A lower bound for the spectral gap of the conjugate Kac process with 3 interacting particles

<p style='text-indent:20px;'>In this paper, we proceed as suggested in the final section of [<xref ref-type="bibr" rid="b2">2</xref>] and prove a lower bound for the spectral gap of the conjugate Kac process with 3 interacting particles. This bound turns out to be around <inline-formula><tex-math id="M1">\begin{document}$ 0.02 $\end{document}</tex-math></inline-formula>, which is already physically meaningful, and we perform Monte Carlo simulations to provide a better empirical estimate for this value via entropy production inequalities. This finishes a complete quantitative estimate of the spectral gap of the Kac process.</p>

Predicting porosity, permeability, and tortuosity of porous media from images by deep learning

Convolutional neural networks (CNN) are utilized to encode the relation between initial configurations of obstacles and three fundamental quantities in porous media: porosity ($$\varphi$$ φ ), permeability (k), and tortuosity (T). The two-dimensional systems with obstacles are considered. The fluid flow through a porous medium is simulated with the lattice Boltzmann method. The analysis has been performed for the systems with $$\varphi \in (0.37,0.99)$$ φ ∈ ( 0.37 , 0.99 ) which covers five orders of magnitude a span for permeability $$k \in (0.78, 2.1\times 10^5)$$ k ∈ ( 0.78 , 2.1 × 10 5 ) and tortuosity $$T \in (1.03,2.74)$$ T ∈ ( 1.03 , 2.74 ) . It is shown that the CNNs can be used to predict the porosity, permeability, and tortuosity with good accuracy. With the usage of the CNN models, the relation between T and $$\varphi$$ φ has been obtained and compared with the empirical estimate.

DC-MMD-GAN: A New Maximum Mean Discrepancy Generative Adversarial Network Using Divide and Conquer

Generative adversarial networks (GANs) have a revolutionary influence on sample generation. Maximum mean discrepancy GANs (MMD-GANs) own competitive performance when compared with other GANs. However, the loss function of MMD-GANs is an empirical estimate of maximum mean discrepancy (MMD) and not precise in measuring the distance between sample distributions, which inhibits MMD-GANs training. We propose an efficient divide-and-conquer model, called DC-MMD-GANs, which constrains the loss function of MMD to tight bound on the deviation between empirical estimate and expected value of MMD and accelerates the training process. DC-MMD-GANs contain a division step and conquer step. In the division step, we learn the embedding of training images based on auto-encoder, and partition the training images into adaptive subsets through k-means clustering based on the embedding. In the conquer step, sub-models are fed with subsets separately and trained synchronously. The loss function values of all sub-models are integrated to compute a new weight-sum loss function. The new loss function with tight deviation bound provides more precise gradients for improving performance. Experimental results show that with a fixed number of iterations, DC-MMD-GANs can converge faster, and achieve better performance compared with the standard MMD-GANs on celebA and CIFAR-10 datasets.

Spiny lobster fisheries status across time and a mosaic of spatial management regimes

In Belize, the commercial harvest of spiny lobsters has occurred for ∼100 years, provides critical livelihoods, and is the primary seafood export. We determined the first empirical estimate of size at maturity in Belize as well as eight fishery status indicators on several fishing grounds. The carapace lengths (CLs) at 50% maturity varied between males (98 mm) and females (86 mm) and are higher than the existing legal minimum of 76 mm. Time series analysis indicated decreasing proportions of mature individuals, decreasing size, and low spawning potential ratios (SPR) as well as high fishing mortality within fishing grounds. The pattern of decline in population status indicators across fishing grounds is consistent with a historical expansion of effort from north to south and offshore. Many indicators of population status within fishing grounds were improved with increasing area of replenishment zone and opposite to the historical expansion. However, overfishing is a problem across all areas examined. An increase in the legal minimum CL to 86 mm and examination of a maximum size limit will likely have significant positive effects on productivity and SPR, respectively, as well as protecting the pivotal role of spiny lobsters within the ecosystem.