29,323 research outputs found
Convexity in source separation: Models, geometry, and algorithms
Source separation or demixing is the process of extracting multiple
components entangled within a signal. Contemporary signal processing presents a
host of difficult source separation problems, from interference cancellation to
background subtraction, blind deconvolution, and even dictionary learning.
Despite the recent progress in each of these applications, advances in
high-throughput sensor technology place demixing algorithms under pressure to
accommodate extremely high-dimensional signals, separate an ever larger number
of sources, and cope with more sophisticated signal and mixing models. These
difficulties are exacerbated by the need for real-time action in automated
decision-making systems.
Recent advances in convex optimization provide a simple framework for
efficiently solving numerous difficult demixing problems. This article provides
an overview of the emerging field, explains the theory that governs the
underlying procedures, and surveys algorithms that solve them efficiently. We
aim to equip practitioners with a toolkit for constructing their own demixing
algorithms that work, as well as concrete intuition for why they work
Free-space propagation of high dimensional structured optical fields in an urban environment
Spatially structured optical fields have been used to enhance the functionality of a wide variety of systems that use
light for sensing or information transfer. As higher-dimensional modes become a solution of choice in optical
systems, it is important to develop channel models that suitably predict the effect of atmospheric turbulence on
these modes. We investigate the propagation of a set of orthogonal spatial modes across a free-space channel
between two buildings separated by 1.6 km. Given the circular geometry of a common optical lens, the orthogonal
mode set we choose to implement is that described by the Laguerre-Gaussian (LG) field equations. Our study focuses
on the preservation of phase purity, which is vital for spatial multiplexing and any system requiring full quantumstate
tomography. We present experimental data for the modal degradation in a real urban environment and draw a
comparison to recognized theoretical predictions of the link. Our findings indicate that adaptations to channel
models are required to simulate the effects of atmospheric turbulence placed on high-dimensional structured
modes that propagate over a long distance. Our study indicates that with mitigation of vortex splitting, potentially
through precorrection techniques, one could overcome the challenges in a real point-to-point free-space channel in
an urban environment
High Dimensional Data Enrichment: Interpretable, Fast, and Data-Efficient
High dimensional structured data enriched model describes groups of
observations by shared and per-group individual parameters, each with its own
structure such as sparsity or group sparsity. In this paper, we consider the
general form of data enrichment where data comes in a fixed but arbitrary
number of groups G. Any convex function, e.g., norms, can characterize the
structure of both shared and individual parameters. We propose an estimator for
high dimensional data enriched model and provide conditions under which it
consistently estimates both shared and individual parameters. We also delineate
sample complexity of the estimator and present high probability non-asymptotic
bound on estimation error of all parameters. Interestingly the sample
complexity of our estimator translates to conditions on both per-group sample
sizes and the total number of samples. We propose an iterative estimation
algorithm with linear convergence rate and supplement our theoretical analysis
with synthetic and real experimental results. Particularly, we show the
predictive power of data-enriched model along with its interpretable results in
anticancer drug sensitivity analysis
Binding and Normalization of Binary Sparse Distributed Representations by Context-Dependent Thinning
Distributed representations were often criticized as inappropriate for encoding of data with a complex structure. However Plate's Holographic Reduced Representations and Kanerva's Binary Spatter Codes are recent schemes that allow on-the-fly encoding of nested compositional structures by real-valued or dense binary vectors of fixed dimensionality.
In this paper we consider procedures of the Context-Dependent Thinning which were developed for representation of complex hierarchical items in the architecture of Associative-Projective Neural Networks. These procedures provide binding of items represented by sparse binary codevectors (with low probability of 1s). Such an encoding is biologically plausible and allows a high storage capacity of distributed associative memory where the codevectors may be stored.
In contrast to known binding procedures, Context-Dependent Thinning preserves the same low density (or sparseness) of the bound codevector for varied number of component codevectors. Besides, a bound codevector is not only similar to another one with similar component codevectors (as in other schemes), but it is also similar to the component codevectors themselves. This allows the similarity of structures to be estimated just by the overlap of their codevectors, without retrieval of the component codevectors. This also allows an easy retrieval of the component codevectors.
Examples of algorithmic and neural-network implementations of the thinning procedures are considered. We also present representation examples for various types of nested structured data (propositions using role-filler and predicate-arguments representation schemes, trees, directed acyclic graphs) using sparse codevectors of fixed dimension. Such representations may provide a fruitful alternative to the symbolic representations of traditional AI, as well as to the localist and microfeature-based connectionist representations
Vibrating quantum billiards on Riemannian manifolds
Quantum billiards provide an excellent forum for the analysis of quantum
chaos. Toward this end, we consider quantum billiards with time-varying
surfaces, which provide an important example of quantum chaos that does not
require the semiclassical () or high quantum-number
limits. We analyze vibrating quantum billiards using the framework of
Riemannian geometry. First, we derive a theorem detailing necessary conditions
for the existence of chaos in vibrating quantum billiards on Riemannian
manifolds. Numerical observations suggest that these conditions are also
sufficient. We prove the aforementioned theorem in full generality for one
degree-of-freedom boundary vibrations and briefly discuss a generalization to
billiards with two or more degrees-of-vibrations. The requisite conditions are
direct consequences of the separability of the Helmholtz equation in a given
orthogonal coordinate frame, and they arise from orthogonality relations
satisfied by solutions of the Helmholtz equation. We then state and prove a
second theorem that provides a general form for the coupled ordinary
differential equations that describe quantum billiards with one
degree-of-vibration boundaries. This set of equations may be used to illustrate
KAM theory and also provides a simple example of semiquantum chaos. Moreover,
vibrating quantum billiards may be used as models for quantum-well
nanostructures, so this study has both theoretical and practical applications.Comment: 23 pages, 6 figures, a few typos corrected. To appear in
International Journal of Bifurcation and Chaos (9/01
Local optical field variation in the neighborhood of a semiconductor micrograting
The local optical field of a semiconductor micrograting (GaAs, 10x10 micro m)
is recorded in the middle field region using an optical scanning probe in
collection mode at constant height. The recorded image shows the micro-grating
with high contrast and a displaced diffraction image. The finite penetration
depth of the light leads to a reduced edge resolution in the direction to the
illuminating beam direction while the edge contrast in perpendicular direction
remains high (~100nm). We use the discrete dipole model to calculate the local
optical field to show how the displacement of the diffraction image increases
with increasing distance from the surface.Comment: 12 pages, 3 figure
- …