Lakshmanan Kuppusamy

A survey on game theoretic models for community detection in social networks

Community detection in social networks has received much attention from the researchers of multiple disciplines due to its impactful applications such as recommendation systems, link prediction, and anomaly detection. The focus of community detection is to determine the more dense subgraphs of the network which are called communities. The nodes of the community are expected to have similar features and interests. Assuming the nodes as selfish agents, the evolution of communities can be effectively modelled as a community formation game. Game theory provides a systematic framework to model the competition and coordination among the players. In the past decade, there are several contributions from the domain of game theory to address the problem of community detection in social networks. In this paper, we make a comprehensive survey that studies and provides an insight into available game theory-based community detection algorithms. The current study provides the taxonomy of game models and their characteristics along with their performance. We discuss the interesting applications of game theory for social networks and also provide further research directions as well as some open challenges.

Matrix insertion-deletion systems for bio-molecular structures

Insertion and deletion are considered to be the basic operations in Biology, more specifically in DNA processing and RNA editing. Based on these evolutionary transformations, a computing model has been formulated in formal language theory known as insertion-deletion systems. Since the biological macromolecules can be viewed as symbols, the gene sequences can be represented as strings. This suggests that the molecular representations can be theoretically analyzed if a biologically inspired computing model recognizes various bio-molecular structures like pseudoknot, hairpin, stem and loop, cloverleaf and dumbbell. In this paper, we introduce a simple grammar system that encompasses many bio-molecular structures including the above mentioned structures. This new grammar system is based on insertion-deletion and matrix grammar systems and is called Matrix insertion-deletion grammars. Finally, we discuss how the ambiguity levels defined for insertion-deletion grammar systems can be realized in bio-molecular structures, thus the ambiguity issues in gene sequences can be studied in terms of grammar systems.

Modelling DNA and RNA secondary structures using matrix insertion-deletion systems

Abstract Insertion and deletion are operations that occur commonly in DNA processing and RNA editing. Since biological macromolecules can be viewed as symbols, gene sequences can be represented as strings and structures can be interpreted as languages. This suggests that the bio-molecular structures that occur at different levels can be theoretically studied by formal languages. In the literature, there is no unique grammar formalism that captures various bio-molecular structures. To overcome this deficiency, in this paper, we introduce a simple grammar model called the matrix insertion–deletion system, and using it we model several bio-molecular structures that occur at the intramolecular, intermolecular and RNA secondary levels.

Parikh Images of Matrix Ins-Del Systems

Matrix insertion-deletion systems combine the idea of matrix control (as established in regulated rewriting) with that of insertion and deletion (as opposed to replacements). We study families of multisets that can be described as Parikh images of languages generated by this type of systems, focusing on aspects of descriptional complexity. We show that the Parikh images of matrix insertion-deletion systems having length 2 matrices and context-free insertion/deletion contain only semilinear languages and when the matrices length increased to 3, they contain non-semilinear languages. We also characterize the hierarchy of family of languages that is formed with these systems having small sizes. We also introduce a new class, namely, monotone strict context-free matrix ins-del systems and analyze the results connecting with families of context-sensitive languages and Parikh images of regular and context-free matrix languages.

Graph-Controlled Insertion-Deletion Systems Generating Language Classes Beyond Linearity

A regulated extension of an insertion-deletion system known as graph-controlled insertion-deletion (GCID) system has several components and each component contains some insertion-deletion rules. A rule is applied to a string in a component and the resultant string is moved to the target component specified in the rule. When resources are so limited (especially, when deletion is context-free) then GCID systems are not known to describe the class of recursively enumerable languages. Hence, it becomes interesting to find the descriptional complexity of such GCID systems of small sizes with respect to language classes below \(\mathrm {RE}\). To this end, we consider closure classes of linear languages. We show that whenever GCID systems describe \(\mathrm {LIN}\) with t components, we can extend this to GCID systems with just one more component to describe, for instance, 2-\(\mathrm {LIN}\) and with further addition of one more component, we can extend to GCID systems that describe the rational closure of \(\mathrm {LIN}\).

