Binary Process Research Articles

On the approaches to an adequate historiography

The article is devoted to clarifying the essential features of the historiography of Ukrainian literature, which arose on the basis of stories, acquired the meaning of their integration, and comprehended the regularity of historical thinking. To this purpose, an analytical review of the formation and development of the history of Ukrainian literature is made — from the literary and critical publications of Osyp Bodianskyi, Mykola Kostomarov and others, gradual structuring through trial and error in the publications of Mykola Petrov, Omelian Ohonovskyi, who resorted either to ideological and stylistic eclecticism or to prioritisation of the biobibliographical method, raised the question of the essence of the history of literature (Ivan Franko). Serhii Yefremov’s «Istoriia ukrainskoho pysmenstva (History of Ukrainian Literature)» became the first fundamental author’s history with a consistent chromatic series, with the concept of the primacy of ideas over the figurative system, and a sociological understanding of the role of literature. The article traces the evolution of scientific thought from extra-artistic engagement to an immanent understanding of literature as an art, starting with the history of Mykhailo Hrushevsky, corresponding to the provisions of Oleksandr Potebnia’s psycholinguistics and Volodymyr Peretz’s philological school. Such a view, conditioned by literary realities, was emphasised by Mykola Zerov, substantiated by Mykola Hnatyshak, and universalised by Dmytro Chyzhevsky. They presented a new type of history of Ukrainian literature with distinct features of historiosophy. Mykola Hnatyshak and Dmytro Chyzhevsky integrated it into the concept of a wave-like binary literary process, proposed a periodisation adequate to the changing genre and style searches based on the principle of «simple» (idea) to «complex» (metaphor) and, on the contrary, consonant with the European cultural world, and identified (Dmytro Chyzhevsky) the baroque psychotype dominant in the Ukrainian mentality. Each of the author’s stories presents a certain angle of view on the dynamics of literary life, and requires comparison in order to reveal a common understanding of the problem, which is important for historiographical studies, at the intersection of their segments on the principle of overlapping hermeneutical circles. In contrast to previous concepts, the author of the article proposes a history not of biographies or extra-artistic factors, but of literary texts in their immanent characteristics, contexts, chronological coordinates, using the technique of close reading, in the guideline of overcoming the time- spatial distance between the text (author) and the recipient (historiographer).

Protocol-based fault detection filtering for memristive neural networks with dynamic quantization

This study examines the issue of event-triggered fault detection filtering for memristive neural networks with dynamic quantization in discrete-time domain. To facilitate digital transmissions, the system output undergoes dynamic quantized prior to transmission. Beyond the reporting event-triggered protocol, a novel event-triggered protocol is enforced, associating with dynamic quantization parameter, fault occurrence probability and network bandwidth utilization rate, to skillfully schedule the transmission frequency. A random variable that follows a binary Markov process, instead of a Bernoulli distribution, is presented to characterize the dynamic impact of denial-of-service attacks. On account of hidden Markov model and Lyapunov theory, an asynchronous filter framework is formulated to ensure stochastically stable of resulting filtering error systems. Ultimately, a simulation example is conducted to validate the usefulness of the developed methodology.

Phase-domain modulated hybrid phase-shifting structured light based efficient 3D measurement

Phase-shifting profilometry (PSP) measurement technology remains a research hotspot in 3D imaging. However, existing PSP methods require projecting additional patterns, which limits measurement space, or involves compressing fringe amplitudes to eliminate phase ambiguity. These practices result in reduced measurement efficiency and robustness. To overcome these challenges, we present a novel phase-domain modulated hybrid phase-shifting (PDM-HPS) structured light 3D measurement approach to solve the phase error of existing spatial-domain modulated phase-shifting (SDM-PS) methods without imposing additional pattern or space constraints. The method integrates phase-shifting speckle and phase-shifting fringe methodologies to create a hybrid phase-shifting coding pattern. In the decoding phase, the offset speckle phase is detected and corrected by the low-precision phase extracted in the frequency domain. The separation of binary speckle and high-precision wrapped phase is realized. Ultimately, an efficient binary speckle-aided stereo phase matching process is employed to achieve unambiguous phase unwrapping. We test the PDM-HPS method in multiple complex real-world scenarios using binocular structured light systems, and compare its accuracy and efficiency with three existing advanced methods. The qualitative and quantitative results show that the proposed method can achieve the measurement accuracy similar to that of the multi-frequency (MF) method by using only 1/3 projection patterns.

