Topological Data Analysis in Cardiovascular Signals: An Overview.

Topological data analysis (TDA) is a recent approach for analyzing and interpreting complex data sets based on ideas a branch of mathematics called algebraic topology. TDA has proven useful to disentangle non-trivial data structures in a broad range of data analytics problems including the study of cardiovascular signals. Here, we aim to provide an overview of the application of TDA to cardiovascular signals and its potential to enhance the understanding of cardiovascular diseases and their treatment in the form of a literature or narrative review. We first introduce the concept of TDA and its key techniques, including persistent homology, Mapper, and multidimensional scaling. We then discuss the use of TDA in analyzing various cardiovascular signals, including electrocardiography, photoplethysmography, and arterial stiffness. We also discuss the potential of TDA to improve the diagnosis and prognosis of cardiovascular diseases, as well as its limitations and challenges. Finally, we outline future directions for the use of TDA in cardiovascular signal analysis and its potential impact on clinical practice. Overall, TDA shows great promise as a powerful tool for the analysis of complex cardiovascular signals and may offer significant insights into the understanding and management of cardiovascular diseases.

Molecular shape as a key source of prebiotic information.

One of the most striking features of a living system is the self-sustaining functional inner organization, which is only possible when a source of internal references is available from which the system is able to self-organize components and processes. Internal references are intrinsically related to biological information, which is typically understood as genetic information. However, the organization in living systems supports a diversity of intricate processes that enable life to endure, adapt and reproduce because of this organization. In a biological context, information refers to a complex relationship between internal architecture and system functionality. Nongenetic processes, such as conformational recognition, are not considered biological information, although they exert important control over cell processes. In this contribution, we discuss the informational nature in the recognition of molecular shape in living systems. Thus, we highlight supramolecular matching as having a theoretical key role in the origin of life. Based on recent data, we demonstrate that the transfer of molecular conformation is a very likely dynamic of prebiotic information, which is closely related to the origin of biological homochirality and biogenic systems. In light of the current hypothesis, we also revisit the central dogma of molecular biology to assess the consistency of the proposal presented here. We conclude that both spatial (molecular shape) and sequential (genetic) information must be represented in this biological paradigm.

Diminishing return for increased Mappability with longer sequencing reads: implications of the k-mer distributions in the human genome.

BACKGROUND: The amount of non-unique sequence (non-singletons) in a genome directly affects the difficulty of read alignment to a reference assembly for high throughput-sequencing data. Although a longer read is more likely to be uniquely mapped to the reference genome, a quantitative analysis of the influence of read lengths on mappability has been lacking. To address this question, we evaluate the k-mer distribution of the human reference genome. The k-mer frequency is determined for k ranging from 20 bp to 1000 bp. RESULTS: We observe that the proportion of non-singletons k-mers decreases slowly with increasing k, and can be fitted by piecewise power-law functions with different exponents at different ranges of k. A slower decay at greater values for k indicates more limited gains in mappability for read lengths between 200 bp and 1000 bp. The frequency distributions of k-mers exhibit long tails with a power-law-like trend, and rank frequency plots exhibit a concave Zipf's curve. The most frequent 1000-mers comprise 172 regions, which include four large stretches on chromosomes 1 and X, containing genes of biomedical relevance. Comparison with other databases indicates that the 172 regions can be broadly classified into two types: those containing LINE transposable elements and those containing segmental duplications. CONCLUSION: Read mappability as measured by the proportion of singletons increases steadily up to the length scale around 200 bp. When read length increases above 200 bp, smaller gains in mappability are expected. Moreover, the proportion of non-singletons decreases with read lengths much slower than linear. Even a read length of 1000 bp would not allow the unique alignment of reads for many coding regions of human genes. A mix of techniques will be needed for efficiently producing high-quality data that cover the complete human genome.

Spatial Information in the Emergence of Life.

