29,876 research outputs found
Status of the differential transformation method
Further to a recent controversy on whether the differential transformation
method (DTM) for solving a differential equation is purely and solely the
traditional Taylor series method, it is emphasized that the DTM is currently
used, often only, as a technique for (analytically) calculating the power
series of the solution (in terms of the initial value parameters). Sometimes, a
piecewise analytic continuation process is implemented either in a numerical
routine (e.g., within a shooting method) or in a semi-analytical procedure
(e.g., to solve a boundary value problem). Emphasized also is the fact that, at
the time of its invention, the currently-used basic ingredients of the DTM
(that transform a differential equation into a difference equation of same
order that is iteratively solvable) were already known for a long time by the
"traditional"-Taylor-method users (notably in the elaboration of software
packages --numerical routines-- for automatically solving ordinary differential
equations). At now, the defenders of the DTM still ignore the, though much
better developed, studies of the "traditional"-Taylor-method users who, in
turn, seem to ignore similarly the existence of the DTM. The DTM has been given
an apparent strong formalization (set on the same footing as the Fourier,
Laplace or Mellin transformations). Though often used trivially, it is easily
attainable and easily adaptable to different kinds of differentiation
procedures. That has made it very attractive. Hence applications to various
problems of the Taylor method, and more generally of the power series method
(including noninteger powers) has been sketched. It seems that its potential
has not been exploited as it could be. After a discussion on the reasons of the
"misunderstandings" which have caused the controversy, the preceding topics are
concretely illustrated.Comment: To appear in Applied Mathematics and Computation, 29 pages,
references and further considerations adde
COEL: A Web-based Chemistry Simulation Framework
The chemical reaction network (CRN) is a widely used formalism to describe
macroscopic behavior of chemical systems. Available tools for CRN modelling and
simulation require local access, installation, and often involve local file
storage, which is susceptible to loss, lacks searchable structure, and does not
support concurrency. Furthermore, simulations are often single-threaded, and
user interfaces are non-trivial to use. Therefore there are significant hurdles
to conducting efficient and collaborative chemical research. In this paper, we
introduce a new enterprise chemistry simulation framework, COEL, which
addresses these issues. COEL is the first web-based framework of its kind. A
visually pleasing and intuitive user interface, simulations that run on a large
computational grid, reliable database storage, and transactional services make
COEL ideal for collaborative research and education. COEL's most prominent
features include ODE-based simulations of chemical reaction networks and
multicompartment reaction networks, with rich options for user interactions
with those networks. COEL provides DNA-strand displacement transformations and
visualization (and is to our knowledge the first CRN framework to do so), GA
optimization of rate constants, expression validation, an application-wide
plotting engine, and SBML/Octave/Matlab export. We also present an overview of
the underlying software and technologies employed and describe the main
architectural decisions driving our development. COEL is available at
http://coel-sim.org for selected research teams only. We plan to provide a part
of COEL's functionality to the general public in the near future.Comment: 23 pages, 12 figures, 1 tabl
Abstraction of Elementary Hybrid Systems by Variable Transformation
Elementary hybrid systems (EHSs) are those hybrid systems (HSs) containing
elementary functions such as exp, ln, sin, cos, etc. EHSs are very common in
practice, especially in safety-critical domains. Due to the non-polynomial
expressions which lead to undecidable arithmetic, verification of EHSs is very
hard. Existing approaches based on partition of state space or
over-approximation of reachable sets suffer from state explosion or inflation
of numerical errors. In this paper, we propose a symbolic abstraction approach
that reduces EHSs to polynomial hybrid systems (PHSs), by replacing all
non-polynomial terms with newly introduced variables. Thus the verification of
EHSs is reduced to the one of PHSs, enabling us to apply all the
well-established verification techniques and tools for PHSs to EHSs. In this
way, it is possible to avoid the limitations of many existing methods. We
illustrate the abstraction approach and its application in safety verification
of EHSs by several real world examples
Transfer Functions for Protein Signal Transduction: Application to a Model of Striatal Neural Plasticity
We present a novel formulation for biochemical reaction networks in the
context of signal transduction. The model consists of input-output transfer
functions, which are derived from differential equations, using stable
equilibria. We select a set of 'source' species, which receive input signals.
