Higher Entropy Research Articles

Forest Fire Detection via Feature Entropy Guided Neural Network.

Forest fire detection from videos or images is vital to forest firefighting. Most deep learning based approaches rely on converging image loss, which ignores the content from different fire scenes. In fact, complex content of images always has higher entropy. From this perspective, we propose a novel feature entropy guided neural network for forest fire detection, which is used to balance the content complexity of different training samples. Specifically, a larger weight is given to the feature of the sample with a high entropy source when calculating the classification loss. In addition, we also propose a color attention neural network, which mainly consists of several repeated multiple-blocks of color-attention modules (MCM). Each MCM module can extract the color feature information of fire adequately. The experimental results show that the performance of our proposed method outperforms the state-of-the-art methods.

Reaction kinetics, mechanism, and product analysis of the iron catalytic graphitization of cellulose

Biomass based porous graphitic carbon are valuable materials in terms of renewable energy and environmental remediation; however, the catalytic graphitization mechanism of biomass and the solid char evolution process have not been comprehensively studied. Therefore, iron catalytic graphitization process of cellulose was investigated and the reaction kinetics, thermodynamics, pyrolytic behavior, and product properties analyzed in detail. It was found that iron addition lowered cellulose decomposition temperature, but higher average activation energy (230 kJ/mol), and higher entropy (100 J/mol). In-situ-produced Fe3C and Fe promoted secondary reactions and activated C–H bonds, which led to an increase in the production of hydrogen and solid char from 2.9 mmol/g to 8.1 mmol/g and 6.3 wt% to 19.9 wt%, respectively, at the expense of the liquid oil yield. Furthermore, the iron addition promoted the degree of graphitization and etched porosity. The intrinsic reaction kinetics, thermodynamics, and technical analysis reported herein may guide the application of bioenergy for the preparation of porous graphite and hydrogen.

Noninvasive Detection of Respiratory Disorder Due to COVID-19 at the Early Stages in Saudi Arabia

The Kingdom of Saudi Arabia has suffered from COVID-19 disease as part of the global pandemic due to severe acute respiratory syndrome coronavirus 2. The economy of Saudi Arabia also suffered a heavy impact. Several measures were taken to help mitigate its impact and stimulate the economy. In this context, we present a safe and secure WiFi-sensing-based COVID-19 monitoring system exploiting commercially available low-cost wireless devices that can be deployed in different indoor settings within Saudi Arabia. We extracted different activities of daily living and respiratory rates from ubiquitous WiFi signals in terms of channel state information (CSI) and secured them from unauthorized access through permutation and diffusion with multiple substitution boxes using chaos theory. The experiments were performed on healthy participants. We used the variances of the amplitude information of the CSI data and evaluated their security using several security parameters such as the correlation coefficient, mean-squared error (MSE), peak-signal-to-noise ratio (PSNR), entropy, number of pixel change rate (NPCR), and unified average change intensity (UACI). These security metrics, for example, lower correlation and higher entropy, indicate stronger security of the proposed encryption method. Moreover, the NPCR and UACI values were higher than 99% and 30, respectively, which also confirmed the security strength of the encrypted information.

A falling magnetic monopole as a holographic local quench

An analytic static monopole solution is found in global AdS4, in the limit of small backreaction. This solution is mapped in Poincaré patch to a falling monopole configuration, which is dual to a local quench triggered by the injection of a condensate. Choosing boundary conditions which are dual to a time-independent Hamiltonian, we find the same functional form of the energy-momentum tensor as the one of a quench dual to a falling black hole. On the contrary, the details of the spread of entanglement entropy are very different from the falling black hole case, where the quench induces always a higher entropy compared to the vacuum, i.e. ∆S > 0. In the propagation of entanglement entropy for the monopole quench, there is instead a competition between a negative contribution to ∆S due to the scalar condensate and a positive one carried by the freely propagating quasiparticles generated by the energy injection.

Prevalence of spelling errors affects reading behavior across languages.