The relationship between depressive mood and non-suicidal self-injury among secondary vocational school students: the moderating role of borderline personality disorder tendencies.

Non-suicidal self-injury (NSSI) has become an important public health issue of global concern, often occurring in adolescents, and depressive mood is closely related to NSSI. In addition, NSSI is considered a symptom of borderline personality disorder. It has been found that adolescents in secondary vocational schools are more vulnerable to behavior and emotional disorders than those in general high schools. This study investigated the risk factors associated with NSSI affecting secondary vocational school students and analyzed the role of borderline personality disorder tendencies in promoting the occurrence of NSSI among students with depressive moods. A total of 1,848 Chinese secondary vocational students completed a self-report questionnaire. The homemade NSSI behavior questionnaire, Patient Health Questionnaire-9 and Personality Diagnostic Questionnaire-4 were used in this survey. Binary logistic regression and PROCESS software analysis were used to explore the influencing factors associated with NSSI and to test for moderating effects. Female (OR = 3.412, 95% CI 2.301-5.060), drinking history (OR = 2.007, 95% CI 1.383-2.911), history of suicidal death exposure (OR = 3.161, 95% CI 1.999-4.999), depressive mood (OR = 2.436, 95% CI 1.668-3.558) and borderline personality disorder tendencies (OR = 2.558, 95% CI = 1.764-3.711) were independent risk factors for NSSI. Borderline personality disorder tendencies (B = 0.047, p = 0.000) moderated the relationship between depressive mood and NSSI. The stronger the borderline personality tendencies, the more NSSI behavior occurred when they were depressive. Borderline personality disorder tendencies in secondary vocational school adolescents significantly enhance the association of depressive mood with NSSI. There is a moderating role for borderline personality disorder tendencies in depressive mood and NSSI.

Simulation of ranges and sputtering of low energy Helium and Argon ions irradiation on Tungsten surface

The interactions of low energy He and Ar ions with pure W target were simulated by a new Monte-Carlo (MC) based computer code which was designed to insure maximum accuracy. For these irradiation systems, incident ions projected ranges in the target material, sputtering yield, and the percentage of backscattered ions at various incident energies were studied. furthermore, the effect of the angle of incidence on sputtering yield and the percentage of backscattered ions were also simulated. Our simulation results were compared with experimental data and those calculated by the TRIM simulation program. Our code is based on an algorithm that uses detailed numerical solutions for the classical scattering integral for evaluating the binary collision process. This approach has provided sputtering yield data with a higher level of accuracy compared to TRIM's simulation results. Also, a new approach of using a reduced atomic displacement threshold in the top surface monolayer enhances the simulation results in the near sputtering threshold energy range and eliminates its dependence on the selected value of the displacement energy threshold Ed. Nonetheless, both simulation programs produced less contrasting results in terms of incident ions mean projected ranges. Furthermore, fundamental discrepancies in the percentage of backscattered ions between the results of both simulation programs were found.

A novel deep learning-based approach for prediction of neonatal respiratory disorders from chest X-ray images

In recent years, many diseases can be diagnosed in a short time with the use of deep learning models in the field of medicine. Most of the studies in this area focus on adult or pediatric patients. However, deep learning studies for the diagnosis of diseases in neonatal are not sufficient. Also, since it is known that respiratory disorders such as pneumonia have a large place among the causes of neonatal death, early and accurate diagnosis of respiratory diseases in neonates is crucial. For this reason, our study aims to detect the presence of respiratory disorders through the developed deep-learning approach using chest X-ray images of patients hospitalized in the Neonatal Intensive Care Unit. Accordingly, the enhanced version of C+EffxNet, the new hybrid deep learning model, is designed to predict respiratory disorders in neonates. In this version, the features selected by PCA are combined as 100, 200, and 300, then the binary classification process was carried out. In the study, the accuracy and kappa value were obtained as 0.965, and 0.904, respectively before feature merging, while these values were obtained as 0.977, and 0.935 after feature merging. This method, which was developed for the diagnosis of respiratory disorders in neonates, was also subsequently applied to a chest X-ray dataset that is frequently used in the literature for the diagnosis of pediatric pneumonia. For this data set, while the accuracy was 0.992, the kappa value was 0.982. The results obtained confirm the success of the proposed method for both datasets.

