Area Under the Moment Curve (AUMC)

2016 ◽  
Author(s):  
Monica Nordberg ◽  
John H. Duffus ◽  
Douglas M. Templeton
Keyword(s):  
2016 ◽  
Author(s):  
John H. Duffus ◽  
Monica Nordberg ◽  
Douglas M. Templeton
Keyword(s):  

2017 ◽  
Vol 9 (6) ◽  
Author(s):  
Jelle Rommers ◽  
Giuseppe Radaelli ◽  
Just L. Herder

Principles from origami art are applied in the design of mechanisms and robotics increasingly frequent. A large part of the application driven research of these origami-like mechanisms focuses on devices where the creases (hinge lines) are actuated and the facets are constructed as stiff elements. In this paper, a design tool is proposed in which hinge lines with torsional stiffness and flexible facets are used to design passive, instead of active mechanisms. The design tool is an extension of a model of a single vertex compliant facet origami mechanism (SV-COFOM) and is used to approximate a desired moment curve by optimizing the design variables of the mechanism. Three example designs are presented: a constant moment joint (CMJ), a gravity compensating joint (GCJ) and a zero moment joint (ZMJ). The CMJ design has been evaluated experimentally, resulting in a root-mean-squared error (RMSE) of 6.4 × 10−2 N·m on a constant moment value of 0.39 N·m. This indicates that the design tool is suitable for a course estimation of the moment curve of the SV-COFOM in early stages of a design process.


10.37236/4471 ◽  
2017 ◽  
Vol 24 (1) ◽  
Author(s):  
Johannes Rauh

This paper describes the polytope $\mathbf{P}_{k;N}$ of $i$-star counts, for all $i\le k$, for graphs on $N$ nodes.  The vertices correspond to graphs that are regular or as regular as possible.  For even $N$ the polytope is a cyclic polytope, and for odd $N$ the polytope is well-approximated by a cyclic polytope.  As $N$ goes to infinity, $\mathbf{P}_{k;N}$ approaches the convex hull of the moment curve. The affine symmetry group of $\mathbf{P}_{k;N}$ contains just a single non-trivial element, which corresponds to forming the complement of a graph.The results generalize to the polytope $\mathbf{P}_{I;N}$ of $i$-star counts, for $i$ in some set $I$ of non-consecutive integers.  In this case, $\mathbf{P}_{I;N}$ can still be approximated by a cyclic polytope, but it is usually not a cyclic polytope itself.Polytopes of subgraph statistics characterize corresponding exponential random graph models.  The elongated shape of the $k$-star polytope gives a qualitative explanation of some of the degeneracies found in such random graph models.


2021 ◽  
Vol 143 (6) ◽  
pp. 1983-1998
Author(s):  
Shaoming Guo ◽  
Zane Kun Li ◽  
Po-Lam Yung ◽  
Pavel Zorin-Kranich
Keyword(s):  

2016 ◽  
Vol 57 (1) ◽  
pp. 56-70 ◽  
Author(s):  
Micha A. Perles ◽  
Moriah Sigron
Keyword(s):  

2019 ◽  
Vol 72 (2) ◽  
pp. 537-556
Author(s):  
Eran Nevo ◽  
Guillermo Pineda-Villavicencio ◽  
Julien Ugon ◽  
David Yost

AbstractWe study $n$-vertex $d$-dimensional polytopes with at most one nonsimplex facet with, say, $d+s$ vertices, called almost simplicial polytopes. We provide tight lower and upper bound theorems for these polytopes as functions of $d,n$, and $s$, thus generalizing the classical Lower Bound Theorem by Barnette and the Upper Bound Theorem by McMullen, which treat the case where $s=0$. We characterize the minimizers and provide examples of maximizers for any $d$. Our construction of maximizers is a generalization of cyclic polytopes, based on a suitable variation of the moment curve, and is of independent interest.


2016 ◽  
Vol 72 (11) ◽  
pp. 686-692 ◽  
Author(s):  
Ismael Martínez-Cortés ◽  
Lilia Gutierrez ◽  
Graciela Tapia ◽  
Luis Ocampo ◽  
Hector Sumano

The success rate in treatment against Staphylococcus aureus mastitis with antibacterial drugs is marginal. Low antibacterial drug concentrations in the mammary tissue is part of the reason for this failure. Enrofloxacin has only been administered on few occasions through the intramammary route i.e., combined with gentamicin in an undisclosed vehicle or dose. A new solvate form of enrofloxacin (enrofloxacin hydrochloride-dihydrate [enro-C]) prepared as 1.5% suspension pH 5.5 was tested in a field mastitis outbreak due to coagulase-negative S. aureus (CNS) in F1 (Holstein/Zebu) cows aged 5-8 years destined to be culled. Enro-C was administered intramammarily daily (300 mg/infected quarter) for 8 days both to healthy and mastitic cows; milk and serum enro-C concentrations were determined on days 1 and 8. Maximum serum concentration (CMAX) values were similar in both groups (9.4 to 10.7 µg/mL). The area under the moment curve (AUMC) for enrofloxacin increased only by 11% in healthy cows and by 10% in infected cows from day 1 to day 8, a fact that suggests little accumulation with this dose regime. Peak concentrations in milk ranged from 18.5 to 19.8 µg/mL on day 1 and from 20.2 to 22 µg/mL on day 8. Cure rates on day 21 after treatment were 75% (12 out of 16 cows) or 69.4% (26 out of 36 glands). Somatic cell counts and California mastitis test showed a positive trend in cured animals. Uniquely high milk enrofloxacin and ciprofloxacin concentrations were obtained after intramammary administration of enro-C. These concentrations seem effective for treating CNS mastitis. The feasibility of incorporating this experimental pharmaceutical preparation of enrofloxacin is discussed.


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