10,303 research outputs found
For the Jubilee of Vladimir Mikhailovich Chernov
On April 25, 2019, Vladimir Chernov celebrated his 70th birthday, Doctor of Physics and Mathematics, Chief Researcher at the Laboratory of Mathematical Methods of Image Processing of the Image Processing Systems Institute of the Russian Academy of Sciences (IPSI RAS), a branch of the Federal Science Research Center "Crystallography and Photonics RAS and part-Time Professor at the Department of Geoinformatics and Information Security of the Samara National Research University named after academician S.P. Korolev (Samara University). The article briefly describes the scientific and pedagogical achievements of the hero of the day. © Published under licence by IOP Publishing Ltd
A Short Note on the Frame Set of Odd Functions
In this work we derive a simple argument which shows that Gabor systems
consisting of odd functions of variables and symplectic lattices of density
cannot constitute a Gabor frame. In the 1--dimensional, separable case,
this is a special case of a result proved by Lyubarskii and Nes, however, we
use a different approach in this work exploiting the algebraic relation between
the ambiguity function and the Wigner distribution as well as their relation
given by the (symplectic) Fourier transform. Also, we do not need the
assumption that the lattice is separable and, hence, new restrictions are added
to the full frame set of odd functions.Comment: accepted: Bulletin of the Australian Mathematical Society; 12 pages;
Version 3 makes use of symmetric time-frequency shifts. In this case the
appearing phase factors are easier to handle. Also, the main result is
extended to higher dimensions. [In Version 2 a mistake in the assumptions was
corrected. The windows should be chosen from Feichtinger's algebra rather
than from the Hilbert space L2.
Quantum theta functions and Gabor frames for modulation spaces
Representations of the celebrated Heisenberg commutation relations in quantum
mechanics and their exponentiated versions form the starting point for a number
of basic constructions, both in mathematics and mathematical physics (geometric
quantization, quantum tori, classical and quantum theta functions) and signal
analysis (Gabor analysis).
In this paper we try to bridge the two communities, represented by the two
co--authors: that of noncommutative geometry and that of signal analysis. After
providing a brief comparative dictionary of the two languages, we will show
e.g. that the Janssen representation of Gabor frames with generalized Gaussians
as Gabor atoms yields in a natural way quantum theta functions, and that the
Rieffel scalar product and associativity relations underlie both the functional
equations for quantum thetas and the Fundamental Identity of Gabor analysis.Comment: 38 pages, typos corrected, MSC class change
Gabor analysis over finite Abelian groups
The topic of this paper are (multi-window) Gabor frames for signals over
finite Abelian groups, generated by an arbitrary lattice within the finite
time-frequency plane. Our generic approach covers simultaneously
multi-dimensional signals as well as non-separable lattices. The main results
reduce to well-known fundamental facts about Gabor expansions of finite signals
for the case of product lattices, as they have been given by Qiu, Wexler-Raz or
Tolimieri-Orr, Bastiaans and Van-Leest, among others. In our presentation a
central role is given to spreading function of linear operators between
finite-dimensional Hilbert spaces. Another relevant tool is a symplectic
version of Poisson's summation formula over the finite time-frequency plane. It
provides the Fundamental Identity of Gabor Analysis.In addition we highlight
projective representations of the time-frequency plane and its subgroups and
explain the natural connection to twisted group algebras. In the
finite-dimensional setting these twisted group algebras are just matrix
algebras and their structure provides the algebraic framework for the study of
the deeper properties of finite-dimensional Gabor frames.Comment: Revised version: two new sections added, many typos fixe
Relaminarisation of Re_{\tau} = 100 channel flow with globally stabilising linear feedback control
The problems of nonlinearity and high dimension have so far prevented a
complete solution of the control of turbulent flow. Addressing the problem of
nonlinearity, we propose a flow control strategy which ensures that the energy
of any perturbation to the target profile decays monotonically. The
controller's estimate of the flow state is similarly guaranteed to converge to
the true value. We present a one-time off-line synthesis procedure, which
generalises to accommodate more restrictive actuation and sensing arrangements,
with conditions for existence for the controller given in this case. The
control is tested in turbulent channel flow () using full-domain
sensing and actuation on the wall-normal velocity. Concentrated at the point of
maximum inflection in the mean profile, the control directly counters the
supply of turbulence energy arising from the interaction of the wall-normal
perturbations with the flow shear. It is found that the control is only
required for the larger-scale motions, specifically those above the scale of
the mean streak spacing. Minimal control effort is required once laminar flow
is achieved. The response of the near-wall flow is examined in detail, with
particular emphasis on the pressure and wall-normal velocity fields, in the
context of Landahl's theory of sheared turbulence
Discrete Fourier Transform Improves the Prediction of the Electronic Properties of Molecules in Quantum Machine Learning
High-throughput approximations of quantum mechanics calculations and
combinatorial experiments have been traditionally used to reduce the search
space of possible molecules, drugs and materials. However, the interplay of
structural and chemical degrees of freedom introduces enormous complexity,
which the current state-of-the-art tools are not yet designed to handle. The
availability of large molecular databases generated by quantum mechanics (QM)
computations using first principles open new venues for data science to
accelerate the discovery of new compounds. In recent years, models that combine
QM with machine learning (ML) known as QM/ML models have been successful at
delivering the accuracy of QM at the speed of ML. The goals are to develop a
framework that will accelerate the extraction of knowledge and to get insights
from quantitative process-structure-property-performance relationships hidden
in materials data via a better search of the chemical compound space, and to
infer new materials with targeted properties. In this study, we show that by
integrating well-known signal processing techniques such as discrete Fourier
transform in the QM/ML pipeline, the outcomes can be significantly improved in
some cases. We also show that the spectrogram of a molecule may represent an
interesting molecular visualization tool.Comment: 4 pages, 3 figures, 2 tables. Accepted to present at 32nd IEEE
Canadian Conference in Electrical Engineering and Computer Scienc
A Multiscale Pyramid Transform for Graph Signals
Multiscale transforms designed to process analog and discrete-time signals
and images cannot be directly applied to analyze high-dimensional data residing
on the vertices of a weighted graph, as they do not capture the intrinsic
geometric structure of the underlying graph data domain. In this paper, we
adapt the Laplacian pyramid transform for signals on Euclidean domains so that
it can be used to analyze high-dimensional data residing on the vertices of a
weighted graph. Our approach is to study existing methods and develop new
methods for the four fundamental operations of graph downsampling, graph
reduction, and filtering and interpolation of signals on graphs. Equipped with
appropriate notions of these operations, we leverage the basic multiscale
constructs and intuitions from classical signal processing to generate a
transform that yields both a multiresolution of graphs and an associated
multiresolution of a graph signal on the underlying sequence of graphs.Comment: 16 pages, 13 figure
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