Tight frames of k-plane ridgelets and the problem of representing objects that are smooth away from d-dimensional singularities in Rn

For each pair (n, k) with 1 ≤ k < n, we construct a tight frame (ρλ : λ ∈ Λ) for L2 (Rn), which we call a frame of k-plane ridgelets. The intent is to efficiently represent functions that are smooth away from singularities along k-planes in Rn. We also develop tools to help decide whether k-plane ridgelets provide the desired efficient representation. We first construct a wavelet-like tight frame on the X-ray bundle χn,k—the fiber bundle having the Grassman manifold Gn,k of k-planes in Rn for base space, and for fibers the orthocomplements of those planes. This wavelet-like tight frame is the pushout to χn,k, via the smooth local coordinates of Gn,k, of an orthonormal basis of tensor Meyer wavelets on Euclidean space Rk(n−k) × Rn−k. We then use the X-ray isometry [Solmon, D. C. (1976) J. Math. Anal. Appl. 56, 61–83] to map this tight frame isometrically to a tight frame for L2(Rn)—the k-plane ridgelets. This construction makes analysis of a function f ∈ L2(Rn) by k-plane ridgelets identical to the analysis of the k-plane X-ray transform of f by an appropriate wavelet-like system for χn,k. As wavelets are typically effective at representing point singularities, it may be expected that these new systems will be effective at representing objects whose k-plane X-ray transform has a point singularity. Objects with discontinuities across hyperplanes are of this form, for k = n − 1.

Fluid shear stress inhibits TNF-α activation of JNK but not ERK1/2 or p38 in human umbilical vein endothelial cells: Inhibitory crosstalk among MAPK family members

Atherosclerosis preferentially occurs in areas of turbulent flow and low fluid shear stress, whereas laminar flow and high shear stress are atheroprotective. Inflammatory cytokines, such as tumor necrosis factor-α (TNF-α) and IL-1 stimulate expression of endothelial cell (EC) genes that may promote atherosclerosis. TNF-α and IL-1 regulate gene expression in ECs, in part, by stimulating mitogen-activated protein kinases (MAPK), which phosphorylate transcription factors. We hypothesized that steady laminar flow inhibits cytokine-mediated activation of MAPK in EC. To test this hypothesis, we determined the effects of flow (shear stress = 12 dynes/cm2) on TNF-α and IL-1-stimulated activity of three MAPK in human umbilical vein ECs (HUVEC): extracellular signal-regulated kinase (ERK1/2), p38, and c-Jun N-terminal kinase (JNK). Flow alone stimulated ERK1/2 and p38 activity but decreased JNK activity compared with static controls. TNF-α or IL-1 alone activated ERK1/2, p38, and JNK maximally at 15 min in HUVEC. Preexposing HUVEC for 10 min to flow inhibited TNF-α and IL-1 activation of JNK by 46% and 49%, respectively, but had no significant effect on ERK1/2 or p38 activation. Incubation of HUVEC with PD98059, which inhibits flow-mediated ERK1/2 activation, prevented flow from inhibiting cytokine activation of JNK. Phorbol 12-myristate 13-acetate, which strongly activates ERK1/2, also inhibited TNF-α activation of JNK. These findings indicate that fluid shear stress inhibits TNF-α-mediated signaling events in HUVEC via the activation of the ERK1/2 signaling pathway. Inhibition of TNF-α signal transduction represents a mechanism by which steady laminar flow may exert atheroprotective effects on the endothelium.

The cis-acting phorbol ester "12-O-tetradecanoylphorbol 13-acetate"-responsive element is involved in shear stress-induced monocyte chemotactic protein 1 gene expression.

