Implementing Demons and Ratchets*Entropy* **2017**, *19*(1), 34; doi:10.3390/e19010034 (registering DOI) - 14 January 2017**Abstract **

►
Figures
Experimental results show that ratchets may be implemented in semiconductor and chemical systems, bypassing the second law and opening up huge gains in energy production. This paper summarizes or describes experiments and results on systems that effect demons and ratchets operating in chemical

[...] Read more.
Experimental results show that ratchets may be implemented in semiconductor and chemical systems, bypassing the second law and opening up huge gains in energy production. This paper summarizes or describes experiments and results on systems that effect demons and ratchets operating in chemical or electrical domains. One creates temperature differences that can be harvested by a heat engine. A second produces light with only heat input. A third produces harvestable electrical potential directly. These systems share creating particles in one location, destroying them in another and moving them between locations by diffusion (Brownian motion). All absorb ambient heat as they produce other energy forms. None requires an external hot and cold side. The economic and social impacts of these conversions of ambient heat to work are, of course, well-understood and huge. The experimental results beg for serious work on the chance that they are valid.
Full article

Similarity Theory Based Radial Turbine Performance and Loss Mechanism Comparison between R245fa and Air for Heavy-Duty Diesel Engine Organic Rankine Cycles*Entropy* **2017**, *19*(1), 25; doi:10.3390/e19010025 (registering DOI) - 14 January 2017**Abstract **

►
Figures
Organic Rankine Cycles using radial turbines as expanders are considered as one of the most efficient technologies to convert heavy-duty diesel engine waste heat into useful work. Turbine similarity design based on the existing air turbine profiles is time saving. Due to totally

[...] Read more.
Organic Rankine Cycles using radial turbines as expanders are considered as one of the most efficient technologies to convert heavy-duty diesel engine waste heat into useful work. Turbine similarity design based on the existing air turbine profiles is time saving. Due to totally different thermodynamic properties between organic fluids and air, its influence on turbine performance and loss mechanisms need to be analyzed. This paper numerically simulated a radial turbine under similar conditions between R245fa and air, and compared the differences of the turbine performance and loss mechanisms. Larger specific heat ratio of air leads to air turbine operating at higher pressure ratios. As R245fa gas constant is only about one-fifth of air gas constant, reduced rotating speeds of R245fa turbine are only 0.4-fold of those of air turbine, and reduced mass flow rates are about twice of those of air turbine. When using R245fa as working fluid, the nozzle shock wave losses decrease but rotor suction surface separation vortex losses increase, and eventually leads that isentropic efficiencies of R245fa turbine in the commonly used velocity ratio range from 0.5 to 0.9 are 3%–4% lower than those of air turbine.
Full article

Heuristic Approach to Understanding the Accumulation Process in Hydrothermal Pores*Entropy* **2017**, *19*(1), 33; doi:10.3390/e19010033 - 13 January 2017**Abstract **

►
Figures
One of the central questions of humankind is: which chemical and physical conditions are necessary to make life possible? In this “origin-of-life” context, formamide plays an important role, because it has been demonstrated that prebiotic molecules can be synthesized from concentrated formamide solutions.

[...] Read more.
One of the central questions of humankind is: which chemical and physical conditions are necessary to make life possible? In this “origin-of-life” context, formamide plays an important role, because it has been demonstrated that prebiotic molecules can be synthesized from concentrated formamide solutions. Recently, it could be shown, using finite-element calculations combining thermophoresis and convection processes in hydrothermal pores, that sufficiently high formamide concentrations could be accumulated to form prebiotic molecules (Niether et al. (2016)). Depending on the initial formamide concentration, the aspect ratio of the pores, and the ambient temperature, formamide concentrations up to 85 wt % could be reached. The stationary calculations show an effective accumulation, only if the aspect ratio is above a certain threshold, and the corresponding transient studies display a sudden increase of the accumulation after a certain time. Neither of the observations were explained. In this work, we derive a simple heuristic model, which explains both phenomena. The physical idea of the approach is a comparison of the time to reach the top of the pore with the time to cross from the convective upstream towards the convective downstream. If the time to reach the top of the pore is shorter than the crossing time, the formamide molecules are flushed out of the pore. If the time is long enough, the formamide molecules can reach the downstream and accumulate at the bottom of the pore. Analysing the optimal aspect ratio as function of concentration, we find that, at a weight fraction of $w=0.5$ , a minimal pore height is required for effective accumulation. At the same concentration, the transient calculations show a maximum of the accumulation rate.
Full article

