80,404 research outputs found
A Supervisor for Control of Mode-switch Process
Many processes operate only around a limited number of operation points. In order to have adequate control around each operation point, and adaptive controller could be used. When the operation point changes often, a large number of parameters would have to be adapted over and over again. This makes application of conventional adaptive control unattractive, which is more suited for processes with slowly changing parameters. Furthermore, continuous adaptation is not always needed or desired. An extension of adaptive control is presented, in which for each operation point the process behaviour can be stored in a memory, retrieved from it and evaluated. These functions are co-ordinated by a ¿supervisor¿. This concept is referred to as a supervisor for control of mode-switch processes. It leads to an adaptive control structure which quickly adjusts the controller parameters based on retrieval of old information, without the need to fully relearn each time. This approach has been tested on experimental set-ups of a flexible beam and of a flexible two-link robot arm, but it is directly applicable to other processes, for instance, in the (petro) chemical industry
Entanglement generation in continuously coupled parametric generators
We investigate a compact source of entanglement. This device is composed of a
pair of linearly coupled nonlinear waveguides operating by means of degenerate
parametric downconversion. For the vacuum state at the input the generalized
squeeze variance and logarithmic negativity are used to quantify the amount of
nonclassicality and entanglement of output beams. Squeezing and entanglement
generation for various dynamical regimes of the device are discussed.Comment: 6 pages, 7 figure
Entropy of Overcomplete Kernel Dictionaries
In signal analysis and synthesis, linear approximation theory considers a
linear decomposition of any given signal in a set of atoms, collected into a
so-called dictionary. Relevant sparse representations are obtained by relaxing
the orthogonality condition of the atoms, yielding overcomplete dictionaries
with an extended number of atoms. More generally than the linear decomposition,
overcomplete kernel dictionaries provide an elegant nonlinear extension by
defining the atoms through a mapping kernel function (e.g., the gaussian
kernel). Models based on such kernel dictionaries are used in neural networks,
gaussian processes and online learning with kernels.
The quality of an overcomplete dictionary is evaluated with a diversity
measure the distance, the approximation, the coherence and the Babel measures.
In this paper, we develop a framework to examine overcomplete kernel
dictionaries with the entropy from information theory. Indeed, a higher value
of the entropy is associated to a further uniform spread of the atoms over the
space. For each of the aforementioned diversity measures, we derive lower
bounds on the entropy. Several definitions of the entropy are examined, with an
extensive analysis in both the input space and the mapped feature space.Comment: 10 page
Higher order nonclassicalities of finite dimensional coherent states: A comparative study
Conventional coherent states (CSs) are defined in various ways. For example,
CS is defined as an infinite Poissonian expansion in Fock states, as displaced
vacuum state, or as an eigenket of annihilation operator. In the infinite
dimensional Hilbert space, these definitions are equivalent. However, these
definitions are not equivalent for the finite dimensional systems. In this
work, we present a comparative description of the lower- and higher-order
nonclassical properties of the finite dimensional CSs which are also referred
to as qudit CSs (QCSs). For the comparison, nonclassical properties of two
types of QCSs are used: (i) nonlinear QCS produced by applying a truncated
displacement operator on the vacuum and (ii) linear QCS produced by the
Poissonian expansion in Fock states of the CS truncated at (d-1)-photon Fock
state. The comparison is performed using a set of nonclassicality witnesses
(e.g., higher order antiubunching, higher order sub-Poissonian statistics,
higher order squeezing, Agarwal-Tara parameter, Klyshko's criterion) and a set
of quantitative measures of nonclassicality (e.g., negativity potential,
concurrence potential and anticlassicality). The higher order nonclassicality
witness have found to reveal the existence of higher order nonclassical
properties of QCS for the first time.Comment: A comparative description of the higher-order nonclassical properties
of the finite dimensional coherent state
The Generalized Spike Process, Sparsity, and Statistical Independence
A basis under which a given set of realizations of a stochastic process can
be represented most sparsely (the so-called best sparsifying basis (BSB)) and
the one under which such a set becomes as less statistically dependent as
possible (the so-called least statistically-dependent basis (LSDB)) are
important for data compression and have generated interests among computational
neuroscientists as well as applied mathematicians. Here we consider these bases
for a particularly simple stochastic process called ``generalized spike
process'', which puts a single spike--whose amplitude is sampled from the
standard normal distribution--at a random location in the zero vector of length
\ndim for each realization.
