5,525 research outputs found
Two likelihood-based semiparametric estimation methods for panel count data with covariates
We consider estimation in a particular semiparametric regression model for
the mean of a counting process with ``panel count'' data. The basic model
assumption is that the conditional mean function of the counting process is of
the form where is a
vector of covariates and is the baseline mean function. The ``panel
count'' observation scheme involves observation of the counting process
for an individual at a random number of random time points;
both the number and the locations of these time points may differ across
individuals. We study semiparametric maximum pseudo-likelihood and maximum
likelihood estimators of the unknown parameters derived
on the basis of a nonhomogeneous Poisson process assumption. The
pseudo-likelihood estimator is fairly easy to compute, while the maximum
likelihood estimator poses more challenges from the computational perspective.
We study asymptotic properties of both estimators assuming that the
proportional mean model holds, but dropping the Poisson process assumption used
to derive the estimators. In particular we establish asymptotic normality for
the estimators of the regression parameter under appropriate
hypotheses. The results show that our estimation procedures are robust in the
sense that the estimators converge to the truth regardless of the underlying
counting process.Comment: Published in at http://dx.doi.org/10.1214/009053607000000181 the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
New quasi-exactly solvable class of generalized isotonic oscillators
We introduce a new family of quasi-exactly solvable generalized isotonic
oscillators which are based on the pseudo-Hermite exceptional orthogonal
polynomials. We obtain exact closed-form expressions for the energies and
wavefunctions as well as the allowed potential parameters for the first two
members of the family using the Bethe ansatz method. Numerical calculations of
the energies reveal that member potentials have multiple quasi-exactly solvable
eigenstates and the number of states for higher members are parameter
dependent.Comment: 14 pages; 4 figure
Modeling the formation of attentive publics in social media: the case of Donald Trump
Previous research has shown the importance of Donald Trump’s Twitter activity, and that of his Twitter following, in spreading his message during the primary and general election campaigns of 2015–2016. However, we know little about how the publics who followed Trump and amplified his messages took shape. We take this case as an opportunity to theorize and test questions about the assembly of what we call “attentive publics” in social media. We situate our study in the context of current discussions of audience formation, attention flow, and hybridity in the United States’ political media system. From this we derive propositions concerning how attentive publics aggregate around a particular object, in this case Trump himself, which we test using time series modeling. We also present an exploration of the possible role of automated accounts in these processes. Our results reiterate the media hybridity described by others, while emphasizing the importance of news media coverage in building social media attentive publics.Accepted manuscrip
Twisted Quantum Affine Superalgebra , Invariant R-matrices and a New Integrable Electronic Model
We describe the twisted affine superalgebra and its quantized
version . We investigate the tensor product representation
of the 4-dimensional grade star representation for the fixed point
subsuperalgebra . We work out the tensor product decomposition
explicitly and find the decomposition is not completely reducible. Associated
with this 4-dimensional grade star representation we derive two
invariant R-matrices: one of them corresponds to and the
other to . Using the R-matrix for , we
construct a new invariant strongly correlated electronic model,
which is integrable in one dimension. Interestingly, this model reduces, in the
limit, to the one proposed by Essler et al which has a larger, ,
symmetry.Comment: 17 pages, LaTex fil
Solutions of the Yang-Baxter Equation with Extra Non-Additive Parameters II: }
The type-I quantum superalgebras are known to admit non-trivial one-parameter
families of inequivalent finite dimensional irreps, even for generic . We
apply the recently developed technique to construct new solutions to the
quantum Yang-Baxter equation associated with the one-parameter family of irreps
of , thus obtaining R-matrices which depend not only on a
spectral parameter but in addition on further continuous parameters. These
extra parameters enter the Yang-Baxter equation in a similar way to the
spectral parameter but in a non-additive form.Comment: 10 pages, LaTex file (some errors in the Casimirs corrected
On Type-I Quantum Affine Superalgebras
The type-I simple Lie-superalgebras are and . We study
the quantum deformations of their untwisted affine extensions
and . We identify additional
relations between the simple generators (``extra -Serre relations") which
need to be imposed to properly define \uqgh and . We
present a general technique for deriving the spectral parameter dependent
R-matrices from quantum affine superalgebras. We determine the R-matrices for
the type-I affine superalgebra in various representations,
thereby deriving new solutions of the spectral-dependent Yang-Baxter equation.
In particular, because this algebra possesses one-parameter families of
finite-dimensional irreps, we are able to construct R-matrices depending on two
additional spectral-like parameters, providing generalizations of the
free-fermion model.Comment: 23 page
A New Supersymmetric and Exactly Solvable Model of Correlated Electrons
A new lattice model is presented for correlated electrons on the unrestricted
-dimensional electronic Hilbert space (where
is the lattice length). It is a supersymmetric generalization of the
Hubbard model, but differs from the extended Hubbard model proposed by Essler,
Korepin and Schoutens. The supersymmetry algebra of the new model is
superalgebra . The model contains one symmetry-preserving free real
parameter which is the Hubbard interaction parameter , and has its origin
here in the one-parameter family of inequivalent typical 4-dimensional irreps
of . On a one-dimensional lattice, the model is exactly solvable by
the Bethe ansatz.Comment: 10 pages, LaTex. (final version to appear in Phys.Rev.Lett.
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