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Steady two-dimensional Rayleigh–Bénard convection between stress-free isothermal boundaries is studied via numerical computations. We explore properties of steady convective rolls with aspect ratios ${\\rm \\pi} /5\\leqslant \\varGamma \\leqslant 4{\\rm \\pi}$, where $\\varGamma$ is the width-to-height ratio for a pair of counter-rotating rolls, over eight orders of magnitude in the Rayleigh number, $10^3\\leqslant Ra\\leqslant 10^{11}$, and four orders of magnitude in the Prandtl number, $10^{-2}\\leqslant Pr\\leqslant 10^2$. At large $Ra$ where steady rolls are dynamically unstable, the computed rolls display $Ra \\rightarrow \\infty$ asymptotic scaling. In this regime, the Nusselt number $Nu$ that measures heat transport scales as $Ra^{1/3}$ uniformly in $Pr$. The prefactor of this scaling depends on $\\varGamma$ and is largest at $\\varGamma \\approx 1.9$. The Reynolds number $Re$ for large-$Ra$ rolls scales as $Pr^{-1} Ra^{2/3}$ with a prefactor that is largest at $\\varGamma \\approx 4.5$. All of these large-$Ra$ features agree quantitatively with the semi-analytical asymptotic solutions constructed by Chini & Cox (Phys. Fluids, vol. 21, 2009, 083603). Convergence of $Nu$ and $Re$ to their asymptotic scalings occurs more slowly when $Pr$ is larger and when $\\varGamma$ is smaller.

Background Current phenotype-based diagnostic tools often struggle with accurate disease prioritization due to incomplete phenotypic data and the complexity of rare disease presentations. Additionally, they lack the ability to generate patient-centered clinical insights or recommend further symptoms for differential diagnosis. Methods We developed PhenoDP, a deep learning-based toolkit with three modules: Summarizer, Ranker, and Recommender. The Summarizer fine-tuned a distilled large language model to create clinical summaries from a patient’s Human Phenotype Ontology (HPO) terms. The Ranker prioritizes diseases by combining information content-based, phi-based, and semantic-based similarity measures. The Recommender employs contrastive learning to recommend additional HPO terms for enhanced diagnostic accuracy. Results PhenoDP’s Summarizer produces more clinically coherent and patient-centered summaries than the general-purpose language model FlanT5. The Ranker achieves state-of-the-art diagnostic performance, consistently outperforming existing phenotype-based methods across both simulated and real-world datasets. The Recommender also outperformed GPT-4o and PhenoTips in improving diagnostic accuracy when its suggested terms were incorporated into different ranking pipelines. Conclusions PhenoDP enhances Mendelian disease diagnosis through deep learning, offering precise summarization, ranking, and symptom recommendation. Its superior performance and open-source design make it a valuable clinical tool, with potential to accelerate diagnosis and improve patient outcomes. PhenoDP is freely available at https://github.com/TianLab-Bioinfo/PhenoDP .

Background Renal cold ischemia-reperfusion injury (CIRI), a pathological process during kidney transplantation, may result in delayed graft function and negatively impact graft survival and function. There is a lack of an accurate and non-invasive tool for evaluating the degree of CIRI. Multi-parametric MRI has been widely used to detect and evaluate kidney injury. The machine learning algorithms introduced the opportunity to combine biomarkers from different MRI metrics into a single classifier. Objective To evaluate the performance of multi-parametric magnetic resonance imaging for grading renal injury in a rat model of renal cold ischemia-reperfusion injury using a machine learning approach. Methods Eighty male SD rats were selected to establish a renal cold ischemia -reperfusion model, and all performed multiparametric MRI scans (DWI, IVIM, DKI, BOLD, T1mapping and ASL), followed by pathological analysis. A total of 25 parameters of renal cortex and medulla were analyzed as features. The pathology scores were divided into 3 groups using K-means clustering method. Lasso regression was applied for the initial selecting of features. The optimal features and the best techniques for pathological grading were obtained. Multiple classifiers were used to construct models to evaluate the predictive value for pathology grading. Results All rats were categorized into mild, moderate, and severe injury group according the pathologic scores. The 8 features that correlated better with the pathologic classification were medullary and cortical Dp, cortical T2*, cortical Fp, medullary T2*, ∆T1, cortical RBF, medullary T1. The accuracy(0.83, 0.850, 0.81, respectively) and AUC (0.95, 0.93, 0.90, respectively) for pathologic classification of the logistic regression, SVM, and RF are significantly higher than other classifiers. For the logistic model and combining logistic, RF and SVM model of different techniques for pathology grading, the stable and perform are both well. Based on logistic regression, IVIM has the highest AUC (0.93) for pathological grading, followed by BOLD(0.90). Conclusion The multi-parametric MRI-based machine learning model could be valuable for noninvasive assessment of the degree of renal injury.

