351 research outputs found
Chern-Simons theory of multi-component quantum Hall systems
The Chern-Simons approach has been widely used to explain fractional quantum
Hall states in the framework of trial wave functions. In the present paper, we
generalise the concept of Chern-Simons transformations to systems with any
number of components (spin or pseudospin degrees of freedom), extending earlier
results for systems with one or two components. We treat the density
fluctuations by adding auxiliary gauge fields and appropriate constraints. The
Hamiltonian is quadratic in these fields and hence can be treated as a harmonic
oscillator Hamiltonian, with a ground state that is connected to the Halperin
wave functions through the plasma analogy. We investigate several conditions on
the coefficients of the Chern-Simons transformation and on the filling factors
under which our model is valid. Furthermore, we discuss several singular cases,
associated with symmetric states.Comment: 11 pages, shortened version, accepted for publication in Phys. Rev.
Quantum process reconstruction based on mutually unbiased basis
We study a quantum process reconstruction based on the use of mutually
unbiased projectors (MUB-projectors) as input states for a D-dimensional
quantum system, with D being a power of a prime number. This approach connects
the results of quantum-state tomography using mutually unbiased bases (MUB)
with the coefficients of a quantum process, expanded in terms of
MUB-projectors. We also study the performance of the reconstruction scheme
against random errors when measuring probabilities at the MUB-projectors.Comment: 6 pages, 1 figur
Composing and Factoring Generalized Green's Operators and Ordinary Boundary Problems
We consider solution operators of linear ordinary boundary problems with "too
many" boundary conditions, which are not always solvable. These generalized
Green's operators are a certain kind of generalized inverses of differential
operators. We answer the question when the product of two generalized Green's
operators is again a generalized Green's operator for the product of the
corresponding differential operators and which boundary problem it solves.
Moreover, we show that---provided a factorization of the underlying
differential operator---a generalized boundary problem can be factored into
lower order problems corresponding to a factorization of the respective Green's
operators. We illustrate our results by examples using the Maple package
IntDiffOp, where the presented algorithms are implemented.Comment: 19 page
Classical R-Matrices and the Feigin-Odesskii Algebra via Hamiltonian and Poisson Reductions
We present a formula for a classical -matrix of an integrable system
obtained by Hamiltonian reduction of some free field theories using pure gauge
symmetries. The framework of the reduction is restricted only by the assumption
that the respective gauge transformations are Lie group ones. Our formula is in
terms of Dirac brackets, and some new observations on these brackets are made.
We apply our method to derive a classical -matrix for the elliptic
Calogero-Moser system with spin starting from the Higgs bundle over an elliptic
curve with marked points. In the paper we also derive a classical
Feigin-Odesskii algebra by a Poisson reduction of some modification of the
Higgs bundle over an elliptic curve. This allows us to include integrable
lattice models in a Hitchin type construction.Comment: 27 pages LaTe
Kernel Spectral Clustering and applications
In this chapter we review the main literature related to kernel spectral
clustering (KSC), an approach to clustering cast within a kernel-based
optimization setting. KSC represents a least-squares support vector machine
based formulation of spectral clustering described by a weighted kernel PCA
objective. Just as in the classifier case, the binary clustering model is
expressed by a hyperplane in a high dimensional space induced by a kernel. In
addition, the multi-way clustering can be obtained by combining a set of binary
decision functions via an Error Correcting Output Codes (ECOC) encoding scheme.
