19,266 research outputs found
Can we identify non-stationary dynamics of trial-to-trial variability?"
Identifying sources of the apparent variability in non-stationary scenarios is a fundamental problem in many biological data analysis settings. For instance, neurophysiological responses to the same task often vary from each repetition of the same experiment (trial) to the next. The origin and functional role of this observed variability is one of the fundamental questions in neuroscience. The nature of such trial-to-trial dynamics however remains largely elusive to current data analysis approaches. A range of strategies have been proposed in modalities such as electro-encephalography but gaining a fundamental insight into latent sources of trial-to-trial variability in neural recordings is still a major challenge. In this paper, we present a proof-of-concept study to the analysis of trial-to-trial variability dynamics founded on non-autonomous dynamical systems. At this initial stage, we evaluate the capacity of a simple statistic based on the behaviour of trajectories in classification settings, the trajectory coherence, in order to identify trial-to-trial dynamics. First, we derive the conditions leading to observable changes in datasets generated by a compact dynamical system (the Duffing equation). This canonical system plays the role of a ubiquitous model of non-stationary supervised classification problems. Second, we estimate the coherence of class-trajectories in empirically reconstructed space of system states. We show how this analysis can discern variations attributable to non-autonomous deterministic processes from stochastic fluctuations. The analyses are benchmarked using simulated and two different real datasets which have been shown to exhibit attractor dynamics. As an illustrative example, we focused on the analysis of the rat's frontal cortex ensemble dynamics during a decision-making task. Results suggest that, in line with recent hypotheses, rather than internal noise, it is the deterministic trend which most likely underlies the observed trial-to-trial variability. Thus, the empirical tool developed within this study potentially allows us to infer the source of variability in in-vivo neural recordings
Gravitational wave emission from binary supermassive black holes
Massive black hole binaries (MBHBs) are unavoidable outcomes of the
hierarchical structure formation process, and according to the theory of
general relativity are expected to be the loudest gravitational wave (GW)
sources in the Universe. In this article I provide a broad overview of MBHBs as
GW sources. After reviewing the basics of GW emission from binary systems and
of MBHB formation, evolution and dynamics, I describe in some details the
connection between binary properties and the emitted gravitational waveform.
Direct GW observations will provide an unprecedented wealth of information
about the physical nature and the astrophysical properties of these extreme
objects, allowing to reconstruct their cosmic history, dynamics and coupling
with their dense stellar and gas environment. In this context I describe
ongoing and future efforts to make a direct detection with space based
interferometry and pulsar timing arrays, highlighting the invaluable scientific
payouts of such enterprises.Comment: 26 pages, 9 figures, invited article for the focus issue on
astrophysical black holes in Classical and Quantum Gravity, guest editors: D.
Merritt and L. Rezzolla. Submitte
Risk-sensitive Inverse Reinforcement Learning via Semi- and Non-Parametric Methods
The literature on Inverse Reinforcement Learning (IRL) typically assumes that
humans take actions in order to minimize the expected value of a cost function,
i.e., that humans are risk neutral. Yet, in practice, humans are often far from
being risk neutral. To fill this gap, the objective of this paper is to devise
a framework for risk-sensitive IRL in order to explicitly account for a human's
risk sensitivity. To this end, we propose a flexible class of models based on
coherent risk measures, which allow us to capture an entire spectrum of risk
preferences from risk-neutral to worst-case. We propose efficient
non-parametric algorithms based on linear programming and semi-parametric
algorithms based on maximum likelihood for inferring a human's underlying risk
measure and cost function for a rich class of static and dynamic
decision-making settings. The resulting approach is demonstrated on a simulated
driving game with ten human participants. Our method is able to infer and mimic
a wide range of qualitatively different driving styles from highly risk-averse
to risk-neutral in a data-efficient manner. Moreover, comparisons of the
Risk-Sensitive (RS) IRL approach with a risk-neutral model show that the RS-IRL
framework more accurately captures observed participant behavior both
qualitatively and quantitatively, especially in scenarios where catastrophic
outcomes such as collisions can occur.Comment: Submitted to International Journal of Robotics Research; Revision 1:
(i) Clarified minor technical points; (ii) Revised proof for Theorem 3 to
hold under weaker assumptions; (iii) Added additional figures and expanded
discussions to improve readabilit
Chaotic versus stochastic behavior in active-dissipative nonlinear systems
We study the dynamical state of the one-dimensional noisy generalized Kuramoto-Sivashinsky (gKS) equation by making use of time-series techniques based on symbolic dynamics and complex networks. We focus on analyzing temporal signals of global measure in the spatiotemporal patterns as the dispersion parameter of the gKS equation and the strength of the noise are varied, observing that a rich variety of different regimes, from high-dimensional chaos to pure stochastic behavior, emerge. Permutation entropy, permutation spectrum, and network entropy allow us to fully classify the dynamical state exposed to additive noise
- β¦