Single‐cell cis‐regulatory relationships (CRRs) are essential for deciphering transcriptional regulation and understanding the pathogenic mechanisms of disease‐associated non‐coding variants. Existing computational methods struggle to accurately predict single‐cell CRRs due to inadequately integrating causal biological principles and large‐scale single‐cell data. Here, SCRIPT (Single‐cell Cis‐regulatory Relationship Identifier based on Pre‐Trained graph attention networks) is presented for inferring single‐cell CRRs from transcriptomic and chromatin accessibility data. SCRIPT incorporates two key innovations: graph causal attention networks supported by empirical CRR evidence, and representation learning enhanced through pretraining on atlas‐scale single‐cell chromatin accessibility data. Validation using cell‐type‐specific chromatin contact and CRISPR perturbation data demonstrates that SCRIPT achieves a mean AUC of 0.89, significantly outperforming state‐of‐the‐art methods (AUC: 0.7). Notably, SCRIPT obtains an over twofold improvement in predicting long‐range CRRs (>100 Kb) compared to existing methods. By applying SCRIPT to Alzheimer's disease and schizophrenia, a framework is established for prioritizing disease‐causing variants and elucidating their functional effects in a cell‐type‐specific manner. By uncovering molecular genetic mechanisms undetected by existing computational methods, SCRIPT provides a roadmap for advancing genetic diagnosis and target discovery. SCRIPT is a novel method inferring single‐cell cis‐regulatory relationships (CRRs) from transcriptomic and chromatin accessibility data. SCRIPT incorporates two key innovations: graph causal attention networks supported by empirical CRR evidence, and representation learning enhanced through pretraining on atlas‐scale single‐cell data. For complex genetic diseases, SCRIPT facilitates prioritizing disease‐causing variants and elucidating their functional effects in a cell‐type‐specific manner.

We investigate the flow structure and dynamics of moderate-Rayleigh-number ( R a ) thermal convection in a two-dimensional inclined porous layer. High-resolution numerical simulations confirm the emergence of O ( 1 ) aspect-ratio large-scale convective rolls, with one ‘natural’ roll rotating in the counterclockwise direction and one ‘antinatural’ roll rotating in the clockwise direction. As the inclination angle ϕ is increased, the background mean shear flow intensifies the natural-roll motion, while suppressing the antinatural-roll motion. Our numerical simulations also reveal—for the first time in single-species porous medium convection—the existence of spatially-localized convective states at large ϕ , which we suggest are enabled by subcritical instability of the base state at sufficiently large inclination angles. To better understand the physics of inclined porous medium convection at different ϕ , we numerically compute steady convective solutions using Newton iteration and then perform secondary stability analysis of these nonlinear states using Floquet theory. Our analysis indicates that the inclination of the porous layer stabilizes the boundary layers of the natural roll, but intensifies the boundary-layer instability of the antinatural roll. These results facilitate physical understanding of the large-scale cellular flows observed in the numerical simulations at different values of ϕ .

