On the Approximation of the Kolmogorov Complexity for DNA Sequences

Statistical analysis of synonymous and stop codons in pseudo-random and real sequences as a function of GC content

Knowledge of the frequencies of synonymous triplets in protein-coding and non-coding DNA stretches can be used in gene finding. These frequencies depend on the GC content of the genome or parts of it. An example of interest is provided by stop codons. This is relevant for the definition of Open Reading Frames. A generic case is provided by pseudo-random sequences, especially when they code for complex proteins or when they are non-coding and not subject to selection pressure. Here, we calculate, for such sequences and for all 25 known genetic codes, the frequency of each amino acid and stop codon based on their set of codons and as a function of GC content. The amino acids can be classified into five groups according to the GC content where their expected frequency reaches its maximum. We determine the overall Shannon information based on groups of synonymous codons and show that it becomes maximum at a percent GC of 43.3% (for the standard code). This is in line with the observation that in most fungi, plants, and animals, this genomic parameter is in the range from 35 to 50%. By analysing natural sequences, we show that there is a clear bias for triplets corresponding to stop codons near the 5'- and 3'-splice sites in the introns of various clades.

Same but different: The influence of context framing on subjective disgust, eye movements and pupillary responses

The adaptive value of disgust has been associated with situations of threat to our survival. This study explored this topic using eye-tracking, which provides an objective measurement of attention, while solving previous methodological issues (e.g., not considering discrete emotions and comparing across perceptually-different stimuli). We used the same stimuli and manipulated the emotional state via contextual framing. Participants' eye movements and pupillary responses were recorded while they explored pictures of objects held by clean or dirty hands; the latter were framed in a disease or a non-disease context. Pictures were then rated for arousal, disgust, and valence. Framing stimuli in a disease (vs non-disease) context induced a more adverse subjective emotional experience. Importantly, our objective measures revealed that such manipulation also led to a higher information-seeking behavior and greater pupil constriction. Overall, our data suggest that the same stimuli can effectively be used to induce different emotional states by manipulating their framing.

Efficient DNA sequence compression with neural networks

BACKGROUND

The increasing production of genomic data has led to an intensified need for models that can cope efficiently with the lossless compression of DNA sequences. Important applications include long-term storage and compression-based data analysis. In the literature, only a few recent articles propose the use of neural networks for DNA sequence compression. However, they fall short when compared with specific DNA compression tools, such as GeCo2. This limitation is due to the absence of models specifically designed for DNA sequences. In this work, we combine the power of neural networks with specific DNA models. For this purpose, we created GeCo3, a new genomic sequence compressor that uses neural networks for mixing multiple context and substitution-tolerant context models.

FINDINGS

We benchmark GeCo3 as a reference-free DNA compressor in 5 datasets, including a balanced and comprehensive dataset of DNA sequences, the Y-chromosome and human mitogenome, 2 compilations of archaeal and virus genomes, 4 whole genomes, and 2 collections of FASTQ data of a human virome and ancient DNA. GeCo3 achieves a solid improvement in compression over the previous version (GeCo2) of $2.4\%$, $7.1\%$, $6.1\%$, $5.8\%$, and $6.0\%$, respectively. To test its performance as a reference-based DNA compressor, we benchmark GeCo3 in 4 datasets constituted by the pairwise compression of the chromosomes of the genomes of several primates. GeCo3 improves the compression in $12.4\%$, $11.7\%$, $10.8\%$, and $10.1\%$ over the state of the art. The cost of this compression improvement is some additional computational time (1.7-3 times slower than GeCo2). The RAM use is constant, and the tool scales efficiently, independently of the sequence size. Overall, these values outperform the state of the art.

CONCLUSIONS

GeCo3 is a genomic sequence compressor with a neural network mixing approach that provides additional gains over top specific genomic compressors. The proposed mixing method is portable, requiring only the probabilities of the models as inputs, providing easy adaptation to other data compressors or compression-based data analysis tools. GeCo3 is released under GPLv3 and is available for free download at https://github.com/cobilab/geco3.

Statistical Complexity Analysis of Turing Machine tapes with Fixed Algorithmic Complexity Using the Best-Order Markov Model

Sources that generate symbolic sequences with algorithmic nature may differ in statistical complexity because they create structures that follow algorithmic schemes, rather than generating symbols from a probabilistic function assuming independence. In the case of Turing machines, this means that machines with the same algorithmic complexity can create tapes with different statistical complexity. In this paper, we use a compression-based approach to measure global and local statistical complexity of specific Turing machine tapes with the same number of states and alphabet. Both measures are estimated using the best-order Markov model. For the global measure, we use the Normalized Compression (NC), while, for the local measures, we define and use normal and dynamic complexity profiles to quantify and localize lower and higher regions of statistical complexity. We assessed the validity of our methodology on synthetic and real genomic data showing that it is tolerant to increasing rates of editions and block permutations. Regarding the analysis of the tapes, we localize patterns of higher statistical complexity in two regions, for a different number of machine states. We show that these patterns are generated by a decrease of the tape's amplitude, given the setting of small rule cycles. Additionally, we performed a comparison with a measure that uses both algorithmic and statistical approaches (BDM) for analysis of the tapes. Naturally, BDM is efficient given the algorithmic nature of the tapes. However, for a higher number of states, BDM is progressively approximated by our methodology. Finally, we provide a simple algorithm to increase the statistical complexity of a Turing machine tape while retaining the same algorithmic complexity. We supply a publicly available implementation of the algorithm in C++ language under the GPLv3 license. All results can be reproduced in full with scripts provided at the repository.

Computational analysis of the SARS-CoV-2 and other viruses based on the Kolmogorov's complexity and Shannon's information theories

This paper tackles the information of 133 RNA viruses available in public databases under the light of several mathematical and computational tools. First, the formal concepts of distance metrics, Kolmogorov complexity and Shannon information are recalled. Second, the computational tools available presently for tackling and visualizing patterns embedded in datasets, such as the hierarchical clustering and the multidimensional scaling, are discussed. The synergies of the common application of the mathematical and computational resources are then used for exploring the RNA data, cross-evaluating the normalized compression distance, entropy and Jensen-Shannon divergence, versus representations in two and three dimensions. The results of these different perspectives give extra light in what concerns the relations between the distinct RNA viruses.