Signals are transmitted to all other species in the system (the 'target'
species) with a specific delay and transmission strength. The delay is computed
as the maximal reaction time until a stable equilibrium for the target species
is reached, in the context of all other reactions in the system. The
transmission strength is the concentration change of the target species. The
computed input-output transfer functions can be stored in a matrix, fitted with
parameters, and recalled to build discrete dynamical models. By separating
reaction time and concentration we can greatly simplify the model,
circumventing typical problems of complex dynamical systems. The transfer
function transformation can be applied to mass-action kinetic models of signal
transduction. The paper shows that this approach yields significant insight,
while remaining an executable dynamical model for signal transduction. In
particular we can deconstruct the complex system into local transfer functions
between individual species. As an example, we examine modularity and signal
integration using a published model of striatal neural plasticity. The modules
that emerge correspond to a known biological distinction between
calcium-dependent and cAMP-dependent pathways. We also found that overall
interconnectedness depends on the magnitude of input, with high connectivity at
low input and less connectivity at moderate to high input. This general result,
which directly follows from the properties of individual transfer functions,
contradicts notions of ubiquitous complexity by showing input-dependent signal
transmission inactivation.Comment: 13 pages, 5 tables, 15 figure
Weyl's symbols of Heisenberg operators of canonical coordinates and momenta as quantum characteristics
The knowledge of quantum phase flow induced under the Weyl's association rule
by the evolution of Heisenberg operators of canonical coordinates and momenta
allows to find the evolution of symbols of generic Heisenberg operators. The
quantum phase flow curves obey the quantum Hamilton's equations and play the
role of characteristics. At any fixed level of accuracy of semiclassical
expansion, quantum characteristics can be constructed by solving a coupled
system of first-order ordinary differential equations for quantum trajectories
and generalized Jacobi fields. Classical and quantum constraint systems are
discussed. The phase-space analytic geometry based on the star-product
operation can hardly be visualized. The statement "quantum trajectory belongs
to a constraint submanifold" can be changed e.g. to the opposite by a unitary
transformation. Some of relations among quantum objects in phase space are,
however, left invariant by unitary transformations and support partly geometric
relations of belonging and intersection. Quantum phase flow satisfies the
star-composition law and preserves hamiltonian and constraint star-functions.Comment: 27 pages REVTeX, 6 EPS Figures. New references added. Accepted for
publication to JM
Scale-free equilibria of self-gravitating gaseous disks with flat rotation curves
We introduce exact analytical solutions of the steady-state hydrodynamic
equations of scale-free, self-gravitating gaseous disks with flat rotation
curves. We express the velocity field in terms of a stream function and obtain
a third-order ordinary differential equation (ODE) for the angular part of the
stream function. We present the closed-form solutions of the obtained ODE and
construct hydrodynamical counterparts of the power-law and elliptic disks, for
which self-consistent stellar dynamical models are known. We show that the
kinematics of the Large Magellanic Cloud can well be explained by our findings
for scale-free elliptic disks.Comment: AAS preprint format, 21 pages, 8 figures, accepted for publication in
The Astrophysical Journa
Institutional entrepreneurs as translators : a comparative study in an emerging activity.
This paper analyzes the reasons why some institutional entrepreneurship strategies failed to translate an institution while other succeeded, by paying a specific attention to the interaction between material and discursive dimensions in the translation process. A theoretical framework integrating both dimensions of translation is first proposed in order to study strategies of competing entrepreneurs. Then a comparative study of three entrepreneurs translating practices of corporate social evaluation in the French context is used to investigate the processes through which competing translators achieved their objective more or less successfully.neo-institutionalisme; translation; corporate social responsibility;
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