This cross-linguistic study investigated the impact of spelling errors on reading behavior in five languages (Chinese, English, Finnish, Greek, and Hebrew). Learning theories predict that correct and incorrect spelling alternatives (e.g., "tomorrow" and "tommorrow") provide competing cues to the sound and meaning of a word: The closer the alternatives are to each other in their frequency of occurrence, the more uncertain the reader is regarding the spelling of that word. An information-theoretic measure of entropy was used as an index of uncertainty. Based on theories of learning, we predicted that higher entropy would lead to slower recognition of words even when they are spelled correctly. This prediction was confirmed in eye-tracking sentence-reading experiments in five languages widely variable in their writing systems' phonology and morphology. Moreover, in each language, we observed a characteristic Entropy × Frequency interaction; arguably, its functional shape varied as a function of the orthographic transparency of a given written language. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

A Model to Improve Security Questions Through Individualized Assistance

Security questions are considered a viable alternative for secondary and supplementary authentication. Security questions are susceptible to three types of attacks: blind (brute force), focused guess (statistical), and observation (research/personal). This research outlines how informing users of potential security threats through a security meter may improve security with minimal impact on usability and trust. A security-question authentication model is proposed that builds on the strengths of security question responses, chiefly their ease of recall and higher entropy, while mitigating the core weaknesses of the model, which are the lack of uniform answers and public accessibility to answers. Users that were made aware of the entropy of their responses were more likely to provide stronger responses to the security questions without affecting the repeatability of the responses to the questions but negatively impacting the memorability.

The Cost of a True Random Bit—On the Electronic Cost Gain of ASIC Time-Domain-Based TRNGs

Random number generators are of paramount importance in numerous fields. Under certain well-defined adversarial settings, True Random Number Generators (TRNGs) are more secure than their computational (pseudo) random number generator counterparts. TRNGs are also known to be more efficiently implemented on hardware platforms where, for various applications, efficiency in terms of electronic cost factors is critical. In this manuscript, we first provide an evaluation of robustness and reliability of efficient time-domain-based TRNG implementation over FPGA platform. In particular, we demonstrate sensitivities which imply a TRNG construction which is not agnostic to electronic-design-automation tools and to the level of designers’ know-how. This entails a large amount of effort and validation to make the designs robust, as well as requires a high degree of complexity from non-trivial FPGAs flows. This motivates the second part of the manuscript, where we propose an ASIC-based implementation of the TRNG, along with the optimization steps to enhance its characteristics. The optimized design improves the randomness-throughput by 42× for the same entropy level described in previous works, and it can provide maximal entropy level of 0.985 with 7× improvement in randomness throughput over the raw samples (no pre-processing). The proposed design simultaneously provides a reduced energy of 0.1 (mW/bit) for the same entropy level as previous works, and 1.06 (mW/bit) for the higher entropy flavor, and a lower area utilization of 0.000252 (mm2) on a 65 nm technology evaluation, situating it in the top-class of the discuss ratings. This leads to the quantitative question of the gain in electronic cost factors over ASIC TRNGs, and the minimum Cost Per Bit/Source possible to date. Finally, we exemplify a TRNG versus PRNG cost-extrapolation for security architects and designers, targeting an ASIC scenario feeding a lightweight encryption core.

CT texture analysis of tonsil cancer: Discrimination from normal palatine tonsils.

The purposes of the study were to determine whether there are differences in texture analysis parameters between tonsil cancers and normal tonsils, and to correlate texture analysis with 18F-FDG PET/CT to investigate the relationship between texture analysis and metabolic parameters. Sixty-four patients with squamous cell carcinoma of the palatine tonsil were included. A ROI was drawn, including all slices, to involve the entire tumor. The contralateral normal tonsil was used for comparison with the tumors. Texture analysis parameters, mean, standard deviation (SD), entropy, mean positive pixels, skewness, and kurtosis were obtained using commercially available software. Parameters were compared between the tumor and the normal palatine tonsils. Comparisons were also performed among early tonsil cancer, advanced tonsil cancer, and normal tonsils. An ROC curve analysis was performed to assess discrimination of tumor from normal tonsils. Correlation between texture analysis and 18F-FDG PET/CT was performed. Compared to normal tonsils, the tumors showed a significantly lower mean, higher SD, higher entropy, lower skewness, and higher kurtosis on most filters (p<0.001). On comparisons among normal tonsils, early cancers, and advanced tonsil cancers, SD and entropy showed significantly higher values on all filters (p<0.001) between early cancers and normal tonsils. The AUC from the ROC analysis was 0.91, obtained from the entropy. A mild correlation was shown between texture parameters and metabolic parameters. The texture analysis parameters, especially entropy, showed significant differences in contrast-enhanced CT results between tumor and normal tonsils, and between early tonsil cancers and normal tonsils. Texture analysis can be useful as an adjunctive tool for the diagnosis of tonsil cancers.

