Deep Learning for chaos detection.

In this article, we study how a chaos detection problem can be solved using Deep Learning techniques. We consider two classical test examples: the Logistic map as a discrete dynamical system and the Lorenz system as a continuous dynamical system. We train three types of artificial neural networks (multi-layer perceptron, convolutional neural network, and long short-term memory cell) to classify time series from the mentioned systems into regular or chaotic. This approach allows us to study biparametric and triparametric regions in the Lorenz system due to their low computational cost compared to traditional techniques.

Unsupervised Anomaly Detection Applied to Φ-OTDR.

Distributed acoustic sensors (DASs) based on direct-detection Φ-OTDR use the light-matter interaction between light pulses and optical fiber to detect mechanical events in the fiber environment. The signals received in Φ-OTDR come from the coherent interference of the portion of the fiber illuminated by the light pulse. Its high sensitivity to minute phase changes in the fiber results in a severe reduction in the signal to noise ratio in the intensity trace that demands processing techniques be able to isolate events. For this purpose, this paper proposes a method based on Unsupervised Anomaly Detection techniques which make use of concepts from the field of deep learning and allow the removal of much of the noise from the Φ-OTDR signals. The fact that this method is unsupervised means that no human-labeled data are needed for training and only event-free data are used for this purpose. Moreover, this method has been implemented and its performance has been tested with real data showing promising results.

Cooling Effectiveness of a Data Center Room under Overhead Airflow via Entropy Generation Assessment in Transient Scenarios.

Forecasting data center cooling demand remains a primary thermal management challenge in an increasingly larger global energy-consuming industry. This paper proposes a dynamic modeling approach to evaluate two different strategies for delivering cold air into a data center room. The common cooling method provides air through perforated floor tiles by means of a centralized distribution system, hindering flow management at the aisle level. We propose an idealized system such that five overhead heat exchangers are located above the aisle and handle the entire server cooling demand. In one case, the overhead heat exchangers force the airflow downwards into the aisle (Overhead Downward Flow (ODF)); in the other case, the flow is forced to move upwards (Overhead Upward Flow (OUF)). A complete fluid dynamic, heat transfer, and thermodynamic analysis is proposed to model the system's thermal performance under both steady state and transient conditions. Inside the servers and heat exchangers, the flow and heat transfer processes are modeled using a set of differential equations solved in MATLAB™ 2017a. This solution is coupled with ANSYS-Fluent™ 18, which computes the three-dimensional velocity, temperature, and turbulence on the Airside. The two approaches proposed (ODF and OUF) are evaluated and compared by estimating their cooling effectiveness and the local Entropy Generation. The latter allows identifying the zones within the room responsible for increasing the inefficiencies (irreversibilities) of the system. Both approaches demonstrated similar performance, with a small advantage shown by OUF. The results of this investigation demonstrated a promising approach of data center on-demand cooling scenarios.

Electrochemical Instrumentation of an Embedded Potentiostat System (EPS) for a Programmable-System-On-a-Chip.

Under the main features required on portable devices in electrochemical instrumentation is to have a small size, low power consumption, economically affordable and precision in the measurements. This paper describes the development of a programmable Embedded Potentiostat System (EPS) capable of performing electrochemical sensing over system-on-a-chip platforms. Furthermore, the study explains a circuit design and develops some validation of the entire system. The hardware validation is performed by electrochemical experiments such as Double Step Chronoamperometry (DSC), Linear Sweep Voltammetry (LSV) and Cyclic Voltammetry (CV); moreover, a comparison of the experimental signals between a commercial potentiostat and the EPS was done by analysis of errors on the response signal. Results illustrate that the EPS is capable of handling currents in the range of absolute values of 86.44 to 3000 nA and having control voltages in the range of ±2 V. The device can support from 50 to 2000 samples per second. The EPS capabilities were compared with other compact potentiostats. The programmable EPS is an original approach which hugely reduces the hardware complexity and leads the way to create new applications for Point-of-Care or industrial developments with a reusable full electronics module.

Competitive silyl-Prins cyclization versus tandem Sakurai-Prins cyclization: an interesting substitution effect.

