2,507,027 research outputs found
Jet Methods in Time-Dependent Lagrangian Biomechanics
In this paper we propose the time-dependent generalization of an `ordinary'
autonomous human biomechanics, in which total mechanical + biochemical energy
is not conserved. We introduce a general framework for time-dependent
biomechanics in terms of jet manifolds associated to the extended
musculo-skeletal configuration manifold, called the configuration bundle. We
start with an ordinary configuration manifold of human body motion, given as a
set of its all active degrees of freedom (DOF) for a particular movement. This
is a Riemannian manifold with a material metric tensor given by the total
mass-inertia matrix of the human body segments. This is the base manifold for
standard autonomous biomechanics. To make its time-dependent generalization, we
need to extend it with a real time axis. By this extension, using techniques
from fibre bundles, we defined the biomechanical configuration bundle. On the
biomechanical bundle we define vector-fields, differential forms and affine
connections, as well as the associated jet manifolds. Using the formalism of
jet manifolds of velocities and accelerations, we develop the time-dependent
Lagrangian biomechanics. Its underlying geometric evolution is given by the
Ricci flow equation.
Keywords: Human time-dependent biomechanics, configuration bundle, jet
spaces, Ricci flowComment: 13 pages, 3 figure
Exploring the cooperative regimes in a model of agents without memory or "tags": indirect reciprocity vs. selfish incentives
The self-organization in cooperative regimes in a simple mean-field version
of a model based on "selfish" agents which play the Prisoner's Dilemma (PD)
game is studied. The agents have no memory and use strategies not based on
direct reciprocity nor 'tags'. Two variables are assigned to each agent at
time , measuring its capital and its probability of cooperation
. At each time step a pair of agents interact by playing the PD
game. These 2 agents update their probability of cooperation as follows:
they compare the profits they made in this interaction with an
estimator and, if , agent
increases its while if the agent
decreases . The 4!=24 different cases produced by permuting the four
Prisoner's Dilemma canonical payoffs 3, 0, 1, and 5 -
corresponding,respectively, to (reward), (sucker's payoff),
(temptation to defect) and (punishment) - are analyzed. It turns out that
for all these 24 possibilities, after a transient,the system self-organizes
into a stationary state with average equilibrium probability of cooperation
= constant .Depending on the payoff matrix, there are
different equilibrium states characterized by their average probability of
cooperation and average equilibrium per-capita-income
().Comment: 11 pages, 5 figure
Temperature dependence of optical spectral weights in quarter-filled ladder systems
The temperature dependence of the integrated optical conductivity I(T)
reflects the changes of the kinetic energy as spin and charge correlations
develop. It provides a unique way to explore experimentally the kinetic
properties of strongly correlated systems. We calculated I(T) in the frame of a
t-J-V model at quarter-filling for ladder systems, like NaV_2O_5, and show that
the measured strong T dependence of I(T) for NaV_2O_5 can be explained by the
destruction of short range antiferromagnetic correlations. Thus I(T) provides
detailed information about super-exchange and magnetic energy scales.Comment: 4 pages, 5 figure
Comparing Powers of Edge Ideals
Given a nontrivial homogeneous ideal , a
problem of great recent interest has been the comparison of the th ordinary
power of and the th symbolic power .
This comparison has been undertaken directly via an exploration of which
exponents and guarantee the subset containment
and asymptotically via a computation of the resurgence , a number for
which any guarantees .
Recently, a third quantity, the symbolic defect, was introduced; as
, the symbolic defect is the minimal number of generators
required to add to in order to get .
We consider these various means of comparison when is the edge ideal of
certain graphs by describing an ideal for which .
When is the edge ideal of an odd cycle, our description of the structure
of yields solutions to both the direct and asymptotic containment
questions, as well as a partial computation of the sequence of symbolic
defects.Comment: Version 2: Revised based on referee suggestions. Lemma 5.12 was added
to clarify the proof of Theorem 5.13. To appear in the Journal of Algebra and
its Applications. Version 1: 20 pages. This project was supported by Dordt
College's undergraduate research program in summer 201
About the stability of the tangent bundle restricted to a curve
Let C be a smooth projective curve with genus g>1 and Clifford index c(C) and
let L be a line bundle on C generated by its global sections. The morphism i:C
-->P(H^0(L))=P is well-defined and i*T is the restriction to C of the tangent
bundle T of the projective space P. Sharpening a theorem by Paranjape, we show
that if deg L>2g-c(C)-1 then i*T is semi-stable, specifying when it is also
stable. We then prove the existence on many curves of a line bundle L of degree
2g-c(C)-1 such that i*T is not semi-stable. Finally, we completely characterize
the (semi-)stability of i*T when C is hyperelliptic.Comment: 5 page
- âŠ