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Inocybe is the largest genus in the family Inocybaceae, with approximately 1000 species worldwide. Basic data on the species diversity, geographic distribution, and the infrageneric framework of Inocybe are still incomplete because of the intricate nature of this genus, which includes numerous unrecognized taxa that exist around the world. A multigene phylogeny of the I. umbratica–paludinella group, initially designated as the “I. angustifolia subgroup”, was conducted using the ITS-28S-rpb2 nucleotide datasets. The seven species, I. alabamensis, I. angustifolia, I. argenteolutea, I. olivaceonigra, I. paludinella, I. subangustifolia, and I. umbratica, were confirmed as members of this species group. At the genus level, the I. umbratica–paludinella group is a sister to the lineage of the unifying I. castanea and an undescribed species. Inocybe sect. Umbraticae sect. nov. was proposed to accommodate species in the I. umbratica–paludinella group and the I. castanea lineage. This section now comprises eight documented species and nine new species from China, as described in this paper. Additionally, new geographical distributions of I. angustifolia and I. castanea in China are reported. The nine new species and I. angustifolia, I. castanea, I. olivaceonigra, and I. umbratica are described in detail and illustrated herein with color plates based on Chinese materials. A global key to 17 species in the section Umbraticae is provided. The results of the current study provide a more detailed basis for the accurate identification of species in the I. umbratica-paludinella group and a better understanding of their phylogenetic placement. 

Homomorphic Encryption (HE) based secure Neural Networks(NNs) inference is one of the most promising security solutions to emerging Machine Learning as a Service (MLaaS). In the HE-based MLaaS setting, a client encrypts the sensitive data, and uploads the encrypted data to the server that directly processes the encrypted data without decryption, and returns the encrypted result to the client. The clients' data privacy is preserved since only the client has the private key. Existing HE-enabled Neural Networks (HENNs), however, suffer from heavy computational overheads. The state-of-the-art HENNs adopt ciphertext packing techniques to reduce homomorphic multiplications by packing multiple messages into one single ciphertext. Nevertheless, rotations are required in these HENNs to implement the sum of the elements within the same ciphertext. We observed that HENNs have to pay significant computing overhead on rotations, and each of rotations is ∼10× more expensive than homomorphic multiplications between ciphertext and plaintext. So the massive rotations have become a primary obstacle of efficient HENNs. In this paper, we propose a fast, frequency-domain deep neural network called Falcon, for fast inferences on encrypted data. Falcon includes a fast Homomorphic Discrete Fourier Transform (HDFT) using block-circulant matrices to homomorphically support spectral operations. We also propose several efficient methods to reduce inference latency, including Homomorphic Spectral Convolution and Homomorphic Spectral Fully Connected operations by combing the batched HE and block-circulant matrices. Our experimental results show Falcon achieves the state-of-the-art inference accuracy and reduces the inference latency by 45.45%∼85.34% over prior HENNs on MNIST and CIFAR-10.