SPNE: sample-perturbed network entropy for revealing critical states of complex biological systems.

Complex biological systems do not always develop smoothly but occasionally undergo a sharp transition; i.e. there exists a critical transition or tipping point at which a drastic qualitative shift occurs. Hunting for such a critical transition is important to prevent or delay the occurrence of catastrophic consequences, such as disease deterioration. However, the identification of the critical state for complex biological systems is still a challenging problem when using high-dimensional small sample data, especially where only a certain sample is available, which often leads to the failure of most traditional statistical approaches. In this study, a novel quantitative method, sample-perturbed network entropy (SPNE), is developed based on the sample-perturbed directed network to reveal the critical state of complex biological systems at the single-sample level. Specifically, the SPNE approach effectively quantifies the perturbation effect caused by a specific sample on the directed network in terms of network entropy and thus captures the criticality of biological systems. This model-free method was applied to both bulk and single-cell expression data. Our approach was validated by successfully detecting the early warning signals of the critical states for six real datasets, including four tumor datasets from The Cancer Genome Atlas (TCGA) and two single-cell datasets of cell differentiation. In addition, the functional analyses of signaling biomarkers demonstrated the effectiveness of the analytical and computational results.

Specific network information gain for detecting the critical state of colorectal cancer based on gut microbiome.

There generally exists a critical state or tipping point from a stable state to another in the development of colorectal cancer (CRC) beyond which a significant qualitative transition occurs. Gut microbiome sequencing data can be collected non-invasively from fecal samples, making it more convenient to obtain. Furthermore, intestinal microbiome sequencing data contain phylogenetic information at various levels, which can be used to reliably identify critical states, thereby providing early warning signals more accurately and effectively. Yet, pinpointing the critical states using gut microbiome data presents a formidable challenge due to the high dimension and strong noise of gut microbiome data. To address this challenge, we introduce a novel approach termed the specific network information gain (SNIG) method to detect CRC's critical states at various taxonomic levels via gut microbiome data. The numerical simulation indicates that the SNIG method is robust under different noise levels and that it is also superior to the existing methods on detecting the critical states. Moreover, utilizing SNIG on two real CRC datasets enabled us to discern the critical states preceding deterioration and to successfully identify their associated dynamic network biomarkers at different taxonomic levels. Notably, we discovered certain 'dark species' and pathways intimately linked to CRC progression. In addition, we accurately detected the tipping points on an individual dataset of type I diabetes.

MIWE: detecting the critical states of complex biological systems by the mutual information weighted entropy.

Complex biological systems often undergo sudden qualitative changes during their dynamic evolution. These critical transitions are typically characterized by a catastrophic progression of the system. Identifying the critical point is critical to uncovering the underlying mechanisms of complex biological systems. However, the system may exhibit minimal changes in its state until the critical point is reached, and in the face of high throughput and strong noise data, traditional biomarkers may not be effective in distinguishing the critical state. In this study, we propose a novel approach, mutual information weighted entropy (MIWE), which uses mutual information between genes to build networks and identifies critical states by quantifying molecular dynamic differences at each stage through weighted differential entropy. The method is applied to one numerical simulation dataset and four real datasets, including bulk and single-cell expression datasets. The critical states of the system can be recognized and the robustness of MIWE method is verified by numerical simulation under the influence of different noises. Moreover, we identify two key transcription factors (TFs), CREB1 and CREB3, that regulate downstream signaling genes to coordinate cell fate commitment. The dark genes in the single-cell expression datasets are mined to reveal the potential pathway regulation mechanism.

Detecting the critical states during disease development based on temporal network flow entropy.

