7,838 research outputs found
A non-regular Groebner fan
The Groebner fan of an ideal , defined by Mora and
Robbiano, is a complex of polyhedral cones in . The maximal cones of the
fan are in bijection with the distinct monomial initial ideals of as the
term order varies. If is homogeneous the Groebner fan is complete and is
the normal fan of the state polytope of . In general the Groebner fan is not
complete and therefore not the normal fan of a polytope. We may ask if the
restricted Groebner fan, a subdivision of , is regular i.e. the
normal fan of a polyhedron. The main result of this paper is an example of an
ideal in whose restricted Groebner fan is not regular.Comment: 11 page
NaDeA: A Natural Deduction Assistant with a Formalization in Isabelle
We present a new software tool for teaching logic based on natural deduction.
Its proof system is formalized in the proof assistant Isabelle such that its
definition is very precise. Soundness of the formalization has been proved in
Isabelle. The tool is open source software developed in TypeScript / JavaScript
and can thus be used directly in a browser without any further installation.
Although developed for undergraduate computer science students who are used to
study and program concrete computer code in a programming language we consider
the approach relevant for a broader audience and for other proof systems as
well.Comment: Proceedings of the Fourth International Conference on Tools for
Teaching Logic (TTL2015), Rennes, France, June 9-12, 2015. Editors: M.
Antonia Huertas, Jo\~ao Marcos, Mar\'ia Manzano, Sophie Pinchinat,
Fran\c{c}ois Schwarzentrube
An algorithm for lifting points in a tropical variety
The aim of this paper is to give a constructive proof of one of the basic
theorems of tropical geometry: given a point on a tropical variety (defined
using initial ideals), there exists a Puiseux-valued ``lift'' of this point in
the algebraic variety. This theorem is so fundamental because it justifies why
a tropical variety (defined combinatorially using initial ideals) carries
information about algebraic varieties: it is the image of an algebraic variety
over the Puiseux series under the valuation map. We have implemented the
``lifting algorithm'' using Singular and Gfan if the base field are the
rational numbers. As a byproduct we get an algorithm to compute the Puiseux
expansion of a space curve singularity in (K^{n+1},0).Comment: 33 page
Optimal Investment Horizons
In stochastic finance, one traditionally considers the return as a
competitive measure of an asset, {\it i.e.}, the profit generated by that asset
after some fixed time span , say one week or one year. This measures
how well (or how bad) the asset performs over that given period of time. It has
been established that the distribution of returns exhibits ``fat tails''
indicating that large returns occur more frequently than what is expected from
standard Gaussian stochastic processes (Mandelbrot-1967,Stanley1,Doyne).
Instead of estimating this ``fat tail'' distribution of returns, we propose
here an alternative approach, which is outlined by addressing the following
question: What is the smallest time interval needed for an asset to cross a
fixed return level of say 10%? For a particular asset, we refer to this time as
the {\it investment horizon} and the corresponding distribution as the {\it
investment horizon distribution}. This latter distribution complements that of
returns and provides new and possibly crucial information for portfolio design
and risk-management, as well as for pricing of more exotic options. By
considering historical financial data, exemplified by the Dow Jones Industrial
Average, we obtain a novel set of probability distributions for the investment
horizons which can be used to estimate the optimal investment horizon for a
stock or a future contract.Comment: Latex, 5 pages including 4 figur
A model analysis on nitrate leaching under different soil and climate conditions and use of catch crops
The use of crops and catch crops with deep rooting can strongly improve the possibility of retaining nitrate-N that will otherwise be leached to the deeper soil layers and end up in the surrounding environment. But will it always be an advantage for the farmer to
grow a catch crop? This will depend on factors such as soil mineral nitrogen level, soil water holding capacity, winter precipitation, rooting depth and N demand of the scceeding crop. These factors interact, and it can be very difficult for farmers or advisors to use this information to decide whether growing a catch crop will be beneficial. To analyse the effect of catch crops under different Danish soil and precipitation conditions, we used the soil, plant and atmosphere model Daisy
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