Related papers: Weakly Mutually Uncorrelated Codes
In distributed systems where strong consistency is costly when not impossible, causal consistency provides a valuable abstraction to represent program executions as partial orders. In addition to the sequential program order of each…
Computing the similarity between two DNA sequences is of vital importance in bioscience, yet it can be computationally expensive on classical hardware. For example, the edit distance with move operations (EDM), a DNA similarity measure of…
In the present paper, we define the concept of weak topological conjugacy and we establish sufficient conditions to obtain this kind of topological conjugacy between two limit sets. We use the character of recurrence to obtain the results.
Component-based systems evolve as a new component is added or an existing one is replaced by a newer version. Hence, it is appealing to assure the new system still preserves its safety properties. However, instead of inspecting the new…
Relative compression, where a set of similar strings are compressed with respect to a reference string, is a very effective method of compressing DNA datasets containing multiple similar sequences. Relative compression is fast to perform…
In this work, we consider the problem of synchronizing two sets of data where the size of the symmetric difference between the sets is small and, in addition, the elements in the symmetric difference are related through the Hamming distance…
We consider linear codes over a finite field of odd characteristic, derived from determinantal varieties, obtained from symmetric matrices of bounded ranks. A formula for the weight of a code word is derived. Using this formula, we have…
This paper introduces a new family of reconstruction codes which is motivated by applications in DNA data storage and sequencing. In such applications, DNA strands are sequenced by reading some subset of their substrings. While previous…
Harvey Friedman's $ \mathsf{WD} $ is a weak set theory given by the following non-logical axioms: $ \mathsf{(W)} \; \forall x y \, \exists z \, \forall u \left[ \, u \in z \leftrightarrow ( \, u \in x \; \vee \; u = y \, ) \, \right] $; $…
We present new algorithms for the problem of multiple string matching of gapped patterns, where a gapped pattern is a sequence of strings such that there is a gap of fixed length between each two consecutive strings. The problem has…
DNA-coated particles are promising as building blocks for functional and finite-sized assemblies because they can be programmed with orthogonal interactions owing to the sequence-specific hybridization of DNA strands. To fully exploit this…
Our earlier work titled: "Win-move is Coordination-Free (Sometimes)" has shown that the classes of queries that can be distributedly computed in a coordination-free manner form a strict hierarchy depending on the assumptions of the model…
This paper concerns the modeling of multi-way functional data where double or multiple indices are involved. We introduce a concept of weak separability. The weakly separable structure supports the use of factorization methods that…
We examine an error-correcting coding framework in which each coded symbol is constrained to be a function of a fixed subset of the message symbols. With an eye toward distributed storage applications, we seek to design systematic codes…
A method to construct and count all the linear codes (of arbitrary length) in $\mathbb{F}_{4}$ that are invariant under reverse permutation and that contain the repetition code is presented. These codes are suitable for constructing DNA…
Persistent homology is a leading tool in topological data analysis (TDA). Many problems in TDA can be solved via homological -- and indeed, linear -- algebra. However, matrices in this domain are typically large, with rows and columns…
A weak deletion sequence is a sequence $(G_1,\ldots,G_n)$ of graphs so that for each $i\in[n-1]$ either $G_i$ is isomorphic to a subgraph of $G_{i+1}$, or vice versa: $G_{i+1}$ is isomorphic to a subgraph of $G_i$. We prove that determining…
In this letter we consider the ensemble of codes formed by the serial concatenation of a Hamming code and two accumulate codes. We show that this ensemble is asymptotically good, in the sense that most codes in the ensemble have minimum…
We introduce constraints necessary for type checking a higher-order concurrent constraint language, and solve them with an incremental algorithm. Our constraint system extends rational unification by constraints x$\subseteq$ y saying that…
We consider superconductivity in a system with $N$ Fermi surfaces, including intraband and interband effective electron-electron interactions. The effective interaction is described by an $N \times N$ matrix whose elements are assumed to be…