Time Dependent Saddle Node Bifurcation: Breaking Time and the Point of No Return in a Non-Autonomous Model of Critical Transitions

There is a growing awareness that catastrophic phenomena in biology and medicine can be mathematically represented in terms of saddle-node bifurcations. In particular, the term `tipping', or critical transition has in recent years entered the discourse of the general public in relation to ecology, medicine, and public health. The saddle-node bifurcation and its associated theory of catastrophe as put forth by Thom and Zeeman has seen applications in a wide range of fields including molecular biophysics, mesoscopic physics, and climate science. In this paper, we investigate a simple model of a non-autonomous system with a time-dependent parameter $p(\tau)$ and its corresponding `dynamic' (time-dependent) saddle-node bifurcation by the modern theory of non-autonomous dynamical systems. We show that the actual point of no return for a system undergoing tipping can be significantly delayed in comparison to the {\em breaking time} $\hat{\tau}$ at which the corresponding autonomous system with a time-independent parameter $p_{a}= p(\hat{\tau})$ undergoes a bifurcation. A dimensionless parameter $\alpha=\lambda p_0^3V^{-2}$ is introduced, in which $\lambda$ is the curvature of the autonomous saddle-node bifurcation according to parameter $p(\tau)$, which has an initial value of $p_{0}$ and a constant rate of change $V$. We find that the breaking time $\hat{\tau}$ is always less than the actual point of no return $\tau^*$ after which the critical transition is irreversible; specifically, the relation $\tau^*-\hat{\tau}\simeq 2.338(\lambda V)^{-\frac{1}{3}}$ is analytically obtained. For a system with a small $\lambda V$, there exists a significant window of opportunity $(\hat{\tau},\tau^*)$ during which rapid reversal of the environment can save the system from catastrophe

Processes on the emergent landscapes of biochemical reaction networks and heterogeneous cell population dynamics: differentiation in living matters.

The notion of an attractor has been widely employed in thinking about the nonlinear dynamics of organisms and biological phenomena as systems and as processes. The notion of a landscape with valleys and mountains encoding multiple attractors, however, has a rigorous foundation only for closed, thermodynamically non-driven, chemical systems, such as a protein. Recent advances in the theory of nonlinear stochastic dynamical systems and its applications to mesoscopic reaction networks, one reaction at a time, have provided a new basis for a landscape of open, driven biochemical reaction systems under sustained chemostat. The theory is equally applicable not only to intracellular dynamics of biochemical regulatory networks within an individual cell but also to tissue dynamics of heterogeneous interacting cell populations. The landscape for an individual cell, applicable to a population of isogenic non-interacting cells under the same environmental conditions, is defined on the counting space of intracellular chemical composition

Hyperspectral Image Super-Resolution via Dual-domain Network Based on Hybrid Convolution

Since the number of incident energies is limited, it is difficult to directly acquire hyperspectral images (HSI) with high spatial resolution. Considering the high dimensionality and correlation of HSI, super-resolution (SR) of HSI remains a challenge in the absence of auxiliary high-resolution images. Furthermore, it is very important to extract the spatial features effectively and make full use of the spectral information. This paper proposes a novel HSI super-resolution algorithm, termed dual-domain network based on hybrid convolution (SRDNet). Specifically, a dual-domain network is designed to fully exploit the spatial-spectral and frequency information among the hyper-spectral data. To capture inter-spectral self-similarity, a self-attention learning mechanism (HSL) is devised in the spatial domain. Meanwhile the pyramid structure is applied to increase the acceptance field of attention, which further reinforces the feature representation ability of the network. Moreover, to further improve the perceptual quality of HSI, a frequency loss(HFL) is introduced to optimize the model in the frequency domain. The dynamic weighting mechanism drives the network to gradually refine the generated frequency and excessive smoothing caused by spatial loss. Finally, In order to better fully obtain the mapping relationship between high-resolution space and low-resolution space, a hybrid module of 2D and 3D units with progressive upsampling strategy is utilized in our method. Experiments on a widely used benchmark dataset illustrate that the proposed SRDNet method enhances the texture information of HSI and is superior to state-of-the-art methods

Imaging through multimode fibres with physical prior

Imaging through perturbed multimode fibres based on deep learning has been widely researched. However, existing methods mainly use target-speckle pairs in different configurations. It is challenging to reconstruct targets without trained networks. In this paper, we propose a physics-assisted, unsupervised, learning-based fibre imaging scheme. The role of the physical prior is to simplify the mapping relationship between the speckle pattern and the target image, thereby reducing the computational complexity. The unsupervised network learns target features according to the optimized direction provided by the physical prior. Therefore, the reconstruction process of the online learning only requires a few speckle patterns and unpaired targets. The proposed scheme also increases the generalization ability of the learning-based method in perturbed multimode fibres. Our scheme has the potential to extend the application of multimode fibre imaging

Super-resolution imaging through a multimode fiber: the physical upsampling of speckle-driven

Following recent advancements in multimode fiber (MMF), miniaturization of imaging endoscopes has proven crucial for minimally invasive surgery in vivo. Recent progress enabled by super-resolution imaging methods with a data-driven deep learning (DL) framework has balanced the relationship between the core size and resolution. However, most of the DL approaches lack attention to the physical properties of the speckle, which is crucial for reconciling the relationship between the magnification of super-resolution imaging and the quality of reconstruction quality. In the paper, we find that the interferometric process of speckle formation is an essential basis for creating DL models with super-resolution imaging. It physically realizes the upsampling of low-resolution (LR) images and enhances the perceptual capabilities of the models. The finding experimentally validates the role played by the physical upsampling of speckle-driven, effectively complementing the lack of information in data-driven. Experimentally, we break the restriction of the poor reconstruction quality at great magnification by inputting the same size of the speckle with the size of the high-resolution (HR) image to the model. The guidance of our research for endoscopic imaging may accelerate the further development of minimally invasive surgery