Related papers: On Binary de Bruijn Sequences from LFSRs with Arbi…
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…
We introduce a new construction for the balancing of non-binary sequences that make use of Gray codes for prefix coding. Our construction provides full encoding and decoding of sequences, including the prefix. This construction is based on…
Linear Feedback Shift Registers (LFRS) are tools commonly used in cryptography in many different context, for example as pseudo-random numbers generators. In this paper we characterize LFRS with certain symmetry properties. Related to this…
We consider the problem of discovering causal relations from independence constraints selection bias in addition to confounding is present. While the seminal FCI algorithm is sound and complete in this setup, no criterion for the causal…
A De Bruijn cycle is a cyclic sequence in which every word of length $n$ over an alphabet $\mathcal{A}$ appears exactly once. De Bruijn tori are a two-dimensional analogue. Motivated by recent progress on universal partial cycles and words,…
There has been an increasing interest from the scientific community in using likelihood-free inference (LFI) to determine which parameters of a given simulator model could best describe a set of experimental data. Despite exciting recent…
This paper presents a Bayesian approach to learning the connectivity structure of a group of neurons from data on configuration frequencies. A major objective of the research is to provide statistical tools for detecting changes in firing…
In this paper, we employ group rings and automorphism groups of binary linear codes to construct new record-breaking binary linear codes. We consider the semidirect product of abelian groups and cyclic groups and use these groups to…
The rapid expansion of genomic sequence data calls for new methods to achieve robust sequence representations. Existing techniques often neglect intricate structural details, emphasizing mainly contextual information. To address this, we…
An artificial neural network can be used to generate a series of numbers. A boolean perceptron generates bit sequences with a periodic structure. The corresponding spectrum of cycle lengths is investigated analytically and numerically; it…
Cycle prefix digraphs have been proposed as an efficient model of symmetric interconnection networks for parallel architecture. It has been discovered that the cycle prefix networks have many attractive communication properties. In this…
Generating random and pseudorandom numbers with a deterministic system is a long-standing challenge in theoretical research and engineering applications. Several pseudorandom number generators based on the inversive congruential method have…
The skew of a binary string is the difference between the number of zeroes and the number of ones, while the length of the string is the sum of these two numbers. We consider certain suffixes of the lexicographically-least de Bruijn…
De novo DNA assembly is a fundamental task in Bioinformatics, and finding Eulerian paths on de Bruijn graphs is one of the dominant approaches to it. In most of the cases, there may be no one order for the de Bruijn graph that works well…
In this paper, we develop a structure theory for generalized spectral sequences, which are derived from chain complexes that are filtered over arbitrary partially ordered sets. Also, a more general construction method reminiscent of exact…
We present a general algorithm for generating arbitrary standard complementary pairs of sequences (including binary, polyphase, M-PSK and QAM) of length 2^N using Boolean functions. The algorithm follows our earlier paraunitary algorithm,…
A method for encoding and decoding spectrum shaped binary run-length constrained sequences is described. The binary sequences with predefined range of exponential sums are introduced. On the base of Cover's enumerative scheme, recurrence…
This paper presents a framework for binary autoregressive time series in which each observation is a Bernoulli variable whose success probability evolves with past outcomes and probabilities, in the spirit of GARCH-type dynamics,…
An $(m,n,R)$-de Bruijn covering array (dBCA) is a doubly periodic $M \times N$ array over an alphabet of size $q$ such that the set of all its $m \times n$ windows form a covering code with radius $R$. An upper bound of the smallest array…
We present a dynamic prediction framework for binary sequences that is based on a Bernoulli generalization of the auto-regressive process. Our approach lends itself easily to variants of the standard link prediction problem for a sequence…