1,928 research outputs found
Mass Incarceration and Children's Outcomes: Criminal Justice Policy is Education Policy
Parental incarceration leads to an array of cognitive and noncognitive outcomes known to affect children's performance in school. Therefore, the discriminatory incarceration of African American parents makes an important contribution to the racial achievement gap. Educators hoping to narrow the achievement gap should make criminal justice reform a policy priority
Strongly stable ideals and Hilbert polynomials
The \texttt{StronglyStableIdeals} package for \textit{Macaulay2} provides a
method to compute all saturated strongly stable ideals in a given polynomial
ring with a fixed Hilbert polynomial. A description of the main method and
auxiliary tools is given.Comment: Source code available as an ancillary file. Final versio
Evolutionary Neural Gas (ENG): A Model of Self Organizing Network from Input Categorization
Despite their claimed biological plausibility, most self organizing networks
have strict topological constraints and consequently they cannot take into
account a wide range of external stimuli. Furthermore their evolution is
conditioned by deterministic laws which often are not correlated with the
structural parameters and the global status of the network, as it should happen
in a real biological system. In nature the environmental inputs are noise
affected and fuzzy. Which thing sets the problem to investigate the possibility
of emergent behaviour in a not strictly constrained net and subjected to
different inputs. It is here presented a new model of Evolutionary Neural Gas
(ENG) with any topological constraints, trained by probabilistic laws depending
on the local distortion errors and the network dimension. The network is
considered as a population of nodes that coexist in an ecosystem sharing local
and global resources. Those particular features allow the network to quickly
adapt to the environment, according to its dimensions. The ENG model analysis
shows that the net evolves as a scale-free graph, and justifies in a deeply
physical sense- the term gas here used.Comment: 16 pages, 8 figure
A Borel open cover of the Hilbert scheme
Let be an admissible Hilbert polynomial in \PP^n of degree . The
Hilbert scheme \hilb^n_p(t) can be realized as a closed subscheme of a
suitable Grassmannian , hence it could be globally defined by
homogeneous equations in the Plucker coordinates of and covered by
open subsets given by the non-vanishing of a Plucker coordinate, each embedded
as a closed subscheme of the affine space , . However,
the number of Plucker coordinates is so large that effective computations
in this setting are practically impossible. In this paper, taking advantage of
the symmetries of \hilb^n_p(t), we exhibit a new open cover, consisting of
marked schemes over Borel-fixed ideals, whose number is significantly smaller
than . Exploiting the properties of marked schemes, we prove that these open
subsets are defined by equations of degree in their natural
embedding in \Af^D. Furthermore we find new embeddings in affine spaces of
far lower dimension than , and characterize those that are still defined by
equations of degree . The proofs are constructive and use a
polynomial reduction process, similar to the one for Grobner bases, but are
term order free. In this new setting, we can achieve explicit computations in
many non-trivial cases.Comment: 17 pages. This version contains and extends the first part of version
2 (arXiv:0909.2184v2[math.AG]). A new extended version of the second part,
with some new results, is posed at arxiv:1110.0698v3[math.AC]. The title is
slightly changed. Final version accepted for publicatio
A combinatorial description of finite O-sequences and aCM genera
The goal of this paper is to explicitly detect all the arithmetic genera of
arithmetically Cohen-Macaulay projective curves with a given degree . It is
well-known that the arithmetic genus of a curve can be easily deduced
from the -vector of the curve; in the case where is arithmetically
Cohen-Macaulay of degree , must belong to the range of integers
. We develop an algorithmic procedure that
allows one to avoid constructing most of the possible -vectors of . The
essential tools are a combinatorial description of the finite O-sequences of
multiplicity , and a sort of continuity result regarding the generation of
the genera. The efficiency of our method is supported by computational
evidence. As a consequence, we single out the minimal possible
Castelnuovo-Mumford regularity of a curve with Cohen-Macaulay postulation and
given degree and genus.Comment: Final versio
The maximum likelihood degree of Fermat hypersurfaces
We study the critical points of the likelihood function over the Fermat
hypersurface. This problem is related to one of the main problems in
statistical optimization: maximum likelihood estimation. The number of critical
points over a projective variety is a topological invariant of the variety and
is called maximum likelihood degree. We provide closed formulas for the maximum
likelihood degree of any Fermat curve in the projective plane and of Fermat
hypersurfaces of degree 2 in any projective space. Algorithmic methods to
compute the ML degree of a generic Fermat hypersurface are developed throughout
the paper. Such algorithms heavily exploit the symmetries of the varieties we
are considering. A computational comparison of the different methods and a list
of the maximum likelihood degrees of several Fermat hypersurfaces are available
in the last section.Comment: Final version. Accepted for publication on Journal of Algebraic
Statistic
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