The central open question about Rayleigh–Bénard convection – buoyancy-driven flow in a fluid layer heated from below and cooled from above – is how vertical heat flux depends on the imposed temperature gradient in the strongly nonlinear regime where the flows are typically turbulent. The quantitative challenge is to determine how the Nusselt number $Nu$ depends on the Rayleigh number $Ra$ in the $Ra\\to \\infty$ limit for fluids of fixed finite Prandtl number $Pr$ in fixed spatial domains. Laboratory experiments, numerical simulations and analysis of Rayleigh's mathematical model have yet to rule out either of the proposed ‘classical’ $Nu \\sim Ra^{1/3}$ or ‘ultimate’ $Nu \\sim Ra^{1/2}$ asymptotic scaling theories. Among the many solutions of the equations of motion at high $Ra$ are steady convection rolls that are dynamically unstable but share features of the turbulent attractor. We have computed these steady solutions for $Ra$ up to $10^{14}$ with $Pr=1$ and various horizontal periods. By choosing the horizontal period of these rolls at each $Ra$ to maximize $Nu$, we find that steady convection rolls achieve classical asymptotic scaling. Moreover, they transport more heat than turbulent convection in experiments or simulations at comparable parameters. If heat transport in turbulent convection continues to be dominated by heat transport in steady rolls as $Ra\\to \\infty$, it cannot achieve the ultimate scaling.

High-Rayleigh-number ( $Ra$ ) convection in an inclined two-dimensional porous layer is investigated using direct numerical simulations (DNS) and stability and variational upper-bound analyses. When the inclination angle $\\unicode[STIX]{x1D719}$ of the layer satisfies $0^{\\circ }<\\unicode[STIX]{x1D719}\\lesssim 25^{\\circ }$ , DNS confirm that the flow exhibits a three-region wall-normal asymptotic structure in accord with the strictly horizontal ( $\\unicode[STIX]{x1D719}=0^{\\circ }$ ) case, except that as $\\unicode[STIX]{x1D719}$ is increased the time-mean spacing between neighbouring interior plumes also increases substantially. Both DNS and upper-bound analysis indicate that the heat transport enhancement factor (i.e. the Nusselt number) $Nu\\sim CRa$ with a $\\unicode[STIX]{x1D719}$ -dependent prefactor $C$ . When $\\unicode[STIX]{x1D719}>\\unicode[STIX]{x1D719}_{t}$ , however, where $30^{\\circ }<\\unicode[STIX]{x1D719}_{t}<32^{\\circ }$ independently of $Ra$ , the columnar flow structure is completely broken down: the flow transitions to a large-scale travelling-wave convective roll state, and the heat transport is significantly reduced. To better understand the physics of inclined porous medium convection at large $Ra$ and modest inclination angles, a spatial Floquet analysis is performed, yielding predictions of the linear stability of numerically computed, fully nonlinear steady convective states. The results show that there exist two types of instability when $\\unicode[STIX]{x1D719}\\neq 0^{\\circ }$ : a bulk-mode instability and a wall-mode instability, consistent with previous findings for $\\unicode[STIX]{x1D719}=0^{\\circ }$ (Wen et al., J. Fluid Mech., vol. 772, 2015, pp. 197–224). The background flow induced by the inclination of the layer intensifies the bulk-mode instability during its subsequent nonlinear evolution, thereby favouring increased spacing between the interior plumes relative to that observed in convection in a horizontal porous layer.

Motivated by the persistence of natural carbon dioxide ( $\\text{CO}_{2}$ ) fields, we investigate the convective dissolution of $\\text{CO}_{2}$ at low pressure (below 1 MPa) in a closed system, where the pressure in the gas declines as convection proceeds. This introduces a negative feedback that reduces the convective dissolution rate even before the brine becomes saturated. We analyse the case of an ideal gas with a solubility given by Henry’s law, in the limits of very low and very high Rayleigh numbers. The equilibrium state in this system is determined by the dimensionless dissolution capacity, $\\unicode[STIX]{x1D6F1}$ , which gives the fraction of the gas that can be dissolved into the underlying brine. Analytic approximations of the pure diffusion problem with $\\unicode[STIX]{x1D6F1}>0$ show that the diffusive base state is no longer self-similar and that diffusive mass transfer declines rapidly with time. Direct numerical simulations at high Rayleigh numbers show that no constant flux regime exists for $\\unicode[STIX]{x1D6F1}>0$ ; nevertheless, the quantity $F/C_{s}^{2}$ remains constant, where $F$ is the dissolution flux and $C_{s}$ is the dissolved concentration at the top of the domain. Simple mathematical models are developed to predict the evolution of $C_{s}$ and $F$ for high-Rayleigh-number convection in a closed system. The negative feedback that limits convection in closed systems may explain the persistence of natural $\\text{CO}_{2}$ accumulations over millennial time scales.