A Stepwise Assessment of Parsimony and Fuzzy Entropy in Species Distribution Modelling.

Entropy is intrinsic to the geographical distribution of a biological species. A species distribution with higher entropy involves more uncertainty, i.e., is more gradually constrained by the environment. Species distribution modelling tries to yield models with low uncertainty but normally has to reduce uncertainty by increasing their complexity, which is detrimental for another desirable property of the models, parsimony. By modelling the distribution of 18 vertebrate species in mainland Spain, we show that entropy may be computed along the forward-backwards stepwise selection of variables in Logistic Regression Models to check whether uncertainty is reduced at each step. In general, a reduction of entropy was produced asymptotically at each step of the model. This asymptote could be used to distinguish the entropy attributable to the species distribution from that attributable to model misspecification. We discussed the use of fuzzy entropy for this end because it produces results that are commensurable between species and study areas. Using a stepwise approach and fuzzy entropy may be helpful to counterbalance the uncertainty and the complexity of the models. The model yielded at the step with the lowest fuzzy entropy combines the reduction of uncertainty with parsimony, which results in high efficiency.

Radiomics-Based Texture Analysis of 68Ga-DOTATATE Positron Emission Tomography and Computed Tomography Images as a Prognostic Biomarker in Adults With Neuroendocrine Cancers Treated With 177Lu-DOTATATE

PurposeNeuroendocrine tumors (NET) are rare cancers with variable behavior. A better understanding of prognosis would aid individualized management. The aim of this hypothesis-generating pilot study was to investigate the prognostic potential of tumor heterogeneity and tracer avidity in NET using texture analysis (TA) of 68Ga-DOTATATE positron emission tomography (PET) and non-enhanced computed tomography (CT) performed at baseline in patients treated with 177Lu-DOTATATE. It aims to justify a larger-scale study to evaluate its clinical value.MethodsThe pretherapy 68Ga-DOTATATE PET-CT scans of 44 patients with metastatic NET (carcinoid, pancreatic, thyroid, head and neck, catecholamine-secreting, and unknown primary NET) treated with 177Lu-DOTATATE were analyzed retrospectively using commercially available texture analysis research software. Image filtration extracted and enhanced objects of different sizes (fine, medium, coarse), then quantified heterogeneity by statistical and histogram-based parameters (mean intensity, standard deviation, entropy, mean of positive pixels, skewness, and kurtosis). Regions of interest were manually drawn around up to five of the most 68Ga-DOTATATE avid lesions for each patient. 68Gallium uptake on PET was quantified as SUVmax and SUVmean. Associations between imaging and clinical markers with progression-free (PFS) and overall survival (OS) were assessed using univariate Kaplan-Meier analysis. Independence of the significant univariate markers of survival was tested using multivariate Cox regression analysis.ResultsMeasures of heterogeneity (higher kurtosis, higher entropy, and lower skewness) on coarse-texture scale CT and unfiltered PET images predicted shorter PFS (CT coarse kurtosis: p=0.05, PET entropy: p=0.01, PET skewness: p=0.03) and shorter OS (CT coarse kurtosis: p=0.05, PET entropy: p=0.01, PET skewness p=0.02). Conventional PET parameters such as SUVmax and SUVmean showed trends towards predicting outcome but were not statistically significant. Multivariate analysis identified that CT-TA (coarse kurtosis: HR=2.57, 95% CI=1.22–5.38, p=0.013) independently predicted PFS, and PET-TA (unfiltered skewness: HR=9.05, 95% CI=1.19–68.91, p=0.033) independently predicted OS.ConclusionThese preliminary data generate a hypothesis that radiomic analysis of neuroendocrine cancer on 68Ga-DOTATATE PET-CT may be of prognostic value and a valuable addition to the assessment of patients.