On the computational completeness of graph-controlled insertion–deletion systems with binary sizes

Abstract A graph-controlled insertion–deletion (GCID) system is a regulated extension of an insertion–deletion system. Such a system has several components and each component has some insertion–deletion rules. The transition is performed by any applicable rule in the current component on a string and the resultant string is then moved to the target component specified in the rule. The language of the system is the set of all terminal strings collected in the final component. The parameters in the size ( k ; n , i ′ , i ″ ; m , j ′ , j ″ ) of a GCID system denote (from left to right) the maximum number of components, the maximal length of the insertion string, the maximal length of the left context for insertion, the maximal length of the right context for insertion; the last three parameters follow a similar representation with respect to deletion. In this paper, we discuss the computational completeness of the families of GCID systems of size ( k ; 1 , i ′ , i ″ ; 1 , j ′ , j ″ ) with k ∈ { 3 , 5 } and for (nearly) all values of i ′ , i ″ j ′ , j ″ ∈ { 0 , 1 } . All proofs are based on the simulation of type-0 grammars given in Special Geffert Normal Form (SGNF). The novelty in our proof presentation is that the context-free and the non-context-free rules of the given SGNF grammar are simulated by GCID systems of different sizes and finally we combine them by stitching and overlaying to characterize the recursive enumerable languages. This proof presentation greatly simplifies and unifies the proof of such characterization results. We also connect some of the obtained GCID simulations to the domain of insertion–deletion P systems.

Generative Power of Matrix Insertion-Deletion Systems with Context-Free Insertion or Deletion

Matrix insertion-deletion systems combine the idea of matrix control as established in regulated rewriting with that of insertion and deletion as opposed to replacements. We improve on and complement previous computational completeness results for such systems, showing for instance that matrix insertion-deletion systems with matrices of length two, insertion rules of type 1,i?ź1,i?ź1 and context-free deletions are computationally complete. We also show how to simulate Kleene stars of metalinear languages with several types of systems with very limited resources. We also generate non-semilinear languages using matrices of length three with context-free insertion and deletion rules.

On path-controlled insertion–deletion systems

A graph-controlled insertion–deletion system is a regulated extension of an insertion–deletion system. It has several components and each component contains some insertion–deletion rules. These components are the vertices of a directed control graph. A transition is performed by any applicable rule in the current component on a string and the resultant string is then moved to the target component specified in the rule. This also describes the arcs of the control graph. Starting from an axiom in the initial component, strings thus move through the control graph. The language of the system is the set of all terminal strings collected in the final component. In this paper, we investigate a variant of the main question in this area: which combinations of size parameters (the maximum number of components, the maximal length of the insertion string, the maximal length of the left context for insertion, the maximal length of the right context for insertion; plus three similar restrictions with respect to deletion) are sufficient to maintain computational completeness of such restricted systems under the additional restriction that the (undirected) control graph is a path? Notice that these results also bear consequences for the domain of insertion–deletion P systems, improving on a number of previous results from the literature, concerning in particular the number of components (membranes) that are necessary for computational completeness results.

Computational Completeness of Path-Structured Graph-Controlled Insertion-Deletion Systems

A graph-controlled insertion-deletion (GCID) system is a regulated extension of an insertion-deletion system. It has several components and each component contains some insertion-deletion rules. These components are the vertices of a directed control graph. A rule is applied to a string in a component and the resultant string is moved to the target component specified in the rule, describing the arcs of the control graph. We investigate which combinations of size parameters (the maximum number of components, the maximal length of the insertion string, the maximal length of the left context for insertion, the maximal length of the right context for insertion; a similar three restrictions with respect to deletion) are sufficient to maintain the computational completeness of such restricted systems with the additional restriction that the control graph is a path, thus, these results also hold for ins-del P systems.

Discovering vesicle traffic network constraints by model checking

A eukaryotic cell contains multiple membrane-bound compartments. Transport vesicles move cargo between these compartments, just as trucks move cargo between warehouses. These processes are regulated by specific molecular interactions, as summarized in the Rothman-Schekman-Sudhof model of vesicle traffic. The whole structure can be represented as a transport graph: each organelle is a node, and each vesicle route is a directed edge. What constraints must such a graph satisfy, if it is to represent a biologically realizable vesicle traffic network? Graph connectedness is an informative feature: 2-connectedness is necessary and sufficient for mass balance, but stronger conditions are required to ensure correct molecular specificity. Here we use Boolean satisfiability (SAT) and model checking as a framework to discover and verify graph constraints. The poor scalability of SAT model checkers often prevents their broad application. By exploiting the special structure of the problem, we scale our model checker to vesicle traffic systems with reasonably large numbers of molecules and compartments. This allows us to test a range of hypotheses about graph connectivity, which can later be proved in full generality by other methods.