Depth of SCUBA Diving Affects Cardiac Autonomic Nervous System.

The present study investigated the influence of SCUBA dives with compressed air at depths of 10 and 20 m on ECG-derived HRV parameters in apparently healthy individuals. We hypothesized that cardiac sympathetic activity (measured by HRV parameters) adapts proportionally to diving depth, and that both time- and frequency-domain parameters are sensitive enough to track changes in cardiac ANS function during diving activities and subsequently during the recovery period. Eleven healthy middle-aged recreational divers (nine men and two women, age 43 ± 8, all nonsmokers) volunteered to participate in the present study. The participants (all open-circuit divers) were equipped with dry suits and ECG Holter devices and were later randomly assigned to dive pairs and depths (10 m vs. 20 m), and each participant served as his or her own control. No interaction effects (diving depth x time epoch) were found for the most commonly used HRV markers. More precisely, in response to two different diving protocols, a significant post hoc effect of time was observed for HR and SDNN, as these parameters transiently decreased during the dives and returned to baseline after ascent (p < 0.001). The ULF, VLF (p < 0.003), TP, and LF parameters decreased significantly during the dives, while HF significantly increased (p < 0.003). SCUBA diving apparently challenges the cardiac ANS, even in healthy individuals. The observed changes reveal possible underwater methods of influencing the parasympathetic activity of the heart depending on the depth of the dive. These results identify autonomic nervous system markers to track the cardiovascular risk related to diving and point to the possibility of tracking cardiovascular system benefits during underwater activities in selected patients.

Density functional theory study of crown ether-magnesium complexes: from a solvated ion to an ion trap.

Metal ion detection rests on host-guest recognition. We propose a theoretical protocol for designing an optimal trap for a desired metal cation. A host for magnesium ions was sought for among derivatives of crown ethers 12-crown-4, 15-crown-5, and 18-crown-6. Mg-crown complexes and their hydrated counterparts with water molecules bound to the cation were optimized using density functional theory. Based on specific geometric criteria, Interacting quantum atoms analysis and density functional theory-based molecular dynamics of Mg-crown complexes immersed in water, crown ethers for optimal accommodation of Mg2+ in aqueous solution were identified. Selectivity of the chosen crowns towards Na+, K+, and Ca2+ ions is addressed.

On the propensity of formation of cyclobutane dimers in face-to-face and face-to-back uracil stacks in solution.

UV irradiation of RNA leads to the formation of intra- and inter-strand crosslinks of cyclobutane type. Despite the importance of this reaction, relatively little is known about how the mutual orientation of the two bases affects the outcome of the reaction. Here we report a comparative nonadiabatic molecular dynamics study of face-to-back (F2B) and face-to-face (F2F) stacked uracil-water clusters. The computations were performed using the second-order algebraic-diagrammatic-construction (ADC(2)) method. We found that F2B stacked uracil-water clusters either relax non-reactively to the ground state by an ethylenic twist around the CC bond or remain in the lowest nπ* state in which the two bases gradually move away from each other. This finding is consistent with the low propensity for the formation of intra-strand cyclobutane dimers between adjacent RNA bases. On the contrary, in F2F stacked uracil-water clusters, in addition to non-reactive deactivation, we found a pro-reactive deactivation pathway, which may lead to the formation of cyclobutane uracil dimers in the electronic ground state. On a qualitative level, the observed photodynamics of F2F stacked uracil-water clusters explains the greater propensity of RNA to form inter-strand cyclobutane-type crosslinks.

A Lower Level of Post-Vaccinal Antibody Titer against Influenza Virus A H1N1 May Protect Patients with Autoimmune Rheumatic Diseases from Respiratory Viral Infections.

