1,251 research outputs found
Ergodicity, Decisions, and Partial Information
In the simplest sequential decision problem for an ergodic stochastic process
X, at each time n a decision u_n is made as a function of past observations
X_0,...,X_{n-1}, and a loss l(u_n,X_n) is incurred. In this setting, it is
known that one may choose (under a mild integrability assumption) a decision
strategy whose pathwise time-average loss is asymptotically smaller than that
of any other strategy. The corresponding problem in the case of partial
information proves to be much more delicate, however: if the process X is not
observable, but decisions must be based on the observation of a different
process Y, the existence of pathwise optimal strategies is not guaranteed.
The aim of this paper is to exhibit connections between pathwise optimal
strategies and notions from ergodic theory. The sequential decision problem is
developed in the general setting of an ergodic dynamical system (\Omega,B,P,T)
with partial information Y\subseteq B. The existence of pathwise optimal
strategies grounded in two basic properties: the conditional ergodic theory of
the dynamical system, and the complexity of the loss function. When the loss
function is not too complex, a general sufficient condition for the existence
of pathwise optimal strategies is that the dynamical system is a conditional
K-automorphism relative to the past observations \bigvee_n T^n Y. If the
conditional ergodicity assumption is strengthened, the complexity assumption
can be weakened. Several examples demonstrate the interplay between complexity
and ergodicity, which does not arise in the case of full information. Our
results also yield a decision-theoretic characterization of weak mixing in
ergodic theory, and establish pathwise optimality of ergodic nonlinear filters.Comment: 45 page
Single-Particle Self-Excited Oscillator
Electronic feedback is used to self-excite the axial oscillation of a single electron in a Penning trap. Large, stable, easily detected oscillations arise even in an anharmonic potential. Amplitudes are controlled by adjusting the feedback gain, and frequencies can be made nearly independent of amplitude fluctuations. Quantum jump spectroscopy of a perpendicular cyclotron motion reveals the absolute temperature and amplitude of the self-excited oscillation. The possibility to quickly measure parts per billion frequency shifts could open the way to improved measurements of e-, e+, p, and [overline p] magnetic moments
On the exchange of intersection and supremum of sigma-fields in filtering theory
We construct a stationary Markov process with trivial tail sigma-field and a
nondegenerate observation process such that the corresponding nonlinear
filtering process is not uniquely ergodic. This settles in the negative a
conjecture of the author in the ergodic theory of nonlinear filters arising
from an erroneous proof in the classic paper of H. Kunita (1971), wherein an
exchange of intersection and supremum of sigma-fields is taken for granted.Comment: 20 page
A discrete invitation to quantum filtering and feedback control
The engineering and control of devices at the quantum-mechanical level--such
as those consisting of small numbers of atoms and photons--is a delicate
business. The fundamental uncertainty that is inherently present at this scale
manifests itself in the unavoidable presence of noise, making this a novel
field of application for stochastic estimation and control theory. In this
expository paper we demonstrate estimation and feedback control of quantum
mechanical systems in what is essentially a noncommutative version of the
binomial model that is popular in mathematical finance. The model is extremely
rich and allows a full development of the theory, while remaining completely
within the setting of finite-dimensional Hilbert spaces (thus avoiding the
technical complications of the continuous theory). We introduce discretized
models of an atom in interaction with the electromagnetic field, obtain
filtering equations for photon counting and homodyne detection, and solve a
stochastic control problem using dynamic programming and Lyapunov function
methods.Comment: 76 pages, 12 figures. A PDF file with high resolution figures can be
found at http://minty.caltech.edu/papers.ph
Effect of Short Term Exercise and High Fat Diet on Skeletal Muscle miR133a
Micro RNAs (miR) are small non-coding RNA that regulate gene expression at the post-transcriptional level. miR133a is abundant in cardiac and skeletal muscle. In skeletal muscle, miR133a is best known for its regulatory role in myogenesis and differentiation. Nie (2016) found that muscle miR133a expression increased after acute exercise and with 12w of treadmill exercise training in mice. Knockdown of miR133a in transgenic mice resulted in blunted skeletal muscle mitochondrial biogenesis and function in response to exercise training (Nie, 2016) suggesting a role for miR133a in regulating the normal skeletal muscle metabolic adaptive response to exercise. Among other miR, skeletal muscle miR133a is reported as downregulated in insulin-resistant muscle. Insulin resistance in mice fed a high-fat diet is detectable after 3 days on diet (Lee, 2011). In this study, voluntary, rather than forced, exercise was employed to test whether miR133a expression is regulated early in the adoption of increased daily physical activity
Sliding mode control of quantum systems
This paper proposes a new robust control method for quantum systems with
uncertainties involving sliding mode control (SMC). Sliding mode control is a
widely used approach in classical control theory and industrial applications.