Complex diseases progression can be generally divided into three states, which are normal state, predisease/critical state and disease state. The sudden deterioration of diseases can be viewed as a bifurcation or a critical transition. Therefore, hunting for the tipping point or critical state is of great importance to prevent the disease deterioration. However, it is still a challenging task to detect the critical states of complex diseases with high-dimensional data, especially based on an individual. In this study, we develop a new method based on network fluctuation of molecules, temporal network flow entropy (TNFE) or temporal differential network flow entropy, to detect the critical states of complex diseases on the basis of each individual. By applying this method to a simulated dataset and six real diseases, including respiratory viral infections and tumors with four time-course and two stage-course high-dimensional omics datasets, the critical states before deterioration were detected and their dynamic network biomarkers were identified successfully. The results on the simulated dataset indicate that the TNFE method is robust under different noise strengths, and is also superior to the existing methods on detecting the critical states. Moreover, the analysis on the real datasets demonstrated the effectiveness of TNFE for providing early-warning signals on various diseases. In addition, we also predicted disease deterioration risk and identified drug targets for cancers based on stage-wise data.

Superconductivity-driven ferromagnetism and spin manipulation using vortices in the magnetic superconductor EuRbFe4As4.

Magnetic superconductors are specific materials exhibiting two antagonistic phenomena, superconductivity and magnetism, whose mutual interaction induces various emergent phenomena, such as the reentrant superconducting transition associated with the suppression of superconductivity around the magnetic transition temperature (T m), highlighting the impact of magnetism on superconductivity. In this study, we report the experimental observation of the ferromagnetic order induced by superconducting vortices in the high-critical-temperature (high-T c) magnetic superconductor EuRbFe4As4 Although the ground state of the Eu2+ moments in EuRbFe4As4 is helimagnetism below T m, neutron diffraction and magnetization experiments show a ferromagnetic hysteresis of the Eu2+ spin alignment. We demonstrate that the direction of the Eu2+ moments is dominated by the distribution of pinned vortices based on the critical state model. Moreover, we demonstrate the manipulation of spin texture by controlling the direction of superconducting vortices, which can help realize spin manipulation devices using magnetic superconductors.

Coupling Relationships between the Brain and the Central Pattern Generator Based on a Fractional-Order Extended Hindmarsh-Rose Model.

BACKGROUND: The states of the central nervous system (CNS) can be classified into subcritical, critical, and supercritical states that endow the system with information capacity, transmission capabilities, and dynamic range. A further investigation of the relationship between the CNS and the central pattern generators (CPG) is warranted to provide insight into the mechanisms that govern the locomotion system. METHODS: In this study, we established a fractional-order CPG model based on an extended Hindmarsh-Rose model with time delay. A CNS model was further established using a recurrent excitation-inhibition neuronal network. Coupling between these CNS and CPG models was then explored, demonstrating a potential means by which oscillations generated by a neural network respond to periodic stimuli. RESULTS AND CONCLUSIONS: These simulations yielded two key sets of findings. First, frequency sliding was observed when the CPG was sent to the CNS in the subcritical, critical, and supercritical states with different external stimulus and fractional-order index values, indicating that frequency sliding regulates brain function on multiple spatiotemporal scales when the CPG and CNS are coupled together. The main frequency range for these simulations was observed in the gamma band. Second, with increasing external inputs the coherence index for the CNS decreases, demonstrating that strong external inputs introduce neuronal stochasticity. Neural network synchronization is then reduced, triggering irregular neuronal firing. Together these results provide novel insight into the potential mechanisms that may underlie the locomotion system.

Identifying the critical states and dynamic network biomarkers of cancers based on network entropy.

