Kalpana Mahalingam

Bio: Kalpana Mahalingam is an academic researcher from Indian Institute of Technology Madras. The author has contributed to research in topics: Palindrome & Combinatorics on words. The author has an hindex of 11, co-authored 62 publications receiving 436 citations. Previous affiliations of Kalpana Mahalingam include University of Western Ontario & University of South Florida.

Watson–Crick Jumping Finite Automata: Combination, Comparison and Closure

Abstract: A new model of computation called Watson–Crick jumping finite automata was introduced by Mahalingam et al., and the authors study the computing power and closure properties of the variants of the model. There are four variants of the model: no state, 1-limited, all-final and simple Watson–Crick jumping finite automata. In this paper, we introduce a restricted version that is a combination of variants of the existing model. It becomes essential to explore the computing power and closure properties of these combinations. The combination variants are extensively compared with Chomsky hierarchy, general jumping finite automata family and among themselves. We also explore the closure properties of such restricted automata.

k-involution codes and related sets

Abstract: This study was motivated by the problem of optimally encoding information on DNA for biocomputational purposes. Our formalization of intermolecular hybridization (binding) with bulges led to the notion, interesting in its own right, of k-involution codes. An involution code refers to any of the generalizations of the classical notion of codes in which the identity function is replaced by an involution function. (An involution function θ is such that θ2 equals the identity. An antimorphic involution is the natural formalization of the notion of DNA complementarity.) We namely define and study the notions of k-θ-prefix, k-θ-suffix and k-θ-bifix codes. We also extend the notion of k-insertion set and k-deletion set of a language to incorporate the notion of an involution function. Thus, to an involution map θ and a language L, we associate a set k-θ-ins(L) (k-θ-del(L)) with the property that its k-insertion (k-deletion) into any word of L yields words which belongs to θ(L). We study the properties o...

Palindromes in two-dimensional Words

Abstract: A two-dimensional ($2$D) word is a $2$D palindrome if it is equal to its reverse and it is an HV-palindrome if all its columns and rows are $1$D palindromes. We study some combinatorial and structural properties of HV-palindromes and its comparison with $2$D palindromes. We investigate the maximum number number of distinct non-empty HV-palindromic sub-arrays in any finite $2$D word, thus, proving the conjecture given by Anisiua et al. We also find the least number of HV-palindromes in an infinite $2$D word over a finite alphabet size $q$.

Operation Insertion on the Conjugacy and Commutativity of Words

Abstract: In this paper, we do a theoretical study of some of the notions in combinatorics of words with respect to the insertion operation on words. We generalize the classical notions of conjugacy and commutativity of words to insertion-conjugacy and insertion-commutativity of words. We define and study properties of such words (i.e.) of words u, v and w such that \(u\leftarrow v = v\leftarrow u\) and \(u\leftarrow v = v\leftarrow w\).

Towards practical, high-capacity, low-maintenance information storage in synthesized DNA

Abstract: Digital production, transmission and storage have revolutionized how we access and use information but have also made archiving an increasingly complex task that requires active, continuing maintenance of digital media. This challenge has focused some interest on DNA as an attractive target for information storage because of its capacity for high-density information encoding, longevity under easily achieved conditions and proven track record as an information bearer. Previous DNA-based information storage approaches have encoded only trivial amounts of information or were not amenable to scaling-up, and used no robust error-correction and lacked examination of their cost-efficiency for large-scale information archival. Here we describe a scalable method that can reliably store more information than has been handled before. We encoded computer files totalling 739 kilobytes of hard-disk storage and with an estimated Shannon information of 5.2 × 10(6) bits into a DNA code, synthesized this DNA, sequenced it and reconstructed the original files with 100% accuracy. Theoretical analysis indicates that our DNA-based storage scheme could be scaled far beyond current global information volumes and offers a realistic technology for large-scale, long-term and infrequently accessed digital archiving. In fact, current trends in technological advances are reducing DNA synthesis costs at a pace that should make our scheme cost-effective for sub-50-year archiving within a decade.

Molecular Biology of the Gene.

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Discrete Applied Mathematics

Abstract: : Significant progress has been made with solution of location problems and in preprocessing and decomposition for discrete optimization. There has also been research on the application of techniques from combinational optimization to nonlinear problems.

Computation in Living Cells: Gene Assembly in Ciliates

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Watson---Crick palindromes in DNA computing

Abstract: This paper provides an overview of existing approaches to encoding information on DNA strands for biocomputing, with a focus on the notion of Watson---Crick (WK) palindromes. We obtain a closed form for, as well as several properties of WK palindromes: The set of WK-palindromes is dense, context-free, but not regular, and is in general not closed under catenation and insertion. We obtain some properties that link the WK palindromes to classical notions such as that of primitive words. For example we show that the set of WK-palindromic words that cannot be written as the product of two nonempty WK-palindromes equals the set of primitive WK-palindromes. We also investigate various simultaneous Watson---Crick conjugate equations of words and show that the equations have, in most cases, only Watson---Crick palindromic solutions. Our results hold for more general functions, such as arbitrary morphic and antimorphic involutions.