We show that SMC is also a useful method for robust control of quantum systems.
In this paper, we define two specific classes of sliding modes (i.e.,
eigenstates and state subspaces) and propose two novel methods combining
unitary control and periodic projective measurements for the design of quantum
sliding mode control systems. Two examples including a two-level system and a
three-level system are presented to demonstrate the proposed SMC method. One of
main features of the proposed method is that the designed control laws can
guarantee desired control performance in the presence of uncertainties in the
system Hamiltonian. This sliding mode control approach provides a useful
control theoretic tool for robust quantum information processing with
uncertainties.Comment: 18 pages, 4 figure
The impact of low erythrocyte density in human blood on the fitness and energetic reserves of the African malaria vector Anopheles gambiae
Background
Anaemia is a common health problem in the developing world. This condition is characterized by a reduction in erythrocyte density, primarily from malnutrition and/or
infectious diseases such as malaria. As red blood cells are the primary source of protein for haematophagous mosquitoes, any reduction could impede the ability of mosquito vectors to transmit malaria by influencing their fitness or that of the parasites they transmit. The aim of this study was to determine the impact of differences in the density of red blood cells in human blood on malaria vector (Anopheles gambiae sensu stricto) fitness. The hypotheses tested are that mosquito vector energetic reserves and fitness are negatively influenced by reductions in the red cell density of host human blood meals commensurate with those expected from severe anaemia.
Methods
Mosquitoes (An. gambiae s.s.) were offered blood meals of different packed cell volume(PCV) of human blood consistent with those arising from severe anaemia (15%) and normalPCV (50%). Associations between mosquito energetic reserves (lipid, glucose and glycogen)and fitness measures (reproduction and survival) and blood meal PCV were investigated.
Results
The amount of protein that malaria vectors acquired from blood feeding (indexed by
haematin excretion) was significantly reduced at low blood PCV. However, mosquitoes
feeding on blood of low PCV had the same oviposition rates as those feeding on blood of normal PCV, and showed an increase in egg production of around 15%. The long-term survival of An. gambiae s.s was reduced after feeding on low PCV blood, but PCV had no significant impact on the proportion of mosquitoes surviving through the minimal period required to develop and transmit malaria parasites (estimated as 14 days post-blood feeding). The impact of blood PCV on the energetic reserves of mosquitoes was relatively minor.
Conclusions
These results suggest that feeding on human hosts whose PCV has been depleted due to severe anaemia does not significantly reduce the fitness or transmission potential of malaria vectors, and indicates that mosquitoes may be able exploit resources for reproduction more
efficiently from blood of low rather than normal PCV
Bellman equations for optimal feedback control of qubit states
Using results from quantum filtering theory and methods from classical
control theory, we derive an optimal control strategy for an open two-level
system (a qubit in interaction with the electromagnetic field) controlled by a
laser. The aim is to optimally choose the laser's amplitude and phase in order
to drive the system into a desired state. The Bellman equations are obtained
for the case of diffusive and counting measurements for vacuum field states. A
full exact solution of the optimal control problem is given for a system with
simpler, linear, dynamics. These linear dynamics can be obtained physically by
considering a two-level atom in a strongly driven, heavily damped, optical
cavity.Comment: 10 pages, no figures, replaced the simpler model in section
How much time does a measurement take?
We consider the problem of measurement using the Lindblad equation, which
allows the introduction of time in the interaction between the measured system
and the measurement apparatus. We use analytic results, valid for weak
system-environment coupling, obtained for a two-level system in contact with a
measurer (Markovian interaction) and a thermal bath (non-Markovian
interaction), where the measured observable may or may not commute with the
system-environment interaction. Analysing the behavior of the coherence, which
tends to a value asymptotically close to zero, we obtain an expression for the
time of measurement which depends only on the system-measurer coupling, and
which does not depend on whether the observable commutes with the system-bath
interaction. The behavior of the coherences in the case of strong
system-environment coupling, found numerically, indicates that an increase in
this coupling decreases the measurement time, thus allowing our expression to
be considered the upper limit for the duration of the process.Comment: REVISED VERSION: 17 pages, 2 figure
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