1,608 research outputs found
Generic Initial Ideals And Graded Artinian Level Algebras Not Having The Weak-Lefschetz Property
We find a sufficient condition that \H is not level based on a reduction
number. In particular, we prove that a graded Artinian algebra of codimension 3
with Hilbert function cannot be level
if , and that there exists a level O-sequence of codimension 3 of
type \H for for . Furthermore, we show that \H is
not level if , and also
prove that any codimension 3 Artinian graded algebra cannot be level if
\beta_{1,d+2}(\Gin(I))=\beta_{2,d+2}(\Gin(I)). In this case, the Hilbert
function of does not have to satisfy the condition .
Moreover, we show that every codimension graded Artinian level algebra
having the Weak-Lefschetz Property has the strictly unimodal Hilbert function
having a growth condition on for every
where
In particular, we find that if is of codimension 3, then for every and , and prove that
if is a codimension 3 Artinian algebra with an -vector
such that h_{d-1}-h_d=2(h_d-h_{d+1})>0 \quad \text{and}
\quad \soc(A)_{d-1}=0 for some , then is
-regular and \dim_k\soc(A)_d=h_d-h_{d+1}.Comment: 25 page
The Gotzmann coefficients of Hilbert functions
AbstractIn this paper we investigate some algebraic and geometric consequences which arise from an extremal bound on the Hilbert function of the general hyperplane section of a variety (Green's Hyperplane Restriction Theorem). These geometric consequences improve some results in this direction first given by Green and extend others by Bigatti, Geramita, and Migliore.Other applications of our detailed investigation of how the Hilbert polynomial is written as a sum of binomials, are to conditions that must be satisfied by a polynomial if it is to be the Hilbert polynomial of a non-degenerate integral subscheme of Pn (a problem posed by R.P. Stanley). We also give some new restrictions on the Hilbert function of a zero-dimensional reduced scheme with the Uniform Position Property
Optimal Multiuser Diversity in Multi-Cell MIMO Uplink Networks: User Scaling Law and Beamforming Design
We introduce a distributed protocol to achieve multiuser diversity in a multicell multiple-input multiple-output (MIMO) uplink network, referred to as a MIMO interfering multiple-access channel (IMAC). Assuming both no information exchange among base stations (BS) and local channel state information at the transmitters for the MIMO IMAC, we propose a joint beamforming and user scheduling protocol, and then show that the proposed protocol can achieve the optimal multiuser diversity gain, i.e., KM log (SNR log N), as long as the number of mobile stations (MSs) in a cell, N, scales faster than SNRKM-L/1-epsilon for a small constant epsilon > 0, where M, L, K, and SNR denote the number of receive antennas at each BS, the number of transmit antennas at each MS, the number of cells, and the signal-to-noise ratio, respectively. Our result indicates that multiuser diversity can be achieved in the presence of intra-cell and inter-cell interference even in a distributed fashion. As a result, vital information on how to design distributed algorithms in interference-limited cellular environments is provided
The EPOCH Project: I. Periodic variable stars in the EROS-2 LMC database
The EPOCH (EROS-2 periodic variable star classification using machine
learning) project aims to detect periodic variable stars in the EROS-2 light
curve database. In this paper, we present the first result of the
classification of periodic variable stars in the EROS-2 LMC database. To
classify these variables, we first built a training set by compiling known
variables in the Large Magellanic Cloud area from the OGLE and MACHO surveys.
We crossmatched these variables with the EROS-2 sources and extracted 22
variability features from 28 392 light curves of the corresponding EROS-2
sources. We then used the random forest method to classify the EROS-2 sources
in the training set. We designed the model to separate not only Scuti
stars, RR Lyraes, Cepheids, eclipsing binaries, and long-period variables, the
superclasses, but also their subclasses, such as RRab, RRc, RRd, and RRe for RR
Lyraes, and similarly for the other variable types. The model trained using
only the superclasses shows 99% recall and precision, while the model trained
on all subclasses shows 87% recall and precision. We applied the trained model
to the entire EROS-2 LMC database, which contains about 29 million sources, and
found 117 234 periodic variable candidates. Out of these 117 234 periodic
variables, 55 285 have not been discovered by either OGLE or MACHO variability
studies. This set comprises 1 906 Scuti stars, 6 607 RR Lyraes, 638
Cepheids, 178 Type II Cepheids, 34 562 eclipsing binaries, and 11 394
long-period variables. A catalog of these EROS-2 LMC periodic variable stars
will be available online at http://stardb.yonsei.ac.kr and at the CDS website
(http://vizier.u-strasbg.fr/viz-bin/VizieR).Comment: 18 pages, 20 figures, suggseted language-editing by the A&A editorial
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