Unlike the ``simple spike process'' which we dealt with in our previous paper
and whose amplitude is constant, we need to consider the kurtosis-maximizing
basis (KMB) instead of the LSDB due to the difficulty of evaluating
differential entropy and mutual information of the generalized spike process.
By computing the marginal densities and moments, we prove that: 1) the BSB and
the KMB selects the standard basis if we restrict our basis search within all
possible orthonormal bases in ; 2) if we extend our basis search
to all possible volume-preserving invertible linear transformations, then the
BSB exists and is again the standard basis whereas the KMB does not exist.
Thus, the KMB is rather sensitive to the orthonormality of the transformations
under consideration whereas the BSB is insensitive to that. Our results once
again support the preference of the BSB over the LSDB/KMB for data compression
applications as our previous work did.Comment: 26 pages, 2 figure
Multiphoton Quantum Optics and Quantum State Engineering
We present a review of theoretical and experimental aspects of multiphoton
quantum optics. Multiphoton processes occur and are important for many aspects
of matter-radiation interactions that include the efficient ionization of atoms
and molecules, and, more generally, atomic transition mechanisms;
system-environment couplings and dissipative quantum dynamics; laser physics,
optical parametric processes, and interferometry. A single review cannot
account for all aspects of such an enormously vast subject. Here we choose to
concentrate our attention on parametric processes in nonlinear media, with
special emphasis on the engineering of nonclassical states of photons and
atoms. We present a detailed analysis of the methods and techniques for the
production of genuinely quantum multiphoton processes in nonlinear media, and
the corresponding models of multiphoton effective interactions. We review
existing proposals for the classification, engineering, and manipulation of
nonclassical states, including Fock states, macroscopic superposition states,
and multiphoton generalized coherent states. We introduce and discuss the
structure of canonical multiphoton quantum optics and the associated one- and
two-mode canonical multiphoton squeezed states. This framework provides a
consistent multiphoton generalization of two-photon quantum optics and a
consistent Hamiltonian description of multiphoton processes associated to
higher-order nonlinearities. Finally, we discuss very recent advances that by
combining linear and nonlinear optical devices allow to realize multiphoton
entangled states of the electromnagnetic field, that are relevant for
applications to efficient quantum computation, quantum teleportation, and
related problems in quantum communication and information.Comment: 198 pages, 36 eps figure
Optimal model-free prediction from multivariate time series
Forecasting a time series from multivariate predictors constitutes a
challenging problem, especially using model-free approaches. Most techniques,
such as nearest-neighbor prediction, quickly suffer from the curse of
dimensionality and overfitting for more than a few predictors which has limited
their application mostly to the univariate case. Therefore, selection
strategies are needed that harness the available information as efficiently as
possible. Since often the right combination of predictors matters, ideally all
subsets of possible predictors should be tested for their predictive power, but
the exponentially growing number of combinations makes such an approach
computationally prohibitive. Here a prediction scheme that overcomes this
strong limitation is introduced utilizing a causal pre-selection step which
drastically reduces the number of possible predictors to the most predictive
set of causal drivers making a globally optimal search scheme tractable. The
information-theoretic optimality is derived and practical selection criteria
are discussed. As demonstrated for multivariate nonlinear stochastic delay
processes, the optimal scheme can even be less computationally expensive than
commonly used sub-optimal schemes like forward selection. The method suggests a
general framework to apply the optimal model-free approach to select variables
and subsequently fit a model to further improve a prediction or learn
statistical dependencies. The performance of this framework is illustrated on a
climatological index of El Ni\~no Southern Oscillation.Comment: 14 pages, 9 figure
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