Intrinsic Entropy Research Articles

On the choice of multiscale entropy algorithm for quantification of complexity in gait data

The present study aimed at identifying a suitable multiscale entropy (MSE) algorithm for assessment of complexity in a stride-to-stride time interval time series. Five different algorithms were included (the original MSE, refine composite multiscale entropy (RCMSE), multiscale fuzzy entropy, generalized multiscale entropy and intrinsic mode entropy) and applied to twenty iterations of white noise, pink noise, or a sine wave with added white noise. Based on their ability to differentiate the level of complexity in the three different generated signal types, and their sensitivity and parameter consistency, MSE and RCMSE were deemed most appropriate. These two algorithms were applied to stride-to-stride time interval time series recorded from fourteen healthy subjects during one hour of overground and treadmill walking. In general, acceptable sensitivity and good parameter consistency were observed for both algorithms; however, they were not able to differentiate the complexity of the stride-to-stride time interval time series between the two walking conditions. Thus, the present study recommends the use of either MSE or RCMSE for quantification of complexity in stride-to-stride time interval time series.

Quantifying the Intrinsic Conformation Energy Landscape Topography of Proteins with Large-Scale Open-Closed Transition.

Large-scale conformational changes of proteins, including the open–closed transitions, are crucial for a variety of protein functions. These open–closed transitions are often associated with ligand binding. However, the understandings of the underlying mechanisms of the conformational changes within proteins during the open–closed transitions are still challenging at present. In this study, we quantified the intrinsic underlying conformational energy landscapes of five different proteins with large-scale open–closed transitions. This is realized by exploring the underlying density of states and the intrinsic conformational energy landscape topography measure Λ. Λ is a dimensionless ratio of conformational energy gap δE versus conformational energy roughness δE and configurational entropy S or size of the intrinsic conformational energy landscape. By quantifying the Λ of intrinsic open–closed conformational (Λoc) and intrinsic global folding (Λglobal) energy landscapes, we show that both intrinsic open–closed conformation energy and entropy landscapes are funneled toward the closed state. Furthermore, our results indicate the strong correlations between Λ and thermodynamics (conformational state transition temperature against trapping temperature) as well as between Λ and kinetics (open–closed kinetic time) of these proteins. This shows that the intrinsic conformational landscape topography determines both the conformational thermodynamic stability and kinetic speed of the conformational dynamics. Our investigations provide important insights for understanding the fundamental mechanisms of the protein conformational dynamics in a physical and global way.

Isentropic correction for collocated Lagrange-Remap scheme

We study an Eulerian scheme of Lagrange-Remap type, which simulates compressible multi-material fluid flows. The Lagrangian phase is based on a collocated scheme called EUCCLHYD (Explicit Unstructured Cell-Centered Lagrangian HYDrodynamics, Maire et al., 2007), whereas the remap phase uses alternate directions with interface reconstruction of PLIC type. The EUCCLHYD scheme, which is built on the resolution of acoustic Riemann problems at nodes, is totally conservative, second order in time and space, and captures shock waves accurately. However, the intrinsic entropy production is inaccurate for isentropic flows (rarefaction/expansion waves, isentropic compression). In this framework we suggest a correction, inspired by Braeunig (2016), to improve accuracy in flows with isentropic behavior. This is achieved by modifying the scheme in order to nullify the entropy production in expansion zones.

Inter-scale information flow as a surrogate for downward causation that maintains spiral waves.

A rotor, the rotation center of spiral waves, has been proposed as a causal mechanism to maintain atrial fibrillation (AF) in human. However, our current understanding of the causality between rotors and spiral waves remains incomplete. One approach to improving our understanding is to determine the relationship between rotors and downward causation from the macro-scale collective behavior of spiral waves to the micro-scale behavior of individual components in a cardiac system. This downward causation is quantifiable as inter-scale information flow that can be used as a surrogate for the mechanism that maintains spiral waves. We used a numerical model of a cardiac system and generated a renormalization group with system descriptions at multiple scales. We found that transfer entropy quantified the upward and downward inter-scale information flow between micro- and macro-scale descriptions of the cardiac system with spiral waves. In addition, because the spatial profile of transfer entropy and intrinsic transfer entropy was identical, there were no synergistic effects in the system. Furthermore, inter-scale information flow significantly decreased as the description of the system became more macro-scale. Finally, downward information flow was significantly correlated with the number of rotors, but the higher numbers of rotors were not necessarily associated with higher downward information flow. This finding contradicts the concept that the rotors are the causal mechanism that maintains spiral waves, and may account for the conflicting evidence from clinical studies targeting rotors to eliminate AF.

