Nonnegative Tensor Factorization, Completely Positive Tensors and an Hierarchical Elimination Algorithm

Nonnegative tensor factorization has applications in statistics, computer vision, exploratory multiway data analysis and blind source separation. A symmetric nonnegative tensor, which has a symmetric nonnegative factorization, is called a completely positive (CP) tensor. The H-eigenvalues of a CP tensor are always nonnegative. When the order is even, the Z-eigenvalue of a CP tensor are all nonnegative. When the order is odd, a Z-eigenvector associated with a positive (negative) Z-eigenvalue of a CP tensor is always nonnegative (nonpositive). The entries of a CP tensor obey some dominance properties. The CP tensor cone and the copositive tensor cone of the same order are dual to each other. We introduce strongly symmetric tensors and show that a symmetric tensor has a symmetric binary decomposition if and only if it is strongly symmetric. Then we show that a strongly symmetric, hierarchically dominated nonnegative tensor is a CP tensor, and present a hierarchical elimination algorithm for checking this. Numerical examples are also given

Inhibition of GABAergic Neurotransmission by HIV-1 Tat and Opioid Treatment in the Striatum Involves μ-Opioid Receptors

Due to combined antiretroviral therapy (cART), human immunodeficiency virus type 1 (HIV-1) is considered a chronic disease with high prevalence of mild forms of neurocognitive impairments, also referred to as HIV-associated neurocognitive disorders (HAND). Although opiate drug use can exacerbate HIV-1 Tat-induced neuronal damage, it remains unknown how and to what extent opioids interact with Tat on the GABAergic system. We conducted whole-cell recordings in mouse striatal slices and examined the effects of HIV-1 Tat in the presence and absence of morphine (1 μM) and damgo (1 μM) on GABAergic neurotransmission. Results indicated a decrease in the frequency and amplitude of spontaneous inhibitory postsynaptic currents (sIPSCs) and miniature IPSCs (mIPSCs) by Tat (5 – 50 nM) in a concentration-dependent manner. The significant Tat-induced decrease in IPSCs was abolished when removing extracellular and/or intracellular calcium. Treatment with morphine or damgo alone significantly decreased the frequency, but not amplitude of IPSCs. Interestingly, morphine but not damgo indicated an additional downregulation of the mean frequency of mIPSCs in combination with Tat. Pretreatment with naloxone (1 μM) and CTAP (1 μM) prevented the Tat-induced decrease in sIPSCs frequency but only naloxone prevented the combined Tat and morphine effect on mIPSCs frequency. Results indicate a Tat- or opioid-induced decrease in GABAergic neurotransmission via µ-opioid receptors with combined Tat and morphine effects involving additional opioid receptor-related mechanisms. Exploring the interactions between Tat and opioids on the GABAergic system may help to guide future research on HAND in the context of opiate drug use

Inhibition of GABAergic Neurotransmission by HIV-1 Tat and Opioid Treatment in the Striatum Involves μ-Opioid Receptors

Due to combined antiretroviral therapy (cART), human immunodeficiency virus type 1 (HIV-1) is considered a chronic disease with high prevalence of mild forms of neurocognitive impairments, also referred to as HIV-associated neurocognitive disorders (HAND). Although opiate drug use can exacerbate HIV-1 Tat-induced neuronal damage, it remains unknown how and to what extent opioids interact with Tat on the GABAergic system. We conducted whole-cell recordings in mouse striatal slices and examined the effects of HIV-1 Tat in the presence and absence of morphine (1 μM) and damgo (1 μM) on GABAergic neurotransmission. Results indicated a decrease in the frequency and amplitude of spontaneous inhibitory postsynaptic currents (sIPSCs) and miniature IPSCs (mIPSCs) by Tat (5–50 nM) in a concentration-dependent manner. The significant Tat-induced decrease in IPSCs was abolished when removing extracellular and/or intracellular calcium. Treatment with morphine or damgo alone significantly decreased the frequency, but not amplitude of IPSCs. Interestingly, morphine but not damgo indicated an additional downregulation of the mean frequency of mIPSCs in combination with Tat. Pretreatment with naloxone (1 μM) and CTAP (1 μM) prevented the Tat-induced decrease in sIPSCs frequency but only naloxone prevented the combined Tat and morphine effect on mIPSCs frequency. Results indicate a Tat- or opioid-induced decrease in GABAergic neurotransmission via μ-opioid receptors with combined Tat and morphine effects involving additional opioid receptor-related mechanisms. Exploring the interactions between Tat and opioids on the GABAergic system may help to guide future research on HAND in the context of opiate drug use

SLSSNN: High energy efficiency spike-train level spiking neural networks with spatio-temporal conversion

Brain-inspired spiking neuron networks (SNNs) have attracted widespread research interest due to their low power features, high biological plausibility, and strong spatiotemporal information processing capability. Although adopting a surrogate gradient (SG) makes the non-differentiability SNN trainable, achieving comparable accuracy for ANNs and keeping low-power features simultaneously is still tricky. In this paper, we proposed an energy-efficient spike-train level spiking neural network (SLSSNN) with low computational cost and high accuracy. In the SLSSNN, spatio-temporal conversion blocks (STCBs) are applied to replace the convolutional and ReLU layers to keep the low power features of SNNs and improve accuracy. However, SLSSNN cannot adopt backpropagation algorithms directly due to the non-differentiability nature of spike trains. We proposed a suitable learning rule for SLSSNNs by deducing the equivalent gradient of STCB. We evaluate the proposed SLSSNN on static and neuromorphic datasets, including Fashion-Mnist, Cifar10, Cifar100, TinyImageNet, and DVS-Cifar10. The experiment results show that our proposed SLSSNN outperforms the state-of-the-art accuracy on nearly all datasets, using fewer time steps and being highly energy-efficient