27,726 research outputs found
Viterbi Sequences and Polytopes
A Viterbi path of length n of a discrete Markov chain is a sequence of n+1
states that has the greatest probability of ocurring in the Markov chain. We
divide the space of all Markov chains into Viterbi regions in which two Markov
chains are in the same region if they have the same set of Viterbi paths. The
Viterbi paths of regions of positive measure are called Viterbi sequences. Our
main results are (1) each Viterbi sequence can be divided into a prefix,
periodic interior, and suffix, and (2) as n increases to infinity (and the
number of states remains fixed), the number of Viterbi regions remains bounded.
The Viterbi regions correspond to the vertices of a Newton polytope of a
polynomial whose terms are the probabilities of sequences of length n. We
characterize Viterbi sequences and polytopes for two- and three-state Markov
chains.Comment: 15 pages, 2 figures, to appear in Journal of Symbolic Computatio
Applications of Graphical Condensation for Enumerating Matchings and Tilings
A technique called graphical condensation is used to prove various
combinatorial identities among numbers of (perfect) matchings of planar
bipartite graphs and tilings of regions. Graphical condensation involves
superimposing matchings of a graph onto matchings of a smaller subgraph, and
then re-partitioning the united matching (actually a multigraph) into matchings
of two other subgraphs, in one of two possible ways. This technique can be used
to enumerate perfect matchings of a wide variety of bipartite planar graphs.
Applications include domino tilings of Aztec diamonds and rectangles, diabolo
tilings of fortresses, plane partitions, and transpose complement plane
partitions.Comment: 25 pages; 21 figures Corrected typos; Updated references; Some text
revised, but content essentially the sam
Designers manual for circuit design by analog/digital techniques Final report
Manual for designing circuits by hybrid compute
Light-emitting current of electrically driven single-photon sources
The time-dependent tunnelling current arising from the electron-hole
recombination of exciton state is theoretically studied using the
nonequilibrium Green's function technique and the Anderson model with two
energy levels. The charge conservation and gauge invariance are satisfied in
the tunnelling current. Apart from the classical capacitive charging and
discharging behavior, interesting oscillations superimpose on the tunnelling
current for the applied rectangular pulse voltage.Comment: 14 pages, 5 figure
Flavor Mixing and the Permutation Symmetry among Generations
In the standard model, the permutation symmetry among the three generations
of fundamental fermions is usually regarded to be broken by the Higgs
couplings. It is found that the symmetry is restored if we include the mass
matrix parameters as physical variables which transform appropriately under the
symmetry operation. Known relations between these variables, such as the
renormalization group equations, as well as formulas for neutrino oscillations
(in vacuum and in matter), are shown to be covariant tensor equations under the
permutation symmetry group.Comment: 12 page
Renormalization of the Neutrino Mass Matrix
In terms of a rephasing invariant parametrization, the set of renormalization
group equations (RGE) for Dirac neutrino parameters can be cast in a compact
and simple form. These equations exhibit manifest symmetry under flavor
permutations. We obtain both exact and approximate RGE invariants, in addition
to some approximate solutions and examples of numerical solutions.Comment: 15 pages, 1figur
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