Univariate and Multivariate Generalized Multiscale Entropy to Characterise EEG Signals in Alzheimer’s Disease*Entropy* **2017**, *19*(1), 31; doi:10.3390/e19010031 - 12 January 2017**Abstract **

►
Figures
Alzheimer’s disease (AD) is a degenerative brain disorder leading to memory loss and changes in other cognitive abilities. The complexity of electroencephalogram (EEG) signals may help to characterise AD. To this end, we propose an extension of multiscale entropy based on variance (MSE_{}

[...] Read more.
Alzheimer’s disease (AD) is a degenerative brain disorder leading to memory loss and changes in other cognitive abilities. The complexity of electroencephalogram (EEG) signals may help to characterise AD. To this end, we propose an extension of multiscale entropy based on variance (MSE_{σ2}) to multichannel signals, termed multivariate MSE_{σ2} (mvMSE_{σ2}), to take into account both the spatial and time domains of time series. Then, we investigate the mvMSE_{σ2} of EEGs at different frequency bands, including the broadband signals filtered between 1 and 40 Hz, *θ*, *α*, and *β* bands, and compare it with the previously-proposed multiscale entropy based on mean (MSE_{µ}), multivariate MSE_{µ} (mvMSE_{µ}), and MSE_{σ2}, to distinguish different kinds of dynamical properties of the spread and the mean in the signals. Results from 11 AD patients and 11 age-matched controls suggest that the presence of broadband activity of EEGs is required for a proper evaluation of complexity. MSE_{σ2} and mvMSE_{σ2} results, showing a loss of complexity in AD signals, led to smaller *p*-values in comparison with MSE_{µ} and mvMSE_{µ} ones, suggesting that the variance-based MSE and mvMSE can characterise changes in EEGs as a result of AD in a more detailed way. The *p*-values for the slope values of the mvMSE curves were smaller than for MSE at large scale factors, also showing the possible usefulness of multivariate techniques.
Full article

Acknowledgement to Reviewers of *Entropy* in 2016*Entropy* **2017**, *19*(1), 28; doi:10.3390/e19010028 - 11 January 2017**Abstract **
The editors of Entropy would like to express their sincere gratitude to the following reviewers for assessing manuscripts in 2016.[...]
Full article

Face Detection Based on Skin Color Segmentation Using Fuzzy Entropy*Entropy* **2017**, *19*(1), 26; doi:10.3390/e19010026 - 11 January 2017**Abstract **

►
Figures
Face detection is the first step of any automated face recognition system. One of the most popular approaches to detect faces in color images is using a skin color segmentation scheme, which in many cases needs a proper representation of color spaces to

[...] Read more.
Face detection is the first step of any automated face recognition system. One of the most popular approaches to detect faces in color images is using a skin color segmentation scheme, which in many cases needs a proper representation of color spaces to interpret image information. In this paper, we propose a fuzzy system for detecting skin in color images, so that each color tone is assumed to be a fuzzy set. The Red, Green, and Blue (RGB), the Hue, Saturation and Value (HSV), and the YCbCr (where Y is the luminance and Cb,Cr are the chroma components) color systems are used for the development of our fuzzy design. Thus, a fuzzy three-partition entropy approach is used to calculate all of the parameters needed for the fuzzy systems, and then, a face detection method is also developed to validate the segmentation results. The results of the experiments show a correct skin detection rate between 94% and 96% for our fuzzy segmentation methods, with a false positive rate of about 0.5% in all cases. Furthermore, the average correct face detection rate is above 93%, and even when working with heterogeneous backgrounds and different light conditions, it achieves almost 88% correct detections. Thus, our method leads to accurate face detection results with low false positive and false negative rates.
Full article

Comparing Relational and Ontological Triple Stores in Healthcare Domain*Entropy* **2017**, *19*(1), 30; doi:10.3390/e19010030 - 11 January 2017**Abstract **

►
Figures
Today’s technological improvements have made ubiquitous healthcare systems that converge into smart healthcare applications in order to solve patients’ problems, to communicate effectively with patients, and to improve healthcare service quality. The first step of building a smart healthcare information system is representing

