The interface between morphology and action planning: a comparison of two species of New World monkeys

Recent research with several species of nonhuman primates suggests sophisticated motor-planning abilities observed in human adults may be ubiquitous among primates. However, there is considerable variability in the extent to which these abilities are expressed across primate species. In the present experiment, we explore whether the variability in the expression of anticipatory motor-planning abilities may be attributed to cognitive differences (such as tool use abilities) or whether they may be due to the consequences of morphological differences (such as being able to deploy a precision grasp). We compared two species of New World monkeys that differ in their tool use abilities and manual dexterity: squirrel monkeys, Saimiri sciureus (less dexterous with little evidence for tool use) and tufted capuchins, Sapajus apella (more dexterous and known tool users). The monkeys were presented with baited cups in an untrained food extraction task. Consistent with the morphological constraint hypothesis, squirrel monkeys frequently showed second-order motor planning by inverting their grasp when picking up an inverted cup, while capuchins frequently deployed canonical upright grasping postures. Findings suggest that the lack of ability for precision grasping may elicit more consistent second-order motor planning, as the squirrel monkeys (and other species that have shown a high rate of second-order planning) have fewer means of compensating for inefficient initial postures. Thus, the interface between morphology and motor planning likely represents an important factor for understanding both the ontogenetic and phylogenetic origins of sophisticated motor-planning abilities.

The Interface Between Morphology and Action Planning: a Comparison of Two Species of New World Monkeys

Recent research with several species of nonhuman primates suggests sophisticated motor-planning abilities observed in human adults may be ubiquitous among primates. However, there is considerable variability in the extent to which these abilities are expressed across primate species. In the present experiment, we explore whether the variability in the expression of anticipatory motor-planning abilities may be attributed to cognitive differences (such as tool use abilities) or whether they may be due to the consequences of morphological differences (such as being able to deploy a precision grasp). We compared two species of New World monkeys that differ in their tool use abilities and manual dexterity: squirrel monkeys, Saimiri sciureus (less dexterous with little evidence for tool use) and tufted capuchins, Sapajus apella (more dexterous and known tool users). The monkeys were presented with baited cups in an untrained food extraction task. Consistent with the morphological constraint hypothesis, squirrel monkeys frequently showed second-order motor planning by inverting their grasp when picking up an inverted cup, while capuchins frequently deployed canonical upright grasping postures. Findings suggest that the lack of ability for precision grasping may elicit more consistent second-order motor planning, as the squirrel monkeys (and other species that have shown a high rate of second-order planning) have fewer means of compensating for inefficient initial postures. Thus, the interface between morphology and motor planning likely represents an important factor for understanding both the ontogenetic and phylogenetic origins of sophisticated motor-planning abilities. (C) 2013 The Association for the Study of Animal Behaviour. Published by Elsevier Ltd. All rights reserved.

Using the Natural Period of a Structure as an Indicator of the Significance of Second-Order Effects

This study investigates the feasibility of predicting the momentamplification in beam-column elements of steel moment-resisting frames using the structure's natural period. Unlike previous methods, which perform moment-amplification on a story-by-story basis, this study develops and tests two models that aim to predict a global amplification factor indicative of the largest relevant instance of local moment amplification in the structure. To thisend, a variety of two-dimensional frames is investigated using first and secondorder finite element analysis. The observed moment amplification is then compared with the predicted amplification based on the structure's natural period, which is calculated by first-order finite element analysis. As a benchmark, design moment amplification factors are calculated for each story using the story stiffness approach, and serve to demonstrate the relativeconservatism and accuracy of the proposed models with respect to current practice in design. The study finds that the observed moment amplification factors may vastly exceed expectations when internal member stresses are initially very small. Where the internal stresses are small relative to the member capacities, thesecases are inconsequential for design. To qualify the significance of the observed amplification factors, two parameters are used: the second-order moment normalized to the plastic moment capacity, and the combined flexural and axial stress interaction equations developed by AISC

hp-dGFEM for Second-Order Elliptic Problems in Plyhedra I: Stability and Quasioptimality on Geometric Meshes

We introduce and analyze hp-version discontinuous Galerkin (dG) finite element methods for the numerical approximation of linear second-order elliptic boundary-value problems in three-dimensional polyhedral domains. To resolve possible corner-, edge- and corner-edge singularities, we consider hexahedral meshes that are geometrically and anisotropically refined toward the corresponding neighborhoods. Similarly, the local polynomial degrees are increased linearly and possibly anisotropically away from singularities. We design interior penalty hp-dG methods and prove that they are well-defined for problems with singular solutions and stable under the proposed hp-refinements. We establish (abstract) error bounds that will allow us to prove exponential rates of convergence in the second part of this work.

hp-dGFEM for Second-Order Elliptic Problems in Plyhedra II: Exponential Convergence

The goal of this paper is to establish exponential convergence of $hp$-version interior penalty (IP) discontinuous Galerkin (dG) finite element methods for the numerical approximation of linear second-order elliptic boundary-value problems with homogeneous Dirichlet boundary conditions and piecewise analytic data in three-dimensional polyhedral domains. More precisely, we shall analyze the convergence of the $hp$-IP dG methods considered in [D. Schötzau, C. Schwab, T. P. Wihler, SIAM J. Numer. Anal., 51 (2013), pp. 1610--1633] based on axiparallel $\sigma$-geometric anisotropic meshes and $\bm{s}$-linear anisotropic polynomial degree distributions.

