18 research outputs found
The influence of isospin conservation on pion multiplicity distribution in independent emission models
We discuss two models for multiple pion production in which strict conservation of isospin generates strong correlations in multiplicity distribution. The first model is a particular version of the uncorrelated jet model in which pions are produced in an eigenstate of total isospin and charge, the second one is the hadronic bremsstrahlung model of pion emission by an isospinor nucleon current. The predictions of these models concerning multiplicity distribution are almost identical : 1. linear rise of the dispersion of the negative pion multiplicity distribution with the average multiplicity which agrees with the data very well, and 2. strong negative correlations between charged and neutral pions which is in disagreement with the data
Taylor Series Revisited
We propose a renovated approach around the use of Taylor expansions to provide polynomial approximations. We introduce a coinductive type scheme and finely-tuned operations that altogether constitute an algebra, where our multivariate Taylor expansions are first-class objects. As for applications, beyond providing classical expansions of integro-differential and algebraic expressions mixed with elementary functions, we demonstrate that solving ODE and PDE in a direct way, without external solvers, is also possible. We also discuss the possibility of computing certified errors within our scheme
A Library for Declarative Resolution-Independent 2D Graphics
The design of most 2D graphics frameworks has been guided by what the computer can draw efficiently, instead of by how graphics can best be expressed and composed. As a result, such frameworks restrict expressivity by providing a limited set of shape primitives, a limited set of textures and only affine transformations. For example, non-affine transformations can only be added by invasive modification or complex tricks rather than by simple composition. More general frameworks exist, but they make it harder to describe and analyze shapes. We present a new declarative approach to resolution-independent 2D graphics that generalizes and simplifies the functionality of traditional frameworks, while preserving their efficiency. As a real-world example, we show the implementation of a form of focus+context lenses that gives better image quality and better performance than the state-of-the-art solution at a fraction of the code. Our approach can serve as a versatile foundation for the creation of advanced graphics and higher level frameworks
A Grassmann integral equation
The present study introduces and investigates a new type of equation which is
called Grassmann integral equation in analogy to integral equations studied in
real analysis. A Grassmann integral equation is an equation which involves
Grassmann integrations and which is to be obeyed by an unknown function over a
(finite-dimensional) Grassmann algebra G_m. A particular type of Grassmann
integral equations is explicitly studied for certain low-dimensional Grassmann
algebras. The choice of the equation under investigation is motivated by the
effective action formalism of (lattice) quantum field theory. In a very general
setting, for the Grassmann algebras G_2n, n = 2,3,4, the finite-dimensional
analogues of the generating functionals of the Green functions are worked out
explicitly by solving a coupled system of nonlinear matrix equations. Finally,
by imposing the condition G[{\bar\Psi},{\Psi}] = G_0[{\lambda\bar\Psi},
{\lambda\Psi}] + const., 0<\lambda\in R (\bar\Psi_k, \Psi_k, k=1,...,n, are the
generators of the Grassmann algebra G_2n), between the finite-dimensional
analogues G_0 and G of the (``classical'') action and effective action
functionals, respectively, a special Grassmann integral equation is being
established and solved which also is equivalent to a coupled system of
nonlinear matrix equations. If \lambda \not= 1, solutions to this Grassmann
integral equation exist for n=2 (and consequently, also for any even value of
n, specifically, for n=4) but not for n=3. If \lambda=1, the considered
Grassmann integral equation has always a solution which corresponds to a
Gaussian integral, but remarkably in the case n=4 a further solution is found
which corresponds to a non-Gaussian integral. The investigation sheds light on
the structures to be met for Grassmann algebras G_2n with arbitrarily chosen n.Comment: 58 pages LaTeX (v2: mainly, minor updates and corrections to the
reference section; v3: references [4], [17]-[21], [39], [46], [49]-[54],
[61], [64], [139] added
A Library for Declarative Resolution-Independent 2D Graphics
htmlabstractThe design of most 2D graphics frameworks has been guided by what the computer can draw efficiently, instead of by how graphics can best be expressed and composed. As a result, such frameworks restrict expressivity by providing a limited set of shape primitives, a limited set of textures and only affine transformations. For example, non-affine transformations can only be added by invasive modification or complex tricks rather than by simple composition. More general frameworks exist, but they make it harder to describe and analyze shapes. We present a new declarative approach to resolution-independent 2D graphics that generalizes and simplifies the functionality of traditional frameworks, while preserving their efficiency. As a real-world example, we show the implementation of a form of focus+context lenses that gives better image quality and better performance than the state-of-the-art solution at a fraction of the code. Our approach can serve as a versatile foundation for the creation of advanced graphics and higher level frameworks
Lazy Multivariate Higher-Order Forward-Mode AD
A method is presented for computing all higher-order partial
derivatives of a multivariate function Rn → R. This method works
by evaluating the function under a nonstandard interpretation, lifting
reals to multivariate power series. Multivariate power series,
with potentially an infinite number of terms with nonzero coefficients,
are represented using a lazy data structure constructed
out of linear terms. A complete implementation of this method
in SCHEME is presented, along with a straightforward exposition,
based on Taylor expansions, of the method’s correctness
Taylor Series Revisited
International audienceWe propose a renovated approach around the use of Taylor expansions to provide polynomial approximations. We introduce a coinductive type scheme and finely-tuned operations that altogether constitute an algebra, where our multivariate Taylor expansions are first-class objects. As for applications, beyond providing classical expansions of integro-differential and algebraic expressions mixed with elementary functions, we demonstrate that solving ODE and PDE in a direct way, without external solvers, is also possible. We also discuss the possibility of computing certified errors within our scheme
3-1 野生ニホンザルにおける毛づくろい前の音声使用の様態に関する調査(X.共同利用研究 2.研究成果)
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)298649-6