Information in living systems is part of a complex relationship between the internal organization and functionality of life. In a cell, both genetic-coding sequences and molecular-shape recognition are sources of biological information. For folded polymers, its spatial arrangement contains general references about conditions that shaped them, as imprints, defining the data for spatial (conformational) information. Considering the origin of life problem, prebiotic dynamics of matching and transfer of molecular shapes may emerge as a flow of information in prebiotic assemblages. The property of carrying information in molecular conformations is only displayed at this system organization level. Accordingly, spatial information is a resource for active system responses toward milieu disturbances. Propagation of resilient conformations could be the substrate for structural maintenance through dynamical molecular scaffolding. The above is a basis for adaptive behavior in potentially biogenic systems. Starting from non-structured populations of carrying-information polymers, in the present contribution, we advance toward an entire theoretical framework considering the active role of these polymers to support the emergence of adaptive response in systems that manage conformational information flow. We discuss this scenario as a previous step for the arising of sequential information carried out by genetic polymers.

Multiwall and bamboo-like carbon nanotubes from the Allende chondrite: A probable source of asymmetry.

This study presents multiwall and bamboo-like carbon nanotubes found in samples from the Allende carbonaceous chondrite using high-resolution transmission electron microscopy (HRTEM). A highly disordered lattice observed in this material suggests the presence of chiral domains in it. Our results also show amorphous and poorly-graphitized carbon, nanodiamonds, and onion-like fullerenes. The presence of multiwall and bamboo-like carbon nanotubes have important implications for hypotheses that explain how a probable source of asymmetry in carbonaceous chondrites might have contributed to the enantiomeric excess in soluble organics under extraterrestrial scenarios. This is the first study proving the existence of carbon nanotubes in carbonaceous chondrites.

The Color of Noise and Weak Stationarity at the NREM to REM Sleep Transition in Mild Cognitive Impaired Subjects.

In Older Adults (OAs), Electroencephalogram (EEG) slowing in frontal lobes and a diminished muscle atonia during Rapid Eye Movement sleep (REM) have each been effective tracers of Mild Cognitive Impairment (MCI), but this relationship remains to be explored by non-linear analysis. Likewise, data provided by EEG, EMG (Electromyogram) and EOG (Electrooculogram)-the three required sleep indicators-during the transition from REM to Non-REM (NREM) sleep have not been related jointly to MCI. Therefore, the main aim of the study was to explore, with results for Detrended Fluctuation Analysis (DFA) and multichannel DFA (mDFA), the Color of Noise (CN) at the NREM to REM transition in OAs with MCI vs. subjects with good performances. The comparisons for the transition from NREM to REM were made for each group at each cerebral area, taking bilateral derivations to evaluate interhemispheric coupling and anteroposterior and posterior networks. In addition, stationarity analysis was carried out to explore if the three markers distinguished between the groups. Neuropsi and the Mini-Mental State Examination (MMSE) were administered, as well as other geriatric tests. One night polysomnography was applied to 6 OAs with MCI (68.1 ± 3) and to 7 subjects without it (CTRL) (64.5 ± 9), and pre-REM and REM epochs were analyzed for each subject. Lower scores for attention, memory and executive funcions and a greater index of arousals during sleep were found for the MCI group. Results confirmed that EOGs constituted significant markers of MCI, increasing the CN for the MCI group in REM sleep. The CN of the EEG from the pre-REM to REM was higher for the MCI group vs. the opposite for the CTRL group at frontotemporal areas. Frontopolar interhemispheric scaling values also followed this trend as well as right anteroposterior networks. EMG Hurst values for both groups were lower than those for EEG and EOG. Stationarity analyses showed differences between stages in frontal areas and right and left EOGs for both groups. These results may demonstrate the breakdown of fractality of areas especially involved in executive functioning and the way weak stationarity analyses may help to distinguish between sleep stages in OAs.

Population patterns in World's administrative units.