Regimes of the Pomeron and its intrinsic entropy

We suggest that the perturbative and non-perturbative descriptions of the Pomeron can be viewed as complementary descriptions of different phases in the Pomeron phase diagram, with a phase boundary where the proper description of the produced systems is “string balls”. Their intrinsic entropy is calculated and turned out to be the same, as the recently reported perturbative entanglement entropy. The distribution of large multiplicities stemming from the string balls is also wide, with its moments close to those reported for hadrons in pp collisions at the LHC. At low-x, the quantum string is so entangled that sufficiently weak string self-attraction can cause it to turn to a string ball dual to a black hole. We suggest that low-x saturation occurs when the density of wee-strings reaches the Bekenstein bound, with a proton size that freezes with increasing rapidity. Some of these observations maybe checked at the future eIC.

Design of two-tail compounds with rotationally fixed benzenesulfonamide ring as inhibitors of carbonic anhydrases

Rational design of compounds that would bind specific pockets of the target proteins is a difficult task in drug design. The 12 isoforms of catalytically active human carbonic anhydrases (CAs) have highly similar active sites that make it difficult to design inhibitors selective for one or several CA isoforms. A series of CA inhibitors based on 2-chloro/bromo-benzenesulfonamide that is largely fixed in the CA active site together with one or two tails yielded compounds that were synthesized and evaluated as inhibitors of CA isoforms. Introduction of a second tail had significant influence on the binding affinity and two-tailed compounds in most cases provided high affinity and selectivity for CA IX and CA XIV. The contacts between several compounds and CA amino acids were determined by X-ray crystallography. Together with the intrinsic enthalpy and entropy of binding they provided the structure-thermodynamics correlations for this series of compounds with the insight how to rationally build compounds with desired CA isoform as a target.

Minimum Data Rate for Exponential Stability of Networked Control Systems with Medium Access Constraints

In this paper, we investigate the minimum data rate problem to guarantee the stability of the networked control systems (NCSs) suffered to the medium access constraints in the digital communication channel. Under the effect of medium access constraints, the data rate of each communication node switches between its pre-set value and zero according to the medium access status assigned by the scheduler. In order to guarantee the exponential stability, a new analysis approach combined with the average dwell time technique and entropy theory is established for the unstable scalar systems and vector systems to obtain the sufficient and necessary conditions for each subsystem. The obtained minimum data rate are related to the intrinsic entropy rate of the system and the duty factor allocated by the scheduler. An numerical example is given to illustrate the effectiveness of the designed minimum data rate for the NCSs which composed by a collection of subsystems.

Intrinsic entropy perturbations from the dark sector

Perfect fluids are modeled by using an effective field theory approach which naturally gives a self-consistent and unambiguous description of the intrinsic non-adiabatic contribution to pressure variations. We study the impact of intrinsic entropy perturbation on the superhorizon dynamics of the curvature perturbation ℛ in the dark sector. The dark sector, made of dark matter and dark energy is described as a single perfect fluid. The non-perturbative vorticity's dynamics and the Weinberg theorem violation for perfect fluids are also studied.

Two new proofs concerning the intrinsic algebraic entropy

ABSTRACTWe provide simpler and more direct proofs of the Addition Theorem and of the Intrinsic Algebraic Yuzvinski Formula for the intrinsic algebraic entropy of endomorphisms of Abelian groups.

Crystal structure correlations with the intrinsic thermodynamics of human carbonic anhydrase inhibitor binding.

The structure-thermodynamics correlation analysis was performed for a series of fluorine- and chlorine-substituted benzenesulfonamide inhibitors binding to several human carbonic anhydrase (CA) isoforms. The total of 24 crystal structures of 16 inhibitors bound to isoforms CA I, CA II, CA XII, and CA XIII provided the structural information of selective recognition between a compound and CA isoform. The binding thermodynamics of all structures was determined by the analysis of binding-linked protonation events, yielding the intrinsic parameters, i.e., the enthalpy, entropy, and Gibbs energy of binding. Inhibitor binding was compared within structurally similar pairs that differ by para- or meta-substituents enabling to obtain the contributing energies of ligand fragments. The pairs were divided into two groups. First, similar binders—the pairs that keep the same orientation of the benzene ring exhibited classical hydrophobic effect, a less exothermic enthalpy and a more favorable entropy upon addition of the hydrophobic fragments. Second, dissimilar binders—the pairs of binders that demonstrated altered positions of the benzene rings exhibited the non-classical hydrophobic effect, a more favorable enthalpy and variable entropy contribution. A deeper understanding of the energies contributing to the protein-ligand recognition should lead toward the eventual goal of rational drug design where chemical structures of ligands could be designed based on the target protein structure.

