Representations in complete and irreducible forms for tensor functions allow general consistent invariant forms of the nonlinear constitutive equations and specify the number and type of the scalar variables involved. They have proved to be even more pertinent in attempts to model mechanical behavior of anisotropic materials, since here invariant conditions predominate and the number and type of independent scalar variables cannot be found by simple arguments. In the last few years, the theory of representations for tensor functions has been well established, including three fundamental principles, a number of essential theorems and a large amount of complete and irreducible representations for both isotropic and anisotropic tensor functions in three- and two-dimensional physical spaces. The objective of the present monograph is to summarize and recapitulate the up-to-date developments and results in the theory of representations for tensor functions for the convenience of further applications in contemporary applied mechanics. Some general topics on unified invariant formulation of constitutive laws are investigated.

Endothelial cell proliferation is a critical step in angiogenesis and requires a coordinated response to soluble growth factors and the extracellular matrix. As focal adhesion kinase (FAK) integrates signals from both adhesion events and growth factor stimulation, we investigated its role in endothelial cell proliferation. Expression of a dominant-negative FAK protein, FAK-related nonkinase (FRNK), impaired phosphorylation of FAK and blocked DNA synthesis in response to multiple angiogenic stimuli. These results coincided with elevated cyclin-dependent kinase inhibitors (CDKIs) p21/Cip and p27/Kip, as a consequence of impaired degradation. FRNK inhibited the expression of Skp2, an F-box protein that targets CDKIs, by inhibiting mitogen-induced mRNA. The FAK-regulated degradation of p27/Kip was Skp2 dependent, while levels of p21/Cip were regulated independent of Skp2. Skp2 is required for endothelial cell proliferation as a consequence of degrading p27. Finally, knockdown of both p21 and p27 in FRNK-expressing cells completely restored mitogen-induced endothelial cell proliferation. These data demonstrate a critical role for FAK in the regulation of CDKIs through two independent mechanisms: Skp2 dependent and Skp2 independent. They also provide important insights into the requirement of focal adhesion kinase for normal vascular development and reveal novel regulatory control points for angiogenesis.

Neurofibromatosis is a well known familial tumor syndrome, however these patients also suffer from a number of vascular anomalies. The loss of NFl from the endothelium is embryonically lethal in mouse developmental models, however little is known regarding the molecular regulation by NF1 in endothelium. We investigated the consequences of losing NF1 expression on the function of endothelial cells using shRNA. The loss of NF1 was sufficient to elevate levels of active Ras under non-stimulated conditions. These elevations in Ras activity were associated with activation of downstream signaling including activation of ERK, AKT and mTOR. Cells knocked down in NF1 expression exhibited no cellular senescence. Rather, they demonstrated augmented proliferation and autonomous entry into the cell cycle. These proliferative changes were accompanied by enhanced expression of cyclin D, phosphorylation of p27KIP, and decreases in total p27KIP levels, even under growth factor free conditions. In addition, NF1-deficient cells failed to undergo normal branching morphogenesis in a co-culture assay, instead forming planar islands with few tubules and branches. We find the changes induced by the loss of NF1 could be mitigated by co-expression of the GAP-related domain of NF1 implicating Ras regulation in these effects. Using doxycycline-inducible shRNA, targeting NF1, we find that the morphogenic changes are reversible. Similarly, in fully differentiated and stable vascular-like structures, the silencing of NF1 results in the appearance of abnormal vascular structures. Finally, the proliferative changes and the abnormal vascular morphogenesis are normalized by low-dose rapamycin treatment. These data provide a detailed analysis of the molecular and functional consequences of NF1 loss in human endothelial cells. These insights may provide new approaches to therapeutically addressing vascular abnormalities in these patients while underscoring a critical role for normal Ras regulation in maintaining the health and function of the vasculature.

Breast cancer heterogeneity determines cancer progression, treatment effects, and prognosis. However, the precise mechanism for this heterogeneity remains unknown owing to its complexity. Here, we summarize the origins of breast cancer heterogeneity and its influence on disease progression, recurrence, and therapeutic resistance. We review the possible mechanisms of heterogeneity and the research methods used to analyze it. We also highlight the importance of cell interactions for the origins of breast cancer heterogeneity, which can be further categorized into cooperative and competitive interactions. Finally, we provide new insights into precise individual treatments based on heterogeneity.

We report a novel phenomenon in carbon nanotube (CNT) based devices, the transphonon effects, which resemble the transonic effects in aerodynamics. It is caused by dissipative resonance of nanotube phonons similar to the radial breathing mode, and subsequent drastic surge of the dragging force on the sliding tube, and multiple phonon barriers are encountered as the intertube sliding velocity reaches critical values. It is found that the transphonon effects can be tuned by applying geometric constraints or varying chirality combinations of the nanotubes.It was widely perceived prior to World War II that supersonic flights were prohibited by the sound barrier due to catastrophes that occurred when flying vessels approached the sound speed. Thanks to von Karman and many other pioneers, great progress has been made to understand the transonic effect which had caused drastic reductions of the plane-lifting forces in the catastrophic events. Consequently, supersonic flights have become reality 1 . Figure 1A depicts a US navy aircraft flying at or near the speed of sound. A condensation cloud was generated around the aircraft due to the transonic effect. Now imagine a nanoscale train travelling inside a nanoscale tunnel. Will similar speed barriers be encountered by the superfast nano-train? We have performed a molecular dynamics study of a fasting moving carbon nanotube inside a