Classification of Links Up to 0-Solvability

The $n$-solvable filtration of the $m$-component smooth (string) link concordance group, $$\dots \subset \mathcal{F}^m_{n+1} \subset \mathcal{F}^m_{n.5} \subset \mathcal{F}^m_n \dots \subset \mathcal{F}^m_1 \subset \mathcal{F}^m_{0.5} \subset \mathcal{F}^m_0 \subset \mathcal{F}^m_{-0.5} \subset \mathcal{C}^m,$$ as defined by Cochran, Orr, and Teichner, is a tool for studying smooth knot and link concordance that yields important results in low-dimensional topology. The focus of this paper is to give a characterization of the set of 0-solvable links. We introduce a new equivalence relation on links called 0-solve equivalence and establish both an algebraic and a geometric classification of $\mathbb{L}_0^m$, the set of links up to 0-solve equivalence. We show that $\mathbb{L}_0^m$ has a group structure isomorphic to the quotient $\mathcal{F}_{-0.5}/\mathcal{F}_0$ of concordance classes of string links and classify this group, showing that $$\mathbb{L}_0^m \cong \mathcal{F}_{-0.5}^m/\mathcal{F}_0^m \cong \mathbb{Z}_2^m \oplus \mathbb{Z}^{m \choose 3} \oplus \mathbb{Z}_2^{m \choose 2}.$$ Finally, using results of Conant, Schneiderman, and Teichner, we show that 0-solvable links are precisely the links that bound class 2 gropes and support order 2 Whitney towers in the 4-ball.Comment: 34 page

A definitive heat of vaporization of silicon through benchmark ab initio calculations on SiF_4

In order to resolve a significant uncertainty in the heat of vaporization of silicon -- a fundamental parameter in gas-phase thermochemistry -- $\Delta H^\circ_{f,0}$[Si(g)] has been determined from a thermochemical cycle involving the precisely known experimental heats of formation of SiF_4(g) and F(g) and a benchmark calculation of the total atomization energy (TAE_0) of SiF_4 using coupled-cluster methods. Basis sets up to $[8s7p6d4f2g1h]$ on Si and $[7s6p5d4f3g2h]$ on F have been employed, and extrapolations for residual basis set incompleteness applied. The contributions of inner-shell correlation (-0.08 kcal/mol), scalar relativistic effects (-1.88 kcal/mol), atomic spin-orbit splitting (-1.97 kcal/mol), and anharmonicity in the zero-point energy (+0.04 kcal/mol) have all been explicitly accounted for. Our benchmark TAE_0=565.89 \pm 0.22 kcal/mol leads to $\Delta H^\circ_{f,0}$[Si(g)]=107.15 \pm 0.38 kcal/mol ($\Delta H^\circ_{f,298}$[Si(g)]=108.19 \pm 0.38 kcal/mol): between the JANAF/CODATA value of 106.5 \pm 1.9 kcal/mol and the revised value proposed by Grev and Schaefer [J. Chem. Phys. 97, 8389 (1992}], 108.1 \pm 0.5 kcal/mol. The revision will be relevant for future computational studies on heats of formation of silicon compounds.Comment: J. Phys. Chem. A, submitted Feb 1, 199

A comparison of the efficiency of producers under collective and individual modes of organisation

This paper compares collective and individuals production systems' technical and allocative efficiency. The producers being studied belong to Honduran agrarian reform cooperatives engaging in colective and/or individual maize production. Debreu-Farrell technical efficiency related to stochastic production is calculated. Allocative efficiency is obtained from an analytically derived cost frontier. Results indicate that collective systems are slightly more efficient than individual production systems. Worker-shirking (one of the most cited theoretical arguments against colective form of enterprise) would seem to have no empirical basis from these results.cooperative

Influence of wear algorithm formulation on computational-experimental corroboration