[...] Read more.
Today’s technological improvements have made ubiquitous healthcare systems that converge into smart healthcare applications in order to solve patients’ problems, to communicate effectively with patients, and to improve healthcare service quality. The first step of building a smart healthcare information system is representing the healthcare data as connected, reachable, and sharable. In order to achieve this representation, ontologies are used to describe the healthcare data. Combining ontological healthcare data with the used and obtained data can be maintained by storing the entire health domain data inside big data stores that support both relational and graph-based ontological data. There are several big data stores and different types of big data sets in the healthcare domain. The goal of this paper is to determine the most applicable ontology data store for storing the big healthcare data. For this purpose, AllegroGraph and Oracle 12c data stores are compared based on their infrastructural capacity, loading time, and query response times. Hence, healthcare ontologies (GENE Ontology, Gene Expression Ontology (GEXO), Regulation of Transcription Ontology (RETO), Regulation of Gene Expression Ontology (REXO)) are used to measure the ontology loading time. Thereafter, various queries are constructed and executed for GENE ontology in order to measure the capacity and query response times for the performance comparison between AllegroGraph and Oracle 12c triple stores.
Full article

Local Entropy Generation in Compressible Flow through a High Pressure Turbine with Delayed Detached Eddy Simulation*Entropy* **2017**, *19*(1), 29; doi:10.3390/e19010029 - 11 January 2017**Abstract **

►
Figures
Gas turbines are important energy-converting equipment in many industries. The flow inside gas turbines is very complicated and the knowledge about the flow loss mechanism is critical to the advanced design. The current design system heavily relies on empirical formulas or Reynolds Averaged

[...] Read more.
Gas turbines are important energy-converting equipment in many industries. The flow inside gas turbines is very complicated and the knowledge about the flow loss mechanism is critical to the advanced design. The current design system heavily relies on empirical formulas or Reynolds Averaged Navier–Stokes (RANS), which faces big challenges in dealing with highly unsteady complex flow and accurately predicting flow losses. Further improving the efficiency needs more insights into the loss generation in gas turbines. Conventional Unsteady Reynolds Averaged Simulation (URANS) methods have defects in modeling multi-frequency, multi-length, highly unsteady flow, especially when mixing or separation occurs, while Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES) are too costly for the high-Reynolds number flow. In this work, the Delayed Detached Eddy Simulation (DDES) method is used with a low-dissipation numerical scheme to capture the detailed flow structures of the complicated flow in a high pressure turbine guide vane. DDES accurately predicts the wake vortex behavior and produces much more details than RANS and URANS. The experimental findings of the wake vortex length characteristics, which RANS and URANS fail to predict, are successfully captured by DDES. Accurate flow simulation builds up a solid foundation for accurate losses prediction. Based on the detailed DDES results, loss analysis in terms of entropy generation rate is conducted from two aspects. The first aspect is to apportion losses by its physical resources: viscous irreversibility and heat transfer irreversibility. The viscous irreversibility is found to be much stronger than the heat transfer irreversibility in the flow. The second aspect is weighing the contributions of steady effects and unsteady effects. Losses due to unsteady effects account for a large part of total losses. Effects of unsteadiness should not be neglected in the flow physics study and design process.
Full article

Research Entropy Complexity about the Nonlinear Dynamic Delay Game Model*Entropy* **2017**, *19*(1), 22; doi:10.3390/e19010022 - 9 January 2017**Abstract **

►
Figures
Based on the research of domestic and foreign scholars, this paper has improved and established a double oligopoly market model of renewable energy, and analyzed the complex dynamic characteristics of a system based on entropy theory and chaos theory, such as equilibrium point,

[...] Read more.
Based on the research of domestic and foreign scholars, this paper has improved and established a double oligopoly market model of renewable energy, and analyzed the complex dynamic characteristics of a system based on entropy theory and chaos theory, such as equilibrium point, stability, Hopf bifurcation conditions, etc. This paper also studied and simulated the effects of the natural growth rate of energy and the single delay decision on the renewable energy system by minimizing the entropy of the system and reducing the system instability to a minimum, so that the degree of disorder within the system was reduced. The results show that with the increase of the natural growth rate of energy, the stability of the system is not affected, but the market demand of the oligopoly 1 is gradually reducing and the market demand of the oligopoly 2 is gradually increasing. At the same time, a single oligopoly making the time delay decision will affect the stability of the two oligopolies. With the increase of delay, the time required to reach the stable state will grow, and the system will eventually enter the Hopf bifurcation, thus the system will have its entropy increased and fall into an unstable state. Therefore, in the actual market of renewable energy, oligopolies should pay attention to the natural growth rate of energy and time delay, ensuring the stability of the game process and the orderliness of the system.
Full article

