 7 undergrad + 11 grad = 5 math + 4 EECS + 3 physics + 3 engineering + 3 othe