1,468 research outputs found
Positive contraction mappings for classical and quantum Schrodinger systems
The classical Schrodinger bridge seeks the most likely probability law for a
diffusion process, in path space, that matches marginals at two end points in
time; the likelihood is quantified by the relative entropy between the sought
law and a prior, and the law dictates a controlled path that abides by the
specified marginals. Schrodinger proved that the optimal steering of the
density between the two end points is effected by a multiplicative functional
transformation of the prior; this transformation represents an automorphism on
the space of probability measures and has since been studied by Fortet,
Beurling and others. A similar question can be raised for processes evolving in
a discrete time and space as well as for processes defined over non-commutative
probability spaces. The present paper builds on earlier work by Pavon and
Ticozzi and begins with the problem of steering a Markov chain between given
marginals. Our approach is based on the Hilbert metric and leads to an
alternative proof which, however, is constructive. More specifically, we show
that the solution to the Schrodinger bridge is provided by the fixed point of a
contractive map. We approach in a similar manner the steering of a quantum
system across a quantum channel. We are able to establish existence of quantum
transitions that are multiplicative functional transformations of a given Kraus
map, but only for the case of uniform marginals. As in the Markov chain case,
and for uniform density matrices, the solution of the quantum bridge can be
constructed from the fixed point of a certain contractive map. For arbitrary
marginal densities, extensive numerical simulations indicate that iteration of
a similar map leads to fixed points from which we can construct a quantum
bridge. For this general case, however, a proof of convergence remains elusive.Comment: 27 page
Longitudinal magnon in the tetrahedral spin system Cu2Te2O5Br2 near quantum criticality
We present a comprehensive study of the coupled tetrahedra-compound
Cu2Te2O5Br2 by theory and experiments in external magnetic fields. We report
the observation of a longitudinal magnon in Raman scattering in the ordered
state close to quantum criticality. We show that the excited
tetrahedral-singlet sets the energy scale for the magnetic ordering temperature
T_N. This energy is determined experimentally. The ordering temperature T_N has
an inverse-log dependence on the coupling parameters near quantum criticality
Regulating the Market in Human Research Participants
Lemmens and Miller critically examine "finder's fees" and other recruitment incentives issued to physicians for successfully referring patients to clinical trial investigators
Stability and convergence in discrete convex monotone dynamical systems
We study the stable behaviour of discrete dynamical systems where the map is
convex and monotone with respect to the standard positive cone. The notion of
tangential stability for fixed points and periodic points is introduced, which
is weaker than Lyapunov stability. Among others we show that the set of
tangentially stable fixed points is isomorphic to a convex inf-semilattice, and
a criterion is given for the existence of a unique tangentially stable fixed
point. We also show that periods of tangentially stable periodic points are
orders of permutations on letters, where is the dimension of the
underlying space, and a sufficient condition for global convergence to periodic
orbits is presented.Comment: 36 pages, 1 fugur
DNA double-strand break repair in Caenorhabditis elegans
Faithful repair of DNA double-strand breaks (DSBs) is vital for animal development, as inappropriate repair can cause gross chromosomal alterations that result in cellular dysfunction, ultimately leading to cancer, or cell death. Correct processing of DSBs is not only essential for maintaining genomic integrity, but is also required in developmental programs, such as gametogenesis, in which DSBs are deliberately generated. Accordingly, DSB repair deficiencies are associated with various developmental disorders including cancer predisposition and infertility. To avoid this threat, cells are equipped with an elaborate and evolutionarily well-conserved network of DSB repair pathways. In recent years, Caenorhabditis elegans has become a successful model system in which to study DSB repair, leading to important insights in this process during animal development. This review will discuss the major contributions and recent progress in the C. elegans field to elucidate the complex networks involved in DSB repair, the impact of which extends well beyond the nematode phylum
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