Abstract: A computer-implemented method and system for generating large families of sequences with desirable properties for many applications, including communications and radar applications, applies constraints to a sequence in the Zak space, modulates the constrained sequence in the Zak space, and determines permutations of the modulated sequence in the Zak space. The constraints are associated with predetermined properties, including predetermined autocorrelation and cross-correlation properties. Other embodiments of the computer-implemented method and system transform an input sequence into a transformed sequence using the finite Zak transform and determine at least one other different sequence based on the transformed sequence. The at least one other different sequence can be determined by collecting a plurality of sequences that are finitely supported on an algebraic line in the Zak space and modulating and/or determining permutations of some or all of the sequences.

Abstract: The present invention relates to methods and apparatus for rapid assessment of genomic sequences using the difference set model. The invention provides methods to determine the presence and identity of similarities and differences in genomic sequences. In particular, the invention provides methods and apparatus to assess homology, the presence and identity of insertion and deletion segments and the presence and identity of single nucleotide polymorphisms in genomic sequences.

Abstract: Methods, systems and computer program products of DNA sequence alignment using a symmetric phase only matched filter (SPOMF) are described herein. SPOMF is useful for both global alignment and local alignment. Also described herein is a prime-length cross correlation algorithm for enhancing the robustness of the SPOMF.

Abstract: A computer-implemented method and system for generating large families of sequences with desirable properties for many applications, including communications and radar applications, applies constraints to a sequence in the Zak space, modulates the constrained sequence in the Zak space, and determines permutations of the modulated sequence in the Zak space. The constraints are associated with predetermined properties, including predetermined autocorrelation and cross-correlation properties. Other embodiments of the computer-implemented method and system transform an input sequence into a transformed sequence using the finite Zak transform and determine at least one other different sequence based on the transformed sequence. The at least one other different sequence can be determined by collecting a plurality of sequences that are finitely supported on an algebraic line in the Zak space and modulating and/or determining permutations of some or all of the sequences.

Abstract: A method of detecting and outputting tandem repeats in a sequence of symbols comprising a) mapping the symbols to quaternions; b) constructing a Quaternionic Periodicity Transform (QPT); c) computing the QPT of the sequence to determine the tandem repeats of the sequence; d) post-processing of the QPT; e) outputting a list of tandem repeats obtained from step d) to a computer's memory. In embodiments, the sequence of symbols is a sequence of letters representing nucleotides in a DNA or RNA sequence.

Abstract: Methods, systems and computer program products of DNA sequence alignment using a symmetric phase only matched filter (SPOMF) are described herein. SPOMF is useful for both global alignment and local alignment. Also described herein is a prime-length cross correlation algorithm for enhancing the robustness of the SPOMF.