The stable index of digraphs

The stable index of a digraph $D$ is defined to be the smallest integer $k$ such that $D$ contains two distinct $(k+1)$-walks with the same initial vertex and terminal vertex if such an integer exists; otherwise the stable index of $D$ is defined to be $\infty$. We characterize the set of stable indices of digraphs with a given order

Study on Single-Polarized Holey Fibers with Double-Hole Unit Cores for Cross-Talk Free Polarization Splitter

A single-polarization single-mode (SPSM) photonic crystal fiber (PCF) based on double-hole unit core is proposed in this paper for application to cross-talk free polarization splitter (PS). Birefringence of the PCF is obtained by adopting double-hole unit cells into the core to destroy its symmetry. With an appropriate cladding hole size, single x- or y-polarized PCF can be achieved by arranging the double-hole unit in the core along the x- or y-axis, respectively. Moreover, our proposed SPSM PCF has the potential to be applied to consist a cross-talk free PS. The simulation result by employing a vectorial finite element beam propagation method (FE-BPM) demonstrates that an arbitrary polarized incident light can be completely separated into two orthogonal single-polarized components through the PS. The structural tolerance and wavelength dependence of the PS have also been discussed in detail

Optical and chemical control of the wettability of nanoporous photoswitchable films

Wettability is a central surface property of functional thin films. Here, we present a nanoporous film made of an azobenzene-containing metal-organic framework material where the wettability is controlled by photoswitching of the fluorinated azobenzene moieties and by reversible incorporation of guest molecules with different polarities in the pores. Using both, the optical and the chemical stimuli, the water contact angle was modified over a wide range, from 23° to 97°

Optical and chemical control of the wettability of nanoporous photoswitchable films

Wettability is a central surface property of functional thin films. Here, we present a nanoporous film made of an azobenzene-containing metal-organic framework material where the wettability is controlled by photoswitching of the fluorinated azobenzene moieties and by reversible incorporation of guest molecules with different polarities in the pores. Using both, the optical and the chemical stimuli, the water contact angle was modified over a wide range, from 23° to 97°

High-efficient deep learning-based DTI reconstruction with flexible diffusion gradient encoding scheme

Purpose: To develop and evaluate a novel dynamic-convolution-based method called FlexDTI for high-efficient diffusion tensor reconstruction with flexible diffusion encoding gradient schemes. Methods: FlexDTI was developed to achieve high-quality DTI parametric mapping with flexible number and directions of diffusion encoding gradients. The proposed method used dynamic convolution kernels to embed diffusion gradient direction information into feature maps of the corresponding diffusion signal. Besides, our method realized the generalization of a flexible number of diffusion gradient directions by setting the maximum number of input channels of the network. The network was trained and tested using data sets from the Human Connectome Project and a local hospital. Results from FlexDTI and other advanced tensor parameter estimation methods were compared. Results: Compared to other methods, FlexDTI successfully achieves high-quality diffusion tensor-derived variables even if the number and directions of diffusion encoding gradients are variable. It increases peak signal-to-noise ratio (PSNR) by about 10 dB on Fractional Anisotropy (FA) and Mean Diffusivity (MD), compared with the state-of-the-art deep learning method with flexible diffusion encoding gradient schemes. Conclusion: FlexDTI can well learn diffusion gradient direction information to achieve generalized DTI reconstruction with flexible diffusion gradient schemes. Both flexibility and reconstruction quality can be taken into account in this network.Comment: 11 pages,6 figures,3 table

Deep Learning in Predicting Real Estate Property Prices: A Comparative Study

The dominant methods for real estate property price prediction or valuation are multi-regression based. Regression-based methods are, however, imperfect because they suffer from issues such as multicollinearity and heteroscedasticity. Recent years have witnessed the use of machine learning methods but the results are mixed. This paper introduces the application of a new approach using deep learning models to real estate property price prediction. The paper uses a deep learning approach for modeling to improve the accuracy of real estate property price prediction with data representing sales transactions in a large metropolitan area. Three deep learning models, LSTM, GRU and Transformer, are created and compared with other machine learning and traditional models. The results obtained for the data set with all features clearly show that the RF and Transformer models outperformed the other models. LSTM and GRU models produced the worst results, suggesting that they are perhaps not suitable to predict the real estate price. Furthermore, the implementations of Transformer and RF on a data set with feature reduction produced even more accurate prediction results. In conclusion, our research shows that the performance of the Transformer model is close to the RF model. Both models produce significantly better prediction results than existing approaches in terms of accuracy

Graph Contrastive Learning with Implicit Augmentations

Existing graph contrastive learning methods rely on augmentation techniques based on random perturbations (e.g., randomly adding or dropping edges and nodes). Nevertheless, altering certain edges or nodes can unexpectedly change the graph characteristics, and choosing the optimal perturbing ratio for each dataset requires onerous manual tuning. In this paper, we introduce Implicit Graph Contrastive Learning (iGCL), which utilizes augmentations in the latent space learned from a Variational Graph Auto-Encoder by reconstructing graph topological structure. Importantly, instead of explicitly sampling augmentations from latent distributions, we further propose an upper bound for the expected contrastive loss to improve the efficiency of our learning algorithm. Thus, graph semantics can be preserved within the augmentations in an intelligent way without arbitrary manual design or prior human knowledge. Experimental results on both graph-level and node-level tasks show that the proposed method achieves state-of-the-art performance compared to other benchmarks, where ablation studies in the end demonstrate the effectiveness of modules in iGCL