7,760 research outputs found
Continuity of the spectra for families of magnetic operators on Z^d
For families of magnetic self-adjoint operators on whose
symbols and magnetic fields depend continuously on a parameter , it
is shown that the main spectral properties of these operators also vary
continuously with respect to . The proof is based on an algebraic
setting involving twisted crossed product C*-algebras.Comment: 13 page
Stable dark and bright soliton Kerr combs can coexist in normal dispersion resonators
Using the Lugiato-Lefever model, we analyze the effects of third order
chromatic dispersion on the existence and stability of dark and bright soliton
Kerr frequency combs in the normal dispersion regime. While in the absence of
third order dispersion only dark solitons exist over an extended parameter
range, we find that third order dispersion allows for stable dark and bright
solitons to coexist. Reversibility is broken and the shape of the switching
waves connecting the top and bottom homogeneous solutions is modified. Bright
solitons come into existence thanks to the generation of oscillations in the
switching wave profiles. Finally, oscillatory instabilities of dark solitons
are also suppressed in the presence of sufficiently strong third order
dispersion
Visualizing recommendations to support exploration, transparency and controllability
Research on recommender systems has traditionally focused on the development of algorithms to improve accuracy of recommendations. So far, little research has been done to enable user interaction with such systems as a basis to support exploration and control by end users. In this paper, we present our research on the use of information visualization techniques to interact with recommender systems. We investigated how information visualization can improve user understanding of the typically black-box rationale behind recommendations in order to increase their perceived relevance and meaning and to support exploration and user involvement in the recommendation process. Our study has been performed using TalkExplorer, an interactive visualization tool developed for attendees of academic conferences. The results of user studies performed at two conferences allowed us to obtain interesting insights to enhance user interfaces that integrate recommendation technology. More specifically, effectiveness and probability of item selection both increase when users are able to explore and interrelate multiple entities - i.e. items bookmarked by users, recommendations and tags. Copyright © 2013 ACM
Interaction of solitons and the formation of bound states in the generalized Lugiato-Lefever equation
Bound states, also called soliton molecules, can form as a result of the
interaction between individual solitons. This interaction is mediated through
the tails of each soliton that overlap with one another. When such soliton
tails have spatial oscillations, locking or pinning between two solitons can
occur at fixed distances related with the wavelength of these oscillations,
thus forming a bound state. In this work, we study the formation and stability
of various types of bound states in the Lugiato-Lefever equation by computing
their interaction potential and by analyzing the properties of the oscillatory
tails. Moreover, we study the effect of higher order dispersion and noise in
the pump intensity on the dynamics of bound states. In doing so, we reveal that
perturbations to the Lugiato-Lefever equation that maintain reversibility, such
as fourth order dispersion, lead to bound states that tend to separate from one
another in time when noise is added. This separation force is determined by the
shape of the envelope of the interaction potential, as well as an additional
Brownian ratchet effect. In systems with broken reversibility, such as third
order dispersion, this ratchet effect continues to push solitons within a bound
state apart. However, the force generated by the envelope of the potential is
now such that it pushes the solitons towards each other, leading to a null net
drift of the solitons.Comment: 13 pages, 13 figure
Single-trial analysis of EEG during rapid visual discrimination: enabling cortically-coupled computer vision
We describe our work using linear discrimination of multi-channel electroencephalography
for single-trial detection of neural signatures of visual recognition events. We demonstrate
the approach as a methodology for relating neural variability to response variability, describing
studies for response accuracy and response latency during visual target detection.
We then show how the approach can be utilized to construct a novel type of brain-computer
interface, which we term cortically-coupled computer vision. In this application, a large
database of images is triaged using the detected neural signatures. We show how ‘corticaltriaging’
improves image search over a strictly behavioral response
Intrinsic noise and two-dimensional maps: Quasicycles, quasiperiodicity, and chaos
We develop a formalism to describe the discrete-time dynamics of systems
containing an arbitrary number of interacting species. The individual-based
model, which forms our starting point, is described by a Markov chain, which in
the limit of large system sizes is shown to be very well-approximated by a
Fokker-Planck-like equation, or equivalently by a set of stochastic difference
equations. This formalism is applied to the specific case of two species: one
predator species and its prey species. Quasi-cycles --- stochastic cycles
sustained and amplified by the demographic noise --- previously found in
continuous-time predator-prey models are shown to exist, and their behavior
predicted from a linear noise analysis is shown to be in very good agreement
with simulations. The effects of the noise on other attractors in the
corresponding deterministic map, such as periodic cycles, quasiperiodicity and
chaos, are also investigated.Comment: 21 pages, 12 figure
Suppressing escape events in maps of the unit interval with demographic noise
We explore the properties of discrete-time stochastic processes with a
bounded state space, whose deterministic limit is given by a map of the unit
interval. We find that, in the mesoscopic description of the system, the large
jumps between successive iterates of the process can result in probability
leaking out of the unit interval, despite the fact that the noise is
multiplicative and vanishes at the boundaries. By including higher-order terms
in the mesoscopic expansion, we are able to capture the non-Gaussian nature of
the noise distribution near the boundaries, but this does not preclude the
possibility of a trajectory leaving the interval. We propose a number of
prescriptions for treating these escape events, and we compare the results with
those obtained for the metastable behavior of the microscopic model, where
escape events are not possible. We find that, rather than truncating the noise
distribution, censoring this distribution to prevent escape events leads to
results which are more consistent with the microscopic model. The addition of
higher moments to the noise distribution does not increase the accuracy of the
final results, and it can be replaced by the simpler Gaussian noise.Comment: 14 pages, 13 figure
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