Relative Predicativity and dependent recursion in second-order set theory and higher-orders theories

This article reports that some robustness of the notions of predicativity and of autonomous progression is broken down if as the given infinite total entity we choose some mathematical entities other than the traditional ω. Namely, the equivalence between normal transfinite recursion scheme and new dependent transfinite recursion scheme, which does hold in the context of subsystems of second order number theory, does not hold in the context of subsystems of second order set theory where the universe V of sets is treated as the given totality (nor in the contexts of those of n+3-th order number or set theories, where the class of all n+2-th order objects is treated as the given totality).

hp-DGFEM for second-order mixed elliptic problems polyhedra

We prove exponential rates of convergence of hp-version discontinuous Galerkin (dG) interior penalty finite element methods for second-order elliptic problems with mixed Dirichlet-Neumann boundary conditions in axiparallel polyhedra. The dG discretizations are based on axiparallel, σ-geometric anisotropic meshes of mapped hexahedra and anisotropic polynomial degree distributions of μ-bounded variation. We consider piecewise analytic solutions which belong to a larger analytic class than those for the pure Dirichlet problem considered in [11, 12]. For such solutions, we establish the exponential convergence of a nonconforming dG interpolant given by local L 2 -projections on elements away from corners and edges, and by suitable local low-order quasi-interpolants on elements at corners and edges. Due to the appearance of non-homogeneous, weighted norms in the analytic regularity class, new arguments are introduced to bound the dG consistency errors in elements abutting on Neumann edges. The non-homogeneous norms also entail some crucial modifications of the stability and quasi-optimality proofs, as well as of the analysis for the anisotropic interpolation operators. The exponential convergence bounds for the dG interpolant constructed in this paper generalize the results of [11, 12] for the pure Dirichlet case.

COMPREHENSIVE CALCULATION-BASED IMRT QA USING R&V DATA, TREATMENT RECORDS, AND A SECOND TREATMENT PLANNING SYSTEM

Purpose: Traditional patient-specific IMRT QA measurements are labor intensive and consume machine time. Calculation-based IMRT QA methods typically are not comprehensive. We have developed a comprehensive calculation-based IMRT QA method to detect uncertainties introduced by the initial dose calculation, the data transfer through the Record-and-Verify (R&V) system, and various aspects of the physical delivery. Methods: We recomputed the treatment plans in the patient geometry for 48 cases using data from the R&V, and from the delivery unit to calculate the “as-transferred” and “as-delivered” doses respectively. These data were sent to the original TPS to verify transfer and delivery or to a second TPS to verify the original calculation. For each dataset we examined the dose computed from the R&V record (RV) and from the delivery records (Tx), and the dose computed with a second verification TPS (vTPS). Each verification dose was compared to the clinical dose distribution using 3D gamma analysis and by comparison of mean dose and ROI-specific dose levels to target volumes. Plans were also compared to IMRT QA absolute and relative dose measurements. Results: The average 3D gamma passing percentages using 3%-3mm, 2%-2mm, and 1%-1mm criteria for the RV plan were 100.0 (σ=0.0), 100.0 (σ=0.0), and 100.0 (σ=0.1); for the Tx plan they were 100.0 (σ=0.0), 100.0 (σ=0.0), and 99.0 (σ=1.4); and for the vTPS plan they were 99.3 (σ=0.6), 97.2 (σ=1.5), and 79.0 (σ=8.6). When comparing target volume doses in the RV, Tx, and vTPS plans to the clinical plans, the average ratios of ROI mean doses were 0.999 (σ=0.001), 1.001 (σ=0.002), and 0.990 (σ=0.009) and ROI-specific dose levels were 0.999 (σ=0.001), 1.001 (σ=0.002), and 0.980 (σ=0.043), respectively. Comparing the clinical, RV, TR, and vTPS calculated doses to the IMRT QA measurements for all 48 patients, the average ratios for absolute doses were 0.999 (σ=0.013), 0.998 (σ=0.013), 0.999 σ=0.015), and 0.990 (σ=0.012), respectively, and the average 2D gamma(5%-3mm) passing percentages for relative doses for 9 patients was were 99.36 (σ=0.68), 99.50 (σ=0.49), 99.13 (σ=0.84), and 98.76 (σ=1.66), respectively. Conclusions: Together with mechanical and dosimetric QA, our calculation-based IMRT QA method promises to minimize the need for patient-specific QA measurements by identifying outliers in need of further review.

Differential invariants of second-order ordinary differential equations

The notion of a differential invariant for systems of second-order differential equations on a manifold M with respect to the group of vertical automorphisms of the projection is de?ned and the Chern connection attached to a SODE allows one to determine a basis for second-order differential invariants of a SODE.

Second-order Lagrangians admitting a first-order Hamiltonian formalism

Let p: E —» JV be an arbitrary fibred manifold over a connected n-dimensional manifold N oriented by a volume form v = dx1^-...^dxn, and let pk: JkE → N be the bundle of K-jets of local sections of p, with projections Plk : JkE → JlE for every k ≥ 1