A systematic investigation of unstable steady-state solutions of the Darcy–Oberbeck–Boussinesq equations at large values of the Rayleigh number $\\mathit{Ra}$ is performed to gain insight into two-dimensional porous medium convection in domains of varying aspect ratio $L$ . The steady convective states are shown to transport less heat than the statistically steady ‘turbulent’ flow realised at the same parameter values: the Nusselt number $\\mathit{Nu}\\sim \\mathit{Ra}$ for turbulent porous medium convection, while $\\mathit{Nu}\\sim \\mathit{Ra}^{0.6}$ for the maximum heat-transporting steady solutions. A key finding is that the lateral scale of the heat-flux-maximising solutions shrinks roughly as $L\\sim \\mathit{Ra}^{-0.5}$ , reminiscent of the decrease of the mean inter-plume spacing observed in turbulent porous medium convection as the thermal forcing is increased. A spatial Floquet analysis is performed to investigate the linear stability of the fully nonlinear steady convective states, extending a recent study by Hewitt et al. (J. Fluid Mech., vol. 737, 2013, pp. 205–231) by treating a base convective state, and secondary stability modes, that satisfy appropriate boundary conditions along plane parallel walls. As in that study, a bulk instability mode is found for sufficiently small-aspect-ratio base states. However, the growth rate of this bulk mode is shown to be significantly reduced by the presence of the walls. Beyond a certain critical $\\mathit{Ra}$ -dependent aspect ratio, the base state is most strongly unstable to a secondary mode that is localised near the heated and cooled walls. Direct numerical simulations, strategically initialised to investigate the fully nonlinear evolution of the most dangerous secondary instability modes, suggest that the (long time) mean inter-plume spacing in statistically steady porous medium convection results from a balance between the competing effects of these two types of instability.

Buoyancy-driven convection in fluid-saturated porous media is a key environmental and technological process, with applications ranging from carbon dioxide storage in terrestrial aquifers to the design of compact heat exchangers. Porous medium convection is also a paradigm for forced-dissipative infinite-dimensional dynamical systems, exhibiting spatiotemporally chaotic dynamics if not \"true\" turbulence. The objective of this dissertation research is to quantitatively characterize the dynamics and heat transport in two-dimensional horizontal and inclined porous medium convection between isothermal plane parallel boundaries at asymptotically large values of the Rayleigh number Ra by investigating the emergent, quasi-coherent flow. This investigation employs a complement of direct numerical simulations (DNS), secondary stability and dynamical systems theory, and variational analysis. The DNS confirm the remarkable tendency for the interior flow to self-organize into closely-spaced columnar plumes at sufficiently large Ra (up to Ra ≃ 105), with more complex spatiotemporal features being confined to boundary layers near the heated and cooled walls. The relatively simple form of the interior flow motivates investigation of unstable steady and time-periodic convective states at large Ra as a function of the domain aspect ratio L. To gain insight into the development of spatiotemporally chaotic convection, the (secondary) stability of these fully nonlinear states to small-amplitude disturbances is investigated using a spatial Floquet analysis. The results indicate that there exist two distinct modes of instability at large Ra: a bulk instability mode and a wall instability mode. The former usually is excited by long-wavelength disturbances and is generally much weaker than the latter. DNS, strategically initialized to investigate the fully nonlinear evolution of the most dangerous secondary instability modes, suggest that the (long time) mean inter-plume spacing in statistically-steady porous medium convection results from an interplay between the competing effects of these two types of instability. Upper bound analysis is then employed to investigate the dependence of the heat transport enhancement factor, i.e. the Nusselt number Nu, on Ra and L. To solve the optimization problems arising from the \"background field\" upper-bound variational analysis, a novel two-step algorithm in which time is introduced into the formulation is developed. The new algorithm obviates the need for numerical continuation, thereby enabling the best available bounds to be computed up to Ra ≈ 2.65 × 104. A mathematical proof is given to demonstrate that the only steady state to which this numerical algorithm can converge is the required global optimal of the variational problem. Using this algorithm, the dependence of the bounds on L( Ra) is explored, and a \"minimal flow unit\" is identified. Finally, the upper bound variational methodology is also shown to yield quantitatively useful predictions of Nu and to furnish a functional basis that is naturally adapted to the boundary layer dynamics at large Ra.