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"Eccentrics"
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What we found in the sofa and how it saved the world
Finding a rare zucchini-colored crayon leads twelve-year-old River Monroe and his friends on an adventure with their eccentric neighbor to save Earth from invading interstellar storm troopers.
Book
On the eccentricity-based invariants of uniform hypergraphs
Let G = (V, E) be a simple connected hypergraph with V the vertex set and E the edge set, respectively. The eccentricity of vertex v refers to the farthest distance of vertex v from other vertices of G, denoted by εG
(v). The eccentric adjacency index (EAI) of G is described as
ξ
a
d
(
G
)
=
∑
u
∈
V
(
G
)
S
G
(
u
)
ε
G
(
u
)
, where
S
G
(
u
)
=
∑
υ
∈
N
G
(
u
)
d
G
(
υ
)
. In this work, we consider the gerneralation of the EAI for hypergraphs to draw several conclusions related to extremal problems to EAI. We first propose several bounds on the EAI of k-uniform hypertrees with fixed maximum degree, diameter and edges, respectively, and characterize the corresponding extremal k-uniform hypertrees. Then we investigate the relationsip between EAI and the adjacent eccentric distance sum. Finally, we present the upper bounds for the difference between the eccentricity distance sum and eccentric connectivity index in the k-uniform hypergraph with diameter 2. It generalizes the previous results of the current authors from the simple graphs to hypergraphs for graph parameters based on eccentricity.
Journal Article
The extraordinary Mr. Qwerty
Mr. Qwerty worries that his ideas might seem strange...so he keeps them under his hat. But extraordinary ideas refuse to stay hidden for long.
Book
Hill-type muscle model with serial damping and eccentric force–velocity relation
Hill-type muscle models are commonly used in biomechanical simulations to predict passive and active muscle forces. Here, a model is presented which consists of four elements: a contractile element with force–length and force–velocity relations for concentric and eccentric contractions, a parallel elastic element, a series elastic element, and a serial damping element. With this, it combines previously published effects relevant for muscular contraction, i.e. serial damping and eccentric force–velocity relation. The model is exemplarily applied to arm movements. The more realistic representation of the eccentric force–velocity relation results in human-like elbow-joint flexion. The model is provided as ready to use Matlab ® and Simulink ® code.
Journal Article
Sprint versus isolated eccentric training: Comparative effects on hamstring architecture and performance in soccer players
The purpose of this study was to compare the effects of hamstring eccentric (NHE) strength training versus sprint training programmed as complements to regular soccer practice, on sprint performance and its mechanical underpinnings, as well as biceps femoris long head (BFlh) architecture.
In this prospective interventional control study, sprint performance, sprint mechanics and BFlh architecture variables were compared before versus after six weeks of training during the first six preseason weeks, and between three different random match-pair groups of soccer players: \"Soccer group\" (n = 10), \"Nordic group\" (n = 12) and \"Sprint group\" (n = 10).
For sprint performance and mechanics, small to large pre-post improvements were reported in \"Sprint group\" (except maximal running velocity), whereas only trivial to small negative changes were reported in \"Soccer group\" and \"Nordic group\". For BFlh architecture variables, \"Sprint\" group showed moderate increase in fascicle length compared to smaller augment for the \"Nordic\" group with trivial changes for \"Soccer group\". Only \"Nordic\" group presented small increases at pennation angle.
The results suggest that sprint training was superior to NHE in order to increase BFlh fascicle length although only the sprint training was able to both provide a preventive stimulus (increase fascicle length) and at the same time improve both sprint performance and mechanics. Further studies with advanced imaging techniques are needed to confirm the validity of the findings.
Journal Article
Biases among classes of rank-crank partitions\\(\\pmod{11}\\)
In this paper, we prove inequalities for ranks, cranks, and partitions among different classes modulo 11. These were conjectured by Borozenets.
Paper