Experimental wear testing is well-established as an important part of the TKR design process. Recently, in-silico models have proved their value to corroborate long-term in-vitro results on a much shorter timescale [1]. Both FE-based models & multi-body dynamics can be used to predict contact pressures, sliding distances and cross-shear (CS). The precise mechanisms of wear are not sufficiently understood to permit analytical calculations, and so empirical formulations are used to estimate wear depths & volumes.Most early simulations were based on a modified Archard/Lancaster formulation; more recently a number of alternative formulations for cross shear have been proposed; it is unclear which is the most robust or accurate for the widest range of activities. The aim of this study was to develop and corroborate a fast in-silico wear model, and use this to compare different wear formulations

Performance of the resurfaced hip. Part 1: the influence of the prosthesis size and positioning on the remodelling and fracture of the femoral neck

Hip resurfacing is an established treatment for osteoarthritis in young active patients. Failure modes include femoral neck fracture and prosthesis loosening, which may be associated with medium-term bone adaptation, including femoral neck narrowing and densification around the prosthesis stem.Finite element modelling was used to indicate the effects of prosthesis sizing and positioning on the bone remodelling and fracture strength under a range of normal and traumatic loads, with the aim of understanding these failure modes better.The simulations predicted increased superior femoral neck stress shielding in young patients with small prostheses, which required shortening of the femoral neck to give an acceptable implant–bone interface. However, with a larger prosthesis, natural femoral head centre recreation in the implanted state was possible; therefore stress shielding was restricted to the prosthesis interior, and its extent was less sensitive to prosthesis orientation. With valgus orientation, the implanted neck strength was, at worst, within 3 per cent of its intact strength.The study suggests that femoral neck narrowing may be linked to a reduction in the horizontal femoral offset, occurring if the prosthesis is excessively undersized. As such, hip resurfacing should aim to reproduce the natural femoral head centre, and, for valgus prosthesis orientation, to avoid femoral neck fracture

The Biequivalence of Locally Cartesian Closed Categories and Martin-L\"of Type Theories

Seely's paper "Locally cartesian closed categories and type theory" contains a well-known result in categorical type theory: that the category of locally cartesian closed categories is equivalent to the category of Martin-L\"of type theories with Pi-types, Sigma-types and extensional identity types. However, Seely's proof relies on the problematic assumption that substitution in types can be interpreted by pullbacks. Here we prove a corrected version of Seely's theorem: that the B\'enabou-Hofmann interpretation of Martin-L\"of type theory in locally cartesian closed categories yields a biequivalence of 2-categories. To facilitate the technical development we employ categories with families as a substitute for syntactic Martin-L\"of type theories. As a second result we prove that if we remove Pi-types the resulting categories with families are biequivalent to left exact categories.Comment: TLCA 2011 - 10th Typed Lambda Calculi and Applications, Novi Sad : Serbia (2011

Use of functional near-infrared spectroscopy to evaluate cognitive change when using healthcare simulation tools

This is an accepted manuscript of an article published by BMJ on 01/11/2020, available online: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8936993/ The accepted version of the publication may differ from the final published version.Background The use of brain imaging techniques in healthcare simulation is relatively rare. However, the use of mobile, wireless technique, such as functional nearinfrared spectroscopy (fNIRS), is becoming a useful tool for assessing the unique demands of simulation learning. For this study, this imaging technique was used to evaluate cognitive load during simulation learning events. Methods This study took place in relation to six simulation activities, paired for similarity, and evaluated comparative cognitive change between the three task pairs. The three paired tasks were: receiving a (1) face-toface and (2) video patient handover; observing a simulated scene in (1) two dimensions and (2) 360° field of vision; and on a simulated patient (1) taking a pulse and (2) taking a pulse and respiratory rate simultaneously. The total number of participants was n=12. Results In this study, fNIRS was sensitive to variations in task difficulty in common simulation tools and scenarios, showing an increase in oxygenated haemoglobin concentration and a decrease in deoxygenated haemoglobin concentration, as tasks increased in cognitive load. Conclusion Overall, findings confirmed the usefulness of neurohaemoglobin concentration markers as an evaluation tool of cognitive change in healthcare simulation. Study findings suggested that cognitive load increases in more complex cognitive tasks in simulation learning events. Task performance that increased in complexity therefore affected cognitive markers, with increase in mental effort required