93 research outputs found
Flat Connections for Characters in Irrational Conformal Field Theory
Following the paradigm on the sphere, we begin the study of irrational
conformal field theory (ICFT) on the torus. In particular, we find that the
affine-Virasoro characters of ICFT satisfy heat-like differential equations
with flat connections. As a first example, we solve the system for the general
coset construction, obtaining an integral representation for the general
coset characters. In a second application, we solve for the high-level
characters of the general ICFT on simple , noting a simplification for the
subspace of theories which possess a non-trivial symmetry group. Finally, we
give a geometric formulation of the system in which the flat connections are
generalized Laplacians on the centrally-extended loop group.Comment: harvmac (answer b to question) 40 pages. LBL-35718, UCB-PTH-94/1
Singular vectors by Fusions in affine su(2)
Explicit expressions for the singular vectors in the highest weight
representations of are obtained using the fusion formalism of
conformal field theory.Comment: 7 page
Fusion and singular vectors in A1{(1)} highest weight cyclic modules
We show how the interplay between the fusion formalism of conformal field
theory and the Knizhnik--Zamolodchikov equation leads to explicit formulae for
the singular vectors in the highest weight representations of A1{(1)}.Comment: 42 page
Physical States in G/G Models and 2d Gravity
An analysis of the BRST cohomology of the G/G topological models is performed
for the case of . Invoking a special free field parametrization of
the various currents, the cohomology on the corresponding Fock space is
extracted. We employ the singular vector structure and fusion rules to
translate the latter into the cohomology on the space of irreducible
representations. Using the physical states we calculate the characters and
partition function, and verify the index interpretation. We twist the
energy-momentum tensor to establish an intriguing correspondence between the
model with level and models
coupled to gravity.Comment: 42 page
-Strands
A -strand is a map for a Lie
group that follows from Hamilton's principle for a certain class of
-invariant Lagrangians. The SO(3)-strand is the -strand version of the
rigid body equation and it may be regarded physically as a continuous spin
chain. Here, -strand dynamics for ellipsoidal rotations is derived as
an Euler-Poincar\'e system for a certain class of variations and recast as a
Lie-Poisson system for coadjoint flow with the same Hamiltonian structure as
for a perfect complex fluid. For a special Hamiltonian, the -strand is
mapped into a completely integrable generalization of the classical chiral
model for the SO(3)-strand. Analogous results are obtained for the
-strand. The -strand is the -strand version of the
Bloch-Iserles ordinary differential equation, whose solutions exhibit dynamical
sorting. Numerical solutions show nonlinear interactions of coherent wave-like
solutions in both cases. -strand equations on the
diffeomorphism group are also introduced and shown
to admit solutions with singular support (e.g., peakons).Comment: 35 pages, 5 figures, 3rd version. To appear in J Nonlin Sc
Антиутопия как диагноз будущему
Материалы XIV Междунар. науч. конф. студентов, магистрантов, аспирантов и молодых ученых, Гомель, 13–14 мая 2021 г
On the geometry of classically integrable two-dimensional non-linear sigma models
A master equation expressing the classical integrability of two-dimensional
non-linear sigma models is found. The geometrical properties of this equation
are outlined. In particular, a closer connection between integrability and
T-duality transformations is emphasised. Finally, a whole new class of
integrable non-linear sigma models is found and all their corresponding Lax
pairs depend on a spectral parameter.Comment: 16 pages. Major changes (almost a new paper). To be published in
Nuclear Physics B (2010
Improving the predictive potential of diffusion MRI in schizophrenia using normative models-Towards subject-level classification.
Diffusion MRI studies consistently report group differences in white matter between individuals diagnosed with schizophrenia and healthy controls. Nevertheless, the abnormalities found at the group-level are often not observed at the individual level. Among the different approaches aiming to study white matter abnormalities at the subject level, normative modeling analysis takes a step towards subject-level predictions by identifying affected brain locations in individual subjects based on extreme deviations from a normative range. Here, we leveraged a large harmonized diffusion MRI dataset from 512 healthy controls and 601 individuals diagnosed with schizophrenia, to study whether normative modeling can improve subject-level predictions from a binary classifier. To this aim, individual deviations from a normative model of standard (fractional anisotropy) and advanced (free-water) dMRI measures, were calculated by means of age and sex-adjusted z-scores relative to control data, in 18 white matter regions. Even though larger effect sizes are found when testing for group differences in z-scores than are found with raw values (p < .001), predictions based on summary z-score measures achieved low predictive power (AUC < 0.63). Instead, we find that combining information from the different white matter tracts, while using multiple imaging measures simultaneously, improves prediction performance (the best predictor achieved AUC = 0.726). Our findings suggest that extreme deviations from a normative model are not optimal features for prediction. However, including the complete distribution of deviations across multiple imaging measures improves prediction, and could aid in subject-level classification
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