Background and Objectives: The concentration of antibodies against virus influenza A H1N1 in the titer (≥1:32) positively correlates with resistance to flu in healthy persons. In elderly and immune-compromised patients, an influenza vaccine may be less immunogenic. Hypothesis: A lower post-vaccinal antibody titer (≥1:16) may be sero-protective against respiratory viral infections in patients with autoimmune rheumatic diseases. Materials and Methods: Fifty patients with autoimmune rheumatic diseases (Systemic Lupus Erythematosus-24; Rheumatoid Arthritis-15; and Sjögren's Syndrome-11), who were at least 65 years old or whose relative disease duration (disease duration/age) was greater than 1/8, were examined. Thirty-four of them were vaccinated with a trivalent inactivated non-adjuvant influenza vaccine. The antibody concentration against influenza virus A H1N1 was measured using the standardized hemagglutination inhibition test and patients who got any respiratory viral infection were registered. To test the hypothesis, a correlative analysis was applied, followed by a binary logistic regression that included potential confounding variables, such as age, disease duration and therapy (personal/health-related conditions). Results: Vaccinated patients were significantly less affected by respiratory viral infections (21% vs. 75%). The lower titer considered (≥1:16) was significantly present more often among vaccinated patients (68% vs. 6%). The correlation between its presence/absence and that of respiratory viral infections was -0.34 (p < 0.05). The binary logistic regression evidenced the relevance of this correlation, confirming the hypothesis. Vaccination was associated with the 87.3% reduction in the likelihood of getting respiratory viral infections, whereas the lower antibody titer (≥1:16) was associated with the 77.6% reduction in the likelihood of getting respiratory viral infections. The vaccine was well tolerated by all patients and after vaccination no exacerbation of the underlying disease was observed. Conclusions: A lower antibody titer (≥1:16) against influenza virus A H1N1 could be protective against respiratory viral infections for certain autoimmune rheumatic diseases patients, which confirms the clinical effectiveness of influenza vaccination.

Proton leap: shuttling of protons onto benzonitrile.

The detailed description of chemical transformations in the interstellar medium allows deciphering the origin of a number of small and medium - sized organic molecules. We present density functional theory analysis of proton transfer from the trihydrogen cation and the ethenium cation to benzonitrile, a recently discovered species in the Taurus Molecular Cloud 1. Detailed energy transformations along the reaction paths were analyzed using the interacting quantum atoms methodology, which elucidated how the proton carrier influences the lightness to deliver the proton to benzonitrile's nitrogen atom. The proton carriers' deformation energy represents the largest destabilizing effect, whereas a proton's promotion energy, the benzonitrile-proton Coulomb attraction, as well as non-classical benzonitrile-proton and carrier-proton interaction are the dominant stabilizing energy components. As two ion-molecule reactions proceed without energy barriers, rate constants were estimated using the classical capture theory and were found to be an order of magnitude larger for the reaction with the trihydrogen cation compared to that with the ethenium cation (∼10-8 and 10-9 cm3 s-1, respectively). These results were obtained both with quantum chemical and ab initio molecular dynamics simulations (the latter performed at 10 K and 100 K), confirming that up to 100 K both systems choose energetically undemanding routes by tracking the corresponding minimum energy paths. A concept of a turning point is introduced, which is an equivalent to the transition state in barrierless reactions.

Alkaline earth cations binding mode tailors excited-state charge transfer properties of guanine quadruplex: A TDDFT study.

Quadruplexes formed by nucleic acids and their derivates tend to chelate different monovalent and bivalent cations, which simultaneously affect their excited electronic states properties. Cation binding to every and every other cavity of the central ion channel could be exploited for tuning exited-state charge transfer properties. In this work we utilize set of descriptors constructed on the basis of the one-electron transition density matrix obtained using linear-response TDDFT to study excited states properties of four crystallized tetramolecular quadruplexes that chelate alkaline earth cations (Ca2+, Sr2+ and Ba2+). Here, we show that alkaline earth cations situated at adjacent vacancies promote existence of the nucleobase-metal charge separation (CS) states, contrary to the structures with cations that occupy every second available vacancy. We argued that stabilization of these CS states is due to the strong electric field that stabilizes d orbitals of the cations which accept an excited-electron. Moreover, CS content is increased and redshifted below the first bright transition when number of the chelated cations is increased. Hydration effects stabilized CS states and increased their relative content. We also identified electron detachment states in the broad energy range for the Ca2+ containing system. These findings are valuable for understanding and development of the novel nanostructures based on the quadruplex scaffold with adjustable optical properties.

Water-Mediated Interactions Enhance Alkaline Earth Cation Chelation in Neighboring Cavities of a Cytosine Quartet in the DNA Quadruplex.