Optimizing vaccine distribution in developing countries under natural disaster risk

AbstractFor many developing countries, COVID‐19 vaccination roll‐out programs are not only slow but vaccination centers are also exposed to the risk of natural disaster, like flooding, which may slow down vaccination progress even further. Policy‐makers in developing countries therefore seek to implement strategies that hedge against distribution risk in order for vaccination campaigns to run smoothly and without delays. We propose a stochastic‐dynamic facility location model that allows policy‐makers to choose vaccination facilities while accounting for possible facility failure. The model is a multi‐stage stochastic variant of the classic facility location problem where disruption risk is modelled as a binary multivariate random process–a problem class that has not yet been studied in the extant literature. To solve the problem, we propose a novel approximate dynamic programming algorithm which trains the shadow price of opening a flood‐prone facility on historical data, thereby alleviating the need to fit a stochastic model. We trained the model using rainfall data provided by the local government of several major cities in the Philippines which are exposed to multiple flooding events per year. Numerical results demonstrate that the solution approach yields approximately 30%–40% lower cost than a baseline approach that does not consider the risk of flooding. Recommendations based on this model were implemented following a collaboration with two large cities in the Philippines which are exposed to multiple flooding events per year.

Significance of Arrhenius activation energy and binary chemical reaction in ternary hybrid nanofluid flow over a convectively heated porous curved surface: A passive control strategy

The convective flow of Jeffrey ternary hybrid nanoliquid over a curved stretching sheet, water-based aluminum oxide and graphene nanoparticles and single wall carbon nanotubes had been employed in this work to explore the hydrothermal variation. In the process of modeling the mechanism of mass transfer, activation energy and binary chemical processes are taken into consideration. The expressions of energy and mass are computed with the extra influence of Brownian diffusion and the thermophoresis characteristics. The initial step in evaluating leading equations involves transforming them into dimensionless forms through similarity transformations. To supplement the assessment, a diverse range of graphs and tables are utilized. The exploration and discussion of various parameters and their impact on involved fields are also presented. In ternary hybrid nanoliquids, an increase in thermophoresis and Brownian motion parameters positively impacts heat transfer capacity. The Biot number exhibits a positive influence on heat transport, while the Schmidt number reduces mass transfer. The curvature parameter has a beneficial impact on the heat transmission rate. Furthermore, as the activation energy parameter rises, the mass transport increases, while it decreases as the chemical reaction rate parameter increases.

A Point-Process Approach for Tracking Valence using a Respiration Belt.

Emotional valence is difficult to be inferred since it is related to several psychological factors and is affected by inter- and intra-subject variability. Changes in emotional valence have been found to cause a physiological response in respiration signals. In this study, we propose a state-space model and decode the valence by analyzing a person's respiration pattern. Particularly, we generate a binary point process based on features that are indicative of changes in respiration pattern as a result of an emotional valence response. High valence is typically associated with faster and deeper breathing. As a result, (i)depth of breath, (ii)rate of respiration, and (iii) breathing cycle time are indicators of high valence and used to generate the binary point process representing underlying neural stimuli associated with changes in valence. We utilize an expectation-maximization (EM) framework to decode a hidden valence state and the associated valence index. This predicted valence state is compared to self-reported valence ratings to optimize the parameters and determine the accuracy of the model. The accuracy of the model in predicting high and low valence events is found to be 77% and 73%, respectively. Our study can be applied towards the long term analysis of valence. Additionally, it has applications in a closed-loop system procedures and wearable design paradigm to track and regulate the emotional valence.

Wrapper and Hybrid Feature Selection Methods Using Metaheuristic Algorithm for Chest X-Ray Images Classification

Covid-19 virus has led to a tremendous pandemic in more than 200 countries across the globe, leading to severe impacts on the lives and health of a large number of people globally. The emergence of Omicron (SARS-CoV-2), which is a coronavirus 2 variant, an acute respiratory syndrome which is highly mutated, has again caused social limitations around the world because of infectious and vaccine escape mutations. One of the most significant steps in the fight against covid-19 is to identify those who were infected with the virus as early as possible, to start their treatment and to minimize the risk of transmission. Detection of this disease from radiographic and radiological images is perhaps one of the quickest and most accessible methods of diagnosing patients. In this study, a computer aided system based on deep learning is proposed for rapid diagnosis of COVID-19 from chest x-ray images. First, a dataset of 5380 Chest x-ray images was collected from publicly available datasets. In the first step, the deep features of the images in the dataset are extracted by using the dataset pre-trained convolutional neural network (CNN) model. In the second step, Differential Evolution (DE), Ant Colony Optimization (ACO) and Particle Swarm Optimization (PSO) algorithms were used for feature selection in order to find the features that are effective for classification of these deep features. Finally, the features obtained in two stages, Decision Tree (DT), Naive Bayes (NB), support vector machine (SVM), k-Nearest Neighbours (k-NN) and Neural Network (NN) classifiers are used for binary, triple and quadruple classification. In order to measure the success of the models objectively, 10 folds cross validation was used. As a result, 1000 features were extracted with the SqueezeNet CNN model. In the binary, triple and quadruple classification process using these features, the SVM method was found to be the best classifier. The classification successes of the SVM model are 96.02%, 86.84% and 79.87%, respectively. The results obtained from the classification process with deep feature extraction were achieved by selecting the features in the proposed method in less time and with less features. While the performance achieved is very good, further analysis is required on a larger set of COVID-19 images to obtain higher estimates of accuracy.