Because of its model-based nature, the KSC method encompasses three main steps:
training, validation, testing. In the validation stage model selection is
performed to obtain tuning parameters, like the number of clusters present in
the data. This is a major advantage compared to classical spectral clustering
where the determination of the clustering parameters is unclear and relies on
heuristics. Once a KSC model is trained on a small subset of the entire data,
it is able to generalize well to unseen test points. Beyond the basic
formulation, sparse KSC algorithms based on the Incomplete Cholesky
Decomposition (ICD) and , , Group Lasso regularization are
reviewed. In that respect, we show how it is possible to handle large scale
data. Also, two possible ways to perform hierarchical clustering and a soft
clustering method are presented. Finally, real-world applications such as image
segmentation, power load time-series clustering, document clustering and big
data learning are considered.Comment: chapter contribution to the book "Unsupervised Learning Algorithms
Mass and Angular Momentum in General Relativity
We present an introduction to mass and angular momentum in General
Relativity. After briefly reviewing energy-momentum for matter fields, first in
the flat Minkowski case (Special Relativity) and then in curved spacetimes with
or without symmetries, we focus on the discussion of energy-momentum for the
gravitational field. We illustrate the difficulties rooted in the Equivalence
Principle for defining a local energy-momentum density for the gravitational
field. This leads to the understanding of gravitational energy-momentum and
angular momentum as non-local observables that make sense, at best, for
extended domains of spacetime. After introducing Komar quantities associated
with spacetime symmetries, it is shown how total energy-momentum can be
unambiguously defined for isolated systems, providing fundamental tests for the
internal consistency of General Relativity as well as setting the conceptual
basis for the understanding of energy loss by gravitational radiation. Finally,
several attempts to formulate quasi-local notions of mass and angular momentum
associated with extended but finite spacetime domains are presented, together
with some illustrations of the relations between total and quasi-local
quantities in the particular context of black hole spacetimes. This article is
not intended to be a rigorous and exhaustive review of the subject, but rather
an invitation to the topic for non-experts. In this sense we follow essentially
the expositions in Szabados 2004, Gourgoulhon 2007, Poisson 2004 and Wald 84,
and refer the reader interested in further developments to the existing
literature, in particular to the excellent and comprehensive review by Szabados
(2004).Comment: 41 pages. Notes based on the lecture given at the C.N.R.S. "School on
Mass" (June 2008) in Orleans, France. To appear as proceedings in the book
"Mass and Motion in General Relativity", eds. L. Blanchet, A. Spallicci and
B. Whiting. Some comments and references added
Vector Continued Fractions using a Generalised Inverse
A real vector space combined with an inverse for vectors is sufficient to
define a vector continued fraction whose parameters consist of vector shifts
and changes of scale. The choice of sign for different components of the vector
inverse permits construction of vector analogues of the Jacobi continued
fraction. These vector Jacobi fractions are related to vector and scalar-valued
polynomial functions of the vectors, which satisfy recurrence relations similar
to those of orthogonal polynomials. The vector Jacobi fraction has strong
convergence properties which are demonstrated analytically, and illustrated
numerically.Comment: Published form - minor change
EBI2 is highly expressed in multiple sclerosis lesions and promotes early CNS migration of encephalitogenic CD4Â T cells
Arrival of encephalitogenic T cells at inflammatory foci represents a critical step in development of experimental autoimmune encephalomyelitis (EAE), the animal model for multiple sclerosis. EBI2 and its ligand, 7{alpha},25-OHC, direct immune cell localization in secondary lymphoid organs. CH25H and CYP7B1 hydroxylate cholesterol to 7{alpha},25-OHC. During EAE, we found increased expression of CH25H by microglia and CYP7B1 by CNS-infiltrating immune cells elevating the ligand concentration in the CNS. Two critical pro-inflammatory cytokines, interleukin-23 (IL-23) and interleukin-1 beta (IL-1{beta}), maintained expression of EBI2 in differentiating Th17 cells. In line with this, EBI2 enhanced early migration of encephalitogenic T cells into the CNS in a transfer EAE model. Nonetheless, EBI2 was dispensable in active EAE. Human Th17 cells do also express EBI2, and EBI2 expressing cells are abundant within multiple sclerosis (MS) white matter lesions. These findings implicate EBI2 as a mediator of CNS autoimmunity and describe mechanistically its contribution to the migration of autoreactive T cells into inflamed organs
The Medium Is the Danger: Discourse about Television among Amish and Ultra-Orthodox (Haredi) Women
This study shows how Old Order Amish and ultra-Orthodox women’s discourse about television can help develop a better understanding of the creation, construction, and strengthening of limits and boundaries separating enclave cultures from the world. Based on questionnaires containing both closed- and open-ended questions completed by 82 participants, approximately half from each community, I argue that both communities can be understood as interpretive communities that negatively interpret not only television content, like other religious communities, but also the medium itself. Their various negative interpretive strategies is discussed and the article shows how they are part of an “us-versus-them” attitude created to mark the boundaries and walls that enclave cultures build around themselves. The comparison between the two communities found only a few small differences but one marked similarity: The communities perceive avoidance of a tool for communication, in this case television, as part of the communities’ sharing, participation, and common culture
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