Larger Coulombic repulsion between divalent cations compared to the monovalent counterparts dictates the cation-cation distance in the central ion channel of quadruplexes. In this work, density functional theory and a continuum solvation model were employed to study bond energies of alkaline earth cations in adjacent cavities of the central ion channel. Four crystallized tetramolecular quadruplexes with various geometric constraints and structural motifs available in the Protein Data Bank were examined in order to understand how the cation binding affinities could be increased in aqueous solution. A cytosine quartet sandwiched between guanine quartets has a larger bond energy of the second alkaline earth cation in comparison with guanine and uracil quartets. Four highly conserved hydrogen-bonded water molecules in the center of the cytosine quartet are responsible for a higher electrostatic interaction with the cations in comparison with guanines' carbonyl groups. The reported findings are valuable for the design of synthetic quadruplexes templated with divalent cations for optoelectronic applications.

Assessment of Autonomic Nervous System Dysfunction in the Early Phase of Infection With SARS-CoV-2 Virus.

BACKGROUND: We are facing the outburst of coronavirus disease 2019 (COVID-19) defined as a serious, multisystem, disorder, including various neurological manifestations in its presentation. So far, autonomic dysfunction (AD) has not been reported in patients with COVID-19 infection. AIM: Assessment of AD in the early phase of infection with severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2 virus). PATIENTS AND METHODS: We analyzed 116 PCR positive COVID-19 patients. After the exclusion of 41 patients with associate diseases (CADG), partitioned to patients with diabetes mellitus, hypertension, and syncope, the remaining patients were included into a severe group (45 patients with confirmed interstitial pneumonia) and mild group (30 patients). Basic cardiovascular autonomic reflex tests (CART) were performed, followed by beat-to-beat heart rate variability (HRV) and systolic and diastolic blood pressure variability (BPV) analysis, along with baroreceptor sensitivity (BRS). Non-linear analysis of HRV was provided by Poincare Plot. Results were compared to 77 sex and age-matched controls. RESULTS: AD (sympathetic, parasympathetic, or both) in our study has been revealed in 51.5% of severe, 78.0% of mild COVID-19 patients, and the difference compared to healthy controls was significant (p = 0.018). Orthostatic hypotension has been established in 33.0% COVID-19 patients compared to 2.6% controls (p = 0.001). Most of the spectral parameters of HRV and BPV confirmed AD, most prominent in the severe COVID-19 group. BRS was significantly lower in all patients (severe, mild, CADG), indicating significant sudden cardiac death risk. CONCLUSION: Cardiovascular autonomic neuropathy should be taken into account in COVID-19 patients' assessment. It can be an explanation for a variety of registered manifestations, enabling a comprehensive diagnostic approach and further treatment.

Self-assembly of rylene-decorated guanine ribbons on graphene surface for optoelectronic applications: a theoretical study.

We are witnessing a change of paradigm from the conventional top-down to the bottom-up fabrication of nanodevices and particularly optoelectronic devices. A promising example of the bottom-up approach is self-assembling of molecules into layers with predictable and reproducible structural, electronic and optical properties. Nucleobases possess extraordinary ability to self-assembly into one-, two-, and three-dimensional structures. Optical properties of nucleotides are not suitable for wider application to optoelectronics and photovoltaics due to their large optical band gap, which is in contrast to rylene-based dyes that have been intensively investigated in organic optoelectronics. However, these lack the self-assembly capability of nucleobases. Combinations of covalently decorated guanine molecules with rylene type chromophores present 'the best of the both worlds'. Due to the large size of such compounds and its flexible nature their self-assemblies have not been fully understood yet. Here, we use a theoretical approach to study the structural, energetic and optical properties of rylene-based dye decorated guanine (GPDI), as self-assembled on a graphene sheet. Particularly we utilize the density-functional based tight-binding method to study atomic structure of these systems including the potential energy surface of GPDI and stability and organization of single- and multilayered GPDIs on graphene sheet. Using density-functional theory (DFT) we employ the energy decomposition analysis to gain a deeper insight into the contributions of different moieties to stability of GPDI films. Using time dependent DFT we analyze optical properties of these systems. We find that atomically thin films consisting of only a few molecular layers with large surface areas are more favorable than isolated thick islands. Our study of excited states indicates existence of charge separated states similar to ones found in the well-studied hydrogen bonded organic frameworks. The self-assembly characterized with a large homogeneous coverage and long-living charge-separated states provide the great potential for optoelectronic applications.

Entropy Analysis of COVID-19 Cardiovascular Signals.