Large population limit of the spectrum of killed birth-and-death processes

We consider a general class of birth-and-death processes with state space {0,1,2,3,…} which describes the size of a population going eventually to extinction with probability one. We obtain the complete spectrum of the generator of the process killed at 0 in the large population limit, that is, we scale the process by a parameter K, and take the limit K→+∞. We assume that the differential equation dx/dt=b(x)−d(x) describing the infinite population limit (in any finite-time interval) has a repulsive fixed point at 0, and an attractive fixed point x⁎>0. We prove that, asymptotically, the spectrum is the superposition of two spectra. One is the spectrum of the generator of an Ornstein-Uhlenbeck process, which is n(b′(x⁎)−d′(x⁎)), n≥0. The other one is the spectrum of a continuous-time binary branching process conditioned on non-extinction, and is given by n(d′(0)−b′(0)), n≥1. A major difficulty is that different scales and function spaces are involved. We work at the level of the eigenfunctions that we split over different regions, and study their asymptotic dependence on K in each region. In particular, we prove that the spectral gap goes to min⁡{b′(0)−d′(0),d′(x⁎)−b′(x⁎)}. This work complements a previous work of ours in which we studied the approximation of the quasi-stationary distribution and of the mean time to extinction.

An RGB Color Image Steganography Scheme by Binary Lower Triangular Matrix

Steganography is an area where researchers focus on how to develop novel hiding techniques that are aided by the mathematical or computational model. In order to conceal the secret bits in a cover image, the imperceptible property and embedding payload capacity must be maintained. In most of the developed methods, some selective least significant bits (LSBs) of each pixel of the cover image is modified to hide the data which may lead to substantial distortion in the stego-image especially when the payload size is large. Therefore, to attain the trade-off between payload capacity and image quality, the authors have devised a binary lower triangular matrix-based secret message embedding process in which data can be hidden in the color pixel. In this secret message embedding process, the secret data is embedded aided by the binary lower triangular matrix. The formulated mathematical model for the secret message embedding process has ensured a secure embedding technique with reduced aberration on the stego-image. The proposed steganography scheme is preserving significant visual quality while emphasizing the security aspect by adopting an indirect data-hiding mechanism in contrast to the conventional mechanism. Furthermore, for the betterment of the visual properties of the stego-image, we have generically extended the formulation and tested it to check the visual quality. The empirical results of the proposed steganography scheme depict outcomes satisfactorily for the RGB color images. Researchers can explore and apply this novel data-hiding scheme in different data communication applications.

Second-generation protoplanetary discs around evolved binaries: a high-resolution polarimetric view with SPHERE/IRDIS

ABSTRACT Binary post-asymptotic giant branch (post-AGB) stars are products of a poorly understood binary interaction process that occurs during the AGB phase. These systems comprise a post-AGB primary star, a main-sequence secondary companion and a stable circumbinary disc. Studying the structure and properties of these circumbinary discs is crucial for gaining insight into the binary interaction process that governs post-AGB binaries as well as comprehending the disc’s creation, evolution, and its interaction with the post-AGB binary system. We aim to use near-infrared polarimetric imaging to investigate the morphology and potential substructures of circumbinary discs around eight representative post-AGB binary stars. To achieve this, we performed polarimetric differential imaging in H and Y bands using the high-angular resolution capabilities of the European Southern Observatory-Very Large Telescope/SPHERE-Infra-Red Dual-beam Imaging and Spectroscopy instrument. We resolved the extended circumbinary disc structure for a diverse sample of eight post-AGB binary systems. Our analysis provided the first estimates of the disc scale height for two of the systems: IW Car and IRAS 15469–5311. We also investigated the morphological differences between the full discs (with the inner rim at the dust sublimation radius) and transition discs (which are expected to have larger inner cavities), as well as similarities to protoplanetary discs around young stellar objects. We found that the transition discs displayed a more intricate and asymmetric configuration. Surprisingly, no correlation was found between the overresolved flux in near-infrared interferometric data and the polarimetric observations, suggesting that scattering of light on the disc surface may not be the primary cause of the observed overresolved flux component.

