On flushed partitions and concave compositions

In this work, we give combinatorial proofs for generating functions of two problems, i.e., flushed partitions and concave compositions of even length. We also give combinatorial interpretation of one problem posed by Sylvester involving flushed partitions and then prove it. For these purposes, we first describe an involution and use it to prove core identities. Using this involution with modifications, we prove several problems of different nature, including Andrews' partition identities involving initial repetitions and partition theoretical interpretations of three mock theta functions of third order $f(q)$, $\phi(q)$ and $\psi(q)$. An identity of Ramanujan is proved combinatorially. Several new identities are also established.Comment: 19 page

Determination of the interfacial heat transfer coefficient in hot stamping of aluminium alloys

The characteristic properties of aluminium alloys, e.g. their high strength-weight ratio, high thermal conductance, excellent corrosion resistance and good recyclability, render them ideal materials to reduce air pollution and improve the fuel economy of vehicles. However, their low formability at room temperature limits their application in industry. In recent years, hot stamping was developed as a promising technology to form sheet metal components from aluminium alloys at elevated temperatures to increase their formability. The interfacial heat transfer coefficient (IHTC), an essential thermophysical parameter in hot stamping processes, should therefore be identified not only to retain the full mechanical strength of the formed components by achieving the critical quenching rates for different aluminium alloys, but also to optimise the production rate by controlling the quenching process. The present research aims to determine the IHTC values for 7075 and 6082 aluminium alloys under different experimental conditions. A dedicated IHTC test facility, IHTC-mate, was developed to precisely measure the temperature evolutions of the specimens and thus accurately determine their IHTC values with high stability and repeatability. Subsequently, the effects of the contact pressure, tool material, coating material, specimen thickness, lubricant and initial blank temperature on the IHTC were identified. It was found that the IHTC increased logarithmically with increasing contact pressure. In addition, the applications of tools, coatings and lubricants with higher thermal conductivities, as well as specimens with larger thickness and higher initial blank temperature could raise the IHTC values. Furthermore, a mechanism-based IHTC model was developed to predict the IHTC evolutions as a function of those influential factors, and enable the interaction between the IHTC evolutions and lubricant layer thickness diminution with sliding distance at different contact pressures and sliding speeds. Hemispherical dome and B-pillar forming tests were conducted to form 7075 and 6082 aluminium alloys. The good agreements between the experimental and simulated temperature evolutions of the components being formed validated the determined IHTC results and developed IHTC model. Consequently, the temperature evolutions and cooling rates of the components being formed in hot stamping processes could be predicted. Furthermore, the processing window and tool design could be optimised to achieve the critical cooling rates and thus retain the full mechanical strength of the formed components.Open Acces

Single Molecule Michaelis-Menten Equation beyond Quasi-Static Disorder

The classic Michaelis-Menten equation describes the catalytic activities for ensembles of enzyme molecules very well. But recent single-molecule experiment showed that the waiting time distribution and other properties of single enzyme molecule are not consistent with the prediction based on the viewpoint of ensemble. It has been contributed to the slow inner conformational changes of single enzyme in the catalytic processes. In this work we study the general dynamics of single enzyme in the presence of dynamic disorder. We find that at two limiting cases, the slow reaction and nondiffusion limits, Michaelis-Menten equation exactly holds although the waiting time distribution has a multiexponential decay behaviors in the nondiffusion limit.Particularly, the classic Michaelis-Menten equation still is an excellent approximation other than the two limits.Comment: 10 pages, 1 figur

A Targeted Quantitative Proteomic Method Revealed a Substantial Reprogramming of Kinome during Melanoma Metastasis.

Kinases are involved in numerous critical cell signaling processes, and dysregulation in kinase signaling is implicated in many types of human cancers. In this study, we applied a parallel-reaction monitoring (PRM)-based targeted proteomic method to assess kinome reprogramming during melanoma metastasis in three pairs of matched primary/metastatic human melanoma cell lines. Around 300 kinases were detected in each pair of cell lines, and the results showed that Janus kinase 3 (JAK3) was with reduced expression in the metastatic lines of all three pairs of melanoma cells. Interrogation of The Cancer Genome Atlas (TCGA) data showed that reduced expression of JAK3 is correlated with poorer prognosis in melanoma patients. Additionally, metastatic human melanoma cells/tissues exhibited diminished levels of JAK3 mRNA relative to primary melanoma cells/tissues. Moreover, JAK3 suppresses the migration and invasion of cultured melanoma cells by modulating the activities of matrix metalloproteinases 2 and 9 (MMP-2 and MMP-9). In summary, our targeted kinome profiling method provided by far the most comprehensive dataset for kinome reprogramming associated with melanoma progression, which builds a solid foundation for examining the functions of other kinases in melanoma metastasis. Moreover, our results reveal a role of JAK3 as a potential suppressor for melanoma metastasis

Talbot effect for the Manakov System on the torus

In this paper, the Talbot effect for the multi-component linear and nonlinear systems of the dispersive evolution equations on a bounded interval subject to periodic boundary conditions and discontinuous initial profiles is investigated. Firstly, for a class of two-component linear systems satisfying the dispersive quantization conditions, we discuss the fractal solutions at irrational times. Next, the investigation to nonlinear regime is extended, we prove that, for the concrete example of the Manakov system, the solutions of the corresponding periodic initial-boundary value problem subject to initial data of bounded variation are continuous but nowhere differentiable fractal-like curve with Minkowski dimension $3/2$ at irrational times. Finally, numerical experiments for the periodic initial-boundary value problem of the Manakov system, are used to justify how such effects persist into the multi-component nonlinear regime. Furthermore, it is shown in the nonlinear multi-component regime that the interplay of different components may induce subtle different qualitative profile between the jump discontinuities, especially in the case that two nonlinearly coupled components start with different initial profile

Preserving Specificity in Federated Graph Learning for fMRI-based Neurological Disorder Identification

Resting-state functional magnetic resonance imaging (rs-fMRI) offers a non-invasive approach to examining abnormal brain connectivity associated with brain disorders. Graph neural network (GNN) gains popularity in fMRI representation learning and brain disorder analysis with powerful graph representation capabilities. Training a general GNN often necessitates a large-scale dataset from multiple imaging centers/sites, but centralizing multi-site data generally faces inherent challenges related to data privacy, security, and storage burden. Federated Learning (FL) enables collaborative model training without centralized multi-site fMRI data. Unfortunately, previous FL approaches for fMRI analysis often ignore site-specificity, including demographic factors such as age, gender, and education level. To this end, we propose a specificity-aware federated graph learning (SFGL) framework for rs-fMRI analysis and automated brain disorder identification, with a server and multiple clients/sites for federated model aggregation and prediction. At each client, our model consists of a shared and a personalized branch, where parameters of the shared branch are sent to the server while those of the personalized branch remain local. This can facilitate knowledge sharing among sites and also helps preserve site specificity. In the shared branch, we employ a spatio-temporal attention graph isomorphism network to learn dynamic fMRI representations. In the personalized branch, we integrate vectorized demographic information (i.e., age, gender, and education years) and functional connectivity networks to preserve site-specific characteristics. Representations generated by the two branches are then fused for classification. Experimental results on two fMRI datasets with a total of 1,218 subjects suggest that SFGL outperforms several state-of-the-art approaches