The world has faced a coronavirus outbreak, which, in addition to lung complications, has caused other serious problems, including cardiovascular. There is still no explanation for the mechanisms of coronavirus that trigger dysfunction of the cardiac autonomic nervous system (ANS). We believe that the complex mechanisms that change the status of ANS could only be solved by advanced multidimensional analysis of many variables, obtained both from the original cardiovascular signals and from laboratory analysis and detailed patient history. The aim of this paper is to analyze different measures of entropy as potential dimensions of the multidimensional space of cardiovascular data. The measures were applied to heart rate and systolic blood pressure signals collected from 116 patients with COVID-19 and 77 healthy controls. Methods that indicate a statistically significant difference between patients with different levels of infection and healthy controls will be used for further multivariate research. As a result, it was shown that a statistically significant difference between healthy controls and patients with COVID-19 was shown by sample entropy applied to integrated transformed probability signals, common symbolic dynamics entropy, and copula parameters. Statistical significance between serious and mild patients with COVID-19 can only be achieved by cross-entropies of heart rate signals and systolic pressure. This result contributes to the hypothesis that the severity of COVID-19 disease is associated with ANS disorder and encourages further research.

Simulation of UV absorption spectra and relaxation dynamics of uracil and uracil-water clusters.

Despite many studies, the mechanisms of nonradiative relaxation of uracil in the gas phase and in aqueous solution are still not fully resolved. Here we combine theoretical UV absorption spectroscopy with nonadiabatic dynamics simulations to identify the photophysical mechanisms that can give rise to experimentally observed decay time constants. We first compute and theoretically assign the electronic spectra of uracil using the second-order algebraic-diagrammatic-construction (ADC(2)) method. The obtained electronic states, their energy differences and state-specific solvation effects are the prerequisites for understanding the photodynamics. We then use nonadiabatic trajectory-surface-hopping dynamics simulations to investigate the photoinduced dynamics of uracil and uracil-water clusters. In contrast to previous studies, we found that a single mechanism - the ethylenic twist around the C[double bond, length as m-dash]C bond - is responsible for the ultrafast component of the nonradiative decay, both in the gas phase and in solution. Very good agreement with the experimentally determined ultrashort decay time constants is obtained.

The significance of the metal cation in guanine-quartet - metalloporphyrin complexes.

The planarity and the appropriate size of the porphyrin ring make porphyrin derivatives ideal ligands for stacking to guanine quartets and they could thus be used as anti-cancer drugs. In this contribution we analyzed complexes of a guanine quartet with a porphyrin molecule, magnesium porphyrin and calcium porphyrin. As magnesium and calcium ions are located in the center and above the porphyrin ring, respectively, the two metalloporphyrins are expected to have different impacts on the target. The optimized structures of the three systems revealed geometrical changes in the guanine quartet upon complexation: while stacking of porphyrin and magnesium porphyrin does not induce significant changes, calcium porphyrin considerably distorts the quartet's structure, which has significant implications for the binding properties among guanine molecules. Ab initio molecular dynamics simulations revealed that the systems perform small fluctuations around the equilibrium structures. The largest atom displacements are performed by the calcium ion. The interacting quantum atoms methodology enabled analysis of the binding properties in the studied complexes. Interestingly, although the proximity of the calcium ion is responsible for the quartet's pronounced deformation and weakening of guanine-guanine binding, it also enables stronger binding of the metal ion to the quartet, resulting in a more stable complex. These results imply that metalloporphyrin-like ligands with out-of-plane central ions might represent promising drug candidates in anti-tumor treatment.

Modulating Excited Charge-Transfer States of G-Quartet Self-Assemblies by Earth Alkaline Cations and Hydration.

Guanine self-assemblies are promising supramolecular platforms for optoelectronic applications. The study (Hua et al., J. Phys. Chem. C 2012, 116, 14,682-14,689) reported that alkaline cations cannot modulate the electronic absorption spectrum of G-quadruplexes, although a cation effect is observable during electronic relaxation due to different mobility of Na+ and K+ cations. In this work, we theoretically examined whether divalent Mg2+ and Ca2+ cations and hydration might shift excited charge-transfer states of a cation-templated stacked G-quartet to the absorption red tail. Our results showed that earth alkaline cations blue-shifted nπ* states and stabilized charge-transfer ππ* states relative to those of complexes with alkaline cations, although the number of charge-separation states was not significantly modified. Earth alkaline cations were not able to considerably increase the amount of charge-transfer states below the Lb excitonic states. Hydration shifted charge-transfer states of the Na+-coordinated G-octet to the absorption red tail, although this part of the spectrum was still dominated by monomer-like excitations. We found G-octet electron detachment states at low excitation energies in aqueous solution. These states were distributed over a broad range of excitation energies and could be responsible for oxidative damage observed upon UV irradiation of biological G-quadruplexes.

