2,184 research outputs found
Irregular and multi--channel sampling of operators
The classical sampling theorem for bandlimited functions has recently been
generalized to apply to so-called bandlimited operators, that is, to operators
with band-limited Kohn-Nirenberg symbols. Here, we discuss operator sampling
versions of two of the most central extensions to the classical sampling
theorem. In irregular operator sampling, the sampling set is not periodic with
uniform distance. In multi-channel operator sampling, we obtain complete
information on an operator by multiple operator sampling outputs
Sparse Volterra and Polynomial Regression Models: Recoverability and Estimation
Volterra and polynomial regression models play a major role in nonlinear
system identification and inference tasks. Exciting applications ranging from
neuroscience to genome-wide association analysis build on these models with the
additional requirement of parsimony. This requirement has high interpretative
value, but unfortunately cannot be met by least-squares based or kernel
regression methods. To this end, compressed sampling (CS) approaches, already
successful in linear regression settings, can offer a viable alternative. The
viability of CS for sparse Volterra and polynomial models is the core theme of
this work. A common sparse regression task is initially posed for the two
models. Building on (weighted) Lasso-based schemes, an adaptive RLS-type
algorithm is developed for sparse polynomial regressions. The identifiability
of polynomial models is critically challenged by dimensionality. However,
following the CS principle, when these models are sparse, they could be
recovered by far fewer measurements. To quantify the sufficient number of
measurements for a given level of sparsity, restricted isometry properties
(RIP) are investigated in commonly met polynomial regression settings,
generalizing known results for their linear counterparts. The merits of the
novel (weighted) adaptive CS algorithms to sparse polynomial modeling are
verified through synthetic as well as real data tests for genotype-phenotype
analysis.Comment: 20 pages, to appear in IEEE Trans. on Signal Processin
Exponentially Localized Wannier Functions in Periodic Zero Flux Magnetic Fields
In this work, we investigate conditions which ensure the existence of an
exponentially localized Wannier basis for a given periodic hamiltonian. We
extend previous results in [Pan07] to include periodic zero flux magnetic
fields which is the setting also investigated in [Kuc09]. The new notion of
magnetic symmetry plays a crucial role; to a large class of symmetries for a
non-magnetic system, one can associate "magnetic" symmetries of the related
magnetic system. Observing that the existence of an exponentially localized
Wannier basis is equivalent to the triviality of the so-called Bloch bundle, a
rank m hermitian vector bundle over the Brillouin zone, we prove that magnetic
time-reversal symmetry is sufficient to ensure the triviality of the Bloch
bundle in spatial dimension d=1,2,3. For d=4, an exponentially localized
Wannier basis exists provided that the trace per unit volume of a suitable
function of the Fermi projection vanishes. For d>4 and d \leq 2m (stable rank
regime) only the exponential localization of a subset of Wannier functions is
shown; this improves part of the analysis of [Kuc09]. Finally, for d>4 and d>2m
(unstable rank regime) we show that the mere analysis of Chern classes does not
suffice in order to prove trivility and thus exponential localization.Comment: 48 pages, updated introduction and bibliograph
Adaptive cancelation of self-generated sensory signals in a whisking robot
Sensory signals are often caused by one's own active movements. This raises a problem of discriminating between self-generated sensory signals and signals generated by the external world. Such discrimination is of general importance for robotic systems, where operational robustness is dependent on the correct interpretation of sensory signals. Here, we investigate this problem in the context of a whiskered robot. The whisker sensory signal comprises two components: one due to contact with an object (externally generated) and another due to active movement of the whisker (self-generated). We propose a solution to this discrimination problem based on adaptive noise cancelation, where the robot learns to predict the sensory consequences of its own movements using an adaptive filter. The filter inputs (copy of motor commands) are transformed by Laguerre functions instead of the often-used tapped-delay line, which reduces model order and, therefore, computational complexity. Results from a contact-detection task demonstrate that false positives are significantly reduced using the proposed scheme
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