Whereas there has been an extended discussion concerning city population distribution, little has been said about that of administrative divisions. In this work, we investigate the population distribution of second-level administrative units of 150 countries and territories and propose the discrete generalized beta distribution (DGBD) rank-size function to describe the data. After testing the balance between the goodness of fit and number of parameters of this function compared with a power law, which is the most common model for city population, the DGBD is a good statistical model for 96% of our datasets and preferred over a power law in almost every case. Moreover, the DGBD is preferred over a power law for fitting country population data, which can be seen as the zeroth-level administrative unit. We present a computational toy model to simulate the formation of administrative divisions in one dimension and give numerical evidence that the DGBD arises from a particular case of this model. This model, along with the fitting of the DGBD, proves adequate in reproducing and describing local unit evolution and its effect on the population distribution.

Modeling the dynamics of chromosomal alteration progression in cervical cancer: A computational model.

Computational modeling has been applied to simulate the heterogeneity of cancer behavior. The development of Cervical Cancer (CC) is a process in which the cell acquires dynamic behavior from non-deleterious and deleterious mutations, exhibiting chromosomal alterations as a manifestation of this dynamic. To further determine the progression of chromosomal alterations in precursor lesions and CC, we introduce a computational model to study the dynamics of deleterious and non-deleterious mutations as an outcome of tumor progression. The analysis of chromosomal alterations mediated by our model reveals that multiple deleterious mutations are more frequent in precursor lesions than in CC. Cells with lethal deleterious mutations would be eliminated, which would mitigate cancer progression; on the other hand, cells with non-deleterious mutations would become dominant, which could predispose them to cancer progression. The study of somatic alterations through computer simulations of cancer progression provides a feasible pathway for insights into the transformation of cell mechanisms in humans. During cancer progression, tumors may acquire new phenotype traits, such as the ability to invade and metastasize or to become clinically important when they develop drug resistance. Non-deleterious chromosomal alterations contribute to this progression.

Large-scale oscillation of structure-related DNA sequence features in human chromosome 21.

Human chromosome 21 is the only chromosome in the human genome that exhibits oscillation of the (G+C) content of a cycle length of hundreds kilobases (kb) ( 500 kb near the right telomere). We aim at establishing the existence of a similar periodicity in structure-related sequence features in order to relate this (G+C)% oscillation to other biological phenomena. The following quantities are shown to oscillate with the same 500 kb periodicity in human chromosome 21: binding energy calculated by two sets of dinucleotide-based thermodynamic parameters, AA/TT and AAA/TTT bi- and tri-nucleotide density, 5'-TA-3' dinucleotide density, and signal for 10- or 11-base periodicity of AA/TT or AAA/TTT. These intrinsic quantities are related to structural features of the double helix of DNA molecules, such as base-pair binding, untwisting or unwinding, stiffness, and a putative tendency for nucleosome formation.

A theoretical framework for defining some concepts in evolution.

We present a theoretical framework for biological evolution with the intention of giving precise mathematical definitions of some concepts in evolutionary biology such as fitness, evolutionary pressure, specialization and natural selection. In this framework, such concepts are identified with well-known mathematical terms within the theory of dynamical systems. We also discuss some more general implications in evolution; for instance, the fact that our model naturally exhibits a frequency spectrum of the type 1/f for low frequencies of evolutionary events.

Size distribution of function-based human gene sets and the split-merge model.

The sizes of paralogues-gene families produced by ancestral duplication-are known to follow a power-law distribution. We examine the size distribution of gene sets or gene families where genes are grouped by a similar function or share a common property. The size distribution of Human Gene Nomenclature Committee (HGNC) gene sets deviate from the power-law, and can be fitted much better by a beta rank function. We propose a simple mechanism to break a power-law size distribution by a combination of splitting and merging operations. The largest gene sets are split into two to account for the subfunctional categories, and a small proportion of other gene sets are merged into larger sets as new common themes might be realized. These operations are not uncommon for a curator of gene sets. A simulation shows that iteration of these operations changes the size distribution of Ensembl paralogues and could lead to a distribution fitted by a rank beta function. We further illustrate application of beta rank function by the example of distribution of transcription factors and drug target genes among HGNC gene families.

