Minimum-Energy Bivariate Wavelet Frame with Arbitrary Dilation Matrix

In order to characterize the bivariate signals, minimum-energy bivariate wavelet frames with arbitrary dilation matrix are studied, which are based on superiority of the minimum-energy frame and the significant properties of bivariate wavelet. Firstly, the concept of minimum-energy bivariate wavelet frame is defined, and its equivalent characterizations and a necessary condition are presented. Secondly, based on polyphase form of symbol functions of scaling function and wavelet function, two sufficient conditions and an explicit constructed method are given. Finally, the decomposition algorithm, reconstruction algorithm, and numerical examples are designed

Minimum-Energy Multiwavelet Frames with Arbitrary Integer Dilation Factor

In order to organically combine the minimum-energy frame with the significant properties of multiwavelets, minimum-energy multiwavelet frames with arbitrary integer dilation factor are studied. Firstly, we define the concept of minimum-energy multiwavelet frame with arbitrary dilation factor and present its equivalent characterizations. Secondly, some necessary conditions and sufficient conditions for minimum-energy multiwavelet frame are given. Thirdly, the decomposition and reconstruction formulas of minimum-energy multiwavelet frame with arbitrary integer dilation factor are deduced. Finally, we give several numerical examples based on B-spline functions

Minimum-Energy Bivariate Wavelet Frame with Arbitrary Dilation Matrix

In order to characterize the bivariate signals, minimum-energy bivariate wavelet frames with arbitrary dilation matrix are studied, which are based on superiority of the minimum-energy frame and the significant properties of bivariate wavelet. Firstly, the concept of minimum-energy bivariate wavelet frame is defined, and its equivalent characterizations and a necessary condition are presented. Secondly, based on polyphase form of symbol functions of scaling function and wavelet function, two sufficient conditions and an explicit constructed method are given. Finally, the decomposition algorithm, reconstruction algorithm, and numerical examples are designed

Minimum-Energy Multiwavelet Frame on the Interval [0,1]

Drawing inspiration from the idea of combining multiwavelets on the interval with frame theory organically, we study minimum-energy multiwavelet frame on the interval [0,1] (MEMWFI). Firstly, left boundary multiscaling functions, right boundary multiscaling functions, and the definition of MEMWFI are put forward, and the equivalent characterizations of MEMWFI are given. Then, two algorithms of constructing MEMWFI are proposed. Finally, the decomposition formula, reconstruction formulas, and numerical examples are given

Activation Template Matching Loss for Explainable Face Recognition

Can we construct an explainable face recognition network able to learn a facial part-based feature like eyes, nose, mouth and so forth, without any manual annotation or additionalsion datasets? In this paper, we propose a generic Explainable Channel Loss (ECLoss) to construct an explainable face recognition network. The explainable network trained with ECLoss can easily learn the facial part-based representation on the target convolutional layer, where an individual channel can detect a certain face part. Our experiments on dozens of datasets show that ECLoss achieves superior explainability metrics, and at the same time improves the performance of face verification without face alignment. In addition, our visualization results also illustrate the effectiveness of the proposed ECLoss.Comment: 13 pages, 7 figures, 5 table

Proper development of relay somatic sensory neurons and D2/D4 interneurons requires homeobox genes Rnx/Tlx-3 and Tlx-1

Trigeminal nuclei and the dorsal spinal cord are first-order relay stations for processing somatic sensory information such as touch, pain, and temperature. The origins and development of these neurons are poorly understood. Here we show that relay somatic sensory neurons and D2/D4 dorsal interneurons likely derive from Mash1-positive neural precursors, and depend on two related homeobox genes, Rnx and Tlx-1, for proper formation. Rnx and Tlx-1 maintain expression of Drg11, a homeobox gene critical for the development of pain circuitry, and are essential for the ingrowth of trkA+ nociceptive/thermoceptive sensory afferents to their central targets. We showed previously that Rnx is necessary for proper formation of the nucleus of solitary tract, the target for visceral sensory afferents. Together, our studies demonstrate a central role for Rnx and Tlx-1 in the development of two major classes of relay sensory neurons, somatic and visceral

Suppression of Cancer Cell Stemness and Drug Resistance via MYC Destabilization by Deubiquitinase USP45 Inhibition with a Natural Small Molecule

Cancer stem cells (CSCs) play significant roles in cancer development, drug resistance and cancer recurrence. In cancer treatments based on the CSC characteristics and inducing factors, MYC is a promising target for therapeutic molecules. Although it has been regarded as an undrugable target, its stability tightly regulated by the ubiquitin–proteasome system offers a new direction for molecule targeting and cancer treatment. Herein we report our discoveries in this research area, and we have found that deubiquitinase USP45 can directly bind with MYC, resulting in its deubiquitination and stabilization. Further, USP45 overexpressing can upregulate MYC, and this overexpressing can significantly enhance cancer development, cancer cell stemness and drug resistance. Interestingly, without enhancing cancer development, MYC silencing with shRNA can only suppress USP45-induced stemness and drug resistance. Moreover, we have identified that USP45 can be specifically bound and inhibited by a natural small molecule (α-mangostin), in turn significantly suppressing USP45-induced stemness and drug resistance. Since USP45 is significantly expressed in cervical tumors, we have discovered that the combination of α-mangostin and doxorubicin can significantly inhibit USP45-induced cervical tumorigenesis in an animal model. In general, on the basis of our USP45 discoveries on its MYC deubiquitination and α-mangostin inhibition, suppressing USP45 has opened a new window for suppressing cancer development, stemness and drug resistance