Analyzing Hydration Differences in Cocrystal Polymorphs: High-Resolution X-ray Investigation of Caffeine–Glutaric Acid Cocrystals

Two polymorphic forms of caffeine (CAF)–glutaric acid (GLU) cocrystals have been studied via high-resolution X-ray crystallography and Bader’s quantum theory of atoms in molecules (QTAIM). For both the monoclinic, 1, and triclinic, 2, systems the experimental charge density distributions of the 1:1 ratio of CAF and GLU polymorphs have been determined and compared. Previous studies have determined that 1 is less stable than 2, in relative humidity (RH) testing. A topological analysis of the electron density distribution (EDD) revealed little difference between the two polymorph internal systems. The packing densities (0.76 vs 0.74) and lattice energies (−101.1 vs −107.1 kJ mol–1) of 1 and 2, respectively, are nearly equivalent, implying that the differences in hygroscopicity between the two polymorphs are not due to crystal lattice porosity or stability. A topological analysis of the number and strength of hydrogen bonds for 1 and 2 revealed nine hydrogen bonds in both polymorphs. “Classical” (O–H···X) hydrogen bonds were similarly present in both polymorphs, stabilizing the cocrystals. However, the sum of the stability produced from the “nonclassical” (C–H···X) bonds is higher in 2: −27.6 vs −38.2 kJ mol–1 for 1 and 2, respectively. One of the nine hydrogen bonds in 1 and 2 varies from the others, caused by the torsional rotation of the aliphatic carbon chain in GLU. This bond is critical for packing stabilization, creating a parallelogram-like packing arrangement in 2 in comparison to ribboning in 1. A Hirshfeld surface analysis found that the percentages of O–H···X hydrogen bonds were nearly identical in 1 and 2 (23.9% vs 22.1%); however, the H···H contacts were higher in 2 (61.4% vs 65.8% for 1 and 2, respectively), suggesting that more hydrogen-based contacts require competitive displacement by water in the hydration of 2 in comparison to 1. Additionally, a stabilizing aromatic cycle stack between CAF molecules is present in 2 due to the varied parallelogram packing arrangement, which was absent in 1; this provided ∼11.3 kJ mol–1 of stability to the system of 2. The solid-state entropies and molecular dipole moments (MDMs) of 1 and 2 supported the relative stability of the individual polymorphs, with 1 having a higher entropy and dipole moment in comparison to 2 (123.2 vs 112.8 J K–1 mol–1 and 7.45 and 4.93 D for 1 and 2, respectively), implying that it has the potential to hydrate more rapidly. These findings are in good agreement with previous experimental RH stability studies, giving further insight into the information gained from thermally averaged ground-state crystal electron density data.

Abstract 173: Efficient representations of tumor diversity with paired DNA-RNA aberrations

