7,148 research outputs found
An Emergent Space for Distributed Data with Hidden Internal Order through Manifold Learning
Manifold-learning techniques are routinely used in mining complex
spatiotemporal data to extract useful, parsimonious data
representations/parametrizations; these are, in turn, useful in nonlinear model
identification tasks. We focus here on the case of time series data that can
ultimately be modelled as a spatially distributed system (e.g. a partial
differential equation, PDE), but where we do not know the space in which this
PDE should be formulated. Hence, even the spatial coordinates for the
distributed system themselves need to be identified - to emerge from - the data
mining process. We will first validate this emergent space reconstruction for
time series sampled without space labels in known PDEs; this brings up the
issue of observability of physical space from temporal observation data, and
the transition from spatially resolved to lumped (order-parameter-based)
representations by tuning the scale of the data mining kernels. We will then
present actual emergent space discovery illustrations. Our illustrative
examples include chimera states (states of coexisting coherent and incoherent
dynamics), and chaotic as well as quasiperiodic spatiotemporal dynamics,
arising in partial differential equations and/or in heterogeneous networks. We
also discuss how data-driven spatial coordinates can be extracted in ways
invariant to the nature of the measuring instrument. Such gauge-invariant data
mining can go beyond the fusion of heterogeneous observations of the same
system, to the possible matching of apparently different systems
Space-by-time non-negative matrix factorization for single-trial decoding of M/EEG activity
We develop a novel methodology for the single-trial analysis of multichannel time-varying neuroimaging signals. We introduce the space-by-time M/EEG decomposition, based on Non-negative Matrix Factorization (NMF), which describes single-trial M/EEG signals using a set of non-negative spatial and temporal components that are linearly combined with signed scalar activation coefficients. We illustrate the effectiveness of the proposed approach on an EEG dataset recorded during the performance of a visual categorization task. Our method extracts three temporal and two spatial functional components achieving a compact yet full representation of the underlying structure, which validates and summarizes succinctly results from previous studies. Furthermore, we introduce a decoding analysis that allows determining the distinct functional role of each component and relating them to experimental conditions and task parameters. In particular, we demonstrate that the presented stimulus and the task difficulty of each trial can be reliably decoded using specific combinations of components from the identified space-by-time representation. When comparing with a sliding-window linear discriminant algorithm, we show that our approach yields more robust decoding performance across participants. Overall, our findings suggest that the proposed space-by-time decomposition is a meaningful low-dimensional representation that carries the relevant information of single-trial M/EEG signals
Nonlinearity Mitigation in WDM Systems: Models, Strategies, and Achievable Rates
After reviewing models and mitigation strategies for interchannel nonlinear
interference (NLI), we focus on the frequency-resolved logarithmic perturbation
model to study the coherence properties of NLI. Based on this study, we devise
an NLI mitigation strategy which exploits the synergic effect of phase and
polarization noise compensation (PPN) and subcarrier multiplexing with
symbol-rate optimization. This synergy persists even for high-order modulation
alphabets and Gaussian symbols. A particle method for the computation of the
resulting achievable information rate and spectral efficiency (SE) is presented
and employed to lower-bound the channel capacity. The dependence of the SE on
the link length, amplifier spacing, and presence or absence of inline
dispersion compensation is studied. Single-polarization and dual-polarization
scenarios with either independent or joint processing of the two polarizations
are considered. Numerical results show that, in links with ideal distributed
amplification, an SE gain of about 1 bit/s/Hz/polarization can be obtained (or,
in alternative, the system reach can be doubled at a given SE) with respect to
single-carrier systems without PPN mitigation. The gain is lower with lumped
amplification, increases with the number of spans, decreases with the span
length, and is further reduced by in-line dispersion compensation. For
instance, considering a dispersion-unmanaged link with lumped amplification and
an amplifier spacing of 60 km, the SE after 80 spans can be be increased from
4.5 to 4.8 bit/s/Hz/polarization, or the reach raised up to 100 spans (+25%)
for a fixed SE.Comment: Submitted to Journal of Lightwave Technolog
Photon temporal modes: a complete framework for quantum information science
Field-orthogonal temporal modes of photonic quantum states provide a new
framework for quantum information science (QIS). They intrinsically span a
high-dimensional Hilbert space and lend themselves to integration into existing
single-mode fiber communication networks. We show that the three main
requirements to construct a valid framework for QIS -- the controlled
generation of resource states, the targeted and highly efficient manipulation
of temporal modes and their efficient detection -- can be fulfilled with
current technology. We suggest implementations of diverse QIS applications
based on this complete set of building blocks.Comment: 17 pages, 13 figure
Representation Learning: A Review and New Perspectives
The success of machine learning algorithms generally depends on data
representation, and we hypothesize that this is because different
representations can entangle and hide more or less the different explanatory
factors of variation behind the data. Although specific domain knowledge can be
used to help design representations, learning with generic priors can also be
used, and the quest for AI is motivating the design of more powerful
representation-learning algorithms implementing such priors. This paper reviews
recent work in the area of unsupervised feature learning and deep learning,
covering advances in probabilistic models, auto-encoders, manifold learning,
and deep networks. This motivates longer-term unanswered questions about the
appropriate objectives for learning good representations, for computing
representations (i.e., inference), and the geometrical connections between
representation learning, density estimation and manifold learning
Mapping Atomic Motions with Electrons: Toward the Quantum Limit to Imaging Chemistry
Recent advances in ultrafast electron and X-ray diffraction have pushed imaging of structural dynamics into the femtosecond time domain, that is, the fundamental time scale of atomic motion. New physics can be reached beyond the scope of traditional diffraction or reciprocal space imaging. By exploiting the high time resolution, it has been possible to directly observe the collapse of nearly innumerable possible nuclear motions to a few key reaction modes that direct chemistry. It is this reduction in dimensionality in the transition state region that makes chemistry a transferable concept, with the same class of reactions being applicable to synthetic strategies to nearly arbitrary levels of complexity. The ability to image the underlying key reaction modes has been achieved with resolution to relative changes in atomic positions to better than 0.01 Å, that is, comparable to thermal motions. We have effectively reached the fundamental space-time limit with respect to the reaction energetics and imaging the acting forces. In the process of ensemble measured structural changes, we have missed the quantum aspects of chemistry. This perspective reviews the current state of the art in imaging chemistry in action and poses the challenge to access quantum information on the dynamics. There is the possibility with the present ultrabright electron and X-ray sources, at least in principle, to do tomographic reconstruction of quantum states in the form of a Wigner function and density matrix for the vibrational, rotational, and electronic degrees of freedom. Accessing this quantum information constitutes the ultimate demand on the spatial and temporal resolution of reciprocal space imaging of chemistry. Given the much shorter wavelength and corresponding intrinsically higher spatial resolution of current electron sources over X-rays, this Perspective will focus on electrons to provide an overview of the challenge on both the theory and the experimental fronts to extract the quantum aspects of molecular dynamics
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