Two different mechanism pathways are observed for the reaction of allylsilyl alcohols 1 and aldehydes in the presence of trimethylsilyl trifluoromethanesulfonate (TMSOTf). In the case of allylsilyl alcohols without allylic substituents, the reaction gives dioxaspirodecanes, which are the products of a tandem Sakurai-Prins cyclization. In contrast, allylsilyl alcohols with an allylic substituent (R(2)≠H) selectively provide oxepanes, thus corresponding to a direct silyl-Prins cyclization. Both types of product are obtained with excellent stereoselectivity. Theoretical studies have been performed to obtain some rationalization for the observed stereoselectivity.

Experimental and theoretical studies on the effect of the oxo group in 1,4-benzodiazepines.

Two families of regioisomeric 1,4-benzodiazepines, 4-benzyl-3H-benzo[e][1,4]diazepin-5-ones and 4-benzoyl-4,5-dihydro-3H-benzo[e][1,4]diazepines, have been synthesized through a similar Ugi/reduction cyclization sequence. Their conformation and stability depend on the position of the tautomeric imine/enamine equilibrium present in the diazepine nucleus, which in turn depends on the relative position of the carbonyl group adjacent to the nitrogen at the 4-position in the benzodiazepine system. Moreover, the electrophilic center on the imine tautomer is essential for the antitumor activity of some benzodiazepines as a DNA binding position. The mechanism of tautomerization in the presence or absence of the oxo group has been studied computationally using DFT methods (B3LYP/6-31G** level).

Automatic Voice Disorder Detection from a Practical Perspective.

Voice disorders, such as dysphonia, are common among the general population. These pathologies often remain untreated until they reach a high level of severity. Assisting the detection of voice disorders could facilitate early diagnosis and subsequent treatment. In this study, we address the practical aspects of automatic voice disorders detection (AVDD). In real-world scenarios, data annotated for voice disorders is usually scarce due to various challenges involved in the collection and annotation of such data. However, some relatively large datasets are available for a reduced number of domains. In this context, we propose the use of a combination of out-of-domain and in-domain data for training a deep neural network-based AVDD system, and offer guidance on the minimum amount of in-domain data required to achieve acceptable performance. Further, we propose the use of a cost-based metric, the normalized expected cost (EC), to evaluate performance of AVDD systems in a way that closely reflects the needs of the application. As an added benefit, optimal decisions for the EC can be made in a principled way given by Bayes decision theory. Finally, we argue that for medical applications like AVDD, the categorical decisions need to be accompanied by interpretable scores that reflect the confidence of the system. Even very accurate models often produce scores that are not suited for interpretation. Here, we show that such models can be easily improved by adding a calibration stage-trained with just a few minutes of in-domain data. The outputs of the resulting calibrated system can then better support practitioners in their decision-making process.

Enzymes Involved in Antioxidant and Detoxification Processes Present Changes in the Expression Levels of Their Coding Genes under the Stress Caused by the Presence of Antimony in Tomato.

Currently, there is an increasing presence of heavy metals and metalloids in soils and water due to anthropogenic activities. However, the biggest problem caused by this increase is the difficulty in recycling these elements and their high permanence in soils. There are plants with great capacity to assimilate these elements or make them less accessible to other organisms. We analyzed the behavior of Solanum lycopersicum L., a crop with great agronomic interest, under the stress caused by antimony (Sb). We evaluated the antioxidant response throughout different exposure times to the metalloid. Our results showed that the enzymes involved in the AsA-GSH cycle show changes in their expression level under the stress caused by Sb but could not find a relationship between the NITROSOGLUTATHIONE REDUCTASE (GSNOR) expression data and nitric oxide (NO) content in tomato roots exposed to Sb. We hypothesize that a better understanding of how these enzymes work could be key to develop more tolerant varieties to this kind of abiotic stress and could explain a greater or lesser phytoremediation capacity. Moreover, we deepened our knowledge about Glutathione S-transferase (GST) and Glutathione Reductase (GR) due to their involvement in the elimination of the xenobiotic component.

Complementary regioselectivity in the synthesis of iminohydantoins: remarkable effect of amide substitution on the cyclization.

Complementary regioselective synthesis of iminohydantoins from isocyanoacetamides controlled by the substituent on the amide group has been described. 4-Iminohydantoins were the major products when the starting materials were N-alkyl isocyanoamides, whereas 2-iminohydantoins were the major products with N-aryl isocyanoamides.

Effect of Thallium(I) on Growth, Nutrient Absorption, Photosynthetic Pigments, and Antioxidant Response of Dittrichia Plants.