Abstract In this work we develop a framework which allows for a systematic analysis of joint DNA and putative downstream RNA effects in cancer data cohorts. Using the Reactome database, we extract gene pairs that are linked by known mechanistic connections. Such pairs, which we refer to as 'Source Target Pairs' or STPs, consist of a source gene for which we examine aberrant activity in the DNA profile, and a target gene that is affected by said source gene, for which we examine aberrant activity in the RNA profile. Using TCGA data for six different cancer types (breast, colon, kidney, liver, lung and prostate), we use mutation and copy number variation information to compile DNA aberrant activity data. For the same cancer cohorts, we use RNASeq gene expression data to quantify RNA aberrant activity via the previous 'divergence' method we have developed. In the divergence framework, normal samples from the same cancer are used to estimate a normal range of expression for target genes of interest and deviation from the normal range is assumed to indicate aberrant activity which may result from upstream DNA aberrations. Then for a given sample, an STP can be represented as a binary variable, indicating presence or absence of joint DNA-RNA aberrant activity. We utilize integer programming to discover a small set of such STPs for each cancer type such that every sample displays aberrant activity in at least one STP. We refer to these reduced STP configurations as 'minimal coverings' of that cancer. These configurations then allow for the quantification of heterogeneity for that cancer type, as well as for phenotypical groups of interest. This is made possible due to the fact that sample to sample variability can be compared via the entropy of the distribution of the minimal covering, where the small number of STPs in such a configuration makes the computation more tractable. Our results reveal many known putative drivers of cancer, as well as identify some novel genes of interest for further consideration. Comparison of heterogeneity across phenotypes of interest show higher entropy in more pathological phenotypes, indicating increasing heterogeneity with severity of disease. Citation Format: Qian Ke, Wikum Dinalankara, Laurent Younes, Donald Geman, Luigi Marchionni. Efficient representations of tumor diversity with paired DNA-RNA aberrations [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2021; 2021 Apr 10-15 and May 17-21. Philadelphia (PA): AACR; Cancer Res 2021;81(13_Suppl):Abstract nr 173.

Increased Entropic Brain Dynamics during DeepDream-Induced Altered Perceptual Phenomenology.

In recent years, the use of psychedelic drugs to study brain dynamics has flourished due to the unique opportunity they offer to investigate the neural mechanisms of conscious perception. Unfortunately, there are many difficulties to conduct experiments on pharmacologically-induced hallucinations, especially regarding ethical and legal issues. In addition, it is difficult to isolate the neural effects of psychedelic states from other physiological effects elicited by the drug ingestion. Here, we used the DeepDream algorithm to create visual stimuli that mimic the perception of hallucinatory states. Participants were first exposed to a regular video, followed by its modified version, while recording electroencephalography (EEG). Results showed that the frontal region’s activity was characterized by a higher entropy and lower complexity during the modified video, with respect to the regular one, at different time scales. Moreover, we found an increased undirected connectivity and a greater level of entropy in functional connectivity networks elicited by the modified video. These findings suggest that DeepDream and psychedelic drugs induced similar altered brain patterns and demonstrate the potential of adopting this method to study altered perceptual phenomenology in neuroimaging research.

Quantitative software project management with mixed data: A comparison of radial, nonradial, and ensemble data envelopment analysis models

AbstractData envelopment analysis (DEA) models are often used for benchmarking software projects, and traditional DEA models only allow for the use of continuous variables. This study considers the use of DEA for datasets with mixed continuous and discrete variables to ranking software projects. It uses the existing radial DEA model and extends the nonradial DEA model to allow for the use of mixed variables. Further efficiency scores from the two DEA models are averaged in an ensemble DEA score. Using three real‐world software engineering datasets, this study finds that the nonradial DEA and the ensemble DEA models have better discriminating power (lower tied efficiency scores) to rank software projects, and the radial DEA model generates more general ranking distribution (higher entropy) of normalized efficiency scores. The choice between selecting radial and nonradial DEA models for ranking software projects appears to depend on the extent to which managers want to introduce bias into the efficiency score ranking distribution. Radial models appear to have a lower bias than nonradial models. The ensemble DEA model appears to be the best performing DEA model for datasets containing two or more discrete and continuous variables.

Phase diagram of the charged black hole bomb system

We find the phase diagram of solutions of the charged black hole bomb system. In particular, we find the static hairy black holes of Einstein-Maxwell-Scalar theory confined in a Minkowski box. We impose boundary conditions such that the scalar field vanishes at and outside a cavity of constant radius. These hairy black holes are asymptotically flat with a scalar condensate floating above the horizon. We identify four critical scalar charges which mark significant changes in the qualitative features of the phase diagram. When they coexist, hairy black holes always have higher entropy than the Reissner-Nordström black hole with the same quasilocal mass and charge. So hairy black holes are natural candidates for the endpoint of the superradiant/near-horizon instabilities of the black hole bomb system. We also relate hairy black holes to the boson stars of the theory. When it has a zero horizon radius limit, the hairy black hole family terminates on the boson star family. Finally, we find the Israel surface tensor of the box required to confine the scalar condensate and that it can obey suitable energy conditions.

