Sweeping the cd-Index and the Toric h-Vector

We derive formulas for the cd-index and the toric h-vector of a convex polytope P from a sweeping by a hyperplane. These arise from interpreting the corresponding S-shelling of the dual of P. We describe a partition of the faces of the complete truncation of P to reflect explicitly the nonnegativity of its cd-index and what its components are counting. One corollary is a quick way to compute the toric h-vector directly from the cd-index. We also propose an "extended toric" h-vector that fully captures the information in the flag h-vector.Comment: 23 page

On k-stacked polytopes

AbstractIt is proved that equality in the Generalized Simplicial Lower Bound Conjecture can always be obtained by k-stacked polytopes

Key Equations in the Tuljapurkar-Lee Model of the Social Security System

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On a triangulation of the 3-ball and the solid torus

AbstractWe show that neither the 3-ball nor the solid torus admits a triangulation in which (i) every vertex is on the boundary, and (ii) every tetrahedron has exactly one triangle on the boundary. Such triangulations are relevant to an unresolved conjecture of Perles

Using Structure from Motion Mapping to Record and Analyze Details of the Colossal Hats (Pukao) of Monumental Statues on Rapa Nui (Easter Island)

Structure from motion (SfM) mapping is a photogrammetric technique that offers a cost-effective means of creating three-dimensional (3-D) visual representations from overlapping digital photographs. The technique is now used more frequently to document the archaeological record. We demonstrate the utility of SfM by studying red scoria bodies known as pukao from Rapa Nui (Easter Island, Chile). We created 3-D images of 50 pukao that once adorned the massive statues (moai) of Rapa Nui and compare them to 13 additional pukao located in Puna Pau, the island’s red scoria pukao quarry. Through SfM, we demonstrate that the majority of these bodies have petroglyphs and other surface features that are relevant to archaeological explanation and are currently at risk of continued degradation

The Pukao of Rapa Nui (Easter Island, Chile)

Structure from motion (SfM) mapping is a photogrammetric technique that offers a cost-effective means of creating three-dimensional visual representations from overlapping digital photographs. The technique has seen increasing uses for documenting the archaeological record. We demonstrate the utility of SfM through a study of the form of red scoria bodies known as pukao from Rapa Nui (Easter Island, Chile). We study 50 pukao that once adorned the massive statues (moai) of Rapa Nui, and compare them to 13 additional pukao located in Puna Pau: the island’s red scoria pukao quarry. Through SfM, we demonstrate that the majority of these bodies have petroglyphs and other surface features that are relevant to archaeological explanation and are currently at risk of continued degradation

Spectral estimates of bed shear stress using suspended-sediment concentrations in a wave-current boundary layer

High-resolution time series of suspended-sediment profiles have been obtained using an acoustic backscatter system at an inner shelf site (North Carolina) where flows are dominated by wind-driven currents and waves. We analyzed the spatial and temporal structure of near-bed turbulence in particle-transporting flows and scalar-like fluctuations of suspended-sediment concentrations. An important element of our analysis is a new inertial dissipation method for passive tracers to estimate the shear stress acting on the seabed, using the spectral properties of suspended sediment concentrations observed by acoustic backscatter sensors. In flows that provide adequate separation of the scales of turbulence production and dissipation, a sufficiently thick constant stress wall layer, and significant sediment suspension, frequency (or associated wave number) spectra of near-bed sediment concentration exhibit a -5/3 slope in the inertial subrange that spans frequencies of order 1 Hz. This observation suggests that the suspended sediment is effectively a passive tracer of turbulent fluid motions. Inversion of the relevant, Kolmogorov scaling equations yields estimates of the shear velocity that agree reasonably well with other, independent and widely used measures. High- and low-frequency limits on application of the inertial dissipation method to sediment concentration are related to the inertial response time of sediment particles and the sediment settling timescale. We propose that, in future applications, the inertial dissipation method for passive tracers can be used to estimate either the shear velocity, effective settling velocity of suspended sediment (or equivalent particle size) or dynamic bed roughness if two of these three quantities are independently known

Computerized adaptive testing and short form development for child and adolescent oral health patient-reported outcomes measurement.

ObjectivesTo develop computerized adaptive testing (CAT) and short forms of self-report oral health measures that are predictive of both the children's oral health status index (COHSI) and the children's oral health referral recommendation (COHRR) scales, for children and adolescents, ages 8-17.Material and methodsUsing final item calibration parameters (discrimination and difficulty parameters) from the item response theory analysis, we performed post hoc CAT simulation. Items most frequently administered in the simulation were incorporated for possible inclusion in final oral health assessment toolkits, to select the best performing eight items for COHSI and COHRR.ResultsTwo previously identified unidimensional sets of self-report items consisting of 19 items for the COHSI and 22 items for the COHRR were administered through CAT resulting in eight-item short forms for both the COHSI and COHRR. Correlations between the simulated CAT scores and the full item bank representing the latent trait are r = .94 for COHSI and r = .96 for COHRR, respectively, which demonstrated high reliability of the CAT and short form.ConclusionsUsing established rigorous measurement development standards, the CAT and corresponding eight-item short form items for COHSI and COHRR were developed to assess the oral health status of children and adolescents, ages 8-17. These measures demonstrated good psychometric properties and can have clinical utility in oral health screening and evaluation and clinical referral recommendations