Vascular endothelial cells, serving as a barrier between vessel and blood, are exposed to shear stress in the body. Although endothelial responses to shear stress are important in physiological adaption to the hemodynamic environments, they can also contribute to pathological conditions--e.g., in atherosclerosis and reperfusion injury. We have previously shown that shear stress mediates a biphasic response of monocyte chemotactic protein 1 (MCP-1) gene expression in vascular endothelial cells and that the regulation is at the transcriptional level. These observations led us to functionally analyze the 550-bp promoter region of the MCP-1-encoding gene to define the cis element responding to shear stress. The shear stress/luciferase assay on the deletion constructs revealed that a 38-bp segment (-53 to -90 bp relative to the transcription initiation site) containing two divergent phorbol ester "12-O-tetradecanoylphorbol 13-acetate" (TPA)-responsive elements (TRE) is critical for shear inducibility. Site-specific mutations on these two sites further demonstrated that the proximal one (TGACTCC) but not the distal one (TCACTCA) was shear-responsive. Shear inducibility was lost after the mutation or deletion of the proximal site. This molecular mechanism of shear inducibility of the MCP-1 gene was functional in both the epithelial-like HeLa cells and bovine aortic endothelial cells (BAEC). In a construct with four copies of the TRE consensus sequences TGACTACA followed by the rat prolactin minimal promoter and luciferase gene, shear stress induced the reporter activities by 35-fold and 7-fold in HeLa cells and BAEC, respectively. The application of shear stress on BAEC also induced a rapid and transient phosphorylation of mitogen-activated protein kinases. Pretreatment of BAEC with TPA attenuated the shear-induced mitogen-activated protein kinase phosphorylation, suggesting that shear stress and TPA share a similar signal transduction pathway in activating cells. The present study provides a molecular basis for the transient induction of MCP-1 gene by shear stress.

Shear wave velocity estimation in the metropolitan area of Málaga (S Spain)

We carry out a seismic noise study based on array measurements at three sites in the Málaga basin, South Spain, for the further estimation of shear wave velocity profiles. For this purpose, we use both the H/V method and the f–k technique in order to characterize the different materials present in the zone, i.e., Quaternary sediments and Pliocene sedimentary rocks above the bedrock. The H/V analysis shows frequency peaks going from 1 Hz, in areas close to the border of the basin, to 0.3 Hz in places located toward the center of the formation. The f–k analysis allows obtaining the dispersion curves associated with each site and subsequently, estimating the Vs profiles by inversion of the respective group velocities. In this way, the basin basement can be characterized by S-wave velocities greater than 2000 m/s. Regarding the basin fill, it is divided into three layers defined by different wave velocity intervals. The shallowest one is featured by velocities ranging from 150 to 400 m/s and comprises the Quaternary sediments, while velocities going from 550–700 to1200–1600 m/s characterize the two underlying layers composed by Pliocene sediments. Finally, the information provided by the three Vs profiles is integrated in a 2D cross-section of the basin to have a spatial view of its sedimentary structure. The results obtained here, in addition to providing useful information about the infill of the basin near the metropolitan area of Málaga, will be very helpful for future seismic zonation studies in the region.

Investigating the Role of cAMP-Signaling in the Regulation of Vascular Endothelial Cell Adaptive Responses to Fluid Shear Stress

The circulating blood exerts a force on the vascular endothelium, termed fluid shear stress (FSS), which directly impacts numerous vascular endothelial cell (VEC) functions. For example, high rates of linear and undisturbed (i.e. laminar) blood flow maintains a protective and quiescent VEC phenotype. Meanwhile, deviations in blood flow, which can occur at vascular branchpoints and large curvatures, create areas of low, and/or oscillatory FSS, and promote a pro-inflammatory, pro-thrombotic and hyperpermeable phenotype. Indeed, it is known that these areas are prone to the development of atherosclerotic lesions. Herein, we show that cyclic nucleotide phosphodiesterase (PDE) 4D (PDE4D) activity is increased by FSS in human arterial endothelial cells (HAECs) and that this activation regulates the activity of cAMP-effector protein, Exchange Protein-activated by cAMP-1 (EPAC1), in these cells. Importantly, we also show that these events directly and critically impact HAEC responses to FSS, especially when FSS levels are low. Both morphological events induced by FSS, as measured by changes in cell alignment and elongation in the direction of FSS, and the expression of critical FSS-regulated genes, including Krüppel-like factor 2 (KLF2), endothelial nitric oxide synthase (eNOS) and thrombomodlin (TM), are mediated by EPAC1/PDE4D signaling. At a mechanistic level, we show that EPAC1/PDE4D acts through the vascular endothelial-cadherin (VECAD)/ platelet-cell adhesion molecule-1 (PECAM1)/vascular endothelial growth factor receptor 2 (VEGFR2) mechanosensor to activate downstream signaling though Akt. Given the critical role of PDE4D in mediating these effects, we also investigated the impact of various patterns of FSS on the expression of individual PDE genes in HAECs. Notably, PDE2A was significantly upregulated in response to high, laminar FSS, while PDE3A was upregulated under low, oscillatory FSS conditions only. These data may provide novel therapeutic targets to limit FSS-dependent endothelial cell dysfunction (ECD) and atherosclerotic development.

