256 research outputs found
Supplementary Material for the Article âUsing Chatbots for Literature Searches and Scholarly Writing: Is the Integrity of the Scientific Discourse in Jeopardy?â
Supplementing our paper âUsing Chatbots for Literature Searches and Scholarly Writing: Is the Integrity of the Scientific Discourse in Jeopardy?â, we present complete transcripts of two conversations with ChatGPT that corroborate the assertions in the paper
Real-time modelling and interpolation of spatio-temporal marine pollution
Due to the complexity of the interactions
involved in various dynamic systems, known physical,
biological or chemical laws cannot adequately describe
the dynamics behind these processes. The study of these
systems thus depends on measurements often taken at
various discrete spatial locations through time by noisy
sensors. For this reason, scientists often necessitate interpolative, visualisation and analytical tools to deal
with the large volumes of data common to these systems. The starting point of this study is the seminal
research by C. Shannon on sampling and reconstruction
theory and its various extensions. Based on recent work
on the reconstruction of stochastic processes, this paper
develops a novel real-time estimation method for non-
stationary stochastic spatio-temporal behaviour based
on the Integro-Di erence Equation (IDE). This meth-
odology is applied to collected marine pollution data
from a Norwegian fjord. Comparison of the results obtained by the proposed method with interpolators from
state-of-the-art Geographical Information System (GIS)
packages will show, that signifi cantly superior results are
obtained by including the temporal evolution in the spatial interpolations.peer-reviewe
Sampling from a system-theoretic viewpoint: Part II - Noncausal solutions
This paper puts to use concepts and tools introduced in Part I to address a wide spectrum of noncausal sampling and reconstruction problems. Particularly, we follow the system-theoretic paradigm by using systems as signal generators to account for available information and system norms (L2 and Lâ) as performance measures. The proposed optimization-based approach recovers many known solutions, derived hitherto by different methods, as special cases under different assumptions about acquisition or reconstructing devices (e.g., polynomial and exponential cardinal splines for fixed samplers and the Sampling Theorem and its modifications in the case when both sampler and interpolator are design parameters). We also derive new results, such as versions of the Sampling Theorem for downsampling and reconstruction from noisy measurements, the continuous-time invariance of a wide class of optimal sampling-and-reconstruction circuits, etcetera
Hard-constrained neural networks for modelling nonlinear acoustics
We model acoustic dynamics in space and time from synthetic sensor data. The
tasks are (i) to predict and extrapolate the spatiotemporal dynamics, and (ii)
reconstruct the acoustic state from partial observations. To achieve this, we
develop acoustic neural networks that learn from sensor data, whilst being
constrained by prior knowledge on acoustic and wave physics by both informing
the training and constraining parts of the network's architecture as an
inductive bias. First, we show that standard feedforward neural networks are
unable to extrapolate in time, even in the simplest case of periodic
oscillations. Second, we constrain the prior knowledge on acoustics in
increasingly effective ways by (i) employing periodic activations (periodically
activated neural networks); (ii) informing the training of the networks with a
penalty term that favours solutions that fulfil the governing equations
(soft-constrained); (iii) constraining the architecture in a
physically-motivated solution space (hard-constrained); and (iv) combination of
these. Third, we apply the networks on two testcases for two tasks in nonlinear
regimes, from periodic to chaotic oscillations. The first testcase is a twin
experiment, in which the data is produced by a prototypical time-delayed model.
In the second testcase, the data is generated by a higher-fidelity model with
mean-flow effects and a kinematic model for the flame source. We find that (i)
constraining the physics in the architecture improves interpolation whilst
requiring smaller network sizes, (ii) extrapolation in time is achieved by
periodic activations, and (iii) velocity can be reconstructed accurately from
only pressure measurements with a combination of physics-based hard and soft
constraints. In and beyond acoustics, this work opens strategies for
constraining the physics in the architecture, rather than the training
Fast T2 Mapping with Improved Accuracy Using Undersampled Spin-echo MRI and Model-based Reconstructions with a Generating Function
A model-based reconstruction technique for accelerated T2 mapping with
improved accuracy is proposed using undersampled Cartesian spin-echo MRI data.
The technique employs an advanced signal model for T2 relaxation that accounts
for contributions from indirect echoes in a train of multiple spin echoes. An
iterative solution of the nonlinear inverse reconstruction problem directly
estimates spin-density and T2 maps from undersampled raw data. The algorithm is
validated for simulated data as well as phantom and human brain MRI at 3 T. The
performance of the advanced model is compared to conventional pixel-based
fitting of echo-time images from fully sampled data. The proposed method yields
more accurate T2 values than the mono-exponential model and allows for
undersampling factors of at least 6. Although limitations are observed for very
long T2 relaxation times, respective reconstruction problems may be overcome by
a gradient dampening approach. The analytical gradient of the utilized cost
function is included as Appendix.Comment: 10 pages, 7 figure
On causal extrapolation of sequences with applications to forecasting
The paper suggests a method of extrapolation of notion of one-sided
semi-infinite sequences representing traces of two-sided band-limited
sequences; this features ensure uniqueness of this extrapolation and
possibility to use this for forecasting. This lead to a forecasting method for
more general sequences without this feature based on minimization of the mean
square error between the observed path and a predicable sequence. These
procedure involves calculation of this predictable path; the procedure can be
interpreted as causal smoothing. The corresponding smoothed sequences allow
unique extrapolations to future times that can be interpreted as optimal
forecasts.Comment: arXiv admin note: substantial text overlap with arXiv:1111.670
Nonideal Sampling and Interpolation from Noisy Observations in Shift-Invariant Spaces
Digital analysis and processing of signals inherently relies on the existence of methods for reconstructing a continuous-time signal from a sequence of corrupted discrete-time samples. In this paper, a general formulation of this problem is developed that treats the interpolation problem from ideal, noisy samples, and the deconvolution problem in which the signal is filtered prior to sampling, in a unified way. The signal reconstruction is performed in a shift-invariant subspace spanned by the integer shifts of a generating function, where the expansion coefficients are obtained by processing the noisy samples with a digital correction filter. Several alternative approaches to designing the correction filter are suggested, which differ in their assumptions on the signal and noise. The classical deconvolution solutions (least-squares, Tikhonov, and Wiener) are adapted to our particular situation, and new methods that are optimal in a minimax sense are also proposed. The solutions often have a similar structure and can be computed simply and efficiently by digital filtering. Some concrete examples of reconstruction filters are presented, as well as simple guidelines for selecting the free parameters (e.g., regularization) of the various algorithms
Multichannel Sampling of Pulse Streams at the Rate of Innovation
We consider minimal-rate sampling schemes for infinite streams of delayed and
weighted versions of a known pulse shape. The minimal sampling rate for these
parametric signals is referred to as the rate of innovation and is equal to the
number of degrees of freedom per unit time. Although sampling of infinite pulse
streams was treated in previous works, either the rate of innovation was not
achieved, or the pulse shape was limited to Diracs. In this paper we propose a
multichannel architecture for sampling pulse streams with arbitrary shape,
operating at the rate of innovation. Our approach is based on modulating the
input signal with a set of properly chosen waveforms, followed by a bank of
integrators. This architecture is motivated by recent work on sub-Nyquist
sampling of multiband signals. We show that the pulse stream can be recovered
from the proposed minimal-rate samples using standard tools taken from spectral
estimation in a stable way even at high rates of innovation. In addition, we
address practical implementation issues, such as reduction of hardware
complexity and immunity to failure in the sampling channels. The resulting
scheme is flexible and exhibits better noise robustness than previous
approaches
- âŠ