Coarse-Graining Approaches in Univariate Multiscale Sample and Dispersion Entropy

The evaluation of complexity in univariate signals has attracted considerable attention in recent years. This is often done using the framework of Multiscale Entropy, which entails two basic steps: coarse-graining to consider multiple temporal scales, and evaluation of irregularity for each of those scales with entropy estimators. Recent developments in the field have proposed modifications to this approach to facilitate the analysis of short-time series. However, the role of the downsampling in the classical coarse-graining process and its relationships with alternative filtering techniques has not been systematically explored yet. Here, we assess the impact of coarse-graining in multiscale entropy estimations based on both Sample Entropy and Dispersion Entropy. We compare the classical moving average approach with low-pass Butterworth filtering, both with and without downsampling, and empirical mode decomposition in Intrinsic Multiscale Entropy, in selected synthetic data and two real physiological datasets. The results show that when the sampling frequency is low or high, downsampling respectively decreases or increases the entropy values. Our results suggest that, when dealing with long signals and relatively low levels of noise, the refine composite method makes little difference in the quality of the entropy estimation at the expense of considerable additional computational cost. It is also found that downsampling within the coarse-graining procedure may not be required to quantify the complexity of signals, especially for short ones. Overall, we expect these results to contribute to the ongoing discussion about the development of stable, fast and robust-to-noise multiscale entropy techniques suited for either short or long recordings.

Thermodynamic, kinetic, and structural parameterization of human carbonic anhydrase interactions toward enhanced inhibitor design.

The aim of rational drug design is to develop small molecules using a quantitative approach to optimize affinity. This should enhance the development of chemical compounds that would specifically, selectively, reversibly, and with high affinity interact with a target protein. It is not yet possible to develop such compounds using computational (i.e., in silico) approach and instead the lead molecules are discovered in high-throughput screening searches of large compound libraries. The main reason why in silico methods are not capable to deliver is our poor understanding of the compound structure-thermodynamics and structure-kinetics correlations. There is a need for databases of intrinsic binding parameters (e.g., the change upon binding in standard Gibbs energy (ΔGint), enthalpy (ΔHint), entropy (ΔSint), volume (ΔVintr), heat capacity (ΔCp,int), association rate (ka,int), and dissociation rate (kd,int)) between a series of closely related proteins and a chemically diverse, but pharmacophoric group-guided library of compounds together with the co-crystal structures that could help explain the structure-energetics correlations and rationally design novel compounds. Assembly of these data will facilitate attempts to provide correlations and train data for modeling of compound binding. Here, we report large datasets of the intrinsic thermodynamic and kinetic data including over 400 primary sulfonamide compound binding to a family of 12 catalytically active human carbonic anhydrases (CA). Thermodynamic parameters have been determined by the fluorescent thermal shift assay, isothermal titration calorimetry, and by the stopped-flow assay of the inhibition of enzymatic activity. Kinetic measurements were performed using surface plasmon resonance. Intrinsic thermodynamic and kinetic parameters of binding were determined by dissecting the binding-linked protonation reactions of the protein and sulfonamide. The compound structure-thermodynamics and kinetics correlations reported here helped to discover compounds that exhibited picomolar affinities, hour-long residence times, and million-fold selectivities over non-target CA isoforms. Drug-lead compounds are suggested for anticancer target CA IX and CA XII, antiglaucoma CA IV, antiobesity CA VA and CA VB, and other isoforms. Together with 85 X-ray crystallographic structures of 60 compounds bound to six CA isoforms, the database should be of help to continue developing the principles of rational target-based drug design.

Intrinsic Entropies of Log-Concave Distributions

The entropy of a random variable is well-known to equal the exponential growth rate of the volumes of its typical sets. In this paper, we show that for any log-concave random variable $X$ , the sequence of the $\lfloor n\theta \rfloor ^{\text {th}}$ intrinsic volumes of the typical sets of $X$ in dimensions $n \geq 1$ grows exponentially with a well-defined rate. We denote this rate by $h_{X}(\theta )$ , and call it the $\theta ^{\text {th}}$ intrinsic entropy of $X$ . We show that $h_{X}(\theta )$ is a continuous function of $\theta $ over the range [0, 1], thereby providing a smooth interpolation between the values 0 and $h(X)$ at the endpoints 0 and 1, respectively.

