34,516 research outputs found
A program for the Bayesian Neural Network in the ROOT framework
We present a Bayesian Neural Network algorithm implemented in the TMVA
package, within the ROOT framework. Comparing to the conventional utilization
of Neural Network as discriminator, this new implementation has more advantages
as a non-parametric regression tool, particularly for fitting probabilities. It
provides functionalities including cost function selection, complexity control
and uncertainty estimation. An example of such application in High Energy
Physics is shown. The algorithm is available with ROOT release later than 5.29.Comment: 12 pages, 6 figure
New Acceleration of Nearly Optimal Univariate Polynomial Root-findERS
Univariate polynomial root-finding has been studied for four millennia and is
still the subject of intensive research. Hundreds of efficient algorithms for
this task have been proposed. Two of them are nearly optimal. The first one,
proposed in 1995, relies on recursive factorization of a polynomial, is quite
involved, and has never been implemented. The second one, proposed in 2016,
relies on subdivision iterations, was implemented in 2018, and promises to be
practically competitive, although user's current choice for univariate
polynomial root-finding is the package MPSolve, proposed in 2000, revised in
2014, and based on Ehrlich's functional iterations. By proposing and
incorporating some novel techniques we significantly accelerate both
subdivision and Ehrlich's iterations. Moreover our acceleration of the known
subdivision root-finders is dramatic in the case of sparse input polynomials.
Our techniques can be of some independent interest for the design and analysis
of polynomial root-finders.Comment: 89 pages, 5 figures, 2 table
Logarithm laws for flows on homogeneous spaces
We prove that almost all geodesics on a noncompact locally symmetric space of
finite volume grow with a logarithmic speed -- the higher rank generalization
of a theorem of D. Sullivan (1982). More generally, under certain conditions on
a sequence of subsets of a homogeneous space ( a semisimple
Lie group, a non-uniform lattice) and a sequence of elements of
we prove that for almost all points of the space, one has for infinitely many .
The main tool is exponential decay of correlation coefficients of smooth
functions on . Besides the aforementioned application to geodesic
flows, as a corollary we obtain a new proof of the classical Khinchin-Groshev
theorem in simultaneous Diophantine approximation, and settle a related
conjecture recently made by M. Skriganov
Near Optimal Subdivision Algorithms for Real Root Isolation
We describe a subroutine that improves the running time of any subdivision
algorithm for real root isolation. The subroutine first detects clusters of
roots using a result of Ostrowski, and then uses Newton iteration to converge
to them. Near a cluster, we switch to subdivision, and proceed recursively. The
subroutine has the advantage that it is independent of the predicates used to
terminate the subdivision. This gives us an alternative and simpler approach to
recent developments of Sagraloff (2012) and Sagraloff-Mehlhorn (2013), assuming
exact arithmetic.
The subdivision tree size of our algorithm using predicates based on
Descartes's rule of signs is bounded by , which is better by
compared to known results. Our analysis differs in two key
aspects. First, we use the general technique of continuous amortization from
Burr-Krahmer-Yap (2009), and second, we use the geometry of clusters of roots
instead of the Davenport-Mahler bound. The analysis naturally extends to other
predicates.Comment: 19 pages, 3 figure
Subdynamics as a mechanism for objective description
The relationship between microsystems and macrosystems is considered in the
context of quantum field formulation of statistical mechanics: it is argued
that problems on foundations of quantum mechanics can be solved relying on this
relationship. This discussion requires some improvement of non-equilibrium
statistical mechanics that is briefly presented.Comment: latex, 15 pages. Paper submitted to Proc. Conference "Mysteries,
Puzzles And Paradoxes In Quantum Mechanics, Workshop on Entanglement And
Decoherence, Palazzo Feltrinelli, Gargnano, Garda Lake, Italy, 20-25
September, 199
Can non-linear real shocks explain the persistence of PPP exchange rate disequilibria?
A core stylized fact of the empirical exchange rate literature is that half-life deviations of equilibrium real exchange rates from levels implied by Purchasing Power Parity (PPP) are very persistent. Empirical efforts to explain this persistence typically proceed along two distinct paths, resorting either to the presence of real shocks such as productivity differentials that drive equilibrium exchange rates away from levels implied by PPP, or the presence of non-linearities in the adjustment process around PPP. By contrast, we combine these two explanations in the context of an innovative panel estimation methodology. We conclude that both explanations are relevant to the behavior of exchange rates and that resulting half-lives are much shorter than estimated using linear PPP and more consistent with the observed volatility of nominal and real exchange rates. JEL Classification: F31, C23, L6-L9Balassa-Samuelson, EPSTAR, exchange rate, PPP, productivity
Hot new directions for quasi-Monte Carlo research in step with applications
This article provides an overview of some interfaces between the theory of
quasi-Monte Carlo (QMC) methods and applications. We summarize three QMC
theoretical settings: first order QMC methods in the unit cube and in
, and higher order QMC methods in the unit cube. One important
feature is that their error bounds can be independent of the dimension
under appropriate conditions on the function spaces. Another important feature
is that good parameters for these QMC methods can be obtained by fast efficient
algorithms even when is large. We outline three different applications and
explain how they can tap into the different QMC theory. We also discuss three
cost saving strategies that can be combined with QMC in these applications.
Many of these recent QMC theory and methods are developed not in isolation, but
in close connection with applications
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