Representations for the Drazin inverse of the sum P+Q+R+S and its applications

AbstractLet P, Q, R and S be complex square matrices and M=P+Q+R+S. A quadruple (P,Q,R,S) is called a pseudo-block decomposition of M ifPQ=QP=0PS=SQ=QR=RP=0andRD=SD=0,where RD and SD are the Drazin inverses of R and S, respectively. We investigate the problem of finding formulae for the Drazin inverse of M. The explicit representations for the Drazin inverses of M and P+Q+R are developed, under some assumptions. As its application, some representations are presented for 2×2 block matricesAB0CandABDC, where the blocks A and C are square matrices. Several results of this paper extend the well known representation for the Drazin inverse ofAB0Cgiven by Hartwig and Shoaf, Meyer and Rose in 1977. An illustrative example is given to verify our new representations

CR-SFP: Learning Consistent Representation for Soft Filter Pruning

Soft filter pruning~(SFP) has emerged as an effective pruning technique for allowing pruned filters to update and the opportunity for them to regrow to the network. However, this pruning strategy applies training and pruning in an alternative manner, which inevitably causes inconsistent representations between the reconstructed network~(R-NN) at the training and the pruned network~(P-NN) at the inference, resulting in performance degradation. In this paper, we propose to mitigate this gap by learning consistent representation for soft filter pruning, dubbed as CR-SFP. Specifically, for each training step, CR-SFP optimizes the R-NN and P-NN simultaneously with different distorted versions of the same training data, while forcing them to be consistent by minimizing their posterior distribution via the bidirectional KL-divergence loss. Meanwhile, the R-NN and P-NN share backbone parameters thus only additional classifier parameters are introduced. After training, we can export the P-NN for inference. CR-SFP is a simple yet effective training framework to improve the accuracy of P-NN without introducing any additional inference cost. It can also be combined with a variety of pruning criteria and loss functions. Extensive experiments demonstrate our CR-SFP achieves consistent improvements across various CNN architectures. Notably, on ImageNet, our CR-SFP reduces more than 41.8\% FLOPs on ResNet18 with 69.2\% top-1 accuracy, improving SFP by 2.1\% under the same training settings. The code will be publicly available on GitHub.Comment: 11 pages, 4 figure

ABT-869, a promising multi-targeted tyrosine kinase inhibitor: from bench to bedside

Tyrosine Kinase Inhibitors (TKI) have significantly changed the landscape of current cancer therapy. Understanding of mechanisms of aberrant TK signaling and strategies to inhibit TKs in cancer, further promote the development of novel agents

PRL-3, a Metastasis Associated Tyrosine Phosphatase, Is Involved in FLT3-ITD Signaling and Implicated in Anti-AML Therapy

Combination with other small molecule drugs represents a promising strategy to improve therapeutic efficacy of FLT3 inhibitors in the clinic. We demonstrated that combining ABT-869, a FLT3 inhibitor, with SAHA, a HDAC inhibitor, led to synergistic killing of the AML cells with FLT3 mutations and suppression of colony formation. We identified a core gene signature that is uniquely induced by the combination treatment in 2 different leukemia cell lines. Among these, we showed that downregulation of PTP4A3 (PRL-3) played a role in this synergism. PRL-3 is downstream of FLT3 signaling and ectopic expression of PRL-3 conferred therapeutic resistance through upregulation of STAT (signal transducers and activators of transcription) pathway activity and anti-apoptotic Mcl-1 protein. PRL-3 interacts with HDAC4 and SAHA downregulates PRL-3 via a proteasome dependent pathway. In addition, PRL-3 protein was identified in 47% of AML cases, but was absent in myeloid cells in normal bone marrows. Our results suggest such combination therapies may significantly improve the therapeutic efficacy of FLT3 inhibitors. PRL-3 plays a potential pathological role in AML and it might be a useful therapeutic target in AML, and warrant clinical investigation

Baicalein-corrected gut microbiota may underlie the amelioration of memory and cognitive deficits in APP/PS1 mice