An efficient kinetic Monte Carlo scheme for computing Helmholtz free energy and entropy in bulk fluids and adsorption systems

We present an efficient kinetic Monte Carlo scheme to determine the Helmholtz free energy and entropy of bulk fluids and adsorption systems. The method is made possible because this technique enables the accurate determination of the chemical potential. The Helmholtz free energy, A, is obtained by integrating the chemical potential with respect to the number of molecules, at constant volume and temperature, and the entropy is then determined from the fundamental thermodynamic equation A = E − TS. The entropy of bulk argon is found to be in excellent agreement with values calculated from the established equation of state (EOS). In a system with two co-existing phases we show that our method can determine the surface tension at the Gibbs dividing surface, without recourse to the mechanical route of Irving, Kirkwood and Buff.We show that the intrinsic integral molecular Helmholtz free energy and entropy of the adsorbed phase, corrected for the surface excess, are independent of the size of the simulation box for all chemical potentials tested.The new procedure is illustrated for a range of gases commonly used in the characterization of porous solids (argon, nitrogen, carbon dioxide and ammonia) as adsorbates and a graphitic slit pore as the model adsorbent.

Size effects of electrocaloric cooling in ferroelectric nanowires

AbstractConsidering finite size effect, ferroelectric nanowires may show novel phenomena compared to ferroelectric thin film and bulk. Here we investigated the effect of width and surface compressive stress on electrocaloric cooling in ferroelectric nanowire by using thermodynamic calculations and phase‐field simulations. It was found that the isothermal entropy change and adiabatic temperature change in nanowire are 50% larger than that in thin film due to different mechanical boundary conditions of nanowire and thin film. The largest electrocaloric temperature changes were shown to increase significantly either with the decrease in nanowire width or the increase with the surface compressive stress. It was also revealed that the largest intrinsic entropy changes are almost the same for different nanowires with different widths and various stresses. The present study therefore contributes to the understanding of size effects of electrocaloric cooling and provides guidance for experiments to design high‐efficiency cooling devices using ferroelectric nanosystems.

Stacking fault energies of face-centered cubic concentrated solid solution alloys

We report the stacking fault energy (SFE) for a series of face-centered cubic (fcc) equiatomic concentrated solid solution alloys (CSAs) derived as subsystems from the NiCoFeCrMn and NiCoFeCrPd high entropy alloys based on ab initio calculations. At low temperatures, these CSAs display very low even negative SFEs, indicating that hexagonal close-pack (hcp) is more energy favorable than fcc structure. The temperature dependence of SFE for some CSAs is studied. With increasing temperature, a hcp-to-fcc transition is revealed for those CSAs with negative SFEs, which can be attributed to the role of intrinsic vibrational entropy. The analysis of the vibrational modes suggests that the vibrational entropy arises from the high frequency states in the hcp structure that originate from local vibrational mode. Our results underscore the importance of vibrational entropy in determining the temperature dependence of SFE for CSAs.

Wear behavior of high entropy alloys containing soft dispersoids (Pb, Bi)

Intrinsic high entropy alloys (HEAs) exhibit superior mechanical properties (hardness, strength, ductility, toughness etc.) and hence, they are considered as potential candidates for wear resistance applications. Wear resistance of HEAs can further be improved by engineering microstructure using various novel design concepts. One of such concepts involves the usages of soft dispersoids (Sn, Pb, Bi, Sb etc.) in the HEA matrix. However, the challenge is to engineer the novel microstructure consisting of soft dispersoids, dispersed uniformly in the HEA matrix, using suitable processing techniques. In this connection, the present work reports the effect of soft dispersoids, such as Pb and Bi on the wear behavior in equiatomic CuCrFeTiZn and AlCrFeMnV HEAs. The alloys containing Pb and Bi were synthesized using mechanical alloying (MA) followed by spark plasma sintering (SPS) in inert argon atmosphere. Phases and microstructure of milled powder and sintered alloys were investigated using XRD, SEM equipped with EDS. Sliding wear tests were also carried out for all the sintered samples at 2N, 5N, 7N and 10N load for various sliding speeds. Wear results indicate coefficient of friction (COF) does not vary much with varying the Pb concentration in HEAs. However, wear rate decreases significantly with increasing the Pb content in the alloys. For HEAs containing Bi, there is considerable decrease in the COF as well as in the wear rate even for a lower (5%) Bi content. Increasing load does not cause any change in the COF in both cases. However, wear rate decreases substantially due to increase of load. In addition, SEM analysis of the worn surface and wear debris were performed and it has been found that oxidative wear is the dominant wear mechanism in these systems. However wear tracks indicate the presence of abrasive wear. Analysis of Raman spectroscopy of wear debris confirms the presence of Fe2O3, Bi2O3 and PbO.

