Another unitarily invariant norm attaining the minimum norm bound for commutators

AbstractBöttcher and Wenzel recently proved that for any unitarily invariant norm ‖·‖, sup‖XY-YX‖‖X‖‖Y‖:XandYaren×nnon-zero complex matrices=C⩾2 and that C=2 when the norm is the Frobenius norm. They also asked whether the Frobenius norm is the only one having such property. In this paper, we answer the question by showing that the dual norm of the (2,2)-norm also has the property that C=2

The effects of knee joint angle on neuromuscular activity during electrostimulation in healthy older adults

Introduction Electrostimulation devices stimulate the common peroneal nerve, producing a calf muscle-pump action to promote venous circulation. Whether knee joint angle influences calf neuromuscular activity remains unclear. Our aim was to determine the effects of knee joint angle on lower limb neuromuscular activity during electrostimulation. Methods Fifteen healthy, older adults underwent 60 min of electrostimulation, with the knee joint at three different angles (0°, 45° or 90° flexion; random order; 20 min each). Outcome variables included electromyography of the peroneus longus, tibialis anterior and gastrocnemius medialis and lateralis and discomfort. Results Knee angle did not influence tibialis anterior and peroneus longus neuromuscular activity during electrostimulation. Neuromuscular activity was greater in the gastrocnemius medialis (p = 0.002) and lateralis (p = 0.002) at 90°, than 0° knee angle. Electrostimulation intensity was positively related to neuromuscular activity for each muscle, with a knee angle effect for the gastrocnemius medialis (p = 0.05). Conclusion Results suggest that during electrostimulation, knee joint angle influenced gastrocnemii neuromuscular activity; increased gastrocnemius medialis activity across all intensities (at 90°), when compared to 0° and 45° flexion; and did not influence peroneus longus and tibialis anterior activity. Greater electrostimulation-evoked gastrocnemii activity has implications for producing a more forceful calf muscle-pump action, potentially further improving venous flow

Reproducibility and day time bias correction of optoelectronic leg volumetry: a prospective cohort study

Background Leg edema is a common manifestation of various underlying pathologies. Reliable measurement tools are required to quantify edema and monitor therapeutic interventions. Aim of the present work was to investigate the reproducibility of optoelectronic leg volumetry over 3 weeks' time period and to eliminate daytime related within-individual variability. Methods Optoelectronic leg volumetry was performed in 63 hairdressers (mean age 45 ± 16 years, 85.7% female) in standing position twice within a minute for each leg and repeated after 3 weeks. Both lower leg (legBD) and whole limb (limbBF) volumetry were analysed. Reproducibility was expressed as analytical and within-individual coefficients of variance (CVA, CVW), and as intra-class correlation coefficients (ICC). Results A total of 492 leg volume measurements were analysed. Both legBD and limbBF volumetry were highly reproducible with CVA of 0.5% and 0.7%, respectively. Within-individual reproducibility of legBD and limbBF volumetry over a three weeks' period was high (CVW 1.3% for both; ICC 0.99 for both). At both visits, the second measurement revealed a significantly higher volume compared to the first measurement with a mean increase of 7.3 ml ± 14.1 (0.33% ± 0.58%) for legBD and 30.1 ml ± 48.5 ml (0.52% ± 0.79%) for limbBF volume. A significant linear correlation between absolute and relative leg volume differences and the difference of exact day time of measurement between the two study visits was found (P < .001). A therefore determined time-correction formula permitted further improvement of CVW. Conclusions Leg volume changes can be reliably assessed by optoelectronic leg volumetry at a single time point and over a 3 weeks' time period. However, volumetry results are biased by orthostatic and daytime-related volume changes. The bias for day-time related volume changes can be minimized by a time-correction formula

Nuclear-Targeted Deleted in Liver Cancer 1 (DLC1) Is Less Efficient in Exerting Its Tumor Suppressive Activity Both In Vitro and In Vivo

BACKGROUND: Deleted in liver cancer 1 (DLC1) serves as an important RhoGTPase activating protein (RhoGAP) protein that terminates active RhoA signaling in human cancers. Increasing evidence has demonstrated that the tumor suppressive activity of DLC1 depends not only on RhoGAP activity, but also relies on proper focal adhesion localization through its interaction with tensin family proteins. Recently, there are reports showing that DLC1 can also be found in the nucleus; however, the existence and the relative tumor suppressive activity of nuclear DLC1 have never been clearly addressed. METHODOLOGY AND PRINCIPAL FINDINGS: We herein provide new evidence that DLC1 protein, which predominantly associated with focal adhesions and localized in cytosol, dynamically shuttled between cytoplasm and nucleus. Treatment of cells with nuclear export blocker, Leptomycin B (LMB), retained DLC1 in the nucleus. To understand the nuclear entry of DLC1, we identified amino acids 600-700 of DLC1 as a novel region that is important for its nuclear localization. The tumor suppressive activity of nuclear DLC1 was directly assessed by employing a nuclear localization signal (NLS) fusion variant of DLC1 (NLS-DLC1) with preferential nuclear localization. In SMMC-7721 HCC cells, expression of NLS-DLC1 failed to suppress colony formation and actin stress fiber formation in vitro. The abrogated tumor suppressive activity of nuclear DLC1 was demonstrated for the first time in vivo by subcutaneously injecting p53(-/-) RasV12 hepatoblasts with stable NLS-DLC1 expression in nude mice. The injected hepatoblasts with NLS-DLC1 expression effectively formed tumors when compared with the non-nuclear targeted DLC1. CONCLUSIONS/SIGNIFICANCE: Our study identified a novel region responsible for the nuclear entry of DLC1 and demonstrated the functional difference of DLC1 in different cellular compartments both in vitro and in vivo

Disruption of p53-p21/WAF1 cell cycle pathway contributes to progression and worse clinical outcome of hepatocellular carcinoma.

p53-p21/WAF1 cell cycle pathway plays an important role in growth control, and the inappropriate deregulation of this pathway has been implicated in carcinogenesis. Although the role of p53 in hepatocellular carcinoma (HCC) has been suggested, its exact molecular mechanism in relation to its down-stream gene p21/WAF1 remains unclear. To investigate the relationship between the expression of p53 and p21/WAF1 and the possible roles of the 2 proteins in HCC, we examined the intracellular expression of p53, p21/WAF1 and PCNA immunohistochemically, together with apoptosis by terminal deoxynucleotidyl transferase-mediated deoxyuridine triphosphate nick-end labeling assay in 35 clinical tissue specimens. The correlation between the clinicopathologic parameters and the intracellular gene expression were analyzed. The results showed that p53 over-expression is a reliable marker for mutational modulation of p53 function. p53 was negatively correlated with p21/WAF1 in hepatitis B virus-related HCC (p=0.024, r=-0.432). Patients with a high p53 expression had a significantly higher Edmondson grading (12/21 vs 13/14, p=0.024) and larger tumor size (10 vs 6 cm, p=0.029). Patients with higher p53 expression had shorter disease-free survival (4 vs 19 months, p=0.0131) and overall survival (11 vs 42 months, p=0.0031). Intracellular expression of p21/WAF1 was positively correlated to proliferating cell nuclear antigen (p=0.001, r=0.776) and apoptosis (p=0.003, r=0.639). Our findings suggest that disruption of p53-p21/WAF1 cell cycle pathways contributes to tumor progression and worse clinical outcome of HCC.link_to_subscribed_fulltex