Thermal degradation of kenaf (Hibiscus cannabinus L.): Impact of torrefaction on pyrolysis kinetics and thermal behavior

Pre-treatment of biomass has garnered significant research attention to facilitate biomass utilization. This study examines the effect of torrefaction on the pyrolysis characteristics of kenaf (Hibiscus cannabinus L.), which grows in South Korea and has a relatively short life cycle as well as a low production cost among herbaceous biomass. In this study, raw kenaf (RK) and torrefied kenaf (TK) were prepared in an inert atmosphere. Torrefaction was carried out in a bed reactor for 30 min at 503, 523 and 553 K, and pyrolysis was performed at six heating rates and analyzed using thermogravimetric analysis. The results showed that the optimal temperature for RK torrefaction based on the energy-mass co-benefit index was 523 K, owing to a higher energy density and low volume. The torrefaction and a higher heating rate resulted in the weight loss and decomposition rate (derivative thermogravimetric) curves moving to a higher temperature region, and improvement in the devolatilization index of the TK. The activation energy was calculated using three methods (Kissinger, Flynn–Wall–Ozawa, and Kissinger–Akahira–Sunose), with all indicating that the activation energy of the TK was greater than that of RK. Additionally, in terms of thermodynamic parameters, the TK had a higher frequency factor, higher enthalpy, slightly lower Gibbs free energy, and higher entropy than those of RK. These kinetic and thermal behavior results are useful for designing pyrolysis processes wherein TK is used as a feedstock; moreover, they provide a useful reference for TK heat conversion applications.

Acoustic Emission Signal Entropy as a Means to Estimate Loads in Fiber Reinforced Polymer Rods

Fibre reinforced polymer (FRP) rods are widely used as corrosion-resistant reinforcing in civil structures. However, developing a method to determine the loads on in-service FRP rods remains a challenge. In this study, the entropy of acoustic emission (AE) emanating from FRP rods is used to estimate the applied loads. As loads increased, the fraction of AE hits with higher entropy also increased. High entropy AE hits are defined using the one-sided Chebyshev’s inequality with parameter k = 2 where the histogram of AE entropy up to 10–15% of ultimate load was used as a baseline. According to the one-sided Chebyshev’s inequality, when more than 20% (k = 2) of AE hits that fall further than two standard deviations away from the mean are classified as high entropy events, a new distribution of high entropy AE hits is assumed to exist. We have found that the fraction of high AE hits. In glass FRP and carbon FRP rods, a high entropy AE hit fraction of 20% was exceeded at approximately 40% and 50% of the ultimate load, respectively. This work demonstrates that monitoring high entropy AE hits may provide a useful means to estimate the loads on FRP rods.

Toward a formal theory of embodied cognition

Since the reduction of uncertainty associated with cognition necessarily implies existence of a ‘dual’ information source, the Source Coding and Rate Distortion Theorems of information theory, in combination with the Data Rate Theorem of control theory, are sufficient to model much of embodied cognition. An iterated Morse Function ‘free energy’ allows construction of a ‘higher entropy’ analog constrained to obey the approximate dynamics of the Onsager gradient model of nonequilibrium thermodynamics. However, since palindromes are unlikely, there is no time reversal symmetry and hence no Onsager reciprocal relations. The group symmetry-breaking associated with physical phase transitions then emerges in terms of groupoids associated with equivalence classes of high probability developmental paths. The formalism is agnostic regarding representation and the Yerkes-Dodson inverted-U relation emerges directly, as do stochastic versions of the underlying dynamics, and a canonical approach to an embodied consciousness model. Contrary to the Western cultural fixation with individual salience at the expense of context, for cognition against and in the real world, context is often central, rather than simply being a screen against which some culturally-specific cartoon is supposed to play.