Fault development and interaction in distributed strike-slip shear zones: an experimental approach

Analogue model experiments using both brittle and viscous materials were performed to investigate the development and interaction of strike-slip faults in zones of distributed shear deformation. At low strain, bulk dextral shear deformation of an initial rectangular model is dominantly accommodated by left-stepping, en echelon strike-slip faults (Riedel shears, R) that form in response to the regional (bulk) stress field. Push-up zones form in the area of interaction between adjacent left-stepping Riedel shears. In cross sections, faults bounding push-up zones have an arcuate shape or merge at depth. Adjacent left-stepping R shears merge by sideways propagation or link by short synthetic shears that strike subparallel to the bulk shear direction. Coalescence of en echelon R shears results in major, through-going faults zones (master faults). Several parallel master faults develop due to the distributed nature of deformation. Spacing between master faults is related to the thickness of the brittle layers overlying the basal viscous layer. Master faults control to a large extent the subsequent fault pattern. With increasing strain, relatively short antithetic and synthetic faults develop mostly between old, but still active master faults. The orientation and evolution of the new faults indicate local modifications of the stress field. In experiments lacking lateral borders, closely spaced parallel antithetic faults (cross faults) define blocks that undergo clockwise rotation about a vertical axis with continuing deformation. Fault development and fault interaction at different stages of shear strain in our models show similarities with natural examples that have undergone distributed shear.

Clay mineralogy and shear strength of subglacial and glaciomarine sediments in the southern Bellingshausen Sea

The Belgica Trough and the adjacent Belgica Trough Mouth Fan in the southern Bellingshausen Sea (Pacific sector of the Southern Ocean) mark the location of a major outlet for the West Antarctic Ice Sheet during the Late Quaternary. The drainage basin of an ice stream that advanced through Belgica Trough across the shelf during the last glacial period comprised an area exceeding 200,000 km**2 in the West Antarctic hinterland. Previous studies, mainly based on marine-geophysical data from the continental shelf and slope, focused on the bathymetry and seafloor bedforms, and the reconstruction of associated depositional processes and ice- drainage patterns. In contrast, there was only sparse information from seabed sediments recovered by coring. In this paper, we present lithological and clay mineralogical data of 21 sediment cores collected from the shelf and slope of the southern Bellingshausen Sea. Most cores recovered three lithological units, which can be attributed to facies types deposited under glacial, transitional and seasonally open-marine conditions. The clay mineral assemblages document coinciding changes in provenance. The relationship between the clay mineral assemblages in the subglacial and proglacial sediments on the shelf and the glacial diamictons on the slope confirms that a grounded ice stream advanced through Belgica Trough to the shelf break during the past, thereby depositing detritus eroded in the West Antarctic hinterland as soft till on the shelf and as glaciogenic debris flows on the slope. The thinness of the transitional and seasonally open-marine sediments in the cores suggests that this ice advance occurred during the last glacial period. Clay mineralogical, acoustic sub-bottom and seismic data furthermore demonstrate that the palaeo-ice stream probably reworked old sedimentary strata, including older tills, on the shelf and incorporated this debris into its till bed. The geographical heterogeneity of the clay mineral assemblages in the sub- and proglacial diamictons and gravelly deposits indicates that they were eroded from underlying sedimentary strata of different ages. These strata may have been deposited during either different phases of the last glacial period or different glacial and interglacial periods. Additionally, the clay mineralogical heterogeneity of the soft tills recovered on the shelf suggests that the drainage area of the palaeo-ice stream flowing through Belgica Trough changed through time.

Basic table of commissioning allowances for 18 plane squadrons regardless of type for use in commissioning VMB, VMD, VMFN, VMJ, Group Headquarters, Wing Headquarters Squadrons. (Short title, BuAero BTCA for VMB, VMD, VMFN, VMJ, etc., Apr. 1943)

At head of title: Bureau of Aeronautics.

Basic research in crashworthiness II - pre-collapse dynamic analysis of plane, ideal elasto-plastic frame structures including the case of collision into a narrow rigid pole obstacle. Interim technical report.

National Highway Traffic Safety Administration, Washington, D.C.

On finding the maximal elements in a set of plane vectors /

"UIUCDCS-R-74-667"