A note on property (gb) and perturbations

An operator $T \in \mathcal{B}(X)$ defined on a Banach space $X$ satisfies property $(gb)$ if the complement in the approximate point spectrum $\sigma_{a}(T)$ of the upper semi-B-Weyl spectrum $\sigma_{SBF_{+}^{-}}(T)$ coincides with the set $\Pi(T)$ of all poles of the resolvent of $T$. In this note we continue to study property $(gb)$ and the stability of it, for a bounded linear operator $T$ acting on a Banach space, under perturbations by nilpotent operators, by finite rank operators, by quasi-nilpotent operators commuting with $T$. Two counterexamples show that property $(gb)$ in general is not preserved under commuting quasi-nilpotent perturbations or commuting finite rank perturbations.Comment: 10 page

Further results on common properties of the products (ac) and (bd)

In this paper, we continue to investigate common properties of the products (ac) and $bd$ in various categories under the assumption $acd=dbd$ and $dba=aca$. These properties include generalized strongly Drazin invertibility and generalized Hirano invertibility in rings, abstract index of Fredholm elements and B-Fredholm elements in the Banach algebra context, complementability of kernels and ranges for bounded linear operators on Banach spaces

LOCALIZED SVEP AND THE COMPONENTS OF QUASI-FREDHOLM RESOLVENT SET

In this paper, new characterizations of the single valued extension property are given, for a bounded linear operator T acting on a Banach space and its adjoint T*, at Λ0 C in the case that Λ0 I - T is quasi-Fredholm. With the help of a classical perturbation result concerning operators with eventual topological uniform descent, we show the constancy of certain subspace valued mappings on the components of quasi-Fredholm resolvent set. As a consequence, we obtain a classification of these components

Porous pyroelectric ceramic with carbon nanotubes for high-performance thermal to electrical energy conversion

The recycling of low-grade thermal energy from our surroundings is an environmental-friendly approach to contribute to sustainability, which remains a grand challenge. Herein, a high-performance porous pyroelectric ceramic formed using carbon nanotubes (CNT) is designed and fabricated using a modified solid-state reaction technique. Localized characterization of PMN-PMS-PZT and PMN-PMS-PZT with 0.3 wt% CNT additions by piezoelectric force microscopy suggests that the presence of porosity and defects in grains can restrict the reversal of domains and weaken the local piezoresponse; that is due to the influence of porosity on the electric field, domain morphology, or screening effects induced by defects at the pore surface. More importantly, the porous ceramics showed enhanced figure of merits, including voltage responsibility and energy harvesting figure of merit, compared to the dense ceramic. The harvested energy increased by 208% when the 0.3 wt% of CNT was added to produce porosity, which has a potential application in thermal energy harvesting and sensing system.</p

SMPLer-X: Scaling Up Expressive Human Pose and Shape Estimation

Expressive human pose and shape estimation (EHPS) unifies body, hands, and face motion capture with numerous applications. Despite encouraging progress, current state-of-the-art methods still depend largely on a confined set of training datasets. In this work, we investigate scaling up EHPS towards the first generalist foundation model (dubbed SMPLer-X), with up to ViT-Huge as the backbone and training with up to 4.5M instances from diverse data sources. With big data and the large model, SMPLer-X exhibits strong performance across diverse test benchmarks and excellent transferability to even unseen environments. 1) For the data scaling, we perform a systematic investigation on 32 EHPS datasets, including a wide range of scenarios that a model trained on any single dataset cannot handle. More importantly, capitalizing on insights obtained from the extensive benchmarking process, we optimize our training scheme and select datasets that lead to a significant leap in EHPS capabilities. 2) For the model scaling, we take advantage of vision transformers to study the scaling law of model sizes in EHPS. Moreover, our finetuning strategy turn SMPLer-X into specialist models, allowing them to achieve further performance boosts. Notably, our foundation model SMPLer-X consistently delivers state-of-the-art results on seven benchmarks such as AGORA (107.2 mm NMVE), UBody (57.4 mm PVE), EgoBody (63.6 mm PVE), and EHF (62.3 mm PVE without finetuning). Homepage: https://caizhongang.github.io/projects/SMPLer-X/Comment: Homepage: https://caizhongang.github.io/projects/SMPLer-X

