6,073 research outputs found
Point particle in general background fields vs. free gauge theories of traceless symmetric tensors
Point particle may interact to traceless symmetric tensors of arbitrary rank.
Free gauge theories of traceless symmetric tensors are constructed, that
provides a possibility for a new type of interactions, when particles exchange
by those gauge fields. The gauge theories are parameterized by the particle's
mass m and otherwise are unique for each rank s. For m=0, they are local gauge
models with actions of 2s-th order in derivatives, known in d=4 as "pure spin",
or "conformal higher spin" actions by Fradkin and Tseytlin. For nonzero m, each
rank-s model undergoes a unique nonlocal deformation which entangles fields of
all ranks, starting from s. There exists a nonlocal transform which maps m > 0
theories onto m=0 ones, however, this map degenerates at some m > 0 fields
whose polarizations are determined by zeros of Bessel functions. Conformal
covariance properties of the m=0 models are analyzed, the space of gauge fields
is shown to admit an action of an infinite-dimensional "conformal higher spin"
Lie algebra which leaves gauge transformations intact.Comment: 21 pages, remarks on nonlinear generalization added, a mistake in the
discussion of degenerate solutions correcte
A Linearization Beam-Hardening Correction Method for X-Ray Computed Tomographic Imaging of Structural Ceramics
Computed tomographic (CT) imaging with both monochromatic and polychromatic x-ray sources can be a powerful NDE method for characterization (e. g., measurement of density gradients) as well as flaw detection (e. g., detection of cracks, voids, inclusions) in ceramics. However, the use of polychromatic x-ray sources can cause image artifacts and overall image degradation through beam hardening (BH) effects [1]. Beam hardening occurs because (i) x-ray attenuation in a given material is energy dependent and (ii) data collection in CT systems is not energy selective. Without an appropriate correction, the BH effect prevents the establishment of an absolute scale for density measurement. Thus, quantitative density comparisons between samples of the same material but of different geometrical shape becomes unreliable [2]
Module networks revisited: computational assessment and prioritization of model predictions
The solution of high-dimensional inference and prediction problems in
computational biology is almost always a compromise between mathematical theory
and practical constraints such as limited computational resources. As time
progresses, computational power increases but well-established inference
methods often remain locked in their initial suboptimal solution. We revisit
the approach of Segal et al. (2003) to infer regulatory modules and their
condition-specific regulators from gene expression data. In contrast to their
direct optimization-based solution we use a more representative centroid-like
solution extracted from an ensemble of possible statistical models to explain
the data. The ensemble method automatically selects a subset of most
informative genes and builds a quantitatively better model for them. Genes
which cluster together in the majority of models produce functionally more
coherent modules. Regulators which are consistently assigned to a module are
more often supported by literature, but a single model always contains many
regulator assignments not supported by the ensemble. Reliably detecting
condition-specific or combinatorial regulation is particularly hard in a single
optimum but can be achieved using ensemble averaging.Comment: 8 pages REVTeX, 6 figure
Transition amplitudes and sewing properties for bosons on the Riemann sphere
We consider scalar quantum fields on the sphere, both massive and massless.