Beyond Zipf's Law: The Lavalette Rank Function and Its Properties.

Although Zipf's law is widespread in natural and social data, one often encounters situations where one or both ends of the ranked data deviate from the power-law function. Previously we proposed the Beta rank function to improve the fitting of data which does not follow a perfect Zipf's law. Here we show that when the two parameters in the Beta rank function have the same value, the Lavalette rank function, the probability density function can be derived analytically. We also show both computationally and analytically that Lavalette distribution is approximately equal, though not identical, to the lognormal distribution. We illustrate the utility of Lavalette rank function in several datasets. We also address three analysis issues on the statistical testing of Lavalette fitting function, comparison between Zipf's law and lognormal distribution through Lavalette function, and comparison between lognormal distribution and Lavalette distribution.

[Abdominal actinomycosis: report of three cases]. / Actinomicosis abdominal. Presentación de tres casos.

We present three cases of abdominal actinomycosis in females, one presenting with an abdominal mass and the two others underwent emergency surgery because of acute abdomen with a diagnosis of complicated acute appendicitis. The first patient (age 36 years) presented with an abdominal mass in the left lower quadrant arising from the colon as observed by abdominal computed tomography (CT). The patient was brought to the operating room and tumoral resection was done. The second and third patients (37 years and 39 years, respectively) were brought to the emergency room because of acute abdominal pain with leucocytosis. Exploratory laparotomy was performed, finding in the second patient a bilateral ovarian abscess and uterine perforation. Hysterectomy and salpingo-oophorectomy were done. In the third patient, the findings were a sigmoid mass and a bilateral tubo-ovarian abscess and these organs were resected. Samples were sent for pathologic analysis. Microscopic analysis of the specimens sent revealed the presence of "sulfur granules," and a diagnosis of actinomycosis was made. Abdominal actinomycosis is a rare disease and preoperative diagnosis is uncommon. It is necessary to complete the full course of antibiotic therapy in order to completely eradicate the disease.

Bacterial genomes lacking long-range correlations may not be modeled by low-order Markov chains: the role of mixing statistics and frame shift of neighboring genes.

We examine the relationship between exponential correlation functions and Markov models in a bacterial genome in detail. Despite the well known fact that Markov models generate sequences with correlation function that decays exponentially, simply constructed Markov models based on nearest-neighbor dimer (first-order), trimer (second-order), up to hexamer (fifth-order), and treating the DNA sequence as being homogeneous all fail to predict the value of exponential decay rate. Even reading-frame-specific Markov models (both first- and fifth-order) could not explain the fact that the exponential decay is very slow. Starting with the in-phase coding-DNA-sequence (CDS), we investigated correlation within a fixed-codon-position subsequence, and in artificially constructed sequences by packing CDSs with out-of-phase spacers, as well as altering CDS length distribution by imposing an upper limit. From these targeted analyses, we conclude that the correlation in the bacterial genomic sequence is mainly due to a mixing of heterogeneous statistics at different codon positions, and the decay of correlation is due to the possible out-of-phase between neighboring CDSs. There are also small contributions to the correlation from bases at the same codon position, as well as by non-coding sequences. These show that the seemingly simple exponential correlation functions in bacterial genome hide a complexity in correlation structure which is not suitable for a modeling by Markov chain in a homogeneous sequence. Other results include: use of the (absolute value) second largest eigenvalue to represent the 16 correlation functions and the prediction of a 10-11 base periodicity from the hexamer frequencies.

Dynamics of high-risk nonvaccine human papillomavirus types after actual vaccination scheme.