Inhibition of IRE1 alpha RNase activity reduces NLRP3 inflammasome assembly and processing of pro-IL1 beta

The inflammasome is a multiprotein complex assembled in response to Pathogen Associated Molecular Patterns (PAMPs) and Danger Associated Molecular Patterns (DAMPS). Inflammasome activation occurs through a two-step mechanism, with the first signal facilitating priming of inflammasome components while the second signal triggers complex assembly. Once assembled, the inflammasome recruits and activates pro-caspase-1, which in turn processes pro-interleukin (IL)-18 and pro-IL-1 beta into their bio-active forms. Owing to its key role in the regulation of innate immune responses, the inflammasome has emerged as a therapeutic target for the treatment of inflammatory conditions. In this study we demonstrate that IRE1 alpha, a key component of the Unfolded Protein Response, contributes to assembly of the NLRP3 inflammasome. Blockade of IRE1 alpha RNase signaling lowered NLRP3 inflammasome assembly, caspase-1 activation and pro-IL-1 beta processing. These results underscore both the importance and potential therapeutic relevance of targeting IRE1 alpha signaling in conditions of excessive inflammasome formation

Expression of Claudin-9 (CLDN9) in breast cancer, the clinical significance in connection with its subcoat anchorage proteins ZO-1 and ZO-3 and impact on drug resistance

(1) Introduction: Claudin-9 (CLDN9) is a member of the claudin protein family, a critical transmembrane protein family for tight junctions that are implemented in the progression of numerous cancer types. The present study investigated the role that CLDN9, along with the subcoat proteins, Zonula Occludens (ZOs), plays in clinical breast cancer and subsequent impact on drug response of patients. (2) Methods: CLDN9 protein and CLDN9 transcript were determined and correlated with clinical and pathological indicators, together with the status of hormonal receptors. The levels of CLDN9 transcript were also assessed against the therapeutic responses of the patients to chemotherapies by using a dataset from the TCGA database. Breast cancer cell models, representing different molecular subtypes of breast cancer, with differential expression of CLDN9 were created and used to assess the biological impact and response to chemotherapeutic drugs. (3) Results: Breast cancer tissues expressed significantly higher levels of the CLDN9, with the high levels being associated with shorter survival. CLDN9 was significantly correlated with its anchorage proteins ZO-1 and ZO-3. Integrated expression of CLDN9, ZO-1 and ZO-3 formed a signature that was significantly linked to overall survival (OS) (p = 0.013) and relapse-free survival (RFS) (p = 0.024) in an independent matter. CLDN9 transcript was significantly higher in patients who were resistant to chemotherapies (p < 0.000001). CLDN9 connection to chemoresistance was particularly prominent in patients of ER-positive (ER(+)), Her-2-negative((Her-2(−)), ER(+)/Her-2(−) and triple-negative breast cancers (TNBCs), but not in patients with HER-2-positive tumors. In Her-2-negative MCF7 and MDA-MB-231 cancer cells, loss of CLDN9 significantly increased sensitivity to several chemotherapeutic drugs including paclitaxel, gemcitabine and methotrexate, which was not seen in Her-2(+) SKBR3 cells. However, suppressing Her-2 using neratinib, a permanent Her-2 inhibitor, sensitized cellular response to these chemodrugs in cells with CLDN9 knockdown. (4) Conclusions: CLDN9 is an important prognostic indicator for patients with breast cancer and also a pivotal factor in assessing patient responses to chemotherapies. Her-2 is a negating factor for the treatment response prediction value by CLDN9 and negating Her-2 and CLDN9 may enhance breast cancer cellular response to chemotherapeutic drugs