19,321 research outputs found
Optimal Control Realizations of Lagrangian Systems with Symmetry
A new relation among a class of optimal control systems and Lagrangian
systems with symmetry is discussed. It will be shown that a family of solutions
of optimal control systems whose control equation are obtained by means of a
group action are in correspondence with the solutions of a mechanical
Lagrangian system with symmetry. This result also explains the equivalence of
the class of Lagrangian systems with symmetry and optimal control problems
discussed in \cite{Bl98}, \cite{Bl00}.
The explicit realization of this correspondence is obtained by a judicious
use of Clebsch variables and Lin constraints, a technique originally developed
to provide simple realizations of Lagrangian systems with symmetry. It is
noteworthy to point out that this correspondence exchanges the role of state
and control variables for control systems with the configuration and Clebsch
variables for the corresponding Lagrangian system.
These results are illustrated with various simple applications
Equivariant Poincar\'e series of filtrations and topology
Earlier, for an action of a finite group on a germ of an analytic
variety, an equivariant -Poincar\'e series of a multi-index filtration in
the ring of germs of functions on the variety was defined as an element of the
Grothendieck ring of -sets with an additional structure. We discuss to which
extend the -Poincar\'e series of a filtration defined by a set of curve or
divisorial valuations on the ring of germs of analytic functions in two
variables determines the (equivariant) topology of the curve or of the set of
divisors
A hierarchical Bayesian model to infer PL(Z) relations using Gaia parallaxes
Aims. We aim at creating a Bayesian model to infer the coefficients of PL or
PLZ relations that propagates uncertainties in the observables in a rigorous
and well founded way. Methods. We propose a directed acyclic graph to encode
the conditional probabilities of the inference model that will allow us to
infer probability distributions for the PL and PL(Z) relations. We evaluate the
model with several semi-synthetic data sets and apply it to a sample of 200
fundamental mode and first overtone mode RR Lyrae stars for which Gaia DR1
parallaxes and literature Ks-band mean magnitudes are available. We define and
test several hyperprior probabilities to verify their adequacy and check the
sensitivity of the solution with respect to the prior choice. Results. The main
conclusion of this work is the absolute necessity of incorporating the existing
correlations between the observed variables (periods, metallicities and
parallaxes) in the form of model priors in order to avoid systematically biased
results, especially in the case of non-negligible uncertainties in the
parallaxes. The tests with the semi-synthetic data based on the data set used
in Gaia Collaboration et al. (2017) reveal the significant impact that the
existing correlations between parallax, metallicity and periods have on the
inferred parameters. The relation coefficients obtained here have been
superseded by those presented in Muraveva et al. (2018a), that incorporates the
findings of this work and the more recent Gaia DR2 measurements.Comment: 14 pages, 12 figures. Submitted to A&
Exact Mapping of the 2+1 Dirac Oscillator onto the Jaynes-Cummings Model: Ion-Trap Experimental Proposal
We study the dynamics of the 2+1 Dirac oscillator exactly and find spin
oscillations due to a {\it Zitterbewegung} of purely relativistic origin. We
find an exact mapping of this quantum-relativistic system onto a
Jaynes-Cummings model, describing the interaction of a two-level atom with a
quantized single-mode field. This equivalence allows us to map a series of
quantum optical phenomena onto the relativistic oscillator, and viceversa. We
make a realistic experimental proposal, at reach with current technology, for
studying the equivalence of both models using a single trapped ion.Comment: Revtex4, submitted for publicatio
Human summating potential using continuous loop averaging deconvolution: Response amplitudes vary with tone burst repetition rate and duration
Electrocochleography (ECochG) to high repetition rate tone bursts may have advantages over ECochG to clicks with standard slow rates. Tone burst stimuli presented at a high repetition rate may enhance summating potential (SP) measurements by reducing neural contributions resulting from neural adaptation to high stimulus repetition rates. To allow for the analysis of the complex ECochG responses to high rates, we deconvolved responses using the Continuous Loop Averaging Deconvolution (CLAD) technique. We examined the effect of high stimulus repetition rate and stimulus duration on SP amplitude measurements made with extratympanic ECochG to tone bursts in 20 adult females with normal hearing. We used 500 and 2,000 Hz tone bursts of various stimulus durations (12, 6, 3 ms) and repetition rates (five rates ranging from 7.1 to 234.38/s). A within-subject repeated measures (rate x duration) analysis of variance was conducted. We found that, for both 500 and 2,000 Hz stimuli, the mean deconvolved SP amplitudes were larger at faster repetition rates (58.59 and 97.66/s) compared to slower repetition rates (7.1 and 19.53/s), and larger at shorter stimulus duration compared longer stimulus duration. Our concluding hypothesis is that large SP amplitude to short duration stimuli may originate primarily from neural excitation, and large SP amplitudes to long duration, fast repetition rate stimuli may originate from hair cell responses. While the hair cell or neural origins of the SP to various stimulus parameters remains to be validated, our results nevertheless provide normative data as a step toward applying the CLAD technique to understanding diseased ears
Bosonic Seesaw in the Unparticle Physics
Recently, conceptually new physics beyond the Standard Model has been
proposed by Georgi, where a new physics sector becomes conformal and provides
"unparticle" which couples to the Standard Model sector through higher
dimensional operators in low energy effective theory. Among several
possibilities, we focus on operators involving the (scalar) unparticle, Higgs
and the gauge bosons. Once the Higgs develops the vacuum expectation value
(VEV), the conformal symmetry is broken and as a result, the mixing between the
unparticle and the Higgs boson emerges. In this paper, we consider a natural
realization of bosonic seesaw in the context of unparticle physics. In this
framework, the negative mass squared or the electroweak symmetry breaking
vacuum is achieved as a result of mass matrix diagonalization. In the
diagonalization process, it is important to have zero value in the
(1,1)-element of the mass matrix. In fact, the conformal invariance in the
hidden sector can actually assure the zero of that element. So, the bosonic
seesaw mechanism for the electroweak symmetry breaking can naturally be
understood in the framework of unparticle physics.Comment: 5 pages, no figure; added one more referenc
Local Unitary Quantum Cellular Automata
In this paper we present a quantization of Cellular Automata. Our formalism
is based on a lattice of qudits, and an update rule consisting of local unitary
operators that commute with their own lattice translations. One purpose of this
model is to act as a theoretical model of quantum computation, similar to the
quantum circuit model. It is also shown to be an appropriate abstraction for
space-homogeneous quantum phenomena, such as quantum lattice gases, spin chains
and others. Some results that show the benefits of basing the model on local
unitary operators are shown: universality, strong connections to the circuit
model, simple implementation on quantum hardware, and a wealth of applications.Comment: To appear in Physical Review
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