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From symmetric fundamental expansions to Schur positivity
We consider families of quasisymmetric functions with the property that if a
symmetric function is a positive sum of functions in one of these families,
then f is necessarily a positive sum of Schur functions. Furthermore, in each
of the families studied, we give a combinatorial description of the Schur
coefficients of . We organize six such families into a poset, where
functions in higher families in the poset are always positive integer sums of
functions in each of the lower families. This poset includes the Schur
functions, the quasisymmetric Schur functions, the fundamental quasisymmetric
generating functions of shifted dual equivalence classes, as well as three new
families of functions --- one of which is conjectured to be a basis of the
vector space of quasisymmetric functions. Each of the six families is realized
as the fundamental quasisymmetric generating functions over the classes of some
refinement of dual Knuth equivalence. Thus, we also produce a poset of
refinements of dual Knuth equivalence. In doing so, we define quasi-dual
equivalence to provide classes that generate quasisymmetric Schur functions
What are the Confining Field Configurations of Strong-Coupling Lattice Gauge Theory?
Starting from the strong-coupling SU(2) Wilson action in D=3 dimensions, we
derive an effective, semi-local action on a lattice of spacing L times the
spacing of the original lattice. It is shown that beyond the adjoint
color-screening distance, i.e. for , thin center vortices are stable
saddlepoints of the corresponding effective action. Since the entropy of these
stable objects exceeds their energy, center vortices percolate throughout the
lattice, and confine color charge in half-integer representations of the SU(2)
gauge group. This result contradicts the folklore that confinement in
strong-coupling lattice gauge theory, for D>2 dimensions, is simply due to
plaquette disorder, as is the case in D=2 dimensions. It also demonstrates
explicitly how the emergence and stability of center vortices is related to the
existence of color screening by gluon fields.Comment: 17 pages, 5 figures, latex2
FPGA based data acquisition system for COMPASS experiment
This paper discusses the present data acquisition system (DAQ) of the COMPASS
experiment at CERN and presents development of a new DAQ. The new DAQ must
preserve present data format and be able to communicate with FPGA cards. Parts
of the new DAQ are based on state machines and they are implemented in C++ with
usage of the QT framework, the DIM library, and the IPBus technology. Prototype
of the system is prepared and communication through DIM between parts was
tested. An implementation of the IPBus technology was prepared and tested. The
new DAQ proved to be able to fulfill requirements.Comment: 8 pages, CHEP 201
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