Dittrichia plants were exposed to thallium (Tl) stress (10, 50, and 100 µM) for 7 days. The Tl toxicity altered the absorption and accumulation of other nutrients. In both the roots and the leaves, there was a decline in K, Mg, and Fe content, but an increase in Ca, Mn, and Zn. Chlorophylls decreased, as did the photosynthetic efficiency, while carotenoids increased. Oxidative stress in the roots was reflected in increased lipid peroxidation. There was more production of superoxide (O2.-), hydrogen peroxide (H2O2), and nitric oxide (NO) in the roots than in the leaves, with increases in both organs in response to Tl toxicity, except for O2.- production in the roots, which fluctuated. There was increased hydrogen sulfide (H2S) production, especially in the leaves. Superoxide dismutase (SOD), ascorbate peroxidase (APX), dehydroascorbate reductase (DHAR), monodehydroascorbate reductase (MDHAR), and glutathione reductase (GR) showed increased activities, except for APX and MDHAR in the roots and GR in the leaves. The components of the ascorbate-glutathione cycle were affected. Thus, ascorbate (AsA) increased, while dehydroascorbate (DHA), reduced glutathione (GSH), and oxidized glutathione (GSSG) decreased, except for in the roots at 100 µM Tl, which showed increased GSH. These Tl toxicity-induced alterations modify the AsA/DHA and GSH/GSSG redox status. The NO and H2S interaction may act by activating the antioxidant system. The effects of Tl could be related to its strong affinity for binding with -SH groups, thus altering the functionality of proteins and the cellular redox state.

Effect of a low versus intermediate tidal volume strategy on pulmonary complications in patients at risk of acute respiratory distress syndrome-a randomized clinical trial.

Introduction: There is no consensus on whether invasive ventilation should use low tidal volumes (VT) to prevent lung complications in patients at risk of acute respiratory distress syndrome (ARDS). The purpose of this study is to determine if a low VT strategy is more effective than an intermediate VT strategy in preventing pulmonary complications. Methods: A randomized clinical trial was conducted in invasively ventilated patients with a lung injury prediction score (LIPS) of >4 performed in the intensive care units of 10 hospitals in Spain and one in the United States of America (USA) from 3 November 2014 to 30 August 2016. Patients were randomized to invasive ventilation using low VT (≤ 6 mL/kg predicted body weight, PBW) (N = 50) or intermediate VT (> 8 mL/kg PBW) (N = 48). The primary endpoint was the development of ARDS during the first 7 days after the initiation of invasive ventilation. Secondary endpoints included the development of pneumonia and severe atelectases; the length of intensive care unit (ICU) and hospital stay; and ICU, hospital, 28- and 90-day mortality. Results: In total, 98 patients [67.3% male], with a median age of 65.5 years [interquartile range 55-73], were enrolled until the study was prematurely stopped because of slow recruitment and loss of equipoise caused by recent study reports. On day 7, five (11.9%) patients in the low VT group and four (9.1%) patients in the intermediate VT group had developed ARDS (risk ratio, 1.16 [95% CI, 0.62-2.17]; p = 0.735). The incidence of pneumonia and severe atelectasis was also not different between the two groups. The use of a low VT strategy did neither affect the length of ICU and hospital stay nor mortality rates. Conclusions: In patients at risk for ARDS, a low VT strategy did not result in a lower incidence of ARDS than an intermediate VT strategy.Clinical Trial Registration: ClinicalTrials.gov, identifier NCT02070666.

Isomeric Aromatic Polyimides Containing Biphenyl Moieties for Gas Separation Applications.

An optimized synthesis of the monomer 2,2'3,3'-biphenyltetracarboxylic dianhydride, iBPDA, was performed to obtain high molecular weight polymers. This monomer has a contorted structure that produces a non-linear shape, hindering the packing of the polymer chain. Aromatic polyimides of high molecular weight were obtained by reaction with the commercial diamine 2,2-bis(4-aminophenyl) hexafluoropropane, 6FpDA, which is a very common monomer in gas separation applications. This diamine has hexafluoroisopropylidine groups which introduce rigidity in the chains, hindering efficient packing. The thermal treatment of the polymers processed as dense membranes had two targets: on the one hand, to achieve the complete elimination of the solvent used, which could remain occluded in the polymeric matrix, and on the other hand to ensure the complete cycloimidization of the polymer. A thermal treatment exceeding the glass transition temperature was performed to ensure the maximum degree of imidization at 350 °C. The good mechanical properties of these materials allow for their use in high-pressure gas purification applications. Moreover, models of the polymers exhibited an Arrhenius-like behavior characteristic of secondary relaxations, normally associated with local motions of the molecular chain. The gas productivity of these membranes was high.

