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Recent sequential pattern mining methods have used the minimum description length (MDL) principle to define an encoding scheme which describes an algorithm for mining the most compressing patterns in a database. We present a novel…
We show that it is possible to algorithmically verify if a given pattern sequence is noncorrelated. As an application, we compute that there are exactly $2272$ noncorrelated binary pattern sequences of length $\leq 4$. If we restrict our…
Recently, Chang and Hyun obtained some classes of binary optimal codes via simplicial complexes. In this letter, we utilize posets of the disjoint union of two chains to construct binary optimal linear codes.
Low-discrepancy sequences have seen widespread adoption in computer graphics thanks to their superior convergence rates. Since rendering integrals often comprise products of lower-dimensional integrals, recent work has focused on developing…
In this paper, we use a linear programming (LP) optimization approach to evaluate the equivocation for a wiretap channel where the main channel is noiseless, and the wiretap channel is a binary symmetric channel (BSC). Using this technique,…
The linear complexity and the $k$-error linear complexity of a binary sequence are important security measures for key stream strength. By studying binary sequences with the minimum Hamming weight, a new tool named as hypercube theory is…
Frequency hopping sequences (FHSs) with favorable partial Hamming correlation properties have important applications in many synchronization and multiple-access systems. In this paper, we investigate constructions of FHS sets with optimal…
We analyze the signum-generation method for creating random dichotomic sequences with prescribed correlation properties. The method is based on a binary mapping of the convolution of continuous random numbers with some function originated…
Self-supervised learning achieves superior performance in many domains by extracting useful representations from the unlabeled data. However, most of traditional self-supervised methods mainly focus on exploring the inter-sample structure…
We introduce an altered version of the four circulant construction over group rings for self-dual codes. We consider this construction over the binary field, the rings F_2 + uF_2 and F_4 + uF_4; using groups of order 3, 7, 9, 13, and 15.…
In this paper, we establish a new bound tying together the effective length and the maximum correlation between the outputs of an arbitrary pair of Boolean functions which operate on two sequences of correlated random variables. We derive a…
Based on Euclid's algorithm, we find a kind of special sequences which play an interesting role in the study of primes. We call them W Sequences. They not only ties up the distribution of primes in short interval but also enables us to give…
Behavior of two-time autocorrelation during the phase separation in solid binary mixtures are studied via numerical solutions of the Cahn-Hilliard equation as well as Monte Carlo simulations of the Ising model. Results are analyzed via…
Locally repairable codes (LRCs), which can recover any symbol of a codeword by reading only a small number of other symbols, have been widely used in real-world distributed storage systems, such as Microsoft Azure Storage and Ceph Storage…
Binary segmentation is the classic greedy algorithm which recursively splits a sequential data set by optimizing some loss or likelihood function. Binary segmentation is widely used for changepoint detection in data sets measured over space…
Over the brief time intervals available for processing retinal output, roughly 50 to 300 msec, the number of extra spikes generated by individual ganglion cells can be quite variable. Here, computer-generated spike trains were used to…
The beam interruptions (interlocks) of particle accelerators, despite being necessary safety measures, lead to abrupt operational changes and a substantial loss of beam time. A novel time series classification approach is applied to…
In recent years, several classes of codes are introduced to provide some fault-tolerance and guarantee system reliability in distributed storage systems, among which locally repairable codes (LRCs for short) play an important role. However,…
Zero correlation zone (ZCZ) sequences and Golay complementary sequences are two kinds of sequences with different preferable correlation properties. Golay-ZCZ sequences are special kinds of complementary sequences which also possess a large…
There has been recent interest in the study of shortest self-orthogonal embeddings of binary linear codes, since many such codes are optimal self-orthogonal codes. Several authors have studied the length of a shortest self-orthogonal…