6,230 research outputs found
A new kernel-based approach to system identification with quantized output data
In this paper we introduce a novel method for linear system identification
with quantized output data. We model the impulse response as a zero-mean
Gaussian process whose covariance (kernel) is given by the recently proposed
stable spline kernel, which encodes information on regularity and exponential
stability. This serves as a starting point to cast our system identification
problem into a Bayesian framework. We employ Markov Chain Monte Carlo methods
to provide an estimate of the system. In particular, we design two methods
based on the so-called Gibbs sampler that allow also to estimate the kernel
hyperparameters by marginal likelihood maximization via the
expectation-maximization method. Numerical simulations show the effectiveness
of the proposed scheme, as compared to the state-of-the-art kernel-based
methods when these are employed in system identification with quantized data.Comment: 10 pages, 4 figure
Solitons and Quasielectrons in the Quantum Hall Matrix Model
We show how to incorporate fractionally charged quasielectrons in the finite
quantum Hall matrix model.The quasielectrons emerge as combinations of BPS
solitons and quasiholes in a finite matrix version of the noncommutative
theory coupled to a noncommutative Chern-Simons gauge field. We also
discuss how to properly define the charge density in the classical matrix
model, and calculate density profiles for droplets, quasiholes and
quasielectrons.Comment: 15 pages, 9 figure
Bell-Type Quantum Field Theories
In [Phys. Rep. 137, 49 (1986)] John S. Bell proposed how to associate
particle trajectories with a lattice quantum field theory, yielding what can be
regarded as a |Psi|^2-distributed Markov process on the appropriate
configuration space. A similar process can be defined in the continuum, for
more or less any regularized quantum field theory; such processes we call
Bell-type quantum field theories. We describe methods for explicitly
constructing these processes. These concern, in addition to the definition of
the Markov processes, the efficient calculation of jump rates, how to obtain
the process from the processes corresponding to the free and interaction
Hamiltonian alone, and how to obtain the free process from the free Hamiltonian
or, alternatively, from the one-particle process by a construction analogous to
"second quantization." As an example, we consider the process for a second
quantized Dirac field in an external electromagnetic field.Comment: 53 pages LaTeX, no figure
From the Hartree equation to the Vlasov-Poisson system: strong convergence for a class of mixed states
We consider the evolution of fermions interacting through a Coulomb or
gravitational potential in the mean-field limit as governed by the nonlinear
Hartree equation with Coulomb or gravitational interaction. In the limit of
large , we study the convergence in trace norm towards the classical
Vlasov-Poisson equation for a special class of mixed quasi-free states.Comment: 21 pages. Typos corrected, references updated and detailed proof of
Lemma 2.4 adde
High-resolution distributed sampling of bandlimited fields with low-precision sensors
The problem of sampling a discrete-time sequence of spatially bandlimited
fields with a bounded dynamic range, in a distributed,
communication-constrained, processing environment is addressed. A central unit,
having access to the data gathered by a dense network of fixed-precision
sensors, operating under stringent inter-node communication constraints, is
required to reconstruct the field snapshots to maximum accuracy. Both
deterministic and stochastic field models are considered. For stochastic
fields, results are established in the almost-sure sense. The feasibility of
having a flexible tradeoff between the oversampling rate (sensor density) and
the analog-to-digital converter (ADC) precision, while achieving an exponential
accuracy in the number of bits per Nyquist-interval per snapshot is
demonstrated. This exposes an underlying ``conservation of bits'' principle:
the bit-budget per Nyquist-interval per snapshot (the rate) can be distributed
along the amplitude axis (sensor-precision) and space (sensor density) in an
almost arbitrary discrete-valued manner, while retaining the same (exponential)
distortion-rate characteristics. Achievable information scaling laws for field
reconstruction over a bounded region are also derived: With N one-bit sensors
per Nyquist-interval, Nyquist-intervals, and total network
bitrate (per-sensor bitrate ), the maximum pointwise distortion goes to zero as
or . This is shown to be possible
with only nearest-neighbor communication, distributed coding, and appropriate
interpolation algorithms. For a fixed, nonzero target distortion, the number of
fixed-precision sensors and the network rate needed is always finite.Comment: 17 pages, 6 figures; paper withdrawn from IEEE Transactions on Signal
Processing and re-submitted to the IEEE Transactions on Information Theor
The Hartree-Fock state for the 2DEG at filling factor 1/2 revisited: analytic solution, dynamics and correlation energy
The CDW Hartree-Fock state at half filling and half electron per unit cell is
examined. Firstly, an exact solution in terms of Bloch-like states is
presented. Using this solution we discuss the dynamics near half filling and
show the mass to diverge logarithmically as this filling is approached. We also
show how a uniform density state may be constructed from a linear combination
of two degenerate solutions. Finally we show the second order correction to the
energy to be an order of magnitude larger than that for competing CDW solutions
with one electron per unit cell.Comment: 14 pages, no figures, extended acknowledgements, two new references
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