Intriguing Intermolecular Interplay in Guanine Quartet Complexes with Alkali and Alkaline Earth Cations.

The possibility to target noncanonical guanine structures with specific ligands for therapeutic purposes inspired numerous theoretical and experimental investigations of a guanine quartet and its stacked composites. In this work, we employed the interacting quantum atoms methodology to study interactions among different fragments in complexes composed of a guanine quartet and alkali (Li+, Na+, K+) or alkaline earth (Be2+, Mg2+, Ca2+) cations in vacuo: metal-quartet interaction, influence of the cation on guanine-guanine interaction, as well as hydrogen bond cooperativity in the guanine quartet and its complexes with metal ions. Interestingly, although the presence of a cation intensifies interaction among guanine molecules, it lowers their binding energy because of notable quartet's distortion which is responsible for guanines' substantial deformation energy. This phenomenon is particularly pronounced with Be2+ which, out of the six analyzed cations, enhances hydrogen bond cooperativity to the greatest extent.

Elucidating Solvent Effects on Strong Intramolecular Hydrogen Bond: DFT-MD Study of Dibenzoylmethane in Methanol Solution.

The dynamic aspect of solvation plays a crucial role in determining properties of strong intramolecular hydrogen bonds since solvent fluctuations modify instantaneous hydrogen-bonded proton transfer barriers. Previous studies pointed out that solvent-solute interactions in the first solvation shell govern the position of the proton but the ability of the electric field due to other solvent molecules to localize the proton remains an important issue. In this work, we examine the structure of the O-H⋅⋅⋅O intramolecular hydrogen bond of dibenzoylmethane in methanol solution by employing density functional theory-based molecular dynamics and quantum chemical calculations. Our computations showed that homogeneous electric fields with intensities corresponding to those found in polar solvents are able to considerably alter the proton transfer barrier height in the gas phase. In methanol solution, the proton position is correlated with the difference in electrostatic potentials on the oxygen atoms of dibenzoylmethane even when dibenzoylmethane-methanol hydrogen bonding is lacking. On a timescale of our simulation, the hydrogen bonding and solvent electrostatics tend to localize the proton on different oxygen atoms. These findings provide an insight into the importance of the solvent electric field on the structure of a strong intramolecular hydrogen bond.

The UVA response of enolic dibenzoylmethane: beyond the static approach.

Enolic dibenzoylmethane is used in cosmetic sunscreens as a UVA filter because it strongly absorbs radiation around 340 nm. Assessing the absorption properties solely on the basis of the vertical excitation spectrum at the minimum of the potential energy surface leads to the conclusion that the nπ* state is not initially photoexcited. Since this molecule exhibits large changes in structure due to nuclear thermal and quantum fluctuations, it is not sufficient to consider one molecular configuration but an ensemble of configurations. In this work, we simulate its UVA response by employing the DFT/MRCI method in conjunction with configurations sampled from density functional theory-based classical and path integral molecular dynamics as well as by computing Franck-Condon factors. Our findings indicate that thermal and nuclear quantum fluctuations symmetrically broaden the excited states' absorption within the semi-classical approximation and thus it is necessary to include vibronic effects in order to correctly reproduce the experimental spectrum. The absorption is largely dominated by the ππ* state but there is a minor contribution from the nπ* state, contrary to the static result. The crossing between these two states occurs during the intramolecular proton transfer. This knowledge is of importance for studying photorelaxation mechanisms of dibenzoylmethane and other ß-diketone compounds.

A Mobile Crowd Sensing Application for Hypertensive Patients.

Mobile crowd sensing (MCS) is an application that collects data from a network of conscientious volunteers and implements it for the common or personal benefit. This contribution proposes an implementation that collects the data from hypertensive patients, thus creating an experimental database using the cloud service Platform as a Service (PaaS). The challenge is to perform the analysis without the main diagnostic feature for hypertension-the blood pressure. The other problems consider the data reliability in an environment full of artifacts and with limited bandwidth and battery resources. In order to motivate the MCS volunteers, a feedback about the patient's current status is created, provided by the means of machine-learning (ML) techniques. Two techniques are investigated and the Random Forest algorithm yielded the best results. The proposed platform, with slight modifications, can be adapted to the patients with other cardiovascular problems.

