2,784 research outputs found
Multisymplectic approach to integrable defects in the sine-Gordon model
Ideas from the theory of multisymplectic systems, introduced recently in integrable systems by the author and Kundu to discuss Liouville integrability in classical field theories with a defect, are applied to the sine-Gordon model. The key ingredient is the introduction of a second Poisson bracket in the theory that allows for a Hamiltonian description of the model that is completely equivalent to the standard one, in the absence of a defect. In the presence of a defect described by frozen Bäcklund transformations, our approach based on the new bracket unifies the various tools used so far to attack the problem. It also gets rid of the known issues related to the evaluation of the Poisson brackets of the defect matrix which involve fields at coinciding space point (the location of the defect). The original Lagrangian approach also finds a nice reinterpretation in terms of the canonical transformation representing the defect conditions
Interplay between Zamolodchikov-Faddeev and Reflection-Transmission algebras
We show that a suitable coset algebra, constructed in terms of an extension
of the Zamolodchikov-Faddeev algebra, is homomorphic to the
Reflection-Transmission algebra, as it appears in the study of integrable
systems with impurity.Comment: 8 pages; a misprint in eq. (2.14) and (2.15) has been correcte
Noncommutative U(1) Instantons in Eight Dimensional Yang-Mills Theory
We study the noncommutative version of the extended ADHM construction in the
eight dimensional U(1) Yang-Mills theory. This construction gives rise to the
solutions of the BPS equations in the Yang-Mills theory, and these solutions
preserve at least 3/16 of supersymmetries. In a wide subspace of the extended
ADHM data, we show that the integer which appears in the extended ADHM
construction should be interpreted as the -brane charge rather than the
-brane charge by explicitly calculating the topological charges in the case
that the noncommutativity parameter is anti-self-dual. We also find the
relationship with the solution generating technique and show that the integer
can be interpreted as the charge of the -brane bound to the -brane
with the -field in the case that the noncommutativity parameter is
self-dual.Comment: 22 page
Exactly solvable potentials of Calogero type for q-deformed Coxeter groups
We establish that by parameterizing the configuration space of a
one-dimensional quantum system by polynomial invariants of q-deformed Coxeter
groups it is possible to construct exactly solvable models of Calogero type. We
adopt the previously introduced notion of solvability which consists of
relating the Hamiltonian to finite dimensional representation spaces of a Lie
algebra. We present explicitly the -case for which we construct the
potentials by means of suitable gauge transformations.Comment: 22 pages Late
Requirements and validation of a prototype learning health system for clinical diagnosis
Introduction Diagnostic error is a major threat to patient safety in the context of family practice. The patient safety implications are severe for both patient and clinician. Traditional approaches to diagnostic decision support have lacked broad acceptance for a number of well-documented reasons: poor integration with electronic health records and clinician workflow, static evidence that lacks transparency and trust, and use of proprietary technical standards hindering wider interoperability. The learning health system (LHS) provides a suitable infrastructure for development of a new breed of learning decision support tools. These tools exploit the potential for appropriate use of the growing volumes of aggregated sources of electronic health records. Methods We describe the experiences of the TRANSFoRm project developing a diagnostic decision support infrastructure consistent with the wider goals of the LHS. We describe an architecture that is model driven, service oriented, constructed using open standards, and supports evidence derived from electronic sources of patient data. We describe the architecture and implementation of 2 critical aspects for a successful LHS: the model representation and translation of clinical evidence into effective practice and the generation of curated clinical evidence that can be used to populate those models, thus closing the LHS loop. Results/Conclusions Six core design requirements for implementing a diagnostic LHS are identified and successfully implemented as part of this research work. A number of significant technical and policy challenges are identified for the LHS community to consider, and these are discussed in the context of evaluating this work: medico-legal responsibility for generated diagnostic evidence, developing trust in the LHS (particularly important from the perspective of decision support), and constraints imposed by clinical terminologies on evidence generation
Polynomials Associated with Equilibria of Affine Toda-Sutherland Systems
An affine Toda-Sutherland system is a quasi-exactly solvable multi-particle
dynamics based on an affine simple root system. It is a `cross' between two
well-known integrable multi-particle dynamics, an affine Toda molecule and a
Sutherland system. Polynomials describing the equilibrium positions of affine
Toda-Sutherland systems are determined for all affine simple root systems.Comment: 9 page
Prochlo: Strong Privacy for Analytics in the Crowd
The large-scale monitoring of computer users' software activities has become
commonplace, e.g., for application telemetry, error reporting, or demographic
profiling. This paper describes a principled systems architecture---Encode,
Shuffle, Analyze (ESA)---for performing such monitoring with high utility while
also protecting user privacy. The ESA design, and its Prochlo implementation,
are informed by our practical experiences with an existing, large deployment of
privacy-preserving software monitoring.
(cont.; see the paper
Yang-Baxter algebra and generation of quantum integrable models
An operator deformed quantum algebra is discovered exploiting the quantum
Yang-Baxter equation with trigonometric R-matrix. This novel Hopf algebra along
with its limit appear to be the most general Yang-Baxter algebra
underlying quantum integrable systems. Three different directions of
application of this algebra in integrable systems depending on different sets
of values of deforming operators are identified. Fixed values on the whole
lattice yield subalgebras linked to standard quantum integrable models, while
the associated Lax operators generate and classify them in an unified way.
Variable values construct a new series of quantum integrable inhomogeneous
models. Fixed but different values at different lattice sites can produce a
novel class of integrable hybrid models including integrable matter-radiation
models and quantum field models with defects, in particular, a new quantum
integrable sine-Gordon model with defect.Comment: 13 pages, revised and bit expanded with additional explanations,
accepted for publication in Theor. Math. Phy
Integrable boundary conditions for classical sine-Gordon theory
The possible boundary conditions consistent with the integrability of the
classical sine-Gordon equation are studied. A boundary value problem on the
half-line with local boundary condition at the origin is considered.
The most general form of this boundary condition is found such that the problem
be integrable. For the resulting system an infinite number of involutive
integrals of motion exist. These integrals are calculated and one is identified
as the Hamiltonian. The results found agree with some recent work of Ghoshal
and Zamolodchikov.Comment: 10 pages, DTP/94-3
Non-Abelian Vortices, Super-Yang-Mills Theory and Spin(7)-Instantons
We consider a complex vector bundle E endowed with a connection A over the
eight-dimensional manifold R^2 x G/H, where G/H = SU(3)/U(1)xU(1) is a
homogeneous space provided with a never integrable almost complex structure and
a family of SU(3)-structures. We establish an equivalence between G-invariant
solutions A of the Spin(7)-instanton equations on R^2 x G/H and general
solutions of non-Abelian coupled vortex equations on R^2. These vortices are
BPS solitons in a d=4 gauge theory obtained from N=1 supersymmetric Yang-Mills
theory in ten dimensions compactified on the coset space G/H with an
SU(3)-structure. The novelty of the obtained vortex equations lies in the fact
that Higgs fields, defining morphisms of vector bundles over R^2, are not
holomorphic in the generic case. Finally, we introduce BPS vortex equations in
N=4 super Yang-Mills theory and show that they have the same feature.Comment: 14 pages; v2: typos fixed, published versio
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