The third generation Calphad description of Al–C including revisions of pure Al and C

New descriptions of pure Al and liquid C were developed and used to describe the Al–C system for the third generation of Calphad databases. The stable phases of the elements are described with a single expression for the entire temperature range. The expression is based on the Einstein model and an important parameter is therefore the Einstein temperature. For the metastable phases, the difference in entropy between stable and metastable phases is used to calculate the Einstein temperature for the metastable allotrope. In this way we avoid breaking the third law of thermodynamics, which would be the consequence if the SGTE lattice stabilities were used. The liquid-amorphous phase for the pure substances and for the binary is described with the two-state model. For the pure substances, we introduce a zero-point entropy that is related to the entropy of melting. The heat capacity of the liquid of the pure substances approaches 3R at high temperatures if the electronic contribution is subtracted. The Al–C system has one stable carbide, Al4C3, which is described with a model equivalent to that used for the solid unary phases but with two Einstein functions. In Al–C, the FCC phase is stable and its metastable end-member, Al1C1, is described with a new model, here called the hybrid model, as it combines the Einstein model (giving the harmonic contribution) and the Neumann–Kopp relationship (adding the additional contributions) to describe the heat capacity. Its Einstein temperature is estimated and its formation energy is obtained from DFT calculations. The total energy of the end-members of the metastable phases BCC(Al1C3) and HCP(Al1C0.5) is calculated with DFT and their Einstein temperatures are estimated using the mass-effect model. The Al–C system was chosen because it is a simple system without magnetism and the results show that the proposed models can reproduce experimental information well. When only one temperature range is used to describe the solid phases, they may be re-stabilized at high temperatures and the recently presented equal-entropy criterion (EEC) is used to exclude solid phases with higher entropy than the liquid.

CT quantification of the heterogeneity of fibrosis boundaries in idiopathic pulmonary fibrosis.

ObjectivesTo quantify the heterogeneity of fibrosis boundaries in idiopathic pulmonary fibrosis (IPF) using the Gaussian curvature analysis for evaluating disease severity and predicting survival.MethodsWe retrospectively included 104 IPF patients and 52 controls who underwent baseline chest CT scans. Normal lungs below − 500 HU were segmented, and the boundary was three-dimensionally reconstructed using in-house software. Gaussian curvature analysis provided histogram features on the heterogeneity of the fibrosis boundary. We analyzed the correlations between histogram features and the gender-age-physiology (GAP) and CT fibrosis scores. We built a regression model to predict diffusing capacity of carbon monoxide (DLCO) using the histogram features and calculated the modified GAP (mGAP) score by replacing DLCO with the predicted DLCO. The performances of the GAP, CT-GAP, and mGAP scores were compared using 100 repeated random-split sets.ResultsPatients with moderate-to-severe IPF had more numerous Gaussian curvatures at the fibrosis boundary, lower uniformity, and lower 10th to 30th percentiles of Gaussian curvature than controls or patients with mild IPF (all p < 0.0033). The 20th percentile was most significantly correlated with the GAP score (r = − 0.357; p < 0.001) and the CT fibrosis score (r = − 0.343; p = 0.001). More numerous Gaussian curvatures, higher entropy, lower uniformity, and 10th to 30th percentiles (p < 0.001–0.041) were associated with mortality. The mGAP score was comparable to the GAP and CT-GAP scores for survival prediction (mean C-indices, 0.76 vs. 0.79 vs. 0.77, respectively).ConclusionsGaussian curvatures of fibrosis boundaries became more heterogeneous as the disease progressed, and heterogeneity was negatively associated with survival in IPF.Key Points • Gaussian curvature of the fibrotic lung boundary was more heterogeneous in patients with moderate-to-severe IPF than those with mild IPF or normal controls. • The 20th percentile of the Gaussian curvature of the fibrosis boundary was linearly correlated with the GAP score and the CT fibrosis score. • A modified GAP score that replaced the diffusing capacity of carbon monoxide with a composite measure using histogram features of the Gaussian curvature of the fibrosis boundary showed a comparable ability to predict survival to both the GAP and the CT-GAP score. Supplementary InformationThe online version contains supplementary material available at 10.1007/s00330-020-07594-y.