25,533 research outputs found
Some resonances between Eastern thought and Integral Biomathics in the framework of the WLIMES formalism for modelling living systems
Forty-two years ago, Capra published âThe Tao of Physicsâ (Capra, 1975). In this book (page 17) he writes: âThe exploration of the atomic and subatomic world in the twentieth century has âŠ. necessitated a radical revision of many of our basic conceptsâ and that, unlike âclassicalâ physics, the sub-atomic and quantum âmodern physicsâ shows resonances with Eastern thoughts and âleads us to a view of the world which is very similar to the views held by mystics of all ages and traditions.â This article stresses an analogous situation in biology with respect to a new theoretical approach for studying living systems, Integral Biomathics (IB), which also exhibits some resonances with Eastern thought. Stepping on earlier research in cybernetics1 and theoretical biology,2 IB has been developed since 2011 by over 100 scientists from a number of disciplines who have been exploring a substantial set of theoretical frameworks. From that effort, the need for a robust core model utilizing advanced mathematics and computation adequate for understanding the behavior of organisms as dynamic wholes was identified. At this end, the authors of this article have proposed WLIMES (Ehresmann and Simeonov, 2012), a formal theory for modeling living systems integrating both the Memory Evolutive Systems (Ehresmann and Vanbremeersch, 2007) and the Wandering Logic Intelligence (Simeonov, 2002b). Its principles will be recalled here with respect to their
resonances to Eastern thought
Tropical Kraus maps for optimal control of switched systems
Kraus maps (completely positive trace preserving maps) arise classically in
quantum information, as they describe the evolution of noncommutative
probability measures. We introduce tropical analogues of Kraus maps, obtained
by replacing the addition of positive semidefinite matrices by a multivalued
supremum with respect to the L\"owner order. We show that non-linear
eigenvectors of tropical Kraus maps determine piecewise quadratic
approximations of the value functions of switched optimal control problems.
This leads to a new approximation method, which we illustrate by two
applications: 1) approximating the joint spectral radius, 2) computing
approximate solutions of Hamilton-Jacobi PDE arising from a class of switched
linear quadratic problems studied previously by McEneaney. We report numerical
experiments, indicating a major improvement in terms of scalability by
comparison with earlier numerical schemes, owing to the "LMI-free" nature of
our method.Comment: 15 page
Grids of stellar models. VIII. From 0.4 to 1.0 Msun at Z=0.020 and Z=0.001, with the MHD equation of state
We present stellar evolutionary models covering the mass range from 0.4 to 1
Msun calculated for metallicities Z=0.020 and 0.001 with the MHD equation of
state (Hummer & Mihalas, 1988; Mihalas et al. 1988; D\"appen et al. 1988). A
parallel calculation using the OPAL (Rogers et al. 1996) equation of state has
been made to demonstrate the adequacy of the MHD equation of state in the range
of 1.0 to 0.8 Msun (the lower end of the OPAL tables). Below, down to 0.4 Msun,
we have justified the use of the MHD equation of state by theoretical arguments
and the findings of Chabrier & Baraffe (1997).
We use the radiative opacities by Iglesias & Rogers (1996), completed with
the atomic and molecular opacities by Alexander & Fergusson (1994). We follow
the evolution from the Hayashi fully convective configuration up to the red
giant tip for the most massive stars, and up to an age of 20 Gyr for the less
massive ones. We compare our solar-metallicity models with recent models
computed by other groups and with observations.
The present stellar models complete the set of grids computed with the same
up-to-date input physics by the Geneva group [Z=0.020 and 0.001, Schaller et
al. (1992), Bernasconi (1996), and Charbonnel et al. (1996); Z=0.008, Schaerer
et al. (1992); Z=0.004, Charbonnel et al. (1993); Z=0.040, Schaerer et al.
(1993); Z=0.10, Mowlavi et al. (1998); enhanced mass loss rate evolutionary
tracks, Meynet et al. (1994)].Comment: Accepted for publication in A&A Supplement Serie
A Family of Iterative Gauss-Newton Shooting Methods for Nonlinear Optimal Control
This paper introduces a family of iterative algorithms for unconstrained
nonlinear optimal control. We generalize the well-known iLQR algorithm to
different multiple-shooting variants, combining advantages like
straight-forward initialization and a closed-loop forward integration. All
algorithms have similar computational complexity, i.e. linear complexity in the
time horizon, and can be derived in the same computational framework. We
compare the full-step variants of our algorithms and present several simulation
examples, including a high-dimensional underactuated robot subject to contact
switches. Simulation results show that our multiple-shooting algorithms can
achieve faster convergence, better local contraction rates and much shorter
runtimes than classical iLQR, which makes them a superior choice for nonlinear
model predictive control applications.Comment: 8 page
Stability Tests for a Class of 2D Continuous-Discrete Linear Systems with Dynamic Boundary Conditions
Repetitive processes are a distinct class of 2D systems of both practical and theoretical interest. Their essential characteristic is repeated sweeps, termed passes, through a set of dynamics defined over a finite duration with explicit interaction between the outputs, or pass profiles, produced as the system evolves. Experience has shown that these processes cannot be studied/controlled by direct application of existing theory (in all but a few very restrictive special cases). This fact, and the growing list of applications areas, has prompted an on-going research programme into the development of a 'mature' systems theory for these processes for onward translation into reliable generally applicable controller design algorithms. This paper develops stability tests for a sub-class of so-called differential linear repetitive processes in the presence of a general set of initial conditions, where it is known that the structure of these conditions is critical to their stability properties
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