222 research outputs found
Role of Categorical Variables in Multicollinearity in the Linear Regression Model
The present article discusses the role of categorical variable in the problem
of multicollinearity in linear regression model. It exposes the diagnostic tool
condition number to linear regression models with categorical explanatory variables
and analyzes how the dummy variables and choice of reference category
can affect the degree of multicollinearity. Such an effect is analyzed analytically
as well as numerically through simulation and real data application
Generalized trace distance measure connecting quantum and classical non-Markovianity
We establish a direct connection of quantum Markovianity of an open quantum
system to its classical counterpart by generalizing the criterion based on the
information flow. Here, the flow is characterized by the time evolution of
Helstrom matrices, given by the weighted difference of statistical operators,
under the action of the quantum dynamical evolution. It turns out that the
introduced criterion is equivalent to P-divisibility of a quantum process,
namely divisibility in terms of positive maps, which provides a direct
connection to classical Markovian stochastic processes. Moreover, it is shown
that similar mathematical representations as those found for the original trace
distance based measure hold true for the associated, generalized measure for
quantum non-Markovianity. That is, we prove orthogonality of optimal states
showing a maximal information backflow and establish a local and universal
representation of the measure. We illustrate some properties of the generalized
criterion by means of examples.Comment: 11 pages, 3 figure
"Mobile Clip"' - Ein Anfang mit Highspeed-Ende. Literatursichtung zum Thema Mobile TV, Handy TV und Micromovies
Efficient and Modular Coalgebraic Partition Refinement
We present a generic partition refinement algorithm that quotients
coalgebraic systems by behavioural equivalence, an important task in system
analysis and verification. Coalgebraic generality allows us to cover not only
classical relational systems but also, e.g. various forms of weighted systems
and furthermore to flexibly combine existing system types. Under assumptions on
the type functor that allow representing its finite coalgebras in terms of
nodes and edges, our algorithm runs in time where
and are the numbers of nodes and edges, respectively. The generic
complexity result and the possibility of combining system types yields a
toolbox for efficient partition refinement algorithms. Instances of our generic
algorithm match the run-time of the best known algorithms for unlabelled
transition systems, Markov chains, deterministic automata (with fixed
alphabets), Segala systems, and for color refinement.Comment: Extended journal version of the conference paper arXiv:1705.08362.
Beside reorganization of the material, the introductory section 3 is entirely
new and the other new section 7 contains new mathematical result
- …