Theoretical Analysis of the Influence of Pore Geometry on Monomolecular Cracking and Dehydrogenation of n-Butane in Brønsted Acidic Zeolites

Recent experimental work has shown that variations in the confinement of n-butane at Bronsted acid sites due to changes in zeolite framework structure strongly affect the apparent and intrinsic enthalpy and entropy of activation for cracking and dehydrogenation. Quantum chemical calculations have provided good estimates of the intrinsic enthalpies and entropies of activation extracted from experimental rate data for MFI, but extending these calculations to less confining zeolites has proven challenging, particularly for activation entropies. Herein, we report our efforts to develop a theoretical model for the cracking and dehydrogenation of n-butane occurring in a series of zeolites containing 10-ring channels and differing in cavity size (TON, FER, -SVR, MFI, MEL, STF, and MWW). We combine a QM/MM approach to calculate intrinsic and apparent activation parameters, with thermal corrections to the apparent barriers obtained from configurational-bias Monte Carlo simulations, to account for configurational c...

Erratum: Big brake singularity is accommodated as an exotic quintessence field [Phys. Rev. D 93 , 043524 (2016)

We describe a big brake singularity in terms of a modified Chaplygin gas equation of state $p=(\ga_{m}-1)\rho+\al\ga_{m}\rho^{-n}$, accommodate this late-time event as an exotic quintessence model obtained from an energy-momentum tensor, and focus on the cosmological behavior of the exotic field, its kinetic energy and the potential energy. At the background level, the exotic field does not blow up whereas its kinetic energy and potential both grow without limit near the future singularity. We evaluate the classical stability of this background solution by examining the scalar perturbations of the metric along with the inclusion of entropy perturbation in the perturbed pressure. Within the Newtonian gauge, the gravitational field approaches a constant near the singularity plus additional regular terms. When the perturbed exotic field is associated with $\al>0$ the perturbed pressure and contrast density both diverge, whereas the perturbed exotic field and the divergence of the exotic field's velocity go to zero exponentially. When the perturbed exotic field is associated with $\al<0$ the contrast density always blows up, but the perturbed pressure can remain bounded. In addition, the perturbed exotic field and the divergence of the exotic field's velocity vanish near the big brake singularity. We also briefly look at the behavior of the intrinsic entropy perturbation near the singular event.

Decoupling interface effect on the phase stability of CdS thin films by van der Waals heteroepitaxy

Wurtzite (W) and zinc-blende (ZB) polytypism has long been observed in epitaxial CdS thin films. The present work, based on van der Waals epitaxial CdS thin films, is an attempt to explain which crystal modification, W or ZB, is favored under different growth conditions. In this van der Waals epitaxy system where the substrate influence is considered weak, it is found that the substrate temperature plays a crucial role in determining the crystal modification of CdS, that is, W and ZB CdS are more stable at low and high ends of substrate temperature, respectively. We attribute this temperature effect to the entropy difference (SW &amp;lt; SZB), a conclusion well supported by the thermodynamic hard sphere model formulation of the entropy difference between hexagonal close-packed and face-centered cubic structures. By summarizing other works, we find that the entropy difference model can also be applied to large mismatched (≳3%) CdS-substrate chemical epitaxy systems but not for small mismatched (≲3%) ones. In the latter case, the energy benefit in terms of high density of bonding contributed by the substrate-film interface is believed to be too overwhelming for the intrinsic entropy difference to overcome. Furthermore, the deposition rate is found to affect the crystalline quality and strain level in CdS films but not the crystal modification of the CdS films. Last, Raman and photoluminescence spectroscopies reveal the strain behaviors in the films. The phase change from W to ZB CdS is well-correlated with the observed peak shifts in Raman and photoluminescence spectroscopies.