In the massive case we show that the correlation functions define amplitudes
which are trace class operators between tensor products of a fixed Hilbert
space. We also establish certain sewing properties between these operators. In
the massless case we consider exponential fields and have a conformal field
theory. In this case the amplitudes are only bilinear forms but still we
establish sewing properties. Our results are obtained in a functional integral
framework.Comment: 33 page
Motif Discovery through Predictive Modeling of Gene Regulation
We present MEDUSA, an integrative method for learning motif models of
transcription factor binding sites by incorporating promoter sequence and gene
expression data. We use a modern large-margin machine learning approach, based
on boosting, to enable feature selection from the high-dimensional search space
of candidate binding sequences while avoiding overfitting. At each iteration of
the algorithm, MEDUSA builds a motif model whose presence in the promoter
region of a gene, coupled with activity of a regulator in an experiment, is
predictive of differential expression. In this way, we learn motifs that are
functional and predictive of regulatory response rather than motifs that are
simply overrepresented in promoter sequences. Moreover, MEDUSA produces a model
of the transcriptional control logic that can predict the expression of any
gene in the organism, given the sequence of the promoter region of the target
gene and the expression state of a set of known or putative transcription
factors and signaling molecules. Each motif model is either a -length
sequence, a dimer, or a PSSM that is built by agglomerative probabilistic
clustering of sequences with similar boosting loss. By applying MEDUSA to a set
of environmental stress response expression data in yeast, we learn motifs
whose ability to predict differential expression of target genes outperforms
motifs from the TRANSFAC dataset and from a previously published candidate set
of PSSMs. We also show that MEDUSA retrieves many experimentally confirmed
binding sites associated with environmental stress response from the
literature.Comment: RECOMB 200
The Yang-Mills equations on the universal cosmos
AbstractGlobal existence and regularity of solutions for the Yang-Mills equations on the universal cosmos M̃, which has the form R1 × S3 for each of an 8-parameter continuum of factorizations of M̃ as time × space, are treated by general methods. The Cauchy problem in the temporal gauge is globally soluble in its abstract evolutionary form with arbitrary data for the field ⊕ potential in L2,r(S3) ⊕ L2,r + 1(S3), where r is an integer >1 and L2,r denotes the class of sections whose first r derivatives are square-integrable; if r = 1, the problem is soluble locally in time. When r is 3 or more the solution is identifiable with a classical one; if infinite, the solution is in C∞(M̃). These results extend earlier work and approaches [1–5]. Solutions of the equations on Minkowski space-time M0 extend canonically (modulo gauge transformations) to solutions on M̃ provided their Cauchy data are moderately smooth and small near spatial infinity. Precise asymptotic structures for solutions on M0 follow, and in turn imply various decay estimates. Thus the energy in regions uniformly bounded in direction away from the light cone is O(¦x0¦−5), where x0 is the Minkowski time coordinate; analysis solely in M0 [8,9] earlier yielded the estimate O(¦x0¦−2) applicable to the region within the light cone. Similarly it follows that the action integral for a solution of the Yang-Mills equations in M0 is finite, in fact absolutely convergent
Segal-Bargmann-Fock modules of monogenic functions
In this paper we introduce the classical Segal-Bargmann transform starting
from the basis of Hermite polynomials and extend it to Clifford algebra-valued
functions. Then we apply the results to monogenic functions and prove that the
Segal-Bargmann kernel corresponds to the kernel of the Fourier-Borel transform
for monogenic functionals. This kernel is also the reproducing kernel for the
monogenic Bargmann module.Comment: 11 page
Birkhoff strata of the Grassmannian Gr: Algebraic curves
Algebraic varieties and curves arising in Birkhoff strata of the Sato
Grassmannian Gr are studied. It is shown that the big cell
contains the tower of families of the normal rational curves of all odd orders.
Strata , contain hyperelliptic curves of genus
and their coordinate rings. Strata , contain
plane curves for and and
curves in , respectively. Curves in the strata
have zero genus.Comment: 14 pages, no figures, improved some definitions, typos correcte
Supergeometry and Quantum Field Theory, or: What is a Classical Configuration?
We discuss of the conceptual difficulties connected with the
anticommutativity of classical fermion fields, and we argue that the "space" of
all classical configurations of a model with such fields should be described as
an infinite-dimensional supermanifold M.
We discuss the two main approaches to supermanifolds, and we examine the
reasons why many physicists tend to prefer the Rogers approach although the
Berezin-Kostant-Leites approach is the more fundamental one. We develop the
infinite-dimensional variant of the latter, and we show that the functionals on
classical configurations considered in a previous paper are nothing but
superfunctions on M. We present a programme for future mathematical work, which
applies to any classical field model with fermion fields. This programme is
(partially) implemented in successor papers.Comment: 46 pages, LateX2E+AMSLaTe
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