504,109 research outputs found
Computing Periods of Hypersurfaces
We give an algorithm to compute the periods of smooth projective
hypersurfaces of any dimension. This is an improvement over existing algorithms
which could only compute the periods of plane curves. Our algorithm reduces the
evaluation of period integrals to an initial value problem for ordinary
differential equations of Picard-Fuchs type. In this way, the periods can be
computed to extreme-precision in order to study their arithmetic properties.
The initial conditions are obtained by an exact determination of the cohomology
pairing on Fermat hypersurfaces with respect to a natural basis.Comment: 33 pages; Final version. Fixed typos, minor expository changes.
Changed code repository lin
Computing periods of rational integrals
A period of a rational integral is the result of integrating, with respect to
one or several variables, a rational function over a closed path. This work
focuses particularly on periods depending on a parameter: in this case the
period under consideration satisfies a linear differential equation, the
Picard-Fuchs equation. I give a reduction algorithm that extends the
Griffiths-Dwork reduction and apply it to the computation of Picard-Fuchs
equations. The resulting algorithm is elementary and has been successfully
applied to problems that were previously out of reach.Comment: To appear in Math. comp. Supplementary material at
http://pierre.lairez.fr/supp/periods
Algorithms for Computing Abelian Periods of Words
Constantinescu and Ilie (Bulletin EATCS 89, 167--170, 2006) introduced the
notion of an \emph{Abelian period} of a word. A word of length over an
alphabet of size can have distinct Abelian periods.
The Brute-Force algorithm computes all the Abelian periods of a word in time
using space. We present an off-line
algorithm based on a \sel function having the same worst-case theoretical
complexity as the Brute-Force one, but outperforming it in practice. We then
present on-line algorithms that also enable to compute all the Abelian periods
of all the prefixes of .Comment: Accepted for publication in Discrete Applied Mathematic
Technology Push, Demand Pull And The Shaping Of Technological Paradigms - Patterns In The Development Of Computing Technology
An assumption generally subscribed in evolutionary economics is thatnew technological paradigms arise from advances is science anddevelopments in technological knowledge. Demand only influences theselection among competing paradigms, and the course the paradigm afterits inception. In this paper we argue that this view needs to beadapted. We demonstrate that in the history of computing technology inthe 20th century a distinction can be made between periods in whicheither demand or knowledge development was the dominant enabler ofinnovation. In the demand enabled periods new technological (sub-)paradigms in computing technology have emerged as well.enablers of innovation;history of computing;technological paradigms
Periods for Calabi--Yau and Landau--Ginzburg Vacua
The complete structure of the moduli space of \cys\ and the associated
Landau-Ginzburg theories, and hence also of the corresponding low-energy
effective theory that results from (2,2) superstring compactification, may be
determined in terms of certain holomorphic functions called periods. These
periods are shown to be readily calculable for a great many such models. We
illustrate this by computing the periods explicitly for a number of classes of
\cys. We also point out that it is possible to read off from the periods
certain important information relating to the mirror manifolds.Comment: 54pp. Use harvmac; WARNING: option l does not work. (Replaces
unTeXable version.
Dark Periods in Rabi Oscillations of Superconducting Phase Qubit Coupled to a Microscopic Two-Level System
We proposed a scheme to demonstrate macroscopic quantum jumps in a
superconducting phase qubit coupled to a microscopic two-level system in the
Josephson tunnel junction. Irradiated with suitable microwaves, the Rabi
oscillations of the qubit exhibit signatures of quantum jumps: a random
telegraph signal with long intervals of intense macroscopic quantum tunneling
events (bright periods) interrupted by the complete absence of tunneling events
(dark periods). An analytical model was developed to describe the width of the
dark periods quantitatively. The numerical simulations indicate that our
analytical model captured underlying physics of the system. Besides calibrating
the quality of the microscopic two-level system, our results have significance
in quantum information process since dark periods in Rabi oscillations are also
responsible for errors in quantum computing with superconducting qubits.Comment: 9 pages, 8 figure
Comparing maximal mean values on different scales
When computing the average speed of a car over different time periods from
given GPS data, it is conventional wisdom that the maximal average speed over
all time intervals of fixed length decreases if the interval length increases.
However, this intuition is wrong. We investigate this phenomenon and make
rigorous in which sense this intuition is still true
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