Relationship between cerebrovascular and valvular manifestations in a Serbian cohort of patients with antiphospholipid syndrome.

OBJECTIVES: Antiphospholipid syndrome (APS) may manifest itself as a primary (PAPS) or secondary disease, most commonly in the context of systemic lupus erythematosus (SLE) with various neurological and cardiac manifestations in its occurrence. The objective of this study was to investigate the relationship between cerebrovascular (stroke and transient ischaemic attack (TIA)) and valvular manifestations in a Serbian cohort of APS patients. METHODS: This is cross sectional study of 508 APS patients: 360 PAPS and 148 APS patients associated with SLE (SAPS). aPL analysis included detection of anticardiolipin antibodies (aCL: IgG/IgM), anti-ß2glycoprotein I (ß2GPI: IgG/IgM), and LA. RESULTS: The prevalence of valvular manifestations (valvular vegetations and valvular thickening and dysfunction not related to age) in our cohort was significantly higher in SAPS group. (28.4% vs. 8.6%, p=0.0001). Age was strong predictor for stroke and TIA occurrence in both groups as well as gender (stroke more likely occurred in male SAPS and TIA in male PAPS patients). Presence of ß2GPI IgG in SAPS patients was significantly related to stroke (p=0.018), whereas ß2GPI IgG negative PAPS patients were more prone to TIA. Valvular manifestations were significantly related to TIA in both groups of patients and were independent risk factors for TIA in PAPS (OR 3.790 CI 1.597-8.998 p=0.003). CONCLUSIONS: In this cross-section analysis of a large cohort of Serbian APS patients, there was a strong relationship between valvular and cerebrovascular manifestations, suggesting a more cautious approach regarding neurological symptoms, especially in PAPS patients with valvular vegetations present.

New Insight into Uracil Stacking in Water from ab Initio Molecular Dynamics.

Nucleobases spontaneously aggregate in water by forming stacked dimers and multimers. It is assumed that the main contributions to the aggregation stem from hydrophobic and base-base dispersion interactions. By studying the uracil monomer and dimer in bulk water with the first principle molecular dynamics, we discuss dimer structure and provide evidence that stacking increases the uracil-water hydrogen bonding strength and alters the hydration structure of uracil. These changes have a significant influence on the intensity and shift of the carbonyl stretching band as revealed by simulated infrared absorption spectra of the monomer and dimer and available experimental spectra. The contributions of dipole-dipole, dispersion, and water mediated forces to the stacking are discussed. The reported findings are valuable for understanding the microscopic mechanism of heteroaromatic association in water which is relevant to a large range of chemical and biological systems.

Binarized cross-approximate entropy in crowdsensing environment.

OBJECTIVES: Personalised monitoring in health applications has been recognised as part of the mobile crowdsensing concept, where subjects equipped with sensors extract information and share them for personal or common benefit. Limited transmission resources impose the use of local analyses methodology, but this approach is incompatible with analytical tools that require stationary and artefact-free data. This paper proposes a computationally efficient binarised cross-approximate entropy, referred to as (X)BinEn, for unsupervised cardiovascular signal processing in environments where energy and processor resources are limited. METHODS: The proposed method is a descendant of the cross-approximate entropy ((X)ApEn). It operates on binary, differentially encoded data series split into m-sized vectors. The Hamming distance is used as a distance measure, while a search for similarities is performed on the vector sets. The procedure is tested on rats under shaker and restraint stress, and compared to the existing (X)ApEn results. RESULTS: The number of processing operations is reduced. (X)BinEn captures entropy changes in a similar manner to (X)ApEn. The coding coarseness yields an adverse effect of reduced sensitivity, but it attenuates parameter inconsistency and binary bias. A special case of (X)BinEn is equivalent to Shannon's entropy. A binary conditional entropy for m =1 vectors is embedded into the (X)BinEn procedure. CONCLUSION: (X)BinEn can be applied to a single time series as an auto-entropy method, or to a pair of time series, as a cross-entropy method. Its low processing requirements makes it suitable for mobile, battery operated, self-attached sensing devices, with limited power and processor resources.