18,573 research outputs found
Adjoint exactness
Plato's ideas and Aristotle's real types from the classical age, Nominalism and Realism of the mediaeval period and Whitehead's modern view of the world as pro- cess all come together in the formal representation by category theory of exactness in adjointness (a). Concepts of exactness and co-exactness arise naturally from ad- jointness and are needed in current global problems of science. If a right co-exact valued left-adjoint functor ( ) in a cartesian closed category has a right-adjoint left- exact functor ( ), then physical stability is satis ed if itself is also a right co-exact left-adjoint functor for the right-adjoint left exact functor ( ): a a . These concepts are discussed here with examples in nuclear fusion, in database interroga- tion and in the cosmological ne structure constant by the Frederick construction
Symmetry classes of alternating sign matrices in the nineteen-vertex model
The nineteen-vertex model on a periodic lattice with an anti-diagonal twist
is investigated. Its inhomogeneous transfer matrix is shown to have a simple
eigenvalue, with the corresponding eigenstate displaying intriguing
combinatorial features. Similar results were previously found for the same
model with a diagonal twist. The eigenstate for the anti-diagonal twist is
explicitly constructed using the quantum separation of variables technique. A
number of sum rules and special components are computed and expressed in terms
of Kuperberg's determinants for partition functions of the inhomogeneous
six-vertex model. The computations of some components of the special eigenstate
for the diagonal twist are also presented. In the homogeneous limit, the
special eigenstates become eigenvectors of the Hamiltonians of the integrable
spin-one XXZ chain with twisted boundary conditions. Their sum rules and
special components for both twists are expressed in terms of generating
functions arising in the weighted enumeration of various symmetry classes of
alternating sign matrices (ASMs). These include half-turn symmetric ASMs,
quarter-turn symmetric ASMs, vertically symmetric ASMs, vertically and
horizontally perverse ASMs and double U-turn ASMs. As side results, new
determinant and pfaffian formulas for the weighted enumeration of various
symmetry classes of alternating sign matrices are obtained.Comment: 61 pages, 13 figure
HeMIS: Hetero-Modal Image Segmentation
We introduce a deep learning image segmentation framework that is extremely
robust to missing imaging modalities. Instead of attempting to impute or
synthesize missing data, the proposed approach learns, for each modality, an
embedding of the input image into a single latent vector space for which
arithmetic operations (such as taking the mean) are well defined. Points in
that space, which are averaged over modalities available at inference time, can
then be further processed to yield the desired segmentation. As such, any
combinatorial subset of available modalities can be provided as input, without
having to learn a combinatorial number of imputation models. Evaluated on two
neurological MRI datasets (brain tumors and MS lesions), the approach yields
state-of-the-art segmentation results when provided with all modalities;
moreover, its performance degrades remarkably gracefully when modalities are
removed, significantly more so than alternative mean-filling or other synthesis
approaches.Comment: Accepted as an oral presentation at MICCAI 201
Probing the Top-Higgs Yukawa CP Structure in dileptonic with -Assisted Reconstruction
Constraining the Higgs boson properties is a cornerstone of the LHC program.
We study the potential to directly probe the Higgs-top CP-structure via the
channel at the LHC with the Higgs boson decaying to a bottom pair
and top-quarks in the dileptonic mode. We show that a combination of laboratory
and rest frame observables display large CP-sensitivity, exploring
the spin correlations in the top decays. To efficiently reconstruct our final
state, we present a method based on simple mass minimization and prove its
robustness to shower, hadronization and detector effects. In addition, the mass
reconstruction works as an extra relevant handle for background suppression.
Based on our results, we demonstrate that the Higgs-top CP-phase can
be probed up to at the high luminosity LHC.Comment: 25 pages, 11 figures, 3 table
Integrable structure of box-ball systems: crystal, Bethe ansatz, ultradiscretization and tropical geometry
The box-ball system is an integrable cellular automaton on one dimensional
lattice. It arises from either quantum or classical integrable systems by the
procedures called crystallization and ultradiscretization, respectively. The
double origin of the integrability has endowed the box-ball system with a
variety of aspects related to Yang-Baxter integrable models in statistical
mechanics, crystal base theory in quantum groups, combinatorial Bethe ansatz,
geometric crystals, classical theory of solitons, tau functions, inverse
scattering method, action-angle variables and invariant tori in completely
integrable systems, spectral curves, tropical geometry and so forth. In this
review article, we demonstrate these integrable structures of the box-ball
system and its generalizations based on the developments in the last two
decades.Comment: 73 page
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