9 research outputs found
Locating regions in a sequence under density constraints
Several biological problems require the identification of regions in a
sequence where some feature occurs within a target density range: examples
including the location of GC-rich regions, identification of CpG islands, and
sequence matching. Mathematically, this corresponds to searching a string of 0s
and 1s for a substring whose relative proportion of 1s lies between given lower
and upper bounds. We consider the algorithmic problem of locating the longest
such substring, as well as other related problems (such as finding the shortest
substring or a maximal set of disjoint substrings). For locating the longest
such substring, we develop an algorithm that runs in O(n) time, improving upon
the previous best-known O(n log n) result. For the related problems we develop
O(n log log n) algorithms, again improving upon the best-known O(n log n)
results. Practical testing verifies that our new algorithms enjoy significantly
smaller time and memory footprints, and can process sequences that are orders
of magnitude longer as a result.Comment: 17 pages, 8 figures; v2: minor revisions, additional explanations; to
appear in SIAM Journal on Computin
Guessing with lies
A practical algorithm was obtained for directly generating an optimal guessing sequence for guessing under lies. An optimal guessing strategy was defined as one which minimizes the number of average number of guesses in determining the correct value of a random variable. The information-theoretic bounds on the average number of guesses for optimal strategies were also derived
Searching a bitstream in linear time for the longest substring of any given density
Given an arbitrary bitstream, we consider the problem of finding the longest
substring whose ratio of ones to zeroes equals a given value. The central
result of this paper is an algorithm that solves this problem in linear time.
The method involves (i) reformulating the problem as a constrained walk through
a sparse matrix, and then (ii) developing a data structure for this sparse
matrix that allows us to perform each step of the walk in amortised constant
time. We also give a linear time algorithm to find the longest substring whose
ratio of ones to zeroes is bounded below by a given value. Both problems have
practical relevance to cryptography and bioinformatics.Comment: 22 pages, 19 figures; v2: minor edits and enhancement
Back to Massey: Impressively fast, scalable and tight security evaluation tools
None of the existing rank estimation algorithms can scale to large cryptographic
keys, such as 4096-bit (512 bytes) RSA keys. In this paper, we present the first
solution to estimate the guessing entropy of arbitrarily large keys, based on
mathematical bounds, resulting in the fastest and most scalable security
evaluation tool to date. Our bounds can be computed within a fraction of a second, with
no memory overhead, and provide a margin of only a few bits for a full 128-bit
AES key
Effect of Ankaferd Blood Stopper on air leakage in the lung and prevention of bleeding: an experimental study
On plateaued functions, linear structures and permutation polynomials
We obtain concrete upper bounds on the algebraic immunity of a class of highly nonlinear plateaued functions without linear structures than the one was given recently in 2017, Cusick. Moreover, we extend Cusick’s class to a much bigger explicit class and we show that our class has better algebraic immunity by an explicit example. We also give a new notion of linear translator, which includes the Frobenius linear translator given in 2018, Cepak, Pasalic and Muratović-Ribić as a special case. We find some applications of our new notion of linear translator to the construction of permutation polynomials. Furthermore, we give explicit classes of permutation polynomials over Fqn using some properties of Fq and some conditions of 2011, Akbary, Ghioca and Wang