Use of Information Measures and Their Approximations to Detect Predictive Gene-Gene Interaction*Entropy* **2017**, *19*(1), 23; doi:10.3390/e19010023 - 7 January 2017**Abstract **

►
Figures
We reconsider the properties and relationships of the interaction information and its modified versions in the context of detecting the interaction of two SNPs for the prediction of a binary outcome when interaction information is positive. This property is called predictive interaction, and

[...] Read more.
We reconsider the properties and relationships of the interaction information and its modified versions in the context of detecting the interaction of two SNPs for the prediction of a binary outcome when interaction information is positive. This property is called predictive interaction, and we state some new sufficient conditions for it to hold true. We also study chi square approximations to these measures. It is argued that interaction information is a different and sometimes more natural measure of interaction than the logistic interaction parameter especially when SNPs are dependent. We introduce a novel measure of predictive interaction based on interaction information and its modified version. In numerical experiments, which use copulas to model dependence, we study examples when the logistic interaction parameter is zero or close to zero for which predictive interaction is detected by the new measure, while it remains undetected by the likelihood ratio test.
Full article

Constructing a Measurement Method of Differences in Group Preferences Based on Relative Entropy*Entropy* **2017**, *19*(1), 24; doi:10.3390/e19010024 - 6 January 2017**Abstract **

In the research and data analysis of the differences involved in group preferences, conventional statistical methods cannot reflect the integrity and preferences of human minds; in particular, it is difficult to exclude humans’ irrational factors. This paper introduces a preference amount model based

[...] Read more.
In the research and data analysis of the differences involved in group preferences, conventional statistical methods cannot reflect the integrity and preferences of human minds; in particular, it is difficult to exclude humans’ irrational factors. This paper introduces a preference amount model based on relative entropy theory. A related expansion is made based on the characteristics of the questionnaire data, and we also construct the parameters to measure differences in the data distribution of different groups on the whole. In this paper, this parameter is called the center distance, and it effectively reflects the preferences of human minds. Using the survey data of securities market participants as an example, this paper analyzes differences in market participants’ attitudes toward the effectiveness of securities regulation. Based on this method, differences between groups that were overlooked by analysis of variance are found, and certain aspects obscured by general data characteristics are also found.
Full article

Misalignment Fault Diagnosis of DFWT Based on IEMD Energy Entropy and PSO-SVM*Entropy* **2017**, *19*(1), 6; doi:10.3390/e19010006 - 1 January 2017**Abstract **

►
Figures
Misalignment is an important cause for the early failure of large doubly-fed wind turbines (DFWT). For the non-stationary characteristics of the signals in the transmission system of DFWT and the reality that it is difficult to obtain a large number of fault samples,

[...] Read more.
Misalignment is an important cause for the early failure of large doubly-fed wind turbines (DFWT). For the non-stationary characteristics of the signals in the transmission system of DFWT and the reality that it is difficult to obtain a large number of fault samples, Solidworks and Adams are used to simulate the different operating conditions of the transmission system of the DFWT to obtain the corresponding characteristic signals. Improved empirical mode decomposition (IEMD), which improves the end effects of empirical mode decomposition (EMD) is used to decompose the signals to get intrinsic mode function (IMF), and the IEMD energy entropy reflecting the working state are extracted as the inputs of the support vector machine (SVM). Particle swarm optimization (PSO) is used to optimize the parameters of SVM to improve the classification performance. The results show that the proposed method can effectively and accurately identify the types of misalignment of the DFWT.
Full article

A New Feature Extraction Method Based on EEMD and Multi-Scale Fuzzy Entropy for Motor Bearing*Entropy* **2017**, *19*(1), 14; doi:10.3390/e19010014 - 31 December 2016**Abstract **