BACKGROUND: There are sudden deterioration phenomena during the progression of many complex diseases, including most cancers; that is, the biological system may go through a critical transition from one stable state (the normal state) to another (the disease state). It is of great importance to predict this critical transition or the so-called pre-disease state so that patients can receive appropriate and timely medical care. In practice, however, this critical transition is usually difficult to identify due to the high nonlinearity and complexity of biological systems. METHODS: In this study, we employed a model-free computational method, local network entropy (LNE), to identify the critical transition/pre-disease states of complex diseases. From a network perspective, this method effectively explores the key associations among biomolecules and captures their dynamic abnormalities. RESULTS: Based on LNE, the pre-disease states of ten cancers were successfully detected. Two types of new prognostic biomarkers, optimistic LNE (O-LNE) and pessimistic LNE (P-LNE) biomarkers, were identified, enabling identification of the pre-disease state and evaluation of prognosis. In addition, LNE helps to find "dark genes" with nondifferential gene expression but differential LNE values. CONCLUSIONS: The proposed method effectively identified the critical transition states of complex diseases at the single-sample level. Our study not only identified the critical transition states of ten cancers but also provides two types of new prognostic biomarkers, O-LNE and P-LNE biomarkers, for further practical application. The method in this study therefore has great potential in personalized disease diagnosis.

A Comprehensive "Real-World Constraints"-Aware Requirements Engineering Related Assessment and a Critical State-of-the-Art Review of the Monitoring of Humans in Bed.

Currently, abnormality detection and/or prediction is a very hot topic. In this paper, we addressed it in the frame of activity monitoring of a human in bed. This paper presents a comprehensive formulation of a requirements engineering dossier for a monitoring system of a "human in bed" for abnormal behavior detection and forecasting. Hereby, practical and real-world constraints and concerns were identified and taken into consideration in the requirements dossier. A comprehensive and holistic discussion of the anomaly concept was extensively conducted and contributed to laying the ground for a realistic specifications book of the anomaly detection system. Some systems engineering relevant issues were also briefly addressed, e.g., verification and validation. A structured critical review of the relevant literature led to identifying four major approaches of interest. These four approaches were evaluated from the perspective of the requirements dossier. It was thereby clearly demonstrated that the approach integrating graph networks and advanced deep-learning schemes (Graph-DL) is the one capable of fully fulfilling the challenging issues expressed in the real-world conditions aware specification book. Nevertheless, to meet immediate market needs, systems based on advanced statistical methods, after a series of adaptations, already ensure and satisfy the important requirements related to, e.g., low cost, solid data security and a fully embedded and self-sufficient implementation. To conclude, some recommendations regarding system architecture and overall systems engineering were formulated.

Detecting the Critical States of Type 2 Diabetes Mellitus Based on Degree Matrix Network Entropy by Cross-Tissue Analysis.

Type 2 diabetes mellitus (T2DM) is a metabolic disease caused by multiple etiologies, the development of which can be divided into three states: normal state, critical state/pre-disease state, and disease state. To avoid irreversible development, it is important to detect the early warning signals before the onset of T2DM. However, detecting critical states of complex diseases based on high-throughput and strongly noisy data remains a challenging task. In this study, we developed a new method, i.e., degree matrix network entropy (DMNE), to detect the critical states of T2DM based on a sample-specific network (SSN). By applying the method to the datasets of three different tissues for experiments involving T2DM in rats, the critical states were detected, and the dynamic network biomarkers (DNBs) were successfully identified. Specifically, for liver and muscle, the critical transitions occur at 4 and 16 weeks. For adipose, the critical transition is at 8 weeks. In addition, we found some "dark genes" that did not exhibit differential expression but displayed sensitivity in terms of their DMNE score, which is closely related to the progression of T2DM. The information uncovered in our study not only provides further evidence regarding the molecular mechanisms of T2DM but may also assist in the development of strategies to prevent this disease.

The effect of organic carbon content on soil compression characteristics.

We investigated the effect of soil organic carbon (SOC) on the consolidation behaviour of soil from two long term field experiments at Rothamsted; the Broadbalk Wheat Experiment and Hoosfield Spring Barley. These experiments are located on soil with similar particle size distributions, and include treatments with SOC contents ranging from approximately 1-3.5 g/100 g. Soils taken from plots with contrasting SOC contents were compressed and deformed in a triaxial cell and the normal consolidation and critical state lines were determined. We found that the compression index was independent of SOC, but the void ratio at any given effective stress was highly correlated with organic carbon content. By comparison with uniaxial compression data, the apparent influence of SOC on the compression index is likely to be due to its effect on soil hydraulic properties rather than any intrinsic effects of strength. The plastic limit test appears to be a useful and simple test to allow direct comparison of soil physical behaviour and expected soil density.