Better prognostic ability of NEWS2, SOFA and SAPS-II in septic patients. / Mejor capacidad pronóstica de NEWS2, SOFA y SAPS-II en pacientes con sepsis.

BACKGROUND AND OBJECTIVES: To compare the ability of qSOFA, NEWS2, SOFA, LODS, SIRS, APACHE-II and SAPS-II scores. MATERIAL AND METHODS: Analysis of in-hospital mortality of 203 patients admitted to the ICU because of sepsis. The scores were compared according to their application. Discrimination was evaluated with AUC-ROC curve and performance with the Akaike's (AIC) and Bayesian information criterion (BIC). RESULTS: In-hospital mortality was 31.53%. NEWS2 showed better mortality discrimination ability and better performance considering the AIC/BIC criterion for mortality tan qSOFA (AUC-ROC=.615 and .536; P=.039). SOFA presented higher performance and AUC-ROC tan LODS (.776 vs .693; P=.01) and both showed higher discrimination ability than SIRS (AUC-ROC=.521; P<.003). Finally, SAPS-II was able to predict mortality with better performance than APACHE-II and presented higher discrimination capacity but without statistical significance compared (AUROC=.738 for SAPS-II and AUROC=.673 for APACHE-II; P=.08). CONCLUSION: NEWS2 is a better predictor of mortality than qSOFA and its implementation for the early recognition of the septic patient or the patient with higher risk in the emergency and hospitalization wards should be addressed. In addition, given that SOFA and SAPS-II showed better performance and are simpler than LODS and APACHE-II, respectively, both should be considered the scores of choice in this setting.

Physiological and Molecular Responses of Vitis vinifera cv. Tempranillo Affected by Esca Disease.

Esca is a multi-fungal disease affecting grapevines. The objective of the study was to evaluate the physiological and molecular response of the grapevine cv. Tempranillo to esca disease, carried out in a vineyard under Mediterranean climatic conditions in western Spain. The photosynthetic pigments in the leaves decreased, with a strong decrease in the photosynthetic efficiency. The proline content increased significantly in the early stages of affected leaves, being possibly involved in the maintenance of lipid peroxidation levels in leaves, which do not increase. The phenol, flavonoid, and phenylpropanoid content decreased in esca-affected leaves, as does the total antioxidant capacity (FRAP), while the polyphenol oxidase (PPO) activity suffers a strong increase with the development of the disease. In affected grapes, the lipid peroxidation and the total phenol content decrease, but not the anthocyanin content. The ascorbate pool decreases with the disease and with time. On the other hand, pool GSH + GSSG is lower in affected leaves, but increases with time. These alterations show a clear change in the redox homeostasis. The expression of genes phenylalanine ammonia lyase (PAL), polyphenol oxidase (PPO), superoxide dismutase (SOD), and chalcone synthase (ChaS1 and ChaS3) become considerably higher in response to esca, being even higher when the infection time increases. The alteration of AsA and GSH levels, phenolic compounds, PPO activity, proline content, and FRAP, together with the increase of the PAL, PPO, SOD,ChaS1, and ChaS3 gene expression, are clearly implicated in the esca response in plants. The expression of these genes, similar to the PPO activity, can be used as markers of state in the development of the disease.

Red blood cell distribution width as prognostic factor in sepsis: A new use for a classical parameter.

