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Free, publicly-accessible full text available November 11, 2025
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Free, publicly-accessible full text available November 11, 2025
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We present a generalization of the geometric phase to pure and thermal states in $\mathcal{PT}$-symmetric quantum mechanics (PTQM) based on the approach of the interferometric geometric phase (IGP). The formalism first introduces the parallel-transport conditions of quantum states and reveals two geometric phases, $\theta^1$ and $\theta^2$, for pure states in PTQM according to the states under parallel-transport. Due to the non-Hermitian Hamiltonian in PTQM, $\theta^1$ is complex and $\theta^2$ is its real part. The imaginary part of $\theta^1$ plays an important role when we generalize the IGP to thermal states in PTQM. The generalized IGP modifies the thermal distribution of a thermal state, thereby introducing effective temperatures. \textcolor{red}{At certain critical points, the generalized IGP may exhibit discrete jumps at finite temperatures, signaling a geometric phase transition. We illustrate the IGP of PTQM through two examples and compare their differences}.more » « lessFree, publicly-accessible full text available June 1, 2025
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Finley, Stacey D (Ed.)
In experiments, the distributions of mRNA or protein numbers in single cells are often fitted to the random telegraph model which includes synthesis and decay of mRNA or protein, and switching of the gene between active and inactive states. While commonly used, this model does not describe how fluctuations are influenced by crucial biological mechanisms such as feedback regulation, non-exponential gene inactivation durations, and multiple gene activation pathways. Here we investigate the dynamical properties of four relatively complex gene expression models by fitting their steady-state mRNA or protein number distributions to the simple telegraph model. We show that despite the underlying complex biological mechanisms, the telegraph model with three effective parameters can accurately capture the steady-state gene product distributions, as well as the conditional distributions in the active gene state, of the complex models. Some effective parameters are reliable and can reflect realistic dynamic behaviors of the complex models, while others may deviate significantly from their real values in the complex models. The effective parameters can also be applied to characterize the capability for a complex model to exhibit multimodality. Using additional information such as single-cell data at multiple time points, we provide an effective method of distinguishing the complex models from the telegraph model. Furthermore, using measurements under varying experimental conditions, we show that fitting the mRNA or protein number distributions to the telegraph model may even reveal the underlying gene regulation mechanisms of the complex models. The effectiveness of these methods is confirmed by analysis of single-cell data for
E. coli and mammalian cells. All these results are robust with respect to cooperative transcriptional regulation and extrinsic noise. In particular, we find that faster relaxation speed to the steady state results in more precise parameter inference under large extrinsic noise.Free, publicly-accessible full text available May 14, 2025 -
In this study, we obtain an exact time-dependent solution of the chemical master equation (CME) of an extension of the two-state telegraph model describing bursty or non-bursty protein expression in the presence of positive or negative autoregulation. Using the method of spectral decomposition, we show that the eigenfunctions of the generating function solution of the CME are Heun functions, while the eigenvalues can be determined by solving a continued fraction equation. Our solution generalizes and corrects a previous time-dependent solution for the CME of a gene circuit describing non-bursty protein expression in the presence of negative autoregulation [Ramos et al., Phys. Rev. E 83, 062902 (2011)]. In particular, we clarify that the eigenvalues are generally not real as previously claimed. We also investigate the relationship between different types of dynamic behavior and the type of feedback, the protein burst size, and the gene switching rate.
Free, publicly-accessible full text available February 21, 2025 -
Due to the incapability of one-dimensional (1D) and two-dimensional (2D) models in simulating the frontal polymerization (FP) process in laminated composites with multiple fiber angles (e.g., cross-ply, angle-ply), modeling a three-dimensional (3D) domain, which is more representative of practical applications, provides critical guidance in the control and optimization of the FP process. In this paper, subroutines are developed to achieve the 3D modeling of FP in unidirectional and cross-ply carbon fiber laminates with finite element analysis, which are validated against the experimental data. The 3D model is employed to study the effect of triggering direction in relevance to the fiber direction on the FP process, which cannot be studied using traditional 1D/2D models. Our findings suggest that triggering in the fiber direction leads to a higher front velocity, in comparison to cases where front was triggered in the direction perpendicular to the fiber. Moreover, the average front velocity in cross-ply laminates is on average 20~25% lower than that in unidirectional laminates. When triggered using two opposite fronts in the in-plane direction, the maximum temperature of the thermal spike in the cross-ply laminate, when two fronts merge, is about 100 °C lower than that in the unidirectional laminate. In cross-ply laminates, a sloped pattern forms across the thickness direction as the front propagates in the in-plane direction, as opposed to the traditionally observed uniform propagation pattern in unidirectional cases. Furthermore, the effect of thermal conductivity is studied using two additional composite laminates with glass (1.14 W/m·K) and Kevlar fibers (0.04 W/m·K). It is shown that the frontal velocity, degree of cure, and the thermal spike temperature decrease as the thermal conductivity reduces.more » « less
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In this paper, we propose a comprehensive unsupervised framework that leverages existing and novel multiview learning models, towards obtaining a single node embedding from a collection of node embeddings, combining the best of all worlds. Through extensive experiments, we demonstrate that the proposed multiview node embedding is able to perform on par or better than the best of its constituents and provide reliable performance across downstream tasks including node classification and graph reconstruction. Index Terms—multiview learning, node embedding, hybrid tensor decomposition, unsupervised learningmore » « less
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null (Ed.)Background The natural history of disease in patients infected with severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) remained obscure during the early pandemic. Aim Our objective was to estimate epidemiological parameters of coronavirus disease (COVID-19) and assess the relative infectivity of the incubation period. Methods We estimated the distributions of four epidemiological parameters of SARS-CoV-2 transmission using a large database of COVID-19 cases and potential transmission pairs of cases, and assessed their heterogeneity by demographics, epidemic phase and geographical region. We further calculated the time of peak infectivity and quantified the proportion of secondary infections during the incubation period. Results The median incubation period was 7.2 (95% confidence interval (CI): 6.9‒7.5) days. The median serial and generation intervals were similar, 4.7 (95% CI: 4.2‒5.3) and 4.6 (95% CI: 4.2‒5.1) days, respectively. Paediatric cases < 18 years had a longer incubation period than adult age groups (p = 0.007). The median incubation period increased from 4.4 days before 25 January to 11.5 days after 31 January (p < 0.001), whereas the median serial (generation) interval contracted from 5.9 (4.8) days before 25 January to 3.4 (3.7) days after. The median time from symptom onset to discharge was also shortened from 18.3 before 22 January to 14.1 days after. Peak infectivity occurred 1 day before symptom onset on average, and the incubation period accounted for 70% of transmission. Conclusion The high infectivity during the incubation period led to short generation and serial intervals, necessitating aggressive control measures such as early case finding and quarantine of close contacts.more » « less