Cell population structure prior to bifurcation predicts efficiency of directed differentiation in human induced pluripotent cells.

Steering the differentiation of induced pluripotent stem cells (iPSCs) toward specific cell types is crucial for patient-specific disease modeling and drug testing. This effort requires the capacity to predict and control when and how multipotent progenitor cells commit to the desired cell fate. Cell fate commitment represents a critical state transition or "tipping point" at which complex systems undergo a sudden qualitative shift. To characterize such transitions during iPSC to cardiomyocyte differentiation, we analyzed the gene expression patterns of 96 developmental genes at single-cell resolution. We identified a bifurcation event early in the trajectory when a primitive streak-like cell population segregated into the mesodermal and endodermal lineages. Before this branching point, we could detect the signature of an imminent critical transition: increase in cell heterogeneity and coordination of gene expression. Correlation analysis of gene expression profiles at the tipping point indicates transcription factors that drive the state transition toward each alternative cell fate and their relationships with specific phenotypic readouts. The latter helps us to facilitate small molecule screening for differentiation efficiency. To this end, we set up an analysis of cell population structure at the tipping point after systematic variation of the protocol to bias the differentiation toward mesodermal or endodermal cell lineage. We were able to predict the proportion of cardiomyocytes many days before cells manifest the differentiated phenotype. The analysis of cell populations undergoing a critical state transition thus affords a tool to forecast cell fate outcomes and can be used to optimize differentiation protocols to obtain desired cell populations.

[Identifying critical state of breast cancer cell differentiation based on landscape dynamic network biomarkers].

Breast cancer is a malignant tumor with the highest morbidity and mortality in female in recent years, and it is a complex disease that affects human health. Studies have shown that dynamic network biomarkers (DNB) can effectively identify critical states at which complex diseases such as breast cancer change from a normal state to a disease state. However, the traditional DNB method requires data from multiple samples in the same disease state, which is usually unachievable in clinical diagnosis. This paper quantitatively analyzes the time series data of MCF-7 breast cancer cells and finds the DNB module of a single sample in the time series based on landscape DNB (L-DNB) method. Then, a comprehensive index is constructed to detect its early warning signals to determine the critical state of breast cancer cell differentiation. The results of this study may be of great significance for the prevention and early diagnosis of breast cancer. It is expected that this paper can provide references for the related research of breast cancer.

Dysfunction of CCT3-associated network signals for the critical state during progression of hepatocellular carcinoma.

Hepatocellular carcinoma (HCC) is one of the most common malignant tumors and is a serious threat to human health; thus, early diagnosis and adequate treatment are essential. However, there are still great challenges in identifying the tipping point and detecting early warning signals of early HCC. In this study, we aimed to identify the tipping point (critical state) of and key molecules involved in hepatocarcinogenesis based on time series transcriptome expression data of HCC patients. The phase from veHCC (very early HCC) to eHCC (early HCC) was identified as the critical state in HCC progression, with 143 genes identified as key candidate molecules by combining the DDRTree (dimensionality reduction via graph structure learning) and DNB (dynamic network biomarker) methods. Then, we ranked the candidate genes to verify their mRNA levels using the diethylnitrosamine (DEN)-induced HCC mouse model and identified five early warning signals, namely, CCT3, DSTYK, EIF3E, IARS2 and TXNRD1; these signals can be regarded as the potential early warning signals for the critical state of HCC. We identified CCT3 as an independent prognostic factor for HCC, and functions of CCT3 involving in the "MYCtargets_V1" and "E2F-Targets" are closely related to the progression of HCC. The predictive method combining the DDRTree and DNB methods can not only identify the key critical state before cancer but also determine candidate molecules of critical state, thus providing new insight into the early diagnosis and preemptive treatment of HCC.