PURPOSE: To evaluate Red blood cell distribution width (RDW) as a sepsis prognostic biomarker. METHODS: 203 septic patients admitted to the ICU. Analysis of RDW dynamics, hospital mortality discrimination ability and the added value when incorporated to the SOFA, LODS, SAPS-II and APACHE-II scores using the AUC-ROC. RESULTS: Non-survivors presented higher RDW values during the first week after ICU admission (p = 0.048). Only SOFA and RDW were independently associated with mortality when adjusted by Charlson, immunosuppression, nosocomial infection, NEWS2, SAPS-II, septic shock and haemoglobin (p < 0.05). After adjustment, AUC-ROC was 0.827, 0.822, 0.824, 0.834 and 0.812 for each model including admission, 24, 48 and 72-h and 7-days RDW, respectively. When added to the scores, 24-h RDW and admission RDW improved their discrimination ability (SOFA AUC-ROC = 0.772 vs 0.812 SOFA + admission RDW, p = 0.041; LODS AUC-ROC = 0.687 vs 0.710, p = 0.002; SAPS-II AUC-ROC = 0.734 vs 0.785, p = 0.021; APACHE-II AUC-ROC = 0.672 vs 0.755, p = 0.003). Admission RDW with SOFA presented the better discrimination ability for mortality. CONCLUSION: RDW is an independent prognostic marker of death in septic patients admitted in the ICU that improves SOFA, LODS, APACHE-II and SAPS-II discrimination ability. This parameter could be incorporated to the prognostic scores as a marker of systemic dysfunction and dysregulated inflammatory response.

Free Volume and Permeability of Mixed Matrix Membranes Made from a Terbutil-M-terphenyl Polyamide and a Porous Polymer Network.

A set of thermally rearranged mixed matrix membranes (TR-MMMs) was manufactured and tested for gas separation. These membranes were obtained through the thermal treatment of a precursor MMM with a microporous polymer network and an o-hydroxypolyamide,(HPA) created through a reaction of 2,2-bis(3-amino-4-hydroxyphenyl)-hexafluoropropane (APAF) and 5'-terbutil-m-terfenilo-3,3″-dicarboxylic acid dichloride (tBTmCl). This HPA was blended with different percentages of a porous polymer network (PPN) filler, which produced gas separation MMMs with enhanced gas permeability but with decreased selectivity. The thermal treatment of these MMMs gave membranes with excellent gas separation properties that did not show the selectivity decreasing trend. It was observed that the use of the PPN load brought about a small decrease in the initial mass losses, which were lower for increasing PPN loads. Regarding the glass transition temperature, it was observed that the use of the filler translated to a slightly lower Tg value. When these MMMs and TR-MMMs were compared with the analogous materials created from the isomeric 5'-terbutil-m-terfenilo-4,4″-dicarboxylic acid dichloride (tBTpCl), the permeability was lower for that of tBTmCl, compared with the one from tBTpCl, although selectivity was quite similar. This fact could be attributed to a lower rigidity as roughly confirmed by the segmental length of the polymer chain as studied by WAXS. A model for FFV calculation was proposed and its predictions compared with those evaluated from density measurements assuming a matrix-filler interaction or ideal independence. It turns out that permeability as a function of FFV for TR-MMMs follows an interaction trend, while those not thermally treated follow the non-interaction trend until relatively high PPN loads were reached.

Early Tracheostomy for Managing ICU Capacity During the COVID-19 Outbreak: A Propensity-Matched Cohort Study.

BACKGROUND: During the first wave of the COVID-19 pandemic, shortages of ventilators and ICU beds overwhelmed health care systems. Whether early tracheostomy reduces the duration of mechanical ventilation and ICU stay is controversial. RESEARCH QUESTION: Can failure-free day outcomes focused on ICU resources help to decide the optimal timing of tracheostomy in overburdened health care systems during viral epidemics? STUDY DESIGN AND METHODS: This retrospective cohort study included consecutive patients with COVID-19 pneumonia who had undergone tracheostomy in 15 Spanish ICUs during the surge, when ICU occupancy modified clinician criteria to perform tracheostomy in Patients with COVID-19. We compared ventilator-free days at 28 and 60 days and ICU- and hospital bed-free days at 28 and 60 days in propensity score-matched cohorts who underwent tracheostomy at different timings (≤ 7 days, 8-10 days, and 11-14 days after intubation). RESULTS: Of 1,939 patients admitted with COVID-19 pneumonia, 682 (35.2%) underwent tracheostomy, 382 (56%) within 14 days. Earlier tracheostomy was associated with more ventilator-free days at 28 days (≤ 7 days vs > 7 days [116 patients included in the analysis]: median, 9 days [interquartile range (IQR), 0-15 days] vs 3 days [IQR, 0-7 days]; difference between groups, 4.5 days; 95% CI, 2.3-6.7 days; 8-10 days vs > 10 days [222 patients analyzed]: 6 days [IQR, 0-10 days] vs 0 days [IQR, 0-6 days]; difference, 3.1 days; 95% CI, 1.7-4.5 days; 11-14 days vs > 14 days [318 patients analyzed]: 4 days [IQR, 0-9 days] vs 0 days [IQR, 0-2 days]; difference, 3 days; 95% CI, 2.1-3.9 days). Except hospital bed-free days at 28 days, all other end points were better with early tracheostomy. INTERPRETATION: Optimal timing of tracheostomy may improve patient outcomes and may alleviate ICU capacity strain during the COVID-19 pandemic without increasing mortality. Tracheostomy within the first work on a ventilator in particular may improve ICU availability.