Multi-treatment casual analysis using improved meta learner and uplift tree

Causality is an appealing but challenging domain for researchers in generations. Recently, researchers have shifted their focus to combining traditional causal inference methods and machine learning models to get both advantages. Meta learner is an algorithm for causal inference, including T-learner, S-learner, and X-learner. Another popular way in causal inference is based on decision tree learning, one of the predictive modeling approaches. Many existing works focus on estimating the causal effect of binary treatment. However, there are also many cases in the real world when the treatment has more than two values. These methods cannot be used directly in multivalued treatment cases. According to the mathematization of causality, we improved the binary meta-learner process to be applicable in multi-treatment situations. At the same time, we also preliminarily explored the technique of uplifting trees. Finally, we applied the two methods to analyze parents' and children's learning situations in hundreds of families to test the effect of improvement.

Estimation of region of attraction with Gaussian process classification

This paper proposes a methodology for assessing the region of attraction (ROA) of stable equilibrium points, a challenging problem for a general nonlinear system, using binary Gaussian process classification (GPC). Interest in this method stems from the fact that an arbitrary point belonging to the system’s state space can be classified in the region of attraction or not. Importantly the proposed GPC approach for determining ROA gives a minimum confidence level associated with the estimate. Moreover, the active learning scheme helps to update the GPC model and yield better predictions by selecting informative observations from the state space sequentially. The methodology is applied to several examples to illustrate the effectiveness of this approach.

Adsorption Isotherms for Removal of Heavy Metal Ions (Copper and Nickel) from Aqueous Solutions in Single and Binary Adsorption Processes

This study deals with the removal of single and binary heavy metals, which cause great problems in terms of the environment and human health, through very low cost, economical and easily obtainable materials. The purpose of this study is to investigate the single- and binary uptake of Copper (II) and Nickel (II) ions onto the Sepiolite in the terms of a thermodynamic perspective. For mono-component systems, the initial effluent concentration, mixing speed and temperature have been studied as a function of time to determine the conditions where the adsorbents show a great deal of affinity towards the Cu (II) and Ni (II) ions in aqueous solutions. Before the metal adsorption experiments, the Physical properties of Sepiolite were identified via Brunauer–Emmett–Teller (BET) analysis. The single metal ion uptake studies were performed at 20, 25, 30, and 35 °C. At equilibrium, the sorption data were individually shown to correlate well with the non-competitive Langmuir, Freundlich, Temkin, and Dubinin-Radushkevich isotherms. Among the applied isotherm models, the one-component sorption values do fit the Langmuir isotherm best. The simultaneous and competitive uptake of Cu (II) and Ni (II) was assessed by the extended Langmuir and Freundlich isotherms. Both adsorption equations complied with the two-component sorption data perfectly. Single- and binary-sorption results unclose that the effect of Sepiolite to Cu (II) is greater than that of Sepiolite to Ni (II).

Multilevel joint model of longitudinal continuous andbinary outcomes for hierarchically structured data.

Joint modeling has been a useful strategy for incorporating latent associations between different types of outcomes simultaneously, often focusing on a longitudinal continuous outcome characterized by an LME submodel and a terminal event subject to a Cox proportional hazard or parametric survival submodel. Applications to hierarchical longitudinal studies have been less frequent, particularly with respect to a binary process, which is commonly specified by a GLMM. Furthermore, many of the joint model developments have not allowed for investigations of nested effects, such as those arising from multicenter studies. To fill this gap, we propose a multilevel joint model that encompasses the LME submodel and GLMM through a Bayesian approach. Motivated by the need for timely detection of pulmonary exacerbation and characterization of irregularly observed lung function measurements in people living with cystic fibrosis (CF) receiving care across multiple centers, we apply the model to the data arising from US CF Foundation Patient Registry. In parallel, we examine the extent of bias induced by a non-hierarchical model. Our simulation study and application results show that incorporating the center effect along with individual stochastic variation over time within the LME submodel improves model estimation and prediction. Given that the center effect is evident in lung function observed in the CF population, accounting for center-specific power parameters by incorporating the symmetric power exponential power (spep) link function in the GLMM can facilitate more accurate conclusions in clinical studies.