►
Figures
Feature extraction is one of the most important, pivotal, and difficult problems in mechanical fault diagnosis, which directly relates to the accuracy of fault diagnosis and the reliability of early fault prediction. Therefore, a new fault feature extraction method, called the EDOMFE method

[...] Read more.
Feature extraction is one of the most important, pivotal, and difficult problems in mechanical fault diagnosis, which directly relates to the accuracy of fault diagnosis and the reliability of early fault prediction. Therefore, a new fault feature extraction method, called the EDOMFE method based on integrating ensemble empirical mode decomposition (EEMD), mode selection, and multi-scale fuzzy entropy is proposed to accurately diagnose fault in this paper. The EEMD method is used to decompose the vibration signal into a series of intrinsic mode functions (IMFs) with a different physical significance. The correlation coefficient analysis method is used to calculate and determine three improved IMFs, which are close to the original signal. The multi-scale fuzzy entropy with the ability of effective distinguishing the complexity of different signals is used to calculate the entropy values of the selected three IMFs in order to form a feature vector with the complexity measure, which is regarded as the inputs of the support vector machine (SVM) model for training and constructing a SVM classifier (EOMSMFD based on EDOMFE and SVM) for fulfilling fault pattern recognition. Finally, the effectiveness of the proposed method is validated by real bearing vibration signals of the motor with different loads and fault severities. The experiment results show that the proposed EDOMFE method can effectively extract fault features from the vibration signal and that the proposed EOMSMFD method can accurately diagnose the fault types and fault severities for the inner race fault, the outer race fault, and rolling element fault of the motor bearing. Therefore, the proposed method provides a new fault diagnosis technology for rotating machinery.
Full article

Information and Self-Organization*Entropy* **2017**, *19*(1), 18; doi:10.3390/e19010018 - 31 December 2016**Abstract **
The process of “*self-organization*” takes place in open and complex systems that acquire spatio-temporal or functional structures without specific ordering instructions from the outside. [...]
Full article

Thermal Conductivity of Suspension of Aggregating Nanometric Rods*Entropy* **2017**, *19*(1), 19; doi:10.3390/e19010019 - 31 December 2016**Abstract **

►
Figures
Enhancing thermal conductivity of simple fluids is of major interest in numerous applicative systems. One possibility of enhancing thermal properties consists of dispersing small conductive particles inside. However, in general, aggregation effects occur and then one must address systems composed of dispersed clusters

[...] Read more.
Enhancing thermal conductivity of simple fluids is of major interest in numerous applicative systems. One possibility of enhancing thermal properties consists of dispersing small conductive particles inside. However, in general, aggregation effects occur and then one must address systems composed of dispersed clusters composed of particles as well as the ones related to percolated networks. This papers analyzes the conductivity enhancement of different microstructures scaling from clusters dispersed into a simple matrix to the ones related to percolated networks exhibiting a fractal morphology.
Full article

Nonlinear Relaxation Phenomena in Metastable Condensed Matter Systems*Entropy* **2017**, *19*(1), 20; doi:10.3390/e19010020 - 31 December 2016**Abstract **

►
Figures
Nonlinear relaxation phenomena in three different systems of condensed matter are investigated. (i) First, the phase dynamics in Josephson junctions is analyzed. Specifically, a superconductor-graphene-superconductor (SGS) system exhibits quantum metastable states, and the average escape time from these metastable states in the presence

[...] Read more.
Nonlinear relaxation phenomena in three different systems of condensed matter are investigated. (i) First, the phase dynamics in Josephson junctions is analyzed. Specifically, a superconductor-graphene-superconductor (SGS) system exhibits quantum metastable states, and the average escape time from these metastable states in the presence of Gaussian and correlated fluctuations is calculated, accounting for variations in the the noise source intensity and the bias frequency. Moreover, the transient dynamics of a long-overlap Josephson junction (JJ) subject to thermal fluctuations and non-Gaussian noise sources is investigated. Noise induced phenomena are observed, such as the noise enhanced stability and the stochastic resonant activation. (ii) Second, the electron spin relaxation process in a n-type GaAs bulk driven by a fluctuating electric field is investigated. In particular, by using a Monte Carlo approach, we study the influence of a random telegraph noise on the spin polarized transport. Our findings show the possibility to raise the spin relaxation length by increasing the amplitude of the external fluctuations. Moreover, we find that, crucially, depending on the value of the external field strength, the electron spin depolarization length versus the noise correlation time increases up to a plateau. (iii) Finally, the stabilization of quantum metastable states by dissipation is presented. Normally, quantum fluctuations enhance the escape from metastable states in the presence of dissipation. We show that dissipation can enhance the stability of a quantum metastable system, consisting of a particle moving in a strongly asymmetric double well potential, interacting with a thermal bath. We find that the escape time from the metastable region has a nonmonotonic behavior versus the system- bath coupling and the temperature, producing a stabilizing effect.
Full article