Simhypo-sand: a simple hypoplastic model for granular materials and SPH implementation.

This paper introduces a new hypoplastic model characterized by a simple and elegant formulation. It requires only 7 material parameters to depict salient mechanical behaviors of granular materials. The numerical implementation employs an explicit integration method, enhanced by a best-fit stress correction algorithm in a smoothed particle hydrodynamics code. The performance of this model in capturing soil behavior across a range of scenarios is demonstrated by conducting various numerical tests, including triaxial and simple shear at low strain rates, as well as granular collapse, rigid penetration and landslide process at high strain rates.

Mechanical behaviour of granular materials undergoing grain dissolution.

Geotechnical engineering projects are often at risk from threats related to mineral dissolution and loss of particles that constitute the matrix of the geomaterial. Moreover, the impact of climate change can exacerbate these risks by accelerating the physical processes. To address such challenges, it is a pre-requisite to understand and quantify the effect of mineral dissolution on geomechanical behaviour. A general theoretical approach to mechanical consequences of geomaterials experiencing mineral dissolution was first proposed. Following, a series of oedometer tests were conducted using mixtures of salt and sand with various salt contents to observe and characterise the effect of dissolution on the mechanical behaviour of granular materials. The dissolution of salt crystals was performed in three different stress states to observe the stress-dependent response of the material. The effect of dissolution was dependent both on the amount of dissolved salt particles and the applied stress state. The laboratory experiments and the discussion followed shares insights into the effect of grain dissolution on the mechanical behaviour of granular materials and proved the potential of the framework presented in this paper. Finally, the paper ends by discussing the engineering implications bearing in mind the climate change we are facing today.

A State-Dependent Elasto-Plastic Model for Hydrate-Bearing Cemented Sand Considering Damage and Cementation Effects.

In order to optimize the efficiency and safety of gas hydrate extraction, it is essential to develop a credible constitutive model for sands containing hydrates. A model incorporating both cementation and damage was constructed to describe the behavior of hydrate-bearing cemented sand. This model is based on the critical state theory and builds upon previous studies. The damage factor Ds is incorporated to consider soil degradation and the reduction in hydrate cementation, as described by plastic shear strain. A computer program was developed to simulate the mechanisms of cementation and damage evolution, as well as the stress-strain curves of hydrate-bearing cemented sand. The results indicate that the model replicates the mechanical behavior of soil cementation and soil deterioration caused by impairment well. By comparing the theoretical curves with the experimental data, the compliance of the model was calculated to be more than 90 percent. The new state-dependent elasto-plastic constitutive model based on cementation and damage of hydrate-bearing cemented sand could provide vital guidance for the construction of deep-buried tunnels, extraction of hydrocarbon compounds, and development of resources.

Stress-dependent Mohr-Coulomb shear strength parameters for intact rock.

Rock strength is imperative for the design and stability analysis of engineering structures. The Mohr-Coulomb (M-C) criterion holds significant prominence in geotechnical engineering. However, the M-C criterion fails to accurately capture the nonlinear strength response and neglects the critical state of rocks, potentially leading to inaccuracies in the design phase of deep engineering projects. This study introduces an innovative stress-dependent friction angle and cohesion (SFC) for the M-C criterion to capture the nonlinear strength responses of intact rocks, spanning from non-critical to critical states (brittle to ductile regions). A novel method for determining these stress-dependent parameters at each corresponding σ 3 is initially introduced. Subsequently, an examination of the confinement dependency of the friction angle and cohesion is conducted, leading to the derivation of the SFC model. The SFC-enhanced M-C criterion, utilizing parameters obtained from triaxial tests under lower σ 3 , demonstrates the capability to delineate the complete non-linear strength envelope from brittle to ductile regions. Validation through triaxial test data confirms that the predictions of the SFC-enhanced M-C criterion accurately correspond to the strength characteristics of the tested rocks.