A Western Diet Modifies the Activation Profile of Circulating Platelets

Background: While it is known that obesity increases the risk for cardiovascular disease (CVD), there has been no clear investigation into the effect an obesogenic diet exerts onto circulating platelets. As platelets are the critical actors in the formation of occlusive clots that manifest as a myocardial infarction or stroke, it is pertinent to establish any potential link between obesity and platelet activity. Methods: To examine the effect of a Western diet on baseline platelet activity, male C57BL6/J mice were fed either a control (10% fat, 7% sucrose, 0.3% salt Research Diets Inc. D12450J) or Western (40% fat, 30% sucrose, 8% salt Research Diets Inc. D06111701) diet ad libitum for 20 weeks beginning at the time of weaning. At 12, 16 and 20 weeks after beginning diet administration whole blood was collected via the retro-orbital sinus. Blood was used to generate platelet rich plasma (PRP) which was stimulated with collagen (20mg/ml) prior to staining for flow cytometry analysis. Flow cytometry staining utilized antibodies to recognize the platelet receptors GPIbα, P-Selectin and the activated form of integrin α IIb β 3 (JON/A). Additionally, body composition was likewise determined at these time points using Echo-MRI while bodyweight was measured weekly. Results: Western diet fed mice gained slightly more weight than control mice and had a higher percentage of body fat (measured by EchoMRI). Surprisingly, the two groups differed in GPIbα and activated α IIb β 3 expression on circulating platelets at all three observed time points. Specifically, platelets from control-fed mice displayed significantly higher GPIbα expression throughout the study while Western diet fed animals had higher levels of activated α IIb β 3 . There was no difference in platelet expression of P-Selectin between the groups at any time point. Conclusions: Platelet activation is not a binary process where platelets display a definitive “active” or “inactive” phenotype. Though terminal platelet activation elicits de-granulation and an increase in P-Selectin expression, the spectrum of platelet stimulation preceding this is marked by variable incidences of integrin activation and GPIbα shedding. Here we demonstrate proof of principle that dietary factors, such as the consumption of a Western diet, can facilitate early changes to the stimulation pattern of circulating platelets which is then maintained long-term. While the consequence of this altered platelet stimulation profile is unknown with regards to the pathways of hemostasis and thrombosis, further investigations of downstream signaling and amplification pathways are needed. Funding: Arkansas Children's Research Institute/Arkansas Bioscience Institute Postgraduate Fellowship: AWD-037176 This is the full abstract presented at the American Physiology Summit 2023 meeting and is only available in HTML format. There are no additional versions or additional content available for this abstract. Physiology was not involved in the peer review process.

On Equivalence between Kinetic Equations and Geodesic Equations in Spaces with Affine Connection

Discrete kinetic equations describing binary processes of agglomeration and fragmentation are considered using formal equivalence between the kinetic equations and the geodesic equations of some affinely connected space A associated with the kinetic equation and called the kinetic space of affine connection. The geometric properties of equations are treated locally in some coordinate chart (x;U). The peculiarity of the space A is that in the coordinates (x) of some selected local chart, the Christoffel symbols defining the affine connection of the space A are constant. Examples of the Smoluchowski equation for agglomeration processes without fragmentation and the exchange-driven growth equation are considered for small dimensions in terms of geodesic equations. When fragmentation is taken into account, the kinetic equations can be written as equations of quasigeodesics. Particular cases of spaces with symmetries are discussed.

Disentangling Phase and Morphological Evolution During the Formation of the Lithium Superionic Conductor Li10 GeP2 S12.

The structural and morphological changes of the Lithium superionic conductor Li10 GeP2 S12 , prepared via a widely used ball milling-heating method over a comprehensive heat treatment range (50-700 °C), are investigated. Based on the phase composition, the formation process can be distinctly separated into four zones: Educt, Intermediary, Formation, and Decomposition zone. It is found that instead of Li4 GeS4 -Li3 PS4 binary crystallization process, diversified intermediate phases, including GeS2 in different space groups, multiphasic lithium phosphosulfides (Lix Py Sz ), and cubic Li7 Ge3 PS12 phase, are involved additionally during the formation and decomposition of Li10 GeP2 S12 . Furthermore, the phase composition at temperatures around the transition temperatures of different formation zones shows a significant deviation. At 600 °C, Li10 GeP2 S12 is fully crystalline, while the sample decomposed to complex phases at 650 °C with 30wt.% impurities, including 20wt.% amorphous phases. These findings over such a wide temperature range are first reported and may help provide previously lacking insights into the formation and crystallinity control of Li10 GeP2 S12 .