Human papillomavirus (HPV) has been identified as the main etiological factor in the developing of cervical cancer (CC). This finding has propitiated the development of vaccines that help to prevent the HPVs 16 and 18 infection. Both genotypes are associated with 70% of CC worldwide. In the present study, we aimed to determine the emergence of high-risk nonvaccine HPV after actual vaccination scheme to estimate the impact of the current HPV vaccines. A SIR-type model was used to study the HPV dynamics after vaccination. According to the results, our model indicates that the application of the vaccine reduces infection by target or vaccine genotypes as expected. However, numerical simulations of the model suggest the presence of the phenomenon called vaccine-induced pathogen strain replacement. Here, we report the following replacement mechanism: if the effectiveness of cross-protective immunity is not larger than the effectiveness of the vaccine, then the high-risk nonvaccine genotypes emerge. In this scenario, further studies of infection dispersion by HPV are necessary to ascertain the real impact of the current vaccines, primarily because of the different high-risk HPV types that are found in CC.

Role reversal in a predator-prey interaction.

Predator-prey relationships are one of the most studied interactions in population ecology. However, little attention has been paid to the possibility of role exchange between species, despite firm field evidence of such phenomena in nature. In this paper, we build a mathematical model capable of reproducing the main phenomenological features of role reversal in a classical system and present results for both the temporal and spatio-temporal cases. We show that, depending on the choice of parameters, our role-reversal dynamical system exhibits excitable-like behaviour, generating waves of species' concentrations that propagate through space. Our findings fill a long-standing gap in modelling ecological interactions and can be applicable to better understanding ecological niche shifts and planning of sustainable ecosystems.

Periodic distribution of a putative nucleosome positioning motif in human, nonhuman primates, and archaea: mutual information analysis.

Recently, Trifonov's group proposed a 10-mer DNA motif YYYYYRRRRR as a solution of the long-standing problem of sequence-based nucleosome positioning. To test whether this generic decamer represents a biological meaningful signal, we compare the distribution of this motif in primates and Archaea, which are known to contain nucleosomes, and in Eubacteria, which do not possess nucleosomes. The distribution of the motif is analyzed by the mutual information function (MIF) with a shifted version of itself (MIF profile). We found common features in the patterns of this generic decamer on MIF profiles among primate species, and interestingly we found conspicuous but dissimilar MIF profiles for each Archaea tested. The overall MIF profiles for each chromosome in each primate species also follow a similar pattern. Trifonov's generic decamer may be a highly conserved motif for the nucleosome positioning, but we argue that this is not the only motif. The distribution of this generic decamer exhibits previously unidentified periodicities, which are associated to highly repetitive sequences in the genome. Alu repetitive elements contribute to the most fundamental structure of nucleosome positioning in higher Eukaryotes. In some regions of primate chromosomes, the distribution of the decamer shows symmetrical patterns including inverted repeats.

Universality of rank-ordering distributions in the arts and sciences.

Searching for generic behaviors has been one of the driving forces leading to a deep understanding and classification of diverse phenomena. Usually a starting point is the development of a phenomenology based on observations. Such is the case for power law distributions encountered in a wealth of situations coming from physics, geophysics, biology, lexicography as well as social and financial networks. This finding is however restricted to a range of values outside of which finite size corrections are often invoked. Here we uncover a universal behavior of the way in which elements of a system are distributed according to their rank with respect to a given property, valid for the full range of values, regardless of whether or not a power law has previously been suggested. We propose a two parameter functional form for these rank-ordered distributions that gives excellent fits to an impressive amount of very diverse phenomena, coming from the arts, social and natural sciences. It is a discrete version of a generalized beta distribution, given by f(r) = A(N+1-r)(b)/r(a), where r is the rank, N its maximum value, A the normalization constant and (a, b) two fitting exponents. Prompted by our genetic sequence observations we present a growth probabilistic model incorporating mutation-duplication features that generates data complying with this distribution. The competition between permanence and change appears to be a relevant, though not necessary feature. Additionally, our observations mainly of social phenomena suggest that a multifactorial quality resulting from the convergence of several heterogeneous underlying processes is an important feature. We also explore the significance of the distribution parameters and their classifying potential. The ubiquity of our findings suggests that there must be a fundamental underlying explanation, most probably of a statistical nature, such as an appropriate central limit theorem formulation.