Hematocytological Clues of Peripheral Blood in Different Clinical Presentations of COVID-19.

Background: To gain insight into the pathogenesis and clinical course of COVID-19 from a historical perspective, we reviewed paraclinical diagnostic tools of this disease and prioritized the patients with a more severe form of disease admitted to intensive care units (ICUs). The objective was to better predict the course and severity of the disease by collecting more paraclinical data, specifically by examining the relationship between hematological findings and cytological variation of blood neutrophils and monocytes. Methods: This retrospective study was conducted on 112 patients with confirmed COVID-19 admitted to Imam Hossein Hospital (Tehran, Iran) from August to September 2020. Peripheral blood smears of these patients were differentiated according to several cytological variations of neutrophils and monocytes, and the correlation to the severity of the disease was specified. Results: The mean percentages of degenerated monocytes, degenerated granulocytes, and spiky biky neutrophils were significantly different among critical and non-critical patients (P<0.05). Degenerated monocytes and granulocytes were higher in critical patients as opposed to spiky biky neutrophils, which were higher among non-critical ones. Comparing the peripheral blood smears of COVID-19 patients (regarding pulmonary involvement in chest computed tomography [CT] scans [subtle, mild, moderate, and severe groups]), the twisted form of neutrophils was significantly higher in the subtle group than in the mild and moderate groups (P=0.003). Conclusion: Different cytological morphologies of neutrophils and monocytes, including degenerated monocytes, degenerated granulocytes, and spiky biky and twisted neutrophils, could help to predict the course and severity of the disease.

Identifying the critical state of cancers by single-sample Markov flow entropy.

Background: The progression of complex diseases sometimes undergoes a drastic critical transition, at which the biological system abruptly shifts from a relatively healthy state (before-transition stage) to a disease state (after-transition stage). Searching for such a critical transition or critical state is crucial to provide timely and effective scientific treatment to patients. However, in most conditions where only a small sample size of clinical data is available, resulting in failure when detecting the critical states of complex diseases, particularly only single-sample data. Methods: In this study, different from traditional methods that require multiple samples at each time, a model-free computational method, single-sample Markov flow entropy (sMFE), provides a solution to the identification problem of critical states/pre-disease states of complex diseases, solely based on a single-sample. Our proposed method was employed to characterize the dynamic changes of complex diseases from the perspective of network entropy. Results: The proposed approach was verified by unmistakably identifying the critical state just before the occurrence of disease deterioration for four tumor datasets from The Cancer Genome Atlas (TCGA) database. In addition, two new prognostic biomarkers, optimistic sMFE (O-sMFE) and pessimistic sMFE (P-sMFE) biomarkers, were identified by our method and enable the prognosis evaluation of tumors. Conclusions: The proposed method has shown its capability to accurately detect pre-disease states of four cancers and provide two novel prognostic biomarkers, O-sMFE and P-sMFE biomarkers, to facilitate the personalized prognosis of patients. This is a remarkable achievement that could have a major impact on the diagnosis and treatment of complex diseases.

Buckling Analysis of Laminated Plates with Asymmetric Layup by Approximation Method.

This study investigated thin-walled plate elements with a central cut-out under axial compression. The plates were manufactured from epoxy/carbon laminate (CFRP) with an asymmetric layup. The study involved analyzing the buckling and post-buckling behavior of the plates using experimental and numerical methods. The experiments provided the post-buckling equilibrium paths (P-u), which were then used to determine the critical load using the straight-line intersection method. Along with the experiments, a numerical analysis was conducted using the Finite Element Method (FEM) and using the ABAQUS® software. A linear analysis of an eigenvalue problem was conducted, the results of which led to the determination of the critical loads for the developed numerical model. The second part of the calculations involved conducting a non-linear analysis of a plate with an initial geometric imperfection corresponding to structural buckling. The numerical results were validated by the experimental findings, which showed that the numerical model of the structure was correct.