Response to Antimony Toxicity in Dittrichia viscosa Plants: ROS, NO, H2S, and the Antioxidant System.

Dittrichia viscosa plants were grown hydroponically with different concentrations of Sb. There was preferential accumulation of Sb in roots. Fe and Cu decreased, while Mn decreased in roots but not in leaves. Chlorophyll content declined, but the carotenoid content increased, and photosynthetic efficiency was unaltered. O2●- generation increased slightly, while lipid peroxidation increased only in roots. H2O2, NO, ONOO-, S-nitrosothiols, and H2S showed significant increases, and the enzymatic antioxidant system was altered. In roots, superoxide dismutase (SOD) and monodehydroascorbate reductase (MDAR) activities declined, dehydroscorbate reductase (DHAR) rose, and ascorbate peroxidase (APX), peroxidase (POX), and glutathione reductase (GR) were unaffected. In leaves, SOD and POX increased, MDAR decreased, and APX was unaltered, while GR increased. S-nitrosoglutathione reductase (GSNOR) and l-cysteine desulfhydrilase (l-DES) increased in activity, while glutathione S-transferase (GST) decreased in leaves but was enhanced in roots. Components of the AsA/GSH cycle decreased. The great capacity of Dittrichia roots to accumulate Sb is the reason for the differing behaviour observed in the enzymatic antioxidant systems of the two organs. Sb appears to act by binding to thiol groups, which can alter free GSH content and SOD and GST activities. The coniferyl alcohol peroxidase activity increased, possibly to lignify the roots' cell walls. Sb altered the ROS balance, especially with respect to H2O2. This led to an increase in NO and H2S acting on the antioxidant system to limit that Sb-induced redox imbalance. The interaction NO, H2S and H2O2 appears key to the response to stress induced by Sb. The interaction between ROS, NO, and H2S appears to be involved in the response to Sb.

Gas Separation by Mixed Matrix Membranes with Porous Organic Polymer Inclusions within o-Hydroxypolyamides Containing m-Terphenyl Moieties.

A hydroxypolyamide (HPA) manufactured from 2,2-bis(3-amino-4-hydroxy phenyl)-hexafluoropropane (APAF) diamine and 5'-terbutyl-m-terphenyl-4,4''-dicarboxylic acid chloride (tBTpCl), and a copolyimide produced by stochiometric copolymerization of APAF and 4,4'-(hexafluoroisopropylidene) diamine (6FpDA), using the same diacid chloride, were obtained and used as polymeric matrixes in mixed matrix membranes (MMMs) loaded with 20% (w/w) of two porous polymer networks (triptycene-isatin, PPN-1, and triptycene-trifluoroacetophenone, PPN-2). These MMMs, and also the thermally rearranged membranes (TR-MMMs) that underwent a thermal treatment process to convert the o-hydroxypolyamide moieties to polybenzoxazole ones, were characterized, and their gas separation properties evaluated for H2, N2, O2, CH4, and CO2. Both TR process and the addition of PPN increased permeability with minor decreases in selectivity for all gases tested. Excellent results were obtained, in terms of the permeability versus selectivity compromise, for H2/CH4 and H2/N2 separations with membranes approaching the 2008 Robeson's trade-off line. The best gas separation properties were obtained when PPN-2 was used. Finally, gas permeation was characterized in terms of chain intersegmental distance and fraction of free volume of the membrane along with the kinetic diameters of the permeated gases. The intersegmental distance increased after TR and/or the addition of PPN-2. Permeability followed an exponential dependence with free volume and a quadratic function of the kinetic diameter of the gas.