10,812 research outputs found
The Geometry of Border Bases
The main topic of the paper is the construction of various explicit flat
families of border bases. To begin with, we cover the punctual Hilbert scheme
Hilb^\mu(A^n) by border basis schemes and work out the base changes. This
enables us to control flat families obtained by linear changes of coordinates.
Next we provide an explicit construction of the principal component of the
border basis scheme, and we use it to find flat families of maximal dimension
at each radical point. Finally, we connect radical points to each other and to
the monomial point via explicit flat families on the principal component
Deformations of Border Bases
Here we study the problem of generalizing one of the main tools of Groebner
basis theory, namely the flat deformation to the leading term ideal, to the
border basis setting. After showing that the straightforward approach based on
the deformation to the degree form ideal works only under additional
hypotheses, we introduce border basis schemes and universal border basis
families. With their help the problem can be rephrased as the search for a
certain rational curve on a border basis scheme. We construct the system of
generators of the vanishing ideal of the border basis scheme in different ways
and study the question of how to minimalize it. For homogeneous ideals, we also
introduce a homogeneous border basis scheme and prove that it is an affine
space in certain cases. In these cases it is then easy to write down the
desired deformations explicitly.Comment: 21 page
Relativistic Shocks: Particle Acceleration and Magnetization
We review the physics of relativistic shocks, which are often invoked as the
sources of non-thermal particles in pulsar wind nebulae (PWNe), gamma-ray
bursts (GRBs), and active galactic nuclei (AGN) jets, and as possible sources
of ultra-high energy cosmic-rays. We focus on particle acceleration and
magnetic field generation, and describe the recent progress in the field driven
by theory advances and by the rapid development of particle-in-cell (PIC)
simulations. In weakly magnetized or quasi parallel-shocks (where the magnetic
field is nearly aligned with the flow), particle acceleration is efficient. The
accelerated particles stream ahead of the shock, where they generate strong
magnetic waves which in turn scatter the particles back and forth across the
shock, mediating their acceleration. In contrast, in strongly magnetized
quasi-perpendicular shocks, the efficiencies of both particle acceleration and
magnetic field generation are suppressed. Particle acceleration, when
efficient, modifies the turbulence around the shock on a long time scale, and
the accelerated particles have a characteristic energy spectral index of ~ 2.2
in the ultra-relativistic limit. We discuss how this novel understanding of
particle acceleration and magnetic field generation in relativistic shocks can
be applied to high-energy astrophysical phenomena, with an emphasis on PWNe and
GRB afterglows.Comment: 32 pages; 9 figures; invited topical review, comments welcome;
submitted for publication in "The Strongest Magnetic Fields in the Universe"
(Space Sciences Series of ISSI, Springer), Space Science Review
Portfolio Optimization and Model Predictive Control: A Kinetic Approach
In this paper, we introduce a large system of interacting financial agents in
which each agent is faced with the decision of how to allocate his capital
between a risky stock or a risk-less bond. The investment decision of
investors, derived through an optimization, drives the stock price. The model
has been inspired by the econophysical Levy-Levy-Solomon model (Economics
Letters, 45). The goal of this work is to gain insights into the stock price
and wealth distribution. We especially want to discover the causes for the
appearance of power-laws in financial data. We follow a kinetic approach
similar to (D. Maldarella, L. Pareschi, Physica A, 391) and derive the mean
field limit of our microscopic agent dynamics. The novelty in our approach is
that the financial agents apply model predictive control (MPC) to approximate
and solve the optimization of their utility function. Interestingly, the MPC
approach gives a mathematical connection between the two opponent economic
concepts of modeling financial agents to be rational or boundedly rational.
Furthermore, this is to our knowledge the first kinetic portfolio model which
considers a wealth and stock price distribution simultaneously. Due to our
kinetic approach, we can study the wealth and price distribution on a
mesoscopic level. The wealth distribution is characterized by a lognormal law.
For the stock price distribution, we can either observe a lognormal behavior in
the case of long-term investors or a power-law in the case of high-frequency
trader. Furthermore, the stock return data exhibits a fat-tail, which is a well
known characteristic of real financial data
Coverage Centrality Maximization in Undirected Networks
Centrality metrics are among the main tools in social network analysis. Being
central for a user of a network leads to several benefits to the user: central
users are highly influential and play key roles within the network. Therefore,
the optimization problem of increasing the centrality of a network user
recently received considerable attention. Given a network and a target user
, the centrality maximization problem consists in creating new links
incident to in such a way that the centrality of is maximized,
according to some centrality metric. Most of the algorithms proposed in the
literature are based on showing that a given centrality metric is monotone and
submodular with respect to link addition. However, this property does not hold
for several shortest-path based centrality metrics if the links are undirected.
In this paper we study the centrality maximization problem in undirected
networks for one of the most important shortest-path based centrality measures,
the coverage centrality. We provide several hardness and approximation results.
We first show that the problem cannot be approximated within a factor greater
than , unless , and, under the stronger gap-ETH hypothesis, the
problem cannot be approximated within a factor better than , where
is the number of users. We then propose two greedy approximation
algorithms, and show that, by suitably combining them, we can guarantee an
approximation factor of . We experimentally compare the
solutions provided by our approximation algorithm with optimal solutions
computed by means of an exact IP formulation. We show that our algorithm
produces solutions that are very close to the optimum.Comment: Accepted to AAAI 201
Development and implantation of a Thesaurus of Manufacturing Engineering terms
Present work shows the teaching-learning experience developed in the Department of Manufacturing Engineering of the University of Malaga. This experience is based on the need to generate a specific glossary of manufacturing engineering terms to be used as a study guide by the students. Eventually, it was decided to make a Thesaurus that would be aimed at a teaching activity. Also, it would take part in the educational innovation project PIE 13-025 of the University of Malaga, within the biennium 2013/2015. The first step consisted of the design of Thesaurus pattern, taking into account the kind of information that it was necessary include in it. Afterward, this pattern would be place on the Virtual Campus and the student would have to complete the information required. Finally, the results obtained in the different applications of this activity would be analyzed and evaluated.Universidad de MĂĄlaga. Campus de Excelencia Internacional AndalucĂa Tech
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