Perturbative Treatment of the Non-Linear *q*-Schrödinger and *q*-Klein–Gordon Equations*Entropy* **2017**, *19*(1), 21; doi:10.3390/e19010021 - 31 December 2016**Abstract **

►
Figures
Interesting non-linear generalization of both Schrödinger’s and Klein–Gordon’s equations have been recently advanced by Tsallis, Rego-Monteiro and Tsallis (NRT) in Nobre et al. (*Phys. Rev. Lett.* 2011, 106, 140601). There is much current activity going on in this area. The non-linearity is

[...] Read more.
Interesting non-linear generalization of both Schrödinger’s and Klein–Gordon’s equations have been recently advanced by Tsallis, Rego-Monteiro and Tsallis (NRT) in Nobre et al. (*Phys. Rev. Lett.* 2011, 106, 140601). There is much current activity going on in this area. The non-linearity is governed by a real parameter *q*. Empiric hints suggest that the ensuing non-linear *q*-Schrödinger and *q*-Klein–Gordon equations are a natural manifestations of very high energy phenomena, as verified by LHC-experiments. This happens for $q-$ values close to unity (Plastino et al. (*Nucl. Phys. A* 2016, 955, 16–26, *Nucl. Phys. A* 2016, 948, 19–27)). It might thus be difficult for *q*-values close to unity to ascertain whether one is dealing with solutions to the ordinary Schrödinger equation (whose free particle solutions are exponentials and for which $q=1$ ) or with its NRT non-linear *q*-generalizations, whose free particle solutions are *q*-exponentials. In this work, we provide a careful analysis of the $q\sim 1$ instance via a perturbative analysis of the NRT equations.
Full article

Humans Outperform Machines at the Bilingual Shannon Game*Entropy* **2017**, *19*(1), 15; doi:10.3390/e19010015 - 30 December 2016**Abstract **

►
Figures
We provide an upper bound for the amount of information a human translator adds to an original text, i.e., how many bits of information we need to store a translation, given the original. We do this by creating a Bilingual Shannon Game that

[...] Read more.
We provide an upper bound for the amount of information a human translator adds to an original text, i.e., how many bits of information we need to store a translation, given the original. We do this by creating a Bilingual Shannon Game that elicits character guesses from human subjects, then developing models to estimate the entropy of those guess sequences.
Full article

One-Parameter Fisher–Rényi Complexity: Notion and Hydrogenic Applications*Entropy* **2017**, *19*(1), 16; doi:10.3390/e19010016 - 30 December 2016**Abstract **

►
Figures
In this work, the one-parameter Fisher–Rényi measure of complexity for general *d*-dimensional probability distributions is introduced and its main analytic properties are discussed. Then, this quantity is determined for the hydrogenic systems in terms of the quantum numbers of the quantum states

[...] Read more.
In this work, the one-parameter Fisher–Rényi measure of complexity for general *d*-dimensional probability distributions is introduced and its main analytic properties are discussed. Then, this quantity is determined for the hydrogenic systems in terms of the quantum numbers of the quantum states and the nuclear charge.
Full article

The Information Recovery Problem*Entropy* **2017**, *19*(1), 17; doi:10.3390/e19010017 - 30 December 2016**Abstract **

►
Figures
The issue of unitary evolution during creation and evaporation of a black hole remains controversial. We argue that some prominent cures are more troubling than the disease, demonstrate that their central element—forming of the event horizon before the evaporation begins—is not necessarily true,

[...] Read more.
The issue of unitary evolution during creation and evaporation of a black hole remains controversial. We argue that some prominent cures are more troubling than the disease, demonstrate that their central element—forming of the event horizon before the evaporation begins—is not necessarily true, and describe a fully coupled matter-gravity system which is manifestly unitary.
Full article