Background: Baicalein is an active ingredient extracted from the root of S. baicalensis Georgi, which exhibits cardiovascular protection, anti-inflammatory, and anti-microbial properties. Our previous study showed that chronic treatment of Baicalein ameliorated cognitive dysfunction in a mouse model of Alzheimer's disease (AD). However, it remains unknown whether Baicalein ameliorates cognitive deficits in AD mouse models by altering gut microbiota and its metabolites.Methods: Behavioral tests, metagenomic and untargeted metabolomics analyses were used to evaluate the effects of Baicalein on the APP/PS1 mice.Results: Our research showed that treatment of Baicalein for 2 weeks ameliorated cognition and memory in a dose-dependent manner, as indicated by the significant increases in the Discrimination index and Number of crossings and decrease in latency to the previous platform location in 8-month of age APP/PS1 mice in novel object recognition and water maze tests. The metagenomic analysis showed the abundance of the dominant phyla in all groups, including Bacteroidetes (14.59%–67.02%) and Firmicutes (20.19%–61.39%). LEfSe analysis of metagenomics identified three species such as s__Roseburia_sp_1XD42_69, s__Muribaculaceae_bacterium_Isolate_104_HZI, s__Muribaculaceae_bacterium_Isolate_110_HZI as Baicalein-treated potential biomarkers. Metabolite analysis revealed the increment of metabolites, including glutamate, thymine and hexanoyl-CoA.Conclusion: The effects of Baicalein on memory and cognition may relate to the metabolism of nucleotides, lipids and glucose

Aberrant non-canonical NF-κB signalling reprograms the epigenome landscape to drive oncogenic transcriptomes in multiple myeloma

In multiple myeloma, abnormal plasma cells establish oncogenic niches within the bone marrow by engaging the NF-κB pathway to nurture their survival while they accumulate pro-proliferative mutations. Under these conditions, many cases eventually develop genetic abnormalities endowing them with constitutive NF-κB activation. Here, we find that sustained NF-κB/p52 levels resulting from such mutations favours the recruitment of enhancers beyond the normal B-cell repertoire. Furthermore, through targeted disruption of p52, we characterise how such enhancers are complicit in the formation of super-enhancers and the establishment of cis-regulatory interactions with myeloma dependencies during constitutive activation of p52. Finally, we functionally validate the pathological impact of these cis-regulatory modules on cell and tumour phenotypes using in vitro and in vivo models, confirming RGS1 as a p52-dependent myeloma driver. We conclude that the divergent epigenomic reprogramming enforced by aberrant non-canonical NF-κB signalling potentiates transcriptional programs beneficial for multiple myeloma progression

The Slow-Releasing Hydrogen Sulfide Donor, GYY4137, Exhibits Novel Anti-Cancer Effects In Vitro and In Vivo

The slow-releasing hydrogen sulfide (H2S) donor, GYY4137, caused concentration-dependent killing of seven different human cancer cell lines (HeLa, HCT-116, Hep G2, HL-60, MCF-7, MV4-11 and U2OS) but did not affect survival of normal human lung fibroblasts (IMR90, WI-38) as determined by trypan blue exclusion. Sodium hydrosulfide (NaHS) was less potent and not active in all cell lines. A structural analogue of GYY4137 (ZYJ1122) lacking sulfur and thence not able to release H2S was inactive. Similar results were obtained using a clonogenic assay. Incubation of GYY4137 (400 µM) in culture medium led to the generation of low (<20 µM) concentrations of H2S sustained over 7 days. In contrast, incubation of NaHS (400 µM) in the same way led to much higher (up to 400 µM) concentrations of H2S which persisted for only 1 hour. Mechanistic studies revealed that GYY4137 (400 µM) incubated for 5 days with MCF-7 but not IMR90 cells caused the generation of cleaved PARP and cleaved caspase 9, indicative of a pro-apoptotic effect. GYY4137 (but not ZYJ1122) also caused partial G2/M arrest of these cells. Mice xenograft studies using HL-60 and MV4-11 cells showed that GYY4137 (100–300 mg/kg/day for 14 days) significantly reduced tumor growth. We conclude that GYY4137 exhibits anti-cancer activity by releasing H2S over a period of days. We also propose that a combination of apoptosis and cell cycle arrest contributes to this effect and that H2S donors should be investigated further as potential anti-cancer agents

THE INVERSE EIGENVALUE PROBLEM FOR REAL EVENTUALLY POSITIVE MATRICES 9

The eventually positive inverse eigenvalue problem(EPIEP) asks when a list σ = (ρ, λ2,..., λn) of n complex numbers is the spectrum of a real n × n eventually positive matrix. In this paper, a constructive method is presented to solve the EPIEP. Using this method, it is easy to find the realizing matrix, i.e., a real eventually positive matrix with the spectrum σ. And a complete answer to the EPIEP prescribed the left and the right Perron eigenvectors of the realizing matrix is also given. 1